I Question of accuracy of galactic collision simulations

[Halc]

TL;DR

Galaxy collisions seem to involve considerable friction which seems absent in simulations.

There are countless time lapse simulations of galactic collisions, squashing say 20 billion years into a few minutes or even seconds. Many of these involve the upcoming collision with Andromeda, but my question is more general.
No, I don't have a specific video in mind.

Most of these show a pair of fairly neat spiral galaxies with defined arms. The near arms distort first and the symmetry is lost. The cores of the galaxies represent considerable mass and their close pass causes at one point a sort of explosion of stars being flung away by gravitational acceleration (which robs especially the central black holes of much momentum). This part is fine and expected. Most of that material was already close to one of the central masses. Point is, those simulated flung objects tend to exit the maelstrom at speed without slowing, and I question this.

Compare this to observations of some recent galactic collisions. You have this disorganized mess shortly after what is concluded was a fairly high speed collision. What stands out with some of these is that each carried a cloud of dark matter which for the most part kept going and exited the combined galaxy whose rotation curve is now far lower than it would be with the DM. The baryonic matter coming in at those speeds all managed to slow down by interaction with matter from the other galaxy, when the dark matter did not. That demonstrates significant friction preventing these galaxies from just parting again like the dark matter did. Sure, some stuff was flung away, but if there was that much friction and it came from the combined core, it probably lost much of its speed to friction on the way out, dropping much of it back below escape velocity. The simulation don't seem to account for this.
I know they can't separately compute the effect between each planet, star, rock, dust, whatever, but to ignore average friction seems to be an oversight, and it would significantly alter the videos created. I'm not sure if there's a way to measure the actual baryonic mass ejected at escape velocity from a collision and compare it to the simulation.


Irrelevant to the question:
I presume the dark matter will eventually find its way back, but will always have this larger 'orbit' which prevents it from clustering significantly around the new galaxy. Its cloud will remain more dispersed that ones from lower speed collisions. I don't thing Andromeda is considered to be particularly high speed. In peculiar velocity terms, we're actually moving away from it and it is overtaking us from behind.

 

[.Scott]

No, I don't have a specific video in mind.

Which, of course, will limit the usefulness of the discussion.

What stands out with some of these is that each carried a cloud of dark matter which for the most part kept going and exited the combined galaxy whose rotation curve is now far lower than it would be with the DM. The baryonic matter coming in at those speeds all managed to slow down by interaction with matter from the other galaxy, when the dark matter did not. That demonstrates significant friction preventing these galaxies from just parting again like the dark matter did. Sure, some stuff was flung away, but if there was that much friction and it came from the combined core, it probably lost much of its speed to friction on the way out, dropping much of it back below escape velocity.

I think you are over-stating how much friction is involved. Wherever there is substantial and immediate friction, there will be enormous heat. The overall contribution of friction to the dynamics of the first "moments" of the collision (the first full rotation of the galactic masses around each other) is likely small - even for the baryonic matter.
As an example, the Earth is moving through space and encountering friction. But not enough to drive us to a lower orbit around the sun any time soon. And the primary component of Lunar friction as it orbits the Earth are due to the tidal effects - the friction occurs with the tides at our coastlines.

 

[ohwilleke]

Astronomy/cosmology simulations do two main things:

1. They rely on a set of assumptions about the physics involved, which are physics informed, but generally never fully reproduce the known laws of physics and the actual distribution of matter in a galaxy. In part, galaxy scale simulations typically use Newtonian mechanics and gravity as a weak field approximations of GR, and in part, the simulations make assumptions about the exact physics of dark matter phenomena in the absence of a scientific consensus about this issue. They also make assumptions about the interstellar baryonic matter present in the simulated system which is better understood than it once was, but which still isn't known to great precision. Processes that give rise to feedback interactions are particularly poorly understood.

2. They oversimplify the interactions to a level of detail that is computationally manageable. At a minimum, they are more coarse grained than reality and simulate the behavior of oversized discrete clumps of matter (far larger than individual stars and planets or solar systems), rather than actual, real life sized particles or solid bodies. Some approximations are based upon documented phenomenological relationships, others are based simply on mathematical and programming convenience.

Quantifying uncertainties in these simulations is non-trivial because a simulation isn't engaged in the much easier to quantify task of estimating the value of a single numerical parameter. Instead, a simulation of a galaxy collision is simulating all the measurable properties of the combined two galaxy system at once. Saying that a simulation is, for example, "30% accurate" is meaningless until you have a good global metric for its overall accuracy. And, there really isn't a single consensus global metric that is a good measurement of galaxy scale simulation accuracy in all of its various aspects.

Another factor that makes quantifying the accuracy of a simulation is that while quantifying the uncertainty in each particular input and assumption of the simulation can be quantified well, figuring out how the combinations of those uncertainties influence the aggregate final result when the interactions are non-linear is, as a practical matter, impossible to calculate analytically (i.e. with equations and calculations, rather than Monte Carlo methods or lattice simulation methods).

Often the sensitivity of the simulation to uncertainties in particular inputs is estimated using Monte Carlo methods. Each input is varied randomly within its known uncertainties, and the simulation is run hundreds or thousands or even millions of times to see how similar the final results are to each other. The empirical range of various in the simulation outputs that arise from varying the inputs within their known uncertainties is then used to estimate how inaccurate the simulation is as a result of imprecisely known inputs (as opposed to any inaccuracy that results from fundamentally incorrect assumptions or key omitted inputs).

Similarly, it is common to use Monte Carlo methods to estimate the accuracy costs of being coarse grained, by running the simulation many times at several different levels of coarse v. fine grained models to determine empirically how much of a difference it makes. Quantum chromodynamics (QCD) physicists using discrete lattice QCD methods to describe high energy physics interactions do the same thing.

Most simulations are going to be better at accurately reproducing some of the properties of the combined two galaxy system than others.

For example, it may be good at predicting what percentage of the mass of the initial two galaxies escapes the combined two galaxy system, and what percentage of the mass of the initial two galaxies remains gravitationally bound to the resulting combined two galaxy system.

But, it might have large systemic errors in estimating the dynamics of stars that remain in the combined system because a naïve coarse grained model might miss key sources of those dynamics that are taking place at a more finely grained level than the simulation, which the method of coarse graining used in the simulation isn't approximating well. Better simulations often impose some forms of global constraints at each iteration to mitigate these kinds of problems (such as global conservation of momentum rules that are applied in addition to the rules applied to each component of the system separately).

That's just an example, of course. Each simulation is going to have aspects of the overall system in which it reproduces comparable real world galaxy collisions relatively well, and aspects of the overall system it simulates resulting from the collision that it gets badly wrong.

In much the same way, different ways of projecting the Earth's geography onto a flat surface each have their own strengths and weaknesses. Some preserve area well but mangle shapes and distances, or aren't continuous (reproducing the reality in finite chunks that don't perfectly match up to each other in an undistorted way). Others are good at preserving shapes and at getting relative distances right on some parts of the image, but get areas and distances badly wrong on other parts of the image. Similar pros and cons are present when choosing different approaches to setting up astronomy simulations.

Of course, when simulations differ materially from the various instants of a galaxy collision process that astronomers see, this isn't the end of the story.

The scientists doing the simulations go back to the drawing board and try to figure out what aspect of their simulation (which is often buried deep in computer code, or even worse, in the black box of a machine learning model), is out of whack, and try to come up with a way to fix it that better matches what astronomers observe.

This is hard. Even if scientists know exactly what their models are getting wrong in terms of end outputs, figuring out what parts of their models are doing that, when the models themselves have many moving parts, is more art than science.

The whole point of a simulation is to test whether the assumptions that went into it are good enough to be sufficiently similar to astronomy observations in an informed, but subjective sense, in the eyes of the astrophysicists who work with them. The closer the match between the simulation and the astronomy observations is, the more confidence we can have in our understanding of the astrophysics involved. And, the bigger the gap between the simulation and the astronomy observations is, the more certain we can be that one or more of the physics informed assumptions or oversimplifications in the model has a material flaw in it.

We have certainly not yet reached the promised land where simulations can accurately model events like the collisions of two galaxies to high precision in a way that is indistinguishable from astronomy observations of different phases of the same kinds of processes (these processes take vastly too long to observe with astronomy from start to finish in a single collision). But just how flawed the existing simulations are is hard to quantify or describe, and the process of improving them is an active area of scientific investigation.

 

[FactChecker]

An amateur question:
Can it be that the observed collisions display a bias? When there is a lot of friction, therefore heat, would they be more visible to us? Could that cause our observations to differ significantly from the results of theoretical analysis?

PS. I ask this because @.Scott says that the friction is small, but the OP states that observations indicate the consequence of significant friction.

 

[ohwilleke]

An amateur question:
Can it be that the observed collisions display a bias? When there is a lot of friction, therefore heat, would they be more visible to us? Could that cause our observations to differ significantly from the results of theoretical analysis?

PS. I ask this because @.Scott says that the friction is small, but the OP states that observations indicate the consequence of significant friction.

This is definitely a possibility. When you are comparing simulations to astronomy observations, I focused on the issues with the simulation. But the astronomy observations have their own issues.

One of the great things about a simulation is that, subject to its limitation of being coarse grained, you can have effectively 100% perfect observations of what your simulation is predicting at any moment of the process from a "god's eye view".

In contrast, we only have a single perspective for all practical purposes in most astronomy observations of galaxies. And, astronomers are so used to working with imprecise data that their standard metric of measuring errors is the "dex" (where the error is expressed in factors of 10^dex relative to the observation, rather than ± X). Many kinds of astronomy observations are routinely accurate only at order of magnitude levels.

There are all sorts of selection biases and observation limitations that are present in any decent sized set of astronomy data.

I personally doubt that this is a big factor for "friction" type behavior in astronomy observations of galaxy behavior. My intuition is that the apparent discrepancy is mostly a simulation problem and not an astronomy observation problem (although I'd be hard pressed to tell you exactly why I have that intuition without some lengthy and thoughtful introspection). But, the general concern that the astronomy observations may themselves be imprecise or drawn from a biased sample is absolutely valid.

 

[ohwilleke]

After giving it some more thought, the reason that I think that the simulation rather than the astronomy observations are the main problem is that the precision and bias issues in the astronomy observations, while very real, are also well understood.

In contrast, the kinds of dark matter phenomena models used in these simulations (usually NFW distributions of completely sterile dark matter) have serious known defects at the galaxy scale, the big improvements in our understanding of interstellar media (which are less than a year old) are probably too recent to have been included in any simulations being discussed right now at PF, and the feedback uncertainty issues, while somewhat tamed from a few years ago, are still huge.

So, on balance, I think it is more likely that the simulation is flawed in ways that are hard for astrophysicists to quantify than it is for the astronomy observations to have similar problems to the same extent.

 

[FactChecker]

My intuition is that the apparent discrepancy is mostly a simulation problem and not an astronomy observation problem (although I'd be hard pressed to tell you exactly why I have that intuition without some lengthy and thoughtful introspection).

I spent my entire career in simulation (not this type). This strikes me as an exceedingly difficult subject to simulate. The numbers make it impossible to track all individual objects. (Even the three-body problem is trouble.) It is more like "lumpy" fluid dynamics, sort of like blood flow. Even simulating aerodynamics, which is relatively simple, using supercomputers is not to be trusted, and must be carefully verified with step-by-step testing.

 

[ohwilleke]

I presume the dark matter will eventually find its way back, but will always have this larger 'orbit' which prevents it from clustering significantly around the new galaxy. Its cloud will remain more dispersed that ones from lower speed collisions. I don't thing Andromeda is considered to be particularly high speed. In peculiar velocity terms, we're actually moving away from it and it is overtaking us from behind.

One of the rather surprising observational facts about dark matter distributions in galaxies is that they show surprising similarities to each other without much regard to the history of mass assembly in that galaxy, rather than great diversity based upon their varied histories of mass assembly.

The only kind of galaxies where you see great diversity in inferred dark matter distributions are in low surface brightness dwarf galaxies which have a bimodal distribution between having very large proportionate shares of inferred dark matter in the large majority of cases and apparently almost no inferred dark matter in a minority of cases.

So, your intuition about the ultimate distribution of inferred dark matter from two source galaxies following a galaxy merger is in tension with the astronomy evidence.

 

[ohwilleke]

Even simulating aerodynamics, which is relatively simple, using supercomputers is not to be trusted, and must be carefully verified with step-by-step testing.

The reason that this particular example is so hard is not because it is, fundamentally, a huge many body problem, but because the underlying deterministic Newtonian physics equations (the Navier-Stokes equations) are inherently "chaotic" in the mathematical sense that large scale behavior is highly sensitive to small scale differences in initial conditions (see, e.g., the Butterfly effect).

I don't know for certain, but strongly suspect, that the large scale physics involved in galaxy collisions are not chaotic in this mathematical sense.

This isn't to detract, however, from your core observation that colliding galaxies are indeed particularly difficult to simulate. It just probably isn't a problem as a result of deterministic but chaotic dynamics (which are also what makes the three-body problem so difficult).