Astrophysics of extreme mass ratio inspiral sources

Compact remnants on orbits with peri-apses close to the Schwarzschild radius of a massive black hole (MBH) lose orbital energy by emitting gravitational waves (GWs) and spiral in. Scattering with other stars allows successful inspiral of such extreme mass ratio inspiral sources (EMRIs) only within small distances, a < few \times 0.01 pc from the MBH. The event rate of EMRIs is therefore dominated by the stellar dynamics and content in the inner few \times 0.01 pc. I discuss the relevant dynamical aspects and resulting estimated event rates of EMRIs. Subjects considered include the loss-cone treatment of inspiral sources; mass segregation; resonant relaxation; and alternative routes to EMRI formation such as tidal binary disruptions, stellar formation in disks and tidal capture of massive main sequence stars. The EMRI event rate is estimated to be of order few \times 10^2/Gyr per MBH, giving excellent prospects for observation by LISA.Comment: Invited contribution to the 6th International LISA Symposiu

The orbital statistics of stellar inspiral and relaxation near a massive black hole: characterizing gravitational wave sources

We study the orbital parameters distribution of stars that are scattered into nearly radial orbits and then spiral into a massive black hole (MBH) due to dissipation, in particular by emission of gravitational waves (GW). This is important for GW detection, e.g. by the Laser Interferometer Space Antenna (LISA). Signal identification requires knowledge of the waveforms, which depend on the orbital parameters. We use analytical and Monte Carlo methods to analyze the interplay between GW dissipation and scattering in the presence of a mass sink during the transition from the initial scattering-dominated phase to the final dissipation-dominated phase of the inspiral. Our main results are (1) Stars typically enter the GW-emitting phase with high eccentricities. (2) The GW event rate per galaxy is a few per Gyr for typical central stellar cusps, almost independently of the relaxation time or the MBH mass. (3) For intermediate mass black holes (IBHs) of ~a thousand solar masses such as may exist in dense stellar clusters, the orbits are very eccentric and the inspiral is rapid, so the sources are very short-lived.Comment: ApJ Accepte

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

Analytic study of mass segregation around a massive black hole

We analyze the distribution of stars of arbitrary mass function xi(m) around a massive black hole (MBH). Unless xi is strongly dominated by light stars, the steady-state distribution function approaches a power-law in specific energy x=-E/(m*sigma^2)<x_max with index p=m/4M_0, where E is the energy, sigma is the typical velocity dispersion of unbound stars, and M_0 is the mass averaged over m*xi*x_{max}^p. For light-dominated xi, p can grow as large as 3/2 - much steeper than previously thought. A simple prescription for the stellar density profile around MBHs is provided. We illustrate our results by applying them to stars around the MBH in the Milky Way.Comment: Revised version published in Astrophys. J. Let

Gravitational waves from remnants of ultraluminous X-ray sources

Ultraluminous X-ray sources (ULXs) with X-ray luminosities larger than the Eddington luminosity of stellar mass objects may be powered by intermediate mass black holes (IBHs) of masses Mbh~10^3Msun. If IBHs form in young dense stellar clusters, they can be fed by Roche lobe overflow from a tidally captured massive (Ms>10Msun) stellar companion. After the donor leaves the main sequence it forms a compact remnant, which spirals in due to gravitational wave (GW) emission. We show that space based detectors such as the Laser Interferometer Space Antenna are likely to detect several of these sources. GW sources stemming from this scenario have small eccentricities which give distinct GW signals. Detection of such a GW signal will unambiguously prove the existence of IBHs, and support the hypothesis that some ULXs are powered by IBHs with captured companions.Comment: Minor changes; MNRAS letters accepte

The effect of mass-segregation on gravitational wave sources near massive black holes

Gravitational waves (GWs) from the inspiral of compact remnants (CRs) into massive black holes (MBHs) will be observable to cosmological distances. While a CR spirals in, 2-body scattering by field stars may cause it to fall into the MBH before reaching a short period orbit that would give an observable signal. As a result, only CRs very near (~0.01 pc) the MBH can spiral in successfully. In a multi-mass stellar population, the heaviest objects sink to the center, where they are more likely to slowly spiral into the MBH without being swallowed prematurely. We study how mass-segregation modifies the stellar distribution and the rate of GW events. We find that the inspiral rate per galaxy for white dwarfs is 30 per Gyr, for neutron stars 6 per Gyr, and for stellar black holes (SBHs) 250 per Gyr. The high rate for SBHs is due to their extremely steep density profile, n_{BH}(r)\propto r^{-2}. The GW detection rate will be dominated by SBHs.Comment: Submitted to ApJ

Ultraluminous X-ray Sources as Intermediate Mass Black Holes Fed by Tidally Captured Stars

The nature of ultraluminous X-ray sources (ULXs) is presently unknown. A possible explanation is that they are accreting intermediate mass black holes (IBHs) that are fed by Roche lobe overflow from a tidally captured stellar companion. We show that a star can circularize around an IBH without being destroyed by tidal heating (in contrast to the case of M_bh> 10^6 M_sun massive black holes in galactic centers, where survival is unlikely). We find that the capture and circularization rate is of the order of 5 \times 10^-8 yr^-1, almost independently of the cluster's relaxation time. We follow the luminosity evolution of the binary system during the main sequence Roche lobe overflow phase and show it can maintain ULX-like luminosities for >10 Myr. In particular, we show that the ULX in the young cluster MGG-11 in star-burst galaxy M82, which possibly harbors an IBH, is well explained by this mechanism, and we predict that \gtrsim 10% of similar clusters with IBHs have a tidally captured circularized star. The cluster can evaporate on a time-scale shorter than the lifetime of the binary. This raises the possibility of a ULX that outlives its host cluster, or even lights up only after the cluster has evaporated, in agreement with observations of host-less ULXs.Comment: Accepted version (ApJL), new figure, typos correcte