This is one of the webpages of Libarid A. Maljian at the Department of Physics at CSLA at NJIT.

 

 

 

New Jersey Institute of Technology

College of Science and Liberal Arts

Department of Physics

Introductory Astronomy and Cosmology

Phys 202

Spring 2023

Fourth (Final) Examination lecture notes

 

 

 

Our Galaxy, the Milky Way Galaxy

 

A galaxy is a collection of billions of star systems held together by gravity.  Our Milky Way Galaxy is composed of roughly one hundred billion star systems, and our Solar System is just one of these one hundred billion star systems that together compose our Milky Way Galaxy.  Since most star systems are binary star systems, our Milky Way Galaxy is composed of roughly two hundred billion stars.  If we regard the average mass of a star to be roughly 1M☉ (one solar mass), we might suspect that the total mass of our Milky Way Galaxy is roughly one or two hundred billion solar masses.  However, the total mass of our Milky Way Galaxy is much larger, roughly one trillion solar masses, for reasons we will discuss shortly.  Most of the star systems that compose our Milky Way Galaxy are arranged into the shape of a flat disk with spiral arms, making the Milky Way Galaxy rather like a pinwheel in appearance.  Therefore, the Milky Way Galaxy is classified as a spiral-disk galaxy.  The galactic disk is roughly thirty kiloparsecs (roughly one hundred thousand light-years) in diameter; therefore, the galactic disk is roughly fifteen kiloparsecs (roughly fifty thousand light-years) in radius.  Our Solar System is in the galactic disk roughly halfway out from the center of our Milky Way Galaxy, making our Solar System roughly eight kiloparsecs (roughly twenty-five thousand light-years) from the center of our Milky Way Galaxy.  The galactic disk is only roughly three hundred parsecs (roughly one thousand light-years) thick.  Therefore, the galactic disk has a diameter roughly one hundred times its own thickness; that is, the thickness of the galactic disk is roughly one-hundredth of its own diameter.  More plainly, the galactic disk is very thin.  Our Solar System is roughly midway within the thickness of the galactic disk, being roughly one hundred and fifty parsecs (roughly five hundred light-years) from either the top edge or the bottom edge of the galactic disk.  The galactic bulge is a collection of stars arranged into a more rounded shape near the center of our Milky Way Galaxy.  If we could observe our Milky Way Galaxy edge on, its galactic disk together with its galactic bulge would give it the appearance of a fried egg.  There are some stars around the galactic disk (above and below the galactic disk); this is called the galactic halo.

 

All the stars of the Milky Way Galaxy move along giant orbits around the center of the Milky Way Galaxy.  All of the star systems within the galactic disk, including our own Solar System, orbit the center of our Milky Way Galaxy in roughly the same angular (orbital) direction.  Therefore, we may regard our Milky Way Galaxy as rotating due to the orbits of all of its individual star systems, but this rotation is certainly not rigid body rotation.  A galaxy is not a solid object; a galaxy is composed of billions of individual star systems each on their own orbit around the center of the galaxy.  Therefore, the shape of a galaxy continuously changes as all its star systems move along their individual orbits.  Of course, we would need to wait millions of years to notice significant changes in the shape of a galaxy.  Nevertheless, over timescales of millions of years, we would observe that the spiral arms of a spiral-disk galaxy are not permanent structures.  The stars closer to the center of a galaxy take less time to complete one orbit, since they have less distance to travel.  The stars further from the center of a galaxy take more time to complete one orbit, since they have more distance to travel.  Therefore, if we could observe a spiral-disk galaxy over timescales of millions of years, we would see its shape continuously change as some spiral arms disperse and new spiral arms coalesce depending on where the individual star systems happen to be located on their orbits.  There are also variations in the concentration of stars throughout the Milky Way Galaxy.  Stars are somewhat closer together in some regions of our Milky Way Galaxy, while stars are somewhat further apart in other regions of our Milky Way Galaxy.  Moreover, these variations in stellar concentrations propagate throughout all the stars that together form our Milky Way Galaxy.  These propagating disturbances are called spiral density waves, since they contribute to the changing structure of the spiral arms of the Milky Way Galaxy.  These spiral density waves also cause variations in the density of gases within the Milky Way Galaxy, as we will discuss shortly.  Since galaxies do not suffer from rigid body rotation, it is not meaningful to ask how long it takes a galaxy to complete one rotation, since each star system is on its own orbit, each taking a different amount of time to orbit around the center of the galaxy.  We could however ask for the average duration of time it takes a galaxy to complete one rotation.  Since our own Solar System is roughly halfway out from the center of our Milky Way Galaxy, we may regard the time it takes our Solar System to complete one orbit around the center of our Milky Way Galaxy as the average duration of time it takes our Milky Way Galaxy to complete one rotation.  This is called one galactic year, and it is between two hundred million years and two hundred and fifty million years.  Our Milky Way Galaxy is roughly ten billion years old, as we will discuss shortly.  Therefore, our Milky Way Galaxy has not completed a large number of rotations over its entire history.  Ten billion divided by two hundred and fifty million is only forty, and ten billion divided by two hundred million is only fifty.  Therefore, our Milky Way Galaxy has only rotated between forty and fifty times over its entire ten-billion-year history.  Our Solar System is only roughly five billion years old, roughly one-half of the age of the Milky Way Galaxy.  Therefore, our Solar System has only completed between twenty to twenty-five orbits around the center of the Milky Way Galaxy over its own particular history.

 

The study of the structure and the evolution of galaxies is called galactic dynamics, and astrophysicists who study the structure and the evolution of galaxies are called galactic dynamicists.  Both the structure and the evolution of galaxies is studied through the orbital motions of the individual star systems that compose a galaxy.  Theoretical galactic dynamicists program a computer with billions of stars attracting each other gravitationally.  While running the simulation, the computer can display various images of the positions of the stars over the course of the simulated time.  In this way, theoretical galactic dynamicists can study the changing structure (the changing shape) of a galaxy.  Observational galactic dynamicists collect light from other galaxies.  For example, most of the star systems of a spiral-disk galaxy rotate in roughly the same angular (orbital) direction.  Therefore, most of the stars on one side of a spiral-disk galaxy will happen to be moving toward us, while most of the stars on the other side of a spiral-disk galaxy will happen to be moving away from us.  Thus, the light from one side of the galaxy will be blueshifted relative to its galactic center, and the light from the other side of the galaxy will be redshifted relative to its galactic center.  By measuring these blueshifts and redshifts, we can calculate the speed with which the stars are moving within the galaxy, and galactic dynamicists can then predict the structure (the shape) the galaxy will have in the future as well as the structure (the shape) the galaxy had in the past.

 

By observing the orbits of stars near the center of our Milky Way Galaxy and by calculating the gravitational force acting on these stars, galactic dynamicists have determined that there is a supermassive black hole at the center of our Milky Way Galaxy.  A supermassive black hole has a mass at least in the millions of solar masses.  Presumably, a supermassive black hole was initially born a stellar black hole from the Type II supernova of a very high mass star.  Over billions of years, the stellar black hole continuously devoured all of the gas around it and thus continued to grow in mass until it became a supermassive black hole.  By observing the orbits of stars near the center of other galaxies and by calculating the gravitational force acting on them, galactic dynamicists have determined that there is a supermassive black hole at the center of every major galaxy in the universe.  Much more recently, astronomers have actually succeeded in imaging these supermassive black holes.  Using many radio telescopes working together as a single interferometer, astronomers have produced radio images of the black event horizon of supermassive black holes against the gases of the surrounding space.  In the year 2019, astronomers imaged the event horizon of the supermassive black hole at the center of a galaxy roughly sixteen megaparsecs (roughly fifty million light-years) distant.  In the year 2022, astronomers imaged the event horizon of the supermassive black hole at the center of our own Milky Way Galaxy.  Although supermassive black holes are incredibly massive as compared with stellar black holes, they still have a small mass as compared with the mass of an entire galaxy.  Although the gravity of a supermassive black hole is strong enough to determine the orbits of stars near a galactic center, the gravity of a supermassive black hole is nowhere nearly strong enough to hold an entire galaxy together.  For example, the supermassive black hole at the center of our Milky Way Galaxy is roughly four million solar masses, but the mass of our entire Milky Way Galaxy is roughly one trillion solar masses.  Thus, the mass of the supermassive black hole at the center of our Milky Way Galaxy is roughly four ten-thousandths of one percent of the mass of the entire Milky Way Galaxy.  This tiny fraction (tiny percentage) should be contrasted with our Solar System, where the mass of our Sun is roughly 99.9 percent of the mass of the entire Solar System.  Thus, the Sun’s gravity does indeed dominate our Solar System, and so it is indeed the Sun’s gravity that holds our Solar System together.  Since the mass of a supermassive black hole is such a tiny fraction (tiny percentage) of the mass of an entire galaxy, supermassive black holes do not hold galaxies together.  Something much more mysterious than black holes is responsible for holding galaxies together.

 

A rotation curve is a graph of the orbital speed of stars around the center of a galaxy as a function of their distance from the center of the galaxy.  By measuring the orbits of stars far from the center of our Milky Way Galaxy, galactic dynamicists have determined that our Milky Way Galaxy’s rotation curve flattens far from the galactic center.  In fact, the rotation curve of all spiral-disk galaxies flattens far from their galactic center.  It is not difficult to use the mathematical laws of gravitation to determine the distribution of mass that would exert the gravitational force necessary to cause a flat rotation curve.  We conclude that the billions of star systems that compose a galaxy only account for roughly one-tenth (roughly ten percent) of the mass of an entire galaxy.  Roughly ninety percent of the mass of a galaxy is distributed throughout an enormous sphere surrounding all the star systems of the galaxy.  As we discussed earlier in the course, we determine the composition of anything in the universe such as planets, stars, and nebulae through spectroscopy, the measuring of the spectrum of the light we receive from the object.  Whether the light has an absorption spectrum or an emission spectrum, we consult tabulated spectral lines to determine which atoms absorbed or emitted those wavelengths of light.  However, we receive no light whatsoever from anywhere across the entire Electromagnetic Spectrum from the enormous distribution of mass dominating galaxies.  All atoms interact with photons, and atoms are composed of protons, neutrons, and electrons.  Protons and electrons certainly interact with photons, since they carry electric charge.  Although neutrons are neutral, they nevertheless also interact with photons, since neutrons still have electromagnetic properties.  If the enormous distribution of mass dominating galaxies does not interact with any photons at all, then this dominating mass cannot be composed of atoms, nor can this dominating mass be composed of the constituents of atoms (protons, neutrons, or electrons).  Therefore, astronomers have no idea what composes this mysterious mass that dominates galaxies.  In their complete ignorance, astronomers use the term dark matter for this mysterious mass.  Therefore, roughly ninety percent of the mass of our Milky Way Galaxy is dark matter distributed over an enormous sphere surrounding all the star systems of our Milky Way Galaxy.  This enormous sphere is called the dark matter halo.  Since every spiral-disk galaxy in the universe has a flat rotation curve, we deduce that roughly ninety percent of the mass of every spiral-disk galaxy in the universe is distributed over a mysterious dark matter halo surrounding the star systems of the galaxy.  As we will discuss shortly, dark matter in fact composes roughly ninety percent of the mass of all galaxies in the universe, not just spiral-disk galaxies.  Therefore, dark matter composes roughly ninety percent of the mass of the entire universe.  The remaining ten percent of the mass of the universe that is composed of atoms is called normal matter.  However, if dark matter composes roughly ninety percent of the mass of the universe, perhaps dark matter should be renamed as normal matter; it is stars and planets and mountains and buildings and humans and mobile telephones that are composed of abnormal (atomic) matter!  As we will discuss shortly, there is further evidence in addition to flat rotation curves for the predominance of dark matter in the universe.  The ten percent normal (atomic) mass of the universe is composed overwhelmingly of stars and gas.  Planets, moons, asteroids, and comets compose a tiny fraction (tiny percentage) of this normal (atomic) mass.  Therefore, we will often refer to normal (atomic) mass as luminous mass, since stars are luminous.  It is appropriate to summarize the composition of matter in the universe.  Roughly ninety percent of the mass of the universe is composed of dark matter.  The remaining roughly ten percent of the mass of the universe is composed of normal (atomic) matter.  Roughly three-quarters (roughly seventy-five percent) of this roughly ten percent normal (atomic) matter is hydrogen, roughly one-quarter (roughly twenty-five percent) of this roughly ten percent normal (atomic) matter is helium, and all the other atoms on the Periodic Table of Elements compose a tiny fraction (tiny percentage) of this roughly ten percent normal (atomic) matter.

 

It is unsettling to discover that we do not know the composition of roughly ninety percent of the mass of the universe.  We are certain that dark matter has mass that exerts gravitational forces in the same way as normal (atomic) matter; this is how we discovered dark matter in the first place.  Other than mass that exerts normal gravitational forces, what is the dark matter exactly?  There are two opposing theories to explain the composition of dark matter.  One theory claims that dark matter is actually composed of normal matter.  Brown dwarf stars are very cool and dim, as we discussed earlier in the course.  According to this first theory, the dark matter is actually an enormous number of brown dwarf stars in the galactic halo surrounding all the other stars of a galaxy.  Consequently, these brown dwarf stars are called massive astrophysical compact halo objects, which astrophysicists always abbreviate as MACHOs.  This MACHO theory is probably not correct.  Although brown dwarf stars radiate very little visible light, they radiate a fair amount of infrared light at their cool temperatures.  To account for the predominance of dark matter, we would need such an enormous number of brown dwarf stars distributed throughout the galactic halo that all of their infrared light would add to a significant amount.  However, we do not receive any infrared light or any other type of photons whatsoever from dark matter.  Moreover, cosmological observations and cosmological calculations place constraints upon the amount of normal matter that formed shortly after the Big Bang that created the universe, as we will discuss shortly.  To account for the predominance of dark matter, the number of brown dwarf stars we would need would exceed these cosmological constraints upon the amount of normal matter that fills the universe.  Therefore, many astrophysicists agree that dark matter cannot be composed of normal (atomic) matter.  The opposing theory to explain the composition of dark matter claims that dark matter is composed of exotic quantum-mechanical particles.  There is a highly speculative theory called Supersymmetric Relativistic Quantum Field Theory, or Supersymmetry for short.  According to Supersymmetric Relativistic Quantum Field Theory, for every particle of matter or antimatter in the universe, there is a corresponding supersymmetric particle.  In particular, this speculative theory claims that there are supersymmetric electrons called selectrons, there are supersymmetric quarks called squarks, there are supersymmetric photons called photinos, there are supersymmetric gluons called gluinos, and there are supersymmetric gravitons called gravitinos.  Other supersymmetric particles include winos and zinos.  No supersymmetric particle has ever actually been observed.  In other words, selectrons, squarks, photinos, gluinos, gravitinos, winos, and zinos are all purely hypothetical particles.  However, subatomic particle accelerators may be able to create these supersymmetric particles, as we will discuss shortly.  Although Supersymmetric Relativistic Quantum Field Theory is highly speculative, some astrophysicists believe that dark matter is composed of these supersymmetric particles.  These supersymmetric particles must have a significant amount of mass to account for the predominance of dark matter in the universe.  Therefore, these hypothetical supersymmetric particles are also called weakly interacting massive particles, which astrophysicists always abbreviate as WIMPs.  To summarize the two opposing theories to explain the composition of dark matter, some astrophysicists believe that the dark matter is composed of MACHOs (massive astrophysical compact halo objects) while other astrophysicists believe that the dark matter is composed of WIMPs (weakly interacting massive particles), and more astrophysicists side with the WIMPs over the MACHOs!

 

It is a common misconception that outer space is perfect vacuum, but there is no such thing as perfect vacuum.  In fact, a perfect vacuum would violate the laws of physics.  Outer space is actually filled with very diffuse gas called the interstellar medium, which astrophysicists always abbreviate ISM.  The interstellar medium fills the space between stars, hence its name.  The interstellar medium is concentrated within the galactic disk.  The interstellar medium is composed of roughly three-quarters (roughly seventy-five percent) hydrogen, roughly one-quarter (roughly twenty-five percent) helium, and tiny amounts of all the other atoms on the Periodic Table of Elements.  We determine the composition of the interstellar medium through spectroscopy.  We find absorption lines in the starlight that passes through the interstellar medium.  By measuring the wavelengths of these absorption lines and consulting tables of spectra, we can determine which atoms absorbed these spectral lines and thus determine the composition of the interstellar medium.  We also find emission lines within the light from the interstellar medium.  Again, by measuring the wavelengths of these emission lines and consulting tables of spectra, we can determine which atoms emitted these spectral lines and again determine the composition of the interstellar medium.  The gases within the interstellar medium are pushed by many different forces, including thermal pressures, gravitational forces, magnetic pressures, and even cosmic rays (ultra high-energy particles).  All these different forces are comparable in strength with each other in interstellar space (the space between star systems).  Thus, the gases within the interstellar medium are pushed in seemingly random directions, causing some regions within the interstellar medium to be more dense than average and other regions within the interstellar medium to be less dense (or more tenuous) than average.  A region of the interstellar medium that is more dense than average is called a diffuse nebula, since even these more dense regions of the interstellar medium are still diffuse (low density) by human standards.  The gases within these diffuse nebulae are sufficiently cool that they radiate more infrared light and less visible light.  Consequently, infrared images of a diffuse nebula typically reveal its gases much more clearly than optical images.  Within a diffuse nebula, gases are pushed by many different forces that are all comparable in strength with each other.  Hence, the gases even within a diffuse nebula are pushed in seemingly random directions, causing variations in density within a diffuse nebula.  Small regions within a diffuse nebula may become dense enough that gravity dominates over all the other forces.  Thus, those small regions of the diffuse nebula will collapse from their self-gravity (under their own weight), eventually becoming star systems.  Note however that stars born within a diffuse nebula provide heat and thus thermal pressures that may balance or even exceed gravitational forces.  Moreover, the radiation pressure from the light radiated from stars born within a nebula will push the surrounding gases outward.  The stellar winds from stars born within a nebula will also push the surrounding gases outward.  As a result of thermal pressures, radiation pressures, and stellar winds from the stars that are born within a diffuse nebula, most of the gases of a diffuse nebula will not form stars; only a tiny fraction of the total mass of a diffuse nebula will form stars.  On the other hand, the energy from a nearby supernova may compress the gases of a particular region of the interstellar medium to sufficient densities for gravity to dominate over all other forces, thus inducing star formation.  A spiral density wave may also compress the gases of a particular region of the interstellar medium to sufficient densities for gravity to dominate over all other forces, thus inducing star formation.  Since the interstellar medium is concentrated within the galactic disk, this is where star formation occurs in the Milky Way Galaxy.  Stars are continuously born within the spiral arms of the galactic disk of the Milky Way Galaxy.  There is virtually no star formation in the galactic halo, the region around (above and below) the galactic disk, since there are virtually no interstellar gases outside of the galactic disk.  Therefore, the stars in the galactic halo must be relatively old, since without active star formation there would be no newly born stars.  The stars in the galactic disk must be relatively young, since stars are continuously born from diffuse nebulae within the interstellar medium within the galactic disk.  Astronomers have named the stars within the galactic disk Population I (Roman numeral) stars, and astronomers have named the stars within the galactic halo Population II (Roman numeral) stars.  Again, Population I stars are comparatively young, while Population II stars are comparatively old.  Since our Sun is in the galactic disk, our Sun is classified as a Population I star.  Since star formation is still active in the galactic disk, some newly born stars will be high mass, hot, luminous, and blue (early-type) main sequence stars.  Such stars have short lifetimes ending with a violent supernova, as we discussed earlier in the course.  The supernova explosion synthesizes all the atoms across the entire Periodic Table of Elements and throws them into the surrounding interstellar medium through the hot and rapidly expanding supernova remnant, as we discussed earlier in the course.  Thus, the interstellar medium is polluted or enriched with these new nuclei, causing future diffuse nebulae to be similarly polluted or enriched.  Hence, Population I stars have comparatively higher mass fractions of these nuclei.  Since Population II stars are comparatively old, they must be low mass, cool, dim, and red (late-type) main sequence stars, since these stars have longer lifetimes.  These old stars were born when the universe was younger; therefore, there was less time for high mass stars to synthesize heavier elements.  Thus, Population II stars have comparatively lower mass fractions of these heavier nuclei.  Recall that the normal (atomic) mass of the universe is roughly three-quarters (roughly seventy-five percent) hydrogen, roughly one-quarter (roughly twenty-five percent) helium, and tiny amounts of all the other atoms on the Periodic Table of Elements.  Therefore, astrophysicists place all the atoms on the Periodic Table of Elements into only three categories: hydrogen, helium, and metals.  In other words, astrophysicists use the word metal for any atom besides hydrogen or helium.  Many students are offended by this categorization, claiming that oxygen and nitrogen and neon for example are not metals.  In a chemistry course, this is certainly the case.  Nevertheless, astrophysicists classify all atoms besides hydrogen and helium as metals.  The metallicity of a star or a nebula or even an entire galaxy is the fraction (percentage) of its normal (atomic) mass that is composed of metals (all atoms besides hydrogen and helium).  Population I stars have relatively higher metallicities, since they are a later (more recent) generation of stars polluted or enriched by metals from the supernova explosions of an earlier generation of high-mass stars.  Caution: by higher metallicity we mean at most one percent or two percent; all stars in the universe are composed of roughly three-quarters (roughly seventy-five percent) hydrogen, roughly one-quarter (roughly twenty-five percent) helium, and only tiny amounts of metals.  Population II stars have relatively lower metallicities, since they are an older generation of stars that were not significantly polluted or enriched by metals, since they were born when the universe was younger and therefore there was less time for high mass stars to synthesize metals.  The metallicities of Population II stars is roughly 0.1%, roughly ten times smaller than the metallicities of Population I stars.  That is, the metallicities of Population I stars is roughly ten times greater than the metallicities of Population II stars.  The very first generation of stars born in the entire universe had zero metallicity, since they were composed of pure hydrogen and helium since there was no earlier generation of stars to synthesize any metals.  These stars are called Population III (Roman numeral) stars.  In other words, Population III stars should really be renamed first-generation stars, Population II stars should really be renamed second-generation stars, and Population I stars should really be renamed third-generation stars!  Nevertheless, we will continue to use the standard Roman numeral designations.  In summary, Population I stars are within the galactic disk and are comparatively high mass, hot, luminous, blue, young, high-metallicity stars, while Population II stars are within the galactic halo and are comparatively low mass, cool, dim, red, old, low-metallicity stars.

 

As we discussed earlier in the course, the main sequence is a population abundance sequence.  That is, most stars are born late-type main sequence stars (cool, dim, red, and low-mass with long lifetimes), while few stars are born early-type main sequence stars (hot, luminous, blue, and high-mass with short lifetimes).  If the very first generation of stars born in the entire universe, Population III stars with zero metallicity, formed in the same way that stars continue to form today, then most of them would still remain to the present day, since most stars are born low-mass with long lifetimes.  However, no Population III stars with zero metallicity have ever been discovered.  This strongly suggests that the first generation of stars born in the universe formed by a mechanism different from later star formation mechanisms.  Although astrophysicists continue to debate the mechanism by which Population III stars formed, it seems that we must conclude that all Population III stars were born early-type main sequence stars (hot, luminous, blue, and high-mass with short lifetimes).  This would explain why there are no Population III stars remaining in the universe today; all of them were born high-mass main sequence stars with short lifetimes and hence all of them died within only millions of years after their birth.  As we will discuss shortly, there is further evidence that all Population III stars were born high-mass stars with short lifetimes.

 

All stars are born in clusters, since many stars are born within a diffuse nebula simultaneously.  However, most stars do not remain in clusters indefinitely.  After a star cluster is born from a diffuse nebula, the individual stars drift apart from one another as they move along their own orbital trajectories through our Milky Way Galaxy.  Therefore, most stars are not members of star clusters.  For example, our Sun is not presently a member of a star cluster, although our Sun was presumably born a member of an ancient star cluster that has long since dispersed.  Star clusters within the galactic disk that are composed of Population I stars are called open star clusters.  The Pleiades Cluster in the constellation Taurus (the bull) and the Ptolemy Cluster in the constellation Scorpius (the scorpion) are beautiful examples of open star clusters.  Star clusters within the galactic halo (outside of the galactic disk) that are composed of Population II stars are called globular star clusters.  The Hercules Cluster in the constellation Hercules (the hero) and Omega Centauri in the constellation Centaurus (the centaur) are beautiful examples of globular star clusters.  The closest star cluster to our Solar System is the Hyades Cluster, an open star cluster within the galactic disk roughly fifty parsecs (roughly 150 light-years) distant in the direction of the constellation Taurus (the bull).  However, there are several other groups of stars even closer than the Hyades Cluster.  These stellar groups were probably born as open star clusters, and they are currently in the process of dispersing.  The closest such stellar group is the Ursa Major Stellar Group located within the galactic disk roughly twenty-five parsecs (roughly eighty light-years) distant in the direction of the constellation Ursa Major (the big bear).

 

Everything we have discussed about Population I stars and Population II stars applies to open star clusters and globular star clusters, respectively.  In particular, open star clusters are composed of comparatively high mass, hot, luminous, blue, young, high-metallicity stars as compared with globular star clusters which are composed of comparatively low mass, cool, dim, red, old, low-metallicity stars.  As we discussed earlier in the course, the Hertzsprung-Russell diagram of a star cluster reveals the history of the cluster.  For example, we can calculate the age of a star cluster from the main sequence turnoff on its Hertzsprung-Russell diagram.  We know that open star clusters are young, since the main sequence turnoff on their Hertzsprung-Russell diagrams is early.  Conversely, we know that globular star clusters are old, since the main sequence turnoff on their Hertzsprung-Russell diagrams is late.  In fact, globular star clusters are the oldest organizations in the Milky Way Galaxy; many globular star clusters are roughly ten billion years old.  This is how we know the age of the entire Milky Way Galaxy, from the age of its oldest organizations.  Globular star clusters contain an abundance of white dwarfs, since globular star clusters are old and hence there has been sufficient time for many low-mass stars in the cluster to live their long lifetimes and reach the very end of their evolutions, finally ending their lives as white dwarfs.  Conversely, open star clusters contain few white dwarfs, since open star clusters are young and hence there has only been sufficient time for very few of the low-mass stars in the cluster to live their lifetimes and reach the very end of their evolutions, finally ending their lives as white dwarfs.  If an open star cluster is particularly young, there may be no white dwarfs within the cluster at all, since there has only been sufficient time for high-mass stars in the cluster to live their short lifetimes and reach the very end of their evolutions, finally ending their lives with supernova explosions and leaving behind neutron stars or black holes.  Particularly young open star clusters are often still embedded within the diffuse nebula from which they formed.  These are called embedded star clusters.

 

Open star clusters are irregularly shaped, hence the term open.  Globular star clusters are spherically shaped, hence the term globular.  Open star clusters are within the galactic disk orbiting the center of the Milky Way Galaxy together with most of the stars that compose the Milky Way Galaxy.  Therefore, many open star clusters move at slow speeds relative to our Solar System, since we are actually moving together in roughly the same angular (orbital) direction at roughly the same speed.  Globular star clusters move at fast speeds relative to our Solar System, since they are within the galactic halo (outside of the galactic disk) moving along random orbits around the center of the Milky Way Galaxy.  Open star clusters typically contain only several hundred stars.  Consequently, the mutual gravitational attraction of all the stars within an open star cluster is insufficient to hold the cluster together.  Thus, stars are not gravitationally bound to each other within an open cluster, and therefore within only several million years the stars within the open star cluster will disperse from one another.  Globular star clusters typically contain hundreds of thousands of stars.  Consequently, the mutual gravitational attraction of all the stars within a globular star cluster is sufficient to hold the cluster together.  Thus, stars are gravitationally bound to each other within a globular star cluster.

 

Just as diffuse nebulae are regions of the interstellar medium that are more dense than average, bubbles are regions of the interstellar medium that are less dense than average.  As we discussed earlier in the course, the hottest and most luminous main sequence stars have spectral type either O or B.  An O-type or a B-type star is so luminous that the strong radiation pressure from its light will push gases within the interstellar medium away from the star.  The stellar wind of an O-type or B-type star is also sufficiently strong to push gases within the interstellar medium away from the star.  The result is a bubble: a spherical region around the O-type or B-type star where the interstellar medium is less dense than average.  Every O-type or B-type star has a bubble surrounding it.  Star clusters with a significant number of O-type and B-type stars are called OB associations.  The combined luminosities and the combined stellar winds from all the O-type and B-type stars within these OB associations push the gases of the interstellar medium so strongly that the entire OB association is surrounded by a superbubble.  Every OB association has a superbubble surrounding it.  These superbubbles are enormous, hundreds of light-years across.  The galactic disk is only roughly one thousand light-years thick, as we discussed.  Therefore, a superbubble can grow to sufficient size to burst out of the galactic disk, ejecting material out of the galactic disk.  The gravity of the galactic disk does pull this material back toward the galactic disk however, and the subsequent collision of this ejected material with the gases of the interstellar medium within the galactic disk may induce star formation.  As we discussed earlier in the course, O-type and B-type stars live short main sequence lifetimes and die with a violent supernova.  It is not difficult to calculate that the supernova remnant ejected by a supernova at first moves so fast that its gases should be able to escape from the gravitational attraction of the entire Milky Way Galaxy.  However, this rapidly expanding supernova remnant soon collides with the gases of the surrounding interstellar medium.  Firstly, the collision slows the expanding supernova remnant to speeds slower than the galactic escape speed, thus keeping the gases within the galactic disk.  Moreover, the collision compresses the surrounding gases of the interstellar medium.  These gases may be compressed to sufficient densities for gravity to dominate over other forces within small parts of the surrounding interstellar medium, thus inducing star formation.  In summary, high mass stars often trigger the birth of new stars, either through superbubbles that burst out from and then fall back toward the galactic disk or through the collision of supernova remnants with the surrounding interstellar medium.

 

There are three different types of diffuse nebulae: absorption nebulae, emission nebulae, and reflection nebulae.  Absorption nebulae tend to appear black in color, since they absorb photons.  Note however that an infrared image of an absorption nebula often clearly reveals the gases within it.  The Horsehead Nebula in the constellation Orion (the hunter) is a beautiful example of an absorption nebula.  Other diffuse nebulae have stars within them that were recently born from the gases within the nebula itself.  The light radiated by these stars within the nebula are absorbed by the surrounding gases of the nebula.  This transitions the electrons within the atoms composing the nebula to higher-energy quantum states.  The electrons then transition back down to lower-energy quantum states, thus emitting photons.  The result is an emission nebula.  All nebulae are composed of mostly hydrogen gas, and there is a particular photon within the emission spectrum of the hydrogen atom that falls within the red part of the visible light spectrum, causing emission nebulae to often appear red in color.  Note however that an emission nebula often displays a variety of colors, caused by photons emitted from other transitions of electrons within the hydrogen atom and also transitions of electrons within other atoms composing the nebula in addition to hydrogen.  There are many transitions within the hydrogen atom and other atoms that result in the emission of ultraviolet photons.  Therefore, an ultraviolet image of an emission nebula often more clearly reveals the gases within it than a visible light image.  The Orion Nebula in the constellation Orion (the hunter) is a beautiful example of an emission nebula.  Reflection nebulae tend to appear blue in color, since shorter wavelengths of light are more preferentially scattered than longer wavelengths of light, and blue is the short-wavelength end of the visible light spectrum.  The Witch Head Nebula in the constellation Orion (the hunter) is a beautiful example of a reflection nebula.  Note that most diffuse nebulae are a combination of all three types (absorption, emission, and reflection), such as the Trifid Nebula in the constellation Sagittarius (the centaur archer).

 

The molecules of the Earth’s atmosphere scatter our Sun’s light.  The shorter wavelengths are more preferentially scattered than the longer wavelengths, causing the daytime sky to appear blue.  The sky during sunrises and sunsets is red for the same reason.  Blue light has been scattered out of sunlight, causing the daytime sky to appear blue.  By the time sunlight has traveled through the Earth’s atmosphere to arrive at someone on the cusp of the daytime side of the Earth where it is sunrise or sunset, most of the short-wavelength blue light has been subtracted from sunlight, leaving only the long-wavelength red light.  The same effect occurs within the interstellar medium.  As light traverses interstellar space, photons are absorbed and scattered by the gases of the interstellar medium.  The shorter-wavelength blue light is more preferentially scattered, leaving the longer-wavelength red light.  Astronomers call this effect reddening, although this term reddening is misleading, since it implies that red light has been added to the starlight.  In actuality, blue light has been subtracted; hence, astronomers should rename this reddening effect as de-bluing instead!  Nevertheless, all astronomers call this effect reddening.  As a result of reddening, whenever we calculate the temperature of a star using color indices as we discussed earlier in the course, we are actually calculating an incorrect temperature for the star.  The temperature we calculate is cooler than the true temperature of the star, since red light corresponds to cooler temperatures.  The actual temperature of the star is hotter than the temperature we calculate.  Astronomers try to estimate the total amount of reddening that has occurred while the starlight traversed interstellar space through the interstellar medium.  Astronomers then add this total reddening (actually scattered blue light) back into the color index calculations to determine the true temperature of the star.  More strictly, astronomers must estimate the total extinction to determine the true temperature of the star.  Extinction is the total amount of light that has been either scattered or absorbed by the interstellar medium.  The total extinction of light as it traverses through the galactic disk is quite severe.  After traveling just a few kiloparsecs (several thousand light-years) through the interstellar medium of the galactic disk, one hundred percent extinction is attained, meaning that none of the starlight remains!  In other words, we cannot observe visible light beyond a few kiloparsecs (several thousand light-years) within our own galactic disk!  Observing other galaxies beyond our Milky Way Galaxy along the direction of our galactic disk is therefore hopeless.  Fortunately, our galactic disk is rather thin, as we discussed.  Therefore, extinction is less severe along directions perpendicular to the galactic disk.  Therefore, we are only able to observe the extragalactic universe (the universe beyond our Milky Way Galaxy) in directions perpendicular to our galactic disk, above and below the galactic plane.  Although the galactic disk is essentially opaque to visible light, astronomers use other wavelengths of light to observe through our galactic disk, such as high-energy X-rays.  Some low-energy photons are also able to traverse through the galactic disk with minimal extinction.  The primary photon that astronomers use to observe through our galactic disk is twenty-one centimeter wavelength photons.  Hydrogen is the most abundant atom composing the interstellar medium.  Hydrogen is also the simplest atom in the universe; it has only one electron around its nucleus, and its nucleus is composed of a single proton.  As we discussed earlier in the course, quantum-mechanical particles have an intrinsic angular momentum, commonly known as spin.  Within the hydrogen atom, the spins of the proton and the electron can be either parallel to each other or antiparallel to each other.  The antiparallel configuration is at a lower-energy quantum state than the parallel configuration.  Therefore, if the spins of the proton and the electron within the hydrogen atom happen to be parallel, the spins may attain the antiparallel configuration to lower the energy of the entire atom.  With this transition from the parallel configuration to the antiparallel configuration, the hydrogen atom will emit a photon with a frequency of roughly 1420 megahertz and a wavelength of roughly twenty-one centimeters.  Since roughly three-quarters (roughly seventy-five percent) of the normal (atomic) mass of the universe is hydrogen atoms that continuously emit twenty-one centimeter photons, the universe is filled with photons with a wavelength of twenty-one centimeters.  These particular photons fall in the microwave band of the Electromagnetic Spectrum, and microwaves suffer minimal extinction while traversing through the interstellar medium.  Therefore, astronomers have determined the structure (the shape) of our galactic disk by mapping the twenty-one centimeter photons emitted by hydrogen atoms.

 

Again, our Milky Way Galaxy is a spiral-disk galaxy, meaning that most of its star systems are arranged in a flat disk with spiral arms while orbiting the center of our Milky Way Galaxy in roughly the same angular (orbital) direction.  The galactic disk has two major spiral arms: the Perseus Arm and the Scutum-Centaurus-Crux Arm.  There are a number of minor spiral arms, such as the Norma Arm, the Carina-Sagittarius Arm, and the Orion Arm.  As we discussed, our Solar System is roughly halfway from the center of our Milky Way Galaxy, roughly eight kiloparsecs (roughly twenty-five thousand light-years) from the galactic center.  More precisely, our Solar System is within the minor Orion Arm, which is itself next to the major Perseus Arm.  From our location, the galactic center is in the direction of the constellation Sagittarius (the centaur archer).  Astronomers have determined the location of the galactic center from the distribution of globular star clusters in the galactic halo.  The locations of globular star clusters are roughly spherically distributed throughout the galactic halo around the galactic bulge, roughly eight kiloparsecs (roughly twenty-five thousand light-years) from our Solar System in the direction of the constellation Sagittarius (the centaur archer).  The galactic disk is thin as compared with its diameter, as we discussed.  The flatness of our galactic disk manifests itself in the sky.  As we discussed earlier in the course, for thousands of years humans observed a band of milk around the entire sky they called the milky way.  Galileo Galilei used his primitive telescope to discover that the milky way is not in fact milk; even a primitive telescope reveals that the milky way is actually innumerable stars sufficiently crowded together in the sky that with the naked eye all of their light blends together so as to appear to be milk.  Today we realize that this milky way in the sky is actually our flat galactic disk projected onto our sky.  When we observe into the direction of the milky way in the sky, we are actually observing into our galactic disk.  When we observe into the direction of the milky way in the sky in the direction of the constellation Sagittarius (the centaur archer), we are actually observing into our galactic disk and toward our galactic center.  When we observe into the direction of the milky way in the sky in the opposite direction of the constellation Sagittarius (the centaur archer), we are actually observing into our galactic disk but away from our galactic center.  This is often called the galactic anticenter, and it is in the direction of the milky way in the sky but in the opposite direction of the constellation Sagittarius (the centaur archer).  More precisely, this galactic anticenter is near the intersection of the three constellations Auriga (the charioteer), Gemini (the twins), and Taurus (the bull).  If we observe directions off of the milky way in the sky, we are actually observing along directions above or below our galactic disk, which are the only directions where we may observe the extragalactic universe, the universe beyond our Milky Way Galaxy.

 

Galactic Properties

 

There are a few dozen small galaxies near our Milky Way Galaxy.  These are satellite galaxies, since they orbit our Milky Way Galaxy.  Caution: anything orbiting anything else is considered a satellite.  The Moon is a satellite of the Earth, the Earth is a satellite of the Sun, and entire galaxies can be satellites of other galaxies.  The two closest small satellite galaxies to our Milky Way Galaxy are the Canis Major Dwarf Galaxy and the Sagittarius Dwarf Galaxy.  These galaxies are named for the constellations wherein they reside in our sky, the constellation Canis Major (the big dog) and the constellation Sagittarius (the centaur archer).  The Canis Major Dwarf Galaxy is roughly eight kiloparsecs (roughly twenty-five thousand light-years) from our Solar System.  The constellation Canis Major (the big dog) lies close to the milky way in the sky.  Therefore, the Canis Major Dwarf Galaxy is in physical contact with our galactic disk.  The Sagittarius Dwarf Galaxy is roughly twenty-five kiloparsecs (roughly seventy-five thousand light-years) from our Solar System.  The constellation Sagittarius (the centaur archer) lies close to the milky way in the sky in the direction toward our galactic center, as we discussed.  Therefore, the Sagittarius Dwarf Galaxy is on the other side of our own Milky Way Galaxy, also in physical contact with our galactic disk.  Another small satellite galaxy of our Milky Way Galaxy is the Large Magellanic Cloud, which astronomers always abbreviate the LMC.  The Large Magellanic Cloud is roughly fifty kiloparsecs (roughly one hundred and fifty thousand light-years) from our Solar System.  Note that the famous supernova SN1987A occurred in the Large Magellanic Cloud, as we discussed earlier in the course.  Yet another small satellite galaxy of our Milky Way Galaxy is the Small Magellanic Cloud, which astronomers always abbreviate the SMC.  The Small Magellanic Cloud is roughly sixty kiloparsecs (roughly two hundred thousand light-years) from our Solar System.  The two Magellanic Clouds are visible from the southern hemisphere without the aid of a telescope or even a pair of binoculars.  To the naked eye, the two Magellanic Clouds appear to be colorful clouds several times larger than the Full Moon in the sky.  The two Magellanic Clouds are named for the Portuguese explorer Ferdinand Magellan, who led the first mission to successfully circumnavigate the entire world in the early sixteenth century (the early 1500s).  The two Magellanic Clouds are classified as irregular galaxies.  Other small satellite galaxies of our Milky Way Galaxy include the Draco Dwarf Galaxy, the Sculptor Dwarf Galaxy, the Carina Dwarf Galaxy, the Fornax Dwarf Galaxy, and the Phoenix Dwarf Galaxy.  Each small satellite galaxy of our Milky Way Galaxy is composed of roughly one billion stars.  As these small satellite galaxies move along their orbits, the gravity of our Milky Way Galaxy perturbs the motion of the stars within these small satellite galaxies.  As a result, our Milky Way Galaxy slowly rips apart these small satellite galaxies.  Ultimately, our Milky Way Galaxy will devour some of these small satellite galaxies, causing our Milky Way Galaxy to gradually grow larger and larger over billions of years.  In fact, there is evidence that some groups of stars within our Milky Way Galaxy were formerly small satellite galaxies that our Milky Way Galaxy completely devoured.

 

The nearest major galaxy to our Milky Way Galaxy is the Andromeda Galaxy, roughly eight hundred kiloparsecs (roughly 2.5 million light-years) distant.  The Andromeda Galaxy is a spiral-disk galaxy similar in size, mass, and structure (shape) to our own Milky Way Galaxy.  The Andromeda Galaxy also has its own small satellite galaxies, the two most prominent being M32 (also designated NGC 221) and M110 (also designated NGC 205).  Other small satellite galaxies of the Andromeda Galaxy include NGC 185 and NGC 147.  The uppercase (capital) letter M stands for the Messier deep sky catalogue, a list of one hundred and ten faint objects in the sky compiled by the French astronomer Charles Messier in the eighteenth century (the 1700s).  The objects on the Messier deep sky catalogue that we have discussed in this course include M1 the Crab Nebula (a supernova remnant), M7 the Ptolemy Cluster (an open star cluster), M13 the Hercules Cluster (a globular star cluster), M20 the Trifid Nebula (a diffuse nebula), M31 the Andromeda Galaxy (a spiral-disk galaxy), M32 (a small satellite galaxy of M31), M33 the Triangulum Galaxy (a spiral-disk galaxy that we will discuss shortly), M42 the Orion Nebula (a diffuse nebula), M45 the Pleiades Cluster (an open star cluster), M57 the Ring Nebula (a planetary nebula), and M110 (a small satellite galaxy of M31).  The New General Catalogue, which astronomers always abbreviate NGC, is a more comprehensive deep sky catalogue compiled in the late nineteenth century (the late 1800s).  The Index Catalogue, which astronomers always abbreviate IC, is an even more comprehensive deep sky catalogue than the New General Catalogue.  Caution: a particular deep sky object may have one Messier Catalogue number, a different New General Catalogue number, and yet another Index Catalogue number!  A similar confusion occurs with stellar designations.  Any particular star may have one CPD number (from the Cape Photographic Durchmusterung Catalogue), another GSC number (from the Guide Star Catalog), yet another HD number (from the Henry Draper Catalogue), yet another SAO number (from the Smithsonian Astrophysical Observatory Catalog), and yet another HIP number (from the Hipparcos Catalogue)!  The light from the Andromeda Galaxy is blueshifted, revealing that the Andromeda Galaxy is moving toward our Milky Way Galaxy.  In actuality, our Milky Way Galaxy and the Andromeda Galaxy are falling toward each other due to their mutual gravitational attraction.  These two galaxies will collide in roughly five billion years.  The Triangulum Galaxy is another nearby major spiral-disk galaxy, although it is significantly smaller than our Milky Way Galaxy or the Andromeda Galaxy; the Triangulum Galaxy is composed of roughly ten billion stars.  The Triangulum Galaxy is more than eight hundred kiloparsecs (almost three million light-years) distant.  The Local Galactic Group is the collection of several dozen galaxies that define our galactic neighborhood.  Most of the galaxies in the Local Galactic Group are small irregular galaxies, such as the two Magellanic Clouds.  There are only three major galaxies in the Local Galactic Group: our own Milky Way Galaxy, the Andromeda Galaxy, and the Triangulum Galaxy.  The Local Galactic Group is roughly three megaparsecs (roughly ten million light-years) in diameter.

 

We cannot measure the distances to our satellite galaxies such as the two Magellanic Clouds using the main sequence fitting method, and measuring the distance to the Andromeda Galaxy or the Triangulum Galaxy is out of the question using this main sequence fitting method.  Therefore, we need a higher rung of the Cosmological Distance Ladder to measure these extragalactic distances.  The next major rung of the Cosmological Distance Ladder above the main sequence fitting method is the variable star method.  A variable star has a luminosity (absolute magnitude or intrinsic brightness) that varies significantly.  These significant variations are caused by pulsations within the star; as a variable star expands and contracts, its surface area changes, thus varying its luminosity.  There are many different classes of variable stars, such as Cepheid variable stars, Lyrae variable stars, and Tauri variable stars.  As we discussed earlier in the course, Tauri variable stars are protostars, Cepheid variable stars are asymptotic-giant-branch stars, and Lyrae variable stars are horizontal-branch stars.  All variable stars are transitioning from one equilibrium evolutionary stage to another equilibrium evolutionary stage.  A transition is essentially an instability, thus causing pulsations within the star, causing its size to oscillate from large to small and back again.  As a result, the luminosity of a variable star oscillates from bright to dim and back again.  At the beginning of the twentieth century (the early 1900s), the American astronomer Henrietta Leavitt discovered an equation relating the average luminosity of Cepheid variable stars with their pulsation period.  This equation is called the Leavitt period-luminosity relation in her honor.  Other similar equations have been discovered for other classes of variable stars, and all such equations are known as period-luminosity relations.  We can use these period-luminosity relations to measure extragalactic distances.  First, we determine the distance to nearby variable stars within our own Milky Way Galaxy using the parallax method or the main sequence fitting method.  We combine their distance with their average apparent magnitude to calculate their average absolute magnitude.  We also measure the pulsation period of these nearby variable stars; their pulsation period together with their average luminosity establishes the period-luminosity relations.  Now suppose we discover variable stars within another galaxy.  Even nearby galaxies are sufficiently distant that we cannot use the parallax method or the main sequence fitting method to measure their distance.  Instead, we measure the pulsation periods of variable stars within these galaxies.  Using the established period-luminosity relations, we can now calculate the average luminosity of these variable stars.  Finally, we combine their average luminosity with their average apparent magnitude to determine the distance to these variable stars and hence the distance to the galaxy wherein they reside.  This procedure is called the variable star method, the next major rung of the Cosmological Distance Ladder above the main sequence fitting method.  To determine the distance to a nearby galaxy, we measure the pulsation periods of variable stars within the galaxy.  We then use the established period-luminosity relations to determine their average luminosity, and finally we combine the average luminosity with the average apparent magnitude to calculate the distance.  This variable star method is used to determine distances not only to galaxies within the Local Galactic Group.  This variable star method is used to measure distances to galaxies even beyond the Local Galactic Group, out to distances as far as roughly one hundred megaparsecs (roughly three hundred million light-years) from our Milky Way Galaxy.

 

During the eighteenth century (the 1700s), moderately powerful telescopes began to reveal faint irregular objects in the sky that astronomers called nebulae.  Somewhat more powerful telescopes in the nineteenth century (the 1800s) magnified these nebulae.  Some of these nebulae still appeared irregularly shaped when magnified, but other nebulae appeared to have spiral shapes when magnified.  Astronomers named these objects spiral nebulae.  At the beginning of the twentieth century (the early 1900s), some astronomers claimed that these spiral nebulae were not nebulae at all.  These astronomers claimed that these objects were actually collections of billions of stars held together by gravity.  In other words, these astronomers claimed that the universe is not homogeneously filled with stars; these astronomers claimed that stars are clumped into gigantic organizations that they called island universes.  These astronomers also claimed that we live within one of these island universes as revealed by the band of milk that wraps around our sky.  Other astronomers were opposed to this new idea; these astronomers claimed that spiral nebulae were clouds of gas and nothing more.  The debate over the true nature of spiral nebulae is called the Great Debate in the history of astronomy.  This Great Debate occurred on April 26, 1920, at the Smithsonian Museum of Natural History in Washington, D.C., between the two American astronomers Harlow Shapley and Heber Curtis.  Therefore, the Great Debate is also called the Shapley-Curtis Debate.  Curtis argued in favor of island universes, while Shapley argued against island universes.  Neither of these astronomers settled this Great Debate.  The greatest American astronomer of the twentieth century, Edwin Hubble, settled this Great Debate a few years later.  In the year 1924, Edwin Hubble discovered Cepheid variable stars in what was then called the Andromeda Spiral Nebula and the Triangulum Spiral Nebula.  Using the Leavitt period-luminosity relation, Edwin Hubble calculated the distances to these so-called spiral nebulae to be in the hundreds of kiloparsecs (millions of light-years).  The only way we could ever see anything at such incredible distances is if it shines with the luminosity of billions of stars.  Therefore, astronomers realized that Heber Curtis was correct.  These so-called spiral nebulae are not nebulae at all; they are island universes of billions of stars, and we live within one of these island universes.  Eventually, these island universes were renamed galaxies.  The word galaxy is derived from the Greek root galacto- for milk.  For example, galactose and glucose are two simple sugars that compose the milk sugar lactose.  The Andromeda Spiral Nebula was renamed the Andromeda Galaxy, the Triangulum Spiral Nebula was renamed the Triangulum Galaxy, and our home galaxy was named the Milky Way Galaxy, which literally means milky milk!

 

As we observe galaxies beyond the Local Galactic Group, we discover that there are two main types of galaxies in our universe.  One type is spiral-disk galaxies, such as our own Milky Way Galaxy, the Andromeda Galaxy, and the Triangulum Galaxy.  The other major type of galaxy in our universe is elliptical galaxies.  These elliptical galaxies should really be called ellipsoidal galaxies, since their true shape is a three-dimensional ellipse, and a three-dimensional ellipse is called an ellipsoid.  Nevertheless, astronomers named them elliptical galaxies, since their shapes appear to be ellipses in photographs.  Spiral-disk galaxies are more flat in structure (shape), while elliptical galaxies are more round in structure (shape).  Spiral-disk galaxies are more flat because most of their stars orbit their galactic center in nearly the same plane in nearly the same angular (orbital) direction.  The orbits of all of these stars add together to give spiral-disk galaxies high angular momentum.  Elliptical galaxies are more round because most of their stars orbit their galactic center in random orbits in random directions.  The orbits of all these stars mostly cancel each other to give elliptical galaxies low angular momentum.  Spiral-disk galaxies have an abundance of interstellar gas resulting in active star formation, making their stellar populations relatively high mass, hot, luminous, and blue (early-type stars) with high metallicities.  Elliptical galaxies have little interstellar gas and hence little star formation, making their stellar populations relatively low mass, cool, dim, and red (late-type stars) with low metallicities.  Of course, when an elliptical galaxy was first born, some of its stars must have been high mass, hot, luminous, and blue (early-type stars).  However, these stars have short main sequence lifetimes, as we discussed earlier in the course.  With very little interstellar gas to give birth to new stars, the only stars remaining in an elliptical galaxy after the short lifetimes of the early-type stars are low mass, cool, dim, and red (late-type stars) with low metallicities.  The stellar populations within spiral-disk galaxies and elliptical galaxies should sound familiar.  Within our Milky Way Galaxy, the relatively high mass, hot, luminous, and blue (early-type) stars orbiting in roughly the same angular (orbital) direction within the galactic disk where an abundance of interstellar gas results in active star formation are the Population I stars, while the relatively low mass, cool, dim, and red (late-type) stars orbiting in random directions throughout the galactic halo where there is little interstellar gas and hence little star formation are the Population II stars.  We conclude that a spiral-disk galaxy is an entire galaxy of mostly Population I stars, while an elliptical galaxy is an entire galaxy of mostly Population II stars.

 

Spiral-disk galaxies have high angular momentum due to most of its stars orbiting its galactic center in nearly the same plane in nearly the same angular (orbital) direction.  As a result, the light we receive from one side of a spiral-disk galaxy is blueshifted relative to its galactic center, since those stars happen to be moving toward us, while the light we receive from the other side of the spiral-disk galaxy is redshifted relative to its galactic center, since those stars happen to be moving away from us.  From these blueshifts and redshifts, we can calculate the speeds with which the stars orbit the galactic center.  From these speeds, we can calculate the gravitational force acting on these stars, and hence we can calculate the distribution of mass within these galaxies.  Again, we discover that there is roughly ten times as much mass as normal (luminous star) mass.  This is the mysterious dark matter.  Although elliptical galaxies have low angular momentum, we can still measure a dispersion of blueshifts and redshifts in the light from these galaxies, enabling us to calculate a velocity dispersion.  Again, we can calculate the gravitational force acting on these stars to cause the velocity dispersion, and again we can calculate the distribution of mass within these galaxies.  Yet again, we discover that there is roughly ten times as much dark matter as normal (luminous star) matter.  Evidently, all galaxies in the universe are composed of roughly ninety percent dark matter and only roughly ten percent normal (luminous star) matter.  All of these observations provide us with another method of determining distance.  The Tully-Fisher relation is an equation that correlates the orbital speed of stars within a spiral-disk galaxy to the luminosity of the spiral-disk galaxy, named for the astronomers R. Brent Tully and J. Richard Fisher who together first formulated this equation.  The orbital speed of the stars within a spiral-disk galaxy is caused by the gravitational force, which is exerted by the total mass of the galaxy.  Although the total mass of the galaxy is mostly dark matter, there is still a correlation between the total amount of mass and the amount of normal (luminous star) mass.  If blueshifts and redshifts are more severe, the stars must be orbiting faster from a stronger gravitational force caused by a greater quantity of total mass, both dark matter and normal (luminous star) matter.  If blueshifts and redshifts are more modest, the stars must be orbiting slower from a weaker gravitational force caused by a lesser quantity of total mass, both dark matter and normal (luminous star) matter.  In brief, the Tully-Fisher relation states that if a spiral-disk galaxy rotates faster, then it must be more luminous, and if a spiral-disk galaxy rotates slower, then it must be less luminous.  The Faber-Jackson relation is a similar equation that correlates the velocity dispersion of stars within an elliptical galaxy to the luminosity of the elliptical galaxy, named for the astronomers Sandra Faber and Robert Jackson who together first formulated this equation.  To use the Tully-Fisher relation and the Faber-Jackson relation to determine the distance to distant galaxies, we first use the variable star method to determine the distance to somewhat closer galaxies.  We combine their distance with their apparent magnitude to calculate the luminosity or the absolute magnitude or the intrinsic brightness of these somewhat closer galaxies.  Some of these somewhat closer galaxies are spiral-disk galaxies, while others are elliptical galaxies.  We measure the orbital speed of stars within the spiral-disk galaxies to establish the Tully-Fisher relation, and we measure the velocity dispersion of stars within the elliptical galaxies to establish the Faber-Jackson relation.  Now suppose we wish to measure the distances to galaxies so distant that we cannot use the variable star method, since even our most powerful telescopes cannot resolve variable stars within these distant galaxies.  For distant spiral-disk galaxies, we measure the orbital speed of its stars, and we use the established Tully-Fisher relation to calculate the luminosity of the spiral-disk galaxy.  For distant elliptical galaxies, we measure the velocity dispersion of its stars, and we use the established Faber-Jackson relation to calculate the luminosity of the elliptical galaxy.  In either case, we combine the luminosity with the apparent magnitude to finally calculate the distance to the galaxy.  The Tully-Fisher relation and the Faber-Jackson relation together are the next major rung of the Cosmological Distance Ladder above the variable star method.

 

Not only are stars clumped together to form galaxies, but galaxies are themselves clumped together to form even larger organizations called galactic groups or galactic clusters.  Galactic groups are composed of several dozen galaxies, although most of these galaxies are small minor galaxies.  A typical galactic group is composed of less than ten large major galaxies.  For example, our Local Galactic Group is composed of several dozen small minor galaxies but only three large major galaxies: our own Milky Way Galaxy, the Andromeda Galaxy, and the Triangulum Galaxy.  The nearest galactic group to our own Local Galactic Group is the Maffei Galactic Group, roughly three megaparsecs (roughly ten million light-years) distant.  Other nearby galactic groups include the Bode Galactic Group at roughly 3.5 megaparsecs (more than eleven million light-years) distant, the Sculptor Galactic Group at nearly four megaparsecs (nearly thirteen million light-years) distant, and the Leo Triplet Galactic Group at nearly eleven megaparsecs (roughly thirty-five million light-years) distant.  Each of these galactic groups is composed of only a few large major galaxies and several dozen small minor galaxies.  Galactic clusters on the other hand are composed of hundreds of large major galaxies.  The nearest galactic cluster is the Virgo Galactic Cluster, roughly seventeen megaparsecs (more than fifty-six million light-years) distant.  Other nearby galactic clusters include the Fornax Galactic Cluster at nearly twenty megaparsecs (more than sixty million light-years) distant, the Eridanus Galactic Cluster at roughly twenty-three megaparsecs (roughly seventy-five million light-years) distant, the Antila Galactic Cluster at more than forty megaparsecs (more than 130 million light-years) distant, the Centaurus Galactic Cluster at more than fifty megaparsecs (more than 170 million light-years) distant, and the Hydra Galactic Cluster at nearly sixty megaparsecs (nearly two hundred million light-years) distant.  Each of these galactic clusters is composed of hundreds of large major galaxies.  We can determine the distance to a galactic cluster by applying the Tully-Fisher relation to its spiral-disk members and the Faber-Jackson relation to its elliptical members.  The results using these two different methods on galaxies within the same galactic cluster have always been found to be roughly consistent with each other, confirming the reliability of these two methods for determining distance.  We can also measure the blueshifts and the redshifts of entire galaxies within a galactic cluster relative to the center of the galactic cluster to determine the orbital speeds of entire galaxies within the galactic cluster.  We can then calculate the gravitational force responsible for these orbital speeds, and thus we can calculate the total mass that exerts this gravitational force.  We discover that galactic clusters are composed of roughly ten times as much dark matter as normal (luminous star) matter.  There is also diffuse gas that fills the space between galaxies within galactic clusters.  This diffuse gas is called the intergalactic medium, since this gas is distributed among many galaxies.  This diffuse gas is also called the intracluster medium, since this gas is distributed within a galactic cluster.  Caution: the prefix inter- means among, while the prefix intra- means within.  Recall that the gas that fills the space among the stars of the galactic disk of our Milky Way Galaxy is called the interstellar medium, since this gas is distributed among many stars.  Note however that this interstellar medium could also be called the intragalactic medium, since this gas is within our Milky Way Galaxy.  We have measured the temperature of the intergalactic/intracluster medium within galactic clusters to be in the millions of kelvins, since this gas radiates primarily X-rays.  Note therefore that the intergalactic/intracluster medium within galactic clusters was not discovered until after astronomers placed X-ray telescopes in orbit around the Earth, since the Earth’s atmosphere is opaque to X-rays, as we discussed earlier in the course.  We can calculate the gravitational force necessary to heat the intergalactic/intracluster medium to these extremely hot temperatures, and again we can calculate the total mass necessary to exert this gravitational force.  Yet again, we discover that galactic clusters are composed of roughly ten times as much dark matter as normal (luminous star) matter.  A galactic cluster contains so much mass that the gravity of a galactic cluster acts as a gravitational lens, bending the light from even more distant galaxies from behind the cluster along our line of sight, as we discussed earlier in the course.  We can use the curved images of these distant galaxies to calculate the gravitational force that causes this lensing, and yet again we can calculate the total mass necessary to exert this gravitational force.  Yet again, we discover that galactic clusters are composed of roughly ten times as much dark matter as normal (luminous star) matter.  Whenever we use these three different methods to calculate the total mass of any particular galactic cluster (the orbital speeds of entire galaxies within the galactic cluster, the temperature of the intergalactic/intracluster medium within the galactic cluster, and the gravitational lensing of distant galaxies caused by the galactic cluster), the results have always been found to be roughly consistent with one another.  Not only does this consistency confirm the reliability of these three methods of determining the total mass of galactic clusters, but this consistency together with rotation curves of individual spiral-disk galaxies (the Tully-Fisher relation) and velocity dispersions of individual elliptical galaxies (the Faber-Jackson relation) all provide strong evidence that the entire universe is composed of roughly ten times as much dark matter as normal (luminous star) matter.

 

Not only are stars clumped together to form galaxies and not only are galaxies themselves clumped together to form galactic groups or galactic clusters, but galactic groups and galactic clusters are clumped into enormous organizations called galactic superclusters.  Our own Local Galactic Group, the Maffei Galactic Group, the Bode Galactic Group, the Sculptor Galactic Group, the Leo Triplet Galactic Group, and innumerable other galactic groups as well as the Virgo Galactic Cluster, the Fornax Galactic Cluster, the Eridanus Galactic Cluster, the Antila Galactic Cluster, the Centaurus Galactic Cluster, the Hydra Galactic Cluster, and several other galactic clusters all together form the Laniakea Galactic Supercluster.  The Laniakea Galactic Supercluster is more than 150 megaparsecs (more than five hundred million light-years) in diameter, and our own Local Galactic Group as well as the nearby Maffei Galactic Group, the Bode Galactic Group, the Sculptor Galactic Group, and the Leo Triplet Galactic Group are all on the outskirts of the Laniakea Galactic Supercluster.  Nearby galactic superclusters to our own Laniakea Galactic Supercluster include the Hydra-Centaurus Galactic Supercluster at roughly seventy megaparsecs (more than 200 million light-years) distant, the Perseus-Pisces Galactic Supercluster at nearly eighty megaparsecs (roughly 250 million light-years) distant, the Coma Galactic Supercluster at more than ninety megaparsecs (roughly three hundred million light-years) distant, and the Shapley Galactic Supercluster at roughly two hundred megaparsecs (roughly 650 million light-years) distant.  Each of these galactic superclusters contains many galactic groups and several galactic clusters.  There are enormous regions between galactic superclusters that are nearly completely empty of galaxies.  These enormous regions are called cosmic voids.  Moreover, galactic superclusters are clumped into colossal organizations called galactic great walls, each containing between a few hundred thousand and a few million galaxies.  Our own Laniakea Galactic Supercluster, the Hydra-Centaurus Galactic Supercluster, the Perseus-Pisces Galactic Supercluster, and several other galactic superclusters all together form the Perseus-Pisces-Sculptor-Hercules Galactic Great Wall.  Nearby galactic great walls to our own Perseus-Pisces-Sculptor-Hercules Galactic Great Wall include the Coma-Hercules-Leo Great Galactic Wall, the Sculptor Galactic Great Wall, and the Sloan Galactic Great Wall.  There are colossal regions between galactic great walls that are nearly completely empty of galaxies.  These colossal regions are called cosmic supervoids.  At size scales of hundreds of megaparsecs (hundreds of millions of light-years) and smaller, the universe appears rather clumpy, with stars clumped together to form galaxies, galaxies clumped together to form galactic groups or galactic clusters, galactic groups and galactic clusters clumped together to form galactic superclusters with cosmic voids between them, and galactic superclusters clumped together to form galactic great walls with cosmic supervoids between them.  However, at size scales of gigaparsecs (billions of light-years), the universe appears less clumpy and more homogeneous (more smooth), since many galactic great walls appear close to each other relative to these titanic size scales.  In other words, there are no conglomerations of matter larger than galactic great walls.  Therefore, cosmologists call this homogeneous (smooth) distribution of mass at these titanic size scales the end of greatness.  The observable universe contains hundreds of thousands, perhaps millions, of galactic great walls.  Since each galactic great wall contains between a few hundred thousand and a few million galaxies, the entire observable universe contains roughly one hundred billion galaxies.  Assuming that each galaxy contains on average one hundred billion star systems just like our Milky Way Galaxy, then there are roughly ten sextillion star systems in the observable universe.

 

To measure these incredible distances, we need an even higher rung of the Cosmological Distance Ladder.  As we discussed earlier in the course, high mass stars end their lives with Type II supernova explosions.  Consider instead a white dwarf orbiting a giant star in a close binary star system with a mass transfer from the giant star to the white dwarf through an accretion disk around the white dwarf, as we discussed earlier in the course.  This white dwarf will suffer from a nova once every few decades, once every few centuries, or once every few millennia, periodically ejecting material from its surface triggered by the fusion of hydrogen into helium on its surface, as we also discussed earlier in the course.  These periodic novae do not stop the mass transfer from the giant star to the white dwarf from continuing.  Hence, the mass of the white dwarf will change.  This variation in mass of the white dwarf depends upon the mass transfer rate from the giant star as compared with the mass loss rate from the periodic novae.  If the mass loss rate from the periodic novae happens to be greater than the mass transfer rate from the giant star, then the white dwarf will lose more and more mass over time.  If the mass transfer rate from the giant star happens to be greater than the mass loss rate from the periodic novae, then the white dwarf will gain more and more mass over time.  In this case however, the increasing mass of the white dwarf cannot continue indefinitely.  The maximum mass of a white dwarf is the Chandrasekhar limit, equal to 1.4M☉ (1.4 solar masses), as we discussed earlier in the course.  If a white dwarf gains so much mass that it reaches this Chandrasekhar limit, electron degeneracy pressure will no longer be able to support the white dwarf.  The self-gravity of the white dwarf will force the white dwarf to compress, raising the temperature of the white dwarf until carbon fusion is initiated.  White dwarfs are composed almost entirely of carbon, as we discussed earlier in the course.  Thus, the entire white dwarf suffers from a thermonuclear detonation, obliterating the entire white dwarf in a cataclysmic explosion that liberates energy in the billions of solar luminosities!  This is roughly the total power output of an entire galaxy of stars!  This unique type of explosion is called a Type Ia supernova, as opposed to a Type II supernova.  Observationally, the Type II supernova of a high mass star and the Type Ia supernova of a carbon white dwarf may seem identical, at least at first glance.  However, a Type II supernova occurs when the iron-nickel white dwarf core of a red supergiant can no longer be supported by electron degeneracy pressure.  The photons liberated from the collapse of the iron-nickel white dwarf core must pass through the outer layers of the red supergiant, which are mostly composed of hydrogen.  Therefore, the light we receive from a Type II supernova has strong hydrogen absorption lines.  With a Type Ia supernova however, the carbon white dwarf is mostly naked, aside from the surrounding accretion disk and the nearby giant star that it orbits.  Thus, the photons liberated from a Type Ia supernova pass through hardly any outer gas layers; therefore, the light we receive from a Type Ia supernova has weak hydrogen absorption lines.  This is one way astronomers discriminate between a Type Ia supernova and a Type II supernova.  The light we receive from a Type II supernova that results from the collapse of the iron-nickel white dwarf core of a red supergiant has strong hydrogen absorption lines, while the light we receive from a Type Ia supernova that results from the thermonuclear detonation of a mostly naked carbon white dwarf has weak hydrogen absorption lines.  Astronomers also use light curves to discriminate between Type Ia supernovae and Type II supernovae.  A light curve is a graph of the amount of light we receive from anything in the universe plotted as a function of time.  The light curves from Type Ia supernovae and Type II supernovae have different shapes.  In particular, the light curve of a Type Ia supernova has a more steep decline, while the light curve of a Type II supernova has a more gradual decline.  Notice that all Type Ia supernovae occur in exactly the same way; a carbon white dwarf slowly gains mass until it reaches the Chandrasekhar limit, which is a very specific value.  Therefore, all Type Ia supernovae have the same luminosity.  Notice that all Type II supernovae do not occur in exactly the same way.  There is a wide range of masses for high mass stars, from 7M☉, 8M☉, or 9M☉ (seven, eight, or nine solar masses) all the way up to the Eddington limit of roughly 100M☉ (one hundred solar masses), that may suffer from a Type II supernova.  Therefore, Type II supernovae have a wide range in luminosities.  We conclude that Type Ia supernovae are standard candles, while Type II supernovae are not standard candles.  The term standard candle was used by astronomers more than one hundred years ago when humans still used candles to light their homes!  Perhaps a better term today would be standard lightbulb instead of standard candle.  Nevertheless, astronomers continue to use the term standard candle.  Imagine a candle or a lightbulb we see in the distance.  We cannot determine the distance to that light source unless we knew its luminosity (its power output).  If we knew the luminosity (the power output) of the light source, we could easily combine the luminosity of the light source with the apparent brightness of the light source to calculate its distance from us.  This is what we mean by the term standard candle, a light source with a known luminosity (power output) that we may combine with its apparent brightness to determine its distance.  Type Ia supernovae are standard candles, since they all have the same luminosity.  Type II supernovae are not standard candles, since they have a wide range in luminosities.  We can therefore use Type Ia supernovae to determine the distance to extremely remote galaxies.  We begin by observing Type Ia supernovae within somewhat closer galaxies.  We can use the variable star method or the Tully-Fisher relation or the Faber-Jackson relation to determine the distance to these somewhat closer galaxies.  We then combine the distance with the apparent brightness of the Type Ia supernovae to determine the luminosity or the absolute magnitude or the intrinsic brightness of Type Ia supernovae.  As we discussed earlier in the course, astronomers continuously monitor tens of thousands of galaxies and thus observe hundreds of distant supernovae every year.  If we happen to discover a supernova in an extremely remote galaxy with strong hydrogen absorption lines with a gradual decline in its light curve, then we are out of luck, since this is a Type II supernova, which is not a standard candle.  However, if we happen to discover a supernova in an extremely remote galaxy with weak hydrogen absorption lines with a steep decline in its light curve, then this must be a Type Ia supernova, which is a standard candle.  We combine its apparent brightness with the absolute magnitude of all Type Ia supernovae to determine the distance to that extremely remote galaxy.  This is called the Type Ia supernova method, and it is one of the highest rungs of the Cosmological Distance Ladder, since supernovae are so incredibly luminous that we can observe them practically across the entire observable universe.

 

The Hubble Classification of Galaxies

 

Edwin Hubble, the greatest American astronomer of the twentieth century, classified galaxies based on their shape.  He designated elliptical galaxies that appeared perfectly round as E0.  He designated elliptical galaxies that appeared almost perfectly round but slightly elongated as E1.  The next designation is E2 for elliptical galaxies appearing even less round and hence even more elongated.  The next designation is E3 for elliptical galaxies appearing moderately elongated.  Hubble designated elliptical galaxies that appeared even more elongated as E4.  The E5 elliptical galaxies appear quite elongated, and E6 elliptical galaxies appear even more elongated.  Hubble designated the most elongated elliptical galaxies as E7.  Edwin Hubble grouped spiral-disk galaxies into two subcategories: unbarred spirals and barred spirals.  A barred spiral galaxy happens to have billions of its stars lined up along the shape of a rod or a bar through its central bulge; an unbarred spiral galaxy does not have a bar through its central bulge.  As we discussed, the structure (the shape) of a galaxy is determined by the orbits of all of its individual stars.  Hence, the structure (the shape) of a galaxy continuously changes over millions of years as all of its stars move along their orbits.  The spiral arms of a spiral-disk galaxy are not permanent structures, as we discussed.  Similarly, central bars of spiral-disk galaxies are not permanent structures.  A barred spiral-disk galaxy may have been an unbarred spiral-disk galaxy millions of years ago, and it may become an unbarred spiral-disk galaxy again millions of years from now.  Similarly, an unbarred spiral-disk galaxy may have been a barred spiral-disk galaxy millions of years ago, and it may become a barred spiral-disk galaxy again millions of years from now.  Edwin Hubble also classified spiral-disk galaxies based on the size of their central bulge, the wrapping of their spiral arms, and the smoothness versus the clumpiness of their spiral arms.  The clumpy regions within the arms of some spiral-disk galaxies are star clusters and diffuse nebulae within their interstellar gases.  For unbarred spiral-disk galaxies, beginning with unbarred spirals with a large central bulge and tightly-wrapped, smooth arms, the galaxy types are Sa, Sab, Sb, Sbc, and finally Sc for the unbarred spirals with a small central bulge and loosely-wrapped, clumpy arms.  Barred spiral-disk galaxies have a similar classification, except that Hubble added an uppercase (capital) letter B meaning barred.  Beginning with barred spirals with a large central bulge and tightly-wrapped, smooth arms, the galaxy types are SBa, SBab, SBb, SBbc, and finally SBc for the barred spirals with a small central bulge and loosely-wrapped, clumpy arms.  We would read Sb for example as “unbarred spiral b,” and we would read SBb for example as “barred spiral b.”  Edwin Hubble arranged this classification scheme into a diagram that resembles a tuning fork, with elliptical galaxies from E0 through E7 being the handle of the tuning fork and the spiral galaxies being the two teeth of the tuning fork.  The unbarred spirals from Sa through Sc form one tooth of the tuning fork, while the barred spirals from SBa through SBc form the other tooth of the tuning fork.  Note that Hubble placed irregular galaxies outside of this tuning fork classification diagram, although he did give irregular galaxies the designation Irr.  Also note that there is a fourth type of galaxy called lenticular galaxies that have some properties of spiral-disk galaxies and some properties of elliptical galaxies.  In particular, lenticular galaxies have little interstellar gas resulting in little star formation, making their stellar populations relatively low mass, cool, dim, and red (late-type stars), like elliptical galaxies.  However, lenticular galaxies are more flat in structure (shape) because most of their stars orbit their galactic center in nearly the same plane in nearly the same angular (orbital) direction, giving lenticular galaxies high angular momentum like spiral-disk galaxies.  The flat structure (shape) of a lenticular galaxy may also be either unbarred or barred, again like spiral-disk galaxies.  Note however that the flat structure (shape) of lenticular galaxies does not include strong spiral arms, unlike spiral-disk galaxies.  For all of these reasons, Hubble placed lenticular galaxies between elliptical galaxies and spiral-disk galaxies in his classification scheme, designating the unbarred lenticular galaxies as S0 and the barred lenticular galaxies as SB0.  Therefore, a more complete sequence of unbarred galaxies along one tooth of the Hubble tuning fork is S0, Sa, Sab, Sb, Sbc, and finally Sc.  Similarly, a more complete sequence of barred galaxies along the other tooth of the Hubble tuning fork is SB0, SBa, SBab, SBb, SBbc, and finally SBc.

 

Within this Hubble classification of galaxies, our own Milky Way Galaxy is classified as type SBb, since our Milky Way Galaxy has a bar through its central bulge, its central bulge is moderate in size, its spiral arms are moderately wrapped, and its spiral arms are somewhat smooth yet somewhat clumpy.  In nearly every way imaginable, we live in an ordinary place in the universe.  Firstly, our planet Earth is not the center of our Solar System; our Sun is at the center of our Solar System.  The Earth is not the closest planet to the Sun, nor is the Earth the furthest planet from the Sun.  The Earth is the third planet from the Sun, which is somewhat intermediate in the order of planets of our Solar System.  Our Sun is not a high mass, hot, luminous star, nor is our Sun a low mass, cool, dim star.  Our Sun is intermediate in mass, intermediate in temperature, and intermediate in luminosity.  Our Sun is not a young star, nor is our Sun an old star.  Our sun is intermediate in age.  Our Solar System is not at the center of our Milky Way Galaxy; a supermassive black hole is at the center of a barred galactic bulge at the center of our Milky Way Galaxy.  Our Solar System is not near the galactic center, nor is our Solar System far from the galactic center.  Our Solar System is roughly halfway from the galactic center.  Our Milky Way Galaxy does not have a particularly large central bulge with tightly-wrapped, smooth spiral arms, nor does our Milky Way Galaxy have a particularly small central bulge with loosely-wrapped, clumpy arms.  Our Milky Way Galaxy has a moderately-sized central bulge with moderately-wrapped spiral arms that are moderately smooth yet moderately clumpy.  Again, in nearly every way imaginable, we live in an ordinary place in the universe.

 

When Edwin Hubble first constructed his tuning-fork shaped classification diagram, he believed that this diagram revealed a galactic evolutionary sequence.  In particular, Hubble believed that supposedly all galaxies are born E0 then supposedly become E1 followed by E2 then E3 then E4 then E5 then E6 then E7 followed supposedly by lenticular (either unbarred or barred) followed supposedly by a-type spiral-disk (either unbarred or barred) then ab-type spiral-disk (either unbarred or barred) then b-type spiral-disk (either unbarred or barred) then bc-type spiral-disk (either unbarred or barred) then c-type spiral-disk (either unbarred or barred).  Finally, Hubble believed that all galaxies supposedly die as irregular galaxies.  Today, we realize that this is not correct.  Unfortunately, many astronomers believed Edwin Hubble so strongly that this Hubble classification of galaxies was called the Hubble sequence, and many astronomers believed that the Hubble sequence was an evolutionary sequence.  Hubble and other astronomers believed so strongly that the Hubble sequence was an evolutionary sequence that they called elliptical galaxies early-type galaxies, and they called spiral-disk galaxies late-type galaxies.  Most unfortunately, this incorrect nomenclature persists among astronomers and astrophysicists to the present day, even though astronomers and astrophysicists do recognize that the Hubble sequence is not an evolutionary sequence.  For example, astronomers and astrophysicists may refer to a b-type spiral-disk galaxy as being earlier than a c-type spiral-disk galaxy, even though they recognize that the Hubble sequence is not an evolutionary sequence.  As another example, astronomers and astrophysicists may refer to an E5 elliptical galaxy as being later than an E2 elliptical galaxy, even though they recognize that the Hubble sequence is not an evolutionary sequence.  Nevertheless, since this incorrect nomenclature persists to the present day, we will also use this incorrect nomenclature in this course.  Note the extraordinary historical parallel between the Hubble sequence and the main sequence.  Just as Ejnar Hertzsprung and Henry Norris Russell incorrectly believed that the main sequence is an evolutionary sequence for stars, Edwin Hubble incorrectly believed that the Hubble sequence is an evolutionary sequence for galaxies.  Just as astrophysicists today continue to incorrectly refer to stars as early-type or late-type depending on their position along the main sequence, astrophysicists today continue to incorrectly refer to galaxies as early-type or late-type depending on their position along the Hubble sequence.  We emphasize again that the Hubble sequence is not an evolutionary sequence, but if galaxies do not evolve along the Hubble sequence, then how do galaxies actually evolve?  How are galaxies actually born?  How do galaxies actually live?  How do galaxies actually die?

 

Galactic Evolution: Birth, Life, and Death

 

Unfortunately, galactic evolution is not well understood.  This is forgivable, since a galaxy is a collection of billions of star systems.  In other words, a single galaxy is an incredibly complicated dynamical system.  Presumably, a galaxy is born from a protogalactic cloud, an enormous cloud of gas millions of light-years across, and presumably a galaxy forms from a protogalactic cloud that collapses from its own self-gravity (under its own weight), but precisely how this galactic formation occurs is not well understood.  There are two main competing theories to explain galactic birth: the density-angular-momentum theory and the collision-merger theory.

 

According to the density-angular-momentum theory of galactic birth, a galaxy is born somewhere along the Hubble sequence.  This theory sounds similar to the manner in which stars are born.  A star is born somewhere along the main sequence, as we discussed earlier in the course.  A star is born somewhere along the main sequence depending on its mass.  If a star happens to be born with high mass, it is born early on the main sequence, while if a star happens to be born with low mass, it is born late on the main sequence, as we discussed earlier in the course.  According to the density-angular-momentum theory of galactic birth, a galaxy is born somewhere along the Hubble sequence depending on the density and the angular momentum of the protogalactic cloud from which it formed.  In particular, if the protogalactic cloud happened to have high density and low angular momentum, then the protogalactic cloud will be born as an elliptical galaxy, early on the Hubble sequence.  If the protogalactic cloud happened to have low density and high angular momentum, then the protogalactic cloud will be born as a spiral-disk galaxy, late on the Hubble sequence.  The detailed arguments of this density-angular-momentum theory are as follows.  If the protogalactic cloud happened to have low angular momentum, this means that its gases were moving along random trajectories in random directions.  All these orbits mostly cancel each other, giving the protogalactic cloud low angular momentum.  If in addition the protogalactic cloud happened to have high density, then stars will form from this high-density gas and continue moving along these random orbits.  If the stars that make up the resulting galaxy move along mostly random orbits, then the overall shape of the resulting galaxy will be more round and less flat.  Also, there will be very little gas remaining to form new stars, since the high-density gas was mostly consumed to create the stars in the first place.  The result is a round-shaped galaxy with stars moving along random orbits with very little gas to form new stars, but this is an elliptical galaxy.  If on the other hand the protogalactic cloud happened to have low density, then many stars will not form yet.  We must wait until the protogalactic cloud collapses further for the gases to attain a high enough density to form stars.  If in addition the protogalactic cloud happened to have high angular momentum, then the protogalactic cloud will collapse into a flat, rotating disk perpendicular to its axis of total angular momentum.  More precisely, small higher density regions within the protogalactic cloud will collide more frequently as the protogalactic cloud collapses, since the gravitational collapse brings these regions closer together.  Several higher density regions often merge into larger regions as a result of these collisions.  By the law of conservation of translational (linear) momentum, the resulting larger regions will have less motion along the direction of the axis defined by the total angular momentum of the collapsing protogalactic cloud, since the collisions will average out their more random motions in this direction.  By the law of conservation of angular momentum, the resulting larger regions will have more circular orbits, since the collisions will average out their more random orbits, many of which were more elliptical.  In summary, the laws of physics together cause the gravitationally collapsing protogalactic cloud to flatten into a circular, rotating disk perpendicular to the axis of the total angular momentum of the forming galaxy.  The result is a flat-shaped galaxy with stars all orbiting the galactic center in roughly the same angular (orbital) direction, but this is a spiral-disk galaxy.  Note that a small number of stars would have formed from sufficiently dense regions even before the high-angular momentum protogalactic cloud collapses.  These would be the first stars born within the resulting spiral-disk galaxy.  These particular stars have lower metallicities, since they were born first when the universe was younger and hence there was less time for earlier generations of high mass stars to synthesize metals.  These particular stars would also remain on their original more random orbits around the resulting spiral-disk galaxy, since they formed before the high-angular momentum protogalactic cloud collapsed into a circular, rotating disk.  This small number of stars are the Population II stars within the galactic halo of the resulting spiral-disk galaxy.  Since the protogalactic cloud happened to have low density initially, only a small number of Population II stars would be born, and hence most of the stars are born later after the collapse of the protogalactic cloud.  This large number of stars that are born later are the Population I stars within the galactic disk of the resulting spiral-disk galaxy.  To summarize the density-angular-momentum theory of galactic birth, if the protogalactic cloud happens to have high density and low angular momentum, it will be born an elliptical galaxy, early on the Hubble sequence; if the protogalactic cloud happens to have low density and high angular momentum, it will be born a spiral-disk galaxy, late on the Hubble sequence.

 

According to the collision-merger theory of galactic birth, all galaxies are initially born spiral-disk galaxies, forming from the collision and merger of several small protogalactic clouds.  Spiral-disk galaxies then grow larger by tearing apart and devouring small satellite galaxies around it.  Finally, large elliptical galaxies result from the collision and merger of two large spiral-disk galaxies.  If two spiral-disk galaxies happen to fall toward each other, they will eventually collide.  However, galaxies are not solid objects; a galaxy is a collection of billions of star systems.  Therefore, when two spiral-disk galaxies collide, they actually pass through each other at first.  However, the mutual gravity of the two galaxies severely perturbs the orbits of the star systems in both galaxies, causing the orbits of all the stars to become somewhat randomized and thus disrupting the beautiful spiral arm structures of both galaxies.  After the two galaxies pass through each other, the two galaxies slow down, come to rest, and fall toward each other again due to their mutual gravitational attraction.  Again, the two galaxies pass through each other, and again the mutual gravity of the two galaxies even more severely perturbs the orbits of the stars in both galaxies, causing the orbits of all the stars to become even more randomized and thus further disrupting the beautiful spiral arm structures of both galaxies.  Again, the two galaxies slow down, come to rest, and fall toward each other yet again due to their mutual gravitational attraction.  Ultimately, the two galaxies merge into a single galaxy with a round shape, since the spiral arm structure of both galaxies has been ruined due to the randomized orbits of all the stars.  In other words, the two spiral-disk galaxies have merged into an elliptical galaxy.  Since galactic collisions result in galactic mergers, astrophysicists regard a galactic collision to also be a galactic merger.  As we discussed, our own Milky Way Galaxy and the Andromeda Galaxy are falling toward each other, and they will collide in roughly five billion years.  We now realize that these two spiral-disk galaxies will not only collide, but they will also merge into an elliptical galaxy.  Astrophysicists have named this elliptical galaxy that will be born in roughly five billion years the Milkdromeda Galaxy, since it will be the merger of our Milky Way Galaxy and the Andromeda Galaxy.

 

There is strong evidence in favor of the collision-merger theory of galactic birth.  Firstly, the observable universe was smaller billions of years ago, as we will discuss shortly.  Therefore, galaxies must have been more crowded together and hence collisions among them must have occurred more frequently when they first formed billions of years ago.  Secondly, our own Milky Way Galaxy is ripping apart the small satellite galaxies around it as we discussed, and there is evidence that some groups of stars within our Milky Way Galaxy were formerly small satellite galaxies that our Milky Way Galaxy completely devoured as we also discussed.  Thirdly, computer simulations reveal that the collision of two spiral-disk galaxies does indeed result in a galactic merger into an elliptical galaxy.  Finally, actual photographs of galactic clusters reveal that the galaxies on the outskirts of galactic clusters are predominantly spirals, while the galaxies toward the center of galactic clusters are predominantly ellipticals.  In fact, there is often a single giant elliptical galaxy at the center of a galactic cluster.  This distribution of spirals and ellipticals within galactic clusters suggests that all the large galaxies in the galactic cluster were born spirals.  Over billions of years, as spiral galaxies fell toward the center of the galactic cluster, they collided and merged with each other to form elliptical galaxies.  As these elliptical galaxies continued to fall toward the center of the galactic cluster, they collided and merged with each other to form a giant elliptical galaxy at the center of the galactic cluster.  Although all of these observations and calculations provide strong evidence in favor of the collision-merger theory of galactic birth, there is also strong evidence against the collision-merger theory of galactic birth.  As we discussed, spiral-disk galaxies have an abundance of interstellar gas and therefore have active star formation, while elliptical galaxies have very little interstellar gas and therefore have very little star formation, as we also discussed.  If two spiral-disk galaxies collide and merge, the interstellar gases within these two spiral-disk galaxies should also collide.  The collision of these gases should increase their density and therefore should induce even greater star formation.  Therefore, the collision-merger theory of galactic birth predicts that two colliding spiral-disk galaxies with active star formation should merge into an elliptical galaxy with even more active star formation, but this is not correct.  Elliptical galaxies in fact have very little interstellar gas and thus very little star formation, as we discussed.  This is a strong argument against the collision-merger theory of galactic birth.  We could modify this collision-merger theory to claim that the collision of two spiral-disk galaxies first results in a starburst galaxy, which is a large irregular galaxy with much more active star formation than even spiral-disk galaxies.  Presumably, most of the gas within a starburst galaxy is consumed to form a large number of stars in a fairly short period of time, leaving little gas to form further stars after this relatively short duration of active star formation.  Eventually, the randomized orbits of the stars cause the entire galaxy to settle down into an elliptical galaxy, again with a fairly round shape with little gas to form new stars.  Unfortunately, this modification of the collision-merger theory to correct one false prediction results in a new false prediction.  If elliptical galaxies were formerly starburst galaxies, then a large number of stars of an elliptical galaxy should be young stars, but again this is not correct.  An elliptical galaxy is an entire galaxy of mostly Population II stars, meaning that its stars are mostly old stars with low metallicities.  This is another strong argument against the collision-merger theory of galactic birth.  The density-angular-momentum theory of galactic birth seems reasonable, but it also has strong counterarguments.  According to this density-angular-momentum theory of galactic birth, if the protogalactic cloud happened to have high density and low angular momentum, it will be born an elliptical galaxy; if the protogalactic cloud happened to have low density and high angular momentum, it will be born a spiral-disk galaxy.  However, what happens if the protogalactic cloud happened to have high density and high angular momentum?  We could argue that the galaxy would be born lenticular in this case.  Lenticular galaxies have little gas and more flat shapes, and indeed high-density gas would be consumed to form stars leaving little gas to form further stars and high angular momentum would result in a more flat shape.  This is a strength of the density-angular-momentum theory over the collision-merger theory, since the collision-merger theory offers conflicting explanations for the formation of lenticular galaxies.  However, what prediction does the density-angular-momentum theory make if the protogalactic cloud happened to have low density and low angular momentum?  Even proponents of this density-angular-momentum theory of galactic birth do not have a definitive answer to this question.  In summary, both of these theories of galactic birth each have their own strengths and each have their own weaknesses.  Perhaps both theories are correct, since perhaps galactic birth occurs through two completely different mechanisms.  Perhaps both of these theories are special cases of a more general theory of galactic birth that has not yet been discovered.  Perhaps both of these theories of galactic birth are completely wrong, and perhaps a new theory of galactic birth that has not yet been discovered is the correct theory for the formation of galaxies.

 

The most distant galaxies in the observable universe are gigaparsecs (billions of light-years) distant.  These distances are measured using redshifts and the Hubble law, as we will discuss shortly.  All of these extremely remote galaxies have incredibly luminous centers.  Consequently, these distant galaxies are called active galaxies, and their luminous centers are called active galactic nuclei, which astrophysicists always abbreviate AGNs.  A galaxy that does not have an active galactic nucleus is classified as a normal galaxy or a quiet galaxy.  There are no active galaxies within hundreds of megaparsecs (several hundred million light-years) from our galactic neighborhood; all galaxies within hundreds of megaparsecs (several hundred million light-years) of distance from us are normal/quiet galaxies.  All galaxies sufficiently distant from us are active galaxies with active galactic nuclei.  Although there are several different types of active galaxies, the two most common types are Seyfert galaxies and quasi-stellar objects.  Seyfert galaxies, named for the American astronomer Carl Seyfert who studied them, are active and distant galaxies as compared with normal/quiet galaxies, but Seyfert galaxies are not as active and not as distant as quasi-stellar objects, which are the most active and the most distant galaxies in the observable universe.  These quasi-stellar objects, often referred to quasars or abbreviated as QSOs, are so distant that they appear almost as point-like as stars even through powerful telescopes, hence the name quasi-stellar.  Active galaxies are thousands of times more luminous than normal/quiet galaxies, and much of this luminosity is in the X-ray band of the Electromagnetic Spectrum.  The active galactic nucleus of a quasar is so luminous that it often outshines the entire host galaxy, preventing us from even being able to observe the quasar’s host galaxy surrounding its active galactic nucleus.  Although Seyfert galaxies are very luminous, they are not as luminous as quasars, and hence we are able to observe the Seyfert galaxy’s host galaxy surrounding its active galactic nucleus.

 

For a number of decades, astrophysicists debated the source of the incredible energy that powers active galactic nuclei.  Astronomers made the following observations of all active galactic nuclei.  Firstly, there are variations in the luminosity of active galactic nuclei over timescales shorter than one year.  Since the vacuum speed of light is the speed limit of the universe according to relativity theory as we discussed earlier in the course, variations in the luminosity of anything in the universe places a constraint on the size of the luminous object.  If active galactic nuclei have varying luminosities on timescales shorter than one year, then the size of an active galactic nucleus must be smaller than one light-year, perhaps the size of the Solar System.  In other words, an active galactic nucleus is tiny compared to the overall size of its host galaxy.  Secondly, we can calculate the mass of an active galactic nucleus from the orbiting gases near the center of the host galaxy.  By measuring the blueshifts and the redshifts of the light from these orbiting gases relative to the center of the active galactic nucleus, we can determine their orbital speeds, the gravitational force responsible for these orbital speeds, and hence the mass that exerts this gravitational force.  We determine that the mass of a typical active galactic nucleus is at least millions of solar masses.  With this much mass crammed within such a small region of space, astrophysicists were forced to conclude that a supermassive black hole is the source of the incredible energy that powers active galactic nuclei.  Indeed, it is not difficult to calculate that a black hole converts mass into energy with high efficiency, and just a few solar masses of material per year falling into a supermassive black hole can provide sufficient energy to account for the incredible luminosity of active galactic nuclei.  Thirdly, we often observe narrow columns or jets of high-speed material from quasars.  These jets are often millions of parsecs (millions of light-years) long!  As the jets collide with the gases that surround the active galaxy, radio waves are emitted, resulting in enormous lobes of radio emissions surrounding the jets from some quasars.  As we discussed earlier in the course, the source of the X-rays from X-ray binaries is an accretion disk around a compact object.  Moreover, some of the gas that falls toward the compact object within an X-ray binary may be ejected as narrow columns or jets near the rotational angular momentum axis of the accretion disk around the compact object.  This makes some X-rays binaries similar to quasars, but on a much smaller size scale than quasars.  Indeed, some types of X-ray binaries are called microquasars.  The presence of incredibly long jets from quasars strongly suggests the presence of an enormous accretion disk around a supermassive black hole.  By combining all of this observational and theoretical evidence, astrophysicists eventually formulated the following model for active galactic nuclei.  Consider an enormous accretion disk, perhaps the size of our Solar System, surrounding a supermassive black hole.  Caution: an accretion disk the size of our Solar System is still tiny compared to the size of a galaxy.  As the gas within the accretion disk falls toward the supermassive black hole, the gas is heated to millions of kelvins of temperature, radiating an incredible amount of X-rays from the center of the galaxy, thus powering the active galactic nucleus of the active galaxy.

 

Why are all galaxies in the local universe normal/quiet galaxies, and why are all extremely remote galaxies active galaxies?  What is the difference between the local universe and the distant universe that makes local galaxies and distant galaxies so different?  Perhaps we are asking the wrong question.  We must realize that if we are observing a galaxy ten billion light-years distant for example, this means that it took its light ten billion years to travel from that galaxy to our Milky Way Galaxy.  This means that we are observing that remote galaxy as it appeared ten billion years ago when it was extremely young, presumably when it was first forming.  Hence, all galaxies sufficiently distant from us appear as they did when they were first forming.  Perhaps there is no difference between the local universe and the distant universe.  Perhaps all galaxies are born as active galaxies with active galactic nuclei, and perhaps the supermassive black hole powering the active galactic nucleus spends billions of years devouring the accretion disk around it.  As the supermassive black hole devours the surrounding accretion disk, the active galactic nucleus becomes more and more quiet, and perhaps the active galaxy gradually settles down to become a normal/quiet galaxy.  The distinction between Seyfert galaxies and quasars supports this model of galactic evolution.  As we discussed, quasars are the most distant and the most active galaxies, while Seyfert galaxies are less distant and less active as compared with quasars.  Since quasars are the most distant galaxies, we are observing these galaxies as they first formed.  Since Seyfert galaxies are less distant, we are observing these galaxies somewhat later in their evolution, after the supermassive black hole has devoured a sufficient amount of the surrounding accretion disk that the galaxy is somewhat less luminous as compared to its luminosity when the galaxy first formed as a quasar.  Moreover, there is a supermassive black hole at the center of every major galaxy, including our own Milky Way Galaxy, as we discussed.  This is a spectacular piece of evidence that this theory of galactic evolution is correct.  Presumably, all normal/quiet galaxies, including our Milky Way Galaxy, were born with quasars.  As the supermassive black hole devoured the surrounding accretion disk, the quasar became more and more quiet, becoming a Seyfert galaxy and then eventually settling down to become a normal/quiet galaxy.  Recall that the center of our Milky Way Galaxy is in the direction of the constellation Sagittarius (the centaur archer).  Astronomers have discovered a radio source within the constellation Sagittarius that they have named Sagittarius A, within which is a more distinct radio source astronomers have named Sagittarius A* (pronounced Sagittarius A-star).  This distinct radio source Sagittarius A* surrounds the precise location of the supermassive black hole at our galactic center.  Radio waves are on the opposite end of the Electromagnetic Spectrum from X-rays, as we discussed toward the beginning of the course.  Just as incredibly hot gases emit X-rays, incredibly cool gases emit radio waves.  The radio emissions from Sagittarius A* must come from very cool gas falling toward the supermassive black hole at our galactic center.  This very cool gas must be all that remains of the large, hot accretion disk that once powered the active galactic nucleus when our Milky Way Galaxy was first born.  All of this evidence has brought astrophysicists to a consensus that all major galaxies are born as active galaxies powered by an enormous and incredibly hot accretion disk around a supermassive black hole.  Over billions of years, active galaxies become more and more quiet, transitioning from quasars to Seyfert galaxies and eventually settling down to become normal/quiet galaxies.  When we observe an active galaxy ten billion light-years distant, we must realize that presently at this very moment, that galaxy is actually a normal/quiet galaxy.  If it is presently a normal/quiet galaxy, then intelligent life may exist on one of the planets orbiting one of the stars within that galaxy.  Perhaps those intelligent lifeforms have even built telescopes, and if they point their telescopes toward our Milky Way Galaxy, they would observe our Milky Way Galaxy as an active galaxy!  After all, if it takes ten billion years for light to travel from that galaxy to our Milky Way Galaxy, then it also takes ten billion years for light to travel from our Milky Way Galaxy to that remote galaxy!  Therefore, those intelligent lifeforms would be observing our Milky Way Galaxy as it first formed ten billion years ago with a quasar!  Right now at this very moment in the present day, we observe that distant galaxy as a quasar and that distant galaxy observes our Milky Way Galaxy as a quasar, even though both galaxies are presently at this moment normal/quiet galaxies!

 

Gamma-ray bursts, which astronomers always abbreviate GRBs, are arguably the single greatest mystery in all of astrophysics.  Hundreds of times every year, astronomers detect a burst of gamma-rays from outer space.  Astrophysicists formerly believed that these gamma-ray bursts come from within our own Milky Way Galaxy.  As we discussed earlier in the course, astronomers detect sudden and intense X-ray bursts from X-ray binaries within our Milky Way Galaxy, assuming the compact object is a neutron star.  Gamma-rays have only a little bit more energy than X-rays, and so it would seem reasonable to conclude that on occasion, X-ray binaries would also generate a sudden and intense burst of gamma-rays.  However, the Compton gamma-ray observatory (CGRO) revealed that gamma-ray bursts do not come from within our Milky Way Galaxy.  If gamma-ray bursts came from within our own Milky Way Galaxy, then the distribution of gamma-ray bursts across the sky would be concentrated along the band of milk that wraps around the entire sky, the milky way.  However, when the Compton gamma-ray observatory mapped the distribution of gamma-ray bursts across the sky, gamma-ray bursts were revealed to come roughly equally from all directions in the sky.  In other words, gamma-ray bursts are extragalactic in origin.  Gamma-ray bursts come from extremely distant galaxies, from hundreds of millions to even billions of light-years distant!  Imagine how powerful an explosion must be for us to still detect gamma-rays at these incredible distances!  The supernova explosion of a high mass star is a weak explosion compared with these incredible explosions!

 

If a particular gamma-ray burst came from a galaxy billions of light-years distant, this means that it took the gamma-rays billions of years to travel from that galaxy to our Milky Way Galaxy.  After all, gamma-rays are a form of electromagnetic radiation, a form of light that propagates at the vacuum speed of light.  Therefore, whatever explosion caused the gamma-ray burst actually occurred billions of years ago, when the universe was still very young.  Often, several hours after the gamma-ray burst, optical telescopes detect an increase in visible light from the source galaxy of the gamma-ray burst.  This is called the afterglow of the gamma-ray burst.  The shape of the afterglow’s light curve is nearly identical to the shape of the light curve of a Type II supernova explosion.  This strongly suggests that the gamma-ray burst was caused by the death of a high-mass star.  Since the explosion that caused the gamma-ray burst actually occurred billions of years ago when the universe was still very young, we conclude that the source of the gamma-ray burst and the subsequent afterglow was the death of an ancient Population III star.  As we discussed, Population III stars were the first generation of stars born in the entire universe.   As we also discussed, no Population III stars have ever been discovered, suggesting that all Population III stars were born high-mass main sequence stars with short lifetimes.  However, the explosion that caused the gamma-ray burst is much more energetic than a supernova explosion.  We conclude that the first generation of stars born in the universe, Population III stars with zero metallicity, formed as not just high-mass stars, but as very high-mass stars, perhaps with masses roughly equal to the Eddington limit, the theoretical maximum mass of any star, as we discussed earlier in the course.  After an incredibly short lifetime, perhaps even shorter than one million years, these Eddington-limit stars exploded with significantly greater luminosity than even a supernova.  This violent explosion is called a hypernova, the most powerful explosions in the entire universe.  We conclude that most gamma-ray bursts are caused by the hypernova explosions of ancient Population III stars in distant galaxies.

 

If all Population III stars were born as very high-mass stars with masses roughly equal to the Eddington limit, then we should be bombarded with many more gamma-ray bursts from distant galaxies than we actually observe.  We conclude that a hypernova explosion causes a gamma-burst that does not radiate spherically outward from the hypernova but is instead concentrated into narrow beams.  As such, exploding Population III stars in distant galaxies would emit gamma-rays bursts in particular directions, and therefore most gamma-ray bursts would not be ejected toward our general direction.  Hence, we only observe a small number of the gamma-ray bursts that actually occurred in the ancient and young universe, the gamma-rays bursts that happened to be ejected toward our general direction.  This would also explain the extraordinary energy of gamma-ray bursts from such incredible distances.  If a gamma-ray burst were radiated spherically outward from a hypernova, then its total energy would spread over a larger and larger sphere as it propagates outward, diluting its energy as it travels billions of light-years from the hypernova.  If the gamma-ray burst is instead concentrated into narrow beams, then its total energy would not be significantly diluted as it travels billions of light-years from the hypernova.  Note however that the hypernova also produces a more conventional Type II supernova explosion that does propagate spherically outward.  The energy from this more conventional Type II supernova explosion therefore does become diluted as it travels billions of light-years, which we detect as the visible light afterglow a few hours after the gamma-ray burst.  In summary, the first generation stars born in the entire universe, Population III stars with zero metallicity, were born differently from later generations of stars and also died differently from later generations of stars.  Population III stars were all born as very high mass stars with masses roughly equal to the Eddington limit.  That is, all Population III stars were born hot, luminous, large, and high-mass with short lifetimes.  Population III stars all died with hypernova explosions, much more energetic than supernova explosions, producing gamma-ray bursts concentrated along narrow beams, followed by more typical Type II supernova explosions that propagate spherically outward.  The gamma-ray bursts and the associated afterglows traveled across billions of light-years of space over billions of years of time.  Some of these gamma-ray bursts happened to be ejected in our general direction, which we can observe when they finally arrive at our planet Earth in the present-day universe.

 

Note that not all gamma-ray bursts are caused by the hypernova explosion of an ancient Population III star.  Some gamma-ray bursts are caused by the collision and merger of binary neutron stars in distant galaxies.  Since the spacetime curvature near a neutron star is nearly as severe as the spacetime curvature near a black hole, the collision and merger of binary neutron stars should create gravitational waves that are similar to the collision and merger of binary black holes.  However, electromagnetic waves (light) cannot escape from within the event horizon of a black hole, as we discussed earlier in the course.  Therefore, the collision and merger of binary black holes should not generate a gamma-ray burst.  Neutron stars do however have solid surfaces, and therefore the collision and merger of binary neutron stars should be violent enough to generate electromagnetic waves (light) in addition to gravitational waves.  Most of the gravitational waves that have been directly detected since the historic year 2015 have been from the collision and merger of binary black holes, as we discussed earlier in the course.  However, in the year 2017, the first gravitational waves were directly detected from the collision and merger of binary neutron stars.  A few seconds after this gravitational wave detection, a gamma-ray burst was detected, as we would expect from the collision and merger of binary neutron stars.  Moreover, a visible light afterglow was detected a couple of days after the gamma-ray burst.  Other gamma-ray bursts may be caused by the collision and merger of a black-hole-neutron-star binary.  In this case, the black hole rips apart and devours the neutron star.  The resulting radiation would be similar to the resulting radiation from the collision and merger of binary neutron stars: gravitational waves followed by a gamma-ray burst followed by a visible light afterglow.  There are still other proposed mechanisms to explain other gamma-ray bursts.  In summary, there are several different mechanisms that may cause gamma-ray bursts, and astronomers must combine a variety of observational techniques to determine which mechanism caused a particular gamma-ray burst.

 

Perhaps the most outrageous mechanism that could cause gamma-ray bursts is exploding microscopic primordial black holes.  In the 1970s, the physicist Jacob Bekenstein tried to formulate a theory of the thermodynamics of black holes.  The physicist Stephen Hawking on the other hand claimed that there is no theory of the thermodynamics of black holes.  If there were such a theory, then black holes would have a temperature that would cause them to radiate energy with a continuous blackbody spectrum consistent with their temperature, but by definition nothing can escape from a black hole.  Of course, we do detect X-rays from black holes, but these X-rays are emitted from gas falling toward the black hole before passing the event horizon.  As long as the gas has not yet passed the event horizon, we could still detect X-rays or any other type of radiation from this gas that falls toward the black hole.  Once however the gas has passed the event horizon of the black hole, we can no longer detect any radiation, since nothing can escape from within a black hole.  Not even light can escape from within the event horizon.  This is why these objects are named black holes, since they appear to be holes that are black!  Consider an isolated black hole with no surrounding gases that could fall toward the black hole.  Such an isolated black hole should not radiate any energy whatsoever.  Therefore, an isolated black hole cannot have a temperature; we could regard the temperature of an isolated black hole as absolute zero temperature.  This was Stephen Hawking’s argument, but Jacob Bekenstein disagreed, arguing that a theory of the thermodynamics of black holes could actually be formulated.  These two physicists made a friendly wager between them; Bekenstein wagered that there is a theory of the thermodynamics of black holes, while Hawking wagered that there is no such theory.  As Stephen Hawking developed the theoretical physics necessary to win this wager, he soon realized that Bekenstein was correct; there is a theory of the thermodynamics of black holes.  Stephen Hawking even succeeded in formulating all of the mathematical details of black hole thermodynamics.  At first, Hawking kept the results private.  Firstly, he did not want to lose the wager!  Secondly, he did not believe his own results, at least at first.  Hawking calculated that an isolated black hole has a temperature and therefore does indeed radiate energy with a continuous blackbody spectrum consistent with its temperature, but how could this possibly be the case?  Ultimately, Hawking realized that his new theory is correct, but it must be interpreted within the context of Relativistic Quantum Field Theory.

 

According to Relativistic Quantum Field Theory, there are particles that continuously appear everywhere in the universe out of the vacuum of nothingness.  These are called virtual particles.  We should all protest this theory, since virtual particles appearing everywhere out of the vacuum of nothingness would violate fundamental laws of physics, such as the conservation of mass and the conservation of energy.  However, Relativistic Quantum Field Theory also claims that these virtual particles disappear back into the vacuum of nothingness before we are able to directly observe their existence!  Hence, the fundamental laws of physics are not violated if we do not actually observe any such violation!  We are now inclined to believe that Relativistic Quantum Field Theory is unscientific nonsense, since it claims that fantastic things occur while ensuring that we can never actually observe them occurring!  However, we can observe the effects of these virtual particles, even though we cannot directly observe the virtual particles themselves.  For example, two neutral metal slabs should not attract or repel each other electromagnetically, since they are both neutral.  Of course, they do attract each other gravitationally.  However, virtual particles that continuously appear and disappear around the metal slabs collide with the metal slabs, exerting a pressure on both of them.  Fewer virtual particles appear and disappear between the two neutral metal slabs, since the boundary conditions imposed on the partial differential equations yield solutions with quantized (discrete) energies instead of a continuum of energies.  Therefore, the greater number of virtual particles that appear and disappear on either side of the two neutral metal slabs exert a greater pressure than the fewer number of virtual particles that appear and disappear between the two neutral metal slabs.  Hence, the two neutral metal slabs feel a pressure that pushes them toward each other!  We can interpret this as an attraction in addition to the gravitational contraction.  This is called the Casimir effect, named for the Dutch physicist Hendrik Casimir who first predicted this phenomenon from Relativistic Quantum Field Theory.  This Casimir effect has actually been observed in the laboratory.  This is evidence of the existence of virtual particles, even though we cannot directly detect the virtual particles themselves.  Another spectacular piece of evidence of the existence of these virtual particles despite the fact that we cannot directly observe them is the anomalous g-factor of the electron.  The g-factor of any quantum-mechanical particle is the ratio between its quantum-mechanical magnetic-moment-spin ratio and its classical magnetic-moment-spin ratio.  Without these virtual particles, Relativistic Quantum Mechanics predicts that the g-factor of the electron should be exactly equal to two.  However, as virtual particles continuously appear and disappear around an electron, they change its g-factor slightly.  If we experimentally measure the g-factor of the electron, the result is 2.002319304362; if we theoretically calculate the g-factor of the electron taking into account the effects of virtual particles, the result it 2.002319304467, correct to ten significant figures!  No other theory in the history of science is anywhere nearly this accurate.  Among all theories among all the sciences, no theory is as well proven as the existence of these virtual particles that we cannot directly observe as predicted by Relativistic Quantum Field Theory!

 

If these virtual particles are truly appearing and disappearing everywhere in the universe, Stephen Hawking realized that they would be appearing and disappearing outside of the event horizon of a black hole.  Imagine virtual particles appearing and disappearing in pairs outside of the event horizon of a black hole.  In some cases, both members of the virtual pair disappear outside of the event horizon of the black hole.  In other cases, both members of the virtual pair fall into the event horizon of the black hole.  However, in some cases only one member of a virtual pair may fall into the event horizon, leaving the other virtual particle with no one to disappear with; hence, this virtual particle is forced to become a real particle.  This would truly violate the fundamental laws of physics, such as the conservation of mass and the conservation of energy.  The only way to rescue these fundamental laws of physics is to claim that the virtual particle that fell into the event horizon disappears with a small amount of the mass of the singularity of the black hole.  This reduces the mass of the singularity by a small amount and shrinks the event horizon by a small amount.  Therefore, we may interpret the virtual-converted-to-real particle outside of the black hole as effectively coming from the black hole’s singularity itself, even though this is not precisely what occurred.  If virtual particles are indeed converting to real particles everywhere outside the event horizon of a black hole while other virtual particles fall into the black hole and disappear with a small amount of the singularity’s mass, then there must be streams of real particles flying away from the black hole as the black hole loses mass and therefore energy!  This compelled Stephen Hawking to utter one of his most famous phrases, that even isolated “black holes ain’t so black!”  This stream of real particles radiating away from an isolated black hole is called Hawking radiation.  Although Hawking radiation has never been observed, most physicists agree that Hawking’s theory is correct.  Hawking also calculated that this Hawking radiation has a continuous blackbody spectrum; thus, there is a temperature associated with this Hawking radiation.  This temperature is called the Hawking temperature.  Hawking even calculated the entropy of an isolated black hole.  Entropy is another thermodynamic variable related to temperature and energy.  The entropy of an isolated black hole is called the Hawking entropy.  Thus, Bekenstein won the wager when Hawking finally revealed his theory of the thermodynamics of black holes.  This infuriated Bekenstein for the rest of his life; although Bekenstein won the wager, he only won the wager because of Hawking’s genius!  In brief, Hawking’s theory claims that an isolated black hole loses mass and has a shrinking event horizon as it radiates Hawking radiation.  Hence, these are called evaporating black holes.  Hawking also calculated that the Hawking temperature of these evaporating black holes actually becomes hotter and hotter as the isolated black hole loses more and more mass.  Thus, the Hawking radiation becomes more and more luminous.  At the very end of their lives, these evaporating black holes should explode with nearly infinite luminosity.  These are called exploding black holes.  If the luminosity of an exploding black hole is nearly infinite, we would detect gamma-ray bursts from these exploding black holes even if they were billions of light-years distant.  Unfortunately, a stellar black hole would take much longer than the current age of the universe to evaporate and explode, and a supermassive black hole would take even longer to evaporate and explode.  However, a microscopic black hole with an event horizon roughly the size of the nucleus of an atom would only take roughly fourteen billion years to evaporate and explode; this is roughly equal to the current age of the universe.  The initial Hawking temperature of such a microscopic black hole would be tremendously hot, but as we will discuss shortly the universe was actually this hot shortly after the Big Bang.  Therefore, these microscopic black holes could have been born in the fires of the Big Bang.  For this reason, microscopic black holes are also called primordial black holes.  These microscopic primordial black holes could have been born in the fires of the Big Bang, they could have spent the past fourteen billion years evaporating, and they could be exploding right now.  We would then detect these explosions as gamma-ray bursts.  Therefore, exploding microscopic primordial black holes could be the source of some of the gamma-ray bursts that we continuously observe from distant galaxies.

 

Cosmology and the History of the Universe

 

The word cosmos means universe.  Therefore, cosmology is the study of the universe, and a cosmologist is someone who studies the universe.  Haven’t we been studying cosmology throughout the entire course?  Actually, throughout this entire course we have been studying astronomy and astrophysics, which we strictly define as the study of objects within the universe.  In other words, astronomy and astrophysics is the study of stars, planets, moons, asteroids, comets, nebulae, star clusters, galaxies, galactic groups, galactic clusters, and galactic superclusters.  An astronomer or an astrophysicist is someone who studies any of these objects within the universe.  Cosmology is the study of the entire universe, the universe itself, and a cosmologist is someone who studies the entire universe, the universe itself.  Instead of studying the birth, life, and death of planets, stars, and galaxies, a cosmologist studies the birth, life, and death of the entire universe, the universe itself.  Whenever we discuss properties of the entire universe, such as its age, its size, or its temperature, we are studying cosmology.

 

We begin our discussion of cosmology with a seemingly innocent question: why is the sky dark at night?  The answer to this seemingly innocent question seems obvious at first: isn’t the sky dark at night simply because our Sun is not in the sky?  As we reflect upon this question further, we realize that there is a problem with this simplistic answer.  If the universe is infinitely large with infinitely many stars, then shouldn’t the light from all those infinitely many stars add up to infinity thus making the nighttime sky infinitely bright?  In fact, the daytime sky should also be infinitely bright, shouldn’t it?  Many students argue that the sky is dark at night because most of the stars in the universe are so distant that they appear very dim, but this argument is incorrect.  It does not matter how dim stars appear from their far distances; infinitely many amounts of dim light should still add up to infinity.  Some students argue that the gases that fill outer space blocks the light from distant stars, but argument is also incorrect.  Interstellar gases that absorb an infinite amount of light will become hotter and hotter until an equilibrium is established; the gases themselves begin to radiate as much light as they absorb.  Hence, we are back to where we started: the nighttime sky (as well as the daytime sky) should be infinitely bright.  As we reflect upon all of these arguments, we actually begin to truly wonder, why is the sky dark at night?  The first person to ask this question in this meaningful way was the German astronomer Heinrich Olbers.  Consequently, this is called the Olbers paradox: why is the sky dark at night?  Heinrich Olbers also discovered the asteroids Pallas and Vesta, which we discussed earlier in the course.  The resolution of the Olbers paradox is provided by Einstein’s General Theory of Relativity.  Recall that both of Einstein’s theories of relativity (Special and General) reveal that there is a speed limit of the universe, the vacuum speed of light.  As we will discuss shortly, Einstein’s General Theory of Relativity also reveals that the universe has a finite age; in other words, the universe had a definite beginning at a finite time in the past.  A finite age of the universe together with a finite speed limit of the universe together prevent anyone in the universe from observing the entire universe.  Let us make this argument more clear.  The true age of the universe is roughly fourteen billion years as we will discuss shortly, but let us suppose instead that the age of the universe is fathomably younger, perhaps only one hundred years old.  In this case, we could not see a star two hundred light-years distant for example, since it would take two hundred years for light to travel from that star to us, but we are supposing that the entire universe is only one hundred years old.  In other words, there has not been sufficient time in the entire history of the universe for light to travel from that star to us, since we are supposing that the entire universe is only one hundred years old.  If the entire universe were only one hundred years old, then the furthest stars we could see would be one hundred light-years distant, since light would barely have sufficient time to travel from such stars to us.  The furthest distance we would be able to observe would be one hundred light-years in all directions away from us, and we would not be able to observe anything in the entire universe further than one hundred light-years distant.  We now realize that it would appear as if we were at the center of a sphere that is one hundred light-years in radius, and the finite age of the universe together with the finite speed limit of the universe would forbid us from seeing anything in the entire universe beyond that sphere.  Any other observer living on any other planet orbiting any other star within any other galaxy would observe the same thing; they would appear to be at the center of a sphere that is one hundred light-years in radius, and the universe forbids them from seeing anything in the entire universe beyond their own sphere.  We now realize that even if the universe is infinitely large with infinitely many stars shining with light that adds to infinite luminosity, the finite age of the universe together with the finite speed limit of the universe together forbid us from observing the entire universe.  The laws of physics themselves constrain us to only observe a finite part of the universe within a spherical region centered on wherever we are located in the universe.  This finite part of the universe that we are only permitted to observe is called the observable universe.  Wherever we live in the entire universe, we appear to be at the center of our own observable universe, and our own observable universe is always the shape of a sphere with a radius in light-years equal to the age of the universe in years.  The spherical edge of our own observable universe is called the cosmic horizon, since it is rather like the event horizon of a black hole.  Although, instead of being outside the event horizon of a black hole and being forbidden from observing within that event horizon, we are inside the cosmic horizon of our observable universe, and we are forbidden from observing outside that horizon!  Indeed, the equations of General Relativity suggest that the entire universe is mathematically identical to a black hole turned inside out!  Also notice that with every passing year, the universe is one year older.  Hence, the cosmic horizon must grow by an additional light-year in radius with each passing year.  Thus, wherever we live in the universe, our cosmic horizon must expand away from us at a speed of one light-year per year.  At what speed what must we move to cover a distance of one light-year in a time of one year?  One light-year per year equals the vacuum speed of light of course!  We now conclude that wherever we live in the universe, the cosmic horizon must expand away from us at the speed of light.  As we will discuss shortly, the space within the cosmic horizon is also expanding away from us at proportionally slower speeds.  The actual age of the universe is roughly fourteen billion years, as we will discuss shortly.  We conclude that wherever we happen to be located within the entire universe, we appear to be at the center of our own observable universe.  Wherever we happen to be located within the entire universe, the shape of our own observable universe is a sphere roughly fourteen billion light-years in radius with an edge (our own particular cosmic horizon) that expands away from us at the vacuum speed of light.  The laws of physics constrain us to only observe the stars and galaxies within our finite observable universe, even if the entire universe is infinitely large with infinitely many stars shining with light that adds to infinite luminosity.  The laws of physics forbid us from observing anything outside of our cosmic horizon.  When we add together all of the light from all of the stars only within our observable universe, we calculate a nighttime sky that is dark.  This is the resolution of the Olbers paradox.  In brief, the finite age of the universe together with the finite speed limit of the universe together force the observable universe to have a finite size with a finite amount of light, even if the entire universe is infinitely large with infinitely many stars shining with light that adds to infinite luminosity.

 

The first person to tackle these cosmological questions using advanced mathematics was Albert Einstein using his General Theory of Relativity.  When Einstein solved the equations of his General Theory of Relativity for the spacetime of the entire universe, the equations reveal that our four-dimensional spacetime actually had a beginning at a finite time in the past.  Again, this resolves the Olbers paradox.  According to the equations of General Relativity, the beginning of our four-dimensional spacetime was a single event (a single mathematical point unified with a single instant of time), and this single event that began our four-dimensional spacetime had infinite spacetime curvature.  We could call this beginning the moment of creation, but all cosmologists call this beginning the Big Bang.  It is a common misconception that the Big Bang was a violent explosion within an empty universe.  This is a complete misunderstanding of the equations of General Relativity.  To even imagine an empty universe would be to presuppose that spacetime already existed before the Big Bang, which is not correct.  Again, according to the equations of General Relativity, the Big Bang was the beginning of spacetime.  Therefore, there was no spacetime before the Big Bang.  To even imagine an empty universe before the Big Bang would be to imagine a spacetime that existed before spacetime began, which is obviously a contradiction!  There was absolutely nothing before the Big Bang, but by this nothing we do not mean an empty universe with nothing in it.  The universe itself, the four-dimensional spacetime itself, was nonexistent!  Many students demand an answer to the following question: what happened before the Big Bang?  This is a meaningless question!  This question is just as meaningless as the following question: what is north of the north terrestrial pole?  There is nothing north of the north terrestrial pole since that is the most northern point on planet Earth or any other planet!  There was nothing before the Big Bang since the Big Bang was the beginning of spacetime itself!  How could anything have occurred before time itself began?  In other words, there was no before that was before the Big Bang!

 

According to the equations of General Relativity, spacetime itself expanded after the Big Bang.  We will discuss the origin of matter and energy within spacetime shortly.  For now, the matter within spacetime attracts each other gravitationally.  This mutual gravitational attraction should slow down the expansion of the universe.  Indeed, Einstein calculated that there are three different ways the universe could expand after the Big Bang.  If the density of mass throughout the universe is greater than a certain critical cosmic density, then the gravitational attraction among all this matter would be strong enough to eventually overpower the expansion of the universe.  In this case, the universe would eventually stop expanding and begin contracting until spacetime ends at a single event (a single mathematical point unified with a single instant of time), and this single event that would be the end of spacetime has infinite spacetime curvature.  In other words, spacetime would end with an opposite of the Big Bang.  All cosmologists call this end the Big Crunch, since it is the opposite of the Big Bang.  If the density of mass throughout the universe is less than this certain critical cosmic density, then the gravitational attraction among all this matter would not be strong enough to eventually overpower the expansion of the universe.  In this case, the universe would continue expanding forever.  If the density of mass throughout the universe is exactly equal to this certain critical cosmic density, the universe would also continue to expand forever but at a slower and slower rate due to the gravitational attraction among all the mass within the universe.  According to the equations of General Relativity, these three possible universes have different cosmic geometries.  If the density of mass throughout the universe is greater than the critical cosmic density, then the cosmic geometry of the universe is closed.  In a closed geometry, the sum of the angles in a triangle is greater than 180°, the circumference of a circle is less than 2π multiplied by its radius, and lines that begin parallel do not remain parallel but instead eventually converge toward one another.  A concrete example of a closed geometry is the geometry of a sphere, which is itself a special case of the geometry of an ellipsoid, which is also a closed geometry.  If the density of mass throughout the universe is less than this critical cosmic density, then the cosmic geometry of the universe is open.  In an open geometry, the sum of the angles in a triangle is less than 180°, the circumference of a circle is greater than 2π multiplied by its radius, and lines that begin parallel do not remain parallel but instead eventually diverge away from one another.  A concrete example of an open geometry is the geometry of a hyperboloid.  If the density of mass throughout the universe is exactly equal to this critical cosmic density, then the cosmic geometry of the universe is flat.  A flat geometry is Euclidean (or normal) geometry, where the sum of the angles in a triangle is equal to 180°, the circumference of a circle is equal to 2π multiplied by its radius, and lines that begin parallel do remain parallel to one another.  A concrete example of a flat geometry is the geometry of a plane.  Students often claim that our universe cannot have this third type of cosmic geometry.  According to General Relativity, gravity is the curvature of spacetime, as we discussed earlier in the course.  Therefore, many students claim that a flat universe would have no curvature and therefore would have no gravitation.  However, the cosmic geometry of the universe is the overall geometry of the entire universe.  Even if the cosmic geometry of the universe were flat, the gravitation of planets and stars and galaxies and black holes within the universe create tiny curvatures within this overall flat geometry.  The same is true if the cosmic geometry of the entire universe is closed or open.  There are tiny gravitational curvatures caused by planets and stars and galaxies and black holes, and these tiny gravitational curvatures are superimposed upon the cosmic geometry, which is the overall geometry of the entire universe.

 

Which of these three possible universes do we live in?  There is still some debate among cosmologists on the answer to this question.  If we add together the mass of all the normal (luminous star) matter in the universe, the resulting density is much less than the critical cosmic density.  This would suggest that we certainly live in an open universe that will continue to expand forever.  However, there is also roughly ten times as much dark matter as normal (luminous star) matter.  This tremendous quantity of dark matter is sufficient to cause us to live in a flat universe that will also continue to expand forever.  The dark matter could possibly be sufficient to cause us to live in a closed universe that will not continue to expand forever but will instead eventually begin contracting and end in a Big Crunch.  Again, it is frustrating to have no idea what dark matter is composed of given its extraordinary importance.  Without dark matter, stars within a galaxy would not remain bound within the galaxy, thus causing individual galaxies to disperse.  Without dark matter, galaxies within a galactic cluster would not remain bound within the galactic cluster, thus causing galactic clusters to disperse.  We now realize that without dark matter, the entire universe would also disperse (expand forever)!  The only size scale where dark matter is not necessary is the star system scale.  For example, the dynamics of our Solar System is completely explained through the gravity of the Sun, the planets, the moons, the asteroids, the comets, and so on and so forth.  Without dark matter, our Solar System would not disperse; our Solar System would remain together due to the gravitational attraction of our Sun.

 

In the early twentieth century (the early 1900s), the scientific community did not yet understand the crucial importance of the Big Bang, the beginning of spacetime, in resolving the Olbers paradox.  Consequently, most physicists during the early twentieth century (the early 1900s) did not believe that the universe ever had a beginning.  Einstein himself did not believe that the universe ever had a beginning.  Consequently, he doubted all three cosmic solutions of his own General Theory of Relativity.  He even tried to hide these three solutions by introducing a fudge factor into his General Theory of Relativity, which he called the cosmological constant.  However, in the year 1929, Edwin Hubble discovered that the universe is indeed expanding.  Hubble discovered that the light from all galaxies beyond our Local Galactic Group is redshifted, revealing that all galaxies beyond our Local Galactic Group are moving away from us.  Caution: galaxies within a galactic group or within a galactic cluster actually fall toward each other due to their mutual gravitational attraction.  For example, the light from the Andromeda Galaxy is actually blueshifted, revealing that our Milky Way Galaxy and the Andromeda Galaxy are falling toward each other, as we discussed.  More strictly, Hubble discovered that galactic groups and galactic clusters are expanding away from each other, although even galactic groups and galactic clusters may deviate from this cosmic expansion due to local gravitational attractions.  According to the equations of General Relativity, this expansion is not an actual motion of galactic groups and galactic clusters; the spacetime is itself expanding and thus spacetime itself carries galactic groups and galactic clusters away from each other.  Nevertheless, this cosmic expansion manifests itself as a recession, thus causing redshifted light as galactic groups and galactic clusters recede from each other.  Because of this motion of all galaxies beyond our Local Galactic Group away from us in all directions, Edwin Hubble announced to the world that the universe is expanding.  Hence, Edwin Hubble was given credit for the discovery of the expansion of the universe, even though this originally followed from Einstein’s General Theory of Relativity.  After Hubble’s discovery, Einstein called his own doubts and his introduction of the cosmological constant the “biggest blunder” of his life.  Today, six persons are collectively given credit for formulating the Big Bang model of cosmology, most importantly Edwin Hubble due to his observational work and Albert Einstein for discovering the General Theory of Relativity and first mathematically deriving the Big Bang.  The four cosmologists who further developed the mathematical details of the expansion of the universe include the Russian physicist Alexander Friedmann, the American physicist Howard Robertson, the British mathematician Arthur Walker, and the Belgian Catholic priest Georges Lemaître.  The prediction of the expansion of the universe is the first of the three great triumphs of the Big Bang model of cosmology.  We will discuss the other two great triumphs of the Big Bang model of cosmology shortly.

 

Many students claim that if all galaxies beyond our Local Galactic Group are expanding away from us, doesn’t this prove that we are at the center of the universe?  We must always keep in mind our earlier discussion: wherever we happen to be located in the universe, it would appear that we are the center of our own observable universe, and the universe appears to expand away from our own particular location within the universe.  This is the case with every observer in the entire universe.  There is no center of the entire universe, since every point in the universe appears to be the center of its own observable universe.  As spacetime expands, every galactic group and galactic cluster is carried away from every other galactic group and galactic cluster.  Therefore, anyone living in any galactic group or galactic cluster in the entire universe would observe all other galactic groups and galactic clusters expand away from their own particular galactic group or galactic cluster.  An analogy will help make this more clear.  Imagine a balloon with enough air inside of it to give it a spherical shape, and imagine many ants living on the outer surface of this balloon.  Suppose all of the ants decide to remain stationary, meaning that the ants do not crawl.  Now suppose someone blows more air into the balloon.  As the balloon is further inflated, the material of the balloon stretches, thus causing all of the ants to be further and further apart from one another.  Every one of these ants would see all the other ants apparently moving away from them; therefore, each ant would believe itself to be the center of the expansion.  In actuality, none of the ants is the center of the expansion since every ant observes itself to be the center of the expansion.  Notice also that each ant would see all the other ants appearing to receding even though they are not actually crawling.  In actuality, the material of the balloon is stretching, thus carrying all of the ants away from each other.  All of the ants are analogous to galactic groups and galactic clusters, and the material of the balloon is analogous to the spacetime itself.  As spacetime stretches, galactic groups and galactic clusters appear to move away from each other.  From within any galactic group or galactic cluster anywhere in the entire universe, all other galactic groups and galactic clusters appear to recede, causing their light to become redshifted.  Imagine there is at least one civilization of intelligent lifeforms living in every galactic group or galactic cluster in the entire universe.  Each one of these civilizations would observe every other galactic group or galactic galactic cluster appear to move away from them, as if their own particular galactic group or galactic cluster was the center of the expansion of the entire universe.  In actuality, there is no center of the expansion of the universe because every galactic group or galactic cluster in the universe appears to be the center of its own observable universe.

 

The Hubble law relates the recessional speed of all galaxies beyond our Local Galactic Group to their distance from us.  If a galaxy beyond our Local Galactic Group is a distance d from us, then the speed v (for velocity) with which the galaxy moves away from us is given by the Hubble law, which states v = H0 d, where H0 is called the Hubble constant and is equal to roughly seventy kilometers per second per megaparsec.  In other words, the Hubble law states that the speed with which galaxies beyond our Local Galactic Group move away from us is directly proportional to their distance from us.  We again emphasize that it is the stretching of the spacetime that carries galaxies away from us, and therefore galaxies beyond our Local Galactic Group are not actually moving away from us.  Although we do observe that the light from these distant galaxies is redshifted, this redshift is actually caused by the stretching of the wavelength of light as it journeys from distant galaxies toward us.  The same would be observed from every other galaxy in the universe.  Again, if we imagine that there is at least one civilization of intelligent lifeforms living in every galactic group or galactic cluster in the entire universe, each of these civilizations would observe redshifted light from all galactic groups and galactic clusters outside of their own particular galactic group or galactic cluster.  This redshift is caused by the stretching of the wavelength of light as it journeys from one galactic group or galactic cluster to any other galactic group or galactic cluster.  This is called cosmological redshift, the third type of redshift we have discussed in this course, the other two being kinematic redshift and gravitational redshift.  Although this cosmological redshift is caused by the stretching of spacetime, we may nevertheless interpret this redshift as a kinematic redshift, since it does appear that all galaxies beyond our Local Galactic Group are moving away from us.  Since we may interpret cosmological redshifts as kinematic redshifts, we may calculate recessional speeds from these redshifts that we measure for light from galaxies beyond our Local Galactic Group.  The direct proportionality between this recessional speed and distance according to the Hubble law is a direct consequence of the entire universe beginning with a Big Bang.  An analogy will help make this more clear.  Imagine we are standing in an enormous parking lot, and suppose we are surrounded by a circle of cars all driving directly away from us at sixty miles per hour, and furthermore suppose that all of these cars are sixty miles distant from us.  We would conclude that all of these cars began driving away from where we are standing one hour ago, since it takes one hour for a car to drive a distance of sixty miles at a speed of sixty miles per hour.  Now suppose we are surrounded by an additional circle of cars all driving directly away from us at 120 miles per hour, and furthermore suppose that all of these cars are 120 miles distant from us.  We would again conclude that all of these cars began driving away from where we are standing one hour ago, since it takes one hour for a car to drive a distance of 120 miles at a speed of 120 miles per hour.  Now suppose we are surrounded by yet another circle of cars all driving directly away from us at 180 miles per hour, and furthermore suppose that all of these cars are 180 miles distant from us.  We again conclude that all of these cars began driving away from where we are standing one hour ago, since it takes one hour for a car to drive a distance of 180 miles at a speed of 180 miles per hour.  As long as further and further cars are driving faster and faster away from us in direct proportion to their distance from us, then all cars at all distances began driving away from where we are standing at the same time in the past.  According to the Hubble law v = H0 d, the recessional speeds of all galaxies (beyond our Local Galactic Group) are directly proportional to their distances from us.  Therefore, all galaxies everywhere in the entire universe began moving away from our Local Galactic Group at the same moment in the past, the Big Bang or the beginning of spacetime (the moment of creation).  Warning: this conclusion tempts us to conclude that we are indeed at the center of the entire universe.  In actuality, the stretching of spacetime carries every galactic group or galactic cluster away from every other galactic group or galactic cluster, causing every civilization of intelligent lifeforms across the entire universe to deduce the same Hubble law.  There is no center of the expansion of the universe because every galactic group or galactic cluster in the universe appears to be the center of its own observable universe as the spacetime of the entire universe stretches (expands).  Since the Hubble constant is roughly seventy kilometers per second per megaparsec, every megaparsec of distance from us results in an additional roughly seventy kilometers per second of speed away from us.  In particular, a galaxy one megaparsec distant from us moves at roughly seventy kilometers per second away from us, a galaxy two megaparsecs distant from us moves at roughly 140 kilometers per second away from us, a galaxy three megaparsecs distant from us moves at roughly 210 kilometers per second away from us, and so on and so forth.  Notice that further and further galaxies are moving faster and faster away from us in direct proportion to their distance from us, and therefore all galaxies everywhere in the entire universe began moving away from us at the same moment in the past, the Big Bang or the beginning of spacetime (the moment of creation).

 

Speed equals distance divided by time; therefore, time equals distance divided by speed.  However, if we solve the Hubble law v = H0 d for the Hubble constant H0, we deduce that the Hubble constant equals speed divided by distance; that is, H0 = v / d.  However, speed divided by distance is the reciprocal of time.  Therefore, the reciprocal of the Hubble constant is distance divided by speed, which is time.  We define the reciprocal of the Hubble constant to be the Hubble time, and the Hubble time is a rough estimate of the age of the entire universe, just as the ratio between the distance traveled by all the cars in our imaginary parking lot to their speed is equal to the time all of them began to drive away from where we are standing.  The age of the entire universe is the amount of time all galactic groups and galactic clusters have been expanding away from each other since the Big Bang.  Again, the Hubble constant is roughly equal to seventy kilometers per second per megaparsec.  If we take the reciprocal of seventy kilometers per second per megaparsec and perform a unit conversion, we calculate that the Hubble time is roughly equal to fourteen billion years.  We have finally justified how we know the age of the entire universe.  It truly is as simple as setting the speed of galaxies equal to their distance traveled divided by the time that they have been traveling!  Note that the reciprocal of a large number is a small number, and the reciprocal of a small number is a large number.  Thus, if the Hubble constant is small, then the Hubble time is large; if the Hubble constant is large, then the Hubble time is small.  This stands to reason.  If the universe is expanding slowly (small Hubble constant), then the universe must have been expanding for a long duration of time since the Big Bang (large Hubble time).  If the universe is expanding quickly (large Hubble constant), then the universe must have been expanding for only a short duration of time since the Big Bang (small Hubble time).  Notice that as the universe ages, the Hubble time must become larger and larger and therefore the Hubble constant must become smaller and smaller.  Therefore, the Hubble constant is not truly a constant.  Nevertheless, we would need to wait billions of years to notice a substantial change in its value.  Therefore, it is appropriate to continue to refer to H0 as the Hubble constant.

 

The Hubble law is the highest rung of the Cosmological Distance Ladder.  To use this law to measure distances, first we determine the distances to somewhat nearby galactic groups and galactic clusters using lower rungs of the Cosmological Distance Ladder, such as the Tully-Fisher relation, the Faber-Jackson relation, or the Type Ia supernova method.  We also determine the recessional speed of these galaxies from us by measuring the redshift of their light.  Caution: we are actually interpreting a cosmological redshift as a kinematic redshift, as we discussed.  If we know the recessional speed of galaxies and the distance to these galaxies, then the only unknown remaining in the Hubble law v = H0 d is the Hubble constant H0.  This is how we have determined that the Hubble constant is roughly equal to seventy kilometers per second per megaparsec.  To then measure the distance to incredibly remote galaxies, we simply measure the redshift of their light.  We interpret this cosmological redshift as a kinematic redshift, and hence we calculate the recessional speed of the galaxy.  Since we have already determined the Hubble constant H0, the only unknown remaining in the Hubble law v = H0 d is the distance.  This is how the Dutch astronomer Maarten Schmidt determined that quasars are the most distant galaxies in the universe, by measuring their redshifts.  It is now appropriate to completely summarize the Cosmological Distance Ladder.  The lowest rung is the parallax method, which is only effective for nearby stars in the solar neighborhood.  The next rung is the main sequence fitting method, which is effective for star clusters beyond the solar neighborhood but still within our Milky Way Galaxy.  The next rung is the variable star method, which is effective for nearby galaxies throughout the Local Galactic Group and even beyond the Local Galactic Group, out to distances of roughly one hundred megaparsecs.  The next rung is the Tully-Fisher relation and the Faber-Jackson relation, which is effective for even more distant galaxies.  The next rung is the Type Ia supernova method, which is effective for quite distant galaxies.  Finally, the highest rung of the Cosmological Distance Ladder is the Hubble law, which is effective for the most distant galaxies in the observable universe.

 

The expansion of the universe causes complications when discussing cosmological distances.  As a concrete example, consider a galaxy that is one billion light-years distant at a particular moment in time.  This means that the light from that galaxy would take one billion years to travel toward us, assuming the one-billion-light-year distance remains fixed.  However, as the light traverses this distance, the universe expands, stretching the distance that the light must traverse.  Therefore, the light must actually travel more than one billion light-years from a galaxy that was formerly one billion light-years distant from us.  Moreover, the expansion of the universe also carries the distant galaxy away from us, causing it to be even further from us than the distance traversed by the light we receive from it.  In summary, whenever we observe a distant galaxy, its light has traversed a further distance than the ancient distance that the galaxy was formerly from us when the light that we presently observe first left the galaxy, and moreover the galaxy is presently in actuality even further from us than even the traversed distance of the light that we observe.  For all of these reasons, cosmologists define several different ways of measuring and calculating cosmological distances.  In this course, we will simply define cosmological distances in such a way that preserves the proportionality between recessional speed and distance as determined by the Hubble law.

 

If the universe is expanding, then it is gaining gravitational energy.  This increase in gravitational energy must come at the expense of thermal energy, since energy must be conserved.  Hence, the universe must become cooler and cooler as it expands.  This also implies that the early universe was hot.  The observable universe expanded to its present size from a formerly smaller size and cooled to its present temperature from a formerly hotter temperature.  Therefore, the Big Bang model of cosmology is more properly called the Hot Big Bang model of cosmology.  We can imagine traveling further and further backward in time when the observable universe was smaller and smaller and thus hotter and hotter.  When the universe was sufficiently young, the observable universe may have been so small that all galaxies in the universe were crowded against each other.  At even earlier times, galaxies did not even form yet; the entire universe was filled with stars that were relatively crowded together.  At even earlier times, not even stars had formed; the entire universe was filled with gas that would later form the first stars.  As we run the cosmic clock further and further backward in time, this gas that filled the entire universe was hotter and hotter at earlier and earlier times, when the universe was younger and younger.  We can imagine times shortly after the Big Bang when the observable universe was so incredibly small and so incredibly hot that the laws of physics themselves were actually different from the laws of physics today.  As we discussed earlier in the course, there are presently four fundamental forces in our universe.  Listed in the correct order from strongest to weakest, these fundamental forces are the strong nuclear force, the electromagnetic force, the weak nuclear force, and the gravitational force.  Recall that the gravitational force is by far by far by far by far the weakest force in the entire universe; the gravitational force is much much much much weaker than the three other fundamental forces.  In the 1970s, the American physicist Sheldon Lee Glashow, the Pakistani physicist Abdus Salam, and the American physicist Steven Weinberg formulated a theory that claimed that at incredibly hot temperatures, the electromagnetic force and the weak nuclear force unify into a single force that they called the electroweak force, since it is the unification of the electromagnetic force and the weak nuclear force.  This theory is called electroweak theory.  According to electroweak theory, at incredibly hot temperatures, there should only be three fundamental forces in our universe: the strong nuclear force, the electroweak force, and the gravitational force.  According to electroweak theory, this electroweak unification occurs at a temperature of roughly three quadrillion kelvins!  Note that nowhere in the entire present-day universe is it hot enough for this electroweak unification to occur.  The core temperature of our Sun is roughly fifteen million kelvins; this is incredibly hot by human standards, but this is also incredibly cold by electroweak unification standards!  The core of a helium-burning star is roughly one hundred million kelvins, still too cold for electroweak unification!  Temperatures at the center of a high mass star which then suffers a supernova explosion are in the billions of kelvins, still too cold for electroweak unification!  We might now suspect that electroweak unification is a purely speculative theory that can never be tested experimentally.  However, electroweak unification has been proven experimentally using subatomic particle accelerators.  A subatomic particle accelerator uses electric and magnetic fields to accelerate subatomic particles to incredibly fast speeds.  In the 1980s, physicists succeeded in building subatomic particle accelerators large enough with electric and magnetic fields strong enough to accelerate protons and antiprotons to speeds unimaginably close to the speed limit of the universe, the vacuum speed of light.  These physicists then used these subatomic particle accelerators to accelerate protons and antiprotons in opposite directions and forced them to collide with each other at these incredible speeds.  These collisions were so energetically violent that they effectively had a temperature of a few quadrillion kelvins.  As a result, physicists actually witnessed, for just a fraction of an instant, electroweak unification during these violently energetic proton-antiproton collisions!  Glashow, Salam, and Weinberg received the Nobel Prize in Physics for their correct electroweak theory.  According to electroweak theory, the electroweak force divorces itself into the electromagnetic force and the weak nuclear force below roughly three quadrillion kelvins through a spontaneously broken symmetry involving the Higgs-Englert particle, named for the British physicist Peter Higgs and the Belgian physicist François Englert, both of whom theorized the existence of this particle.  Although electroweak unification was experimentally proven with subatomic particle accelerators in the 1980s, these accelerators were still not large enough to cause particle collisions energetically violent enough to synthesize the Higgs-Englert particle.  The largest particle accelerator in the world is currently the Large Hadron Collider in Europe, abbreviated the LHC, and in the year 2012 this giant subatomic particle accelerator caused particle collisions energetically violent enough to finally synthesize the Higgs-Englert particle.  Both Peter Higgs and François Englert received the Nobel Prize in Physics for their correct prediction of the existence of this particle.  Although the cores of stars and even supernova explosions are too cold for electroweak unification to occur, humans have built subatomic particle accelerators on planet Earth that have achieved the electroweak unification temperature!  Although nowhere in the entire present-day universe is it hot enough for electroweak unification to occur (other than subatomic particle accelerators humans have built on planet Earth), there must have been a very early time shortly after the Big Bang when the universe was so hot that the entire universe only had three fundamental forces: the strong nuclear force, the electroweak force, and the gravitational force.

 

Since electroweak theory has been experimentally proven, other physicists have been motivated to search for theories that unify the strong nuclear force with the electroweak force.  These theories are called grand unification theories, which physicists abbreviate GUTs.  According to these grand unification theories, at an even hotter temperature far beyond the electroweak unification temperature, a grand unification would result in only two fundamental forces in the universe: a grand-unified force and the gravitational force.  We will reveal the grand unification temperature shortly.  For now, we express this grand unification threshold in terms of the appropriate size of a subatomic particle accelerator to achieve grand unification.  Again, the largest particle accelerator in the world is currently the Large Hadron Collider in Europe, abbreviated the LHC.  Unfortunately, even the Large Hadron Collider is not large enough to achieve grand unification.  Although there are many different grand unification theories that predict somewhat different grand unification temperatures, all these different temperatures are roughly equal to each other, and hence we can estimate the size of a subatomic particle accelerator that could achieve grand unification.  According to most grand unification theories, grand unification can only be achieved in a subatomic particle accelerator roughly the size of our Milky Way Galaxy!  Humans will never ever succeed in constructing such an enormous subatomic particle accelerator.  We might now suspect that grand unification theories are purely speculative theories that can never be tested experimentally.  However, there are other methods to test grand unification theories.  According to grand unification theories, the proton is actually an unstable particle that disintegrates after a certain lifetime.  If we were to actually observe a proton disintegrate, this would be experimental evidence that grand unification theories are correct.  Unfortunately, we have never witnessed a proton disintegrate.  Perhaps grand unification theories are correct that the proton is an unstable particle, but perhaps the lifetime of a proton is much longer than the current age of the universe; this would explain why we have never witnessed a proton disintegrate.  Nevertheless, if grand unification theories are correct, then all the protons in the universe should eventually disintegrate.  Stars and planets and mountains and buildings and humans and mobile telephones are all composed of atoms, which are in turn composed of protons.  If the lifetime of a proton is perhaps fourteen billion years, the current age of the universe, then all the protons in the universe could disintegrate at any moment.  Perhaps tomorrow, all stars and planets and mountains and buildings and humans and mobile telephones will spontaneously disintegrate due to their unstable protons as predicted by grand unification theories!  The most popular grand unification theory is Supersymmetric Relativistic Quantum Field Theory, or Supersymmetry for short.  According to Supersymmetric Relativistic Quantum Field Theory, for every particle of matter or antimatter in the universe, there is a corresponding supersymmetric particle.  In particular, this theory claims that there are supersymmetric electrons called selectrons, there are supersymmetric quarks called squarks, there are supersymmetric photons called photinos, there are supersymmetric gluons called gluinos, and supersymmetric gravitons called gravitinos.  Other supersymmetric particles include winos and zinos.  The Large Hadron Collider might be large enough to create one of these supersymmetric particles; this would be experimental evidence for a grand unification theory.  Unfortunately, we have never discovered a supersymmetric particle.  In other words, selectrons, squarks, photinos, gluinos, gravitinos, winos, and zinos are all purely hypothetical particles.  Without ever witnessing a proton disintegrate and without ever discovering a supersymmetric particle, we currently have no experimental evidence that any of the several grand unification theories are correct.  Nevertheless, most physicists do believe in grand unification.  Although nowhere in the entire present-day universe is it hot enough for grand unification to occur, there must have been a very early time shortly after the Big Bang when the universe was so hot that the entire universe only had two fundamental forces: the grand-unified force and the gravitational force.

 

Although we have no experimental evidence that any of the grand unification theories are correct, some physicists claim that at an even hotter temperature the grand-unified force unifies with the gravitational force.  Theories that claim that this occurs are called super unification theories, which physicists abbreviate SUTs, or theories of everything, which physicists abbreviate TOEs.  A super unification theory or a theory of everything would finally achieve Einstein’s ultimate dream to discover the single ultimate equation that explains everything about the entire universe.  According to super unification theories or theories of everything, at fantastically hot temperatures there would be no gravity, no electromagnetism, and no nuclear forces.  There would only be a single force throughout the entire universe, called the super-unified force.  We will reveal the super unification temperature shortly.  For now, we express this super unification threshold in terms of the appropriate size of a subatomic particle accelerator to achieve super unification.  According to super unification theories, super unification can only be achieved in a subatomic particle accelerator roughly the size of our observable universe!  Humans will never ever succeed in constructing such an enormous subatomic particle accelerator.  We might now suspect that super unification theories are purely speculative theories that can never be tested experimentally.  However, there are other methods to test super unification theories.  Just as Quantum Electromagnetic Theory reveals that light is composed of individual photons, super unification theories or theories of everything claim that gravity is composed of individual gravitons.  If we could detect a single graviton, this would be evidence for super unification theories or theories of everything.  Unfortunately, we have never detected a single graviton.  Gravitational waves were just recently detected for the first time in the year 2015, as we discussed earlier in the course.  The most popular super unification theory or theory of everything is string theory, more properly called brane theory.  The word brane is a shortening of the word membrane; a string is a one-dimensional membrane, a drum is a two-dimensional membrane, and so on and so forth.  This string theory or brane theory is also called M-theory, meaning any of the following: membrane theory, matrix theory, mystery theory, mysterious theory, magic theory, magical theory, majestic theory, magnificent theory, monster theory, monstrous theory, mother theory, or mother of all theories.  Some physicists jokingly suspect that the uppercase (capital) letter M is actually an upside-down uppercase (capital) letter W for Witten, since the American theoretical physicist Edward Witten has made the greatest mathematical advances in this proposed super unification theory or theory of everything.  According to string theory or brane theory or M-theory, every particle in the universe and even the curvature of spacetime itself is actually composed of vibrating branes (membranes) that are fantastically tiny, far far far far smaller than the nucleus of an atom and even far far smaller than protons and neutrons.  The different vibrations of these branes (membranes) would create different particles, such as electrons or quarks or photons or even the speculative supersymmetric particles.  The graviton itself is a vibrating brane (membrane) according to M-theory.  We currently have no experimental evidence that any of the several super unification theories are correct.  Nevertheless, most physicists do believe in super unification.  Although nowhere in the entire present-day universe is it hot enough for super unification to occur, there must have been an incredibly early time immediately after the Big Bang when the universe was so fantastically hot that the entire universe only had one fundamental force: the super-unified force.

 

We can use the equations of General Relativity to calculate the cooling temperature of the entire universe as it expands.  From these calculations, cosmologists have determined the history of the entire universe.  Cosmologists have divided the history of the entire universe into cosmic epochs based on cosmic events that occurred throughout the entire universe.  This is similar to human history.  Historians have divided human history into ages based on important events that occurred in human history, beginning with the Stone Ages followed by the Bronze Age, the Iron Age, the Greco-Roman Ages, the Middle Ages, and finally the Modern Ages.  The history of any particular country or culture is similarly divided into periods based on important events.  For example, American history begins with the Pre-British Colonial Period followed by the British Colonial Period, the Revolutionary Period, the Early Nineteenth Century Period, the Sectional Crisis Period, the Late Nineteenth Century Period, the Early Twentieth Century Period, the Superpower Period, and finally the Hyperpower Period.  Geologists have taken the entire history of planet Earth and divided it into geologic eras, again based on important geological events.  These geologic eras include the Paleozoic Era, the Mesozoic Era, and the Cenozoic Era.  Similarly, cosmologists have divided the entire history of the universe into epochs based on cosmic events that occurred throughout the entire universe.  We have arrived at the grand finale of the entire course: a brief history of the entire universe.

 

The Big Bang itself occurred at time zero, the beginning of spacetime.  According to the equations of General Relativity, the temperature and the energy density and the spacetime curvature were all equal to infinity at the Big Bang.  Consequently, the mathematical equations of General Relativity actually break down at the Big Bang, meaning that the mathematical equations of General Relativity fail to answer any questions about the moment of the Big Bang itself.  What exactly occurred at the instant of the Big Bang?  Was it the hand of God?  Science provides no answer.

 

The Planck Epoch occurred from time zero to a time of roughly 5×10–44 seconds, roughly fifty quadrillionths of one quadrillionth of one quadrillionth of one second after God created the universe!  During the Planck Epoch, the temperature of the universe cooled from infinity down to roughly 1032 kelvins, roughly one hundred nonillion kelvins!  During this epoch, there was no gravity, there was no electromagnetism, and there were no nuclear forces.  There was only a single fundamental force in the entire universe: the super-unified force.  Therefore, the universe must have been governed by a super unification theory or theory of everything.  This could have been M-theory (brane theory or string theory), but we are not certain.  Thus, cosmologists are almost completely uncertain about what exactly occurred during the Planck Epoch.  However, all cosmologists do agree that at the end of the Planck Epoch, the universe became so cool (roughly one hundred nonillion kelvins!) that the super-unified force could no longer continue to exist.  At the end of the Planck Epoch, the super-unified force divorced itself into the grand-unified force and the gravitational force.  This was when gravity was born, at the end of the Planck Epoch.  All cosmologists also agree that a tremendous number of gravitons was liberated from this divorce.  These gravitons that filled the entire universe is called the Cosmic Graviton Background Radiation.  This Cosmic Graviton Background Radiation was born at the end of the Planck Epoch at roughly one hundred nonillion kelvins of temperature.  However, fourteen billion years of cosmic expansion has cooled this Cosmic Graviton Background Radiation to nearly absolute zero temperature.  We will reveal the present-day temperature of this Cosmic Graviton Background Radiation shortly.

 

The GUT Epoch occurred from a time of roughly 5×10–44 seconds to a time of roughly 10–34 seconds, roughly one hundred trillionths of one trillionth of one trillionth of one second after God created the universe!  During this GUT Epoch, the temperature of the universe cooled from roughly 1032 kelvins down to roughly 1028 kelvins, roughly ten octillion kelvins!  During this epoch, there were two fundamental forces in the entire universe: the grand-unified force and the gravitational force.  Therefore, the universe must have been governed by a grand unification theory to explain the grand-unified force and Einstein’s General Relativity theory to explain the gravitational force.  The grand unification theory that explained the grand-unified force could have been Supersymmetric Relativistic Quantum Field Theory, but we are not certain.  Thus, cosmologists are nearly completely uncertain about what exactly occurred during the GUT Epoch.  However, all cosmologists do agree that at the end of the GUT Epoch, the universe became so cool (roughly ten octillion kelvins!) that the grand-unified force could no longer continue to exist.  At the end of the GUT Epoch, the grand-unified force divorced itself into the strong nuclear force and the electroweak force.  Many cosmologists also agree that a tremendous amount of energy was liberated from this divorce, causing the universe to expand by a fantastic amount that it would not have suffered otherwise.  This is called the theory of inflation, and it is a recent addition to the Hot Big Bang model of cosmology.

 

The Electroweak Epoch occurred from a time of roughly 10–34 seconds to a time of roughly 10–11 seconds, roughly ten trillionths of one second after God created the universe!  During this Electroweak Epoch, the temperature of the universe cooled from roughly 1028 kelvins down to roughly 3×1015 kelvins, roughly three quadrillion kelvins!  During this epoch, there were three fundamental forces in the entire universe: the strong nuclear force, the electroweak force, and the gravitational force.  This is the earliest cosmic epoch during which cosmologists are somewhat certain what precisely occurred.  The gravitational force is explained by Einstein’s General Relativity theory, the electroweak force is explained by the Glashow-Salam-Weinberg electroweak theory, and the strong nuclear force is explained by the Gross-Wilczek-Politzer theory, named for the three American theoretical physicists David Gross, Frank Wilczek, and Hugh David Politzer who formulated this correct theory of the strong nuclear force.  At the end of the Electroweak Epoch, the universe became so cool (roughly three quadrillion kelvins!) that the electroweak force could no longer continue to exist.  At the end of the Electroweak Epoch, the electroweak force divorced itself into the electromagnetic force and the weak nuclear force.  Thus, the four fundamental forces that continue to exist throughout the universe today only began to exist as four separate forces at the end of the Electroweak Epoch, roughly ten trillionths of one second after the Big Bang, when the electroweak force divorced itself into the electromagnetic force and the weak nuclear force.  The electroweak force would never appear again until roughly fourteen billion years later on planet Earth when humans built large subatomic particle accelerators!

 

The Particle Epoch occurred from a time of roughly 10–11 seconds to a time of roughly 10–2 seconds, roughly one hundredth of one second after God created the universe!  During this Particle Epoch, the temperature of the universe cooled from roughly 3×1015 kelvins down to roughly 1011 kelvins, roughly one hundred billion kelvins!  The Particle Epoch provided the appropriate temperature to possibly create microscopic primordial black holes that would spend the next fourteen billion years evaporating and eventually exploding to possibly cause some gamma-ray bursts.  The Particle Epoch certainly provided appropriate temperatures for quarks and electrons to come into existence out of the energy that filled the entire universe.  The quarks also combined with one another to form protons and neutrons during the Particle Epoch.  Hence, the Particle Epoch is when normal matter came into existence.  Note that we have no idea when dark matter came into existence, since we do not even know what composes dark matter!  If normal matter and normal antimatter appeared in equal amounts during the Particle Epoch, they would have completely annihilated each other, leaving no normal matter or antimatter to eventually form stars and planets.  Although physicists do not yet understand why, we must nevertheless conclude that slightly more matter appeared than antimatter during the Particle Epoch.  When normal matter annihilated with normal antimatter during the Particle Epoch, there would have remained a tiny amount of leftover matter from this cosmic annihilation.  This tiny amount of leftover matter would eventually form the stars and planets of all the galaxies in the universe!  Perhaps there was in actuality slightly more antimatter than matter that appeared during the Particle Epoch.  After the cosmic annihilation during the Particle Epoch, perhaps there instead remained a tiny amount of leftover antimatter, and perhaps it was this tiny amount of leftover antimatter that would eventually form the stars and planets of all the galaxies in the universe.  Perhaps our Sun and our planet Earth and mountains and buildings and humans and mobile telephones are actually composed of antimatter, and perhaps we have mistakenly named these atoms as matter when in fact we are actually composed of antimatter!

 

The Nucleosynthesis Epoch occurred from a time of roughly one hundredth of one second to a time of roughly three minutes after God created the universe.  During this Nucleosynthesis Epoch, the temperature of the universe cooled from roughly one hundred billion kelvins down to roughly one billion kelvins.  During this Nucleosynthesis Epoch, protons and neutrons began to combine, forming atomic nuclei.  This is why this is called the Nucleosynthesis Epoch, since nuclei were synthesized during this epoch.  Cosmological calculations indicate that roughly three-quarters (roughly seventy-five percent) of the normal matter that filled the universe were protons that remained alone, separate from each other and separate from the neutrons.  Cosmological calculations also indicate that the remaining roughly one-quarter (roughly twenty-five percent) of the normal matter that filled the universe were protons and neutrons that combined into quadruplets, two protons and two neutrons fusing into a single nucleus.  Recall that a single proton is the nucleus of the hydrogen atom, and also recall that two protons and two neutrons together form an alpha particle, the nucleus of the helium atom.  Therefore, these cosmological calculations predict that the normal mass of the universe should be roughly three-quarters (roughly seventy-five percent) hydrogen and roughly one-quarter (roughly twenty-five percent) helium.  As we have discussed numerous times throughout the course, this is indeed the case.  This is the second great triumph of the Hot Big Bang model of cosmology, the explanation of the chemical composition of the normal mass of the universe.  Hence, the universe became roughly three-quarters hydrogen and roughly one-quarter helium between roughly one hundredth of one second and roughly three minutes after the Big Bang.  Caution: the universe was still so hot that hydrogen and helium were not neutral atoms yet.  The entire universe was filled with a hot plasma of hydrogen nuclei, helium nuclei, electrons, and photons all colliding with each other.  When protons and neutrons fused to form helium nuclei, a tremendous number of neutrinos was liberated that filled the entire universe.  This is called the Cosmic Neutrino Background Radiation.  This Cosmic Neutrino Background Radiation was born during the Nucleosynthesis Epoch at billions of kelvins of temperature.  However, fourteen billion years of cosmic expansion has cooled this Cosmic Neutrino Background Radiation to nearly absolute zero temperature.  We will reveal the present-day temperature of this Cosmic Neutrino Background Radiation shortly.  Cosmological calculations place constraints upon the relative abundances of the nuclei that were synthesized during the Nucleosynthesis Epoch, and by combining these calculations with our observations of the chemical composition of the normal matter of the universe, we can place constraints upon the amount of normal mass that fills the entire universe.  These constraints reveal that the normal matter that fills the universe should have a mass of roughly one-tenth of the total mass that fills the universe.  Yet again, we are compelled to conclude that the entire universe is composed of roughly ten times as much mysterious dark matter as normal matter.  Unfortunately, this still does not reveal what actually composes dark matter.  Consequently, we have no idea during which epoch of cosmic history the dark matter first formed.

 

The Epoch of Nuclei occurred from a time of roughly three minutes to a time of roughly three hundred thousand years after the Big Bang.  During the Epoch of Nuclei, the temperature of the universe cooled from roughly one billion kelvins down to roughly 3240 kelvins.  During this Epoch of Nuclei, the entire universe was filled with a hot plasma of colliding nuclei, electrons, and photons.  This hot plasma cooled as the universe expanded.  In addition, the entire universe was filled with the Cosmic Graviton Background Radiation and the Cosmic Neutrino Background Radiation.  Both of these background radiations continued to cool as the universe expanded.

 

The Recombination Epoch occurred from a time of roughly three hundred thousand years to a time of roughly four hundred thousand years after the Big Bang.  During this Recombination Epoch, the temperature of the universe cooled from roughly 3240 kelvins down to roughly 2710 kelvins.  We will regard roughly three thousand kelvins as the average temperature of the universe during the Recombination Epoch.  During this epoch, electrons combined with nuclei to form neutral hydrogen and helium atoms.  This is why this epoch is named the Recombination Epoch, since electrons combined with nuclei during this epoch.  When the electrons combined with the nuclei to form neutral atoms, a tremendous number of photons was liberated that filled the entire universe.  This is called the Cosmic Photon Background Radiation.  This Cosmic Photon Background Radiation was born during the Recombination Epoch at roughly three thousand kelvins of temperature.  However, fourteen billion years of cosmic expansion has cooled this Cosmic Photon Background Radiation to nearly absolute zero temperature.  Cosmological calculations reveal that the present-day temperature of the Cosmic Photon Background Radiation should be a miserable three kelvins above absolute zero.  At such an incredibly cold temperature, the Cosmic Photon Background Radiation should have a continuous blackbody spectrum with its primary radiation within the microwave band of the Electromagnetic Spectrum.  In the year 1964, the American astronomers Arno Allan Penzias and Robert Woodrow Wilson built a microwave telescope in New Jersey.  They became frustrated however, since their microwave telescope continuously detected microwaves coming from all directions in the sky with a temperature of roughly three kelvins above absolute zero.  It was only later that other astronomers and cosmologists realized that Penzias and Wilson had accidentally discovered the Cosmic Photon Background Radiation that fills the entire universe.  Penzias and Wilson received the Nobel Prize in Physics for this tremendous, although accidental, achievement.  This is the third great triumph of the Hot Big Bang model of cosmology, the prediction of the three-kelvin Cosmic Photon Background Radiation that fills the entire universe.  The Cosmic Background Explorer was NASA’s great microwave space telescope, in operation from 1989 to 1993.  This microwave telescope mapped the Cosmic Photon Background Radiation to fair resolution.  The Cosmic Background Explorer was replaced by the Wilkinson telescope, in operation from 2001 to 2010, which mapped the Cosmic Photon Background Radiation to incredible resolution.  We may interpret this map as an actual image of how the entire universe appeared during the Recombination Epoch, between roughly three hundred thousand years and roughly four hundred thousand years after the Big Bang.

 

Although the Cosmic Photon Background Radiation is nearly perfectly uniform, the map constructed by the Wilkinson telescope reveals microkelvin variations throughout the universe during the Recombination Epoch.  Variations in temperature must correspond with variations in density.  Some regions of the early universe were more dense than average, while other regions of the early universe were less dense than average.  The regions of the universe that were more dense than average must have collapsed under their self-gravity, ultimately forming galactic great walls.  This would leave more empty space between galactic great walls, ultimately forming cosmic supervoids.  However, computer simulations reveal that more dense regions would have had insufficient self-gravity to collapse and form galactic great walls without roughly ten times as much mass as the normal matter that fills the universe.  Once again, we conclude that roughly ninety percent of the mass of the universe is the mysterious dark matter.  Therefore, the variations in density that existed during the Recombination Epoch were due primarily to variations in the density of dark matter.  Whatever composes this mysterious dark matter, we are forced to conclude that it already existed before the Recombination Epoch, since dark matter density variations certainly existed during the Recombination Epoch.  Over billions of years, galactic superclusters formed within galactic great walls, galactic groups and galactic clusters formed within galactic superclusters, galaxies formed within galactic groups and galactic clusters, and stars formed within galaxies.  The first generation of stars born were Population III stars with zero metallicity, being composed of pure hydrogen and helium.  These stars fused some of their hydrogen to form more helium.  These Population III stars were very high mass stars that ended their lives with supernova explosions, synthesizing all the atoms on the entire Periodic Table of Elements and ejecting hot, rapidly-expanding supernova remnants that polluted or enriched the surrounding universe with these metals.  These gases eventually formed second-generation Population II stars with small but non-zero metallicity.  These stars fused some of their hydrogen to form more helium.  Some of these stars were high mass stars that ended their lives with supernova explosions, synthesizing all the atoms on the entire Periodic Table of Elements and ejecting hot, rapidly-expanding supernova remnants that further polluted or enriched the surrounding universe with even more of these metals.  These gases eventually formed third-generation Population I stars with higher metallicities than Population II stars.  The formation of nuclei by stars is called stellar nucleosynthesis, which continues to occur to the present day.  The formation of nuclei during the Nucleosynthesis Epoch is called Big Bang nucleosynthesis or primordial nucleosynthesis, which only occurred from a time of roughly one hundredth of one second to a time of roughly three minutes after the Big Bang.  Billions of years of stellar nucleosynthesis has increased the fraction (percentage) of helium and decreased the fraction (percentage) of hydrogen throughout the universe.  Nevertheless, fourteen billion years of stellar nucleosynthesis has only changed these fractions (percentages) by small amounts.  The normal (atomic) mass of the universe remains roughly three-quarters (roughly seventy-five percent) hydrogen, roughly one-quarter (roughly twenty-five percent) helium, and a tiny fraction (tiny percentage) of metals.  Over billions of years of cosmic history, the universe continued to expand, causing galactic groups, galactic clusters, galactic superclusters, and galactic great walls to move away from each other and also causing the three cosmic background radiations (photon, neutrino, and graviton) to continue to cool.

 

Presently, the universe is roughly fourteen billion years old.  The universe is filled with a Cosmic Photon Background Radiation at a miserable three kelvins above absolute zero.  The universe is also filled with a Cosmic Neutrino Background Radiation, and cosmological calculations reveal that this radiation should be at a miserable two kelvins above absolute zero.  This Cosmic Neutrino Background Radiation has not yet been detected.  If it is someday detected and if it is measured to have a temperature of roughly two kelvins above absolute zero, this will become the fourth great triumph of the Hot Big Bang model of cosmology.  Again, this has not yet been achieved.  If it is achieved, astronomers will use neutrino telescopes to construct a map of this Cosmic Neutrino Background Radiation, providing a neutrino image of how the entire universe appeared during the Nucleosynthesis Epoch, between roughly one hundredth of one second and roughly three minutes after the Big Bang, since that was when the Cosmic Neutrino Background Radiation was born.  The universe is also filled with a Cosmic Graviton Background Radiation, and cosmological calculations reveal that this radiation should be at a miserable one kelvin above absolute zero.  This Cosmic Graviton Background Radiation has not yet been detected.  If it is someday detected and if it is measured to have a temperature of roughly one kelvin above absolute zero, this will become the fifth great triumph of the Hot Big Bang model of cosmology.  Again, this has not yet been achieved.  If it is achieved, astronomers will use graviton telescopes to construct a map of this Cosmic Graviton Background Radiation, providing a graviton image of how the entire universe appeared at the end of the Planck Epoch, roughly fifty quadrillionths of one quadrillionth of one quadrillionth of one second after the Big Bang, since that was when the Cosmic Graviton Background Radiation was born.  We may never achieve this fifth triumph of the Hot Big Bang model of cosmology.  As we discussed, we have never detected a single graviton, and gravitational waves were just recently detected for the first time in the year 2015.

 

It is now appropriate to summarize the entire universe.  In doing so, we will also summarize the entire course.  The universe is filled with a Cosmic Photon Background Radiation at a miserable three kelvins above absolute zero, but this background radiation was born during the Recombination Epoch at roughly three thousand kelvins of temperature when the universe was between roughly three hundred thousand years old and roughly four hundred thousand years old.  The universe is filled with a Cosmic Neutrino Background Radiation at a miserable two kelvins above absolute zero, but this background radiation was born during the Nucleosynthesis Epoch at billions of kelvins of temperature when the universe was between roughly one hundredth of one second old and roughly three minutes old.  The universe is filled with a Cosmic Graviton Background Radiation at a miserable one kelvin above absolute zero, but this background radiation was born at the end of the Planck Epoch at roughly one hundred nonillion kelvins of temperature when the universe was roughly fifty quadrillionths of one quadrillionth of one quadrillionth of one second old.  Roughly ninety percent of the mass of the universe is dark matter, which exerts normal gravity even though it is not composed of normal (atomic) matter.  The remaining roughly ten percent of the mass of the universe is normal (atomic) matter.  Roughly three-quarters (roughly seventy-five percent) of this normal (atomic) matter is hydrogen, roughly one-quarter (roughly twenty-five percent) of this normal (atomic) matter is helium, and a tiny fraction (tiny percentage) of this normal (atomic) matter is metals.  Most of this normal (atomic) matter is intergalactic/intracluster gases within galactic clusters and interstellar/intragalactic gases within galaxies, and some of these gases have formed stars that fuse hydrogen into helium, increasing the amount of helium and decreasing the amount of hydrogen in the universe by small amounts.  High mass stars synthesize metals.  A tiny fraction (tiny percentage) of this normal (atomic) matter has formed planets, moons, asteroids, and comets.  Stars are clumped together to form galaxies, galaxies are clumped together to form galactic groups and galactic clusters, galactic groups and galactic clusters are clumped together to form galactic superclusters, and galactic superclusters are clumped together to form galactic great walls.  There are roughly one hundred billion star systems within a typical galaxy, and there are roughly one hundred billion galaxies in the observable universe.  Therefore, there are roughly ten sextillion star systems in the observable universe.  The entire universe has been expanding for roughly fourteen billion years, carrying all galactic groups, galactic clusters, galactic superclusters, and galactic great walls away from each other and also causing all three cosmic background radiations (photon, neutrino, and graviton) to cool.  The universe presently has four fundamental forces, but it was born with only one fundamental force described by a super unification theory or a theory of everything.

 

There is one final topic about the universe that we must mention.  This final topic is fascinating, arguably mysterious, and perhaps even beautiful.  Somewhere within this photon and neutrino and graviton filled, dark matter and hydrogen and helium dominated, continuously expanding and cooling universe, there is a seemingly ordinary galactic great wall.  Within that seemingly ordinary galactic great wall, there is a seemingly ordinary galactic supercluster.  Within that seemingly ordinary galactic supercluster, there is a seemingly ordinary galactic group.  Within that seemingly ordinary galactic group, there is a seemingly ordinary disk galaxy.  Within that seemingly ordinary disk galaxy, there is a seemingly ordinary spiral arm.  Within that seemingly ordinary spiral arm, there is a seemingly ordinary middle-aged main sequence star, but this is not an ordinary middle-aged main sequence star at all.  This middle-aged main sequence star is extraordinary, because the third planet orbiting that star actually has life upon it.  If this weren’t unbelievable enough, on a seemingly ordinary continent on that planet, there is a seemingly ordinary school, with a seemingly ordinary building, with a seemingly ordinary classroom, but this is not an ordinary classroom at all.  This classroom is extraordinary, because there is actually a person at the front of that classroom who just explained the nature and the history of the entire universe to a group of students, and perhaps this is the most fantastic thing about the entire universe.

 

 

 

Links

 

Libarid A. Maljian homepage at the Department of Physics at CSLA at NJIT

Libarid A. Maljian profile at the Department of Physics at CSLA at NJIT

Department of Physics at CSLA at NJIT

College of Science and Liberal Arts at NJIT

New Jersey Institute of Technology

 

 

 

This webpage was most recently modified on Monday, the twenty-fourth day of April, anno Domini MMXXIII, at 03:45 ante meridiem EDT.