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

Using semi-analytical modeling of "light" black hole seeds, this study estimates the merger rates of intermediate-mass and supermassive black holes, finding that while LISA and the proposed LGWA detector can detect numerous mergers, their detection capabilities vary significantly depending on the assumed dynamical friction timescales and redshift.

Original authors: Jasbir Singh, Paola Severgnini, Vieri Cammelli, Alessandra De Rosa, Cristian Vignali, Fabio Rigamonti, Rosa Valiante, Pierluigi Monaco, Jonathan C. Tan, Lorenzo Battistini, Roberto Della Ceca, Jan Har

Published 2026-02-11

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CC BY 4.0

Original authors: Jasbir Singh, Paola Severgnini, Vieri Cammelli, Alessandra De Rosa, Cristian Vignali, Fabio Rigamonti, Rosa Valiante, Pierluigi Monaco, Jonathan C. Tan, Lorenzo Battistini, Roberto Della Ceca, Jan Harms, Manali Parvatikar

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

The Cosmic Dance of the Heavyweights: A Simple Guide

Imagine the universe is a vast, dark ocean. Scattered throughout this ocean are massive, swirling whirlpools. In our world, these whirlpools are galaxies, and at the very center of every single one sits a monster: a Black Hole.

Some of these monsters are "Supermassive"—they are so big they could swallow entire solar systems (think of them as Great White Sharks). Others are "Intermediate"—smaller, but still much bigger than anything we’ve ever seen (think of them as Orcas).

Scientists have been trying to find these "Orcas" (Intermediate-Mass Black Holes) for a long time, but they are incredibly good at hiding. This paper is a roadmap for how we are finally going to catch them using "ears" we are building in space.

1. The Problem: The Invisible Giants

Right now, we know the "Great White Sharks" (Supermassive Black Holes) exist because we can see them eating stars and glowing brightly. But the "Orcas" (Intermediate Black Holes) are much harder to spot. They don't always eat enough to glow, and they are much harder to find.

The researchers in this paper wanted to answer one big question: "If we build new, super-sensitive 'ears' in space, how many of these black hole collisions will we actually hear?"

2. The Method: The Cosmic Simulator

Since we can't wait billions of years to see what happens, the scientists built a "Cosmic Video Game."

Using massive supercomputers, they simulated a piece of the universe. They didn't just throw black holes in; they followed a "Light Seed" rule. This rule assumes that the very first stars in the universe were like tiny seeds that eventually grew into these black holes through eating gas and merging with others.

They also had to account for "The Traffic Jam" (Dynamical Friction). When two galaxies collide, their black holes don't just instantly smash together. They have to spiral toward each other, fighting through a "crowd" of stars. It’s like two dancers trying to reach the center of a crowded ballroom; the more people (stars) in the way, the longer it takes them to meet in the middle.

3. The Tools: LISA and LGWA

The paper focuses on two upcoming "ears" (gravitational-wave detectors):

LISA (The Space Listener): A massive detector floating in space. It’s great at hearing the deep, heavy bass of the "Great White Sharks" (Supermassive Black Holes).
LGWA (The Moon Listener): A futuristic detector placed on the surface of the Moon. Because the Moon is quiet and stable, this detector is perfect for hearing the higher-pitched "clicks" of the "Orcas" (Intermediate Black Holes).

4. The Results: What will we hear?

The scientists ran two scenarios: an "Optimistic" one (where black holes move through the star crowd quickly) and a "Pessimistic" one (where they get stuck in traffic for a long time).

The Good News: Even in the "pessimistic" version, we will likely hear some collisions. But in the "optimistic" version, we could hear dozens of collisions every single year!
The Perfect Team: The paper concludes that LISA and LGWA are like a stereo system. LISA hears the deep, low notes, and LGWA hears the mid-range notes. If we use them together, we can hear the "full song" of the universe’s black hole history.

The Big Picture

By listening to these cosmic collisions, we aren't just hearing noise; we are reading the history book of the universe. These collisions tell us how galaxies were born, how they grew, and how the very first stars lived and died. We are about to turn on the volume of the universe, and it’s going to be loud!

This technical summary details the manuscript "Black hole merger rates for LISA and LGWA from semi-analytical modelling of light seeds" (Singh et al., 2025).

1. Problem Statement

The study addresses a major gap in current astrophysics: the lack of observational constraints on the population and evolution of Intermediate-Mass Black Holes (IMBHs) ( $10^3–10^5 M_\odot$ ) and Supermassive Black Holes (SMBHs) ( $>10^5 M_\odot$ ). While stellar-mass BHs and SMBHs are well-documented, the "missing link" (IMBHs) remains elusive. The authors aim to predict the gravitational-wave (GW) merger rates for these populations to determine the scientific potential of two upcoming detectors: the space-based LISA (Laser Interferometer Space Antenna) and the Moon-based LGWA (Lunar Gravitational-wave Antenna).

2. Methodology

The authors employ a multi-layered computational approach to simulate the hierarchical growth of black holes:

Cosmological Framework: They use the pinocchio code (Lagrangian Perturbation Theory) to generate a dark matter (DM) skeleton, providing continuous-time merger trees for DM halos in a 59.7 Mpc box.
Semi-Analytical Modeling (SAM): The DM halos are populated with galaxies and black holes using the GAEA SAM (via the CAM25 framework).
Seeding Scheme: They implement a "light seed" scenario, mimicking the collapse of Population III stars. This allows for the formation of BHs as small as $\sim 5 M_\odot$ , which can subsequently grow into IMBHs or SMBHs through accretion and mergers.
Merging Delays: The model calculates the time elapsed between a DM halo merger and the eventual BH merger by summing two phases:
1. $\tau_{H \to G}$ : The delay from halo merger to galaxy merger (using dynamical friction and halo stripping prescriptions).
2. $\tau_{merge}$ : The delay from galaxy merger to BH merger, modeled using the Chandrasekhar dynamical friction (DF) prescription.
Uncertainty Modeling: To account for the high uncertainty in how much stellar mass accompanies an infalling BH, they provide two scenarios:
- Optimistic (Lower Limit): Assumes the infalling BH retains its host galaxy's stellar mass, speeding up dynamical friction.
- Pessimistic (Upper Limit): Assumes the BH is stripped of its stellar component, slowing down the merger.
Signal Analysis: They use the GWFish3 library and IMRPhenomD waveforms to calculate the Signal-to-Noise Ratio (SNR) for both LISA and LGWA, assuming a detection threshold of $\text{SNR} > 8$ .

3. Key Contributions

Integrated Modeling: A comprehensive pipeline linking large-scale DM structure to specific GW observables for two different detector technologies.
Dual-Detector Comparison: A detailed comparative analysis of how LISA and LGWA complement each other across the mass spectrum.
Dynamical Friction Sensitivity: A demonstration of how sensitive merger rate predictions are to the modeling of "galaxy stripping" and the mass of the infalling object.

4. Results

The study reveals significant differences in detection capabilities based on the mass regime and the assumed merger delays:

Merger Rates:
- Optimistic Case: High detection rates, with both detectors potentially seeing $\sim 26$ mergers per year.
- Pessimistic Case: Low detection rates, with only $\sim 0.5$ mergers per year.
Mass-Specific Performance:
- IMBHs ( $10^3–10^5 M_\odot$ ): LGWA is superior, offering higher SNRs and detecting mergers at higher redshifts (up to $z \sim 11$ ).
- SMBHs ( $10^5–10^7 M_\odot$ ): LISA is superior, detecting more frequent events and reaching higher redshifts for the most massive binaries.
Redshift Distribution: Most detectable mergers occur at relatively low redshifts ( $z < 3$ ), though the optimistic model allows for detections as far back as $z \sim 14$ .
Synergy: The results suggest a powerful synergy: LISA could detect the long-term inspiral phase of a binary, while LGWA could detect the final merger/ringdown at higher frequencies.

5. Significance

This paper provides a roadmap for future GW astronomy. By quantifying the expected event rates, it demonstrates that:

IMBHs are detectable: Even under pessimistic assumptions, these detectors will likely capture a handful of IMBH mergers, finally providing empirical data to test Pop III seeding models.
Multi-Detector Science: The complementary nature of LISA (low frequency/high mass) and LGWA (higher frequency/intermediate mass) is essential for mapping the complete BH mass function.
Model Constraint: Future observations from these missions will be able to distinguish between "light seed" and "heavy seed" scenarios, fundamentally refining our understanding of how the first massive objects in the universe formed.