Using Velocity Dispersion to Estimate Halo Mass: Is the Local Group in Tension with $\Lambda$CDM?

TL;DR

This study investigates whether the low velocity dispersion observed in the Local Group conflicts with $ ext{Lambda}$CDM predictions, finding that observational biases in measuring dispersion can explain the discrepancy.

Contribution

The paper introduces an optimal window in velocity and distance to accurately estimate halo mass from line-of-sight velocity dispersions, reducing bias in such measurements.

Findings

Line-of-sight velocity dispersion is a biased mass proxy.

An optimal window minimizes scatter in dispersion-mass relation.

The Local Group's dispersion is consistent with $ ext{Lambda}$CDM}.

Abstract

Satellite galaxies are commonly used as tracers to measure the line-of-sight velocity dispersion ($\sigma_{\rm LOS}$) 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 $\sigma\sim$50 km/s, which is surprisingly low when compared to the theoretical expectation of $\sigma\sim$100s km/s for systems of their mass. Does this pose a problem for $\Lambda$CDM? We explore this tension using the {\small{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 $\sigma_{\rm LOS}$ of subhaloes and surrounding haloes. Our results demonstrate that $\sigma_{\rm LOS}$ is biased mass proxy. We define an optimal window in $v_{\rm LOS}$ and projected distance ($D_p$) -- $0.5\lesssim D_p/R_{\rm vir}\lesssim1.0$ and $v_{\rm LOS} \lesssim0.5V_{\rm esc}$, where $R_{\rm vir}$ is the virial radius and $V_{\rm esc}$ is the escape velocity -- such that the scatter in LOS to halo dispersion is minimised - $\sigma_{\rm LOS}=(0.5\pm0.1)\sigma_{v,{\rm H}}$. We argue that this window should be used to measure line-of-sight dispersions as a proxy for mass, as it minimises scatter in the $\sigma_{\rm LOS}-M_{\rm vir}$ relation. This bias also naturally explains the results from \cite{mcconnachie2012a}, who used similar cuts when estimating $\sigma_{\rm LOS,LG}$, producing a bias of $\sigma_{\rm LG}=(0.44\pm0.14)\sigma_{v,{\rm H}}$. We conclude that the Local Group's velocity dispersion does not pose a problem for $\Lambda$CDM and has a mass of $\log M_{\rm LG, vir}/M_\odot=12.0^{+0.8}_{-2.0}$.