<p>The peak power (or luminosity) is roughly proportional to <span class="math-container">$\nu^2$</span>, where
<span class="math-container">$$\nu = \frac{m_1 m_2}{(m_1+m_2)^2}$$</span>
is the symmetric mass-ratio (This follows from the fact that the luminosity in general is proportional to <span class="math-container">$\nu^2$</span>.). So, yes, the maximal peak power is reach for equal mass-mergers.</p>
<p>In general, the peak power will depend on the spins (and their orientation), eccentricity, (and if you wish to consider it charges) of the merging binaries. However, there is no way to establish these dependencies analytically. Instead we have to rely on numerical relativity simulations. For example, <a href="https://arxiv.org/abs/1612.09566" rel="nofollow noreferrer">this paper</a>, studies the relation between mass-ratio, spin, and peak luminosity for spin aligned binaries. They find that the maximal peak luminosity seems to be attained in the equal mass case with both spins maximal and aligned, reaching roughly 0.002 in natural units (about a factor two higher than the non-spinning case). The intuitive explanation for this is that aligned spins allow the inspiral phase to continue to much smaller separations, leading to a higher peak luminosity. Following this intuition any misalignment of the spins should result in a lower peak luminosity. A similar intuition applies to the charges case. Adding similar charges to the black holes delays the merger and should increase the peak luminosity. I'm not aware of any systematic NR campaigns that looked specifically at this, though.</p>
<p>People have only fairly recently started exploring the parameter space of eccentric mergers with NR simulations with no (published) reports on the peak luminosity. However, the dependence of the peak luminosity on eccentricity is likely to be fairly weak, because most inspirals will shed most of their eccentricity before merger. Intuitively, one should expect a slight increase in the peak luminosity though.</p>

CC BY-SA 4.0
2021-08-31T11:34:04.667Z
It looks like spin could enhance the luminosity by about a factor of two.
ProfRob
CC BY-SA 4.0
2021-08-31T11:56:32.277Z
@ProfRob, at equal mass, yes. In the small mass-ratio regime by more.
TimRias
CC BY-SA 4.0
2021-08-31T13:07:25.437Z
But a small mass ratio has less power than an equal mass ratio. What combination gives the global maximum and how does that compare with the vanilla scenario?
ProfRob
CC BY-SA 4.0
2021-08-31T13:10:12.937Z
@mmeent: Thanks for all this information!  I appreciate all the effort you've put into this.  I will accept your answer after a waiting a day or two to see if there will be more input from others.
James
CC BY-SA 4.0
2021-08-31T10:23:46.150Z
2021-08-31T12:35:07.317Z
2021-08-31T12:35:07.317Z
TimRias
<p>The peak power output of the <a href="https://en.wikipedia.org/wiki/Binary_black_hole" rel="noreferrer">GW150914</a> black hole merger was 3.6e49 Watts.  These black holes were around 30 solar masses each and about 3 solar masses were converted to gravitational waves during the final 20 ms.</p>
<p><a href="https://physics.stackexchange.com/questions/438952/is-it-true-that-all-symmetric-binary-black-hole-mergings-emit-the-same-power-re">This question</a> on the physics site contains a claim from LIGO that two black holes of equal mass will have approximately the same peak power output.  This seems believable to me, because both the energy output AND the inspiral time will both increase as the black hole masses increase.</p>
<p>What I would like to know is... <strong>Is the peak power achieved when the two black holes are equal in size?  Or, will the peak power be higher when one of the black holes is larger than the other?</strong></p>
<p><strong>Also, would the peak power output depend on the shape of the orbit, the black hole spin, or the black hole magnetic charge?</strong></p>
<p><strong>Has the maximum possible peak power been calculated, or is there even a limit on the peak power?</strong></p>

<black-hole><merger>
What is the maximum possible peak power during a black hole merger?
James
# What is the maximum possible peak power during a black hole merger?

(Asked by: username_0 on 2021-08-30)

The peak power output of the [GW150914](https://en.wikipedia.org/wiki/Binary_black_hole) black hole merger was 3.6e49 Watts. These black holes were around 30 solar masses each and about 3 solar masses were converted to gravitational waves during the final 20 ms.

[This question](https://physics.stackexchange.com/questions/438952/is-it-true-that-all-symmetric-binary-black-hole-mergings-emit-the-same-power-re) on the physics site contains a claim from LIGO that two black holes of equal mass will have approximately the same peak power output. This seems believable to me, because both the energy output AND the inspiral time will both increase as the black hole masses increase.

What I would like to know is... **Is the peak power achieved when the two black holes are equal in size? Or, will the peak power be higher when one of the black holes is larger than the other?**

**Also, would the peak power output depend on the shape of the orbit, the black hole spin, or the black hole magnetic charge?**

**Has the maximum possible peak power been calculated, or is there even a limit on the peak power?**

**Tags:** black-hole, merger

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## 1 answers

### Answer by username_1 on 2021-08-31. Score: 8 | Accepted answer

The peak power (or luminosity) is roughly proportional to $\nu^2$, where
$$\nu = \frac{m\_1 m\_2}{(m\_1+m\_2)^2}$$
is the symmetric mass-ratio (This follows from the fact that the luminosity in general is proportional to $\nu^2$.). So, yes, the maximal peak power is reach for equal mass-mergers.

In general, the peak power will depend on the spins (and their orientation), eccentricity, (and if you wish to consider it charges) of the merging binaries. However, there is no way to establish these dependencies analytically. Instead we have to rely on numerical relativity simulations. For example, [this paper](https://arxiv.org/abs/1612.09566), studies the relation between mass-ratio, spin, and peak luminosity for spin aligned binaries. They find that the maximal peak luminosity seems to be attained in the equal mass case with both spins maximal and aligned, reaching roughly 0.002 in natural units (about a factor two higher than the non-spinning case). The intuitive explanation for this is that aligned spins allow the inspiral phase to continue to much smaller separations, leading to a higher peak luminosity. Following this intuition any misalignment of the spins should result in a lower peak luminosity. A similar intuition applies to the charges case. Adding similar charges to the black holes delays the merger and should increase the peak luminosity. I'm not aware of any systematic NR campaigns that looked specifically at this, though.

People have only fairly recently started exploring the parameter space of eccentric mergers with NR simulations with no (published) reports on the peak luminosity. However, the dependence of the peak luminosity on eccentricity is likely to be fairly weak, because most inspirals will shed most of their eccentricity before merger. Intuitively, one should expect a slight increase in the peak luminosity though.

> **Comments:**
> **username_2**: It looks like spin could enhance the luminosity by about a factor of two.  
> **username_1**: @ProfRob, at equal mass, yes. In the small mass-ratio regime by more.  
> **username_2**: But a small mass ratio has less power than an equal mass ratio. What combination gives the global maximum and how does that compare with the vanilla scenario?  
> **username_0**: @mmeent: Thanks for all this information!  I appreciate all the effort you've put into this.  I will accept your answer after a waiting a day or two to see if there will be more input from others.  

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