Schonberg-Chandrasekhar mass for low mass stars

[Sherrod]

Hi guys,
I am dealing with the following issue: in low mass stars during the main sequence, the core gets filled with He ashes over time until the pressure is not sufficient to keep it in hydrostatic balance. Then the core starts to contract on KH timescale until it hits the full degeneracy where the contraction stops and the star becomes a WD.
My question is: what is the density of the He core just before it reaches the Schonberg-Chandrasekhar limit?
Is it the same as the initial H core density of ~200g/cm3? Or does it change as more He is added over time?
Thank you.

 

[vociferous]

I am not sure that I understand the question.

What do you mean by "low mass star", because I am uncertain if there is a specific definition.

For masses smaller than the sun (and a bit larger), I do not believe the limit is ever reached.

For stars that are slightly larger than the sun, the limit is about 0.1 of the mass of the star.

You can find their original paper here:

http://articles.adsabs.harvard.edu/cgi-bin/nph-iarticle_query?letter=.&classic=YES&bibcode=1942ApJ...96..161S&page=&type=SCREEN_VIEW&data_type=PDF_HIGH&send=GET&filetype=.pdf

You should investigate later research papers and post what you have discovered.

 

[Sherrod]

Hi Vociferous,
I did not find anything on this specific range of stars. Everything I found refers to the paper you posted which holds for stars a bit more massive than the Sun.
By low mass stars, I refer to stars with ~0.1 to 0.5 Sun. Since the pressure of the envelope above the core is smaller, they can burn more than 10% of their hydrogen before they leave the main sequence. But how much is this fraction of the start total mass? This is what I wanted to know.

 

[vociferous]

Hi Vociferous,
I did not find anything on this specific range of stars. Everything I found refers to the paper you posted which holds for stars a bit more massive than the Sun.
By low mass stars, I refer to stars with ~0.1 to 0.5 Sun. Since the pressure of the envelope above the core is smaller, they can burn more than 10% of their hydrogen before they leave the main sequence. But how much is this fraction of the start total mass? This is what I wanted to know.

For very low-mass stars (like the kind you mention), they are fully convective, so shell burning is impossible, at least in theory (the universe is not old enough to test this). The helium from their core gets mixed into the envelope and the hydrogen from their envelope gets mixed into the core.

So basically, I think the answer to your question is that the limit is never reached and since there are no low-mass white dwarfs, we really cannot be certain how they will form or even if they will form. The "best guess" is that they form what is known as a helium white dwarf, something that is thought to exist today (although formed by other means).[1]

I don't believe these stars will ever truly leave the main sequence during their normal lifetime, because they will never ignite helium burning as they cannot get hot enough. Again though, they are so tiny that the Earth won't even be around when we see the first low-mass stars burn out.
[1]http://arxiv.org/pdf/astro-ph/0404291v1.pdf

 

[Ken G]

Well, they'll leave the main sequence when they run out of hydrogen, and contract into helium white dwarfs, but I presume you are not counting that in their "normal" lifetime. You are certainly right that these stars won't have shell burning and won't have a Schonberg-Chandrasekhar limit, that's for stars with convective cores but radiative envelopes, more massive than about 2 solar masses. That limit is the cause of the "Hertsprung gap", a kind of forbidden zone in the H-R diagram where stars cannot have an ideal-gas helium core that can support itself against the weight of its own envelope, so the core is crushed until it goes degenerate, creating a red giant or red supergiant.