Propagation effect of gravitational wave on detector response

TL;DR

This paper develops a frequency-dependent response formula for gravitational wave detectors, reexamines LIGO data, and highlights the importance of photon travel time relative to gravitational wave periods for accurate signal detection.

Contribution

It introduces a new formula for detector response to gravitational waves considering varied frequencies and photon travel times, providing a refined analysis of LIGO data.

Findings

Reanalysis of GW150914 and GW151226 data with the new framework.

Photon travel time relative to gravitational wave period affects signal matching.

Standard templates may not fit well when photon travel time exceeds wave period.

Abstract

The response of a detector to gravitational wave is a function of frequency. When the time a photon moving around in the Fabry-Perot cavities is the same order of the period of a gravitational wave, the phase-difference due to the gravitational wave should be an integral along the path. We present a formula description for detector response to gravitational wave with varied frequencies. The LIGO data for GW150914 and GW 151226 are reexamined in this framework. For GW150924, the traveling time of a photon in the LIGO detector is just a bit larger than a half period of the highest frequency of gravitational wave and the similar result is obtained with LIGO and Virgo collaborations. However, we are not always so luck. In the case of GW151226, the time of a photon traveling in the detector is larger than the period of the highest frequency of gravitational wave and the announced signal cannot match well the template with the initial black hole masses 14.2M$_\odot$ and 7.5M$_\odot$.