Using velocity dispersion to estimate halo mass: Is the Local Group in tension with ΛCDM?

Satellite galaxies are commonly used as tracers to measure the line-of-sight (LOS)velocity dispersion (σLOS) 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 (∧CDM)? 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 σLOS of subhaloes and surrounding haloes. Our results demonstrate that σLOS is biased mass proxy. We define an optimal window in νLOS and projected distance (Dp) - 0.5 ≲ Dp/Rvir ≲ 1.0 and νLOS ≲ 0.5Vesc, where Rvir is the virial radius and Vesc is the escape velocity - such that the scatter in LOS to halo dispersion is minimized - σLOS = (0.5 ± 0.1)σν, H. We argue that this window should be used to measure LOS dispersions as a proxy for mass, as it minimises scatter in the σLOS-Mvir relation. This bias also naturally explains the results from McConnachie (2012), who used similar cuts when estimating σLOS, LG, producing a bias of σLG = (0.44 ± 0.14)σν, H. We conclude that the Local Group's velocity dispersion does not pose a problem for ∧CDM and has a mass of logMLG,vir/M∡ = 12.0-2.0+0.8. [ABSTRACT FROM AUTHOR]