A New Data-Driven Measurement of the Milky Way’s Circular Velocity Curve

Data science extends to the farthest corners of the Galaxy

The circular velocity curve of the Milky Way represents how fast an object would move at a Galactocentric distance (meaning a certain radius from the center of the Galaxy), provided it was on a perfectly circular orbit. It is a measure of the Galaxy’s mass as a function of radius. Most methods of measuring the Milky Way’s circular velocity curve depend strongly on the Sun, and are most precise in the Solar neighborhood. Methods for measuring beyond the Sun’s radius rely on tracing the paths of distant stars and other objects, but these measures are often imprecise, subject to various biases, and based on small numbers of stars to date.

In a new paper, David W. Hogg, Professor of Physics and Data Science, Anna-Christina Eilers and Hans Walter-Rix, Max-Planck-Institute for Astronomy, and Melissa K. Ness, Flatiron Institute and Columbia University, propose a new method for measuring the Milky Way’s circular velocity curve. Their method uses precise phase-space measurements (within ~10% uncertainty) of approximately 23,000 red giant stars at Galactocentric distances between five and twenty-five kiloparsecs (kpc). (A kiloparsec is 1000 parsecs or 3262 light-years.) The measurements come from a data-driven model, derived in another paper co-authored by Hogg, which leverages spectral and photometric datasets from the Sloan Digital Sky Survey and also NASA and ESA to predict the location and movement of the relevant red giant stars — the first wholly data-driven model for predicting or estimating the distances of stars.

The researchers stress the importance of the accuracy of these measurements and explain that their model for red giant stars improves both the precision and accuracy of Milky-Way measurements because the stars in their dataset are both very common and very luminous. They also note that their calculation of the circular velocity at the distance of the Sun (and therefore mass of the Galaxy) has a mere 5% uncertainty. With their dataset, Hogg and collaborators derived this circular velocity measurement from the Jeans equation, which uses the velocity and density distribution of the red giant star population, assuming an axi-symmetric gravitational potential.

The results of their derivation largely agreed with results from previous calculations, although it is much more precise, and the researchers point out that while other calculations find dips in the circular velocity at nine and eleven kiloparsecs, they find no such dips. The mass distribution in the Milky Way looks very smooth, and their measurements of any fluctuations would be precise at the percent level. They were also able to estimate the concentration of dark matter as a function of distance, and according to their calculations the Milky Way is dominated by dark matter past fourteen kiloparsecs from the center of the Galaxy.

Hogg’s work reminds us that data science affects not only the apps we use every day but the farthest reaches of the Galaxy.

By Paul Oliver