Properties of the M31 halo spectroscopic sample. (a) Surface brightness profile of M31's stellar halo based on counts of spectroscopically confirmed M31 red giants (Gilbert et al. 2012). (b) Likelihood distribution of the 4721 stars in the spectroscopic sample (blue histogram). Stars with L_i >0 are more likely to be M31 red giants (dashed histogram), while stars with L_i <0 are more likely to be MW dwarf stars; the two populations present a clear bimodal distribution in likelihood space. The analysis presented here is restricted to stars with L_i >0.5 (black histogram), which are three times more probable to be M31 RGB stars than MW dwarf stars. (c) Velocity distribution of stellar sources in the spectroscopic sample. Line types are the same as in panel (b). M31's systemic velocity is v_M31 = −300 km s⁻¹.