Hanging on the cliff: Extreme mass ratio inspiral formation with local two-body relaxation and post-Newtonian dynamics

Abstract

Extreme mass ratio inspirals (EMRIs) are anticipated to be primary gravitational wave sources for LISA (Laser Interferometer Space Antenna). They form in dense nuclear clusters when a compact object (CO) is captured by the central massive black holes (MBHs) due to frequent two-body interactions among orbiting objects. We present a novel Monte Carlo approach to evolve the post-Newtonian (PN) equations of motion of a CO orbiting an MBH accounting for two-body relaxation locally on the fly, without the assumption of orbit-averaging. We estimate the fraction $S(a_0)$ of EMRIs to total captures (including direct plunges, DPs) as a function of the initial semi-major axis $a_0$ for COs around MBHs of $M_{\bullet }\in [10^4{\mathrm{M}}_{\odot },4\times 10^6{\mathrm{M}}_{\odot }]$. Previous results indicate $S(a_0)\to 0$ at large $a_0$, with a sharp transition from EMRIs to DPs around a critical scale $a_{\mathrm{c}}$. This notion has been recently challenged for low-mass MBHs, with EMRIs forming at $a\gg a_{\mathrm{c}}$, the so-called "cliffhangers''. Our simulations confirm their existence, at larger numbers than previously expected. Cliffhangers start to appear for $M_{\bullet }\lesssim 3\times 10^5{\mathrm{M}}_{\odot }$ and can account for up to 55% of the overall EMRIs formed. We find $S(a_0)\gg 0$ for $a\gg a_{\mathrm{c}}$, reaching values as high as 0.6 for $M_{\bullet }=10^4{\mathrm{M}}_{\odot }$, much larger than previously found. We find that the PN description of the system greatly enhances the number of EMRIs by shifting $a_{\mathrm{c}}$ to larger values at all MBH masses, and that the local treatment of relaxation significantly boosts the number of cliffhangers for small MBHs. Our work shows the limitations of standard assumptions for estimating EMRI formation rates, most importantly their dynamical models. Future estimates of rates and properties of EMRIs detectable by LISA should account for these improvements.

Accepted for publication in A&A; 22 pages, 15 figures, 1 table

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Cited by in corpus (5)

• Eccentricity distribution of extreme mass ratio inspirals
• Gravitational radiation from hyperbolic orbits: comparison between self-force, post-Minkowskian, post-Newtonian, and numerical relativity results
• Co-evolution of Nuclear Star Clusters and Massive Black Holes: Extreme Mass-Ratio Inspirals
• Revealing massive black hole astrophysics: The potential of hierarchical inference with extreme mass-ratio inspiral observations
• Extreme Mass Ratio Inspirals in Light of Quasi-periodic Eruptions: Milli-Hertz Gravitational Wave Background