Propagation effect of gravitational wave on detector response

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${}_{\odot }$.

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