What is the ultimate fate of a cluster of galaxies?

Question

We're fairly aware clusters of galaxies drift apart due to space expansion, which will drive them out of each other's cosmic event horizon eventually, leaving them separate, alone, each a single "body" within its local observable universe with no means to communicate or influence other clusters.

The clusters themselves are held together by gravitational binding that keeps them from being internally torn apart by space expansion, at least assuming density of dark energy doesn't increase drastically eventually.

What will happen to the cluster though? At first I assumed its black holes will swallow all its available matter, and connect into one single, lonely black hole. But then, neither are black holes ultimately eternal, due to Hawking Radiation, nor do they swallow all the stars, supposedly most stars escaping their gravity well.

Well then, what current theories say a local cluster of galaxies will transform into as t→∞ ?

Answer 1

As you point out, in an accelerating Universe, large scale structures will become more and more isolated. So at a certain point you will have gravitationally bound superclusters separated by very large voids and less and less filamentary structures.

Once isolated, we can then study the dynamics of these independent superclusters. On very large time scales, galaxies will collide and merge. After collisions you will tend to form elliptical galaxies. So I think that you will end up with a big single elliptical galaxy.

Then we can be interested in the future of the stars of these galaxies. First we currently see that the star formation rate has already peaked some billion years ago. So as the number of galaxies collision that usually targets star formation, the star formation rate will slowly continue to decrease. Moreover, as heavy elements (all elements apart from hydrogen and helium) are formed in stars, the future generation of stars will have more and more heavy elements. From the nuclear point of view, the most stable element is iron, so on very very large time scales light elements will be converted into iron, whereas heavy elements will decay into iron.

This is a little speculative, but I think that on large time scales, more and more interstellar gas and stars will fall at the center of the gravitational potential of super elliptical galaxy. So as the density will increase at the center, you will mechanically form a heavier and heavier supermassive black hole. Another interesting point is that we do not currently know whether proton are stable or not. So on time scales larger than $10^{30}$ years (see more details here) protons may naturally decay into lighter subatomic particles.

So maybe as $t\rightarrow\infty$ we will end up with supermassive black holes and light particles. But as you mentioned, black holes will themselves slowly lose mass by Hawking radiation. In the same time, the expansion rate may have increased significantly leading ultimately to isolated particles in an expanding Universe.

Note: this is an hypothetical scenario and there are a lot of unknowns

Answer 2

This depends where the cluster is. Large scale features of the universe (both observed and simulated) consist of filaments and voids. Below is a map produced by the Sloan Digital Sky Survey (SDSS) showing these features.

Each dot here is an individual galaxy.

Simulations show remarkably the same thing. Here is a video of the Millennium Simulation. It zooms into smaller and smaller structures, and just at about the smallest scale it zooms to (~4Mpc) is about the size of an individual cluster. It turns out that collections of clusters which form at the intersections of filaments, super clusters, are even more massive, yet are still forming today. If the cluster belongs to these highly overdense regions, it will merge with other clusters to eventually form super clusters. If they live at the boundaries of these regions it is not guaranteed that they will fall into more massive regions. I know this answer is a bit lacking in detail, but structure formation theory is complicating stuff. Hopefully this gives you some idea of where clusters live and what could potentially happen to them as $t \rightarrow \infty$.

Answer 3

The galaxies could either be pulled away or collide with each other. This comes from the two possible theories: The Big Crunch and The Big freeze. But its true if we only consider the two galaxies of interest.

Voids and Black Holes should not ignored as there presence should escalate or demolish any of the existing forces. These two are equally responsible for the fate of galaxies.

EDIT: The Big Crunch and The Big Freeze are two theoretical possibilities that pose a future to our universe. Each of the theories conclude the end, where the universe either starts shrinking as it had once expanded and thus ends in a singularity as it once started, or the universe keeps expanding relentlessly making it colder and colder. Voids and Black Holes should not directly relate to the above fates, but will be the eventual result of them.