Considering lensing effect on gravitational wave signals from black holes in mass gap

TL;DR

The paper investigates whether gravitational lensing can explain the appearance of binary black holes with masses in the PISN mass gap by quantifying how lensing magnification biases inferred source-frame masses. It builds lensed GW templates under the geometric-optics approximation and performs Bayesian parameter estimation with unlensed and lensed templates on GW190521-like and GW231123-like signals in the LVK network. The study finds that lensing magnification can shift inferred masses across the $60\,M_\odot$ boundary, with minimum magnifications $\mu \approx 12.2$ for GW190521 and $\mu \approx 320.1$ for GW231123 (corresponding to $d_L^l \approx 11155$ and $15207$ Mpc), though low-SNR events can exhibit distance biases that complicate recovery. It highlights that third-generation detectors will greatly improve the ability to identify and interpret lensed high-mass BBH events, and advocates incorporating lensing effects into Bayesian inference as a viable alternative viewpoint for high-mass GW events.

Abstract

The pair-instability supernova (PISN) mechanism predicts a mass gap in the black hole population, where no stellar-origin black holes are expected to form. However, the binary black hole merger events GW190521 and GW231123 appear unusual, as current analyses place their component masses within the PISN mass gap. In this work, we investigate the relationship between different lensing magnifications and the inferred source-frame black hole masses for these two events. If the gravitational wave source is lensed, neglecting lensing effect can bias the inferred luminosity distance and hence the redshift, leading to an underestimation of the luminosity distance and consequently an overestimation of the source-frame masses, potentially placing them in the mass-gap region. For the two events in mass gap, when adopting a lower bound of $60 M_{\odot}$ for the mass gap, the minimum magnifications required to shift the inferred source-frame masses below this gap boundary are found to be $μ=12.2$ for GW190521 and $μ=320.1$ for GW231123, corresponding to lensing-corrected luminosity distances of $11155\, \mathrm{Mpc}$ and $15207\, \mathrm{Mpc}$, respectively. These results provide a quantitative reference for assessing the lensing hypothesis as a possible explanation for the existence of black holes in the PISN mass gap.

Figures (6)

• Figure 1: The amplification effect of GW signal by gravitational lensing. The blue line represent the original GW231123-like signal and orange line represent the first image of the original signal magnificated by a lens with $\mu=5$ in H1 detector. We also plot the pure noise of the detector, whose strain is nearly comparable to that of the unlensed signal, but is roughly four times smaller than that of the lensed one in merger phase due to the magnification.
• Figure 2: The relation between the inferred source-frame mass of primary BH (x-axis) and the lensing magnification $\mu$ (left y-axis, log scale), together with the corresponding luminosity distance after accounting for the lensing effect $d_L^l$ (right y-axis, log scale). The stars in upper and lower panels correspond to the median value of the posterior samples for real GW190521 and GW231123 events, respectively. And the black dashed line represents the lower boundary of the mass gap $m= 60\,M_\odot$ as we take.
• Figure 3: Posterior distributions from the PE of a GW190521-like event using unlensed templates. The four parameters shown are the source-frame component masses $m_1$, $m_2$, the luminosity distance $d_L$ and the angle $\theta_{jn}$. The orange lines indicate the injection values (note that the injections were performed using the detector-frame masses; thus, the source-frame masses shown here are obtained by converting the injected detector-frame masses using the corresponding luminosity distance). The blue dashed lines indicate the 15.8% and 84.1% quantiles. The inferred primary mass $m_{1}$ lies within the mass gap.
• Figure 4: Posterior distributions from the parameter estimation of a GW190521-like event using lensed templates with a magnification of $\mu=12.2$. The four parameters shown are same to Fig. \ref{['fig.3']}. The red lines indicate the predicted values through Eqs. (\ref{['eq.15']}) and (\ref{['eq.16']}) (except for $\theta_{jn}$). By including the lensing effect, a larger luminosity distance is recovered, which in turn yields lower source-frame masses, bringing the primary mass close to the lower boundary of the mass gap.
• Figure 5: Similar to Fig. \ref{['fig.3']}, the posterior distributions from the PE of a GW231123-like event using unlensed templates are shown. Both $m_{1}$ and $m_{2}$ lie within the mass gap.