A Volumetric Law For Star Formation

It's well-known that there's a correlation between galaxy gas density and star formation rate. The problem is that no-one's clear on exactly what sort of correlation it is, or what sort of gas it is. In general, galaxies which have significant amounts of atomic hydrogen (which is relatively warm) tend to be forming stars, so there's definitely some sort of connection there. But recent studies have found the correlation is much better when considering only the colder, molecular hydrogen, which gives a much nicer linear relation. And that makes physical sense too, since to form a star you need higher gas density, which is easier if the gas is cold as it can't use thermal pressure to support itself against collapse. Perhaps most convincing were the discovery of holes in the atomic gas component of some spiral galaxies, which seem to be the result of star formation consuming all the gas. Also, the atomic gas has a strict upper density limit, beyond which all gas seems to become molecular.

The shape of the correlation between the gas and star formation rate is somewhat unclear as well. Mostly it's a nice power law, but there's some evidence for a density threshold below which the star formation activity drops sharply. This, say the authors of this work, is quite controversial (more so than I realised, and I'm supposed to know about this stuff), as is the choice of which gas component to use.

There are lots of uncertainties, but perhaps the main one is the gas density (of either the cold or the warm component). We can estimate the gas density per unit area (surface density) easily enough, but the true volume density is much harder because we can't directly measure the thickness of the gas disc. Here the authors attempt to overcome this. They assume the gas is in hydrostatic equilibrium, meaning that its outward pressure (due to thermal and other motions) is balanced by its tendency to collapse under gravity. This isn't straightforward : it requires detailed knowledge of the mass and distribution of stars and dark matter as well as that of the gas, and also it needs the velocity dispersion and overall rotation curve of the gas. This is currently only possible for quite nearby galaxies since you need very detailed, well-resolved data to do this properly. Even then there are still uncertainties and assumptions that have to be made.

This paper is under review, but it seems to me to be a careful, detailed work more in need of correcting typos than methodological revisions. After describing their methods with considerable precision, they find that both the atomic and molecular components show very clear, power-law correlations with star formation. There's no change of slope with density either. They say this could be because the thickness of the gas disc varies significantly depending on where you are in the galaxy : it's much fatter in the low-density outskirts than the centre. The surface density measurement would give a misleadingly high estimate in the outer regions.

The fact that both warm gas correlates with star formation is also very interesting. Previously the tendency had been to assume that this connection would be somewhat secondary : the picture has been shifting to the atomic gas having to transition to molecular gas before forming stars. So the correlation is expected to be rather rough, but in fact it's very clear - certainly no worse than that of the molecular gas. They give two interpretations :
- The warm gas is a good tracer of the cold gas. The connection between atomic gas and star formation could then still be indirect. It would also mean that there could be undetected cold gas (which is very difficult to detect directly - normally other components have to be used) in the outskirts of galaxies, where star formation activity has previously been puzzling.
- The warm gas can form stars directly. This is theoretically possible : there are conditions under which the warm gas could cool so quickly that there's no time for molecular gas to form and it goes directly into stars.

There's a lot of work to be done, but this isn't the only evidence for atomic gas being directly involved in star formation. The idea that actually this complex process is governed by a rather simple condition - true density - but that this condition is hard to measure is very appealing.
https://arxiv.org/abs/1810.03616