<p>There are two ways in which mass transfer may occur. The first way is driven by stellar winds: stars constantly loose mass throught stellar wind, if there is a companion star sweeping around, it will capture some of the wind and increase its mass. This process is always active, but not always significant. For example, the Sun looses about <span class="math-container">$10^{-14} M_\odot \text{yr}^{-1}$</span>; if it had a companion, the mass transfer would be too small to be relevant in any way. This kind of mass transfer becomes more important, the highest is the mass loss rate. So you will have to look for luminous red giants and AGB stars.</p>
<p>More on this in <a href="https://arxiv.org/abs/1406.3473" rel="nofollow noreferrer">Boffin 2014</a>.</p>
<p>The second way is called <a href="https://en.m.wikipedia.org/wiki/Roche_lobe#Mass_transfer" rel="nofollow noreferrer">Roche Lobe Overflow</a>. This kind of mass transfer starts when the radius of one of the two stars becomes larger than its Roche (so this is the condition you were probably asking for). At this point, matter starts flowing through the L1 Lagrange point.</p>
<p>As a consequence of the mass transfer, both the radius of the star and the radius of the Roche lobe will change. If the radius of the star shrinks faster than the Roche lobe, then the mass transfer is said unstable, and will not continue. Otherwise, it is stable and will continue until the above conditions are met.</p>
<p>So, if you want to know when a particular binary will commence a Roche lobe overflow, you need the masses of the stars and the orbital parameters, which allow you to determine the geometry of the Roche lobes. Plus, you need the radii of the stars and how they evolve with time.
Finally, once the mass transfer starts, you will want to know how much mass is transferred, how the orbital parameters are changed by the mass transfer, and how the donating star reacts to being stripped of its envelope.</p>

CC BY-SA 4.0
2022-09-05T04:51:38.003Z
Thank you so much and how to convert units of orbital separation to radius in solar masses, please? https://articles.adsabs.harvard.edu/pdf/1983ApJ...268..368E
Elena Greg
CC BY-SA 4.0
2022-09-05T05:10:41.180Z
@ElenaGreg In the Eggleton's paper that you quote, he just assumes that the orbital separation is equal to 1, so the conversion to solar radii is done by simply multiplying for the value of the quantity you are interested, in solar radii
Prallax
CC BY-SA 4.0
2022-09-05T05:25:11.423Z
`import numpy as np`
`q = 0.49`
`rL = 0.49 * q**(2/3)/(0.6*q**(2/3) + np.log(1+q**(1/3)))`
`print(rL)`

rL is less then 1; thus, when I multiplied that by the radius of the primary, I obtain that Roche lobe radius is less then the radius of the star.
Elena Greg
CC BY-SA 4.0
2022-09-05T05:30:40.237Z
@ElenaGreg You can see it like this: the quantiy you have calculated is the ratio between the radius of the Roche lobe and the orbital separation. If rL=0.5, it means that the Roche lobe radius is half of the orbital separation. Is it clearer now?
Prallax
CC BY-SA 4.0
2022-09-05T05:46:40.820Z
When the semi-major axis a is 40 solRad (a1+a2 = 13+27), then the orbital separation is 40 + 13 * e + 27 * e, where e is the eccentricity. The Roche lobe in solar masses is r_L*(40+13*e+27*e). Is that correct, please?
Elena Greg
CC BY-SA 4.0
2022-09-05T10:14:14.533Z
*in solar radii
Elena Greg
CC BY-SA 4.0
2022-09-05T18:04:15.843Z
@ElenaGreg Yeah, that would be the orbital separation when the stars at apoastron, I think. But It changes during the orbit. In fact, you may also have eccentric binary systems in which the mass transfer only happens near periastron, when the stars are closer
Prallax
CC BY-SA 4.0
2022-09-05T18:08:37.367Z
Thank you. Is there a formula for that?
Elena Greg
CC BY-SA 4.0
2022-09-05T20:04:14.843Z
@ElenaGreg It's a [keplerian orbit](https://en.m.wikipedia.org/wiki/Kepler_orbit), the position of the stars trace ellipses... The maximum separation will be the one you wrote. The minimum, at periastron, will be 40 - 13*e  - 27*e
Prallax
CC BY-SA 4.0
2022-09-04T10:36:36.570Z
2022-09-04T10:36:36.570Z
Prallax
<p>How to estimate when the mass transfer will start? What is the characteristic of pre-mass transfer binaries?</p>

<binary-star><mass>
Binary - when mass transfer starts
Elena Greg
# Binary - when mass transfer starts

(Asked by: username_0 on 2022-09-03)

How to estimate when the mass transfer will start? What is the characteristic of pre-mass transfer binaries?

**Tags:** binary-star, mass


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## 1 answers

### Answer by username_1 on 2022-09-04. Score: 1 | Accepted answer

There are two ways in which mass transfer may occur. The first way is driven by stellar winds: stars constantly loose mass throught stellar wind, if there is a companion star sweeping around, it will capture some of the wind and increase its mass. This process is always active, but not always significant. For example, the Sun looses about $10^{-14} M\_\odot \text{yr}^{-1}$; if it had a companion, the mass transfer would be too small to be relevant in any way. This kind of mass transfer becomes more important, the highest is the mass loss rate. So you will have to look for luminous red giants and AGB stars.

More on this in [Boffin 2014](https://arxiv.org/abs/1406.3473).

The second way is called [Roche Lobe Overflow](https://en.m.wikipedia.org/wiki/Roche_lobe#Mass_transfer). This kind of mass transfer starts when the radius of one of the two stars becomes larger than its Roche (so this is the condition you were probably asking for). At this point, matter starts flowing through the L1 Lagrange point.

As a consequence of the mass transfer, both the radius of the star and the radius of the Roche lobe will change. If the radius of the star shrinks faster than the Roche lobe, then the mass transfer is said unstable, and will not continue. Otherwise, it is stable and will continue until the above conditions are met.

So, if you want to know when a particular binary will commence a Roche lobe overflow, you need the masses of the stars and the orbital parameters, which allow you to determine the geometry of the Roche lobes. Plus, you need the radii of the stars and how they evolve with time.
Finally, once the mass transfer starts, you will want to know how much mass is transferred, how the orbital parameters are changed by the mass transfer, and how the donating star reacts to being stripped of its envelope.

> **Comments:**
> **username_0**: Thank you so much and how to convert units of orbital separation to radius in solar masses, please? https://articles.adsabs.harvard.edu/pdf/1983ApJ...268..368E  
> **username_1**: @username_0 In the Eggleton's paper that you quote, he just assumes that the orbital separation is equal to 1, so the conversion to solar radii is done by simply multiplying for the value of the quantity you are interested, in solar radii  
> **username_0**: `import numpy as np` `q = 0.49` `rL = 0.49 * q**(2/3)/(0.6*q**(2/3) + np.log(1+q**(1/3)))` `print(rL)`  rL is less then 1; thus, when I multiplied that by the radius of the primary, I obtain that Roche lobe radius is less then the radius of the star.  
> **username_1**: @username_0 You can see it like this: the quantiy you have calculated is the ratio between the radius of the Roche lobe and the orbital separation. If rL=0.5, it means that the Roche lobe radius is half of the orbital separation. Is it clearer now?  
> **username_0**: When the semi-major axis a is 40 solRad (a1+a2 = 13+27), then the orbital separation is 40 + 13 * e + 27 * e, where e is the eccentricity. The Roche lobe in solar masses is r_L*(40+13*e+27*e). Is that correct, please?  
> **username_0**: *in solar radii  
> **username_1**: @username_0 Yeah, that would be the orbital separation when the stars at apoastron, I think. But It changes during the orbit. In fact, you may also have eccentric binary systems in which the mass transfer only happens near periastron, when the stars are closer  
> **username_0**: Thank you. Is there a formula for that?  
> **username_1**: @username_0 It's a [keplerian orbit](https://en.m.wikipedia.org/wiki/Kepler_orbit), the position of the stars trace ellipses... The maximum separation will be the one you wrote. The minimum, at periastron, will be 40 - 13*e  - 27*e  

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