Mostly Missing ?

I recently read a news article claiming that it's a myth that college students are all wokeist do-goodies. This it refuted quite sensibly by looking at the fraction of students who align with said wokeist do-goody policies. Fair enough.

But it also occurred to me that in some ways this is slicing things backwards. If you want to say that university life is or isn't dominated by the "woke", then it's perfectly correct. If, however, you want to understand why the popular image of the woke might fit a certain demographic, then it's the wrong way round. What you want to do in that case is analyse the fraction of those identified as woke, e.g. see if the woke are dominated by students, rather than the overall student population being political activists or whatnot. Because the numbers are small, it's entirely possible that only a few percent of students might be called woke, yet all the woke are bobble-hat wearing students.

Or, in other words : not everyone who voted for Brexit was a racist, but all racists voted for Brexit.

But that's more than enough politics for this blog. What it reminds me of is the statistical approach used by those who claim that there's a huge disagreement between observations and cosmological models of galaxy. It goes something like this :

• An observation is found which is intuitively unexpected.
• Simulations are used to assess how frequently such observations should actually occur, according to the particular model.
• The fraction found showing similarities to observations is low, and therefore the observations are proclaimed to be incompatible with the model.

What they do not do is ever look at those rare cases which do show similar features do the observations : though sometimes very rare, it hardly ever happens that the models never show such features at all. And that would be much more interesting, because by examining how such features form in simulations, you could potentially infer the mechanism at work in the real universe.

In today's paper (press release here), the authors return to the old favourite - the missing satellite problem. Simulations generally predict about ten times as many satellite galaxies around the Milky Way as are actually observed. Or rather... they used to. Actually that's been getting a bit better thanks to improved observations and far more sophisticated modelling. But certainly back when simulations generally only used dark matter (to keep things computationally cheap), that was indeed the case. It isn't the case any more, but on the other hand, adding in realistic gas and stars causes all kinds of other horrendous complications.

The important point is that the simulations tended to only use dark matter, whereas what we observe are stars and gas (for a long read on why this matters, see this). So claiming a stark disagreement was entirely warranted at the time, but provisional on better simulations. And this is still the case, though simulations have progressed significantly.

Anyway, what the authors are looking at is how recent the satellites of the Milky Way have arrived in our vicinity. The basic model predicts that they should be the leftover remnants of the Milky Way's assembly process, so they should have been orbiting our galaxy since basically forever. While the missing satellite problem might have alleviated in terms of pure numbers, if in fact most of the satellites are recent arrivals, then the problem is just as bad as it ever was - if not worse.

Now you can't just go an observe something like "arrival time" directly. What they have is data from the Gaia space telescope that gives the proper motions of the galaxies across the sky. Combined with line-of-sight velocity, this can be used to give clues as to the three-dimensional orbital of the satellite around the Milky Way. However, it does not give the full orbit directly : for that, they use independent measurements of the mass of the Milky Way. That's rather tricky, because (ironically) being inside the disc makes such estimates much more difficult than when measuring other galaxies.

Their most important result to me are the phase diagrams they plot for different components. This is just a plot of speed against distance, combined with models to show what speed is expected where. At small distances, a satellite galaxy can be bound to its parent even if it's moving at high velocities, whereas at high distances it must have a much smaller motion to remain bound. So you get characteristic curves, depending on the parent mass, showing whether galaxies are likely to be bound or unbound from the parent host. But remember, the mass of the parent galaxy - the Milky Way in this case - isn't very well constrained.

Still, they show convincingly that the satellite galaxies are generally all at higher velocities than other components in the galactic "halo" beyond the disc (individual stars and globular clusters). While only a very few require the largest possible parent mass to be in a bound orbit, they point out that this doesn't imply the galaxies moving at lower velocities have therefore been present for all that long. Rather, most of them appear to be in a regime where it's much more likely that they're recent infallers.

This is a nice, intriguing result. But as usual, it would be premature to throw out the standard cosmological model just yet. 

For example, one parameter they measure is the tangential velocity compared to the radial velocity, finding that this is in excess compared to expectations. Early authors claimed that such an excess happened in just 1.5% of the simulations, but this is problematic for two reasons : (1) they used pure dark matter, which doesn't have the massive baryonic galactic disc that can cause markedly different tidal effects; (2) it's using the wrong selection criteria - as above, why not look at those 1.5% which did show similarities, and see if those show any other similarities to the observations ? That would potentially be much more informative.

Furthermore, they cite other authors who postulated that maybe this is a survivorship bias. In this scenario, satellites on highly radial orbits are destroyed by the tidal effects of the parent galaxy. But they reject this hypothesis as the observable galaxies don't show the expected distance-based trend in tangential/radial velocity ratio, but I would (naively) assume destruction to be a highly non-linear process, so I'm not sure this is such a big problem.

Now one might expect that an encounter with another massive galaxy would play a huge role in the formation of its satellites. So they also select more advanced simulations, which do employ gas physics, containing pairs of giant galaxies resembling the Milky Way and M31. But they only have ten of these, so this already restricts the possibilities and doesn't let them select similar objects by design - which I think would be a much better approach. One should start by assuming that the mechanism for this velocity excess is unknown and see how the simulations reproduce it, not by seeing if any particular mechanism can explain the results or not. 

It also seems strange to me that they don't try and use the orbits of the galaxies to try and constrain the mass of the Milky Way. While they say there are other reasons to prefer a smaller halo mass, this rapidly escalates in complexity. It definitely feels to me like there is a large aspect of personal preference at work. If you prefer the standard model, you could use the evidence to infer a large halo mass with some anomalies; if you don't, you could say there's a small halo mass with some different anomalies.

Finally, the elephant in the room is that the Milky Way's satellites are in a plane. Long-term readers will know that I'm deeply skeptical about claims for similar features around other galaxies, but that of the Milky Way is virtually certain. So knowing that its satellites are atypical in their positions, should we really expect them to be typical in other parameters ? Probably not. 

All in all, it's an intriguing result. But as usual, I don't think it's anywhere near enough for the standard model to have anything much to worry about.