Black hole merger rates for LISA and LGWA from semi-analytical modelling of light seeds

TL;DR

This study assesses MBH merger observability by LGWA and LISA using a light-seed Pop III-like seeding model embedded in a PINOCCHIO-derived DM skeleton and CAM25/GAEA semi-analytic framework. It propagates halos through two-stage dynamical-friction delays (halo-to-galaxy and galaxy-to-BH) under optimistic and pessimistic limits to bound merger rates, then maps mergers to GW signals and computes detectable events across mass ranges $[10^3,10^5]\,M_\odot$, $[10^5,10^7]$, and $[10^7,10^8]\,M_\odot$ with SNR thresholds. The results show LGWA excels for high-SNR IMBH detections at high redshift, while LISA is more sensitive to SMBH mergers, with joint observations capable of probing the full BH mass spectrum and constraining seed formation models; however, results depend strongly on DF treatment and neglect alternative formation channels. The work highlights the critical role of galaxy-stripping physics in setting delays and demonstrates consistency with other population studies within current uncertainties, supporting the value of multi-detector synergy for future GW astronomy.

Abstract

With the upcoming space- and Moon-based gravitational-wave detectors, LISA and LGWA respectively, a new era of GW astronomy will begin with the possibility of detections of the mergers of intermediate-mass black holes (IMBHs) and supermassive black holes (SMBHs). We generate populations of synthetic black hole (BH) binaries with masses ranging from the intermediate ($10^3-10^5 M_\odot$) to the supermassive regime ($>10^5 M_\odot$), formed from the dynamical processes of merging halos and their residing galaxies, assuming that each galaxy is initially seeded with a single black hole at its centre. The aim is to estimate the rate of these BH mergers which could be detected by LISA and LGWA. Using PINOCCHIO cosmological simulation and a semi-analytical model based on GAEA, we construct a population of merging BHs by implementing a "light" seeding scheme and calculating the merging timescales using the Chandrasekhar prescription. We provide upper and lower limits of dynamical friction timescale by varying the mass of the infalling object to create "pessimistic" and "optimistic" merger rates respectively. We find that for our synthetic population of MBHs, both LGWA and LISA are able to detect more than $15$ binary IMBH mergers per year in the optimistic case, while in the pessimistic case less than $\sim5$ detections would be possible considering the entire lifetime of the detectors. For SMBHs, the rates are slightly lower in both cases. Most mergers below $z\approx4$ are detected in the optimistic case, although mergers beyond $z=8$ are also detectable at a lower rate. We find that LGWA is better suited for high-SNR IMBH detections at higher redshift, while LISA is more sensitive to massive SMBHs. Joint observations will probe the full BH mass spectrum and constrain BH formation and seeding models.

Figures (11)

• Figure 1: Merging rate of seeded halos (per unit redshift per year) below redshift $z\leq19.92$. The time is shown in observer frame units. The highest redshift corresponds to the highest available snapshot from the CAM25 model; we only consider mergers below this redshift.
• Figure 2: Time taken from halo merger to galaxy merger, $\tau_{{\rm H}\rightarrow{\rm G}}$, as a function of the halo mass ratio. The colour of each point represents the mass of the primary halo. The grey dashed line depicts the Hubble time.
• Figure 3: The BH mass, galaxy mass, and the galaxy radius as a function of halo mass from the CAM25 model with ALS seeding at $z=0$.
• Figure 4: Corner plot showing the distribution of the population of BH pairs formed after the galaxy merger. The plot shows the primary mass $m_\mathrm{BH,p}$, the secondary mass $m_\mathrm{BH,s}$ divided by the primary BH mass $m_\mathrm{BH,s}/m_\mathrm{BH,p}$, and the redshift of the galaxy merger $z_\mathrm{merge}^\mathrm{galaxy}$. The contours show the density of the points. Individual points outside the contours are also shown to visualize the extent of the distributions.
• Figure 5: Histogram of the initial BH separations used for computing the DF timescale. $r_0$ corresponds to the separation used to evaluate the upper limits on the timescale (equation \ref{['eq:t_dyn']}), while $r_{0,p}$ is used for the lower limits (equation \ref{['eq:t_dyn_ll']}).