Confusion Noise from LISA Capture Sources

Captures of compact objects (COs) by massive black holes (MBHs) in galactic nuclei will be an important source for LISA, the space-based gravitational-wave (GW) detector. However, a large fraction of captures will not be individually resolvable--either because they are too distant, have unfavorable orientation, or have too many years to go before final plunge--and so will constitute a source of ``confusion noise,'' obscuring other types of sources. Here we estimate the shape and overall magnitude of the spectrum of confusion noise from CO captures. The overall magnitude depends on the capture rates, which are rather uncertain, so we present results for a plausible range of rates. We show that the impact of capture confusion noise on the total LISA noise curve ranges from insignificant to modest, depending on these rates. Capture rates at the high end of estimated ranges would raise LISA's overall (effective) noise level by at most a factor \sim 2. While this slightly elevated noise level would somewhat decrease LISA's sensitivity to other classes of sources, overall, this would be a pleasant problem for LISA to have: It would also imply that detection rates for CO captures were at nearly their maximum possible levels (given LISA's baseline design). This paper includes several other results that should be useful in further studies of LISA capture sources, including (i) a calculation of the total GW energy output from generic inspirals into Kerr MBHs, and (ii) an approximate GW energy spectrum for a typical capture

Towards the solution of the relativistic gravitational radiation reaction problem for binary black holes

Here we present the results of applying the generalized Riemann zeta-function regularization method to the gravitational radiation reaction problem. We analyze in detail the headon collision of two nonspinning black holes with extreme mass ratio. The resulting reaction force on the smaller hole is repulsive. We discuss the possible extensions of these method to generic orbits and spinning black holes. The determination of corrected trajectories allows to add second perturbative corrections with the consequent increase in the accuracy of computed waveforms.Comment: Contribution to the Proceedings of the 3rd LISA Symposiu

Orbital evolution of a particle around a black hole: II. Comparison of contributions of spin-orbit coupling and the self force

We consider the evolution of the orbit of a spinning compact object in a quasi-circular, planar orbit around a Schwarzschild black hole in the extreme mass ratio limit. We compare the contributions to the orbital evolution of both spin-orbit coupling and the local self force. Making assumptions on the behavior of the forces, we suggest that the decay of the orbit is dominated by radiation reaction, and that the conservative effect is typically dominated by the spin force. We propose that a reasonable approximation for the gravitational waveform can be obtained by ignoring the local self force, for adjusted values of the parameters of the system. We argue that this approximation will only introduce small errors in the astronomical determination of these parameters.Comment: 11 pages, 7 figure

Perturbative evolution of particle orbits around Kerr black holes: time domain calculation

Treating the Teukolsky perturbation equation numerically as a 2+1 PDE and smearing the singularities in the particle source term by the use of narrow Gaussian distributions, we have been able to reproduce earlier results for equatorial circular orbits that were computed using the frequency domain formalism. A time domain prescription for a more general evolution of nearly geodesic orbits under the effects of radiation reaction is presented. This approach can be useful when tackling the more realistic problem of a stellar-mass black hole moving on a generic orbit around a supermassive black hole under the influence of radiation reaction forces.Comment: 8 pages, 5 figures, problems with references and double-printing fixe

A Toy Model for Testing Finite Element Methods to Simulate Extreme-Mass-Ratio Binary Systems

Extreme mass ratio binary systems, binaries involving stellar mass objects orbiting massive black holes, are considered to be a primary source of gravitational radiation to be detected by the space-based interferometer LISA. The numerical modelling of these binary systems is extremely challenging because the scales involved expand over several orders of magnitude. One needs to handle large wavelength scales comparable to the size of the massive black hole and, at the same time, to resolve the scales in the vicinity of the small companion where radiation reaction effects play a crucial role. Adaptive finite element methods, in which quantitative control of errors is achieved automatically by finite element mesh adaptivity based on posteriori error estimation, are a natural choice that has great potential for achieving the high level of adaptivity required in these simulations. To demonstrate this, we present the results of simulations of a toy model, consisting of a point-like source orbiting a black hole under the action of a scalar gravitational field.Comment: 29 pages, 37 figures. RevTeX 4.0. Minor changes to match the published versio

Approximating the inspiral of test bodies into Kerr black holes

We present a new approximate method for constructing gravitational radiation driven inspirals of test-bodies orbiting Kerr black holes. Such orbits can be fully described by a semi-latus rectum $p$, an eccentricity $e$, and an inclination angle $\iota$; or, by an energy $E$, an angular momentum component $L_z$, and a third constant $Q$. Our scheme uses expressions that are exact (within an adiabatic approximation) for the rates of change ($\dot{p}$, $\dot{e}$, $\dot{\iota}$) as linear combinations of the fluxes ($\dot{E}$, $\dot{L_z}$, $\dot{Q}$), but uses quadrupole-order formulae for these fluxes. This scheme thus encodes the exact orbital dynamics, augmenting it with approximate radiation reaction. Comparing inspiral trajectories, we find that this approximation agrees well with numerical results for the special cases of eccentric equatorial and circular inclined orbits, far more accurate than corresponding weak-field formulae for ($\dot{p}$, $\dot{e}$, $\dot{\iota}$). We use this technique to study the inspiral of a test-body in inclined, eccentric Kerr orbits. Our results should be useful tools for constructing approximate waveforms that can be used to study data analysis problems for the future LISA gravitational-wave observatory, in lieu of waveforms from more rigorous techniques that are currently under development.Comment: 15 pages, 5 figures, submitted to PR

Gravitational Waves from a Compact Star in a Circular, Inspiral Orbit, in the Equatorial Plane of a Massive, Spinning Black Hole, as Observed by LISA

Results are presented from high-precision computations of the orbital evolution and emitted gravitational waves for a stellar-mass object spiraling into a massive black hole in a slowly shrinking, circular, equatorial orbit. The focus of these computations is inspiral near the innermost stable circular orbit (isco)---more particularly, on orbits for which the angular velocity Omega is 0.03 < Omega/Omega_{isco} < 1. The computations are based on the Teukolsky-Sasaki-Nakamura formalism, and the results are tabulated in a set of functions that are of order unity and represent relativistic corrections to low-orbital-velocity formulas. These tables can form a foundation for future design studies for the LISA space-based gravitational-wave mission. A first survey of applications to LISA is presented: Signal to noise ratios S/N are computed and graphed as functions of the time-evolving gravitational-wave frequency for representative values of the hole's mass M and spin a and the inspiraling object's mass \mu, with the distance to Earth chosen to be r_o = 1 Gpc. These S/N's show a very strong dependence on the black-hole spin, as well as on M and \mu. A comparison with predicted event rates shows strong promise for detecting these waves, but not beyond about 1Gpc if the inspiraling object is a white dwarf or neutron star. This argues for a modest lowering of LISA's noise floor. A brief discussion is given of the prospects for extracting information from the observed wavesComment: Physical Review D, in press; 21 pages, 9 figures, 10 tables it is present in the RevTeX fil

The Carter Constant for Inclined Orbits About a Massive Kerr Black Hole: near-circular, near-polar orbits

In an extreme mass-ratio binary black hole system, a non-equatorial orbit will list (i.e. increase its angle of inclination, {\iota}) as it evolves in Kerr spacetime. The abutment, a set of evolving, near-polar, retrograde orbits, for which the instantaneous Carter constant (Q) is at its maximum value (Q_{X}) for given values of latus rectum (l) and eccentricity (e), has been introduced as a laboratory in which the consistency of dQ/dt with corresponding evolution equations for dl/dt and de/dt might be tested independently of a specific radiation back-reaction model. To demonstrate the use of the abutment as such a laboratory, a derivation of dQ/dt, based only on published formulae for dl/dt and de/dt, was performed for elliptical orbits on the abutment. The resulting expression for dQ/dt matched the published result to the second order in e. We believe the abutment is a potentially useful tool for improving the accuracy of evolution equations to higher orders of e and l^{1}.Comment: 35 Pages, 1 figure, Accepted for publication in Cent Eur J Phy

Intermediate and extreme mass-ratio inspirals — astrophysics, science applications and detection using LISA

Black hole binaries with extreme (gtrsim104:1) or intermediate (~102–104:1) mass ratios are among the most interesting gravitational wave sources that are expected to be detected by the proposed laser interferometer space antenna (LISA). These sources have the potential to tell us much about astrophysics, but are also of unique importance for testing aspects of the general theory of relativity in the strong field regime. Here we discuss these sources from the perspectives of astrophysics, data analysis and applications to testing general relativity, providing both a description of the current state of knowledge and an outline of some of the outstanding questions that still need to be addressed. This review grew out of discussions at a workshop in September 2006 hosted by the Albert Einstein Institute in Golm, Germany

Physics, Astrophysics and Cosmology with Gravitational Waves

Gravitational wave detectors are already operating at interesting sensitivity levels, and they have an upgrade path that should result in secure detections by 2014. We review the physics of gravitational waves, how they interact with detectors (bars and interferometers), and how these detectors operate. We study the most likely sources of gravitational waves and review the data analysis methods that are used to extract their signals from detector noise. Then we consider the consequences of gravitational wave detections and observations for physics, astrophysics, and cosmology.Comment: 137 pages, 16 figures, Published version <http://www.livingreviews.org/lrr-2009-2