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Here a source says that astronomers looked for a black hole in the brightest galaxy in the cluster Abell 2261, A2261-BCG, but found nothing:

However, X-ray observations from NASA's Chandra X-ray Observatory and Hubble Space Telescope have found nothing.

How is it possible for this galaxy to not have a black hole in the center?

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The Brightest Cluster Galaxy (BCG) in Abell 2261 ("Abell 2261-BCG") is a massive elliptical; these almost always seem to have supermassive black holes in their centers. In addition, the center of the galaxy has a large region of relatively low stellar density (a "core"), something usually thought to be produced by the merger of two SMBHs into one, an event which follows the merger of two massive galaxies to form one massive elliptical. (As part of the merger, the two SMBHs form a binary; stars near the center of the merged galaxy can gravitationally interact with this binary, with the usual result being a shrinking of the binary and the ejection of the star to a larger radius; thus, stars get preferentially kicked out of the center into the intermediate or outer parts of the galaxy, and the density of stars in the center gets lower. Eventually, the SMBH binary becomes so small that gravitational radiation shrinks it even further, to the point that the two SMBHs merge to become one in the center of the galaxy.)

The actual paper (Gültekin et al.) behind that article is about looking for X-ray emission from an accretion disk around the possible SMBH in the center of the BCG (and also in a few other locations near the center). Since they don't detect any X-rays, they conclude "there is either no $10^{10} M_{\odot}$ black hole in the core of A2261-BCG, or it is accreting at a low level." So there are really two possibilities:

  1. There is a SMBH in the galaxy center, but it's quiescent (not accreting enough gas to produce a lot of X-rays).

  2. There isn't a SMBH in the galaxy center, which is more exciting because it's unexpected.

Now, there actually is a theoretical mechanism which might occasionally eject a SMBH from the center of a galaxy. When two SMBHs merge to form one SMBH (see above), there can be a "kick" which causes the merged SMBH to be ejected from the galaxy center (the magnitude of this kick depends on things like the mass ratio between the two SMBHs, how fast the individual SMBHs were spinning before the merged, and what the directionw of those spins were relative to the orbit of the binary before the merger). In most cases, the ejected SMBH will fall back into the center of the galaxy -- possibly oscillating in and out a few times before dynamical friction slows its motion down and it settles back in the center of the galaxy. In extreme cases, it might be ejected fast enough so that it escapes the galaxy entirely. This whole process will eject a number of stars from the center of the galaxy, too, which might help explain why its low-density core is so big (i.e., a combination of the SMBH-binary-merger process and a resulting SMBH ejection).

So it's possible something like this happened in Abell 2261-BCG, and the SMBH is currently somewhere outside the galaxy center. (Or it's sitting the center and just doesn't show up in X-rays.) Of course, they didn't find any evidence for an X-ray-emitting SMBH outside the galaxy nucleus, either, so we really don't know -- and I wouldn't be surprised if there is a (quiescent) SMBH in the center after all.

(Rory Alsop is correct that not all galaxies have SMBHs -- for example, the local small spiral galaxy Messier 33 has been studied with the Hubble Space Telescope (Gebhardt et al. 2001, and the modeling of stellar velocities in its center suggests an upper limit of about 1500 $M_{\odot}$ for any possible black hole there. But every massive elliptical that's been studied carefully enough seems to have one, so we would expect Abell 2261-BCG to have one, too.)

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Physics doesn't require a black hole at the centre of a galaxy, it just indicates that it is likely.

All you need is mass. If the mass is not dense enough to form a black hole, it can still be high enough for a galaxy to grow.

(Also, finding nothing is not the same as nothing being there. So nobody is ruling out the existence of a black hole there)

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