[Paper Review] Extreme mass ratio inspirals triggered by massive black hole binaries: from relativistic dynamics to cosmological rates

Lodato, G.|arXiv (Cornell University)|Oct 1, 2022

Galaxies: Formation, Evolution, PhenomenaPhysics and Astronomy69 references23 citations

TL;DR

This paper investigates extreme mass ratio inspirals (EMRIs) triggered by massive black hole binaries (MBHBs) formed after galaxy mergers, using relativistic three-body simulations to model EMRI formation via secular and chaotic dynamics. It finds that MBHBs can trigger EMRI formation in a sharp burst with rates 10–100× higher than standard two-body relaxation, forecasting O(10) EMRIs per year detectable by LISA.

ABSTRACT

Extreme mass ratio inspirals (EMRIs) are compact binary systems characterized by a mass-ratio $q=m/M$ in the range $~10^{-9}-10^{-4}$ and represent primary gravitational wave (GW) sources for the forthcoming Laser Interferometer Space Antenna (LISA). While their standard formation channel involves relaxation processes deflecting compact objects on very low angular momentum orbits around the central massive black hole, a number of alternative formation channels has been proposed, including binary tidal break-up, migration in accretion disks and secular and chaotic dynamics around a massive black hole binary (MBHB). In this work, we take an extensive closer look at this latter scenario, investigating how EMRIs can be triggered by a MBHBs, formed in the aftermath of galaxy mergers. By employing a suite of relativistic three-body simulations, we evaluate the efficiency of EMRI formation for different parameters of the MBHB, assessing the importance of both secular and chaotic dynamics. By modelling the distribution of compact objects in galaxy nuclei, we estimate the resulting EMRI formation rate, finding that EMRI are produced in a sharp burst, with peak rates that are 10-100 times higher than the standard two-body relaxation channel, lasting for 10$^6$--10$^8$ years. By coupling our results with an estimate of the cosmic MBHB merger rate, we finally forecast that LISA could observe ${\cal O}(10)$ EMRIs per year formed by this channel.

Motivation & Objective

• To investigate EMRI formation triggered by massive black hole binaries (MBHBs) in galactic nuclei.
• To assess the relative contributions of secular (e.g., Lidov-Kozai) and chaotic dynamics in EMRI production.
• To estimate cosmological EMRI formation rates from the MBHB-triggered channel and forecast LISA detection rates.
• To evaluate the robustness of results against uncertainties in stellar density profiles and perturbations.
• To explore whether MBHB-triggered EMRIs have distinctive properties for identification without electromagnetic counterparts.

Proposed method

• Conducted relativistic three-body simulations of a stellar black hole (CO) interacting with a massive black hole binary (MBHB) in a relativistic gravitational field.
• Used a simplified analytical stellar potential (SIS-like) to model the central stellar cusp, with Newtonian precession included.
• Varied MBHB parameters (mass ratio 𝑞, total mass, separation) to assess their impact on EMRI formation efficiency.
• Modelled compact object distribution in galactic nuclei and scaled EMRI rates using a semi-analytical cosmological model (L-Galaxies).
• Applied a simplified kludge waveform model (Barack & Cutler 2004) to estimate signal-to-noise ratios and detectability by LISA.
• Performed sensitivity tests by removing the stellar potential and assessing impact on LK oscillations and EMRI rates.

Experimental results

Research questions

• RQ1 How efficiently can massive black hole binaries (MBHBs) trigger EMRI formation via secular and chaotic dynamics?
• RQ2 What is the cosmological EMRI formation rate from the MBHB-triggered channel compared to the standard two-body relaxation mechanism?
• RQ3 How do MBHB parameters (mass ratio, total mass, separation) influence EMRI production rates?
• RQ4 Can MBHB-triggered EMRIs be distinguished from those formed via standard relaxation, enabling electromagnetic-free identification?
• RQ5 What is the expected number of detectable EMRIs per year by the LISA mission from this channel?

Key findings

• EMRI formation via MBHBs occurs in a sharp burst lasting 10⁶–10⁸ years, with peak rates 10–100 times higher than the standard two-body relaxation channel.
• The MBHB-triggered EMRI rate is dominated by chaotic interactions for most systems, especially at higher mass ratios, while secular Lidov-Kozai oscillations contribute significantly only for low-mass-ratio binaries.
• Cosmological EMRI formation rates from the MBHB channel are estimated at O(10) events per year detectable by LISA, assuming standard MBHB merger rates from the L-Galaxies model.
• The results are robust to uncertainties in the stellar potential: even with steeper density profiles, LK oscillations remain sub-dominant for most systems, and EMRI rates are minimally affected.
• Neglecting stochastic perturbations from close stellar encounters may lead to a modest underestimation of rates (up to a factor of ≈2), but the overall contribution remains significant.
• EMRIs triggered by MBHBs are likely to have distinct waveforms and orbital properties, offering a potential pathway to identify MBHB populations without electromagnetic counterparts.