2018MNRAS.477..616E

Satellite galaxies are commonly used as tracers to measure the line-of-sight (LOS)velocity dispersion (σ_LOS) of the dark matter halo associated with their central galaxy, and thereby to estimate the halo's mass. Recent observational dispersion estimates of the Local Group, including the Milky Way and M31, suggest σ ∼50 km s^–1, which is surprisingly low when compared to the theoretical expectation of σ ∼100 km s^–1 for systems of their mass. Does this pose a problem for Lambda cold dark matter (ΛCDM)? We explore this tension using the SURFS suite of N-body simulations, containing over 10000 (sub)haloes with well tracked orbits. We test how well a central galaxy's host halo velocity dispersion can be recovered by sampling σ_LOS of subhaloes and surrounding haloes. Our results demonstrate that σ_LOS is biased mass proxy. We define an optimal window in v_LOS and projected distance (D_p) - 0.5 <= D_p/R_vir <= 1.0 and v_LOS <= 0.5V_esc, where R_vir is the virial radius and V_esc is the escape velocity - such that the scatter in LOS to halo dispersion is minimized - σ_LOS = (0.5 ± 0.1)σ_v, H_. We argue that this window should be used to measure LOS dispersions as a proxy for mass, as it minimises scatter in the σ_LOS-M_vir relation. This bias also naturally explains the results from McConnachie (2012), who used similar cuts when estimating σ_LOS, LG_, producing a bias of σ_LG = (0.44 ± 0.14)σ_v, H_. We conclude that the Local Group's velocity dispersion does not pose a problem for ΛCDM and has a mass of logM_ LG, vir_/M☉_=12.0+0.8^_–2.0.