Sensitivity of Weak Lensing Surveys to Gravitational Waves from Inspiraling Supermassive Black Hole Binaries

TL;DR

This work investigates the feasibility of using weak gravitational lensing to detect low-frequency gravitational waves from inspiraling supermassive black hole binaries, targeting the nanohertz–microhertz band that lies between PTAs and LISA. It develops a comprehensive SNR framework that ties survey depth, angular resolution, and cadence to a measurement-noise PSD and a GW characteristic strain, enabling direct comparison of LSST-like and idealized cosmic-limit surveys. The results show that current surveys are insufficient mainly due to limited angular resolution, while an ideal full-sky survey with milliarcsecond precision could detect continuous GWs from very massive SMBHBs and partially bridge the PTA–LISA gap; SGWB detection, however, remains highly challenging, requiring extremely high angular resolution and cross-correlation with other GW probes. Overall, the paper highlights the potential and limitations of weak-lensing observables for low-frequency GW astronomy and points to future multi-tracer and cross-correlation approaches to enhance sensitivity.

Abstract

We explore the sensitivity of upcoming and idealized weak lensing surveys to gravitational waves (GWs) emitted by inspiraling supermassive black hole binaries (SMBHBs) in the nanohertz to microhertz frequency band. This range, situated between the reach of pulsar timing arrays and space-based interferometers, remains observationally underexplored. Building upon the formalism for GW-induced shear distortions, we develop a signal-to-noise framework that incorporates realistic survey characteristics, including cadence, angular resolution, and depth. We model the effective galaxy population using a redshift- and luminosity-dependent distribution to evaluate the noise power spectral density across the survey. Applying this framework to both LSST-like and idealized survey configurations, we derive characteristic strain sensitivity curves and identify the detectable parameter space for SMBHBs. We find that while current surveys are limited by angular resolution, an ideal full-sky survey with milliarcsecond-level precision and rapid cadence could detect continuous GW signals from SMBHBs at cosmological distances and partially bridge the PTA-LISA sensitivity gap. Our analysis highlights the potential and limitations of weak-lensing surveys for low-frequency GW astronomy, with angular resolution emerging as the dominant constraint.

Figures (7)

• Figure 1: Redshift distribution of galaxies for different r-band AB magnitude thresholds $m_t$.
• Figure 2: The characteristic noise $h_n(f)$ is shown for two weak-lensing survey configurations: (i) an LSST-like survey (purple dashed line) and (ii) a cosmic-limit survey (gray dashed line). For comparison, we also plot the effective sensitivity of NANOGrav 15yr NANOGrav:2023pdq, using $h_n=h_0\sqrt{f T_\mathrm{15yr}}$ with $T_\mathrm{15yr}=15$ years. Straight solid lines show the characteristic strain $h_c(f)$ for circular inspiraling binaries with various chirp masses $\mathcal{M}_c$ and luminosity distances $d_L$, truncated at their ISCO frequencies.
• Figure 3: The detectable region in the chirp mass $\mathcal{M}_c$ and frequency $f$ parameter space for inspiraling binaries at different luminosity distances $d_L$, assuming the cosmic-limit survey configuration. The gray shaded region indicates frequencies above the ISCO for equal-mass binaries.
• Figure 4: Contours of the characteristic noise $h_n$ at $f=10$ nHz as a function of the survey r-band AB magnitude threshold $m_t$ and angular resolution $\sigma_\theta$, assuming full-sky coverage and cadence $\Delta t=1$ day. The top axis shows the corresponding total number of observed galaxies $N_\mathrm{gal}$ in the survey. White dashed lines indicate the parameter values of Vera Rubin's LSST.
• Figure 5: The relative difference in $h_n$, with the baseline given by the $\sigma_\theta = 0.01$ arcsec slice in Fig. \ref{['fig:mt_vs_res']}, is shown for two modified scenarios: (i) fixing all galaxy angular sizes to $\Theta=0.7$ arcsec (blue), and (ii) omitting the K-correction in the distance modulus (red).