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:where by R h we denote the projected half-light radius and by σ 2 los 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 ∼ 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 log 10 (M/M ) 10) at present, showing no clear trend with either galaxy size or luminosity.

Can tides disrupt cold dark matter subhaloes?

“…Furthermore, we fit a power-law r max ∝ M κ max to the subhalo mass-size evolution. The fitted slope κ = 0.415 ± 0.001 is lower than the value found in Errani et al (2018) from an average of re-simulations of the Aquarius A2 merger tree (κ ≈ 0.48). This may be related to strong disc shocking of our subhalo model experienced due to the particularly low pericentre distance (r peri ≈ 2.5 kpc), potentially heating up the subhalo, affecting its mass-size evolution.…”

“…The subhalo therefore has increasing multiples of its dynamical time to relax and reach equilibrium between subsequent tidal interactions. In contrast, κ → 0 for cored subhaloes as the r max evolution flattens off (Errani et al 2018), and t c (r max ) increases during tidal stripping.…”

“…This is shown for subhaloes of initial mass M 0 = 10 8 M and scale radius a 0 = 0.5 kpc (solid lines). For cuspy (cored) profiles, tidal stripping decreases (increases) t c (r) at fixed fractions r/a of the scale radius: dashed (dotted) lines are computed using the Errani et al (2018) tidal tracks (measured from controlled simulations) and show t c (r) when the subhalo has been tidally stripped to a remnant mass fraction of M/M 0 = 1/10 (1/50). An orbital period of T orb = 0.5 Gyrs within the host halo is shown as guidance for the time available for the subhalo to reach dynamical equilibrium between two pericentre passages.…”

“…The evolution of r max is highly sensitive to the spatial resolution of the simulation and artificially flattens off once the simulation fails to resolve the subhalo peak circular velocity. Tidal evolutionary tracks(Errani et al 2018) for cuspy and cored subhaloes are shown as a reference. Dashed curves show fits of equation 6 to the mass evolution (top panel) and the predicted r max evolution assuming power-law scaling r max ∝ M κ max (bottom panel).…”

Fornax globular cluster distributions: implications for the cusp-core problem

“…The data points correspond to the mass estimates by Walker &Peñarrubia (2011) for two chemically distinct sub-populations. There are other mass estimators for Fornax (Amorisco et al 2013;Errani, Peñarrubia & Walker 2018). Plots of density profiles are illustrated in Figure 2.…”