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

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

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 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

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-wave interaction in a beam-plasma system

Coupling coefficient derived for three-wave interaction in beam plasma syste

The influence of preparation methodology on high voltage behaviour of alumina insulators in vacuum

The flashover characteristics of an insulator bridged high voltage vacuum gap can play an important role in the overall performance of a high voltage device, for example in the extreme environments of high energy particle accelerators. The detailed preparation of the insulators is, at present, governed by the commercial production methods and by standard bulk cleaning processes, which for a particular application may be far from optimum. The influence of particular cleaning technique have been investigated for commercially available alumina samples, with measurement of surface characteristics by scanning electron microscopy and laser diffraction and fields up to 200 kV/cm. The results of the different measurements are discussed in the overall context of the problems encountered in the full sized high voltage devices, and suggestions are made as to how the performance of alumina insulators could be improved by modification of the production and preparation specification

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

Focused Ion Beam Milling Strategies of Photonic Crystal Structures in Silicon

We report on optimisation of the side wall angle of focused ion beam (FIB) fabricated submicron diameter holes in silicon. Two optimisation steps were performed. First, we compare two different FIB scanning procedures and show the advantages of using a spiral scanning method for the definition of holes in photonic crystal slab structures. Secondly, we investigate the effect on the geometry, of parameters for reducing the tapering effect. Furthermore, we report on the initial results regarding effects of $Ga^{+}$ ion implantation during FIB milling on optical losses, both before and after an annealing step, showing over a decade reduction of optical loss