<p>The &quot;final parsec problem&quot; describes the difficulty in getting two supermassive black holes close enough together that their merger timescale due to gravitational wave emission becomes shorter than the age of the universe.</p>
<p>Normal stars do not merge due to gravitational wave emission - their masses are too low and their separations too large. The gravitational wave merger timescales would be much longer than the age of the universe even when their photospheres are in contact.</p>
<p>There is something akin to the final parsec problem for merging stellar black holes, neutron stars and white dwarfs. These are compact enough to have mergers driven by gravitational wave emission but they too must get together closer than about <span class="math-container">$10^{10}$</span> m (for black holes) or <span class="math-container">$10^9$</span> m (for neutron stars and white dwarfs) before the gravitational waver merger timescales become shorter than 10 billion years. However, this is very much a solved problem in the sense that their are lots of channels whereby this can happen. Common envelope evolution in isolated binary systems can bring binary components together (e.g., <a href="https://academic.oup.com/mnras/article/481/2/1908/5071961" rel="noreferrer">Kruckow et al. 2018</a>). Multiple dynamical interactions within star clusters (<a href="https://iopscience.iop.org/article/10.3847/2041-8213/abdfcd" rel="noreferrer">Sedda 20121</a>) or as part of ternary or other multiple systems can also do the trick (<a href="https://iopscience.iop.org/article/10.3847/1538-4357/ac4892/meta" rel="noreferrer">Vynethya &amp; Hamers 2022</a>).</p>

CC BY-SA 4.0
2024-03-30T10:22:17.137Z
Thanks Prof! Mind referencing some further materials for further reading? I’m particularly interested in these “channels” and “common evolution envelopes” you mentioned. Why are neutron stars and white dwarf mergers “very much a solved problem” when black hole mergers aren’t?
Shawn Lim
CC BY-SA 4.0
2024-03-30T10:34:12.953Z
@ShawnLim because supermassive black holes don;'t have stellar progenitors with envelopes. They also cannot be brought extremely close together by encounters with things that are a millionth or less of their mass.
ProfRob
CC BY-SA 4.0
2024-03-30T07:43:16.777Z
2024-03-30T10:42:24.050Z
2024-03-30T10:42:24.050Z
ProfRob
<p>The <a href="https://www.skyatnightmagazine.com/space-science/final-parsec-problem" rel="noreferrer">final parsec problem</a> describes the difficulty of two blackholes merging with one another when their distances reach ~3.2 light years apart. Does this also then apply to stellar collisions, perhaps with another distance threshold? If not, why?</p>
<p>Potentially related?: <a href="https://astronomy.stackexchange.com/questions/44256/what-is-the-difference-between-the-terms-collision-and-merger-how-are-they-used">What is the difference between the terms collision and merger? How are they used differently in Astronomy?</a></p>

CC BY-SA 4.0
2024-03-30T03:47:17.347Z
Stars typically don't merge via gravitational wave emission - they are not compact enough. Anyhow any semi-major axis distance can be shrunk sufficiently when using three-body interactions to get rid of the angular momentum of the binary.
AtmosphericPrisonEscape
CC BY-SA 4.0
2024-03-30T03:55:54.810Z
@AtmosphericPrisonEscape Binary White Dwarf and Neutron Star collisions have been known to happen due to gravitational wave emissions, albeit rare. I suppose the point to the question is if black holes inherently have a problem of not having enough material around them to get rid of their angular momentum in the last parsec, then why is this not the case for stellar collisions/mergers as well.
Shawn Lim
CC BY-SA 4.0
2024-03-30T07:57:41.027Z
related and informative: [Why can't supermassive black holes merge? (or can they?)](https://astronomy.stackexchange.com/q/32622/7982) and [How do we know that supermassive black holes can gain mass by means other than merging with other supermassive black holes?](https://astronomy.stackexchange.com/q/43821/7982) and especially  [How do two supermassive black holes reach "the last parsec" in merging galaxies?](https://astronomy.stackexchange.com/q/32634/7982)
uhoh
<galactic-dynamics><star-systems><collision><stellar-dynamics>
Does the Final-Parsec problem apply to stellar collisions?
Shawn Lim
# Does the Final-Parsec problem apply to stellar collisions?

(Asked by: username_0 on 2024-03-30)

The [final parsec problem](https://www.skyatnightmagazine.com/space-science/final-parsec-problem) describes the difficulty of two blackholes merging with one another when their distances reach ~3.2 light years apart. Does this also then apply to stellar collisions, perhaps with another distance threshold? If not, why?

Potentially related?: [What is the difference between the terms collision and merger? How are they used differently in Astronomy?](https://astronomy.stackexchange.com/questions/44256/what-is-the-difference-between-the-terms-collision-and-merger-how-are-they-used)

**Tags:** galactic-dynamics, star-systems, collision, stellar-dynamics
> **Comments:**
> **username_1**: Stars typically don't merge via gravitational wave emission - they are not compact enough. Anyhow any semi-major axis distance can be shrunk sufficiently when using three-body interactions to get rid of the angular momentum of the binary.  
> **username_0**: @AtmosphericPrisonEscape Binary White Dwarf and Neutron Star collisions have been known to happen due to gravitational wave emissions, albeit rare. I suppose the point to the question is if black holes inherently have a problem of not having enough material around them to get rid of their angular momentum in the last parsec, then why is this not the case for stellar collisions/mergers as well.  
> **username_2**: related and informative: [Why can't supermassive black holes merge? (or can they?)](https://astronomy.stackexchange.com/q/32622/7982) and [How do we know that supermassive black holes can gain mass by means other than merging with other supermassive black holes?](https://astronomy.stackexchange.com/q/43821/7982) and especially  [How do two supermassive black holes reach "the last parsec" in merging galaxies?](https://astronomy.stackexchange.com/q/32634/7982)  

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## 1 answers

### Answer by username_3 on 2024-03-30. Score: 7 | Accepted answer

The "final parsec problem" describes the difficulty in getting two supermassive black holes close enough together that their merger timescale due to gravitational wave emission becomes shorter than the age of the universe.

Normal stars do not merge due to gravitational wave emission - their masses are too low and their separations too large. The gravitational wave merger timescales would be much longer than the age of the universe even when their photospheres are in contact.

There is something akin to the final parsec problem for merging stellar black holes, neutron stars and white dwarfs. These are compact enough to have mergers driven by gravitational wave emission but they too must get together closer than about $10^{10}$ m (for black holes) or $10^9$ m (for neutron stars and white dwarfs) before the gravitational waver merger timescales become shorter than 10 billion years. However, this is very much a solved problem in the sense that their are lots of channels whereby this can happen. Common envelope evolution in isolated binary systems can bring binary components together (e.g., [Kruckow et al. 2018](https://academic.oup.com/mnras/article/481/2/1908/5071961)). Multiple dynamical interactions within star clusters ([Sedda 20121](https://iopscience.iop.org/article/10.3847/2041-8213/abdfcd)) or as part of ternary or other multiple systems can also do the trick ([Vynethya & Hamers 2022](https://iopscience.iop.org/article/10.3847/1538-4357/ac4892/meta)).

> **Comments:**
> **username_0**: Thanks Prof! Mind referencing some further materials for further reading? I’m particularly interested in these “channels” and “common evolution envelopes” you mentioned. Why are neutron stars and white dwarf mergers “very much a solved problem” when black hole mergers aren’t?  
> **username_3**: @ShawnLim because supermassive black holes don;'t have stellar progenitors with envelopes. They also cannot be brought extremely close together by encounters with things that are a millionth or less of their mass.  

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