How fast can a small black hole eat?

Question

Edit: I'm not referring to the giants, but to the little ones that might or might not exist.

First:

https://worldbuilding.stackexchange.com/a/202290/264

We have this answer which limits the consumption rate to the speed of sound in the material at the event horizon.

However, I just ran into:

https://arxiv.org/abs/2312.07647

concerning a black hole in a star. They are projecting a consumption rate based on the speed of sound at the distance from the black hole where escape velocity was the speed of sound in the material and ending up with a far more voracious black hole than in the answer cited above.

I find it hard to accept either of these as correct, though. The speed of sound part seems inherent, the question is where the eating surface is. As the material falls in the result will be a traffic jam. I can't see how the material can fall from that whole area unimpeded (as in the star-eating paper), but I also have a hard time with assuming the material doesn't compress at all (as in the planet-eating answer) as it falls.

Is there any better analysis on this?

Answer 1

Phoenix A is the most massive black hole that we know about. Its mass is estimated at a hundred billion solar masses. If we assume it got there linearly since the Big Bang, it might have accreted 7.14 solar masses per year.

But that is very unlikely. Most likely it had different accretion rates over the eras. It probably got so big by merging with other black holes.

Such mergers are practically instantaneous. GW150914 took about two hundred millisseconds from start to finish, and the larger black hole went from 36 to 62 solar masses, so that's like 130 solar masses per second.

I wouldn't be surprised if Phoenix A and TON 618 could merge even faster than that, should they ever be made to collide.

Answer 2

The arXiv paper you mention is probably a better guide than the other source.

The question you are asking is not, strictly speaking, about matter passing the horizon but about matter getting sufficiently close to the horizon that any light or other signals emitted from it cannot be detected by the rest of the universe because it is very dim and only arrives slowly. (I mention this so as to avoid some difficulties arising from the fact that infinite amounts of time may pass elsewhere while the stuff is still falling towards the horizon).

Once you have qualified the question in this way, it becomes a question of accretion and the calculation can in principle be done using standard G.R. and some assumptions about the matter nearby, e.g. at the centre of a star. For purposes of rough estimation you won't go too far wrong using Newtonian gravity at a few $R_S$ from the horizon, where $R_S$ is the Schwarzschild radius, unless the black hole has a high rotation. However if it has accreted a lot then it probably does have a high rotation.

Answer 3

I am afraid there is no good answer to this.

It is estimated M87* consumes about 1 solar mass per decade, and that is a fairly active and huge black hole.

The truly upper bound for how fast you can shove mass past the horizon depends on your assumptions. If we assume a Hard Sci Fi setting, so a world in which materials melt at a given temperature, i suspect you wont get much better feeding rates.

The real issue here is that despite common believes, falling into a black hole is pretty trick as they all spin which causes all trajectories to curve in wild ways. Objects also tend to gain momentum when entering the Ergo sphere of rotating black holes and can be ejected again. For feeding black holes, the outward radiation pressure and astrophysical jet will greatly restrict how much matter can fall in as well.

If you want the absolute most amount of energy added, i suspect the best way would be to shoot lasers into the horizon as light does not interact with itself. So you avoid radiation pressure, well not really but whatever. Even then, there would be limits as the black hole would gain angular momentum from this and eventually spin so fast light cannot enter the horizon anymore.