<p><a href="http://adsabs.harvard.edu/pdf/2002ASPC..263....1S" rel="noreferrer">Fairly good</a>.</p>
<p>Two stars of mass <span class="math-container">$M$</span> falling from infinity straight towards each other until they merge at distance <span class="math-container">$2R$</span> will get kinetic energy <span class="math-container">$GM^2/R$</span>. This is a lot, for two suns it is <span class="math-container">$1.8978\times 10^{41}$</span> J. However, compared to the binding energy of even a single star, <span class="math-container">$\approx 3GM^2/5R$</span> this is less(the sun has binding energy <span class="math-container">$2.2774\times 10^{41}$</span> J, and a double mass <span class="math-container">$2^{1/3}R$</span> radius same density merged star <span class="math-container">$7.2302\times 10^{41}$</span> J, 3.17 times more). So there is not enough energy released to blow up a star, but is is about a quarter of it: a lot of matter is going to get ejected or end up in orbits through a heated envelope that will take a while to simmer down.</p>
<p>The key issue is whether the cores get slowed down enough by the encounter to remain bound, becoming a <a href="https://en.wikipedia.org/wiki/Common_envelope" rel="noreferrer">common envelope</a> binary. A direct hit clearly would work, but glancing collisions may allow the cores to miss each other: now the question is whether the envelope can absorb enough kinetic energy. A rough estimate may be that there is significant slowing if the mass scooped up/pushed aside <span class="math-container">$\pi r_{core}^2 \rho_{envelope} R$</span> becomes comparable to <span class="math-container">$m_{core}$</span>. For two sun-like stars with <span class="math-container">$r_{core}=0.2R_\odot$</span> this seem to happen, but much hydrodynamics may occur complicating things.</p>
<p><a href="https://dspace.library.uu.nl/handle/1874/27801" rel="noreferrer">Glebbek's dissertation on stellar mergers</a> estimates a rough condition for the orbital angular momentum to exceed the maximum spin angular momentum of the merged star as <span class="math-container">$$\frac{r_p}{R_1+R_2} &gt; k^4\frac{(1+q)^{\xi+4}}{2q^2}$$</span> where <span class="math-container">$k^2\approx 0.05$</span>, <span class="math-container">$\xi\approx 0.6$</span>, <span class="math-container">$r_p$</span> the periastron distance, and <span class="math-container">$q=M_2/M_1$</span>. This typically is exceeded: there is a lot of angular momentum that needs to be shed (<a href="https://academic.oup.com/mnras/article/444/4/3209/1023064" rel="noreferrer">for example by blowing off a lot of heated gas</a>). For example, two sun-like stars having <span class="math-container">$r_p=R_\odot/2$</span> has a LHS of 1/4 and a RHS of 0.0303.</p>
<p>That dissertation also contains numerical simulations of various merger cases.</p>

CC BY-SA 4.0
2021-06-08T23:53:13.293Z
Great answer! Any thoughts on [What is the difference between the terms collision and merger? How are they used differently in Astronomy?](https://astronomy.stackexchange.com/q/44256/7982)
uhoh
CC BY-SA 4.0
2021-01-23T16:33:23.460Z
2021-01-23T16:33:23.460Z
Anders Sandberg
<p>After looking at <a href="https://astronomy.stackexchange.com/questions/41000/what-are-the-odds-that-the-sun-hits-another-star">What are the odds that the Sun hits another star?</a> and answering it (crudely), now I'd like to ask the following:</p>
<p>What is the probability that if two stars collide, their cores merge to form one larger, more massive star?</p>

CC BY-SA 4.0
2021-01-22T22:37:52.363Z
I'm not sure how to do the calculations correctly, so I won't write an answer, but I suspect that if 2 normal (Sun-like) stars fall into each other, even from a relatively small distance, the total KE in the rest frame would exceed their gravitational binding energies. So I seriously doubt that a peaceful merger could occur.
PM 2Ring
CC BY-SA 4.0
2021-01-23T00:06:52.763Z
@PM2Ring I don't care how violent the merger is and how messy the debris is after the first strike, just what is the chance that the stars *don't destroy each other and actually merge their cores to form a larger star without a common envelope being shed?*
WarpPrime
CC BY-SA 4.0
2021-01-23T00:26:07.803Z
Sure. And I'm saying the KE of the collision is probably enough to completely unbind both stars. And that's totally ignoring their current thermal energy content, or any energy released via nuclear reactions caused by the increased pressure. Hopefully, one of the professional astrophysicists will be able to give us a more definitive answer.
PM 2Ring
CC BY-SA 4.0
2021-01-23T12:47:38.280Z
That might depend on the other star's mass and size
jng224
<star><orbit><collision><impact-probability>
If two stars collide, what is the probability that they merge to form a single star?
WarpPrime
# If two stars collide, what is the probability that they merge to form a single star?

(Asked by: username_0 on 2021-01-22)

After looking at [What are the odds that the Sun hits another star?](https://astronomy.stackexchange.com/questions/41000/what-are-the-odds-that-the-sun-hits-another-star) and answering it (crudely), now I'd like to ask the following:

What is the probability that if two stars collide, their cores merge to form one larger, more massive star?

**Tags:** star, orbit, collision, impact-probability
> **Comments:**
> **username_1**: I'm not sure how to do the calculations correctly, so I won't write an answer, but I suspect that if 2 normal (Sun-like) stars fall into each other, even from a relatively small distance, the total KE in the rest frame would exceed their gravitational binding energies. So I seriously doubt that a peaceful merger could occur.  
> **username_0**: @PM2Ring I don't care how violent the merger is and how messy the debris is after the first strike, just what is the chance that the stars *don't destroy each other and actually merge their cores to form a larger star without a common envelope being shed?*  
> **username_1**: Sure. And I'm saying the KE of the collision is probably enough to completely unbind both stars. And that's totally ignoring their current thermal energy content, or any energy released via nuclear reactions caused by the increased pressure. Hopefully, one of the professional astrophysicists will be able to give us a more definitive answer.  
> **username_2**: That might depend on the other star's mass and size  

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## 1 answers

### Answer by username_3 on 2021-01-23. Score: 7 | Accepted answer

[Fairly good](http://adsabs.harvard.edu/pdf/2002ASPC..263....1S).

Two stars of mass $M$ falling from infinity straight towards each other until they merge at distance $2R$ will get kinetic energy $GM^2/R$. This is a lot, for two suns it is $1.8978\times 10^{41}$ J. However, compared to the binding energy of even a single star, $\approx 3GM^2/5R$ this is less(the sun has binding energy $2.2774\times 10^{41}$ J, and a double mass $2^{1/3}R$ radius same density merged star $7.2302\times 10^{41}$ J, 3.17 times more). So there is not enough energy released to blow up a star, but is is about a quarter of it: a lot of matter is going to get ejected or end up in orbits through a heated envelope that will take a while to simmer down.

The key issue is whether the cores get slowed down enough by the encounter to remain bound, becoming a [common envelope](https://en.wikipedia.org/wiki/Common_envelope) binary. A direct hit clearly would work, but glancing collisions may allow the cores to miss each other: now the question is whether the envelope can absorb enough kinetic energy. A rough estimate may be that there is significant slowing if the mass scooped up/pushed aside $\pi r\_{core}^2 \rho\_{envelope} R$ becomes comparable to $m\_{core}$. For two sun-like stars with $r\_{core}=0.2R\_\odot$ this seem to happen, but much hydrodynamics may occur complicating things.

[Glebbek's dissertation on stellar mergers](https://dspace.library.uu.nl/handle/1874/27801) estimates a rough condition for the orbital angular momentum to exceed the maximum spin angular momentum of the merged star as $$\frac{r\_p}{R\_1+R\_2} > k^4\frac{(1+q)^{\xi+4}}{2q^2}$$ where $k^2\approx 0.05$, $\xi\approx 0.6$, $r\_p$ the periastron distance, and $q=M\_2/M\_1$. This typically is exceeded: there is a lot of angular momentum that needs to be shed ([for example by blowing off a lot of heated gas](https://academic.oup.com/mnras/article/444/4/3209/1023064)). For example, two sun-like stars having $r\_p=R\_\odot/2$ has a LHS of 1/4 and a RHS of 0.0303.

That dissertation also contains numerical simulations of various merger cases.

> **Comments:**
> **username_4**: Great answer! Any thoughts on [What is the difference between the terms collision and merger? How are they used differently in Astronomy?](https://astronomy.stackexchange.com/q/44256/7982)  

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