For those that remain in the cluster, the black holes would be much more massive than the rest of the stars in the cluster. Globular clusters undergo a phenomenon called mass segregation, where the most massive stars settle to the center of the cluster and lighter stars occupy the outer regions. So over time the black holes would sink to the center of the cluster where they would interact and form binaries with each other. These binary-binary interactions would, over time, kick single black holes out of the cluster. Since these interactions happen on timescales that are much shorter than the lifetime of the cluster, the received wisdom about twenty years ago was that globular clusters should have only a couple of black holes left, if any at all.
In 2007, Thomas Maccarone (who is an author on this paper) discovered a black hole in a globular cluster in another galaxy. It wasn't until 2012 that any were discovered in a globular cluster around the Milky Way. Now that computers have gotten fast enough that it has started to become possible to simulate the dynamics of globular clusters, theorists have found that globular clusters retain a much higher fraction of black holes than they originally thought. The reason for this seems to be that the distribution in black hole masses leads the black hole population to remain better mixed with ordinary stars than was originally thought.
Intuitively, this seems simple, since "heavier objects" should sink further down, no?
But thinking about this for a while, it doesn't seem so simple anymore. No matter what's the mass of the star, if it's already on a given orbit around the cluster, it will tend to stay on that orbit, unless there are close interactions with other stars of comparable mass.
So what would be an intuitive explanation for this phenomenon?
A consequence of this is that stars exchange energy with each other frequently, and when you have frequent energy exchanges, you end up with a system that is in energy equipartition --- i.e., every star has about the same amount of energy as every other. Since more massive stars have the same energy as lighter stars, they must move slower, and consequently sink to the center of the cluster. Ultimately energy equipartition is the same reason that there is gravitational settling in a gas or a liquid on Earth.
Could you support this claim with some explanation? This can be proven for the Maxwell-Boltzmann distribution of velocities, which is valid for gas in thermodynamic equilibrium, but probably not so valid for stars as these interact via long range forces, not through collisions like molecules do.
Also, the stars that move too fast will escape the system so the equipartition cannot be sustained for stars whose mass is lower than some value corresponding to average quadratic speed being equal to escape speed.
How could one possibly conclude that system is ergodic from observation? I thought ergodicity is a property of infinite time averages. Globular clusters do not exist indefinitely in the same macrostate, they lose stars as they evolve.
So for everything that matters: If statistical mechanics works you can conclude that the system is ergodic. And if you observe long-time correlations it’s not.
I'm guessing it should be close enough due to the inverse square root law. Just the shape of hyperbolic trajectories should provide a clue.
> the stars that move too fast will escape the system so the equipartition cannot be sustained
Again, I think this one of those "close enough" things.
Reality tends to dislike either-black-or-white approaches.
I am not sure how the shape of hyperbolic trajectories is of relevance for equipartition, since most of the stars in the cluster do not have such trajectories else it would disintegrate before it could achieve any sort of dynamical equilibrium.
Trenti M., Marel R.: No Energy Equipartition in Globular Clusters
(however I have no idea how/why the mass segregation happens in this instance)
1. Natal kicks. The process of forming a black hole is fairly violent, and could involve a supernova in many cases. If the supernova is asymmetric, this will result in a kick on the black hole. Even if there is no supernova, an asymmetric infall process could produce an asymmetric burst of gravitational waves. Since gravitational waves carry momentum, this will also result in a kick on the new black hole. But it's generally thought that black hole natal kicks are weaker than neutron star natal kicks. The received wisdom seems to be that natal kicks will remove some black holes from a globular cluster, but probably not most.
2. Few-body interactions. A general principle of dynamical interactions (called Heggie's Law) is that if a single star interacts with a binary system, it is likely that the binary will become tighter if its orbital velocity is greater than the velocity of the incoming star, and wider if its orbital velocity is less than the velocity of the incoming star. The BH-BH binaries that would form in the cores of globular clusters would be relatively tight, so almost all interactions they have with other black holes will result in them getting tighter and giving more kinetic energy to the interloping black hole. (Or there may be an exchange and the interloping black hole will take the place of one of the black holes in the binary and kick out one of the original black holes.)
Back when I was in grad school I made a visualization of a binary-binary interaction, which you can watch here: https://www.youtube.com/watch?v=Y3nPOQXl6co
Intelligences could be expected to slowly accrete the mass of their parent star, rather than lifting or collapsing that mass and then inefficiently recreating fusion within the black hole (if the laws of physics even allow the latter, which they may not). In other words, you might absorb your star in a passive and gravitationally-driven process that would look a lot like a low mass X-ray binary (LMXRB) system to external observers, but in which the black hole companion begins as a planet mass black hole on the order of 1000 times less massive than the star companion, which should be a main-sequence star, likely with a spectral class G, like our Sun.
Approximately 100 LMXRBs have been discovered in our galaxy to date, and about 13 of these have been found in the globular clusters, areas at the rim of our galaxy that may not harbor intelligence. They have also been found in many distant galaxies, again often in globular clusters. Few have involved G class stars, and none have yet been discovered with the very high, 1,000:1 mass ratio the hypothesis appears to predict. This may simply be a problem of detection. XRBs emit X-rays only when they are "eating" their companion sun, a transient phenomenon. Chandra, our best X-ray observatory, may also not have the sensitivity or persistence needed to detect very high mass ratio LMXRBs, or those that absorb their star's matter very infrequently or in very small doses. More research and theory is needed in this area.
Microscopic black holes seem more efficient. They are one of the very few ways to achieve total mass conversion (complete conversion of mass into energy).
Why would this be the case? Unless you're extremely close to it, a black hole is just a mass, like any other stellar object.
How do such low mass black holes form?
On the other hand, it did make me click to find out what "binary" was about...
Remember that the original journal is read by astrophysicists, for whom a low-mass X-ray binary is perhaps more detail than they would need in a title.