Emission of gravitational radiation from ultra-relativistic sources

TL;DR

This paper models gravitational waves emitted by ultra-relativistic ejected blobs in astrophysical events, showing their wide angular distribution and beamed energy flux, and estimates detection rates for gravitational-wave observatories.

Contribution

It provides a detailed calculation of gravitational radiation from ultra-relativistic ejecta and estimates detection rates for gravitational-wave detectors based on supernova models.

Findings

Gravitational waves have a wide angular distribution proportional to $1+\cos\theta$.

The frequency of bursts is Doppler shifted and strongly beamed forward.

Estimated detection rate is about 1 per year for advanced LIGO-II.

Abstract

Recent observations suggest that blobs of matter are ejected with ultra-relativistic speeds in various astrophysical phenomena such as supernova explosions, quasars, and microquasars. In this paper we analyze the gravitational radiation emitted when such an ultra-relativistic blob is ejected from a massive object. We express the gravitational wave by the metric perturbation in the transverse-traceless gauge, and calculate its amplitude and angular dependence. We find that in the ultra-relativistic limit the gravitational wave has a wide angular distribution, like $1+\cos\theta$. The typical burst's frequency is Doppler shifted, with the blue-shift factor being strongly beamed in the forward direction. As a consequence, the energy flux carried by the gravitational radiation is beamed. In the second part of the paper we estimate the anticipated detection rate of such bursts by a gravitational-wave detector, for blobs ejected in supernova explosions. Dar and De Rujula recently proposed that ultra-relativistic blobs ejected from the central core in supernova explosions constitute the source of Gamma-ray bursts. Substituting the most likely values of the parameters as suggested by their model, we obtain an estimated detection rate of about 1 per year by the advanced LIGO-II detector.