The proper motion of stars in dwarf galaxies: distinguishing central density cusps from cores

TL;DR

Measuring proper motions of around 2000 stars in dwarf galaxies with 1 km/s accuracy can decisively determine whether their dark matter density profiles have a central core or cusp, greatly advancing our understanding of dark matter distribution.

Contribution

This study demonstrates that proper motion data from future astrometric missions can reliably distinguish between core and cusp dark matter profiles in dwarf galaxies, improving parameter estimates significantly.

Findings

Proper motions help break degeneracies in dark matter profile parameters.

A sample of 2000 stars can distinguish core vs cusp at over 8 sigma.

Uncertainties in mass profile estimates decrease with larger star samples.

Abstract

We show that measuring the proper motion of ${{\sim 2000}}$ stars within a dwarf galaxy, with an uncertainty of 1 km/s at most, can establish whether the Dark Matter (DM) density profile of the dwarf has a central core or cusp. We derive these limits by building mock star catalogues similar to those expected from future astrometric {\it Theia}-like missions and including celestial coordinates, radial velocity and proper motion of the stars. The density field of the DM halo of the dwarf is sampled from an extended Navarro-Frank-White (eNWF) spherical model, whereas the number density distribution of the stars is a Plummer sphere. The velocity field of the stars is set according to the Jeans equations. A Monte Carlo Markov Chain algorithm applied to a sample of $N\gtrsim 2000$ stars returns unbiased estimates of the eNFW DM parameters within $10\%$ of the true values and with $1\sigma$ relative uncertainties $\lesssim 20$\%. The proper motions of the stars lift the degeneracy among the eNFW parameters which appears when the line-of-sight velocities alone are available. {Our analysis demonstrates that, by estimating the log-slope of the mass density profile estimated at the half-light radius, a sample of $N=2000$ stars can distinguish between a core and a cusp at more than $8\sigma$.} Proper motions also return unbiased estimates of the dwarf mass profile with $1\sigma$ uncertainties that decrease, on average, from 2.65 dex to 0.15 dex when the size of the star sample increases from $N=100$ to $N=6000$ stars. The measure of the proper motions can thus strongly constrain the distribution of DM in nearby dwarfs and provides a fundamental contribution to understanding the nature and the properties of DM.