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We determine the velocity vector of M31 with respect to the Milky Way and use this to constrain the mass of the Local Group, based on HST proper-motion measurements presented in Paper I. We construct N-body models for M31 to correct the measurements for the contributions from stellar motions internal to M31. We also estimate the center-of-mass motion independently, using the kinematics of satellite galaxies of M31 and the Local Group. All estimates are mutually consistent, and imply a weighted average M31 heliocentric transverse velocity of (v_W,v_N) = (-125.2+/-30.8, -73.8+/-28.4) km/s. We correct for the reflex motion of the Sun using the most recent insights into the solar motion within the Milky Way. This implies a radial velocity of M31 with respect to the Milky Way of V_rad = -109.3+/-4.4 km/s, and a tangential velocity V_tan = 17.0 km/s (<34.3 km/s at 1-sigma confidence). Hence, the velocity vector of M31 is statistically consistent with a radial (head-on collision) orbit towards the Milky Way. We revise prior estimates for the Local Group timing mass, including corrections for cosmic bias and scatter. Bayesian combination with other mass estimates yields M_LG = M_MW(vir) + M_M31(vir) = (3.17 +/- 0.57) x 10^12 solar masses. The velocity and mass results imply at 95% confidence that M33 is bound to M31, consistent with expectation from observed tidal deformations. (Abridged)
We study the future orbital evolution and merging of the MW-M31-M33 system, using a combination of collisionless N-body simulations and semi-analytic orbit integrations. Monte-Carlo simulations are used to explore the consequences of varying the init
We examine the prevalence, longevity, and causes of planes of satellite dwarf galaxies, as observed in the Local Group. We use 14 Milky Way/Andromeda-(MW/M31) mass host galaxies from the FIRE-2 simulations. We select the 14 most massive satellites by
Measuring the escape velocity of the Milky Way is critical in obtaining the mass of the Milky Way, understanding the dark matter velocity distribution, and building the dark matter density profile. In Necib $&$ Lin (2021), we introduced a strategy to
We present several different statistical methods to determine the transverse velocity vector of M31. The underlying assumptions are that the M31 satellites on average follow the motion of M31 through space, and that the galaxies in the outer parts of
We confirm, quantify, and provide a table of the coherent velocity substructure of the Milky Way disk within 2 kpc of the Sun towards the Galactic anticenter, with 0.2 kpc resolution. We use the radial velocities of ~340,000 F-type stars obtained wit