# Black holes: merged remnants have similar spin - why?

• A
• Vrbic
In summary: No, the limit is the angular momentum to mass ratio, which is effectively what ##a## is. It cannot exceed 1 in geometrised units.
Vrbic
Hello everyone,

I hope I'm asking in the correct section, if not please point me.

I read a list of gravitational wave detection. I focused on black hole - black hole events and I noticed the resulting black hole spin is very similar about a=0.7. I didn't find any explanation for this.

List of events you find here.

My two ideas are:
1) The first idea was the orbital frequency before merge gives the resulting spin and there is some intrinsic physics reason why this orbital frequency (in the final stage of merge) is very same for all masses of black holes.

2) The second idea is connected to the sensitivity of our instruments. We see a resulting spin of about a=0.7 because we are able to detect only sources with such properties (frequency of gravitational waves).

Is one of these ideas correct or I'm out? :-)

vanhees71, PeroK and Drakkith
You need to give a reference. I don't know what "a=0.7" means, and I suspect you are using spin in a non-standard way.

Hornbein said:
You need to give a reference. I don't know what "a=0.7" means, and I suspect you are using spin in a non-standard way.
Reference is in the list of events here. There is also defined a dimensionless black hole spin parameter as a=cj/(GM^2), where c and G are the speed of light and gravitational constant, j is angular momentum and M is the mass of the object. This "a" is mostly connected with a spin of Kerr's black hole.

vanhees71
Vrbic said:
Reference is in the list of events here. There is also defined a dimensionless black hole spin parameter as a=cj/(GM^2), where c and G are the speed of light and gravitational constant, j is angular momentum and M is the mass of the object. This "a" is mostly connected with a spin of Kerr's black hole.
Aha you did give a reference, sorry I missed that. Yes that is interesting, that the spin of the remnants is always about the same.

According to this the absolute maximum value of a is 1, and it is not unusual for supermassive black holes to reach this limit. No smbh had less than 0.6.
https://astronomy.stackexchange.com/questions/20276/maximum-spin-rate-of-a-black-hole

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Hornbein said:
I have a vague memory that there is some similar limit on the spin of black holes. Any faster and the singularity would be exposed. At any rate surely there is a limit of some nature. There is so much energy in a black hole collision I would expect that this limit is usually reached.
Thank you for your comments. The limit of a (standard - Kerr's) rotating black hole is "a=1", if greater, there is no horizon and we call it naked singularity as you mentioned. Actually, the guesses on the rotation of supermassive black holes in many active galactic nuclei are about "a=0.99". So, it was surprising for me very narrow window of final spin after the merge of two black holes.

Vrbic said:
Thank you for your comments. The limit of a (standard - Kerr's) rotating black hole is "a=1", if greater, there is no horizon and we call it naked singularity as you mentioned. Actually, the guesses on the rotation of supermassive black holes in many active galactic nuclei are about "a=0.99". So, it was surprising for me very narrow window of final spin after the merge of two black holes.
Yes the smaller merged holes don't reach the limit. It is a puzzle.

Hornbein said:
I have a vague memory that there is some similar limit on the spin of black holes. Any faster and the singularity would be exposed. At any rate surely there is a limit of some nature. There is so much energy in a black hole collision I would expect that this limit is usually reached.
No, the limit is the angular momentum to mass ratio, which is effectively what ##a## is. It cannot exceed 1 in geometrised units.

@Vrbic, I suspect there's a bias in the remnants' ##a## values. I found the paper below which implies that the expectation is that binary stats becoming binary black holes then merging will have very low ##a##, while binaries formed by capture after becoming black holes can have almost any ##a##.
https://iopscience.iop.org/article/10.3847/2041-8213/ac2f3c

I don't know about SMBHs, but if they mostly grow by absorbing matter from their parent galaxy then pretty much every merger would seem likely to push up ##a##.

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vanhees71
Ibix said:
@Vrbic, I suspect there's a bias in the remnants' ##a## values. I found the paper below which implies that the expectation is that binary stats becoming binary black holes then merging will have very low ##a##, while binaries formed by capture after becoming black holes can have almost any ##a##.
https://iopscience.iop.org/article/10.3847/2041-8213/ac2f3c
Nice, thank you for the interesting reference.
Ibix said:
I don't know about SMBHs, but if they mostly grow by absorbing matter from their parent galaxy then pretty much every merger would seem likely to pish up ##a##.
Or these guesses are wrong. I suppose it is very difficult to do such a guess.

Vrbic said:
Or these guesses are wrong. I suppose it is very difficult to do such a guess.
You can actually look at the dynamics of stars in close orbits around SMBHs, which is one way to estimate their parameters. I don't know how precisely that's been done, though. There's less opportunity to probe smaller black holes that way.

Ibix said:
You can actually look at the dynamics of stars in close orbits around SMBHs, which is one way to estimate their parameters. I don't know how precisely that's been done, though. There's less opportunity to probe smaller black holes that way.
I understand, but I'm not sure if it is possible to do this for very distant sources. It is done for the central black hole in our galaxy (Sgr A*) but I'm not sure how it is for other galaxy centers. I think the guesses I mentioned are based on the position of accretion discs (ISCO position) or the energy of these particles.

Ibix

## 1. What is the significance of black holes merging and having similar spin?

When two black holes merge, they form a larger black hole with a combined spin that is determined by the individual spins of the two smaller black holes. This is significant because it provides insight into the formation and evolution of black holes, as well as the properties of space and time around them.

## 2. How do scientists determine the spin of black holes?

Scientists use a variety of techniques to measure the spin of black holes, including observing the motion of matter around the black hole, analyzing the gravitational waves emitted during a merger, and studying the X-ray emissions from the accretion disk around the black hole.

## 3. What factors can influence the spin of a black hole?

The spin of a black hole can be influenced by a number of factors, including the mass and angular momentum of the matter that formed it, the rate of accretion, and the gravitational interactions with other objects in its vicinity.

## 4. Why is it important to study the spins of black holes?

Studying the spins of black holes can provide valuable information about the nature of gravity, the behavior of matter in extreme environments, and the structure of spacetime. It can also help us better understand the role of black holes in the formation and evolution of galaxies.

## 5. Can the spin of a black hole change over time?

Yes, the spin of a black hole can change over time due to various factors such as accretion, mergers with other black holes, and gravitational interactions. However, the change is typically very slow and can take millions or even billions of years to be noticeable.

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