# How Do You Weigh a Galaxy?

Authors: Laura L. Watkins, Roeland P. Van Der Marel, Sangmo Tony Sohn, and N. Wyn Evans

First Author’s Institution: University of Chicago

Status: Published in ApJ, open access on the arXiv

We can’t put it on a digital scale, we can’t hang it on a balance and compare it against something else, so how does one measure the mass of our home galaxy? The authors of today’s paper use measurements of globular clusters in the halo of the galaxy taken from the Gaia satellite to estimate a mass for the Milky Way.

### What Is Our Galaxy Made of and Why Should We Weigh It?

Our galaxy contains four major parts: the bulge, the disk (which contains the thin disk and the thick disk), the bar, and the halo (see Figure 1). The first three components are made up of baryons, particles that make up protons and neutrons and therefore most of the things around us. The halo, however, is dominated by dark matter, and the percentage of baryonic mass in the halo depends on how much dark matter there is. Dark matter is a mysterious substance that pervades the galaxy, interacting strongly with gravity and weakly with light. We know dark matter is there because of the rotation curve of the galaxy; if the mass was concentrated at the center, the velocity of the outer regions would be slower than the inner regions. In the case of the Milky Way, we see that the rotational velocity stays fairly constant all the way out, which points to some unseen matter being present (matter which we identify as dark matter). Because of its weak interactions with light, it can be really tough to measure the amount of dark matter, and thus how much it weighs. Therefore, calculating a mass of the dark matter in the halo would be a big step in obtaining the mass of the galaxy.

Measuring the mass of our galaxy is very useful for two reasons: first, because the mass of the galaxy and its distribution are linked to the formation and growth of our Universe. Accurately determining the mass will help us understand where our galaxy sits on the scale of the cosmos. Second, it helps us learn about the dynamical history and future of the Local Group and the satellite population (specifically stellar streams).

### How to Weigh a Galaxy

The estimate of the mass of a galaxy is dependent on many things, including which satellites are bound and how long they have been that way, the shape of the Milky Way, and the method used for analysis. Three techniques have been mainly used to measure the mass of the galaxy: the timing argument, abundance-matching studies, and dynamical methods. The timing argument measures the speed at which two galaxies are approaching each other and uses those dynamics to predict a mass. Abundance-matching studies uses the number of galaxies versus their circular velocity and the Tully-Fischer relation to obtain their luminosity, which can be used to estimate their mass. Finally, dynamical methods look at the velocity of tracer objects such as globular clusters; any mass distribution gives rise to a gravitational potential that causes objects to move, so by studying the motions of the objects, we can work backwards to recover the gravitational potential, and thus the mass. The authors of today’s paper use this dynamical method to measure the mass of the Milky Way.

### Using Gaia to Map Motions

The team used data from the Gaia mission’s 2nd data release (DR2) to measure the proper motions of stars, or how they are moving across the sky. Gaia is a space-based instrument whose goal is to make a 3D map of the galaxy, and this data release contained measurements for billions of stars and 75 globular clusters. The Gaia satellite is so precise that it can measure a human hair’s width at 1000 km, which is a resolution 1000-2000x smaller than that of the Hubble Space Telescope! Figure 2 shows just how many sources Gaia has measured. In DR2, they released. (Check out this really cool video on Gaia to learn more about this amazing satellite!)  Out of the 75 globular clusters released on DR2, the authors used 34 of them that spanned a range of 2.0 kiloparsecs (kpc) to 21.1 kiloparsecs from the center of the galaxy, which allowed them to measure out to the outer halo.

In order to map the mass of the galaxy correctly, they need parameters like velocity anisotropy (which measures how the motions of stars vary in different directions), the density of the galaxy, and the potential of the galaxy. The team uses an NFW model, which is a model for how the density is distributed within the galaxy, to describe the potential of the galaxy. The authors then run simulations to determine the radius inside which particles are gravitationally bound to each other (the virial radius) and the mass contained inside the virial radius (the virial mass). By varying the virial parameters and sampling different models of the halo, the team was able to figure out the most probable mass of the galaxy. In addition, they use the velocities of the stars to map the circular velocity of the galaxy out to the radius of the farthest globular cluster. Figure 3 shows the potential of the different components of the galaxy and the results of varying the virial parameters of the halo.

### Evidence for an Intermediate Mass Milky Way

The authors find that the mass of the galaxy is 0.21 x $10^{12}$ solar masses, the circular velocity of the galaxy at the maximum radius they look at (21.1 kpc) to be 206 km/s, and the virial radius to be 1.28 x $10^{12}$ solar masses. This virial mass fits in most with intermediate values found by other studies. The circular velocity measurement the authors made indicates that the velocity is fairly constant in the outer regions, supporting the idea that dark matter is present in our galaxy. Some of the clusters the team used for measurements are on very radial or very tangential orbits, which could have been the result of galactic collisions. If they remove these clusters, the mass and velocity measurements are still within their error bars, showing that these estimates are robust even if there are substructures of globular clusters in the galaxy.

The amazing wealth of data from the Gaia mission has allowed the team to make one of the most precise estimates of the mass of the galaxy that has ever been done. As Gaia continues its mission over the next few years, it will obtain positions and velocities of even more clusters, paving the way for more robust studies of the mass of our galaxy.