Stellar Evolution Continued

• Back to Stellar Evolution

  When we last saw the Sun it was evolving up the red giant branch (also known as First Ascent Giant Branch) with an ever-larger He core that is contracting and heating the surrounding H-fusion shell.

• So where is this heading?

  Eventually the core stops contracting for a Strange Reason .

  You might expect the core to heat up to K where He fusion would start and produce the thermal pressure required to balance gravity and then work in the thermostat mode. But, this is wrong

• The Red Giant core is supported by Electron Degeneracy.

  This comes about because you can only squeeze electrons so close together and no further because of the Pauli Exclusion Principle.

• The Red Giant core is made up of mostly ionized He so it is a gas of nuclei and .

  All subatomic particles have various properties characterized by ``quantum numbers''. One is ``spin''. The quantum world gets split into two flavors of particles according to their spin:

  1. ``spin 1/2'' particles are called Fermions ( are Fermions).

  2. ``spin 1'' particles are called Bosons (neutrons and He nuclei are Bosons)
• Fermions all obey a law called the Pauli Exclusion Principle:

  

  

  Here, the x,y,z refer to position and etc refer to momentum.

• At a given temperature (this means give the mean speed of the ), as the density goes up (packing those closer and closer together), the gas starts to run out phase space in which to put . The inability to increase the density adds up to a form of supporting pressure called Electron Degeneracy Pressure .

• Electron Degeneracy Pressure is what balances gravity in the RGB star core and EDP has a strange property in that it is more-or-less independent of temperature.

• Remember the usual Gas Law:

  This provides a saftey value:

• The Usual Gas Law as a Safety Value:
  1. Suppose the He fusion started in the core. This would release some heat, the temperature and pressure would go up, the core expands and cools off and the fusion rate decreases a little bit.

  2. Alternatively suppose the fusion rates go down. Then gravity starts to compress the core, the Temperature goes up, fusion rates go up and the core re-expands.

• But, because EDP is independent of temperature, when He fusion starts, it is like a bomb going off.
  1. Core Temperature reaches K.

  2. A special form of He fusion starts where 3He Carbon and there is an enormous release of energy and increase in the core temperature.

  3. Because the pressure in the core is due to degeneracy and is T independent, the core does NOT expand and cool, but rather there is a temperature runaway - this is the .

• Although it sounds exciting, the Helium Flash does not add up to all that much. It runs for a few hours until the temperature reaches and at this temperature there is lots of extra phase space available to the electrons and the degeneracy is ``lifted''. The result is a small hiccup and the internal structure now looks like a version of a main-sequence star with . The new equilibrium puts the star in a spot on the H-R Diagram called the ``horizontal branch''.

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Michael Bolte
Tue Feb 17 13:32:05 PST 1998