Why Don't Low Mass Stars Progress Beyond Helium Burning?

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stupid question, but why don't low mass stars experience nuclear burning beyond helium burning? I mean, after the helium's been exhausted, what's to stop the carbon core from contracting enough to trigger Si burning (or whatever element comes next).

 

[Nabeshin]

Quick answer is that there's simply not enough mass in the star to cause the kind of pressures needed at the core to begin fusing helium. What happens in lieu is a little more complicated and tied to more advanced stellar evolution.

 

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Quick answer is that there's simply not enough mass in the star to cause the kind of pressures needed at the core to begin fusing helium. What happens in lieu is a little more complicated and tied to more advanced stellar evolution.

thanks Nabeshin. I guess my question is though, when hydrogen is exhausted, the core can keep on contracting (until ofcourse electrons become degenerate), and as it keeps on contracting the core temperature rises. For He burning to happen, a critical temperature is needed (~10^7) to get through the higher coloumb barrier,

What's to stop the temperature rising enough to pass this coloumb barrier?

 

[Nabeshin]

I'm not sure exactly what you're thinking of, but again there simply isn't enough mass in these small stars. The gravitational collapse is halted by the pressure supplied by the hydrogen shell and helium core that exist at this point. These will be able to provide a certain amount of force outwards which, in small stars, will balance the gravitational collapse. Larger stars continue burning the helium because gravity overpowers the pressure these layers are able to provide.

The answer here is very similar to why brown dwarfs or planets like Jupiter don't begin to fuse their hydrogen. There simply isn't enough mass to create the required temperatures at the core to get the whole process started.

 

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Nabeshin. I think I see the point you are making.

What happens after all the He is converted into C though? I mean nuclear reactions cease, so by the virial theorem the core must contract and heat up (if it radiates away energy). You're saying its low mass doesn't allow it to heat up enough to trigger He burning... so I presume electron degeneracy stops the core from contracting (and thus heating up) enough for He burning?

I'm going to bed now, but if you respond thanks:)

 

[Orion1]

What happens after all the He is converted into C though? I mean nuclear reactions cease, so by the virial theorem the core must contract and heat up (if it radiates away energy). You're saying its low mass doesn't allow it to heat up enough to trigger He burning... so I presume electron degeneracy stops the core from contracting (and thus heating up) enough for He burning?

After all the He is fused to C, its nuclear fuel has been exhausted.

The material in a white dwarf no longer undergoes fusion reactions, so the star has no source of energy, nor is it supported against gravitational collapse by the heat generated by fusion. It is supported only by electron degeneracy pressure, which enables it to be extremely dense.

Note that degenerate White dwarfs do not obey the Ideal gas pressure law, they obey the electron degeneracy pressure law, which is independent of gas temperature.

The physics of degeneracy yields a maximum mass for a nonrotating white dwarf, the Chandrasekhar limit—approximately 1.4 solar masses—beyond which it cannot be supported by degeneracy pressure. A carbon-oxygen white dwarf that approaches this mass limit, typically by mass transfer from a companion star, may explode as a Type Ia supernova via a process known as carbon detonation.

A white dwarf is very hot when it is formed, but since it has no source of energy, it will gradually radiate away its energy and cool down. This means that its radiation, which initially has a high color temperature, will lessen and redden with time. Over a very long time, a white dwarf will cool to temperatures at which it is no longer visible and become a cold black dwarf.[6] However, since no white dwarf can be older than the age of the Universe (approximately 13.7 billion years),[10] even the oldest white dwarfs still radiate at temperatures of a few thousand kelvins, and no black dwarfs are thought to exist yet.

Although white dwarf material is initially plasma—a fluid composed of nuclei and electrons—it was theoretically predicted in the 1960s that at a late stage of cooling, it should crystallize, starting at the center of the star.

The virial theorem does not depend on the notion of temperature and holds even for systems that are not in thermal equilibrium.
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Reference:
http://en.wikipedia.org/wiki/White_dwarf"
http://en.wikipedia.org/wiki/Virial_theorem"

 

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great reply Orion1! thanks:) Just a couple of stupid questions again.

The physics of degeneracy yields a maximum mass for a nonrotating white dwarf, the Chandrasekhar limit—approximately 1.4 solar masses—beyond which it cannot be supported by degeneracy pressure. A carbon-oxygen white dwarf that approaches this mass limit, typically by mass transfer from a companion star, may explode as a Type Ia supernova via a process known as carbon detonation.

where does the energy to ignite the carbon actually come from, when the WD reaches the Chandreskhar mass limit?

Although white dwarf material is initially plasma—a fluid composed of nuclei and electrons—it was theoretically predicted in the 1960s that at a late stage of cooling, it should crystallize, starting at the center of the star.

nuclei, or or protons and neutrons?