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Since we see the Triangulum galaxy M33 from a quite vertical position (contrary to our Milky Way and a bit the Andromeda galaxy) it should be easy to image the black hole in the center of it, shouldn't it? Why did they prefer to first image the black hole in a galaxy which is about 20 times farther and thus harder to photograph the black hole in its center?

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M33 does not appear to contain a supermassive black hole: in fact there's no evidence that it contains a central black hole at all. The upper limit on the mass of a central black hole based on the dynamics of the core region is a few thousand solar masses.

Merritt et al. (2001) "No Supermassive Black Hole in M33?" derive an upper limit of 3000 solar masses on a central compact object in M33, noting that this is still consistent with the M-σ relationship between the mass of a supermassive black hole and the velocity dispersion in the stellar bulge, using which they obtain a predicted mass of 2600–26300 solar masses.

Gebhardt et al. (2001) "M33: A Galaxy with No Supermassive Black Hole" obtain an even smaller upper limit on the mass of a black hole of only 1500 solar masses (their best fit mass is zero, i.e. no central black hole), which they state is significantly lower than the predicted mass from the M-σ relationship.

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    $\begingroup$ @user30007 Most stars in a galaxy don't actually orbit around the central black hole of a galaxy. Despite it's enormous mass, it's only a tiny fraction of the mass of the galaxy. The orbit is more within the entire galaxy's mass, so a central black hole is probably not necessary for orbits. Interestingly, for M33, the stars near the center seem to orbit or rotate around the galaxy more slowly, the opposite of what's expected. science.sciencemag.org/content/293/5532/1116 $\endgroup$ – userLTK Feb 5 at 12:06
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    $\begingroup$ So stars can simply orbit a barycenter which is the very center of the galaxy? $\endgroup$ – user30007 Feb 5 at 12:47
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    $\begingroup$ The papers on the imaged BH explicitly say why other targets were impossible or anyway discarded. $\endgroup$ – Alchimista Feb 5 at 13:25
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    $\begingroup$ @user30007 : Stars (bound to a galaxy, separated widely from other galaxies) only orbit the barycenter of their galaxy. $\endgroup$ – Eric Towers Feb 5 at 19:24
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    $\begingroup$ @user30007 same is true with the sun and the earth, the sun is also slightly wobbling and both are orbiting around a point that is not the center of the sun (also affected by other planets). All following Newton’s law of universal gravitation. $\endgroup$ – Mehdi Feb 6 at 13:15
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M87 was actually the easiest black hole for the Event Horizon Telescope (EHT) to attempt, and was thus sensibly its first target. For the EHT to work you need 1) an active BH accreting matter such that it is a strong radio source, and 2) that it be close and massive enough to be angularly large. While M87 is some 20x further away than, say M31 or M33, it is also extremely massive, thus offering a large resolvable horizon. The only BH larger in angular size is the BH in our own Milky Way galaxy, which while weighing only 1/1500 as much at M87 is far closer by about 2000x, giving a larger target. The small mass of the MW BH, however, means that it has a very short time scale for varying its rate of mass accretion, so that its appearance changes while the EHT is observing it. This is a tricky technical issue that the EHT did not have to address for M87.

WRT other BHs, as a previous respondent did an excellent job of answering, M33 shows no evidence for harboring a central BH. M31, in contrast, does have an ~800M solar mass BH, but it's 1) just a little below EHT's resolving power, and 2) provides very little radio emission.

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