Broken Expectations: The Effects of Modelling Assumptions on the Inferred Dark Matter Distribution in the Milky Way's Satellites

Abstract

The spherical Jeans equation is commonly used to infer dark matter distributions in dwarf spheroidal satellites of the Milky Way to constrain the nature of dark matter. One of its assumptions is that of dynamical equilibrium while the dwarfs are under the influence of Galactic tides. We carry out tailored simulations of Carina, Draco, Fornax, Sculptor and Ursa Minor and test the accuracy of dark matter density profiles and annihilation rates (J-factors) recovered with the Jeans analysis code pyGravSphere. We find that tides do not significantly affect the quality of density profile inference; however, pyGravSphere tends to underestimate the inner densities of dwarf galaxies, which, together with tidal mass loss, leads to an inference of flatter density slopes, although all of our dwarfs have cuspy Navarro-Frenk-White haloes. This is because the default broken power-law model is unable to describe the outer halo density profile. The recovered J-factors are generally underestimated. While the difference with the true J-factor is small, the error bars are also often underestimated. We also test the accuracy of the Wolf et al. 2010 mass estimator and find that it can be sensitive to orbital stage and eccentricity. Still, for our sample of dwarf galaxies, the estimates agree with the truth within 10 percent. Consistency of our simulated dwarfs with the mass-concentration relation in LambdaCDM requires a light Milky Way, or limited action of tides, which may be in tension with a "tidal stirring" origin of dwarf spheroidals.

Figures (16)

• Figure 1: Top: initial masses and concentrations of dSphs in the light and heavy Milky Way potentials, after utilising an iterative procedure based on that from Iorio_2019, which produces snapshots of dSphs at the present day that match the properties of dSphs from observations. The black dashed line and the shaded band are the mass-concentration relation at $z=0$ from Ludlow_2016 and the 0.1 dex errors dutton_maccio. Dwarf galaxies in the 'heavy' and 'light' Milky Way potential are identified in the legend. The blue dashed line and shaded band show the mass-concentartion relation from the dark-matter-only simulations of wang_bose. Bottom: the relation between the concentration parameter, $c_V$, and the maximum circular velocity, $V_{\rm max}$ measured for satellites from cosmological simulations in moline. The grey curves show the average relation for subhaloes of a given $x_{\rm sub}$ range. Colour symbols show our sample of simulated dwarf spheroidals, for which the values of $x_{\rm sub}$ are shown in the legend. The black error bar shows the error in $c_V\approx0.28$ dex at the mass scale of Draco, calculated in massari_draco and is representative of the typical error in the $c_V-V_{\rm max}$ relation in the mass range of our simulated dwarfs.
• Figure 2: Snapshots in the 'light' Milky Way potentials of the dSphs at present day. Black shows the distribution of dark matter and orange the stars. Bound particles, as identified with SUBFIND, are shown in red. Green is the expected (galpy) orbit and magenta is the orbit computed from the centre-of-mass of the bound particles of the dSphs. The Milky Way potential is not depicted here but is centred at the origin.
• Figure 3: Comparison of the present-day surface density (top panels) and line-of-sight velocity dispersion profiles (bottom panels) for Fornax, Carina and Draco in the 'heavy' (solid lines) and the 'light' potential (dashed lines) compared to observational data (dot-dashed lines). The projected radius limit is determined by the extent of the observational data. The shaded bands correspond to Poisson errors in the surface density and Poisson errors combined with measurement errors for the line-of-sight velocity dispersion (2 kms$^{-1}$ measurement errors were assumed for the simulated data). Additionally shown here are the projected half-light radii obtained from fitting a Plummer profile and the corresponding line-of-sight velocity dispersion within the half-light radius from simulations (dotted dark and light green lines and error bars) and observations (purple dotted lines and error bars). The solid purple lines in the top panel show the best-fitting Plummer profiles to the observational data. The observational photometric and kinematic data in this figure and Fig. \ref{['fig:today_obs_comp2']} were obtained from carina_photokoposov_2014flewellingursa_min_stellarfornax_stellardraco_stellar.
• Figure 4: Same as Fig. \ref{['fig:today_obs_comp']}, but for Sculptor and Ursa Minor.
• Figure 5: Left: Ratios of the masses within the projected half-mass radii of the stellar populations computed with the '2-D Wolf' estimator with the true masses within the 3-D half-mass radii. The ratios are shown for the present-day snapshots as well as nearest apocentre and pericentre snapshots in both the 'light' and 'heavy'Milky Way potentials. We average over all $\pm150$ Myr snapshots at each point. The errors were estimated from the Poisson error on the velocity dispersion within the half-light radius and the error on the Plummer profile $a$ fit, as well as the Poisson error on the mass enclosed within the 3-D half-mass radius. Right: The same as the left, but the 2-D Wolf masses are instead computed using the half-mass radius directly obtained from the cumulative mass distribution of the bound particles (using projected radii) and using the mean line-of-sight velocity dispersion within the projected half-mass radius.