# Kinematics of Mass Loss from the Outer Lagrange Point L2

## TL;DR

This paper analyzes the kinematics of mass loss from the L2 point in binary systems, revealing how initial conditions influence whether material escapes, forms a disk, or impacts the binary, aiding interpretation of simulation results.

## Contribution

It provides a detailed characterization of particle trajectories near L2, highlighting the effects of initial velocities and offsets on mass loss outcomes in binary systems.

## Key findings

- Unbound outflows can occur even with initial velocities below corotation.
- Trajectory outcomes depend on initial position offsets and velocity vectors.
- Results help interpret hydrodynamic simulation morphologies.

## Abstract

We investigate kinematics of mass loss from the vicinity of the second Lagrange point L2 with applications to merging binary stars, common envelope evolution and the associated transient brightenings. For ballistic particle trajectories, we characterize initial velocities and positional offsets from L2 which lead to unbound outflow, fall back followed by a formation of a decretion disk, collision with the binary surface, or a hydrodynamic shock close to the binary, where some particle trajectories loop and self-intersect. The latter two final states occur only when the trajectories are initiated with offset from L2 or with velocity vector different from corotation with the binary. We find that competition between the time-dependent and steeply radially decreasing tidal torques from the binary, Coriolis force and initial conditions lead to a non-trivial distribution of outcomes in the vicinity of L2. Specifically, even for initial velocities slower than corotation, we find that a set of initial position offsets lead to unbound outflows. Our results will aid in the interpretation of the morphology of mass loss streams in hydrodynamic simulations.