{
  "id": "2208.14110",
  "version": "v1",
  "published": "2022-08-30T09:47:06.000Z",
  "updated": "2022-08-30T09:47:06.000Z",
  "title": "The proper motion of stars in dwarf galaxies: distinguishing central density cusps from cores",
  "authors": [
    "Ivan de Martino",
    "Antonaldo Diaferio",
    "Luisa Ostorero"
  ],
  "comment": "14 pages, 10 Figures and 5 Tables. Accepted for publication on MNRAS",
  "doi": "10.1093/mnras/stac2336",
  "categories": [
    "astro-ph.GA"
  ],
  "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.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-08-30T09:47:06.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "proper motion",
      "distinguishing central density cusps",
      "dwarf galaxy",
      "mock star catalogues similar",
      "monte carlo markov chain algorithm"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}