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Inspiral of compact stellar remnants into massive black holes (MBHs) is accompanied by the emission of gravitational waves at frequencies that are potentially detectable by space-based interferometers. Event rates computed from statistical (Fokker-Planck, Monte-Carlo) approaches span a wide range due to uncertaintities about the rate coefficients. Here we present results from direct integration of the post-Newtonian N-body equations of motion descrbing dense clusters of compact stars around Schwarzschild MBHs. These simulations embody an essentially exact (at the post-Newtonian level) treatment of the interplay between stellar dynamical relaxation, relativistic precession, and gravitational-wave energy loss. The rate of capture of stars by the MBH is found to be greatly reduced by relativistic precession, which limits the ability of torques from the stellar potential to change orbital angular momenta. Penetration of this Schwarzschild barrier does occasionally occur, resulting in capture of stars onto orbits that gradually inspiral due to gravitational wave emission; we discuss two mechanisms for barrier penetration and find evidence for both in the simulations. We derive an approximate formula for the capture rate, which predicts that captures would be strongly disfavored from orbits with semi-major axes below a certain value; this prediction, as well as the predicted rate, are verified in the N-body integrations. We discuss the implications of our results for the detection of extreme-mass-ratio inspirals from galactic nuclei with a range of physical properties.
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The Laser Interferometer Space Antenna (LISA) will open the mHz frequency window of the gravitational wave (GW) landscape. Among all the new GW sources expected to emit in this frequency band, extreme mass-ratio inspirals (EMRIs) constitute a unique laboratory for astrophysics and fundamental physics. Here we show that EMRIs can also be used to extract relevant cosmological information, complementary to both electromagnetic (EM) and other GW observations. By using the loudest EMRIs (SNR$>$100) detected by LISA as dark standard sirens, statistically matching their sky localisation region with mock galaxy catalogs, we find that constraints on $H_0$ can reach $sim$1.1% ($sim$3.6%) accuracy, at the 90% credible level, in our best (worst) case scenario. By considering a dynamical dark energy (DE) cosmological model, with $Lambda$CDM parameters fixed by other observations, we further show that in our best (worst) case scenario $sim$5.9% ($sim$12.3%) relative uncertainties at the 90% credible level can be obtained on $w_0$, the DE equation of state parameter. Besides being relevant in their own right, EMRI measurements will be affected by different systematics compared to both EM and ground-based GW observations. Cross validation with complementary cosmological measurements will therefore be of paramount importance, especially if convincing evidence of physics beyond $Lambda$CDM emerges from future observations.
We show that the loudest extreme mass-ratio inspirals (EMRIs) detected by the future space-based gravitational wave detector LISA can be used as dark standard sirens, statistically matching their sky localisation region with mock galaxy catalogs. In these Proceedings we focus on a realistic EMRI population scenario and report accuracy predictions for the measure of cosmological parameters, anticipating the potential of EMRIs to simultaneously constrain the Hubble constant, the dark matter, and the dark energy density parameters.
One of the main targets of the Laser Interferometer Space Antenna (LISA) is the detection of extreme mass-ratio inspirals (EMRIs) and extremely large mass-ratio inspirals (X-MRIs). Their orbits are expected to be highly eccentric and relativistic when entering the LISA band. Under these circumstances, the inspiral time-scale given by Peters formula loses precision and the shift of the last-stable orbit (LSO) caused by the massive black hole spin could influence the event rates estimate. We re-derive EMRIs and X-MRIs event rates by implementing two differe
The intermediate mass-ratio inspiral of a stellar compact remnant into an intermediate mass black hole (IMBH) can produce a gravitational wave (GW) signal that is potentially detectable by current ground-based GW detectors (e.g., Advanced LIGO) as well as by planned space-based interferometers (e.g., eLISA). Here, we present results from a direct integration of the post-Newtonian $N$-body equations of motion describing stellar clusters containing an IMBH and a population of stellar-mass black holes (BHs) and solar mass stars. We take particular care to simulate the dynamics closest to the IMBH, including post-Newtonian effects up to order $2.5$. Our simulations show that the IMBH readily forms a binary with a BH companion. This binary is gradually hardened by transient 3-body or 4-body encounters, leading to frequent substitutions of the BH companion, while the binarys eccentricity experiences large amplitude oscillations due to the Lidov-Kozai resonance. We also demonstrate suppression of these resonances by the relativistic precession of the binary orbit. We find an intermediate mass-ratio inspiral in one of the 12 cluster models we evolved for $sim 100$ Myr. This cluster hosts a $100 M_odot$ IMBH embedded in a population of 32 $10M_odot$ BH and 32,000 $1M_odot$ stars. At the end of the simulation, after $sim 100$ Myr of evolution, the IMBH merges with a BH companion. The IMBH--BH binary inspiral starts in the eLISA frequency window ($gtrsim 1rm mHz$) when the binary reaches an eccentricity $1-esimeq 10^{-3}$. After $simeq 10^5$ years the binary moves into the LIGO frequency band with a negligible eccentricity. We comment on the implications for GW searches, with a possible detection within the next decade.
Extreme-mass-ratio inspiral (EMRI) is an important gravitational-wave (GW) source and it normally consists of one stellar-mass black hole (BH) whirling closely around a supermassive black hole (SMBH). In this Letter, we demonstrate that the small body, in fact, could be a BH binary (BHB). Previous numerical scatting experiments have shown that SMBHs can tidally capture BHBs to bound orbits. Here we investigate the subsequent long-term evolution. We find that those BHBs with a semi-major axis of $alesssim5times10^{-3}$ AU can be captured to tightly-bound orbits such that they will successfully inspiral towards the central SMBHs without being scattered away by stellar relaxation processes. We estimate that these binary-EMRIs (b-EMRIs) could constitute at most $10%$ of the EMRI population. Moreover, we show that when the eccentricity of a b-EMRI drops to about $0.85$, the two stellar BHs will quickly merge due to the tidal perturbation by the SMBH. The high-frequency ($sim10^2$ Hz) GWs generated during the coalescence coincide with the low-frequency ($sim10^{-3}$ Hz) waves from the b-EMRI, making this system an ideal target for future multi-band GW observations.
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