# Evolution of low-mass stars

## Main Question or Discussion Point

Let's say we have a star of 0.7 solar masses on the main sequence. Can somebody describe what happens to it when it comes off the main sequence?

Thanks
Maria

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Chronos
Gold Member
They may [according to current models] bypass the red giant phase and evolve more or less directly into white dwarfs due to their inability to fuse helium. This is almost surely true for any star less than .5 solar masses. At .7 solar masses, the issue is less clear. It may enter the red giant phase then rapidly shed its outer atmosphere before settling in as a white dwarf. It is entirely possible, however, the universe is not yet old enough for a star of this size to have died of old age.

Nabeshin
It is entirely possible, however, the universe is not yet old enough for a star of this size to have died of old age.
Very likely the case. The Lifetime proportional to mass^3.5 approximation gives a main sequence lifetime of ~24 billion years for a star of .7 solar masses.

WMAP Universe age:
$$t_u = 1.373 \cdot 10^{10} \; \text{y}$$

$$t_{L} = 1.1 \cdot 10^{10} \; \text{y}$$

$$\tau_{ms} = t_{L} \left( \frac{M_{\odot}}{M_s} \right)^{2.5}$$

$$\boxed{\tau_{ms} \geq t_u}$$

Integration by substitution:
$$t_{L} \left( \frac{M_{\odot}}{M_s} \right)^{2.5} \geq t_u$$

Main sequence minimum stellar mass threshold currently available for red giant phase branch ascention:
$$\boxed{M_s \leq M_{\odot} \left( \frac{t_u}{t_{L}} \right)^{-0.4}}$$

$$\boxed{M_s \leq 0.915 \cdot M_{\odot}}$$

Red Giant phase mass threshold:
$$0.23 \cdot M_{\odot} \leq M_s \leq 10 \cdot M_{\odot}$$

Wikipedia said:
Once a main sequence star consumes the hydrogen at its core, the loss of energy generation causes gravitational collapse to resume. For stars with less than 0.23 solar masses,[1] they are predicted to become white dwarfs once energy generation by nuclear fusion comes to a halt. For stars above this threshold with up to 10 solar masses, the hydrogen surrounding the helium core reaches sufficient temperature and pressure to undergo fusion, forming a hydrogen-burning shell. In consequence of this change, the outer envelope of the star expands and decreases in temperature, turning it into a red giant. At this point the star is evolving off the main sequence and entering the giant branch.

Reference:
http://en.wikipedia.org/wiki/Age_of_the_universe#WMAP"
http://en.wikipedia.org/wiki/Main_sequence#Evolutionary_tracks"
http://www.eso.org/public/outreach/press-rel/pr-2007/images/phot-29-07-normal.jpg" [Broken]

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A better source for low mass stars are the papers by Laughlin, Adams and Bodenheimer - "The End of the Main Sequence" and its follow-up papers - but Wikipedia is more or less correct. A 0.7 solar mass star will eventually burn its helium and it will form a Red Giant, but there hasn't been time for such stars to evolve to such a late stage in the history of the present Universe. There do exist many white-dwarfs of that mass, and smaller, but that's because red-giants undergo a lot of mass loss - a 10 solar mass star will probably return about ~8.6 solar masses of material back to the interstellar medium. Our Sun is likely to return about ~0.46 solar masses, leaving a carbon/oxygen white-dwarf corpse of about 0.54 solar masses.

I do wonder if we can't engineer that final remnant as a gigantic fusion reactor, slowly trickling mass onto it until we creep up to the Chandrasekhar Limit. We could control the stages of collapse into neutronium by encouraging the formation of heavier elements, after carefully fusing the final mass into iron, then collapsing it into heavier and heavier elements before the final (hopefully not too quick) deconfinement of quarks in the core. If we could collapse it into a quark star some 6.96 km in radius (0.000001 solar radii) we can ultimately extract a total of ~1.87 trillion years worth of gravitational energy (counting the energy in years of present solar luminosity.)

Chronos
Gold Member
I flinch at the .23 solar mass limit. I see no way helium fusion of any significance can occur in a star with such low mass.

I flinch at the .23 solar mass limit. I see no way helium fusion of any significance can occur in a star with such low mass.
The lowest I've seen is about 0.3 solar masses, which is what the Adams/Laughlin/Bodenheimer paper says as well.

hydrogen burning shell...

I flinch at the .23 solar mass limit. I see no way helium fusion of any significance can occur in a star with such low mass.
Wikipedia said:
For stars above this threshold with up to 10 solar masses, the hydrogen surrounding the helium core reaches sufficient temperature and pressure to undergo fusion, forming a hydrogen-burning shell.
ref. 1 said:
Upon emerging from its parent cloud core, the lowest mass star capable of burning hydrogen (M∗ ≈ 0.08M⊙).

A star with a slightly larger mass, M∗ = 0.23 M⊙, experiences the onset of a radiative core when the hydrogen mass fraction dips below 50%. The composition gradients which ensue are sufficient to briefly drive the star to lower effective temperature as the luminosity increases. In this sense, stars with mass M∗ = 0.23M⊙ represent the lowest mass objects that can become conventional “Red Giants”. At these low masses, however, the full giant phase is not completed. Stars with initial mass M∗ < 0.5 M⊙ will be unable to generate the high central temperatures (Tc ∼ 10^8 K) required for the helium flash; these stars abort their ascent up the giant branch by veering to the left in the H-R diagram.
At 0.23 solar masses it does not burn helium, the helium remains inert within a purely radiative core and burns a hydrogen shell surrounding the radiative helium core resulting in a red giant star.

Reference:
http://arxiv.org/PS_cache/astro-ph/pdf/9701/9701131v1.pdf" [Broken]

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