Protostar Collapse to Pre-Main-Sequence (PMS) Object

• Cloud gravitational potential energy exceeds internal energy (one half of original potential energy is converted to internal kinetic energy, other half to radiation and stellar wind)
• Free-fall collapse of cloud, no hydrostatic equilibrium established (pressure near zero).
• What collisions do occur heat the gas and dust, but dust is efficient at radiating in the IR, so cloud stays cool and pressure stays low, collapse continues in free-fall.
• Center (densest part) becomes opaque to IR and traps the radiation.  The temperature rises, collision rate increases, and hydrostatic equilibrium is established.  The object is now a PMS object.  Time to this point: few x 10⁵ y.


The evolution of the object as a PMS object can be traced on an H-R diagram, as on the figure below, from Appenzeller and Tscharnuter (1975), Astron. Astrophys. 40, 397.  This and other tracks below are based on computer models of the type we discussed earlier.

As always, the temperatures here are the surface temperatures.  A plot of the location of an object on an H-R diagram at different times during its lifetime is called an evolutionary track.  Such evolutionary tracks for pre-main-sequence (PMS) objects depend on the initial mass of the protostar (or protostellar cloud).  The figure below shows evolutionary tracks for different masses (Iben (1965) Ap. J. 141, 993.).  Notice that they reach the main sequence at different points.

How long do the PMS objects take to travel these paths?

• A 1 solar mass star takes about 50 my (million years) to reach point 8.
• A 5 solar mass star takes only 600,000 y
• A 15 solar mass star takes only 60,000 y.
This is a trend that occurs throughout the life-cycle of stars--more massive stars live a much shorter time than less massive stars.

The turns in the PMS evolutionary paths in the diagram above are due to changes in the structure of the core of the star as it adjusts, fitfully, to nuclear burning in the core.  The diagonal line joining the "8"s in the figure is called the Zero-Age Main-Sequence (ZAMS), and represents the point at which equilibrium nuclear burning of H to He is taking place.  When the star arrives on the ZAMS, it has transitioned from a PMS object to a true star.  We already saw that stars evolve slightly after reaching the main sequence, when we discussed the evolution of the Sun over its lifetime.  The track is a slight motion along the main sequence, upward and to the left as the luminosity increases.

Hydrogen Core Burning
This stage of a star's life lasts for a time proportional to its mass, roughly according to the relation

t_*/t_sun = (M_*/M_sun)^-2.3

where t_sun = 10 billion years.  This is the total time spent on the main sequence (the main-sequence lifetime).

Hydrogen Shell Burning
As the star uses up its initial supply of H in the core, it begins to collapse again and the temperature and density in a region around the core (a shell) reaches high enough temperature to ignite H.  This causes the star to expand and leave the main sequence, rising up the Red Giant Branch (RGB).  During this time, the He in the core is inert, and for sufficiently massive stars it grow denser until it becomes electron degenerate.

Helium Core Burning
Once the star exhausts its supply of H in the shell, the star again collapses and the temperature rises rapidly.  The dense core of Helium suddenly reaches ignition temperature (Helium flash) and the track discontinuously changes to lower luminosity as the star shrinks again from its RGB stage.  Once there, it again is stable, on a "helium main-sequence", but its lifetime in burning He is much shorter than before.

Helium Shell Burning
When the He is exhausted in the core, the star begins to burn He in a shell around the Carbon core, and the track again moves to a red giant stage along the Asymptotic Giant Branch (AGB).  Because of the temperature dependence of He burning, the star is unstable during this stage and thermal pulses begin, which causes the ejection of planetary nebula (PN).

Carbon Burning
More massive stars can repeat this scenario with collapse to a stable carbon burning stage, again with ever shorter lifetime.

End of Life
Stars of various masses behave differently in detail, but ultimately they all suffer the same fate of collapse due to the available nuclear fuel being exhausted.  In the case of stars like the Sun, He burning is the last stage.  For less massive stars, He burning may not take place at all.  Once the final collapse takes place, we have only to look at the violence of the collapse and the forces involved to determine what happens next.

• White dwarf is the fate of solar mass stars, after the PN stage removes all of the outer layers of the star, leaving only a bare carbon core that slowly cools.
• Neutron star is the fate of more massive stars, which are greater than 1.4 solar masses (after the loss of their outer layers).
• Black hole is the fate of stars of more than 3 solar masses (after loss of mass in PN stage).