Of all the galaxies in our surveys of the sky, the biggest, most massive systems are always giant elliptical galaxies. These galaxies are thought to be the end product of repeated galactic collisions, and so the end result is an object, which, though full of stars, no longer resembles the galaxy it was, very early in the lifetime of the Universe.
After so many collisions, the stars within these galaxies no longer orbit in an orderly fashion, like those in our own Milky Way, but are more or less moving randomly with respect to each other. Each star follows its own particular elliptical orbit within the gravitational pull of the galaxy, but with no particular regard for what the other stars are doing around it. As a result, the galaxy has no particular directionality to it. If you could hold it in your hands, you could turn it over and around without finding any particular features to give it an orientation.
The very largest of these ellipticals are found in areas of the Universe where many galaxies gather together; with lots of galaxies in the area, there’s more chance for the galaxy to grow into the size it is by devouring its neighbors. The biggest of all are found lurking at the center of galaxy clusters, which are huge associations of thousands of galaxies. The galaxies within the cluster go whirling around the center of mass of those thousands of galaxies, and like the stars within an elliptical, they do this with no particular order.
There’s a little bit of order; the most massive galaxies sink to the center. And so this is where we find the most massive galaxies in our observable Universe. The current heavyweight sits at the center of the cluster Abell 3827 (shown at the top of the page), and has the entirely unpronounceable name of ESO 146-IG 005. It’s in the process of consuming a number of other galaxies, rapidly growing its own mass in the process. This galaxy is currently measured to be 27 trillion times the mass of our sun, which puts it more then ten times the mass of the Milky Way - it is definitely a giant.
The least massive galaxy, on the other hand, is much harder to find, because it's not very bright. By definition, small galaxies have very few stars, so finding that faint light is an observational challenge. These faintest galaxies are extra hard to find because we’re limited to those which are nearby. A faint galaxy too distant from us will be doubly faint, and impossible to spot.
The other problem with defining the least massive galaxy is that the definition of a galaxy gets a little messy at the low mass end. However, if we use the definition that a galaxy has to have some amount of dark matter surrounding it, the current least massive galaxy seems to be Segue 2. Segue 2 is about 1000 stars, held together by dark matter, orbiting our Milky Way, and is only about 800 times brighter than our Sun!
It's worth noting that both of these objects are likely to be holding temporary titles. As observational methods improve, we may find a galaxy was more massive than we had thought, or find dark matter surrounding stars that we had thought had none. In any case, these two objects are the far ends of the galaxy population - from a thousand stars, loosely held together, in the thrall of the Milky Way’s gravitational pull, to something ten times more massive than our entire Milky Way, itself doing the devouring of other galaxies.
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