# Gravitational wave emission from unstable accretion discs in tidal disruption events

## TL;DR

This paper investigates gravitational wave emissions from unstable accretion disks formed after tidal disruption events, estimating their detectability by LISA through analytical and numerical methods.

## Contribution

It provides the first combined analytical and numerical analysis of gravitational waves from unstable accretion disks post-tidal disruption, highlighting potential detectability.

## Key findings

- Numerical strain measurements are two orders of magnitude lower than analytical estimates.
- Disks affected by the Papaloizou-Pringle instability could be detectable by LISA in certain scenarios.
- Analytical estimates suggest possible gravitational wave signals from these disks.

## Abstract

Gravitational waves can be emitted by accretion discs if they undergo instabilities that generate a time varying mass quadrupole. In this work we investigate the gravitational signal generated by a thick accretion disc of $1 M_{\odot}$ around a static super-massive black hole of $10^{6}M_{\odot}$, assumed to be formed after the tidal disruption of a solar type star. This torus has been shown to be unstable to a global non-axisymmetric hydrodynamic instability, the Papaloizou-Pringle instability, in the case where it is not already accreting and has a weak magnetic field. We start by deriving analytical estimates of the maximum amplitude of the gravitational wave signal, with the aim to establish its detectability by the Laser Interferometer Space Antenna (LISA). Then, we compare these estimates with those obtained through a numerical simulation of the torus, made with a 3D smoothed particle hydrodynamics code. Our numerical analysis shows that the measured strain is two orders of magnitude lower than the maximum value obtained analytically. However, accretion discs affected by the Papaloizou-Pringle instability may still be interesting sources for LISA, if we consider discs generated after deeply penetrating tidal disruptions of main sequence stars of higher mass.