Embedded Files
Distinguishing central density cusps from cores with proper motions
We show that measuring the proper motion of 2000 stars within a dwarf galaxy, with an uncertainty of 1 km/s at most, can establish whether the dark matter density profile of the dwarf has a central core or a cusp [1].
We derive these limits by building mock star catalogues that are similar to those expected from future astrometric Theia-like missions and that include celestial coordinates, radial velocity and proper motion of the stars. The density field of the dark matter 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> 2000 stars returns unbiased estimates of the eNFW dark matter parameters within 10% of the true values and with 1σ relative uncertainties <20%.
Figure: MCMC posterior distributions of the parameters of the model with a core, γ = 0, and an isotropic velocity field, β = 0, estimated from a mock sample with N = 2000 stars and no uncertainty on each velocity component of the stars. The shaded areas with increasing darkness show the 99%, 95%, and 68% confidence regions of the posterior distributions, respectively. The black solid stars show the position of the input parameters used to create the mock catalogue. The input parameters are also indicated by the vertical lines in the top panel of each column. The red solid circles with the error bars are the medians of the posterior distributions with their 68% confidence intervals; they are adopted as the estimated values of the parameters and their uncertainty.
Figure: The 1σ confidence interval (upper and lower curves with the same style) of the parameter estimates as a function of the number of stars of the catalogue for models with a core, γ = 0, and three different values of the velocity anisotropy parameter β, as listed in the inset. The red horizontal lines show the input parameters used to create the mock catalogues.
Figure: The 1σ confidence interval (upper and lower curves with the same style) of the parameter estimates as a function of the number of stars of the catalogue for a model with a core, γ = 0, and an isotropic velocity field, β = 0. Different line styles are for different velocity uncertainty, as listed in the inset. The red horizontal lines show the input parameters used to create the mock catalogues.
Our analysis demonstrates that, by estimating the log-slope λ 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 8σ.
Figure: Posterior distributions of the estimated parameters of the DM density profiles of a dwarf model with a cusp (blue shaded areas) or a core (green shaded areas) and velocity anisotropy parameter β = 0. The panel show the posterior distributions derived from mock catalogues with N = 2000 stars. We assume zero uncertainty on the stellar velocity components. The red and black solid stars and the red and black vertical lines indicate the input parameters of the models. The medians and the 68% confidence intervals of the posterior distributions are shown by the red and black dots with error bars.
The measure of the proper motions can thus strongly constrain the distribution of dark matter in nearby dwarfs and provides a fundamental contribution to understanding the nature and the properties of dark matter.
Bibliography
I. De Martino, A. Diaferio, L. Ostorero, "The proper motion of stars in dwarf galaxies: distinguishing central density cusps from cores", 2022, MNRAS, 516, 3556-3568
Page updated
Google Sites
Report abuse