Numerical wave optics and the lensing of gravitational waves by globular clusters

TL;DR

This paper investigates the wave optical effects of gravitational lensing by globular clusters on gravitational waves from neutron stars, using numerical methods to go beyond geometrical optics, and finds the probability of significant lensing effects to be very small.

Contribution

It introduces a numerical wave optics method for modeling gravitational lensing by globular clusters without relying on geometrical optics approximations.

Findings

Wave optical solutions are necessary for long-wavelength gravitational waves.

The probability of significant lensing effects on gravitational wave detection is very small.

The method allows comparison of different globular cluster lens models numerically.

Abstract

We consider the possible effects of gravitational lensing by globular clusters on gravitational waves from asymmetric neutron stars in our galaxy. In the lensing of gravitational waves, the long wavelength, compared with the usual case of optical lensing, can lead to the geometrical optics approximation being invalid, in which case a wave optical solution is necessary. In general, wave optical solutions can only be obtained numerically. We describe a computational method that is particularly well suited to numerical wave optics. This method enables us to compare the properties of several lens models for globular clusters without ever calling upon the geometrical optics approximation, though that approximation would sometimes have been valid. Finally, we estimate the probability that lensing by a globular cluster will significantly affect the detection, by ground-based laser interferometer detectors such as LIGO, of gravitational waves from an asymmetric neutron star in our galaxy, finding that the probability is insignificantly small.