Resonant relaxation near a massive black hole: the stellar distribution and gravitational wave sources

Resonant relaxation (RR) of orbital angular momenta occurs near massive black holes (MBHs) where the stellar orbits are nearly Keplerian and so do not precess significantly. The resulting coherent torques efficiently change the magnitude of the angular momenta and rotate the orbital inclination in all directions. As a result, many of the tightly bound stars very near the MBH are rapidly destroyed by falling into the MBH on low-angular momentum orbits, while the orbits of the remaining stars are efficiently randomized. We solve numerically the Fokker-Planck equation in energy for the steady state distribution of a single mass population with a RR sink term. We find that the steady state current of stars, which sustains the accelerated drainage close to the MBH, can be up to ~10 times larger than that due to non-coherent 2-body relaxation alone. RR mostly affects tightly bound stars, and so it increases only moderately the total tidal disruption rate, which is dominated by stars originating from less bound orbits farther away. We show that the event rate of gravitational wave (GW) emission from inspiraling stars, originating much closer to the MBH, is dominated by RR dynamics. The GW event rate depends on the uncertain efficiency of RR. The efficiency indicated by the few available simulations implies rates ~10 times higher than those predicted by 2-body relaxation, which would improve the prospects of detecting such events by future GW detectors, such as LISA. However, a higher, but still plausible RR efficiency can lead to the drainage of all tightly bound stars and strong suppression of GW events from inspiraling stars. We apply our results to the Galactic MBH, and show that the observed dynamical properties of stars there are consistent with RR.Comment: Accepted to ApJ; Minor revision

Extreme mass ratio inspiral rates: dependence on the massive black hole mass

We study the rate at which stars spiral into a massive black hole (MBH) due to the emission of gravitational waves (GWs), as a function of the mass M of the MBH. In the context of our model, it is shown analytically that the rate approximately depends on the MBH mass as M^{-1/4}. Numerical simulations confirm this result, and show that for all MBH masses, the event rate is highest for stellar black holes, followed by white dwarfs, and lowest for neutron stars. The Laser Interferometer Space Antenna (LISA) is expected to see hundreds of these extreme mass ratio inspirals per year. Since the event rate derived here formally diverges as M->0, the model presented here cannot hold for MBHs of masses that are too low, and we discuss what the limitations of the model are.Comment: Accepted to CQG, special LISA issu

The impact of realistic models of mass segregation on the event rate of extreme-mass ratio inspirals and cusp re-growth

One of the most interesting sources of gravitational waves (GWs) for LISA is the inspiral of compact objects on to a massive black hole (MBH), commonly referred to as an "extreme-mass ratio inspiral" (EMRI). The small object, typically a stellar black hole (bh), emits significant amounts of GW along each orbit in the detector bandwidth. The slowly, adiabatic inspiral of these sources will allow us to map space-time around MBHs in detail, as well as to test our current conception of gravitation in the strong regime. The event rate of this kind of source has been addressed many times in the literature and the numbers reported fluctuate by orders of magnitude. On the other hand, recent observations of the Galactic center revealed a dearth of giant stars inside the inner parsec relative to the numbers theoretically expected for a fully relaxed stellar cusp. The possibility of unrelaxed nuclei (or, equivalently, with no or only a very shallow cusp) adds substantial uncertainty to the estimates. Having this timely question in mind, we run a significant number of direct-summation $N-$body simulations with up to half a million particles to calibrate a much faster orbit-averaged Fokker-Planck code. We then investigate the regime of strong mass segregation (SMS) for models with two different stellar mass components. We show that, under quite generic initial conditions, the time required for the growth of a relaxed, mass segregated stellar cusp is shorter than a Hubble time for MBHs with $M_\bullet \lesssim 5 \times 10^6 M_\odot$ (i.e. nuclei in the range of LISA). SMS has a significant impact boosting the EMRI rates by a factor of $\sim 10$ for our fiducial models of Milky Way type galactic nuclei.Comment: Accepted by CQG, minor changes, a bit expande

Three-Body Dynamics with Gravitational Wave Emission

We present numerical three-body experiments that include the effects of gravitational radiation reaction by using equations of motion that include the 2.5-order post-Newtonian force terms, which are the leading order terms of energy loss from gravitational waves. We simulate binary-single interactions and show that close approach cross sections for three 1 solar mass objects are unchanged from the purely Newtonian dynamics except for close approaches smaller than 1.0e-5 times the initial semimajor axis of the binary. We also present cross sections for mergers resulting from gravitational radiation during three-body encounters for a range of binary semimajor axes and mass ratios including those of interest for intermediate-mass black holes (IMBHs). Building on previous work, we simulate sequences of high-mass-ratio three-body encounters that include the effects of gravitational radiation. The simulations show that the binaries merge with extremely high eccentricity such that when the gravitational waves are detectable by LISA, most of the binaries will have eccentricities e > 0.9 though all will have circularized by the time they are detectable by LIGO. We also investigate the implications for the formation and growth of IMBHs and find that the inclusion of gravitational waves during the encounter results in roughly half as many black holes ejected from the host cluster for each black hole accreted onto the growing IMBH.Comment: 34 pages, 14 figures, minor corrections to match version accepted by Ap

Towards adiabatic waveforms for inspiral into Kerr black holes: I. A new model of the source for the time domain perturbation equation

We revisit the problem of the emission of gravitational waves from a test mass orbiting and thus perturbing a Kerr black hole. The source term of the Teukolsky perturbation equation contains a Dirac delta function which represents a point particle. We present a technique to effectively model the delta function and its derivatives using as few as four points on a numerical grid. The source term is then incorporated into a code that evolves the Teukolsky equation in the time domain as a (2+1) dimensional PDE. The waveforms and energy fluxes are extracted far from the black hole. Our comparisons with earlier work show an order of magnitude gain in performance (speed) and numerical errors less than 1% for a large fraction of parameter space. As a first application of this code, we analyze the effect of finite extraction radius on the energy fluxes. This paper is the first in a series whose goal is to develop adiabatic waveforms describing the inspiral of a small compact body into a massive Kerr black hole.Comment: 21 pages, 6 figures, accepted by PRD. This version removes the appendix; that content will be subsumed into future wor

Warping the young stellar disc in the Galactic Centre

We examine influence of the circum-nuclear disc (CND) upon the orbital evolution of young stars in the Galactic Centre. We show that gravity of the CND causes precession of the orbits which is highly sensitive upon the semi-major axis and inclination. We consider such a differential precession within the context of an ongoing discussion about the origin of the young stars and suggest a possibility that all of them have originated in a thin disc which was partially destroyed due to the influence of the CND during the period of ~6Myr.Comment: proc. conf. "The Universe Under the Microscope - Astrophysics at High Angular Resolution", 21-25 April 2008, Bad Honnef, German

Simulations of Extreme-Mass-Ratio Inspirals Using Pseudospectral Methods

Extreme-mass-ratio inspirals (EMRIs), stellar-mass compact objects (SCOs) inspiralling into a massive black hole, are one of the main sources of gravitational waves expected for the Laser Interferometer Space Antenna (LISA). To extract the EMRI signals from the expected LISA data stream, which will also contain the instrumental noise as well as other signals, we need very accurate theoretical templates of the gravitational waves that they produce. In order to construct those templates we need to account for the gravitational backreaction, that is, how the gravitational field of the SCO affects its own trajectory. In general relativity, the backreaction can be described in terms of a local self-force, and the foundations to compute it have been laid recently. Due to its complexity, some parts of the calculation of the self-force have to be performed numerically. Here, we report on an ongoing effort towards the computation of the self-force based on time-domain multi-grid pseudospectral methods.Comment: 6 pages, 4 figures, JPCS latex style. Submitted to JPCS (special issue for the proceedings of the 7th International LISA Symposium

Comparison of LISA and Atom Interferometry for Gravitational Wave Astronomy in Space

One of the atom interferometer gravitational wave missions proposed by Dimopoulos et al.1 in 2008 was called AGIS-Sat. 2. It had a suggested gravitational wave sensitivity set by the atom state detection shot noise level that started at 1 mHz, was comparable to LISA sensitivity from 1 to about 20 mHz, and had better sensitivity from 20 to 500 mHz. The separation between the spacecraft was 1,000 km, with atom interferometers 200 m long and shades from sunlight used at each end. A careful analysis of many error sources was included, but requirements on the time-stability of both the laser wavefront aberrations and the atom temperatures in the atom clouds were not investigated. After including these considerations, the laser wavefront aberration stability requirement to meet the quoted sensitivity level is about 1\times10-8 wavelengths, and is far tighter than for LISA. Also, the temperature fluctuations between atom clouds have to be less than 1 pK. An alternate atom interferometer GW mission in Earth orbit called AGIS-LEO with 30 km satellite separation has been suggested recently. The reduction of wavefront aberration noise by sending the laser beam through a high-finesse mode-scrubbing optical cavity is discussed briefly, but the requirements on such a cavity are not given. Unfortunately, such an Earth-orbiting mission seems to be considerably more difficult to design than a non-geocentric mission and does not appear to have comparably attractive scientific goals.Comment: Submitted to Proc. 46th Rencontres de Moriond: Gravitational Waves and Experimental Gravity, March 20 - 27, 2011, La Thuile, Ital

Rates and Characteristics of Intermediate Mass Ratio Inspirals Detectable by Advanced LIGO

Gravitational waves (GWs) from the inspiral of a neutron star (NS) or stellar-mass black hole (BH) into an intermediate-mass black hole (IMBH) with mass between ~50 and ~350 solar masses may be detectable by the planned advanced generation of ground-based GW interferometers. Such intermediate mass ratio inspirals (IMRIs) are most likely to be found in globular clusters. We analyze four possible IMRI formation mechanisms: (1) hardening of an NS-IMBH or BH-IMBH binary via three-body interactions, (2) hardening via Kozai resonance in a hierarchical triple system, (3) direct capture, and (4) inspiral of a compact object from a tidally captured main-sequence star; we also discuss tidal effects when the inspiraling object is an NS. For each mechanism we predict the typical eccentricities of the resulting IMRIs. We find that IMRIs will have largely circularized by the time they enter the sensitivity band of ground-based detectors. Hardening of a binary via three-body interactions, which is likely to be the dominant mechanism for IMRI formation, yields eccentricities under 10^-4 when the GW frequency reaches 10 Hz. Even among IMRIs formed via direct captures, which can have the highest eccentricities, around 90% will circularize to eccentricities under 0.1 before the GW frequency reaches 10 Hz. We estimate the rate of IMRI coalescences in globular clusters and the sensitivity of a network of three Advanced LIGO detectors to the resulting GWs. We show that this detector network may see up to tens of IMRIs per year, although rates of one to a few per year may be more plausible. We also estimate the loss in signal-to-noise ratio that will result from using circular IMRI templates for data analysis and find that, for the eccentricities we expect, this loss is negligible.Comment: Accepted for publication in ApJ; revised version reflects changes made to the article during the acceptance proces