Wibbly-wobbly curvey-wurvey

Fresh from having mastered the art of fitting the baryonic Tully-Fisher relation the hard way, I thought I'd resume a long hiatus from reading papers with a look at this one.

The BTFR is an empirical relation between the rotation speed of a galaxy and its baryonic mass (stars and gas). In logarithmic units, this is a nice straight line with (arguably) no intrinsic scatter. This is rather surprising since even very simple calculations show that star formation and environmental effects ought to disturb the gas and stars - galaxies with low surface brightness (brightness per unit area) ought not to follow the same relation as high surface brightness galaxies, but they do anyway.

It's been argued that this is evidence for alternative theories of gravity. If it's just mass that dictates rotation speed, then it doesn't matter if the mass consists of stars or gas : everything should follow the same relation. Under the standard paradigm of galaxies being dark matter-dominated, this would involve a conspiracy between different components that's comparatively hard to justify.

But while the BTFR has been shown to hold true over a wide range of rotation speeds and masses, for the very largest galaxies this is known not to be the case. Establishing whether this is also the case for the smallest galaxies is harder. Not only are they rare, but to get accurate measurements of the rotation speed requires high resolution observations - and resolving the smallest galaxies of all is naturally more difficult. And since you want the systems to be stable, they need to be isolated. Ideally, you want them to be gas-dominated as well, as it's easier to measure the mass of gas than it is for stars.

So getting a statistically significant sample to probe this end of the BTFR is difficult. That's where this paper comes in. At long last, the authors have obtained just such a sample, of 25 objects. Enough, at least, to say whether galaxies of the lowest mass typically follow the same BTFR as for normal galaxies.

The answer ? They don't. They rotate significantly more slowly than the relation found for more massive galaxies.

The really tricky part comes in demonstrating whether this is consistent with standard model expectations or not. The problem is you can only measure how fast a galaxy is rotating out as far as you can observe its material, whereas the dark matter halo ought to extend much further. To correct for this, they compare with analytic predictions for different dark matter halo density profiles. With enough clever tweaking, it's possible to get a result that agrees really well with numerical simulations.

You may well read a note of skepticism here. Thing is, since we don't know the true distribution of dark matter, there's quite a lot of freedom to choose which one to use to get a result which agrees with simulations. And the corrections are so extreme that these galaxies then have a faster rotation than the BTFR for more massive galaxies predicts. But to be fair, they state their results quite cautiously, emphasising the need for more data. So I have no problem with saying this is an intriguing result that needs to be reported.

That said, I'm more persuaded of the claim that the galaxies are more likely to have a constant density inner "core" than an extremely high-density spike (a.k.a. a "cusp"). Trying to get a self-consistent cusped profile that agrees with observations just doesn't seem to work very well, a well-known problem that might be solved because of all the gas and stars sloshing around in the middle.

The provisional, take-home message, then, is that the BTFR is really more the result of the complicated physics of star formation and galaxy formation than it is something as fundamental as gravity. Naively, while you can reproduce the BTFR for ordinary galaxies using nothing more than dynamics, it looks likely that this is really just an elaborate selection effect : once we go outside the standard range of galaxies we've been accustomed to observing, we don't see the nice neat linear relation any more.

Where does this leave Ultra Diffuse Galaxies, ones of extremely low surface brightness that look to be rotating so slowly they may have no dark matter at all ? The authors say, "dunno". My bet remains that we've simply estimated their velocities incorrectly, but if there is something funky going on with how star formation works at these mass scales, that'd be much more interesting.