The caustic technique uses galaxy redshifts alone to measure the escape velocity and mass profiles of galaxy clusters to clustrocentric distances well beyond the virial radius, where dynamical equilibrium does not necessarily hold. We provide a detailed description of this technique and analyse its possible systematic errors. We apply the caustic technique to clusters with mass M_200>=10^{14}h^{-1} M_sun extracted from a cosmological hydrodynamic simulation of a LambdaCDM universe. With a few tens of redshifts per squared comoving megaparsec within the cluster, the caustic technique, on average, recovers the profile of the escape velocity from the cluster with better than 10 percent accuracy up to r~4 r_200. The caustic technique also recovers the mass profile with better than 10 percent accuracy in the range (0.6-4) r_200, but it overestimates the mass up to 70 percent at smaller radii. This overestimate is a consequence of neglecting the radial dependence of the filling function F_beta(r). The 1-sigma uncertainty on individual escape velocity profiles increases from ~20 to ~50 percent when the radius increases from r~0.1 r_200 to ~4 r_200. Individual mass profiles have 1-sigma uncertainty between 40 and 80 percent within the radial range (0.6-4) r_200. We show that the amplitude of these uncertainties is completely due to the assumption of spherical symmetry, which is difficult to drop. Alternatively, we can apply the technique to synthetic clusters obtained by stacking individual clusters: in this case, the 1-sigma uncertainty on the escape velocity profile is smaller than 20 percent out to 4 r_200. The caustic technique thus provides reliable average profiles which extend to regions difficult or impossible to probe with other techniques.
The Need for Speed: Escape velocity and dynamical mass measurements of the Andromeda galaxy
我们最近的大宇宙学邻居仙女座星系（M31）是一个动力系统，精确测量它的总质量对于我们理解它的组装历史、卫星星系的生命周期以及它在塑造本星系群环境中的作用至关重要。在这里，我们采用一种新的方法来确定M31的动力学质量，使用高速行星状星云（PNe），建立一个分层贝叶斯模型与一个计划，以捕捉潜在的离群值和边缘化的示踪剂未知的距离。由此，我们得到了M31的逃逸速度运行作为银河中心距离的函数，参数和非参数的方法。我们确定M31的逃逸速度为$470\pm{40}$ km s $^{-1}$，在银河系中心距离为15 kpc，还导出了M31的总势，估计银河系的维里质量和半径分别为$0.8\pm{0.1}\times10^{12}\,M_\odot$和$240\pm{10}$ kpc。我们的M31质量处于测量范围的低侧，这支持了从时间和动量参数出发的M31-银河系较低的预期质量，满足$10\lesssim R/\textrm{kpc}<35$之间的圆速度HI约束，并与恒星质量Tully-Fisher关系相一致。为了将这些结果放在更广泛的背景下，我们将它们与$Λ{\rm CDM}$宇宙学范式的关键预测进行比较，包括恒星质量晕质量和暗物质晕浓度维里质量相关性，并发现它是这种关系的异常值。
