[Paper Review] Enhanced Extreme Mass Ratio Inspiral Rates into Intermediate Mass Black Holes

Ismail Qunbar, Nicholas C. Stone|arXiv (Cornell University)|Apr 25, 2023

Pulsars and Gravitational Waves Research4 citations

TL;DR

This paper identifies a new EMRI production channel—'cliffhanger' EMRIs—where plunges into intermediate-mass black holes (IMBHs) with $ M_{ullet} aise.17ex lap{ aise.25ex ext{ extasciitilde}} aise.15ex ext{ extasciitilde} 10^5 M_{igodot} $ can fail and transition into long-lived EMRIs due to gravitational wave dissipation overcoming two-body relaxation. This mechanism can increase volumetric EMRI rates by up to an order of magnitude in dwarf galaxy nuclei with common IMBHs.

ABSTRACT

Extreme mass ratio inspirals (EMRIs) occur when stellar-mass compact objects begin a gravitational wave (GW) driven inspiral into massive black holes. EMRI waveforms can precisely map the surrounding spacetime, making them a key target for future space-based GW interferometers such as {\it LISA}, but their event rates and parameters are massively uncertain. One of the largest uncertainties is the ratio of true EMRIs (which spend at least thousands of orbits in the {\it LISA} band) and direct plunges, which are in-band for at most a handful of orbits and are not detectable in practice. In this paper, we show that the traditional dichotomy between EMRIs and plunges -- EMRIs originate from small semimajor axes, plunges from large -- does not hold for intermediate-mass black holes with masses $M_\bullet \lesssim 10^5 M_\odot$. In this low-mass regime, a plunge always has an $\mathcal{O}(1)$ probability of failing and transitioning into a novel ``cliffhanger'' EMRI. Cliffhanger EMRIs are more easily produced for larger stellar-mass compact objects, and are less likely for smaller ones. This new EMRI production channel can dominate volumetric EMRI rates $\dot{n}_{ m EMRI}$ if intermediate-mass black holes are common in dwarf galactic nuclei, potentially increasing $\dot{n}_{ m EMRI}$ by an order of magnitude.

Motivation & Objective

• To resolve the long-standing uncertainty in EMRI event rates for space-based gravitational wave detectors like LISA.
• To investigate the traditional dichotomy between EMRIs and plunges in the context of intermediate-mass black holes (IMBHs).
• To identify and quantify a new EMRI production mechanism—'cliffhanger' EMRIs—where plunges fail and transition into detectable EMRIs.
• To assess the impact of this mechanism on volumetric EMRI rates and LISA detection prospects, especially in low-mass IMBH regimes.

Proposed method

• Developed analytic criteria to identify the critical black hole mass $ M_{ m c} $ at which the transition from plunge to cliffhanger EMRI becomes likely, based on the balance between gravitational wave (GW) dissipation and two-body relaxation.
• Used Monte Carlo (MC) orbit simulations to model the stochastic angular momentum diffusion from two-body scatterings and GW-driven inspiral in a spherically symmetric, Keplerian potential with a stellar mass function.
• Defined the critical pericenter $ q_{ m IBCO} = 8R_{ m g} $ (or $ x_{ m IBCO} = 8 $) as the threshold for bound orbits, with $ R_{ m g} = GM_{ullet}/c^2 $, to determine when a plunge can become a cliffhanger EMRI.
• Calculated the plunge-to-EMRI ratio $ ilde{ m R} $ as a function of black hole mass $ M_{ullet} $, stellar mass $ m $, and the lower truncation $ M_{ m tr} $ of the MBH mass function.
• Incorporated post-Newtonian corrections for GW inspiral time $ t_{ m GW} $ and angular momentum relaxation time $ t_{ m AM} $, using standard expressions for highly eccentric orbits.
• Explored the effect of black hole spin on $ x_{ m IBCO} $, showing that prograde orbits around rapidly spinning black holes can extend the regime of cliffhanger EMRIs to higher masses.

Experimental results

Research questions

• RQ1 Can the traditional dichotomy between EMRIs and plunges break down for intermediate-mass black holes (IMBHs) with $ M_{ullet} aise.17ex lap{ aise.25ex ext{ extasciitilde}} aise.15ex ext{ extasciitilde} 10^5 M_{igodot} $, leading to a new EMRI production channel?
• RQ2 What is the critical black hole mass $ M_{ m c} $ at which the probability of a plunge transitioning into a cliffhanger EMRI becomes significant?
• RQ3 How do stellar mass and black hole mass influence the likelihood of cliffhanger EMRIs forming?
• RQ4 To what extent can cliffhanger EMRIs increase volumetric EMRI rates $ ilde{n}_{ m EMRI} $, especially in dwarf galaxy nuclei with common IMBHs?
• RQ5 How does black hole spin affect the regime of possible cliffhanger EMRIs, particularly in the context of LISA detection?

Key findings

• For IMBHs with $ M_{ullet} aise.17ex lap{ aise.25ex ext{ extasciitilde}} aise.15ex ext{ extasciitilde} 10^5 M_{igodot} $, a plunge has an $ m O(1) $ probability of failing and transitioning into a cliffhanger EMRI, challenging the classical plunge/EMRI dichotomy.
• The critical mass $ M_{ m c} $, above which cliffhanger EMRIs dominate, depends on the stellar mass $ m $: larger $ m $ increases $ M_{ m c} $, making the effect more prominent for $ m aise.17ex lap{ aise.25ex ext{ extasciitilde}} aise.15ex ext{ extasciitilde} 10 M_{igodot} $.
• If IMBHs in dwarf galaxies have a lower mass truncation $ M_{ m tr} aise.17ex lap{ aise.25ex ext{ extasciitilde}} aise.15ex ext{ extasciitilde} 10^4 M_{igodot} $, the plunge-to-EMRI ratio $ ilde{ m R} $ drops to $ ilde{ m R} aise.17ex lap{ aise.25ex ext{ extasciitilde}} aise.15ex ext{ extasciitilde} 10 $, increasing volumetric EMRI rates by up to an order of magnitude.
• The cliffhanger EMRI channel is most significant for $ M_{ullet} aise.17ex lap{ aise.25ex ext{ extasciitilde}} aise.15ex ext{ extasciitilde} 10^4 - 10^5 M_{igodot} $, where $ ilde{ m R} $ is sensitive to $ M_{ m tr} $, but largely independent of the MBH mass function slope.
• Spin increases the window for cliffhanger EMRIs: for $ m = 10 M_{igodot} $, going from a Schwarzschild to extremal Kerr prograde case increases $ M_{ m c} $ from $ aise.17ex lap{ aise.25ex ext{ extasciitilde}} aise.15ex ext{ extasciitilde} 10^{4.9} M_{igodot} $ to $ aise.17ex lap{ aise.25ex ext{ extasciitilde}} aise.15ex ext{ extasciitilde} 10^{7.1} M_{igodot} $, potentially extending the effect into the SMBH regime.
• The stochastic EMRI background detected by LISA may be dominated by cliffhanger EMRIs around the smallest, most numerous IMBHs, especially if $ M_{ m tr} aise.17ex lap{ aise.25ex ext{ extasciitilde}} aise.15ex ext{ extasciitilde} 10^4 M_{igodot} $.