Systematics in virial mass estimators for pressure-supported systems

Abstract

Mass estimators are a key tool to infer the dark matter content in pressure-supported systems like dwarf spheroidal galaxies (dSphs). We construct an estimator for enclosed masses based on the virial theorem which is insensitive to anisotropy in the velocity dispersion and tailored to yield masses with minimum uncertainty introduced by our ignorance on (i) the shape of the inner halo profile, and (ii) how deeply the stellar component is embedded within the halo: $M(<1.8\,R_\mathrm{h}) \approx 3.5 \times 1.8\,R_\mathrm{h} \langle \sigma_\mathrm{los}^2 \rangle G^{-1}$, where by $R_\mathrm{h}$ we denote the projected half-light radius and by $\langle \sigma_\mathrm{los}^2 \rangle$ the luminosity-averaged squared line-of-sight velocity dispersion. Tests against controlled simulations show that this estimator provides unbiased enclosed masses with an accuracy of $\sim 10$ per cent. This confirms the robustness of similar previously proposed mass estimators. Application to published kinematic data of Milky Way dSphs reveals a tight correlation between enclosed mass and luminosity. Using $N$-body models we show that tidal stripping has little effect on this relation. Comparison against cuspy and cored dark matter haloes extracted from controlled re-simulations of the Aquarius A2 merger tree shows that the high mass densities of ultrafaint galaxies are not compatible with large dark matter cores, and that the (total) halo masses of the classical Milky Way dSphs span a remarkably narrow range ($8 \lesssim \mathrm{log_{10}}\,(M/\mathrm{M_\odot}) \lesssim 10$) at present, showing no clear trend with either galaxy size or luminosity.