Milky Way and Andromeda pastencounters in different gravity models: the impact on the estimated Local Group mass
Abstract
The Twobody problem of $M31$ and the Milky Way (MW) galaxies with a Cosmological Constant background is studied, with emphasis on the possibility that they experienced Past Encounters. By implementing the Timing Argument (TA), it is shown that if $M{31}$ and the MW have had more than one encounter then the deduced mass of the Local Group (LG) would be larger. Past encounters are possible only for nonzero transverse velocity, and their viability is subject to observations of the imprints of such near collisions. Using a recent $Gaia$  based measurement of the transverse velocity we show that the presence of the Cosmological Constant requires the mass for the LG to be $35\%$ higher: $3.36^{+1.14}_{0.70} \cdot 10^{12} M_{\odot}$ with no Cosmological Constant or $4.54^{+1.20}_{0.75} \cdot 10^{12} M_{\odot}$ with a Cosmological Constant background. If the LG has had one past encounter, the LG mass is $9.99^{+2.22}_{1.58}\cdot 10^{12} M_{\odot}$ with a Cosmological Constant background. Modified Newtonian Dynamics (MOND) is studied as the accelerations of the Local Group are fully in the deepMOND regime. MOND yields the order of magnitude for the expected baryonic mass only if at least one encounter occurred. While we only consider the LG as two point masses, our calculations provide a benchmark for future work with simulations to test Dynamical Friction and other effects. This model can be also used to test screening mechanisms and alternative theories of gravity.
 Publication:

arXiv eprints
 Pub Date:
 April 2019
 arXiv:
 arXiv:1904.03153
 Bibcode:
 2019arXiv190403153B
 Keywords:

 Astrophysics  Astrophysics of Galaxies;
 Astrophysics  Cosmology and Nongalactic Astrophysics;
 General Relativity and Quantum Cosmology;
 High Energy Physics  Phenomenology
 EPrint:
 16 pages. A revised version