Paper day! "Fitting the Radial Acceleration Relation to Individual SPARC Galaxies" by our brilliant student Pengfei Li: arxiv.org/abs/1803.00022 A thread will follow!
In arxiv.org/abs/1609.05917 and arxiv.org/abs/1610.08981 we show that baryons and dynamics are tightly linked in galaxies at a *local* level: the observed acceleration (from the gas rotation curve) correlates with that expected from the distribution of baryons (using Newton's law). 
At high accelerations gobs=gbar because baryons fully dominate the dynamics. These data come from the central parts of massive galaxies where there is no need for dark matter. At low accelerations, the data deviates from the 1:1 line. That's the classic indication of dark matter!
We were expecting something like this! @DudeDarkmatter did a similar work back in 2004: arxiv.org/abs/astro-ph/0… What really shocked us was the tightness of the relation! The deviations from the mean relation (aka "scatter") are of the order of 30%!
This scatter is absurdly small for the (poor) standards of galactic astronomy. So we did a simple math exercise: let's propagate the errors on the measurements and compare the resulting expected scatter from errors (black) with the observed scatter (red). The two are consistent!
This means that the relation is consistent with NO intrinsic scatter. The width of the relation can be fully explained by observational errors. In general this happens only when you deal with Laws of Nature, like Kepler's laws. This is a big deal, so we further looked into it.
The problem is that errors in Astronomy are a mess. We don't have complete control on them as Physicists can have with their experiments in their labs. Our lab is the Universe and the Universe doesn't care about what we wanna do. And here comes Pengfei's paper.
There are three main sources of error on gobs and gbar: the galaxy distance, the galaxy inclination, and the conversion from stellar light to stellar mass. If you got them a bit wrong, the galaxy will shift perpendicularly or horizontally from the mean relation, adding scatter.
The fact that the observed scatter is only 30% means that we did a pretty good job in estimating these quantities. But now we want to know whether this 30% can completely disappear when the errors are taken into account.
To do this, Pengfei used Bayesian statistics and a technique called Markov Chain Monte Carlo (MCMC). Essentially you can fit the mean relation to individual galaxies, allowing the light-to-mass conversion, distance, and inclination to vary a little, within the observed errors.
This is an example of how good the fits can be. They are not all this good. But if we measure the mean deviation from the fits for all galaxies, the resulting number is ridiculously small: 13%. We have a recipe that explains rotation curves better than 13% using only baryons!
When we optimize distance, inclination, and mass-to-light conversion, the radial acceleration relation becomes extremely tight. This didn't necessarily have to happen because we are varying *global* quantities while looking at a *local* relation, connecting different galaxy radii
If you are still following me, you may wonder what drives the remaining 13% scatter. Well, part of it could be intrinsic, but most of it must surely come from errors on the rotation velocities (due to non-circular motions and other nuisances) which are indeed of the order of 10%.
To summarize: we have a relation which is very tight for astronomical standards. The deviations from the mean can all be explained by measurement errors. The relation is consistent with no intrinsic scatter. So is this a Law of Nature? Or just another galaxy scaling relation?
Ops! I forgot to add the key plot. Here you see the radial acceleration relation using best-fit distance, inclination, and mass-to-light ratio. The tiny residuals need two tiny Gaussians, but we think we understand why this happens. It's likely how velocity errors are estimated.
