Strong-lensing rates of massive black hole binaries in LISA

TL;DR

This work estimates the rate of strongly lensed MBHBs detectable by LISA by combining six MBHB population models (light and heavy seeds) with three galaxy lens-population models (one redshift-independent and two redshift-dependent). Using an SIS lens framework and optical-depth formalism, the authors propagate MBHB distributions through lensing to predict detectable lensed events, distinguishing single- and two-image detections and analyzing time-delay distributions. They find a wide range of expected lensed events in 4 years, from 0.13 to 231, corresponding to 0.2%–0.9% of all unlensed detections, with time delays between 1 week and 1 year for most two-image events. The results underscore substantial dependencies on source and lens population assumptions and highlight boosted detectability due to lensing, while also noting limitations due to simplified lens models and the neglect of wave-optics effects.

Abstract

Similarly to electromagnetic (EM) signals, gravitational lensing by intervening galaxies can also affect gravitational waves (GWs). In this paper, we estimate the strong-lensing rate of massive black hole mergers observed with LISA. Given the uncertainties in the source populations as well as in the population of galaxies at high redshift, we consider: six different source population models, including light and heavy seeds, as well as three lens population models, including redshift-independent and redshift-dependent evolution properties. Among all the scenarios explored, the expected number of strong lensed events detected in a 4-year observation time in LISA ranges between 0.13-231 with most of them having two (one) images detectable in the heavy (light) seed scenarios. The event numbers obtained correspond to 0.2%-0.9% of all detected unlensed events. Out of all the detectable strong-lensed events, up to 61% (in the light-seed scenario) and 1% (in the heavy-seed scenario) of them are above the detectability threshold solely due to strong lensing effects and would otherwise be undetectable. For detectable pairs of strong-lensed events by galaxy lenses, we also find between 72%-81% of them to have time delays from 1 week to 1 year.

Figures (11)

• Figure 1: Lensing configuration of a MBHB source located at an angular diameter distance $D_S$ from the LISA detector, with a dimensionless impact parameter $y$, which suffers from strong lensing by a galaxy at an angular diameter distance $D_L$ from the detector. The signal can take two trajectories from the source to the detector, as indicated by the dotted lines, which results in two GW signals being detected with different amplitudes and arrival times.
• Figure 2: Intrinsic merger rate distribution of MBHBs in 4 years as a function of total mass $M$ (top) and redshift $z$(bottom), for different source population models.
• Figure 3: Optical depth as function of source redshift, for the three lens population models: $z$-independent, $z$-dependent model 1, and $z$-dependent model 2.
• Figure 4: Redshift distributions of lenses $z_L$ and lensed sources $z_s$ for the population Q3-nod (K+16).
• Figure 5: Intrinsic events for PopIII-d (K+16) and Q3-nod (K+16) simulations in 1 year, as function of total mass $M$ and source redshift $z_s$. Colors indicate the expected mean SNR, with grey dots showing the undetectable events.