Satellite galaxies are commonly used as tracers to measure the line-of-sight velocity dispersion ( \sigma _ { 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 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 _ { LOS } of subhaloes and surrounding haloes .
Our results demonstrate that \sigma _ { LOS } is biased mass proxy .
We define an optimal window in v _ { LOS } and projected distance ( D _ { p } ) – 0.5 \lesssim D _ { p } / R _ { vir } \lesssim 1.0 and v _ { LOS } \lesssim 0.5 V _ { 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 minimised - \sigma _ { LOS } = ( 0.5 \pm 0.1 ) \sigma _ { v, { 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 _ { LOS } - M _ { vir } relation .
This bias also naturally explains the results from ( ) , who used similar cuts when estimating \sigma _ { LOS,LG } , producing a bias of \sigma _ { LG } = ( 0.44 \pm 0.14 ) \sigma _ { v, { 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 _ { LG,vir } / M _ { \odot } = 12.0 ^ { +0.8 } _ { -2.0 } .