It would be interesting to view the evolution over long periods of time.
This simulation is 2D, but it's similar to what happens in globular star clusters. In these, there's a phenomenon called the "gravothermal catastrophe".
The particles (stars, sponge bits) relax to thermal equilibrium, where the kinetic energy of a particle has a distribution where probability declines exponentially in energy/temperature. Some of the particles will have energy high enough to escape to infinity (to "evaporate"). When they leave, the remaining particles are more tightly bound, so the cluster shrinks. The particles then move faster (by the virial theorem, total kinetic energy is always 1/2 the negative of the gravitational potential energy). Evaporation accelerates until the cluster basically explodes.
Why this doesn't happen to actual star clusters was eventually determined to be due to three body collisions that cause binary stars to form, and these stars then inject energy into passing stars (causing the binary star orbits to shrink). This energy injection reheats the cluster, inflating it again and preventing runaway evaporation.
I'm not clear that the simulation here can handle formation of such binaries.
>The only force at play is newtonian gravity, which we modify by adding a softening length, ε.
> This way we avoid numerical instabilities due to divergent forces when two particles get to close together.
So it appears he doesn't handle close encounters that form binaries. Probably reasonable if he's using heavier discrete particles as a proxy for dark matter.
I wrote my own toy gravity simulation. 2 stars that come very close together at a clock tick will experience a massive force that throws them both right out of the system. This is an artefact of artificially dividing time into clock ticks to make the calculation tractable. As I understand it, 'softening length' is a fudge to stop that happening.
You'd have to use a more sophisticated algorithm with variable time steps for closely interacting particles, I think. And then some way to deal with particles that become bound.
yup. molecular dynamics simulations are hard-core. and the parallelization is highly non-trivial so you need fast fabrics and complex message passing to scale. one of the raisons d'être for supercomputers
> Evaporation accelerates until the cluster basically explodes
This sounds very much like what happens at the end of a black hole's lifetime as it evaporates by Hawking radiation. Any chance that's a real connection?
No, but also maybe yes, but it's way over my pay grade as a physicist. In short, I think the fact that gravitational systems have negative specific heat capactiy is very relevant.
As gravitational systems lose energy, the "temperature" of the ensemble of particles goes up. (I.e. objects with smaller orbits have higher velocities.)
It is probably not exactly an accident that this relationship holds for blackholes as well: the hawking radiation formulas suggest a larger and larger temperature for blackholes with smaller and smaller event horizons. The hawking radiation stuff is built upon entropy / temperature relationships so I think there is actually some kind of connection there.
There might even be something baked into the energy conditions / bianchi identities of GR that is manifesting in that way, but I'm speculating.
Well yeah, probably, but sometimes very weird analogies between systems turn out to produce real physics, and it doesn't even seem impossible to me that there's something similar happening behind the event horizon of a black hole. I'm just hoping someone smarter than me has already done the math.
There is a relationship in that both the "Spongebob cluster" and a black hole has negative heat capacity. The math is already there in the virial theorem. See <https://en.wikipedia.org/wiki/Heat_capacity#Negative_heat_ca...>. Detailed treatments of the non-relativistic case you can find in an undergrad astronomy textbook; the relativsitic singleton case ehhhhh I don't think you're ready for it but Wald's General Relativity §12.5 & §§14.3-14.4 would be a good choice (and he shows you the math, which has been known for several decades), and for relativistic orbits I think you need to go beyond textbooks (although you probably could start with numerical relativity textbooks, like Baumgarte & Shapiro or Alcubierre, although I don't have either handy to double-check where they go with thermodynamics. Oh and the paper I linked in a sibling comment has a good and relevant bibliography. <https://academic.oup.com/mnras/article/516/3/3266/6668807>).
However it's best to think of "the black hole" as the entire spacetime (in Hawking's 1974 treatment and similar; or alternatively out to somewhere in the asymptotic flatness), in which there are two regions without a horizon, one to the past of the event horizon formation, and one to the future of final evaporation.
What goes into the horizon doesn't stay in, therefore what happens inside is part of the picture (and has been speculated about for fifty years! Fifty!)
Yeah technically, in the current formulation, but I think at this point the smart money is on Hawking radiation being correlated with something on the inside. For instance this is my favorite solution for the information-loss problem, that the info is carried away by hawking radiation.
As far as I am aware the virtual particles near the event horizon of black hole behave nothing like stars in a galaxy. For a start, stars much more massive (many many orders of magnitude) and aren't influenced by quantum mechanical effects in the same way as individual particles.
I like your comment, it provoked some catch-up reading, so forgive me pecking a bit at what you wrote.
The visualization is pretty limited, and was probably just a fun way for the astrophys student to use his choice of tools. (Which we should encourage! His work is great!)
Digging deeply into the consequences of this example of obviously physically improbable initial conditions could be somewhere between entertaining and enlightening, but would quickly go over the head of early astro students first encountering the virial theorem and negative heat capacity. "Getting the physics right" would be a significant research project. You'd also generally have to do without animations, unless you are very patient and have a big compute time budget (see the acknowledgments section of the MNRAS paper below, and my final paragraph).
Motivated by the previous paragraph's themes I found a recent (2022) MNRAS open access paper which among other things has a good overview of the (recent) state of the art in modelling star clusters, some good teaching material in section 2, and in section 3 we see their software packages. I'd suggest you begin with the summary in section 6.1.
In principle simulating the Spongebob cluster could produce information in the top two graphs of figure 7, and a 2d version of one or two of the graphs in figure 6. The additional information in those figures is certainly interesting, but nowhere near as pretty as the Spongebob animation. And I'm not sure what extracting similar figures for the Spongebob simulation would be useful for.
Conversely, the Spongebob simulation could not generate figure 9, and that figure is especially interesting to me (q.v. §4.2 & final sentence in §3.2).
And finally, "The movies of the full simulations, from which Fig. 6 was produced, will be made available upon reasonable request as well and will be uploaded publicly in the future". Not sure the upload ever happened, although I didn't really search much (e.g. it's not linked at the arxiv <https://arxiv.org/abs/2205.04470> or in DDG media searches on title or a few of the authors).
This simulation is 2D, but it's similar to what happens in globular star clusters. In these, there's a phenomenon called the "gravothermal catastrophe".
The particles (stars, sponge bits) relax to thermal equilibrium, where the kinetic energy of a particle has a distribution where probability declines exponentially in energy/temperature. Some of the particles will have energy high enough to escape to infinity (to "evaporate"). When they leave, the remaining particles are more tightly bound, so the cluster shrinks. The particles then move faster (by the virial theorem, total kinetic energy is always 1/2 the negative of the gravitational potential energy). Evaporation accelerates until the cluster basically explodes.
Why this doesn't happen to actual star clusters was eventually determined to be due to three body collisions that cause binary stars to form, and these stars then inject energy into passing stars (causing the binary star orbits to shrink). This energy injection reheats the cluster, inflating it again and preventing runaway evaporation.
I'm not clear that the simulation here can handle formation of such binaries.