Black Hole Inspirals Research Articles

Influence of conservative corrections on parameter estimation for extreme-mass-ratio inspirals

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{sub {center_dot}} compact object captured by a 10{sup 6}M{sub {center_dot}} SMBH at a signal to noise ratio of 30) we expect to determine the two masses to within a fractional error of {approx}10{sup -4}, measure the spin parameter q to {approx}10{sup -4.5}, and determine the location of the source on the sky and the spin orientation to within 10{sup -3} steradians. We show that, for this kludge model, omitting the conservative corrections leads to a small error overmore » 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.« less

IMEX Evolution of Scalar Fields on Curved Backgrounds

Inspiral of binary black holes occurs over a time-scale of many orbits, far longer than the dynamical time-scale of the individual black holes. Explicit evolutions of a binary system therefore require excessively many time steps to capture interesting dynamics. We present a strategy to overcome the Courant-Friedrichs-Lewy condition in such evolutions, one relying on modern implicit-explicit ODE solvers and multidomain spectral methods for elliptic equations. Our analysis considers the model problem of a forced scalar field propagating on a generic curved background. Nevertheless, we encounter and address a number of issues pertinent to the binary black hole problem in full general relativity. Specializing to the Schwarzschild geometry in Kerr-Schild coordinates, we document the results of several numerical experiments testing our strategy.

LISA detections of massive black hole inspirals: Parameter extraction errors due to inaccurate template waveforms

The planned Laser Interferometer Space Antenna (LISA) is expected to detect the inspiral and merger of massive black hole binaries (MBHBs) at $z\ensuremath{\lesssim}5$ with signal-to-noise ratios (SNRs) of hundreds to thousands. Because of these high SNRs, and because these SNRs accrete over periods of weeks to months, it should be possible to extract the physical parameters of these systems with high accuracy; for instance, for a $\ensuremath{\sim}{10}^{6}{M}_{\ensuremath{\bigodot}}$ MBHBs at $z=1$ it should be possible to determine the two masses to $\ensuremath{\sim}0.1%$ and the sky location to $\ensuremath{\sim}1\ifmmode^\circ\else\textdegree\fi{}$. However, those are just the errors due to noise: there will be additional ``theoretical'' errors due to inaccuracies in our best model waveforms, which are still only approximate. The goal of this paper is to estimate the typical magnitude of these theoretical errors. We develop mathematical tools for this purpose, and apply them to a somewhat simplified version of the MBHB problem, in which we consider just the inspiral part of the waveform and neglect spin-induced precession, eccentricity, and PN amplitude corrections. For this simplified version, we estimate that theoretical uncertainties in sky position will typically be $\ensuremath{\sim}1\ifmmode^\circ\else\textdegree\fi{}$, i.e., comparable to the statistical uncertainty. For the mass and spin parameters, our results suggest that while theoretical errors will be rather small absolutely, they could still dominate over statistical errors (by roughly an order of magnitude) for the strongest sources. The tools developed here should be useful for estimating the magnitude of theoretical errors in many other problems in gravitational-wave astronomy.

Coherent Bayesian analysis of inspiral signals

In this paper we present a Bayesian parameter estimation method for the analysis of interferometric gravitational wave observations of an inspiral of binary compact objects using data recorded simultaneously by a network of several interferometers at different sites. We consider neutron star or black hole inspirals that are modeled to 3.5 post-Newtonian (PN) order in phase and 2.5 PN in amplitude. Inference is facilitated using Markov chain Monte Carlo (MCMC) methods that are adapted in order to efficiently explore the particular parameter space. Examples are shown to illustrate how and what information about the different parameters can be derived from the data. This study uses simulated signals and data with noise characteristics that are assumed to be defined by the LIGO and Virgo detectors operating at their design sensitivities. Nine parameters are estimated, including those associated with the binary system plus its location on the sky. We explain how this technique will be part of a detection pipeline for binary systems of compact objects with masses up to , including cases where the ratio of the individual masses can be extreme.

Maximum Kick from Nonspinning Black-Hole Binary Inspiral

When unequal-mass black holes merge, the final black hole receives a kick due to the asymmetric loss of linear momentum in the gravitational radiation emitted during the merger. The magnitude of this kick has important astrophysical consequences. Recent breakthroughs in numerical relativity allow us to perform the largest parameter study undertaken to date in numerical simulations of binary black-hole inspirals. We study nonspinning black-hole binaries with mass ratios from q=M1/M2=1 to q=0.25 (eta=q/(1+q)2 from 0.25 to 0.16). We accurately calculate the velocity of the kick to within 6%, and the final spin of the black holes to within 2%. A maximum kick of 175.2+/-11 km s(-1) is achieved for eta=0.195+/-0.005.

Application of the probability event horizon filter to constrain the local rate density of binary black hole inspirals with advanced LIGO

The temporal evolution of the gravitational wave background signal resulting from stellar-mass binary black hole (BBH) inspirals has a unique statistical signature. We describe the application of a new filter, based on the ‘probability event horizon’ (PEH) concept, that utilizes both the temporal and spatial source distribution to constrain the local rate density, r0, of BBH inspiral events in the nearby Universe. Assuming advanced LIGO (Laser Interferometer Gravitational Wave Observatory) sensitivities and an upper rate of Galactic BBH inspirals of 30 Myr−1, we simulate gravitational wave data and apply a fitting procedure to the PEH filtered data. To determine the accuracy of the PEH filter in constraining r0, a comparison is made with a fit to the brightness distribution of events. We apply both methods to a data stream containing a background of Gaussian-distributed false alarms. We find that the brightness distribution yields lower standard errors, but is biased by the false alarms. In comparison, the PEH method is less prone to errors resulting from false alarms but has a lower resolution as fewer events contribute to the data. Used in combination, the PEH and brightness distribution methods provide an improved estimate of the rate density.

Short GRB and binary black hole standard sirens as a probe of dark energy

Observations of the gravitational radiation from well-localized, inspiraling compact-object binaries can measure absolute source distances with high accuracy. When coupled with an independent determination of redshift through an electromagnetic counterpart, these standard sirens can provide an excellent probe of the expansion history of the Universe and the dark energy. Short $\ensuremath{\gamma}$-ray bursts, if produced by merging neutron star binaries, would be standard sirens with known redshifts detectable by ground-based gravitational wave (GW) networks such as Advanced Laser Interferometer Gravitational-wave Observatory (LIGO), Virgo, and Australian International Gravitational Observatory (AIGO). Depending upon the collimation of these GRBs, the measurement of about 10 GW-GRB events (corresponding to about 1 yr of observation with an advanced GW detector network and an all-sky GRB monitor) can measure the Hubble constant $h$ to $\ensuremath{\sim}2--3%$. When combined with measurement of the absolute distance to the last scattering surface of the cosmic microwave background, this determines the dark energy equation of state parameter $w$ to $\ensuremath{\sim}9%$. Similarly, supermassive binary black hole inspirals will be standard sirens detectable by Laser Interferometer Space Antenna (LISA). Depending upon the precise redshift distribution, $\ensuremath{\sim}100$ sources could measure $w$ at the $\ensuremath{\sim}4%$ level.

Erratum: Physical template family for gravitational waves from precessing binaries of spinning compact objects: Application to single-spin binaries [Phys. Rev. D69, 104017 (2004)

The detection of the gravitational waves (GWs) emitted by precessing binaries of spinning compact objects is complicated by the large number of parameters (such as the magnitudes and initial directions of the spins, and the position and orientation of the binary with respect to the detector) that are required to model accurately the precession-induced modulations of the GW signal. In this paper we describe a fast matched-filtering search scheme for precessing binaries, and we adopt the physical template family proposed by Buonanno, Chen, and Vallisneri [Phys.Rev.D 67, 104025 (2003)] for ground-based interferometers. This family provides essentially exact waveforms, written directly in terms of the physical parameters, for binaries with a single significant spin, and for which the observed GW signal is emitted during the phase of adiabatic inspiral (for LIGO-I and VIRGO, this corresponds to a total mass M < 15Msun). We show how the detection statistic can be maximized automatically over all the parameters (including the position and orientation of the binary with respect to the detector), except four (the two masses, the magnitude of the single spin, and the opening angle between the spin and the orbital angular momentum), so the template bank used in the search is only four-dimensional; this technique is relevant also to the searches for GW from extreme--mass-ratio inspirals and supermassive blackhole inspirals to be performed using the space-borne detector LISA. Using the LIGO-I design sensitivity, we compute the detection threshold (~10) required for a false-alarm probability of 10^(-3)/year, and the number of templates (~76,000) required for a minimum match of 0.97, for the mass range (m1,m2)=[7,12]Msun*[1,3]Msun.

Erratum: Detection template families for gravitational waves from the final stages of binary–black-hole inspirals: Nonspinning case [Phys. Rev. D67, 024016 (2003)

We investigate the problem of detecting gravitational waves from binaries of nonspinning black holes with masses m = 5--20 Msun, moving on quasicircular orbits, which are arguably the most promising sources for first-generation ground-based detectors. We analyze and compare all the currently available post--Newtonian approximations for the relativistic two-body dynamics; for these binaries, different approximations predict different waveforms. We then construct examples of detection template families that embed all the approximate models, and that could be used to detect the true gravitational-wave signal (but not to characterize accurately its physical parameters). We estimate that the fitting factor for our detection families is >~0.95 (corresponding to an event-rate loss <~15%) and we estimate that the discretization of the template family, for ~10^4 templates, increases the loss to <~20%.

Probing the nonlinear structure of general relativity with black hole binaries

Observations of the inspiral of massive binary black holes (BBH) in the Laser Interferometer Space Antenna (LISA) and stellar mass binary black holes in the European Gravitational Wave Observatory (EGO) offer an unique opportunity to test the nonlinear structure of general relativity. For a binary composed of two nonspinning black holes, the nonlinear general relativistic effects depend only on the masses of the constituents. In a recent paper, we explored the possibility of a test to determine all the post-Newtonian coefficients in the gravitational wave phasing. However, mutual covariances dilute the effectiveness of such a test. In this paper, we propose a more powerful test in which the various post-Newtonian coefficients in the gravitational wave phasing are systematically measured by treating three of them as independent parameters and demanding their mutual consistency. LISA (EGO) will observe BBH inspirals with a signal-to-noise ratio of more than 1000 (100) and thereby test the self-consistency of each of the nine post-Newtonian coefficients that have so-far been computed, by measuring the lower order coefficients to a relative accuracy of ∼10-5 (respectively, ∼10-4) and the higher order coefficients to a relative accuracy in the range 10-4-0.1 (respectively, 10-3-1).

Laser Interferometer Space Antenna double black holes: dynamics in gaseous nuclear discs

We study the inspiral of double black holes, with masses in the Laser Interferometer Space Antenna (LISA) window of detectability, orbiting inside a massive circumnuclear, rotationally supported gaseous disc. Using high-resolution smoothed particle hydrodynamics simulations, we follow the black hole dynamics in the early phase when gas-dynamical friction acts on the black holes individually, and continue our simulation until they form a close binary. We find that in the early sinking the black holes lose memory of their initial orbital eccentricity if they corotate with the gaseous disc. As a consequence, the massive black holes bind forming a binary with a low eccentricity, consistent with zero within our numerical resolution limit. The cause of circularization resides in the rotation present in the gaseous background where dynamical friction operates. Circularization may hinder gravitational waves from taking over and leading the binary to coalescence. In the case of counter-rotating orbits, the initial eccentricity (if present) does not decrease, and the black holes may bind forming an eccentric binary. When dynamical friction has subsided, for equal mass black holes and regardless their initial eccentricity, angular momentum loss, driven by the gravitational torque exerted on the binary by surrounding gas, is nevertheless observable down to the smallest scale probed (≃1 pc). In the case of unequal masses, dynamical friction remains efficient down to our resolution limit, and there is no sign of formation of any ellipsoidal gas distribution that may further harden the binary. During inspiral, gravitational capture of gas by the black holes occurs mainly along circular orbits; eccentric orbits imply high relative velocities and weak gravitational focusing. Thus, the active galactic nucleus activity may be excited during the black hole pairing process and double active nuclei may form when circularization is completed, on distance scales of tens of parsecs.

Search for gravitational waves from binary black hole inspirals in LIGO data

We report on a search for gravitational waves from binary black hole inspirals in the data from the second science run of the LIGO interferometers. The search focused on binary systems with component masses between 3 and 20 solar masses. Optimally oriented binaries with distances up to 1 Mpc could be detected with efficiency of at least 90%. We found no events that could be identified as gravitational waves in the 385.6 hours of data that we searched.

Report on the search for binary black holes inspiral in S3 LIGO data

We report on the search for gravitational waves emitted by non-spinning binary black hole inspirals in the data taken during the third LIGO science run (S3). We give an overview of the data acquired during S3 and the target waveforms that we are searching for in this analysis. We briefly describe how the data was filtered using a BCV detection template family (using an hexagonal template bank placement in the mass parameter plane). Finally, we report on preliminary estimates of the sensitivity of the three LIGO detectors using software injections of effective one-body waveforms with component masses in the range 3-40 M⊙ and total mass M ⩽ 40 M⊙. We show that during S3, the three LIGO detectors have a detection efficiency of 50% up to several Mpc for L1 and H2, and up to 30 Mpc for H1.

Using Gravitational‐Wave Standard Sirens

Gravitational waves (GWs) from supermassive binary black hole (BBH) inspirals are potentially powerful standard sirens (the GW analog to standard candles) (Schutz 1986, 2002). Because these systems are well-modeled, the space-based GW observatory LISA will be able to measure the luminosity distance (but not the redshift) to some distant massive BBH systems with 1-10% accuracy. This accuracy is largely limited by pointing error: GW sources generally are poorly localized on the sky. Localizing the binary independently (e.g., through association with an electromagnetic counterpart) greatly reduces this positional error. An electromagnetic counterpart may also allow determination of the event's redshift. In this case, BBH coalescence would constitute an extremely precise (better than 1%) standard candle visible to high redshift. In practice, gravitational lensing degrades this precision, though the candle remains precise enough to provide useful information about the distance-redshift relation. Even if very rare, these GW standard sirens would complement, and increase confidence in, other standard candles.

Periodic standing-wave approximation: Nonlinear scalar fields, adapted coordinates, and the eigenspectral method

The periodic standing wave (PSW) method for the binary inspiral of black holes and neutron stars computes exact numerical solutions for periodic standing-wave spacetimes and then extracts approximate solutions of the physical problem, with outgoing waves. The method requires solution of a boundary-value problem with a mixed (hyperbolic and elliptic) character. We present here a new numerical method for such problems, based on three innovations: (i) a coordinate system adapted to the geometry of the problem, (ii) an expansion in multipole moments of these coordinates and a filtering out of higher moments, and (iii) the replacement of the continuum multipole moments with their analogs for a discrete grid. We illustrate the efficiency and accuracy of this method with nonlinear scalar model problems. Finally, we take advantage of the ability of this method to handle highly nonlinear models to demonstrate that the outgoing approximations extracted from the standing-wave solutions are highly accurate even in the presence of strong nonlinearities.

Testing alternative theories of gravity using LISA

We investigate the possible bounds which could be placed on alternative theories of gravity using gravitational wave detection from inspiralling compact binaries with the proposed LISA space interferometer. Specifically, we estimate lower bounds on the coupling parameter ω of scalar–tensor theories of the Brans–Dicke type and on the Compton wavelength of the graviton λg in hypothetical massive graviton theories. In these theories, modifications of the gravitational radiation damping formulae or of the propagation of the waves translate into a change in the phase evolution of the observed gravitational waveform. We obtain the bounds through the technique of matched filtering, employing the LISA sensitivity curve generator (SCG), available online. For a non-spinning neutron star on a quasi-circular inspiral into a non-spinning 103M⊙ black hole in the Virgo Cluster, in a two-year integration, we find a lower bound ω > 3 × 105. For lower-mass black holes, the bound could be as large as 2 × 106. The bound is independent of LISA arm length, but is inversely proportional to the LISA position noise error, under the assumption that position error noise dominates laser shot noise. Lower bounds on the graviton Compton wavelength ranging from 1015 km to 5 × 1016 km can be obtained from one-year observations of massive binary black-hole inspirals at cosmological distances (3 Gpc) for masses ranging from 104 to 107M⊙. For the highest-mass systems (107M⊙), the bound is proportional to (LISA arm length)1/2 and to (LISA acceleration noise)−1/2. For the others, the bound is independent of these parameters because of the dominance of white-dwarf confusion noise in the relevant part of the frequency spectrum. These bounds improve and extend earlier work which used analytic formulae for the noise curves.

Physical template family for gravitational waves from precessing binaries of spinning compact objects: Application to single-spin binaries

The detection of the gravitational waves (GWs) emitted by precessing binaries of spinning compact objects is complicated by the large number of parameters (such as the magnitudes and initial directions of the spins, and the position and orientation of the binary with respect to the detector) that are required to model accurately the precession-induced modulations of the GW signal. In this paper we describe a fast matched-filtering search scheme for precessing binaries, and we adopt the physical template family proposed by Buonanno, Chen, and Vallisneri [Phys. Rev. D 67, 104025 (2003)] for ground-based interferometers. This family provides essentially exact waveforms, written directly in terms of the physical parameters, for binaries with a single significant spin, and for which the observed GW signal is emitted during the phase of adiabatic inspiral (for LIGO-I and VIRGO, this corresponds to a total mass $M\ensuremath{\lesssim}{15M}_{\ensuremath{\bigodot}}).$ We show how the detection statistic can be maximized automatically over all the parameters (including the position and orientation of the binary with respect to the detector), except four (the two masses, the magnitude of the single spin, and the opening angle between the spin and the orbital angular momentum), so the template bank used in the search is only four-dimensional; this technique is relevant also to the searches for GW from extreme-mass-ratio inspirals and supermassive black hole inspirals to be performed using the space-borne detector LISA. Using the LIGO-I design sensitivity, we compute the detection threshold $(\ensuremath{\sim}10)$ required for a false-alarm probability of ${10}^{\ensuremath{-}3}/\mathrm{yr}$ and the number of templates $(\ensuremath{\sim}76000)$ required for a minimum match of 0.97 for the mass range ${(m}_{1}{,m}_{2})=[7,12]{M}_{\ensuremath{\bigodot}}\ifmmode\times\else\texttimes\fi{}[1,3]{M}_{\ensuremath{\bigodot}}.$

Editorial

The 4th International LISA Symposium was held at the National Science Foundation Physics Frontier Center for Gravitational Wave Physics at The Pennsylvania State University on 19-24 July 2002. This special issue of Classical and Quantum Gravity is the proceedings of this meeting.LISA - the Laser Interferometer Space Antenna - is part of an international effort to open a new window on the universe. Not all things radiate light, but everything gravitates. Observations of the gravitational waves radiated by black holes and compact binary star systems, in our galaxy and beyond, can reveal details about these systems and their environments that are otherwise inaccessible.The international effort, of which LISA is a part, includes ground-based detectors, and the relationship between LISA and its ground-based detector 'cousins' was an important theme for this Symposium. LISA will observe gravitational waves in the 0.1 mHz to 0.1 Hz band, complementing observations made by ground-based detectors in the 10 Hz to several KHz band. Together they will explore nearly six decades of bandwidth in the gravitational-wave sky. LISA in particular will observe the gravitational waves radiated by the coalescence of black holes at the centres of colliding galaxies, and the inspiral of compact neutron stars or stellar-mass black holes onto these black holes, virtually anywhere in the universe. It will take a census of neutron star or close white dwarf binaries in our own galaxy and observe the formation of large black holes from the very first structures to form and collapse in our universe. In doing all these things, it will shed new 'light' on the first structures to form in the universe, explore the evolution of galaxies and the roles that black holes play in their structure, test relativity near the 'edges' of a black hole, and deepen our understanding of stellar and binary system evolution.A successful conference - and this LISA Symposium, like its predecessors, was very successful - does not just happen. It is the result of the work of many individuals and teams working together on scientific organization, travel, visa, lodging and financial logistics and planning. When all these things come together just right, as they did in July of 2002, it enables the speakers and participants to make something truly remarkable happen. It is my pleasure to thank the local organizing and scientific organizing committees, the accommodating staff of the Penn State Conference Center, and Penn State Transportation Services for their help and cooperation. I would like to single out for special thanks and appreciation the tireless Karen Brewster, whose energy, vigour and focus overcame all logistical obstacles, freeing the participants to focus on the exciting science that LISA will enable. In the end, however, it is the speakers and the participants who make a successful meeting. I look forward to the continued growth of the LISA Community and to meeting you all at the 5th International LISA Symposium, to be held at ESTEC in July 2004.Lee Samuel FinnPenn State University

Detection template families for gravitational waves from the final stages of binary–black-hole inspirals: Nonspinning case

We investigate the problem of detecting gravitational waves from binaries of nonspinning black holes with masses m=5-20M., moving on quasicircular orbits, which are arguably the most promising sources for first-generation ground-based detectors. We analyze and compare all the currently available post-Newtonian approximations for the relativistic two-body dynamics; for these binaries, different approximations predict different waveforms. We then construct examples of detection template families that embed all the approximate models and that could be used to detect the true gravitational-wave signal (but not to characterize accurately its physical parameters). We estimate that the fitting factor for our detection families is greater than or similar to0.95 (corresponding to an event rate loss less than or similar to15%) and we estimate that the discretization of the template family, for similar to10(4) templates, increases the loss to less than or similar to20%.

Dynamics of spinning test particles in Kerr spacetime

We investigate the dynamics of relativistic spinning test particles in the spacetime of a rotating black hole using the Papapetrou equations. We use the method of Lyapunov exponents to determine whether the orbits exhibit sensitive dependence on initial conditions, a signature of chaos. In the case of maximally spinning equal-mass binaries (a limiting case that violates the test-particle approximation) we find unambiguous positive Lyapunov exponents that come in pairs $\ifmmode\pm\else\textpm\fi{}\ensuremath{\lambda},$ a characteristic of Hamiltonian dynamical systems. We find no evidence for nonvanishing Lyapunov exponents for physically realistic spin parameters, which suggests that chaos may not manifest itself in the gravitational radiation of extreme mass-ratio binary black-hole inspirals (as detectable, for example, by LISA, the Laser Interferometer Space Antenna).