# Timing Argument take on the Milky Way and Andromeda past-encounter

## TL;DR

This paper uses the Timing Argument to analyze the past encounter possibility between the Milky Way and Andromeda, concluding that such an encounter is unlikely based on mass predictions.

## Contribution

It applies the Timing Argument with a cosmological constant to assess past galaxy encounters, providing new constraints on the Local Group's collision history.

## Key findings

- Predicted mass doubles if past encounter occurred
- Collision likely happened around 8 billion years ago
- Past encounter is ruled out based on mass estimates

## Abstract

The two-body 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 Encounter (PE). PE are possible only for non-zero 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 have had PE, then the predicted mass of the Local Group (LG) should be twice larger. Since the predicted mass is too large, the MW and $M31$ galaxies should have collided at $\sim 8 Gys$. Therefore, the TA analysis show that PE is not possible for the Local Group (LG) system.