# Final Parsec Problem

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Posted (edited)

I was doing some reading due to a recent thread on Dark Matter, and came across a 'problem' that Dark Matter may provide an answer to.
As I had never heard of this problem, I thought I should investigate, and I'm only just beginning.
Hopefully some of you guys have some insights.

Apparently super massive Black Holes  of the galactic center type have a merging problem.
As they approach each other, an effect termed 'dynamic gravitational drag', stops their orbits from further decay, and establishes a stable orbit at about 3 Light Years ( one parsec ). Apparently this is dictated by the math, which I haven't seen yet, and probably won't understand when I do.
This makes SMBH mergers impossible; although we know they happen, but maybe Dark Matter has a modifying influence on this D G drag, and the 'modified' math will then allow for mergers.

Has anyone else looked into this, or have a clearer understanding of the math and situation ?

Edited by MigL
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From what I've read on such noted reluctance to mergers of large masses, it seems that the energy/angular-momentum decay needed to merge is mostly dissipated by gravitational drag, the flinging of nearby matter away at high speeds, as is typical of 3 body dynamics when one of the bodies masses much less than the other two.

Eventually, the local area is cleaned out and there's nothing left to fling, leaving a fairly stable 2 body orbit, decaying at least by gravitational waves, but that is trivial at that distance.

Dark matter is just more [small] mass, just like regular matter. If it gets close it gets flung away and is cleared out like anything else. I don't see how dark matter is therefore any sort of solution to the effect.

I don't know if 1 parsec is typical, or can be derived from any math. It would seem to be a function of the masses of the respective black holes and of the density of other matter near them.  Clearly black holes do merge since our own galaxy is a collection of dozens of smaller galaxies, many of which contributed their own SMBH.  We have but the one, so they've merged at some point. Some of then recent swallowed galaxies may have central masses that are en-route to the center, but none orbits particularly nearby at this time.  Sgr-A has plenty of stars orbiting within that 1 parsec radius, so there is available mass to be ejected during any upcoming merger.  Notably, in perhaps   10-20 billion years, Sgr-A will be merging with something 10 times its own mass. I wonder how far away you need to be from that for it not to be dangerous.

Edited by Halc
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Sounds very similar to numerous back reaction examinations without a direct reference its difficult to know for sure but sound familiar. However I can't recall the articles I may have come across it.

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I very recently watched a documentary in which this was mentioned. I was not aware of it prior to this. However, it seems to me that the notion of something preventing supermassive black holes from merging is not consistent with general relativity. According to general relativity, if one has a system containing an arbitrary arrangement of black holes, an increase of the masses of all the black holes by a constant factor, as well as an increase of all the distances and times by the same factor will result in the system's behaviour being unchanged. For example, if one has two black holes of mass equal to ten million solar masses in mutual circular orbit ten million astronomical units apart, then the amount of time required for the orbit to decay by emission of gravitational radiation to five million astronomical units apart will be one million times as long as two black holes of ten solar masses in mutual circular orbit ten astronomical units apart decaying by emission of gravitational radiation to five astronomical units apart.

Yes, the supermassive black holes will take a lot longer to merge, but there isn't anything other than time itself preventing the merge.

However, the above does assume a background spacetime that is flat. In a de Sitter or anti-de Sitter background spacetime, the scaling of the cosmological constant is different and will lead to larger black holes behaving differently to smaller black holes.

Edited by KJW

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