[Paper Review] The difficult path to coalescence: massive black hole dynamics in merging low mass dark matter haloes and galaxies

Christian Partmann, Thorsten Naab+4 more|arXiv (Cornell University)|Oct 12, 2023

Adaptive optics and wavefront sensingPhysics and Astronomy3 citations

TL;DR

This study uses high-resolution N-body simulations with unsoftened forces and post-Newtonian corrections to investigate massive black hole (MBH) dynamics in merging low-mass dark matter halos and galaxies. It finds that low-mass MBHs ($\lesssim 10^5\,\mathrm{M}_\odot$) rarely sink to centers or merge, while higher-mass MBHs ($\gtrsim 10^6\,\mathrm{M}_\odot$) trigger core scouring and can merge via three-body interactions, though recoil ejections and dynamical ejections severely hinder merger-assisted seed growth.

ABSTRACT

We present a high resolution numerical study of the sinking and merging of massive black holes (MBHs) with masses in the range of $10^3 - 10^7 \, \mathrm{M}_\odot$ in multiple minor mergers of low mass dark matter halos without and with galaxies ($4 imes 10^8 \, \mathrm{M}_\odot \lesssim \mathrm{M}_{\mathrm{halo}} \lesssim 2 imes 10^{10} \, \mathrm{M}_\odot)$. The Ketju simulation code, a combination of the Gadget tree solver with accurate regularised integration, uses unsoftened forces between the star/dark matter components and the MBHs for an accurate treatment of dynamical friction and scattering of dark matter/stars by MBH binaries or multiples. Post-Newtonian corrections up to order 3.5 for MBH interactions allow for coalescence by gravitational wave emission and gravitational recoil kicks. Low mass MBHs ($\lesssim 10^5 \, \mathrm{M}_\odot$) hardly sink to the centre or merge. Sinking MBHs have various complex evolution paths - binaries, triplets, free-floating MBHs, and dynamically or recoil ejected MBHs. Collisional interactions with dark matter alone can drive MBHs to coalescence. The highest mass MBHs of $\gtrsim 10^6 M_\odot$ mostly sink to the centre and trigger the scouring of dark matter and stellar cores. The scouring can transform a centrally baryon dominated system to a dark matter dominated system. Our idealized high-resolution study highlights the difficulty to bring in and keep low mass MBHs in the centres of low mass halos/galaxies - a remaining challenge for merger assisted MBH seed growth mechanisms.

Motivation & Objective

• To understand the dynamics of massive black holes (MBHs) in merging low-mass dark matter halos and galaxies, particularly focusing on sinking, merging, and ejection mechanisms.
• To assess the viability of merger-assisted growth for MBH seeds in early-universe-like environments with low-mass halos.
• To investigate how dynamical friction, gravitational scattering, and gravitational wave emission influence MBH evolution and coalescence.
• To quantify the impact of MBHs on central density profiles, including core formation and dark matter fraction changes.
• To evaluate the role of three-body interactions and recoil kicks in disrupting or enabling MBH mergers.

Proposed method

• Simulations use the Ketju code, combining the Gadget tree solver with regularized integration for accurate treatment of MBH-dynamical interactions.
• Unsoftened forces between MBHs and stars/dark matter particles ensure precise modeling of dynamical friction and scattering.
• Post-Newtonian corrections up to 3.5PN are included to model gravitational wave-driven hardening and recoil kicks.
• High spatial and mass resolution (20 M⊙ for dark matter, 100 M⊙ for stars) enables accurate capture of individual stellar and dark matter particle interactions.
• Initial conditions model minor mergers of low-mass halos ($4\times10^8 - 2\times10^{10}\,\mathrm{M}_\odot$) with MBHs of $10^3 - 10^7\,\mathrm{M}_\odot$.
• The study tracks MBH evolution over gigayears, analyzing orbital paths, binary hardening, and ejection events.

Figure 1: Dark matter surface densities (greyscale) and massive black hole (MBH) orbits (color coded) for the highest resolution ( $20\,\mathrm{M}_{\odot}$ ) simulations with orbital configuration IC1-20-5 (top row) and IC2-20-5 (bottom row) at initial time (left panels) , after $0.2\,\rm Gyr$ (midd

Experimental results

Research questions

• RQ1 Can low-mass MBHs ($\lesssim 10^5\,\mathrm{M}_\odot$) efficiently sink to the centers of low-mass dark matter halos and galaxies?
• RQ2 What role do three-body interactions and gravitational wave emission play in triggering MBH mergers in low-mass systems?
• RQ3 How do recoil kicks affect the retention of MBH merger remnants in low-mass halos?
• RQ4 To what extent do MBHs induce core formation and alter central mass fractions in dark matter and stellar components?
• RQ5 How does the presence of multiple MBHs lead to dynamical ejections or long-lived binaries in low-mass merger environments?

Key findings

• Low-mass MBHs ($\lesssim 10^5\,\mathrm{M}_\odot$) rarely sink to halo centers and are unlikely to merge, even after multiple mergers.
• MBHs with masses $\gtrsim 10^6\,\mathrm{M}_\odot$ efficiently sink and trigger scouring of both stellar and dark matter cores, leading to mass deficits up to $\sim 10\,M_{\bullet,\rm c}$.
• Binary MBH mergers are rare and typically require a third MBH to excite high eccentricity, pushing the binary into the gravitational wave-driven regime.
• Gravitational recoil kicks frequently eject merger remnants from low-mass halos, especially for non-spinning MBHs, reducing retention efficiency.
• In extreme cases, MBH-induced core scouring can transform a baryon-dominated central region into a dark matter-dominated system.
• The mass deficit in the core scales approximately linearly with the number of MBH sinking events, consistent with Merritt (2006) predictions.

Figure 2: Radial distances of all MBHs (colored lines) from the dark matter density centre of the systems as a function of time. From top to bottom, the central MBH mass increases by factors of 10 from $M_{\bullet,\rm c}=10^{3}\,\mathrm{M}_{\odot}$ to $10^{7}\,\mathrm{M}_{\odot}$ (indicated by the g