<p>This is a well-studied problem. The effect of rotation on the structure of a low-ish mass star (like the Sun) is summarised by <a href="https://www.epj-conferences.org/articles/epjconf/pdf/2013/04/epjconf_liac40_01005.pdf" rel="noreferrer">Eggenberger (2013)</a>.</p>

<p>Such stars are never observed to rotate so fast that the rotation plays any significant role in their hydrostatic equilibrium, however rotation <em>does</em> play a role by causing additional mixing in the star.</p>

<p>This is important for two reasons: (i) it inhibits the gradual diffusion of helium towards the core, this slightly lowers the opacity in the core and raises it in the envelope (compared with a non-rotating star). This results in a slightly higher luminosity and a slightly higher surface temperature. (ii) More importantly, the additional mixing brings additional hydrogen into the core and this increases the lifetime on the main sequence.</p>

<p>The effects on stars of a solar mass are however unlikely to be very significant in practice, because these stars efficiently lose angular momentum via a magnetised wind during their early lives and the effects of rotation are unlikely to be significant even at several times the solar rotation rate.</p>

<p>The effects on more massive stars can be more severe. These can spin at an appreciable fraction of their break-up rate for a large part of their lives and do not lose angular momentum as efficiently as lower mass stars (they do not have magnetised winds). The effects are described in the canonical paper of <a href="http://adsabs.harvard.edu/abs/2000A%26A...361..101M" rel="noreferrer">Meynet &amp; Maeder (2000)</a>; they are more pronounced than for lower mass stars and more complicated because of the radiative envelope and uncertainties in the rotation-dependence of the significant mass-loss. </p>

<p>The hydrostatic effects of rotation <em>are</em> expected to be important early in the main sequence and contribute to a slightly <em>lower</em> surface temperature. At later times the dominant effects are caused by changes in the mixing and diffusion near the core and in the envelope as for the lower mass stars, resulting in higher luminosities and hotter temperatures. The main sequence lifetimes can be extended by 30% due to the additional mixing of fresh hydrogen fuel into the core.</p>

CC BY-SA 4.0
2024-11-21T10:47:00.740Z
Isn't there also an effect that for fast rotators the flattening implied higher gravity and hence temperature at the pole compared to the equator renders their spectrum and even spectral type inclination dependent?
Walter
CC BY-SA 4.0
2024-11-21T11:24:56.033Z
@Walter I think that is true (for high mass stars). One could add a paragraph for that. One could also add a paragraph for the effect on astereoseismology, where rotation leads to frequency splitting in a way that is inclination dependent. This latter point is seen even in lower mass stars (though they don't tend to be fast rotators). But I didn't read the question as wanting to know how it affects observational features of a star.
ProfRob
CC BY-SA 4.0
2024-11-30T21:13:35.550Z
The main sequence (mentioned in the question) is an observational feature. (full stop) Fast rotators seen at different inclinations are at different locations in the HRD and hence don't fall on the same main sequence, even though they are the same stars.
Walter
CC BY-SA 4.0
2018-12-28T19:32:51.667Z
2018-12-28T19:32:51.667Z
ProfRob
<p>I searched and have found that the questions mainly focus on neutron stars, white dwarfs and black holes. This was not what I want.</p>
<p>Basically, the bigger the star's mass is, the more intense its fusion reaction is and the shorter its lifespan is in the main sequence. Now, imagine that a star spins much faster. There will be lower surface gravity at the equator than at the poles. How does a fast rotation affect the star's fusion reaction?</p>
<ol>
<li><p>Will the pressure of the star's mass on its core be lower at the equator and therefore reduce nuclear fusion rate?</p>
</li>
<li><p>Will there be a deeper convection because of the Coriolis effect?</p>
</li>
<li><p>What would we notice in term of longevity on the main sequence, luminosity and the emission spectrum of a fast rotating star compared to a slow rotating one <strong>of the same initial mass</strong>?</p>
</li>
</ol>

<star><rotation><stellar-evolution><main-sequence><spectral-type>
How does a star's rotation affect a star on the main sequence?
Christmas Snow
# How does a star's rotation affect a star on the main sequence?

(Asked by: username_0 on 2018-12-28)

I searched and have found that the questions mainly focus on neutron stars, white dwarfs and black holes. This was not what I want.

Basically, the bigger the star's mass is, the more intense its fusion reaction is and the shorter its lifespan is in the main sequence. Now, imagine that a star spins much faster. There will be lower surface gravity at the equator than at the poles. How does a fast rotation affect the star's fusion reaction?

1. Will the pressure of the star's mass on its core be lower at the equator and therefore reduce nuclear fusion rate?
2. Will there be a deeper convection because of the Coriolis effect?
3. What would we notice in term of longevity on the main sequence, luminosity and the emission spectrum of a fast rotating star compared to a slow rotating one **of the same initial mass**?

**Tags:** star, rotation, stellar-evolution, main-sequence, spectral-type

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## 1 answers

### Answer by username_1 on 2018-12-28. Score: 9 | Accepted answer

This is a well-studied problem. The effect of rotation on the structure of a low-ish mass star (like the Sun) is summarised by [Eggenberger (2013)](https://www.epj-conferences.org/articles/epjconf/pdf/2013/04/epjconf_liac40_01005.pdf).

Such stars are never observed to rotate so fast that the rotation plays any significant role in their hydrostatic equilibrium, however rotation *does* play a role by causing additional mixing in the star.

This is important for two reasons: (i) it inhibits the gradual diffusion of helium towards the core, this slightly lowers the opacity in the core and raises it in the envelope (compared with a non-rotating star). This results in a slightly higher luminosity and a slightly higher surface temperature. (ii) More importantly, the additional mixing brings additional hydrogen into the core and this increases the lifetime on the main sequence.

The effects on stars of a solar mass are however unlikely to be very significant in practice, because these stars efficiently lose angular momentum via a magnetised wind during their early lives and the effects of rotation are unlikely to be significant even at several times the solar rotation rate.

The effects on more massive stars can be more severe. These can spin at an appreciable fraction of their break-up rate for a large part of their lives and do not lose angular momentum as efficiently as lower mass stars (they do not have magnetised winds). The effects are described in the canonical paper of [Meynet & Maeder (2000)](http://adsabs.harvard.edu/abs/2000A%26A...361..101M); they are more pronounced than for lower mass stars and more complicated because of the radiative envelope and uncertainties in the rotation-dependence of the significant mass-loss.

The hydrostatic effects of rotation *are* expected to be important early in the main sequence and contribute to a slightly *lower* surface temperature. At later times the dominant effects are caused by changes in the mixing and diffusion near the core and in the envelope as for the lower mass stars, resulting in higher luminosities and hotter temperatures. The main sequence lifetimes can be extended by 30% due to the additional mixing of fresh hydrogen fuel into the core.

> **Comments:**
> **username_2**: Isn't there also an effect that for fast rotators the flattening implied higher gravity and hence temperature at the pole compared to the equator renders their spectrum and even spectral type inclination dependent?  
> **username_1**: @Walter I think that is true (for high mass stars). One could add a paragraph for that. One could also add a paragraph for the effect on astereoseismology, where rotation leads to frequency splitting in a way that is inclination dependent. This latter point is seen even in lower mass stars (though they don't tend to be fast rotators). But I didn't read the question as wanting to know how it affects observational features of a star.  
> **username_2**: The main sequence (mentioned in the question) is an observational feature. (full stop) Fast rotators seen at different inclinations are at different locations in the HRD and hence don't fall on the same main sequence, even though they are the same stars.  

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