The Decline of the Milky Way’s Rotation
I just noticed an interesting item on the ESA website about results described in a paper by Jiao et al. (on the arXiv here) relating to the rotation of the Milky Way as determined by Gaia’s Data Release 3.
The key result in the paper is summarized in this diagram:
A galaxy rotation curve like this is a diagnostic of the radial distribution of mass. If all the mass were concentrated at the centre, the galaxy would behave like the Solar System (in which most of the mass is contained within the Sun). In such a Keplerian profile the rotation speed falls off with distance, just as the outer planets move more slowly in their orbits than the inner ones. According to modern cosmology, however, there is dark matter not concentrated in the centre, in which case the rotation curve does not decline with distance and may even rise. According to theory, at large distances, the rotation curve of a spiral galaxy should be roughly flat.
The new results seem to contract this notion. The Figure shows a rotation curve that declines for distances about 15 kpc from the Galactic Centre; for reference the Sun orbits at a radius of about 10 kpc.
One of the problems in constructing a rotation curve of our own Galaxy is that we are inside it so it isn’t possible to make measurements across the entire system like we can with other galaxies. Using the Gaia measurements and a plausible model, however, the authors find much less dark matter than anticipated.
With a bit of extrapolation using a model, this measurement leeds to a reduction in the estimated total mass of the Milky Way. The value usually bandied about is around 1012 Solar Masses, while the new measurements imply a much lower mass of about 2 × 1011 Solar Masses.
A factor of five reduction is quite a dramatic change and I’m sure this result will be challenged by those of an orthodox persuasion while also providing encouragement to dark matter sceptics. We’ll just have to wait and see how this pans out.
In the Dark 
September 28, 2023 at 9:22 pm
Constraints on the total mass of the MW at large radii come from (i) kinematics of halo stars and globular clusters, (ii) kinematics of stellar streams, (iii) kinematics of satellite galaxies and (iv) the Timing Argument.
These all probe the mass at much larger radii than Jiao et al’s rotation curve.
Their rotation curve gives out at ~ 30 kpc, so any mass inference beyond that distance is model-dependent.
September 29, 2023 at 10:28 am
How secure is the Timing Argument, really? I’ve never been all that convinced. I take your point about the Jiao estimate though – it is quite an extrapolation and is indeed very model dependent.
September 30, 2023 at 10:38 am
Indeed it is a very nice question. Especially because we have now good evidences that at the M31 location there were a major merger occurring 2 to 3 billion years ago. Since the timing argument is integrating past orbits for at least a Hubble time, how to deal with it with 3 bodies instead of 2?
October 13, 2023 at 2:58 pm
The Timing Argument works remarkably well, even though the (small) errors quoted in some papers only represent the observational errors, assuming no scatter in the relation between kinematics and mass. When that is taken into account, the errors for an individual system are significantly larger. Some earlier works also don’t take into account that, in LCDM, lower mass systems are intrinsically more abundant than higher mass systems.
It is worth saying that the TA constrains only the total mass of the LG, so its constraint on the mass of the MW relies on the assumption that a significant fraction of that mass is in the MW – the TA gives the same kinematics for a system where 50% or 1% of the total mass is in the MW (and, indeed, the TA still works very well at redshifts where both the MW and M31 contain only a tiny fraction of their present mass and of the total mass of the system).
However, given that the MW is one of the two brightest galaxies (and one with many bright satellites) in the LG today, it is probably safe to assume that it does contain a significant fraction of the total mass, which gives the TA power to constrain its mass as well. With all the caveats above, a mass of only 2×10^11 would thus be very unlikely, given the TA (and assuming LCDM).
September 30, 2023 at 9:35 am
The main question with these other tracers is whether or not their orbits are at equilibrium. For example the Magellanic Clouds are at their first passage, and their total orbital energy still contains an important contribution from their initial velocity. Conversely, stars in the Milky Way disk have much more circular velocities that are in equilibrium with the Galaxy potential, i.e., they constitute a much robust tracer.
The fact that they show a Keplerian decrease beyond the Galactic disk also put limits on the contribution of matter outside the disk (inside the error bars, of course).
September 30, 2023 at 10:56 am
I’m not an expert in rotation curves, but from memory I don’t recall seeing any external disk galaxy rotation curve with a decline as steep as this … plenty do decline, but more gently and at larger radii. This would seem to make the MW rather exceptional. Any comment from rotation-curve experts out there ?
October 13, 2023 at 2:42 pm
This would certainly be a spectacular result and at odds with many other measurements. The MW’s total mass would then be comparable to that of the LMC (its most massive satellite), while several of its other satellite galaxies (not only Leo I) would not be on bound orbits (at least without also modifying GR, but this analysis is based on standard gravity).
With an M200 mass of 2×10^11 solar masses, the MW would also be a severe outlier in the stellar / halo mass ratio compared to other galaxies – including those where the halo masses can be measured through weak lensing.