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Also is the total mass of a galaxy and the number of stars it has closely connected to the mass of the supermassive black hole at its heart?
Actually, there is a connection, although it is a little more subtle. It is the M-sigma relation
, which is a relation between the mass (M) of a galaxy's central supermassive black hole (SMBH) and the velocity dispersion (sigma) of the stars in its bulge. Velocity dispersion means how much variation or spread there is in the orbital velocities of the stars, about the mean value. (Think "standard deviation" in statistics). For a system of orbiting particles, the velocity dispersion acts as a measure of the total mass of the system.What the M-sigma relation shows us is that the mass of the SMBH is closely related to the velocity dispersion of stars in the galaxy's bulge. It goes approximately as the velocity dispersion to the 4th to 5th power (depending on the type of galaxy and whether it is active or quiescent).
The relation also holds between the mass of the SMBH and the galaxy's luminosity.
As most relations go, there can be exceptions, like the Ultra Compact Dwarf galaxies Stellarator mentioned. This is because those galaxies have apparently been stripped of most of their stars so that only the core region remains. Aside from those exceptions though, the relation is very robust and is commonly used. Because the relation is so tight, by measuring the velocity dispersion of a galaxy's bulge we can get an accurate measure of the mass of its central black hole. This method even helped resolve discrepancies between other earlier methods of estimating SMBH masses.
The M-sigma relation is also surprising when you think about it. It implies a close connection between black hole growth and the evolution of the host galaxy. But why, when the SMBH is so much smaller by both size and mass than the rest of the galaxy it resides in?
The understanding, which only came about in the last couple decades (and which I am also grossly oversimplifying here), is that the black hole extends its influence not just by gravity, but also by its jets. When the black hole is active and accreting at a higher rate, its jets and outbursts are more effective at blowing away the surrounding intergalactic medium, preventing material from falling in to feed the galaxy. This is called AGN feedback, and represents a way in which the tiny powerhouse at the galactic center is capable of driving large scale dynamics in the galaxy's environment. Black holes are even more remarkably powerful than just their gravitational fields would suggest.
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Do you think that galaxies further away from us would be more massive? Would the earliest galaxies formed probably contain the most mass?
In this case there isn't so strong of a relation, but overall galaxy clusters and especially the giant elliptical galaxies within them do grow more massive with time. This is simply because more material is constantly falling into them: gas and dark matter from the surrounding intergalactic medium, and also other galaxies in the cluster randomly colliding and merging together. As we saw with the earlier image of Laniakea, very large regions of the universe "break off" from the expansion and the material collapses together, especially along those sheets and filaments connecting nearby regions of the cosmic web.