Detecting strong gravitational lensing of gravitational waves with TianQin

Abstract

When gravitational waves (GWs) pass by a massive object on its way to the Earth, strong gravitational lensing effect will happen. Thus the GW signal will be amplified, deflected, and delayed in time. Through analysing the lensed GW waveform, physical properties of the lens can be inferred. On the other hand, neglecting lensing effects in the analysis of GW data may induce systematic errors in the estimating of source parameters. As a space-borne GW detector, TianQin will be launched in the 2030s. It is expected to detect dozens of mergers of massive black hole binary (MBHB) as far as z = 15, and thus will have high probability to detect at least one lensed event during the mission lifetime. In this article, we discuss the capability of TianQin to detect lensed MBHBs signals. Three lens models are considered in this work: the point mass model, the singular isothermal sphere (SIS) model, and the Navarro-Frenk-White (NFW) model. The sensitive frequency band for space-borne GW detectors is around milli-hertz, and the corresponding GW wavelength could be comparable to the lens gravitational length scale, which requires us to account for wave diffraction effects. In calculating lensed waveforms, we adopt the approximation of geometric optics at high frequencies to accelerate computation, while precisely evaluate the diffraction integral at low frequencies. Through a Fisher analysis, we analyse the accuracy to estimate the lens parameters. We find that the accuracy can reach to the level of 10 −3 for the mass of point mass and SIS lens, and to the level of 10 −5 for the density of NFW lens. We also assess the impact on the accuracy of estimating the source parameters, and find that the improvement of the accuracy is dominated by the increasing of signal-to-noise ratio (SNR).

Detecting the gravitational wave memory effect with TianQin

“…TianQin is capable of detecting the GW signals from MB-HBs, providing the potential to constrain the cosmological parameters [24], measure the Hubble constant by gravitational lensing [25,26] and test general relativity [27][28][29][30]. Furthermore, the potential for high signal-to-noise ratios (SNRs) of signals of MBHBs on TianQin, opens up the possibility to study the strong-field gravitational effects.…”