Forecasting properties of detectable massive binary black hole mergers in the era of space based gravitational-wave detectors

TL;DR

This paper forecasts the number and properties of massive black hole binary mergers detectable by space-based gravitational-wave detectors, using the NINJA cosmological hydrodynamical simulation suite. It models MBH growth, merger histories, and post-processing time delays from dynamical friction and stellar hardening, coupled with LISA sensitivity and IMRPhenomA waveforms to estimate SNR for mergers across cosmic time. The study finds an upper detectable MBH total mass of order a few ×10^8 M⊙ for LISA, and shows that including time delays shifts the peak detectable redshift to z≈0.1 while increasing per-event SNR but reducing event counts; it also uncovers a strong SFR–L_bol relation for merging hosts that could enable multimessenger observations. These results inform expectations for MBHB detections and highlight the importance of realistic delay modeling and host-galaxy properties in planning multimessenger strategies with LISA and electromagnetic observatories.

Abstract

Gravitational waves (GWs) from massive black hole (MBH) mergers will provide a novel way to probe the high-redshift universe and are key to understanding galactic dynamics and evolution. In this work, we analyze MBH mergers, their GW signals and detectability, as well as their population properties, using the cosmological hydrodynamical simulation - NINJA Simulation Suite. We discuss the effect of resolution and finite volume on the black hole mass function (BHMF), which in turn limits the mergers associated with low mass black holes, $M_{BH} \lesssim 10^{6.5} M_\odot$. We find the upper limit on the total mass of the MBH binaries detectable by LISA to be $\sim 10^{8.4} M_\odot$. We also find that adding time delays pertaining to dissipative processes like dynamical friction and stellar hardening during the final stages of the inspiral for which the simulation lacks sufficient resolution to model, considerably shifts the peak of redshift distribution of detectable binaries from $z\sim0.5$ to $z\sim0.1$. Time delays reduce the number of detectable GW events but on the other hand their signal-to-noise is increased. From the observational point of view, we find a strong correlation between the SFR and $L_{\rm bol}$ at high redshifts for the detectable LISA binaries. This may prove to be a future application in the coincident observation of MBH binaries by GW and electromagnetic observations.

Figures (11)

• Figure 1: Projected gas (left) and stellar (right) properties from the NINJA L50_N1008 simulation at redshift $z = 0.6$, showing a $500~h^{-1}kpc$ deep projection focused on a halo. Left panel: Gas surface density ($\log \Sigma_{\rm gas}$ [$M_\odot~hMpc^{-2}$]) color-coded by temperature ($\log T_{\rm eff}$ [K]), revealing the multi-phase structure of the interstellar and circumgalactic medium. Right panel: Stellar surface density ($\log \Sigma_{\rm star}$ [$M_\odot~hMpc^{-2}$]) color-coded by formation redshift, illustrating the stellar mass distribution and age structure. The scale bar indicates $100~h^{-1}kpc$. Black holes with $M_\bullet>10^{6.5}h^{-1}M_\odot$ in the region are marked with stars (black crosses in the left panel, red crosses in the right panel). Note the correspondence between cold, clumpy gas patches (blue regions in the left panel) and recent star formation (purple regions in the right panel), particularly along the spiral arms, while multiple black holes near the halo center are in the process of inspiraling and should eventually merge.
• Figure 2: Comparison of the black hole mass function for different simulation volumes of NINJA with other simulations and observations at $z=0$. The green lines represent the results of the NINJA runs (solid for centrals and dashed for satellites), the solid blue, brown and purple lines represent the results from TNG2021MNRAS.503.1940H, Illustris2015MNRAS.452..575S, and the Astrid2025ApJ...993..199W simulations. The pink shaded region and the red, orange and magenta lines are observational constraints from 2013CQGra..30x4001S, 10.1111/j.1365-2966.2008.13472.x, 2014ApJ...786..104U, and Li_2011 respectively. The error estimates from 10.1111/j.1365-2966.2008.13472.x are extremely small and have not been included. The pink shaded region of 2013CQGra..30x4001S represents the $1\sigma$ uncertainty of the mass function assuming the $M_{\textrm{BH}}-\sigma$ relation from 2013ApJ...764..184M.
• Figure 3: An example of a merger tree tracing the evolution of a progenitor black hole through time. The y-axis represents redshift ($z$), with cosmic time increasing downwards. Each circle represents a black hole, with its size proportional to the logarithm of the mass of the black hole $\log_{10}(M_{\textrm{BH}}/M_{\odot})$. The color of each black hole at a given redshift is determined by the logarithm of the signal-to-noise ratio (log(SNR)) as detected by LISA, with the color bar on the right indicating the scale. The connecting lines illustrate the hierarchical merging of black holes over cosmic time.
• Figure 4: Bolometric luminosity as a function of redshift plotted by tracking an ID of a black hole from the merger tree. Each vertical line of distinct color marks a MBBH merger. The solid line corresponds to the merger where the MBBHs are considered merged by the simulation. The number beside each merger denotes the mass ratio of the merger. Dashed line corresponds to the merger redshift after adding time delays due to dynamical friction.
• Figure 5: A comparison of the different methods (panels left to right) used to calculate the SFR of galaxies hosting merging black holes systems with bolometric luminosity, $L_{\rm bol}$, with a GW SNR greater than 8 for the redshifts $0 \leq z \leq 2.5$. Left: SFR and $L_{\rm bol}$ are calculated using their mean values within 20 Myr time merger. Middle: SFR and $L_{\rm bol}$ based on their maximum values within 20 Myr of the merger. Right: SFR and $L_{\rm bol}$ based on the closest snapshot data to the merger. The solid black line in each panel represents the median relation. The contours represent the 68%, 95% of the enclosed population.