A Response to Recent Developments Concerning the Gravitational Potential of the Milky Way

In the series of recent posts I’ve made about the Milky Way, I missed an important reply made in the comments by Francois Hammer, one of the eminent scientists doing the work. I was on to writing the next post when he wrote it, and simply didn’t see it until yesterday. Dr. Hammer has some important things to say that are both illustrative of the specific topic and also of how science should work. I wanted to highlight his concerns with their own post, so, with his permission, I cut & paste his comments below, making this, in effect, a guest post by Francois Hammer.

There are two aspects we’d like to mention, as they may help to clarify part of the debate:
1- When saying “Gaia is great, but has its limits. It is really optimized for nearby stars (within a few kpc). Outside of that, the statistics… leave something to be desired. Is it safe to push out beyond 20 kpc?”, one may wonder whether the significance of Gaia data has been really understood.
In the Eilers et al. 2019 DR2 rotation curve, you may see points with small error bar up to 21-22 kpc. Gaia DR3 provides proper motion (systematics) uncertainties that are 2 times smaller than from Gaia DR2, so it can easily goes to 25 kpc or more.
The gain in quality for parallaxes is indeed smaller (30% gain). However, our results cannot be affected by distance estimates, since the large number of stars with parallax estimates in Wang et al. (2023) is giving the same rotation curve than that from (a lower number of) RGB stars with spectrophotometric distances (Ou et al. 2023), i.e., following Eilers et al. 2019. And both show a Keplerian decline, which was already noticeable with DR2 results from Eilers et al 2019. The latter authors said in their conclusions: “We do see a mild but significant deviation from the straightly declining circular velocity curve at R≈19–21 kpc of Δv≈15 km s−1.” Our work using Gaia DR3 is nothing else than having a factor 2 better in accounting for systematics, and then being able to resolve what looks like a Keplerian decrease of the rotation curve.
We may also mention here that one of us participated to an unprecedented study of the kinematics LMC (Gaia Collaboration 2021, Luri’s paper), which is at 50 kpc. Unless one proves everything that people has done about the LMC and MW is wrong, and that the data are too uncertain to conclude anything about what happens at R=17-25 kpc, the above clarifications about Gaia accuracy are truly necessary for people reading your blog.
2- The argument that the result “violates a gazillion well-established constraints.” has to be taken with some caution, since otherwise, no one can do any progress in the field. In fact, the problem with many probes (so-called “satellites”) in the MW halo, is the fact that one cannot guarantee whether or not their orbits are at equilibrium with the MW potential. This is the reverse for the MW disk, for which stars are rotating in the disk, and, e.g., at 25 kpc, they have likely experience 7-8 orbits since the last merger (Gaia-Sausage-Enceladus), about 9 billion years go. In other words, the mass provided by a system mostly at equilibrium, likely supersedes masses provided by systems that equilibrium conditions are not secured. An interesting example of this is given by globular clusters (GCs). If taken as an ensemble of 156 GCs (from Baumgardt catalog), just by removing Pyxis and Terzan 8, the MW mass inside 50 kpc passes from 5.5 to 2.1 10^11 Msun. This is likely because these two GCs may have come quite recently, meaning that their initial kinetic energy is still contributing to their total energy. A similar mass overestimate could happen if one accounts the LMC or Leo I as MW satellites at equilibrium with the MW potential.
So we agree that near 25 kpc the disk of the MW may show signs of less-equilibrium, or sign of slightly less circular orbits due to different phenomenas discussed in the blog. However, why taking into account objects for which there is no proof they are at equilibrium as being the true measurements?
In our work, we have considerably focused in understanding and expanding the whole contribution of systematics, which may comes from Gaia data, but also from assumptions about stellar profile (i.e., deviations from exponential profiles), from the Sun distance and proper motion and so on. You may find a description in Ou et al.’s Figure 5 and Jiao et al.’s Figure 4, both showing that systematics cannot gives much more than 10% error on circular velocity estimates. This is an area where we are considered by the Local Group community as being quite conservative, and following Gaia specialists with who we have worked to deliver the EDR3 catalog of dwarf galaxy motions (Li, Hammer, Babusiaux et al 2021) up to about 150 kpc. Jiao et al. paper main contribution is the fair accounting of systematics, which analysis shows error bars that are much larger than those from other sources of errors especially in MW outskirts (see Fig. 2).

Francois Hammer, 24 September 2023

The image at top is Fig. 2 from Jiao et al. illustrating their assessment of the rotation curve and its systematic uncertainties.