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This answer mentions that the supermassive black hole at the center of our galaxy is constantly moving.

Sagittarius A Star is 1000 times faster and smaller. Its like a toddler who is moving constantly. In comparison, M87 is much slower, like a big bear

What causes Sgr A* to move?

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    $\begingroup$ Could be related to the fact that, since it’s smaller, the mass of the whole galaxy around it makes it move, like in a similar way the sun moves just a little bit from the orbits of all the bodies around it, but I’m not 100% sure $\endgroup$
    – Justin T
    Commented Apr 18, 2022 at 15:10

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As far as I know, the issue is not that Sgr A* itself moves around so much, but rather it is the gas around Sgr A* (that the event horizon telescope tries to image) that moves around. The typically timescale for variations in the gas is set by the period of the innermost stable circular orbit (ISCO) around Sgr A*. This period is roughly proportion with the mass of the black hole. For Sgr A* this period is of order minutes. For M87*, it is order days.

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If a star of mass $m$ hits a black hole of mass $M$ at velocity $v$, conservation of momentum means that the black hole now moves at velocity $$\Delta v=\frac{mv}{m+M}=\frac{1}{1+\frac{M}{m}}v.$$ The bigger $M$ is compared to $m$, the less the change in velocity.

Sag A* is a fairly small black hole, so the random mergers have given it a bigger velocity than a heavier black hole like M87.

(This is not 100% as straightforward as the above argument: to make a mass $M$ black hole out of $N=M/m$ stars you have to add their random velocities, and a heavy black hole will have more added momentum than a small one. To properly calculate it one needs to add a sum of random velocity vectors rescaled by the mass accumulated to that date. However, $N$ random Gauss-distributed momentum vectors will produce a Gaussian vector with mean 0 and a variance $\sigma^2/N$: even if they all contributed equally the spread of black hole momentum around 0 would tend towards zero. Dividing by the growing mass gives an even slower velocity distribution.)

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  • $\begingroup$ As mmeent’s answer points out, the context of the original quote is clearly about the variability of emission from rapidly moving gas orbiting around the SMBH, not motion of the SMBH itself. $\endgroup$ Commented Apr 19, 2022 at 13:58
  • $\begingroup$ Also, SMBH growth is understood to be primarily from gas accretion via accretion disks, not from collisions with individual stars. $\endgroup$ Commented Apr 19, 2022 at 14:03

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