The Number of Galaxies

Just as our Sun is but one of 100 billion stars that make up our galaxy, so our galaxy is but one of 100 billion galaxies that make up the Universe!  This image from the Hubble Space Telescope gives an idea of how many galaxies there are--this is a tiny region of space in the direction of the Big Dipper.  Check out the new (2004) Ultra Deep Field image. Nearly every object in these pictures is a galaxy, with only a handful of foreground stars from our galaxy visible with diffraction spikes.

Galaxies come in several distinct types.  Some have a spiral structure like the Andromeda Galaxy.  Some show no structure at all, and have a simple, eliptical shape.  Others have no spiral structure, but are not elliptical, either.  These are called irregular galaxies.  Below are some examples of the different kinds.

• Elliptical galaxies: Come in all sizes.  Here is a comparison of M32 (companion of M31, Andromeda Galaxy) and M87.

M32 (companion to Andromeda Galaxy)                                   M87 (Giant Elliptical)

• Spiral galaxies -- dust is key
• Ordinary spiral (AAO)
• Barred spiral (AAO) -- why a bar?  Simulations show bar forms with less dark matter (halo)
• M74: An Sc galaxy in the visible and UV(UO)
• Spiral variations
• Edge-on spiral
• Radio view of M81 and size of galaxy
• Oddball galaxies
• Dwarf irregular (AAO) largest population by number
• M82(Gendler)
• M51(Gendler)
• M51 (NJIT)
• Cartwheel (HST)
• Centaurus A (HST)
• Tuning fork diagram -- Not an evolutionary diagram.
• The morphological mix
• As observed (brightness limited):       77% spirals, 20% ellipticals,   3% irregular
• Space-limited sample (to 9.1 Mpc): 33% spirals, 13% ellipticals, 54% irregulars
• Galaxy colors/spectral types
• Depends on morphology
• Dominated by relatively few giant stars
• Elliptical and early spiral -- K star spectra
• Late spirals -- G or F star spectra, with K spectra in central bulge
• Invisible radiations
• Radio -- H I (21 cm line), H II (recombination lines), CO (mm lines) -- for Sc spirals and Irr I galaxies, the H I is much more extended than the stars -- almost double in radius.
• IR -- measures amount of dust in galaxy
• X-rays from M31 (ROSAT)

Measuring Cosmic Distances

Cepheid Variables
We mentioned earlier that some stars are variable stars.  Some stars change their brightness due to pulsations, in which they alternately grow and shrink in size, over a few days' time.  One kind is the Cepheid variables, which are luminous red supergiant stars that are burning helium in a shell around their cores.  Low-mass stars in this stage have thermal pulses in which they lose most of their mass as a planetary nebula, but the high-mass stars have a thick enough layer of gas that the pulses do not eject the outer layers.  Instead, the outer layers alternately expand and contract, making the star get brighter and dimmer over their cycle.

It turns out that Cepheid variables have a very remarkable and useful property.  Their period of pulsation varies with their luminosity.  If we measure two things about a distant Cepheid variable, 1) its apparent brightness, and 2) its period, then we can combine these to determine its distance.  Luckily, Cepheid variables are among the brightest of stars, so we can actually detect them in other galaxies!

See this very thorough lecture about Cepheids and the distance to the Large Magellanic Cloud.

Hubble's Law
The Hubble Space Telescope is named after Edwin Hubble, who was the first to use Cepheid variables (in 1924) to measure the distance to the nearest spiral galaxy, the Andromeda Galaxy.  Prior to his measurement of the distance to Andromeda Galaxy, we had no way of knowing how far away it was.  In Hubble's time, the 1920's, there was a debate about whether "spiral nebulae" were clouds of gas, or collections of stars.  Using the largest telescope in the world at that time, the 100-inch telescope on Mt. Wilson, CA, Hubble took photographs of the galaxy over many days, and discovered several Cepheid variables.  By measuring their periods and their apparent brightnesses, he showed for the first time that the Andromeda Galaxy is at a great distance--more than 2 million light years!

Even more than this, Hubble went on to measure Cepheid variables in several other galaxies as well.  As part of his analysis, he measured both the distance to the galaxies and their doppler shifts.  He made one of the most remarkable discoveries in science -- that more distant galaxies have a larger redshift.  This has become known as the Hubble Redshift Law, or Hubble's Law, and it holds true throughout the universe.  The farther away a galaxy is, the larger its redshift.  Recall that light is redshifted when objects move away from the observer.  What this is telling us is that the universe is expanding!  The constant of proportionality between distance and redshift is called the Hubble Constant, designated H_o.  Using this constant, we can tell the distance to the most distant objects we can measure!  All we do is measure its spectrum, determine how much the spectral lines are redshifted, convert that to a velocity v, called the recessional velocity, and from the equation v = H_od, we can get its distance.

But we have two practical difficulties that we must solve in order to use this to determine accurate distances.

• Galaxies do not obey Hubble's Law exactly, because they have velocities of their own, in addition to their recessional velocity.  This is especially problematic for nearby galaxies, whose recessional velocities are small compared to their own velocities.
• Even when galaxies do obey Hubble's Law, the distance we measure is only as accurate as the value of H_o.  For many many years it was not known to better than a factor of two--somewhere between 50 and 100 km s^-1 Mpc^-1.

Hubble could measure the constant H_o, but it was not very accurate because it was based on those galaxies within reach of the Cepheid distance-scale.  One of the key projects of the Hubble Space Telescope was to pin down the value of  with much better than the factor of two accuracy it has had for so long.  The final results of this key project are in, and the announced value is

H_o ~ 72 +/- 8 km s^-1 Mpc^-1.

We will discuss the implications of the expansion of the universe in a moment, but first, let's take a look at the complete distance scale.  We discussed this when we talked about parallax measurements of nearby stars, which was one link in the chain.  Here is the entire chain:

Complete Chain of Distance Scale

• Radar to measure distance to planets => determination of the value of 1 Astronomical Unit.  The value can be used to measure distances within our solar system.
• Parallax to measure distance to nearby stars => determination of the value of 1 pc.  Parallax can be measured for stars within about 100 pc of the Sun.
• Main-sequence fitting to measure distance to clusters => determination of the distance to clusters of stars within the galaxy.  This is good for measuring distances out to about 50 kpc, within our galaxy and the Magellanic Clouds (our satellite galaxies).
• Cepheid variables to measure distance to nearby galaxies => good to about 10 Mpc
• Other distance standards (e.g. Tulley-Fisher Relation) => good to 100 Mpc?
• Here is an example: using globular clusters to find distance to M87
• Hubble's Law => good to any distance
• Type Ia supernovae => good to any distance

Distance and Age

Recall that the more distant an object is, the longer it takes for the light to reach us.  Thus, we see distant objects as they were in the past, not as they are now.  For example, it takes 8 minutes for the light from the Sun to reach Earth, so we see the Sun as it was 8 minutes earlier.  We see alpha Centauri (at a distance of 4.3 light years) as it was 4.3 years ago.  And we see the Andromeda Galaxy as it appeared 2 million years ago.

As we look farther and farther into the distance, we are also looking further and further into the past.  This would be true even for a static universe, but Hubble's discovery that the universe is expanding makes things even stranger.

We can think of the expansion of the universe as if the galaxies are painted on the surface of an expanding balloon, or better, as if they were raisins in an expanding loaf of raisin bread.

The expansion of the universe is the expansion of space itself, not a motion through space.  Nearby galaxies appear to move more slowly away, because there is not much space between us and them, but more distant galaxies appear to move more quickly because there is more space separating us from them.  Note that it does not matter which raisin in the bread, or which dot on the balloon, we choose.  All of the raisins and dots move away from all of the others.

But notice that if all of the galaxies are moving away from all of the others due to the expansion of the universe, it is obvious that if we ran the clock backwards the galaxies would all get closer together.  In fact, if we keep running the clock backward, Hubble's Constant tells us when the galaxies would all come together in a single point.  Notice the units of Hubble's Constant -- km s^-1 Mpc^-1.  Both km and Mpc are units of distance, and we could express them in the same units, e.g. km, and cancel them.  Thus, the remaining units are inverse time (s^-1).  So inverting Hubble's Constant must give us a time, in seconds.  The inverse of 72 km s^-1 Mpc^-1 turns out to correspond to about 14 billion years.  This is why we said in the very first lecture that the age of the universe is 14 billion years.  This is the length of time that the universe has been expanding.

Now, following what we said earlier, if the universe is only 14 billion years old, can we see galaxies as far away as 14 billion light years?  If so, we would be seeing all the way back in time to the beginning of the universe -- back to the Big Bang itself.  Obviously, we cannot see back beyond the beginning of the universe, so there is a horizon beyond which we cannot see -- the Cosmological Horizon.  But what about Hubble's Law.  Since the universe is expanding, perhaps the galaxies near 14 billion light years away are moving near the speed of light.  In fact, this is the case, and there are galaxies so far away that they appear to be moving faster than the speed of light relative to us.  Note that we talked about Special Relativity, and the impossibility of anything to move faster than the speed of light through space.  But what we are talking about here is not motion through space -- it is the expansion of space itself.  There is no speed limit on the expansion of space.  So the observable universe has a horizon that we cannot see beyond -- not because it is too far back in time, but because it is moving away so fast that light from beyond it can never reach us.