Detecting gravitational waves from test-mass bodies orbiting a Kerr black hole with P-approximant templates

In this study we apply post-Newtonian (T-approximants) and resummed post-Newtonian (P-approximants) to the case of a test-particle in equatorial orbit around a Kerr black hole. We compare the two approximants by measuring their effectualness (i.e. larger overlaps with the exact signal), and faithfulness (i.e. smaller biases while measuring the parameters of the signal) with the exact (numerical) waveforms. We find that in the case of prograde orbits, T-approximant templates obtain an effectualness of ~0.99 for spins q < 0.75. For 0.75 < q < 0.95, the effectualness drops to about 0.82. The P-approximants achieve effectualness of > 0.99 for all spins up to q = 0.95. The bias in the estimation of parameters is much lower in the case of P-approximants than T-approximants. We find that P-approximants are both effectual and faithful and should be more effective than T-approximants as a detection template family when q > 0. For q < 0 both T- and P-approximants perform equally well so that either of them could be used as a detection template family. However, for parameter estimation, the P-approximant templates still outperforms the T-approximants.Comment: 11 Pages - 9 figures. Accepted for publication. Proceedings of GWDAW 9. Special edition of Classical and Quantum Gravit

Parameter estimation of compact binaries using the inspiral and ringdown waveforms

We analyze the problem of parameter estimation for compact binary systems that could be detected by ground-based gravitational wave detectors. So far this problem has only been dealt with for the inspiral and the ringdown phases separately. In this paper, we combine the information from both signals, and we study the improvement in parameter estimation, at a fixed signal-to-noise ratio, by including the ringdown signal without making any assumption on the merger phase. The study is performed for both initial and advanced LIGO and VIRGO detectors.Comment: matching cqg versio

Inspiral, merger and ringdown of unequal mass black hole binaries: a multipolar analysis

We study the inspiral, merger and ringdown of unequal mass black hole binaries by analyzing a catalogue of numerical simulations for seven different values of the mass ratio (from q=M2/M1=1 to q=4). We compare numerical and Post-Newtonian results by projecting the waveforms onto spin-weighted spherical harmonics, characterized by angular indices (l,m). We find that the Post-Newtonian equations predict remarkably well the relation between the wave amplitude and the orbital frequency for each (l,m), and that the convergence of the Post-Newtonian series to the numerical results is non-monotonic. To leading order the total energy emitted in the merger phase scales like eta^2 and the spin of the final black hole scales like eta, where eta=q/(1+q)^2 is the symmetric mass ratio. We study the multipolar distribution of the radiation, finding that odd-l multipoles are suppressed in the equal mass limit. Higher multipoles carry a larger fraction of the total energy as q increases. We introduce and compare three different definitions for the ringdown starting time. Applying linear estimation methods (the so-called Prony methods) to the ringdown phase, we find resolution-dependent time variations in the fitted parameters of the final black hole. By cross-correlating information from different multipoles we show that ringdown fits can be used to obtain precise estimates of the mass and spin of the final black hole, which are in remarkable agreement with energy and angular momentum balance calculations.Comment: 51 pages, 28 figures, 16 tables. Many improvements throughout the text in response to the referee report. The calculation of multipolar components in Appendix A now uses slightly different conventions. Matches version in press in PR

Gravitational radiation for extreme mass ratio inspirals to the 14th post-Newtonian order

We derive gravitational waveforms needed to compute the 14th post-Newtonian (14PN) order energy flux for a particle in circular orbit around a Schwarzschild black hole, i.e. $v^{28}$ beyond the leading Newtonian approximation where $v$ is the orbital velocity of a test particle. We investigate the convergence of the energy flux in the PN expansion and suggest a fitting formula which can be used to extract unknown higher order PN coefficients from accurate numerical data for more general orbits around a Kerr black hole. The phase difference between the 14PN waveforms and numerical waveforms after two years inspiral is shown to be about $10^{-7}$ for $\mu/M=10^{-4}$ and $10^{-3}$ for $\mu/M=10^{-5}$ where $\mu$ is the mass of a compact object and $M$ the mass of the central supermassive black hole. In first order black hole perturbation theory, for extreme mass ratio inspirals which are one of the main targets of Laser Interferometer Space Antenna, the 14PN expressions will lead to the data analysis accuracies comparable to the ones resulting from high precision numerical waveforms.Comment: 8 pages, 2 figure

An efficient iterative method to reduce eccentricity in numerical-relativity simulations of compact binary inspiral

We present a new iterative method to reduce eccentricity in black-hole-binary simulations. Given a good first estimate of low-eccentricity starting momenta, we evolve puncture initial data for ~4 orbits and construct improved initial parameters by comparing the inspiral with post-Newtonian calculations. Our method is the first to be applied directly to the gravitational-wave (GW) signal, rather than the orbital motion. The GW signal is in general less contaminated by gauge effects, which, in moving-puncture simulations, limit orbital-motion-based measurements of the eccentricity to an uncertainty of $\Delta e \sim 0.002$, making it difficult to reduce the eccentricity below this value. Our new method can reach eccentricities below $10^{-3}$ in one or two iteration steps; we find that this is well below the requirements for GW astronomy in the advanced detector era. Our method can be readily adapted to any compact-binary simulation with GW emission, including black-hole-binary simulations that use alternative approaches, and neutron-star-binary simulations. We also comment on the differences in eccentricity estimates based on the strain $h$, and the Newman-Penrose scalar $\Psi_4$.Comment: 24 pages, 25 figures, pdflatex; v2: minor change

An Effective Search Method for Gravitational Ringing of Black Holes

We develop a search method for gravitational ringing of black holes. The gravitational ringing is due to complex frequency modes called the quasi-normal modes that are excited when a black hole geometry is perturbed. The detection of it will be a direct confirmation of the existence of a black hole. Assuming that the ringdown waves are dominated by the fundamental mode with least imaginary part, we consider matched filtering and develop an optimal method to search for the ringdown waves that have damped sinusoidal wave forms. When we use the matched filtering method, the data analysis with a lot of templates required. Here we have to ensure a proper match between the filter as a template and the real wave. It is necessary to keep the detection efficiency as high as possible under limited computational costs. First, we consider the white noise case for which the matched filtering can be studied analytically. We construct an efficient method for tiling the template space. Then, using a fitting curve of the TAMA300 DT6 noise spectrum, we numerically consider the case of colored noise. We find our tiling method developed for the white noise case is still valid even if the noise is colored.Comment: 17 pages, 9 figures. Accepted to Phys. Rev. D, Note correction to Eq. (3-25), A few comments added and minor typos correcte