Undergrad Red Dwarfs: Is 100% Hydrogen Conversion Practically True?

[bbbl67]

Now, it's been said that red dwarfs are completely convective, therefore they can convert 100% of their hydrogen supply into helium. However, is this really practically true? One would think that at some point in its lifespan that there simply won't be enough hydrogen left to sustain a practical fusion reaction, because there's more helium around than hydrogen, which would make it harder and harder for hydrogen to find other hydrogen to fuse with. Just as a guess, let's say that's about at the level where helium makes up 90% of the mass or perhaps volume of the star? Is there any theories that discuss this issue?

 

[unusually_wrong]

There wouldn't be enough mass to start fusion of the helium and should eventually cool. Over trillions of years it will cool to a point where is it no longer visible ( a black dwarf). That is all I can remember from my class.

 

[mathman]

Bit of irony - red dwarfs will outlive most other stars.

 

[CygnusX-1]

Not all red dwarfs are completely convective; only those with masses below about a third solar. Also, not all red dwarfs that are completely convective destroy all of their hydrogen.

However, the lowest-mass red dwarfs DO eventually exhaust all of their hydrogen. See the details for a 0.1 solar mass red dwarf in the inset of Figure 1 of this paper and notice how the hydrogen content drops to zero after 6 trillion years.

 

[Simon Peach]

you can still get it on DVD!

 

[snorkack]

However, the lowest-mass red dwarfs DO eventually exhaust all of their hydrogen. See the details for a 0.1 solar mass red dwarf in the inset of Figure 1 of this paper and notice how the hydrogen content drops to zero after 6 trillion years.

If so, then a bad approximation - a detail not well checked.

Of the massive stars that have fused helium and become white dwarfs, 80 % are DA class - so have not exhausted all their hydrogen. And the remaining 20 % includes hot stars that also have not exhausted hydrogen but that are hot enough to show He lines.

Red dwarfs have not become white dwarfs yet. When they will, how much hydrogen remains in them?

 

[stefan r]

If so, then a bad approximation - a detail not well checked.

Of the massive stars that have fused helium and become white dwarfs, 80 % are DA class - so have not exhausted all their hydrogen. And the remaining 20 % includes hot stars that also have not exhausted hydrogen but that are hot enough to show He lines.

Red dwarfs have not become white dwarfs yet. When they will, how much hydrogen remains in them?

I believe you are referencing the observed light signature. If you look at a photo image of Earth you see mostly water. However, Earth's mantel and core are very water depleted. The outer surface of a white dwarf is often made of material that fell onto the surface after it cooled. Hydrogen would not sink so it remains visible as a surface coating.

...is this really practically true? One would think that at some point in its lifespan that there simply won't be enough hydrogen left to sustain a practical fusion reaction, because there's more helium around than hydrogen, which would make it harder and harder for hydrogen to find other hydrogen to fuse with. ...

A blue dwarf is more compact. Increasing the density increases temperature and pressure. The fusion rate is determined by temperature and pressure. So it will become easier and easier for hydrogen to react.
Stars without any fusion reactions are still hot. The energy comes from gravitational collapse. When fusion is nearly complete the temperature can rise. At 15 megakelvins protons can find carbon and nitrogen with which to fuse. Convection will stop when fuel runs out. Any remnant hydrogen will be near the surface.

The lack of any examples of blue dwarfs does not mean that the theory is wrong. If something takes longer than 1.3 x 10¹⁰ years to form then it should not be visible yet. Creating a blue dwarf to demonstrate would be an expensive experiment. Research budgets would need to increase by several dozen orders of magnitude and be adjusted to inflation.

 

[snorkack]

A blue dwarf is more compact. Increasing the density increases temperature and pressure. The fusion rate is determined by temperature and pressure.

Increasing the density has no inevitable effect on temperature. Fusion rate is determined by temperature, pressure and composition.

So it will become easier and easier for hydrogen to react.
Stars without any fusion reactions are still hot. The energy comes from gravitational collapse.

Energy from gravitational collapse is rapidly exhausted.

When fusion is nearly complete the temperature can rise. At 15 megakelvins protons can find carbon and nitrogen with which to fuse. Convection will stop when fuel runs out.

As the temperature increases (with increase of molecular mass a contributing factor) the gas gets more transparent, which also favours radiation over convection.

Any remnant hydrogen will be near the surface.

There are effects favouring more remnant hydrogen near surface, yes.