Davide Mancieri, Luca Broggi, Matteo Bonetti, Alberto Sesana
{"title":"Hanging on the cliff: EMRI formation with local two-body relaxation and post-Newtonian dynamics","authors":"Davide Mancieri, Luca Broggi, Matteo Bonetti, Alberto Sesana","doi":"arxiv-2409.09122","DOIUrl":null,"url":null,"abstract":"Extreme mass ratio inspirals (EMRIs) are anticipated to be primary\ngravitational wave sources for LISA (Laser Interferometer Space Antenna). They\nform in dense nuclear clusters when a compact object (CO) is captured by the\ncentral massive black holes (MBHs) due to frequent two-body interactions among\norbiting objects. We present a novel Monte Carlo approach to evolve the\npost-Newtonian (PN) equations of motion of a CO orbiting an MBH accounting for\ntwo-body relaxation locally on the fly, without the assumption of\norbit-averaging. We estimate the fraction $S(a_0)$ of EMRIs to total captures\n(including direct plunges, DPs) as a function of the initial semi-major axis\n$a_0$ for COs around MBHs of $M_\\bullet\\in[10^4\\,{\\rm\nM}_\\odot,4\\times10^6\\,{\\rm M}_\\odot]$. Previous results indicate\n$S(a_0)\\rightarrow 0$ at large $a_0$, with a sharp transition from EMRIs to DPs\naround a critical scale $a_{\\rm c}$. This notion has been recently challenged\nfor low-mass MBHs, with EMRIs forming at $a\\gg a_{\\rm c}$, the so-called\n\"cliffhangers''. Our simulations confirm their existence, at larger numbers\nthan previously expected. Cliffhangers start to appear for\n$M_\\bullet\\lesssim3\\times 10^5\\,{\\rm M}_\\odot$ and can account for up to 55% of\nthe overall EMRIs formed. We find $S(a_0)\\gg 0$ for $a\\gg a_{\\rm c}$, reaching\nvalues as high as 0.6 for $M_\\bullet=10^4\\,{\\rm M}_\\odot$, much larger than\npreviously found. We find that the PN description of the system greatly\nenhances the number of EMRIs by shifting $a_{\\rm c}$ to larger values at all\nMBH masses, and that the local treatment of relaxation significantly boosts the\nnumber of cliffhangers for small MBHs. Our work shows the limitations of\nstandard assumptions for estimating EMRI formation rates, most importantly\ntheir dynamical models. Future estimates of rates and properties of EMRIs\ndetectable by LISA should account for these improvements.","PeriodicalId":501041,"journal":{"name":"arXiv - PHYS - General Relativity and Quantum Cosmology","volume":"5 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-09-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - PHYS - General Relativity and Quantum Cosmology","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2409.09122","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
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 $M_\bullet\in[10^4\,{\rm
M}_\odot,4\times10^6\,{\rm M}_\odot]$. Previous results indicate
$S(a_0)\rightarrow 0$ at large $a_0$, with a sharp transition from EMRIs to DPs
around a critical scale $a_{\rm c}$. This notion has been recently challenged
for low-mass MBHs, with EMRIs forming at $a\gg a_{\rm c}$, the so-called
"cliffhangers''. Our simulations confirm their existence, at larger numbers
than previously expected. Cliffhangers start to appear for
$M_\bullet\lesssim3\times 10^5\,{\rm M}_\odot$ and can account for up to 55% of
the overall EMRIs formed. We find $S(a_0)\gg 0$ for $a\gg a_{\rm c}$, reaching
values as high as 0.6 for $M_\bullet=10^4\,{\rm M}_\odot$, much larger than
previously found. We find that the PN description of the system greatly
enhances the number of EMRIs by shifting $a_{\rm c}$ 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.