Thread by @DudeDarkmatter

Who wants to hear about our Galaxy, the Milky Way?
I’m slowly recovering from jet lag induced from visiting Bonn for a conference last week. As it happened, a paper was accepted while there. Managed to post it on the arXiv from the hotel, but haven’t had time to talk about it.

Our home Galaxy is a normal spiral galaxy. So I wondered what we might learn by putting it in that context with known scaling relations for external spirals like the radial acceleration relation (RAR; see, e.g., arxiv.org/abs/1909.02011).

Quite a lot, as it turns out.

I started this a few years ago with arxiv.org/abs/1511.06387 in which I used the RAR to infer the surface density profile of the Milky Way from the observed terminal velocities. Which is to say, one can figure out where the mass is based on how things move. In considerable detail.

There are bumps & wiggles in the terminal velocities that correspond to bumps & wiggles in the mass profile. These are spiral arms. The locations of the spirals indicated by the kinematics correspond well to their locations as traced by GMCs (blue points) and HII regions (red).

Sorry for the jargon: hit the character limit. GMCs are giant molecular clouds where stats form. HII regions are sites of recent star formation. Both congregate and trace the spiral arms.

One uncertainty in this exercise is the absolute size of the Milky Way. I had assumed a reasonable value, but recently the GRAVITY collaboration provided a much more accurate value from relativistic effects on the orbit of a star that passed close to the MW’s central black hole.

That was cool. And useful, as having the distance the center of the Galaxy allows me to estimate its stellar mass: 62 billion times the mass of the sun. That’s a lot more stars in the Milky Way than there are people on Earth. But fairly typical for a bright “~L*” spiral galaxy.

This change to the size was a minor tweak to the 2016 work, so I just wrote a short note about it (arxiv.org/abs/1808.09435). Thought I was done with it, but then a nice rotation curve extending much further out was reported by Eilers et al. (arxiv.org/abs/1810.09466).

That was nifty because the terminal velocities only trace interior to the solar circle (< 8 kpc). Eilers et al. trace the rotation curve out to over 20 kpc! The model I built was only got to small radii, but it makes a prediction out to larger radii. So their data provide a test.

One of the things they found surprising was a gradient in outer rotation speed of a mild -1.7 km/s/kpc. I could query the model to see what it predicted over the same range of radii. The answer? -1.7 km/s/kpc. Spot on. (Both have a formal uncertainty of +/- 0.1 km/s/kpc).

Here is the model rotation curve (blue line) along with the data to which it was fit (light grey points) and the data of Eilers et al. (black points going much farther out). That’s a big extrapolation of a model fit to R < 8 kpc, but it works remarkably well.

The agreement between the Eilers data and the data to which the model was fit is not all that good over the range where they overlap. I got curious about this, & to make a long story short, it is all in the assumptions. There’s a term in the Jeans equation that one has to assume.

The usual assumption is a smooth “exponential disk” (red dotted line). But I have a model for this, complete with bumps and wiggles (blue line). So what happens if I use that to estimate the term for the logarithmic density gradient in the Jeans equation?

It fixes the discrepancy, that’s what. Here is a zoom in on the affected region. Gray points are the terminal velocities to which I had fit the blue line. Red points are the Eilers data with the exponential assumption. While close, red does not overlap with grey as it should.

The modest but formally significant discrepancy is reconciled if instead we use the model with bumps & wiggles (black and green points - 2 different realizations). So the Milky Way has stricture. It matters. And it works to take the Jeans equation literally.

One lesson I take from this is that we have reached a level of precision that formerly reasonable assumptions (like exponential disks) are no longer adequate. We need nonparametric numerical models going forward. Which is probably a good point at which to move on...