<p>I asked this on the physics SE but it received little attention:</p>
<p>Consider a high-mass zero-age main-sequence (ZAMS) (e.g., <span class="math-container">$m_{\rm ZAMS} \gtrsim 30\,$</span>M<span class="math-container">$_{\odot}$</span>) star.</p>
<p>I understand that the core-envelope boundary is only (semi-) well defined for Main Sequence stars that do have a core, and that in principle the final spin (angular velocity) of the core should depend on the spin of the star prior to losing its envelope due to strong wind mass-loss in late-stage evolution if the star is in isolation (or due to a mass transfer event if the star is in a binary). I've read, <a href="http://adsabs.harvard.edu/abs/2000MNRAS.315..543H" rel="nofollow noreferrer">here</a> for instance, that the core should be nearly completely uncoupled from the envelope, however in <a href="https://arxiv.org/abs/1706.07053" rel="nofollow noreferrer">this</a> recent paper they assume that the coupling is sufficient enough to determine the natal spin of the stellar core (see figure 1). <a href="https://arxiv.org/abs/2010.00078" rel="nofollow noreferrer">Here</a>, they treat core-envelope coupling of high mass stars as a great uncertainty. I understand that this coupling is uncertain (observationally poorly constrained) and is theoretically uncertain due to many complicated processes involved in sustaining the transfer of angular momentum through the star.</p>
<p>Is there a (preferably) simple way to understand the strength of core-envelope coupling in terms of the ZAMS quantities of the star, without performing full stellar population synthesis?... and without introducing another uncertain parameter, such as a timescale? Is there a known parameterization of the effects of this process on single-star evolution, i.e. with the ZAMS mass and metallicity?</p>

CC BY-SA 4.0
2021-03-27T14:29:31.180Z
It is not known how strong this coupling is. Natal spin is usually determined assuming solid body rotation since extremely young stars are fully convective. What "mass transfer event"? Are you talking about binary systems - in which case there are tidal forces to consider. The question seems to be missing links to references.
ProfRob
CC BY-SA 4.0
2021-03-27T17:24:05.247Z
@ProfRob Thanks for letting me know, I forgot to copy the links from PSE. Links are added. There are tons of papers about the physics of core-envelope coupling in single stars and its effects in binary stellar evolution (usually using population synthesis simulation of some kind). So I don't want to add too many links because its a rabbit-hole My question is really about whether there exists a known parameterization of the effects of the coupling, say, on a star's spin as it ages? I hope that makes sense. Tried to clarify in OP.
Daddy Kropotkin
CC BY-SA 4.0
2021-03-27T18:29:05.200Z
Looking at your links we seem to be talking at cross purposes. I really don't know about core envelope coupling in very massive stars. Your Q just asks about main sequence stars, 99.9% of which don't fall into that category. Angular momentum transfer between core and envelope is an unsolved problem in solar-type stars.
ProfRob
CC BY-SA 4.0
2021-03-27T20:17:35.493Z
"very massive stars" is quite vague. I'm talking about "high mass" stars, e.g., $m_{\rm ZAMS} \gtrsim 30$ solar masses. Most high mass stars we've observed exist with companion. I don't know what you mean by "99.9% of which don't fall into this category."
Daddy Kropotkin
CC BY-SA 4.0
2021-03-28T01:10:44.427Z
I think I see what you mean.... you mean that most stars are not "high mass." That's fair, and I forgot to say that I'm asking specifically about high mass stars. Sorry about that confusion. I've edited it.
Daddy Kropotkin
<star><stellar-evolution><stellar-astrophysics><main-sequence><metallicity>
Strength of core-envelope coupling in stars (again)
Daddy Kropotkin
# Strength of core-envelope coupling in stars (again)

(Asked by: username_0 on 2021-03-27)

I asked this on the physics SE but it received little attention:

Consider a high-mass zero-age main-sequence (ZAMS) (e.g., $m\_{\rm ZAMS} \gtrsim 30\,$M$\_{\odot}$) star.

I understand that the core-envelope boundary is only (semi-) well defined for Main Sequence stars that do have a core, and that in principle the final spin (angular velocity) of the core should depend on the spin of the star prior to losing its envelope due to strong wind mass-loss in late-stage evolution if the star is in isolation (or due to a mass transfer event if the star is in a binary). I've read, [here](http://adsabs.harvard.edu/abs/2000MNRAS.315..543H) for instance, that the core should be nearly completely uncoupled from the envelope, however in [this](https://arxiv.org/abs/1706.07053) recent paper they assume that the coupling is sufficient enough to determine the natal spin of the stellar core (see figure 1). [Here](https://arxiv.org/abs/2010.00078), they treat core-envelope coupling of high mass stars as a great uncertainty. I understand that this coupling is uncertain (observationally poorly constrained) and is theoretically uncertain due to many complicated processes involved in sustaining the transfer of angular momentum through the star.

Is there a (preferably) simple way to understand the strength of core-envelope coupling in terms of the ZAMS quantities of the star, without performing full stellar population synthesis?... and without introducing another uncertain parameter, such as a timescale? Is there a known parameterization of the effects of this process on single-star evolution, i.e. with the ZAMS mass and metallicity?

**Tags:** star, stellar-evolution, stellar-astrophysics, main-sequence, metallicity

> **Comments:**
> **username_1**: It is not known how strong this coupling is. Natal spin is usually determined assuming solid body rotation since extremely young stars are fully convective. What "mass transfer event"? Are you talking about binary systems - in which case there are tidal forces to consider. The question seems to be missing links to references.  
> **username_0**: @username_1 Thanks for letting me know, I forgot to copy the links from PSE. Links are added. There are tons of papers about the physics of core-envelope coupling in single stars and its effects in binary stellar evolution (usually using population synthesis simulation of some kind). So I don't want to add too many links because its a rabbit-hole My question is really about whether there exists a known parameterization of the effects of the coupling, say, on a star's spin as it ages? I hope that makes sense. Tried to clarify in OP.  
> **username_1**: Looking at your links we seem to be talking at cross purposes. I really don't know about core envelope coupling in very massive stars. Your Q just asks about main sequence stars, 99.9% of which don't fall into that category. Angular momentum transfer between core and envelope is an unsolved problem in solar-type stars.  
> **username_0**: "very massive stars" is quite vague. I'm talking about "high mass" stars, e.g., $m_{\rm ZAMS} \gtrsim 30$ solar masses. Most high mass stars we've observed exist with companion. I don't know what you mean by "99.9% of which don't fall into this category."  
> **username_0**: I think I see what you mean.... you mean that most stars are not "high mass." That's fair, and I forgot to say that I'm asking specifically about high mass stars. Sorry about that confusion. I've edited it.  

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## 0 answers

