Gravitational lensing effects on detection of gravitational waves from black hole binary systems

Abstract

[eng] Gravitational wave astronomy has become a reality after the first gravitational wave detections done by advanced LIGO detectors. The availability of accurate waveform templates is crucial for the optimal detection of signals, and for the reliable identification of the source, in order to filter the astrophysical signals from the noise of the detector. In this work we treat a phenomenon that can significantly affect the gravitational wave signal: gravitational lensing. The presence of matter inhomogeneities in the propagating path of gravitational waves from the source to the detector can modify the signals, both in amplitude and phase. If these effects are not included in the search templates, there can be a loss of detected signals. However, as in the well-known case of gravitational lensing of light, lensing magnification can increase the number of detectable events if lensing effects are included in the search templates. For gravitational lensing of light, the geometrical optics framework is sufficient for analyzing almost all astrophysical situations of interest, but in the last decade the work of Takahashi, Nakamura and others showed that for lensing of gravitational waves the correct framework is wave optics. In this work we discuss the fundamental theory for understanding lensing effects on gravitational wave signals in the wave optics formalism, and we study two interesting situations of lensing of coalescing black hole binary signals, currently the only detected systems by gravitational wave detectors. First, we study how the signal-to-noise ratio of a lensed signal can decrease by the employ of unlensed templates for the search, and how the estimated binary parameters can be biased with respect the right ones due to the incomplete templates. Second, we study the increase in the number of detectable events per year for advanced LIGO due to lensing magnification if lensing effects are included in the templates.