# Why can't supermassive black holes merge? (or can they?)

Supermassive black holes are usually found at the center of galaxies, including our own, and during a galaxy merger they end up beginning a dance of death, spinning around each other in a near-endless waltz, until finally merging. However, researchers are currently unclear as to the time it takes for black holes to merge -- or indeed, if they merge at all.

"It's a major embarrassment for astronomy that we don't know if supermassive black holes merge," said Jenny Greene, a professor of astrophysical sciences at Princeton and co-author of the study. "For everyone in black hole physics, observationally this is a long-standing puzzle that we need to solve."

This puzzle is dubbed the "final-parsec problem." Some astronomers believes that once two supermassive black holes get close enough together, reducing their distance to 1 parsec (3.2 light years), they may dance for an eternity.

Question: If it turns out that supermassive black holes can't merge, or have a tough time doing so, what might the reasons be?

The main problem is angular momentum. In order for two gravitationally bound objects to merge (whether black holes, supermassive black holes, planets, stars, etc.), they must shed enough angular momentum for their orbital separation to become small enough. Average orbital separation (semi-major axis) is determined entirely from the angular momentum of the orbit (at least in classical mechanics; I don't know if that is true for relativistic situations such as merging black holes when they get close together). Removal of angular momentum requires interactions with other objects.

When two galaxies merge, their supermassive black holes both have angular momentum. Through a phenomenon known as "dynamical friction," gravitational interactions with other stars sap the black holes of much of their angular momentum, until they are brought within a few parsecs or so of each other. At this point, the black holes have flung out all of the stars that were in the region and there is (presumably) nothing left for dynamical friction to sap their angular momentum. Once the black holes are close enough (I don't know off the top of my head how close), emission of gravitational waves will sap the orbiting pair of their remaining angular momentum and a merger becomes inevitable.

So to answer your question, the reason for supermassive black holes to be unable to merge is that they are too close together for there to be any remaining material (stars, gas, etc.) in the center of the galaxy to remove angular momentum from the orbiting pair, having already removed the material themselves, but are not close enough for emission of gravitational waves to remove angular momentum fast enough for their merger to occur any time soon (in an astronomical sense).

• This is a great answer! I learned several different things from it, nice.
– uhoh
Jul 12 '19 at 13:34
• It's safe to use Newtonian approximations when the separation between the BHs is large. To get a rough idea of where relativistic effects become too large to ignore, use the Schwarzschild time dilation ratio $\sqrt{1-r_s/r}$, where $r_s$ is the Schwarzschild radius, and $r$ is the distance. Jul 12 '19 at 13:39
• To be a bit pedantic, there are two processes at work 1. Dynamical friction, which is the mean interaction of the individual BHs with the general population of stars (and dark matter) in their vicinity, and which is effective down to scales of a few hundred parsecs... Jul 12 '19 at 19:00
• ... and 2. Gravitational three-body interactions between the binary BH and individual stars, which is how you get stars "flung out" from the inner regions. This dominates for BH separations of less than a few hundred pc; if there aren't enough stars in the very center for the binary to interact with, it may not be able to shrink its orbit smaller than a parsec or so -- the "final parsec" problem. Jul 12 '19 at 19:03
• I feel like trying to merge them with a well-aimed chain of smaller black holes forming a bridge. Jul 13 '19 at 3:47