[Paper Review] Implications of pulsar timing array observations for LISA detections of massive black hole binaries

Nathan Steinle, H. Middleton+7 more|arXiv (Cornell University)|May 10, 2023

Pulsars and Gravitational Waves Research4 citations

TL;DR

This paper forecasts LISA's detection rate of massive black hole binaries (MBHBs) by leveraging pulsar timing array (PTA) constraints on a stochastic gravitational-wave background, assuming the signal originates from a population of MBHBs. Using Bayesian inference and LISA’s sensitivity to spin-aligned waveforms, it predicts an upper limit of 134 yr⁻¹ for MBHBs with total masses 10⁷–10⁸ M☉, rising to 11 yr⁻¹ if LISA’s sensitivity extends to 10⁻⁵ Hz.

ABSTRACT

Pulsar timing arrays (PTAs) and the Laser Interferometer Space Antenna (LISA) will open complementary observational windows on massive black-hole binaries (MBHBs), i.e., with masses in the range $\sim 10^6 - 10^{10}\,$ M$_{\odot}$. While PTAs may detect a stochastic gravitational-wave background from a population of MBHBs, during operation LISA will detect individual merging MBHBs. To demonstrate the profound interplay between LISA and PTAs, we estimate the number of MBHB mergers that one can expect to observe with LISA by extrapolating direct observational constraints on the MBHB merger rate inferred from PTA data. For this, we postulate that the common signal observed by PTAs (and consistent with the increased evidence recently reported) is an astrophysical background sourced by a single MBHB population. We then constrain the LISA detection rate, $\mathcal{R}$, in the mass-redshift space by combining our Bayesian-inferred merger rate with LISA's sensitivity to spin-aligned, inspiral-merger-ringdown waveforms. Using an astrophysically-informed formation model, we predict a 95$\%$ upper limit on the detection rate of $\mathcal{R} < 134\,{ m yr}^{-1}$ for binaries with total masses in the range $10^7 - 10^8\,$ M$_{\odot}$. For higher masses, i.e., $>10^8\,$ M$_{\odot}$, we find $\mathcal{R} < 2\,(1)\,\mathrm{yr}^{-1}$ using an astrophysically-informed (agnostic) formation model, rising to $11\,(6)\,\mathrm{yr}^{-1}$ if the LISA sensitivity bandwidth extends down to $10^{-5}$ Hz. Forecasts of LISA science potential with PTA background measurements should improve as PTAs continue their search.

Motivation & Objective

• To quantify how PTA observations of a stochastic gravitational-wave background can inform LISA’s expected detection rate of massive black hole binaries (MBHBs).
• To establish a predictive framework linking PTAs’ astrophysical constraints to LISA’s science potential, leveraging Bayesian inference and waveform sensitivity.
• To explore the synergy between PTAs and LISA in constraining the cosmic MBHB population across mass-redshift space.
• To assess the impact of formation model assumptions and LISA sensitivity bandwidth on detection rate forecasts.
• To provide falsifiable predictions for LISA based on emerging PTA results, enhancing multi-band gravitational-wave astronomy.

Proposed method

• Assumes the common red-stochastic signal in PTA data (from IPTA DR2) is a stochastic gravitational-wave background (SGWB) from a single population of MBHBs.
• Applies Bayesian inference to constrain the MBHB merger rate density in mass-redshift space using PTA data.
• Combines the inferred merger rate with LISA’s sensitivity to spin-aligned, inspiral-merger-ringdown waveforms to compute detection rates.
• Uses two formation models—astrophysically-informed and agnostic—to explore systematic uncertainties in detection rate predictions.
• Extends the LISA sensitivity bandwidth down to 10⁻⁵ Hz in a sensitivity-scenario analysis to assess potential improvements.
• Employs the balrog codesuite and standard astrophysical tools (e.g., astropy, corner, numpy) for population synthesis and posterior sampling.

Experimental results

Research questions

• RQ1 How does the PTA-observed stochastic gravitational-wave background constrain the merger rate of massive black hole binaries (MBHBs) in the mass-redshift plane?
• RQ2 What is the expected number of MBHB mergers that LISA will detect, given constraints from PTA observations assuming a universal MBHB population?
• RQ3 How do different MBHB formation models (astrophysically-informed vs. agnostic) affect the predicted LISA detection rate?
• RQ4 How does extending LISA’s sensitivity bandwidth to 10⁻⁵ Hz impact the forecasted detection rate for high-mass MBHBs?
• RQ5 To what extent can PTA observations enable falsifiable predictions for LISA’s science potential before its launch in 2034?

Key findings

• The study predicts a 95% upper limit of 134 yr⁻¹ on the LISA detection rate for MBHBs with total masses between 10⁷ and 10⁸ M☉, based on an astrophysically-informed formation model.
• For higher-mass binaries (>10⁸ M☉), the 95% upper limit is 2 yr⁻¹ under an agnostic formation model, increasing to 11 yr⁻¹ if LISA’s sensitivity extends to 10⁻⁵ Hz.
• The detection rate is most sensitive to spin magnitudes and directions in the high-mass regime (M ≳ 10⁷ M☉), where higher-mode contributions to the signal-to-noise ratio become significant.
• The results demonstrate a strong synergy between PTAs and LISA, where PTA constraints can directly inform LISA’s expected science output.
• The framework provides falsifiable predictions for LISA based on current PTA data, with growing support from recent 2σ–4σ evidence for a GW origin of the common signal.
• Future improvements in PTA data quality and modeling of MBHB populations will enhance the accuracy of such forecasts, enabling tighter constraints on MBHB evolution and cosmology.