No abstract available

No abstract available

[en] One of the most exciting potential sources of gravitational waves for low-frequency, space-based gravitational wave (GW) detectors such as the proposed Laser Interferometer Space Antenna (LISA) is the inspiral of compact objects into massive black holes in the centers of galaxies. The detection of waves from such 'extreme mass ratio inspiral' systems (EMRIs) and extraction of information from those waves require template waveforms. The systems' extreme mass ratio means that their waveforms can be determined accurately using black hole perturbation theory. Such calculations are computationally very expensive. There is a pressing need for families of approximate waveforms that may be generated cheaply and quickly but which still capture the main features of true waveforms. In this paper, we introduce a family of such kludge waveforms and describe ways to generate them. Different kinds of kludges have already been used to scope out data analysis issues for LISA. The models we study here are based on computing a particle's inspiral trajectory in Boyer-Lindquist coordinates, and subsequent identification of these coordinates with flat-space spherical polar coordinates. A gravitational waveform may then be computed from the multipole moments of the trajectory in these coordinates, using well-known solutions of the linearised gravitational perturbation equations in flat space time. We compute waveforms using a standard slow-motion quadrupole formula, a quadrupole/octupole formula, and a fast-motion, weak-field formula originally developed by Press. We assess these approximations by comparing to accurate waveforms obtained by solving the Teukolsky equation in the adiabatic limit (neglecting GW backreaction). We find that the kludge waveforms do extremely well at approximating the true gravitational waveform, having overlaps with the Teukolsky waveforms of 95% or higher over most of the parameter space for which comparisons can currently be made. Indeed, we find these kludges to be of such high quality (despite their ease of calculation) that it is possible they may play some role in the final search of LISA data for EMRIs

No abstract available

[en] We explore the precision with which the Einstein Telescope will be able to measure the parameters of intermediate-mass-ratio inspirals, i.e., the inspirals of stellar mass compact objects into intermediate-mass black holes (IMBHs). We calculate the parameter estimation errors using the Fisher Matrix formalism and present results of Monte Carlo simulations of these errors over choices for the extrinsic parameters of the source. These results are obtained using two different models for the gravitational waveform which were introduced in paper I of this series. These two waveform models include the inspiral, merger, and ringdown phases in a consistent way. One of the models, based on the transition scheme of Ori and Thorne [A. Ori and K. S. Thorne, Phys. Rev. D 62, 124022 (2000).], is valid for IMBHs of arbitrary spin; whereas, the second model, based on the effective-one-body approach, has been developed to cross-check our results in the nonspinning limit. In paper I of this series, we demonstrated the excellent agreement in both phase and amplitude between these two models for nonspinning black holes, and that their predictions for signal-to-noise ratios are consistent to within 10%. We now use these waveform models to estimate parameter estimation errors for binary systems with masses 1.4M_·+100M_·, 10M_·+100M_·, 1.4M_·+500M_·, and 10M_·+500M_· and various choices for the spin of the central IMBH. Assuming a detector network of three Einstein Telescopes, the analysis shows that for a 10M_· compact object inspiralling into a 100M_· IMBH with spin q=0.3, detected with a signal-to-noise ratio of 30, we should be able to determine the compact object and IMBH masses, and the IMBH spin magnitude to fractional accuracies of ∼10^-3, ∼10^-3.5, and ∼10^-3, respectively. We also expect to determine the location of the source in the sky and the luminosity distance to within ∼0.003 steradians and ∼10%, respectively. We also compute results for several different possible configurations of the detector network to assess how the precision of parameter determination depends on the network configuration.

[en] We investigate the linearized form of metric f(R)-gravity, assuming that f(R) is analytic about R=0 so it may be expanded as f(R)=R+a₂R²/2+.... Gravitational radiation is modified, admitting an extra mode of oscillation, that of the Ricci scalar. We derive an effective energy-momentum tensor for the radiation. We also present weak-field metrics for simple sources. These are distinct from the equivalent Kerr (or Schwarzschild) forms. We apply the metrics to tests that could constrain f(R). We show that light deflection experiments cannot distinguish f(R)-gravity from general relativity as both have an effective post-Newtonian parameter γ=1. We find that planetary precession rates are enhanced relative to general relativity; from the orbit of Mercury we derive the bound |a₂| < or approx. 1.2x10¹⁸ m². Gravitational-wave astronomy may be more useful: considering the phase of a gravitational waveform we estimate deviations from general relativity could be measurable for an extreme-mass-ratio inspiral about a 10⁶M_· black hole if |a₂| > or approx. 10¹⁷m², assuming that the weak-field metric of the black hole coincides with that of a point mass. However Eoet-Wash experiments provide the strictest bound |a₂| < or approx. 2x10^-9 m². Although the astronomical bounds are weaker, they are still of interest in the case that the effective form of f(R) is modified in different regions, perhaps through the chameleon mechanism. Assuming the laboratory bound is universal, we conclude that the propagating Ricci scalar mode cannot be excited by astrophysical sources.

[en] We derive an analytic expression for the energy spectrum of gravitational waves from a parabolic Keplerian binary by taking the limit of the Peters and Mathews spectrum for eccentric orbits. This demonstrates that the location of the peak of the energy spectrum depends primarily on the orbital periapse rather than the eccentricity. We compare this weak-field result to strong-field calculations and find it is reasonably accurate (∼10%) provided that the azimuthal and radial orbital frequencies do not differ by more than ∼10%. For equatorial orbits in the Kerr spacetime, this corresponds to periapse radii of r_p > or approx. 20M. These results can be used to model radiation bursts from compact objects on highly eccentric orbits about massive black holes in the local Universe, which could be detected by the Laser Interferometer Space Antenna (LISA).

[en] The Einstein Telescope (ET) is a proposed third-generation ground-based interferometric gravitational wave detector, for which the target is a sensitivity that is a factor of 10 better than Advanced LIGO and a frequency range that extends down to ∼1 Hz. Such a third-generation interferometer will provide opportunities to test Einstein's theory of relativity in the strong field and will realize precision gravitational wave astronomy with a thousandfold increase in the expected number of events over the advanced ground-based detectors. A design study for ET is currently underway, so it is timely to assess the science that could be done with such an instrument. This paper is the first in a series that will carry out a detailed study of intermediate-mass-ratio inspirals (IMRIs) for ET. In the context of ET, an IMRI is the inspiral of a neutron star or stellar-mass black hole into an intermediate mass black hole (IMBH). In this paper we focus on the development of IMRI waveform models for circular and equatorial inspirals. We consider two approximations for the waveforms, which both incorporate the inspiral, merger, and ringdown phases in a consistent way. One approximation, valid for IMBHs of arbitrary spin, uses the transition model of Ori and Thorne [A. Ori and K. S. Thorne, Phys. Rev. D 62, 124022 (2000).] to describe the merger, and this is then matched smoothly onto a ringdown waveform. The second approximation uses the effective one body approach to model the merger phase of the waveform and is valid for nonspinning IMBHs. In this paper, we use both waveform models to compute signal-to-noise ratios for IMRI sources detectable by ET. At a redshift of z=1, we find typical signal-to-noise ratios for IMRI systems with masses 1.4M_·+100M_·, 10M_·+100M_·, 1.4M_·+500M_· and 10M_·+500M_· of ∼10-25, ∼40-80, ∼3-15, and ∼10-60, respectively. We also find that the two models make predictions for nonspinning inspirals that are consistent to about 10%.

[en] We present an improved numerical kludge waveform model for circular, equatorial extreme-mass-ratio inspirals (EMRIs). The model is based on true Kerr geodesics, augmented by radiative self-force corrections derived from perturbative calculations, and in this paper for the first time we include conservative self-force corrections that we derive by comparison to post-Newtonian results. We present results of a Monte Carlo simulation of parameter estimation errors computed using the Fisher matrix and also assess the theoretical errors that would arise from omitting the conservative correction terms we include here. We present results for three different types of system, namely, the inspirals of black holes, neutron stars, or white dwarfs into a supermassive black hole (SMBH). The analysis shows that for a typical source (a 10M_· compact object captured by a 10⁶M_· SMBH at a signal to noise ratio of 30) we expect to determine the two masses to within a fractional error of ∼10^-4, measure the spin parameter q to ∼10^-4.5, and determine the location of the source on the sky and the spin orientation to within 10^-3 steradians. We show that, for this kludge model, omitting the conservative corrections leads to a small error over much of the parameter space, i.e., the ratio R of the theoretical model error to the Fisher matrix error is R<1 for all ten parameters in the model. For the few systems with larger errors typically R<3 and hence the conservative corrections can be marginally ignored. In addition, we use our model and first-order self-force results for Schwarzschild black holes to estimate the error that arises from omitting the second-order radiative piece of the self-force. This indicates that it may not be necessary to go beyond first order to recover accurate parameter estimates.

[en] One of the most exciting potential sources of gravitational waves for the Laser Interferometer Space Antenna (LISA) are the inspirals of approximately solar mass compact objects into massive black holes in the centres of galaxies-extreme mass ratio inspirals (EMRIs). LISA should observe between a few tens and a few hundred EMRIs over the mission lifetime, mostly at low redshifts (z∼< 1). Each observation will provide a measurement of the parameters of the host system to unprecendented precision. LISA EMRI observations will thus offer a new and unique way to probe black holes at low redshift. In this paper we provide a description of the population of EMRI events that LISA is likely to observe, and describe how the numbers of events vary with changes in the underlying assumptions about the black hole population. We also provide fitting functions that characterize LISA's ability to detect EMRIs and which will allow LISA event rates to be computed for arbitrary population models. We finish with a discussion of an ongoing programme that will use these results to assess what constraints LISA observations could place on galaxy evolution models.