<p>The two main forms of mass loss in stellar evolution are 1. stellar winds, and 2. mass transfer events.</p>
<p>Stars experience stellar winds throughout their lives, which is mass loss from the star's surface due to the pressure and temperature gradient that exists within the star. Depending on the type of star, i.e., small, large, cool, hot, etc... there are various mechanisms that drive the stellar winds. Regardless of the mechanism that drives the wind mass loss, <strong>the mass carries angular momentum from the star and thus decreases the rotation rate of the star.</strong></p>
<p>For example, winds from hot, luminous stars, such as O type main sequence stars or Wolf-Rayet stars, are driven by spectral lines, and hence are called &quot;line-driven&quot; winds. There is a very rich literature about stellar winds, for example see the classic <a href="https://ui.adsabs.harvard.edu/abs/1999isw..book.....L/abstract" rel="nofollow noreferrer">textbook</a> <em>Introduction to Stellar Winds</em> by Lamers &amp; Casinelli (1999) (free abridged version <a href="https://ui.adsabs.harvard.edu/abs/2000M%26PS...35..206W/abstract" rel="nofollow noreferrer">here</a>), or this review by Kudritzki <span class="math-container">$et~al.$</span> (2000) on <a href="https://ui.adsabs.harvard.edu/abs/2000ARA%26A..38..613K/abstract" rel="nofollow noreferrer">winds from hot stars.</a></p>
<p>The strength of the stellar wind depends on the luminosity L and metallicity Z of the star, since atoms that are more massive will carry more momentum from the star's surface. So the mass loss rate is typically modeled in stellar evolution models by power laws, i.e. <span class="math-container">$\dot{m} \propto L^m Z^n$</span>, where <span class="math-container">$m$</span> and <span class="math-container">$n$</span> are positive numbers that depend on the type of star. <a href="http://www.astronomy.ohio-state.edu/%7Ethompson/1144/Lecture9.html" rel="nofollow noreferrer">Since the luminosity is proportional to the star's radius</a>, the mass loss rate is also proportional to the star's radius. <strong>Thus, a higher metallicity star will experience stronger winds, more mass loss, and thus a greater decrease in spin angular momentum.</strong></p>
<p>EDIT: In practice, depending on the type of star, its mass, and metallicity, additional mechanisms for transporting angular momentum from the surface of the star are required to achieve significant angular momentum loss via wind mass loss. A common example is magnetic breaking, where the presence of magnetic fields at the stellar surface provide longer lever arms.</p>
<p>A star generally expands in radius as it evolves. If it evolves in isolation, like in a stellar cluster, it will continue to expand in radius until late in its life where the envelope is blown away nearly completely by strong stellar winds (due to the very large radius). These strong winds blow the envelope away from the stellar core, resulting in a nebula, and the core emerges as a core helium-burning star, a typical example is the Wolf-Rayet star. However, if we instead consider stars in a gravitationally bound system, like a binary star, then <a href="https://en.wikipedia.org/wiki/Roche_lobe#Mass_transfer" rel="nofollow noreferrer">mass transfer events</a> can occur between the two stars in the binary, depending on various things: if the separation is sufficiently small for one of the components to fill and overflow its Roche lobe, is the orbit circular or eccentric, are the stars rotating? Such mass transfer is, roughly speaking, either stable (a little bit of mass is lost and then stops), dynamically stable (mass is transferred while the Roche lobe of the donor can shrink controllably), or dynamically unstable (known as common envelope evolution in which the accretor cannot keep with the mass transfer rate). <strong>In the latter two cases, the donor star loses its envelope, and the loss of this envelope can result in angular momentum extraction from the stellar core, depending on how strongly coupled the stellar core's spin is to the envelope's spin</strong>: if the coupling is strong, then the core is depleted of spin, leaving a slowly spinning Wolf-Rayet star; if the coupling is weak, then losing the envelope has no effect on the spin of the Wolf-Rayet star (i.e., the emergent core) and thus is parameterized by some fraction of its breakup spin.</p>
<blockquote>
<p>will interstellar medium slow down the rotation of stars?</p>
</blockquote>
<p>An isolated star moving through the interstellar medium (ISM) is likely to be unaffected by the dust, because the star expells its own low energy cosmic rays (i.e., stellar winds) and electromagnetic radiation pressure. In the case where a star is able to accrete from the ISM, which would require a dense region of ISM (known as an <a href="https://en.wikipedia.org/wiki/Interstellar_cloud" rel="nofollow noreferrer">interstellar cloud</a>) and/or a star with very weak stellar winds, then this <a href="https://ui.adsabs.harvard.edu/abs/1979A%26A....72..104W/abstract" rel="nofollow noreferrer">can be modeled as Bondi-Hoyle accretion</a>, but this would have a negligible effect on the star's rotation rate compared to the effect of strong wind mass loss.</p>
<p>EDIT: it seems more likely to be the other way around: star formation and death impacts the ISM, and <a href="https://arxiv.org/abs/2102.01352" rel="nofollow noreferrer">supernovae may contribute a larger portion</a> of heavy metals to the ISM than stellar winds.</p>
<p>Lastly, when a star ends its life in gravitational collapse, further mass loss might accompany the ensuing supernova process, but such mass loss is highly uncertain currently.</p>

CC BY-SA 4.0
2021-08-18T07:17:59.807Z
You don't explain how mass loss results in slower rotation. Losing angular momentum is insufficient, since the moment of inertia also decreases. Most hot stars are quite rapid rotators and are not slowed in this way. For cool stars, although the spin down mechanism involves a stellar wind, it is not that alone that exerts a torque on the star.
ProfRob
CC BY-SA 4.0
2021-08-18T13:09:11.063Z
As to how much angular momentum is lost due to mass loss without the presence of other mechanisms, such as magnetic fields which cause magnetic breaking by supplying a larger lever arm for the winds, it greatly depends on the type of star being considered. In detailed models of stellar evolution, such things like magnetic fields are necessary, but in models of binary evolution, magnetic fields are usually ignored and spin-down due to winds is principally due to mass loss. IN principle, the mass loss itself can reduce the spin of the star significantly if the mass and/or metallicity are high...
Daddy Kropotkin
CC BY-SA 4.0
2021-08-18T13:10:46.813Z
But I agree with your point that for most stars (since most stars are not high mass nor high metallicity), things like magnetic breaking are important for spinning down the star. I've added an edit.
Daddy Kropotkin
CC BY-SA 4.0
2021-08-18T13:14:21.203Z
And about the moment of inertia... indeed it will change, but even if the mass is lost isotropically, the star's spin can decrease significantly without magnetic breaking if the change in the star's radius is not significant.
Daddy Kropotkin
CC BY-SA 4.0
2021-08-18T14:04:20.243Z
$L = I\omega$.  $\dot{L} = I\dot{\omega} + \omega \dot{I}$. If the mass loss rate is $\dot{m}$ and is lost from the stellar surface, then $\dot{L} = \omega R^2 \dot{m}$ and $\dot{I} =k\dot{m}R^2$, where $I=kmR^2$. So $\dot{\omega}/\omega = (k^{-1}-1) \dot{m}/{m}$. Thus the spin-down timescale is the same as the mass loss timescale. This would be $\gg$ the main-sequence lifetime, so is unimportant for main sequence stars of any mass, but may become important for evolved stars. In binaries it is important because the lever arm is to the COM of the binary.
ProfRob
CC BY-SA 4.0
2021-08-17T12:43:40.850Z
2021-08-18T13:17:09.780Z
2021-08-18T13:17:09.780Z
Daddy Kropotkin
<p>This is a side question from my previous <a href="https://astronomy.stackexchange.com/q/45342/36851">one</a>, will interstellar medium slow down the rotation of stars? Will it be significant enough to be considered as a factor? What are the other factors that slow down stars?</p>

CC BY-SA 4.0
2021-08-17T11:37:18.107Z
Why would you think the ISM can slow down the rotation of stars?
AtmosphericPrisonEscape
CC BY-SA 4.0
2021-08-17T11:41:51.687Z
@AtmosphericPrisonEscape Well, interstellar medium is composed of gas and dust, so I was wondering will it have any impact on the rotation of stars.
Jack the Ranger
CC BY-SA 4.0
2021-08-17T16:54:09.597Z
Pulsars and Stars loose angular momentum to the plasma that they themselves expel (see the answer below), but I don't think the ISM is involved, except in forming the star..
AtmosphericPrisonEscape
<star><star-evolution>
Will interstellar medium slow down the rotation of stars?
Jack the Ranger
# Will interstellar medium slow down the rotation of stars?

(Asked by: username_0 on 2021-08-17)

This is a side question from my previous [one](https://astronomy.stackexchange.com/q/45342/36851), will interstellar medium slow down the rotation of stars? Will it be significant enough to be considered as a factor? What are the other factors that slow down stars?

**Tags:** star, star-evolution
> **Comments:**
> **username_1**: Why would you think the ISM can slow down the rotation of stars?  
> **username_0**: @AtmosphericPrisonEscape Well, interstellar medium is composed of gas and dust, so I was wondering will it have any impact on the rotation of stars.  
> **username_1**: Pulsars and Stars loose angular momentum to the plasma that they themselves expel (see the answer below), but I don't think the ISM is involved, except in forming the star..  

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## 1 answers

### Answer by username_2 on 2021-08-17. Score: 10 | Accepted answer

The two main forms of mass loss in stellar evolution are 1. stellar winds, and 2. mass transfer events.

Stars experience stellar winds throughout their lives, which is mass loss from the star's surface due to the pressure and temperature gradient that exists within the star. Depending on the type of star, i.e., small, large, cool, hot, etc... there are various mechanisms that drive the stellar winds. Regardless of the mechanism that drives the wind mass loss, **the mass carries angular momentum from the star and thus decreases the rotation rate of the star.**

For example, winds from hot, luminous stars, such as O type main sequence stars or Wolf-Rayet stars, are driven by spectral lines, and hence are called "line-driven" winds. There is a very rich literature about stellar winds, for example see the classic [textbook](https://ui.adsabs.harvard.edu/abs/1999isw..book.....L/abstract) *Introduction to Stellar Winds* by Lamers & Casinelli (1999) (free abridged version [here](https://ui.adsabs.harvard.edu/abs/2000M%26PS...35..206W/abstract)), or this review by Kudritzki $et~al.$ (2000) on [winds from hot stars.](https://ui.adsabs.harvard.edu/abs/2000ARA%26A..38..613K/abstract)

The strength of the stellar wind depends on the luminosity L and metallicity Z of the star, since atoms that are more massive will carry more momentum from the star's surface. So the mass loss rate is typically modeled in stellar evolution models by power laws, i.e. $\dot{m} \propto L^m Z^n$, where $m$ and $n$ are positive numbers that depend on the type of star. [Since the luminosity is proportional to the star's radius](http://www.astronomy.ohio-state.edu/%7Ethompson/1144/Lecture9.html), the mass loss rate is also proportional to the star's radius. **Thus, a higher metallicity star will experience stronger winds, more mass loss, and thus a greater decrease in spin angular momentum.**

EDIT: In practice, depending on the type of star, its mass, and metallicity, additional mechanisms for transporting angular momentum from the surface of the star are required to achieve significant angular momentum loss via wind mass loss. A common example is magnetic breaking, where the presence of magnetic fields at the stellar surface provide longer lever arms.

A star generally expands in radius as it evolves. If it evolves in isolation, like in a stellar cluster, it will continue to expand in radius until late in its life where the envelope is blown away nearly completely by strong stellar winds (due to the very large radius). These strong winds blow the envelope away from the stellar core, resulting in a nebula, and the core emerges as a core helium-burning star, a typical example is the Wolf-Rayet star. However, if we instead consider stars in a gravitationally bound system, like a binary star, then [mass transfer events](https://en.wikipedia.org/wiki/Roche_lobe#Mass_transfer) can occur between the two stars in the binary, depending on various things: if the separation is sufficiently small for one of the components to fill and overflow its Roche lobe, is the orbit circular or eccentric, are the stars rotating? Such mass transfer is, roughly speaking, either stable (a little bit of mass is lost and then stops), dynamically stable (mass is transferred while the Roche lobe of the donor can shrink controllably), or dynamically unstable (known as common envelope evolution in which the accretor cannot keep with the mass transfer rate). **In the latter two cases, the donor star loses its envelope, and the loss of this envelope can result in angular momentum extraction from the stellar core, depending on how strongly coupled the stellar core's spin is to the envelope's spin**: if the coupling is strong, then the core is depleted of spin, leaving a slowly spinning Wolf-Rayet star; if the coupling is weak, then losing the envelope has no effect on the spin of the Wolf-Rayet star (i.e., the emergent core) and thus is parameterized by some fraction of its breakup spin.

> will interstellar medium slow down the rotation of stars?

An isolated star moving through the interstellar medium (ISM) is likely to be unaffected by the dust, because the star expells its own low energy cosmic rays (i.e., stellar winds) and electromagnetic radiation pressure. In the case where a star is able to accrete from the ISM, which would require a dense region of ISM (known as an [interstellar cloud](https://en.wikipedia.org/wiki/Interstellar_cloud)) and/or a star with very weak stellar winds, then this [can be modeled as Bondi-Hoyle accretion](https://ui.adsabs.harvard.edu/abs/1979A%26A....72..104W/abstract), but this would have a negligible effect on the star's rotation rate compared to the effect of strong wind mass loss.

EDIT: it seems more likely to be the other way around: star formation and death impacts the ISM, and [supernovae may contribute a larger portion](https://arxiv.org/abs/2102.01352) of heavy metals to the ISM than stellar winds.

Lastly, when a star ends its life in gravitational collapse, further mass loss might accompany the ensuing supernova process, but such mass loss is highly uncertain currently.

> **Comments:**
> **username_3**: You don't explain how mass loss results in slower rotation. Losing angular momentum is insufficient, since the moment of inertia also decreases. Most hot stars are quite rapid rotators and are not slowed in this way. For cool stars, although the spin down mechanism involves a stellar wind, it is not that alone that exerts a torque on the star.  
> **username_2**: As to how much angular momentum is lost due to mass loss without the presence of other mechanisms, such as magnetic fields which cause magnetic breaking by supplying a larger lever arm for the winds, it greatly depends on the type of star being considered. In detailed models of stellar evolution, such things like magnetic fields are necessary, but in models of binary evolution, magnetic fields are usually ignored and spin-down due to winds is principally due to mass loss. IN principle, the mass loss itself can reduce the spin of the star significantly if the mass and/or metallicity are high...  
> **username_2**: But I agree with your point that for most stars (since most stars are not high mass nor high metallicity), things like magnetic breaking are important for spinning down the star. I've added an edit.  
> **username_2**: And about the moment of inertia... indeed it will change, but even if the mass is lost isotropically, the star's spin can decrease significantly without magnetic breaking if the change in the star's radius is not significant.  
> **username_3**: $L = I\omega$.  $\dot{L} = I\dot{\omega} + \omega \dot{I}$. If the mass loss rate is $\dot{m}$ and is lost from the stellar surface, then $\dot{L} = \omega R^2 \dot{m}$ and $\dot{I} =k\dot{m}R^2$, where $I=kmR^2$. So $\dot{\omega}/\omega = (k^{-1}-1) \dot{m}/{m}$. Thus the spin-down timescale is the same as the mass loss timescale. This would be $\gg$ the main-sequence lifetime, so is unimportant for main sequence stars of any mass, but may become important for evolved stars. In binaries it is important because the lever arm is to the COM of the binary.  

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