Applying scale-free mass estimators to the Local Group in Constrained Local Universe Simulations

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We use the recently proposed scale-free mass estimators to determine the masses of the Milky Way (MW) and Andromeda (M31) galaxy in a dark matter only Constrained Local UniversE Simulation (CLUES). While these mass estimators work rather well for isolated spherical host systems, we examine here their applicability to a simulated binary system with a unique satellite population similar to the observed satellites of MW and M31. We confirm that the scale-free estimators work also very well in our simulated Local Group galaxies with the right number of satellites which follow the observed radial distribution. In the isotropic case and under the assumption that the satellites are tracking the total gravitating mass, the power-law index of the radial satellite distribution $N(<r)\propto r^{3-\gamma}$ is directly related to the host's mass profile $M(<r)\propto r^{1-\alpha}$ as $\alpha=\gamma-2$. The use of this relation for any given $\gamma$ leads to highly accurate mass estimations which is a crucial point for observer, since they do not know a priori the mass profile of the MW and M31 haloes. We discuss possible bias in the mass estimators and conclude that the scale-free mass estimators can be satisfactorily applied to the real MW and M31 system.