# Mass loss through the L2 Lagrange point - Application to Main Sequence EMRI

## TL;DR

This paper investigates stable mass transfer in extreme mass ratio binaries, highlighting the role of L2 mass loss in gravitational wave signals from systems like a main-sequence star and a supermassive black hole, with implications for future detections.

## Contribution

It provides an analytical estimate of L2 mass leakage and explores its impact on gravitational wave signals, a novel aspect in modeling such binary systems.

## Key findings

- Mass leakage through L2 can be comparable to L1 transfer under certain conditions.
- L2 mass loss can accelerate the evolution of gravitational wave signals.
- L2 ejection significantly affects the gravitational wave signal's frequency and amplitude evolution.

## Abstract

We consider stable mass transfer from the secondary to the primary of an extreme mass ratio binary system. We show that when the mass transfer is sufficiently fast, mass leakage occurs through the outer Lagrange point L2, in addition to the usual transfer through L1. We provide an analytical estimate for the mass leakage rate through L2 and find the conditions in which it is comparable to the mass transfer rate through L1. Focusing on a binary system of a main-sequence star and a super-massive black hole, driven by the emission of gravitational radiation, we show that it may sustain stable mass transfer, along with mass loss through L2. If such a mass-transferring system occurs at our Galactic Centre, it produces a gravitational wave signal detectable by future detectors, such as eLISA. The signal evolves according to the star's adiabatic index and cooling time. For low mass stars, the evolution is faster than the Kelvin-Helmholtz cooling rate driving the star out of the main-sequence. In some cases, the frequency and amplitude of the signal may both decrease with time, contrary to the standard chirp of a coalescing binary. Mass loss through L2, when occurs, decreases the evolution timescale of the emitted gravitational wave signal by up to a few tens of per cent. We conclude that L2 mass ejection is a crucial factor in analyzing gravitational waves signals produced by such systems.