Timing argument take on the Milky Way and Andromeda past encounter

¹ Frankfurt Institute for Advanced Studies, Ruth-Moufang-Strasse 1, 60438 Frankfurt am Main, Germany
e-mail: benidav@post.bgu.ac.il
² Physics Department, Ben-Gurion University of the Negev, Beer-Sheva 84105, Israel
³ Kavli Institute of Cosmology (KICC), University of Cambridge, Madingley Road, Cambridge CB3 0HA, UK
⁴ DAMTP, Centre for Mathematical Sciences, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, UK

Received: 26 August 2021
Accepted: 17 September 2021

Abstract

The two-body problem of the M 31 and Milky Way (MW) galaxies with a cosmological constant background is studied, with an emphasis on the possibility that they experienced a past encounter (PE). Past encounters are possible only for a nonzero transverse velocity, and their viability is subject to observations of the imprints of such near collisions. By implementing the timing argument (TA) for two isolated point bodies, it is shown that if M 31 and the MW had experienced a PE, then the predicted mass of the Local Group (LG) would be twice larger. This predicted mass is too large and implies that the MW and M 31 galaxies would have collided at ∼8 Gys. Therefore, the TA analysis shows that a PE is not possible for the LG system.