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Register a new userUsing Velocity Dispersion to Estimate Halo Mass: Is the Local Group in Tension with $Lambda$CDM?
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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 halos mass. Recent observational dispersion estimates of the Local Group, including the Milky Way and M31, suggest $sigmasim$50 km/s, which is surprisingly low when compared to the theoretical expectation of $sigmasim$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 galaxys 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 ($D_p$) -- $0.5lesssim D_p/R_{rm vir}lesssim1.0$ 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 - $sigma_{rm LOS}=(0.5pm0.1)sigma_{v,{rm H}}$. 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 $sigma_{rm LG}=(0.44pm0.14)sigma_{v,{rm H}}$. We conclude that the Local Groups velocity dispersion does not pose a problem for $Lambda$CDM and has a mass of $log M_{rm LG, vir}/M_odot=12.0^{+0.8}_{-2.0}$.
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We present a new method for embedding a stellar disc in a cosmological dark matter halo and provide a worked example from a {Lambda}CDM zoom-in simulation. The disc is inserted into the halo at a redshift z = 3 as a zero-mass rigid body. Its mass and size are then increased adiabatically while its position, velocity, and orientation are determined from rigid-body dynamics. At z = 1, the rigid disc is replaced by an N-body disc whose particles sample a three-integral distribution function (DF). The simulation then proceeds to z = 0 with live disc and halo particles. By comparison, other methods assume one or more of the following: the centre of the rigid disc during the growth phase is pinned to the minimum of the halo potential, the orientation of the rigid disc is fixed, or the live N-body disc is constructed from a two rather than three-integral DF. In general, the presence of a disc makes the halo rounder, more centrally concentrated, and smoother, especially in the innermost regions. We find that methods in which the disc is pinned to the minimum of the halo potential tend to overestimate the amount of adiabatic contraction. Additionally, the effect of the disc on the subhalo distribution appears to be rather insensitive to the disc insertion method. The live disc in our simulation develops a bar that is consistent with the bars seen in late-type spiral galaxies. In addition, particles from the disc are launched or kicked up to high galactic latitudes.
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