<p>There is no gravitational separation of elements as such for a self-gravitating system (held together by <span class="math-container">$1/r^2$</span> forces only). At all phases during star formation (and afterwards) you can assume the virial theorem to hold, by which the average kinetic energy = -1/2x average gravitational potential energy. As both the kinetic and potential energy are proportional to the mass of the elements, this ratio is therefore the same for all elements and no separation will occur.</p>
<p>You may be thinking of the gravitational separation in the Earth's atmosphere for instance or in context with buoyancy. The atmosphere is not a self-gravitating system though. The kinetic energy of a molecule in the Earth's atmosphere is less than 1% of its gravitational potential energy provided by the mass of the Earth. So the Earth's atmosphere is far from being in state of a virial equilibrium and separation of elements does occur here. A virial equilibrium for the Earth  would require a temperature of about <span class="math-container">$10^5 K$</span>. This is not even achieved in the Earth's interior, so elements are gravitationally separated here as well.</p>

CC BY-SA 4.0
2022-04-30T15:25:48.677Z
Maintaining the viral theorem does not imply you will not find chemical segregation. Nor do I follow your argument of Earth's atmosphere. Earth *is* a self-gravitating body, and as such its atmosphere and its segregation is actually a counter-argument to what you argue. And so is the chemical segregation of Earth's interior. It's the temperature gradient being greater than the adiabatic, thus (reasonably strong) convection which counters segregation.
planetmaker
CC BY-SA 4.0
2022-04-30T15:48:33.273Z
@planetmaker That's not what I said. What I said is that You will NOT find chemical segregation if the virial theorem DOES apply (as for e.g. the Sun). In order for the virial theorem to apply to the Earth you would need a temperature of about 10^5 K given the mass of the Earth. You have this neither in the Earth's atmosphere nor in its interior, so segregation will occur.
Thomas
CC BY-SA 4.0
2022-04-30T15:19:44.120Z
2022-05-01T07:59:49.623Z
2022-05-01T07:59:49.623Z
Thomas
<p>No. The diffusion process you describe does not take place to any significant extent in regions that are thoroughly mixed by convection.</p>
<p>Protostars are fully convective and as such have a uniform composition.</p>

CC BY-SA 4.0
2022-04-29T22:52:43.300Z
2022-04-29T22:52:43.300Z
ProfRob
<p>After the death of the universe’s first generation of stars, the clouds from which new stars form will include elements heavier than hydrogen.  In the formation of a protostar from such a cloud, do heavier elements sink down toward the center?  If so, does this sinking dilute the concentration of hydrogen at the protostar’s core, and thus, delay the time until initiation of hydrogen fusion (i.e., a delay relative to when a first generation protostar would have initiated hydrogen fusion)? I suspect the concentration of heavier elements in the cloud is so small that any such delay would be small.</p>

CC BY-SA 4.0
2022-04-29T18:04:29.297Z
I don’t know the answer, but I can confirm your suspicions that metallicity has a measurable effect on when fusion takes place; as small as the percentages of the metallicity are, they end up having a surprisingly large impact on a lot of things.
Justin T
CC BY-SA 4.0
2022-04-29T18:06:30.167Z
Also related but not the same: https://physics.stackexchange.com/questions/168437/metal-rich-star-formation
Justin T
CC BY-SA 4.0
2022-04-29T20:56:05.133Z
Metals affect the rate that the gas cloud collapses. As I said here: https://physics.stackexchange.com/a/413603/123208 Carbon is very important in star formation: it can radiate away energy in frequencies that hydrogen and helium are transparent to. This allows a collapsing gas cloud with carbon in it to shed excess heat far more effectively than a pure hydrogen + helium cloud can.
PM 2Ring
<protostar>
Do protostars take longer to achieve H fusion due to gravitational sinking of heavy elements?
MarkVonTexas
# Do protostars take longer to achieve H fusion due to gravitational sinking of heavy elements?

(Asked by: username_0 on 2022-04-29)

After the death of the universe’s first generation of stars, the clouds from which new stars form will include elements heavier than hydrogen. In the formation of a protostar from such a cloud, do heavier elements sink down toward the center? If so, does this sinking dilute the concentration of hydrogen at the protostar’s core, and thus, delay the time until initiation of hydrogen fusion (i.e., a delay relative to when a first generation protostar would have initiated hydrogen fusion)? I suspect the concentration of heavier elements in the cloud is so small that any such delay would be small.

**Tags:** protostar
> **Comments:**
> **username_1**: I don’t know the answer, but I can confirm your suspicions that metallicity has a measurable effect on when fusion takes place; as small as the percentages of the metallicity are, they end up having a surprisingly large impact on a lot of things.  
> **username_1**: Also related but not the same: https://physics.stackexchange.com/questions/168437/metal-rich-star-formation  
> **username_2**: Metals affect the rate that the gas cloud collapses. As I said here: https://physics.stackexchange.com/a/413603/123208 Carbon is very important in star formation: it can radiate away energy in frequencies that hydrogen and helium are transparent to. This allows a collapsing gas cloud with carbon in it to shed excess heat far more effectively than a pure hydrogen + helium cloud can.  

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## 2 answers

### Answer by username_5 on 2022-04-29. Score: 8 | Accepted answer

No. The diffusion process you describe does not take place to any significant extent in regions that are thoroughly mixed by convection.

Protostars are fully convective and as such have a uniform composition.


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### Answer by username_3 on 2022-04-30. Score: -2

There is no gravitational separation of elements as such for a self-gravitating system (held together by $1/r^2$ forces only). At all phases during star formation (and afterwards) you can assume the virial theorem to hold, by which the average kinetic energy = -1/2x average gravitational potential energy. As both the kinetic and potential energy are proportional to the mass of the elements, this ratio is therefore the same for all elements and no separation will occur.

You may be thinking of the gravitational separation in the Earth's atmosphere for instance or in context with buoyancy. The atmosphere is not a self-gravitating system though. The kinetic energy of a molecule in the Earth's atmosphere is less than 1% of its gravitational potential energy provided by the mass of the Earth. So the Earth's atmosphere is far from being in state of a virial equilibrium and separation of elements does occur here. A virial equilibrium for the Earth would require a temperature of about $10^5 K$. This is not even achieved in the Earth's interior, so elements are gravitationally separated here as well.

> **Comments:**
> **username_4**: Maintaining the viral theorem does not imply you will not find chemical segregation. Nor do I follow your argument of Earth's atmosphere. Earth *is* a self-gravitating body, and as such its atmosphere and its segregation is actually a counter-argument to what you argue. And so is the chemical segregation of Earth's interior. It's the temperature gradient being greater than the adiabatic, thus (reasonably strong) convection which counters segregation.  
> **username_3**: @planetmaker That's not what I said. What I said is that You will NOT find chemical segregation if the virial theorem DOES apply (as for e.g. the Sun). In order for the virial theorem to apply to the Earth you would need a temperature of about 10^5 K given the mass of the Earth. You have this neither in the Earth's atmosphere nor in its interior, so segregation will occur.  

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