results for au:Lousto_C in:gr-qc

- We present the results of 74 new simulations of nonprecessing spinning black hole binaries with mass ratios $q=m_1/m_2$ in the range $1/7\leq q\leq1$ and individual spins covering the parameter space $-0.95\leq\alpha_{1,2}\leq0.95$ with one runs with spins of $\pm0.95$. We supplement those runs with 107 previous simulations to study the hangup effect in black hole mergers, i.e. the delay or prompt merger of spinning holes with respect to non spinning binaries. We perform the numerical evolution for typically the last ten orbits before the merger and down to the formation of the final remnant black hole. This allows us to study the hangup effect for unequal mass binaries leading us to identify the spin variable that controls the number of orbits before merger as $\vec{S}_{hu}\cdot{\hat{L}},$ where $\vec{S}_{hu}=(1+\frac12\frac{m_2}{m_1})\vec{S}_1+(1+\frac12\frac{m_1}{m_2})\vec{S}_2$. We also combine the total results of those 181 simulations to obtain improved fitting formulae for the remnant final black hole mass, spin and recoil velocity as well as for the peak luminosity and peak frequency of the gravitational strain, and find new correlations among them. This accurate new set of simulations enhances the number of available numerical relativity waveforms available for parameter estimation of gravitational wave observations.
- Dec 19 2017 gr-qc astro-ph.GA arXiv:1712.05836v2In response to LIGO's observation of GW170104, we performed a series of full numerical simulations of binary black holes, each designed to replicate likely realizations of its dynamics and radiation. These simulations have been performed at multiple resolutions and with two independent techniques to solve Einstein's equations. For the nonprecessing and precessing simulations, we demonstrate the two techniques agree mode by mode, at a precision substantially in excess of statistical uncertainties in current LIGO's observations. Conversely, we demonstrate our full numerical solutions contain information which is not accurately captured with the approximate phenomenological models commonly used to infer compact binary parameters. To quantify the impact of these differences on parameter inference for GW170104 specifically, we compare the predictions of our simulations and these approximate models to LIGO's observations of GW170104.
- Dec 05 2017 gr-qc astro-ph.CO arXiv:1712.01168v1Cosmic strings are topological defects which can be formed in GUT-scale phase transitions in the early universe. They are also predicted to form in the context of string theory. The main mechanism for a network of Nambu-Goto cosmic strings to lose energy is through the production of loops and the subsequent emission of gravitational waves, thus offering an experimental signature for the existence of cosmic strings. Here we report on the analysis conducted to specifically search for gravitational-wave bursts from cosmic string loops in the data of Advanced LIGO 2015-2016 observing run (O1). No evidence of such signals was found in the data, and as a result we set upper limits on the cosmic string parameters for three recent loop distribution models. In this paper, we initially derive constraints on the string tension $G\mu$ and the intercommutation probability, using not only the burst analysis performed on the O1 data set, but also results from the previously published LIGO stochastic O1 analysis, pulsar timing arrays, cosmic microwave background and Big-Bang nucleosynthesis experiments. We show that these data sets are complementary in that they probe gravitational waves produced by cosmic string loops during very different epochs. Finally, we show that the data sets exclude large parts of the parameter space of the three loop distribution models we consider.
- We evolve a binary black hole system bearing a mass ratio of $q=m_1/m_2=2/3$ and individual spins of $S^z_1/m_1^2=0.95$ and $S^z_2/m_2^2=-0.95$ in a configuration where the large black hole has its spin antialigned with the orbital angular momentum, $L^z$, and the small black hole has its spin aligned with $L^z$. This configuration was chosen to measure the maximum recoil of the remnant black hole for nonprecessing binaries. We find that the remnant black hole recoils at 500km/s, the largest recorded value from numerical simulations for aligned spin configurations. The remnant mass, spin, and gravitational waveform peak luminosity and frequency also provide a valuable point in parameter space for source modeling.
- Nov 16 2017 astro-ph.HE gr-qc arXiv:1711.05578v1On June 8, 2017 at 02:01:16.49 UTC, a gravitational-wave signal from the merger of two stellar-mass black holes was observed by the two Advanced LIGO detectors with a network signal-to-noise ratio of 13. This system is the lightest black hole binary so far observed, with component masses $12^{+7}_{-2}\,M_\odot$ and $7^{+2}_{-2}\,M_\odot$ (90% credible intervals). These lie in the range of measured black hole masses in low-mass X-ray binaries, thus allowing us to compare black holes detected through gravitational waves with electromagnetic observations. The source's luminosity distance is $340^{+140}_{-140}$ Mpc, corresponding to redshift $0.07^{+0.03}_{-0.03}$. We verify that the signal waveform is consistent with the predictions of general relativity.
- Oct 26 2017 astro-ph.HE gr-qc arXiv:1710.09320v1The first observation of a binary neutron star coalescence by the Advanced LIGO and Advanced Virgo gravitational-wave detectors offers an unprecedented opportunity to study matter under the most extreme conditions. After such a merger, a compact remnant is left over whose nature depends primarily on the masses of the inspiralling objects and on the equation of state of nuclear matter. This could be either a black hole or a neutron star (NS), with the latter being either long-lived or too massive for stability implying delayed collapse to a black hole. Here, we present a search for gravitational waves from the remnant of the binary neutron star merger GW170817 using data from Advanced LIGO and Advanced Virgo. We search for short ($\lesssim1$ s) and intermediate-duration ($\lesssim 500$ s) signals, which includes gravitational-wave emission from a hypermassive NS or supramassive NS, respectively. We find no signal from the post-merger remnant. Our derived strain upper limits are more than an order of magnitude larger than those predicted by most models. For short signals, our best upper limit on the root-sum-square of the gravitational-wave strain emitted from 1--4 kHz is $h_{\rm rss}^{50\%}=2.1\times 10^{-22}$ Hz$^{-1/2}$ at 50% detection efficiency. For intermediate-duration signals, our best upper limit at 50% detection efficiency is $h_{\rm rss}^{50\%}=8.4\times 10^{-22}$ Hz$^{-1/2}$ for a millisecond magnetar model, and $h_{\rm rss}^{50\%}=5.9\times 10^{-22}$ Hz$^{-1/2}$ for a bar-mode model. These results indicate that post-merger emission from a similar event may be detectable when advanced detectors reach design sensitivity or with next-generation detectors.
- Oct 17 2017 gr-qc arXiv:1710.05837v1The LIGO Scientific and Virgo Collaborations have announced the first detection of gravitational waves from the coalescence of two neutron stars. The merger rate of binary neutron stars estimated from this event suggests that distant, unresolvable binary neutron stars create a significant astrophysical stochastic gravitational-wave background. The binary neutron star background will add to the background from binary black holes, increasing the amplitude of the total astrophysical background relative to previous expectations. In the Advanced LIGO-Virgo frequency band most sensitive to stochastic backgrounds (near 25 Hz), we predict a total astrophysical background with amplitude $\Omega_{\rm GW} (f=25 \text{Hz}) = 1.8_{-1.3}^{+2.7} \times 10^{-9}$ with $90\%$ confidence, compared with $\Omega_{\rm GW} (f=25 \text{Hz}) = 1.1_{-0.7}^{+1.2} \times 10^{-9}$ from binary black holes alone. Assuming the most probable rate for compact binary mergers, we find that the total background may be detectable with a signal-to-noise-ratio of 3 after 40 months of total observation time, based on the expected timeline for Advanced LIGO and Virgo to reach their design sensitivity.
- Sep 28 2017 gr-qc arXiv:1709.09203v1We present results from the first directed search for nontensorial gravitational waves. While general relativity allows for tensorial (plus and cross) modes only, a generic metric theory may, in principle, predict waves with up to six different polarizations. This analysis is sensitive to continuous signals of scalar, vector or tensor polarizations, and does not rely on any specific theory of gravity. After searching data from the first observation run of the advanced LIGO detectors for signals at twice the rotational frequency of 200 known pulsars, we find no evidence of gravitational waves of any polarization. We report the first upper limits for scalar and vector strains, finding values comparable in magnitude to previously-published limits for tensor strain. Our results may be translated into constraints on specific alternative theories of gravity.
- Sep 28 2017 gr-qc astro-ph.HE arXiv:1709.09660v3On August 14, 2017 at 10:30:43 UTC, the Advanced Virgo detector and the two Advanced LIGO detectors coherently observed a transient gravitational-wave signal produced by the coalescence of two stellar mass black holes, with a false-alarm-rate of $\lesssim$ 1 in 27000 years. The signal was observed with a three-detector network matched-filter signal-to-noise ratio of 18. The inferred masses of the initial black holes are $30.5_{-3.0}^{+5.7}$ Msun and $25.3_{-4.2}^{+2.8}$ Msun (at the 90% credible level). The luminosity distance of the source is $540_{-210}^{+130}~\mathrm{Mpc}$, corresponding to a redshift of $z=0.11_{-0.04}^{+0.03}$. A network of three detectors improves the sky localization of the source, reducing the area of the 90% credible region from 1160 deg$^2$ using only the two LIGO detectors to 60 deg$^2$ using all three detectors. For the first time, we can test the nature of gravitational wave polarizations from the antenna response of the LIGO-Virgo network, thus enabling a new class of phenomenological tests of gravity.
- Jun 13 2017 astro-ph.HE gr-qc arXiv:1706.03119v3We present the results of a semicoherent search for continuous gravitational waves from the low-mass X-ray binary Scorpius X-1, using data from the first Advanced LIGO observing run. The search method uses details of the modelled, parametrized continuous signal to combine coherently data separated by less than a specified coherence time, which can be adjusted to trade off sensitivity against computational cost. A search was conducted over the frequency range from 25 Hz to 2000 Hz, spanning the current observationally-constrained range of the binary orbital parameters. No significant detection candidates were found, and frequency-dependent upper limits were set using a combination of sensitivity estimates and simulated signal injections. The most stringent upper limit was set at 175 Hz, with comparable limits set across the most sensitive frequency range from 100 Hz to 200 Hz. At this frequency, the 95 pct upper limit on signal amplitude h0 is 2.3e-25 marginalized over the unknown inclination angle of the neutron star's spin, and 8.03e-26 assuming the best orientation (which results in circularly polarized gravitational waves). These limits are a factor of 3-4 stronger than those set by other analyses of the same data, and a factor of about 7 stronger than the best upper limits set using initial LIGO data. In the vicinity of 100 Hz, the limits are a factor of between 1.2 and 3.5 above the predictions of the torque balance model, depending on inclination angle, if the most likely inclination angle of 44 degrees is assumed, they are within a factor of 1.7.
- Jun 08 2017 gr-qc astro-ph.HE arXiv:1706.01980v2We demonstrate that numerical relativity codes based on the moving punctures formalism are capable of evolving nearly maximally spinning black hole binaries. We compare a new evolution of an equal-mass, aligned-spin binary with dimensionless spin chi=0.99 using puncture-based data with recent simulations of the SXS Collaboration. We find that the overlap of our new waveform with the published results of the SXS Collaboration is larger than 0.999. To generate our new waveform, we use the recently introduced HiSpID puncture data, the CCZ4 evolution system, and a modified lapse condition that helps keep the horizon radii reasonably large.
- May 30 2017 gr-qc arXiv:1705.09833v1We present and assess a Bayesian method to interpret gravitational wave signals from binary black holes. Our method directly compares gravitational wave data to numerical relativity simulations. This procedure bypasses approximations used in semi-analytical models for compact binary coalescence. In this work, we use only the full posterior parameter distribution for generic nonprecessing binaries, drawing inferences away from the set of NR simulations used, via interpolation of a single scalar quantity (the marginalized log-likelihood, $\ln {\cal L}$) evaluated by comparing data to nonprecessing binary black hole simulations. We also compare the data to generic simulations, and discuss the effectiveness of this procedure for generic sources. We specifically assess the impact of higher order modes, repeating our interpretation with both $l\le2$ as well as $l\le3$ harmonic modes. Using the $l\le3$ higher modes, we gain more information from the signal and can better constrain the parameters of the gravitational wave signal. We assess and quantify several sources of systematic error that our procedure could introduce, including simulation resolution and duration; most are negligible. We show through examples that our method can recover the parameters for equal mass, zero spin; GW150914-like; and unequal mass, precessing spin sources. Our study of this new parameter estimation method demonstrates we can quantify and understand the systematic and statistical error. This method allows us to use higher order modes from numerical relativity simulations to better constrain the black hole binary parameters.
- We present the results of 14 simulations of nonspinning black hole binaries with mass ratios $q=m_1/m_2$ in the range $1/100\leq q\leq1$. For each of these simulations we perform three runs at increasing resolution to assess the finite difference errors and to extrapolate the results to infinite resolution. For $q\geq 1/6$, we follow the evolution of the binary typically for the last ten orbits prior to merger. By fitting the results of these simulations, we accurately model the peak luminosity, peak waveform frequency and amplitude, and the recoil of the remnant hole for unequal mass nonspinning binaries. We verify the accuracy of these new models and compare them to previously existing empirical formulas. These new fits provide a basis for a hierarchical approach to produce more accurate remnant formulas in the generic precessing case. They also provide input to gravitational waveform modeling.
- Apr 18 2017 gr-qc arXiv:1704.04628v4During their first observational run, the two Advanced LIGO detectors attained an unprecedented sensitivity, resulting in the first direct detections of gravitational-wave signals and GW151226, produced by stellar-mass binary black hole systems. This paper reports on an all-sky search for gravitational waves (GWs) from merging intermediate mass black hole binaries (IMBHBs). The combined results from two independent search techniques were used in this study: the first employs a matched-filter algorithm that uses a bank of filters covering the GW signal parameter space, while the second is a generic search for GW transients (bursts). No GWs from IMBHBs were detected, therefore, we constrain the rate of several classes of IMBHB mergers. The most stringent limit is obtained for black holes of individual mass $100\,M_\odot$, with spins aligned with the binary orbital angular momentum. For such systems, the merger rate is constrained to be less than $0.93~\mathrm{Gpc^{-3}\,yr}^{-1}$ in comoving units at the $90\%$ confidence level, an improvement of nearly 2 orders of magnitude over previous upper limits.
- Recent detailed observations of the radio-loud quasar 3C 186 indicate the possibility that a supermassive recoiling black hole is moving away from the host galaxy at a speed of nearly 2100km/s. If this is the case, we can model the mass ratio and spins of the progenitor binary black hole using the results of numerical relativity simulations. We find that the black holes in the progenitor must have comparable masses with a mass ratio $q=m_1/m_2>1/4$ and the spin of the primary black hole must be $\alpha_2=S_2/m_2^2>0.4$. The final remnant of the merger is bounded by $\alpha_f>0.45$ and at least $4\%$ of the total mass of the binary system is radiated into gravitational waves. We consider four different pre-merger scenarios that further narrow those values. Assuming, for instance, a cold accretion driven merger model, we find that the binary had comparable masses with $q=0.70^{+0.29}_{-0.21}$ and the normalized spins of the larger and smaller black holes were $\alpha_2=0.94^{+0.06}_{-0.22}$ and $\alpha_1=0.95^{+0.05}_{-0.09}$. We can also estimate the final recoiling black hole spin $\alpha_f=0.93^{+0.02}_{-0.03}$ and that the system radiated $9.6^{+0.8}_{-1.4}\%$ of its total mass, making the merger of those black holes the most energetic event ever observed.
- The RIT numerical relativity group is releasing a public catalog of black-hole-binary waveforms. The initial release of the catalog consists of 126 recent simulations that include precessing and non precessing systems with mass ratios $q=m_1/m_2$ in the range $1/6\leq q\leq1$. The catalog contains information about the initial data of the simulation, the waveforms extrapolated to infinity, as well as information about the peak luminosity and final remnant black hole properties. These waveforms can be used to independently interpret gravitational wave signals from laser interferometric detectors and
- Feb 06 2017 gr-qc astro-ph.CO arXiv:1702.00872v1We use post-Newtonian (PN) approximations to determine the initial orbital and spin parameters of black hole binaries that lead to low-eccentricity inspirals when evolved with numerical relativity techniques. In particular, we seek initial configurations that lead to very small eccentricities at small separations, as is expected for astrophysical systems. We consider three cases: (i) quasicircular orbits with no radial velocity, (ii) quasicircular orbits with an initial radial velocity determined by radiation reaction, and (iii) parameters obtained form evolution of the PN equations of motion from much larger separations. We study seven cases of spinning, nonprecessing, unequal mass binaries. We then use several definitions of the eccentricity, based on orbital separations and waveform phase and amplitude, and find that using the complete 3PN Hamiltonian for quasicircular orbits to obtain the tangential orbital momentum, and using the highest-known-order radiation reaction expressions to obtain the radial momentum, leads to the lowest eccentricity. The accuracy of this method even exceeds that of inspiral data based on 3PN and 4PN evolutions.
- Jan 27 2017 astro-ph.HE gr-qc arXiv:1701.07709v5We present the result of searches for gravitational waves from 200 pulsars using data from the first observing run of the Advanced LIGO detectors. We find no significant evidence for a gravitational-wave signal from any of these pulsars, but we are able to set the most constraining upper limits yet on their gravitational-wave amplitudes and ellipticities. For eight of these pulsars, our upper limits give bounds that are improvements over the indirect spin-down limit values. For another 32, we are within a factor of 10 of the spin-down limit, and it is likely that some of these will be reachable in future runs of the advanced detector. Taken as a whole, these new results improve on previous limits by more than a factor of two.
- Nov 10 2016 gr-qc astro-ph.HE arXiv:1611.02972v1We present the results from an all-sky search for short-duration gravitational waves in the data of the first run of the Advanced LIGO detectors between September 2015 and January 2016. The search algorithms use minimal assumptions on the signal morphology, so they are sensitive to a wide range of sources emitting gravitational waves. The analyses target transient signals with duration ranging from milliseconds to seconds over the frequency band of 32 to 4096 Hz. The first observed gravitational-wave event, GW150914, has been detected with high confidence in this search; other known gravitational-wave events fall below the search's sensitivity. Besides GW150914, all of the search results are consistent with the expected rate of accidental noise coincidences. Finally, we estimate rate-density limits for a broad range of non-BBH transient gravitational-wave sources as a function of their gravitational radiation emission energy and their characteristic frequency. These rate-density upper-limits are stricter than those previously published by an order-of-magnitude.
- Nov 01 2016 gr-qc arXiv:1610.09713v2We present the results of 61 new simulations of nonprecessing spinning black hole binaries with mass ratios $q=m_1/m_2$ in the range $1/3\leq q\leq1$ and individual spins covering the parameter space $-0.85\leq\alpha_{1,2}\leq0.85$. We additionally perform 10 new simulations of nonspinning black hole binaries with mass ratios covering the range $1/6\leq q<1$. We follow the evolution for typically the last ten orbits before merger down to the formation of the final remnant black hole. This allows for assessment of the accuracy of our previous empirical formulae for relating the binary parameters to the remnant final black hole mass, spin and recoil. We use the new simulation to improve the fit to the above remnant formulae and add a formula for the peak luminosity of gravitational waves, produced around the merger of the two horizons into one. We find excellent agreement (typical errors $\sim0.1-0.2\%$) for the mass and spin, and within $\sim5\%$ for the recoil and peak luminosity. These formulae have direct application to parameter estimation techniques applied to LIGO observations of gravitational waves from binary black hole mergers.
- Jul 20 2016 gr-qc astro-ph.HE arXiv:1607.05377v1In fall of 2015, the two LIGO detectors measured the gravitational wave signal GW150914, which originated from a pair of merging black holes. In the final 0.2 seconds (about 8 gravitational-wave cycles) before the amplitude reached its maximum, the observed signal swept up in amplitude and frequency, from 35 Hz to 150 Hz. The theoretical gravitational-wave signal for merging black holes, as predicted by general relativity, can be computed only by full numerical relativity, because analytic approximations fail near the time of merger. Moreover, the nearly-equal masses, moderate spins, and small number of orbits of GW150914 are especially straightforward and efficient to simulate with modern numerical-relativity codes. In this paper, we report the modeling of GW150914 with numerical-relativity simulations, using black-hole masses and spins consistent with those inferred from LIGO's measurement. In particular, we employ two independent numerical-relativity codes that use completely different analytical and numerical methods to model the same merging black holes and to compute the emitted gravitational waveform; we find excellent agreement between the waveforms produced by the two independent codes. These results demonstrate the validity, impact, and potential of current and future studies using rapid-response, targeted numerical-relativity simulations for better understanding gravitational-wave observations.
- Jun 16 2016 gr-qc astro-ph.CO arXiv:1606.04856v3The first observational run of the Advanced LIGO detectors, from September 12, 2015 to January 19, 2016, saw the first detections of gravitational waves from binary black hole mergers. In this paper we present full results from a search for binary black hole merger signals with total masses up to $100 M_\odot$ and detailed implications from our observations of these systems. Our search, based on general-relativistic models of gravitational wave signals from binary black hole systems, unambiguously identified two signals, GW150914 and GW151226, with a significance of greater than $5\sigma$ over the observing period. It also identified a third possible signal, LVT151012, with substantially lower significance, and with an 87% probability of being of astrophysical origin. We provide detailed estimates of the parameters of the observed systems. Both GW150914 and GW151226 provide an unprecedented opportunity to study the two-body motion of a compact-object binary in the large velocity, highly nonlinear regime. We do not observe any deviations from general relativity, and place improved empirical bounds on several high-order post-Newtonian coefficients. From our observations we infer stellar-mass binary black hole merger rates lying in the range $9-240 \mathrm{Gpc}^{-3} \mathrm{yr}^{-1}$. These observations are beginning to inform astrophysical predictions of binary black hole formation rates, and indicate that future observing runs of the Advanced detector network will yield many more gravitational wave detections.
- We compare GW150914 directly to simulations of coalescing binary black holes in full general relativity, accounting for all the spin-weighted quadrupolar modes, and separately accounting for all the quadrupolar and octopolar modes. Consistent with the posterior distributions reported in LVC_PE[1] (at 90% confidence), we find the data are compatible with a wide range of nonprecessing and precessing simulations. Followup simulations performed using previously-estimated binary parameters most resemble the data. Comparisons including only the quadrupolar modes constrain the total redshifted mass Mz ∈[64 - 82M_⊙], mass ratio q = m2/m1 ∈[0.6,1], and effective aligned spin \chi_eff ∈[-0.3, 0.2], where \chi_eff = (S1/m1 + S2/m2) ⋅\hatL /M. Including both quadrupolar and octopolar modes, we find the mass ratio is even more tightly constrained. Simulations with extreme mass ratios and effective spins are highly inconsistent with the data, at any mass. Several nonprecessing and precessing simulations with similar mass ratio and \chi_eff are consistent with the data. Though correlated, the components' spins (both in magnitude and directions) are not significantly constrained by the data. For nonprecessing binaries, interpolating between simulations, we reconstruct a posterior distribution consistent with previous results. The final black hole's redshifted mass is consistent with Mf,z between 64.0 - 73.5M_⊙and the final black hole's dimensionless spin parameter is consistent with af = 0.62 - 0.73. As our approach invokes no intermediate approximations to general relativity and can strongly reject binaries whose radiation is inconsistent with the data, our analysis provides a valuable complement to LVC_PE[1].
- Jun 06 2016 gr-qc astro-ph.HE arXiv:1606.01210v1This paper presents updated estimates of source parameters for GW150914, a binary black-hole coalescence event detected by the Laser Interferometer Gravitational-wave Observatory (LIGO) on September 14, 2015 [1]. Reference presented parameter estimation [2] of the source using a 13-dimensional, phenomenological precessing-spin model (precessing IMRPhenom) and a 11-dimensional nonprecessing effective-one-body (EOB) model calibrated to numerical-relativity simulations, which forces spin alignment (nonprecessing EOBNR). Here we present new results that include a 15-dimensional precessing-spin waveform model (precessing EOBNR) developed within the EOB formalism. We find good agreement with the parameters estimated previously [2], and we quote updated component masses of $35^{+5}_{-3}\mathrm{M}_\odot$ and $30^{+3}_{-4}\mathrm{M}_\odot$ (where errors correspond to 90% symmetric credible intervals). We also present slightly tighter constraints on the dimensionless spin magnitudes of the two black holes, with a primary spin estimate $0.65$ and a secondary spin estimate $0.75$ at 90% probability. Reference [2] estimated the systematic parameter-extraction errors due to waveform-model uncertainty by combining the posterior probability densities of precessing IMRPhenom and nonprecessing EOBNR. Here we find that the two precessing-spin models are in closer agreement, suggesting that these systematic errors are smaller than previously quoted.
- Feb 12 2016 gr-qc astro-ph.HE arXiv:1602.03840v2On September 14, 2015, the Laser Interferometer Gravitational-wave Observatory (LIGO) detected a gravitational-wave transient (GW150914); we characterize the properties of the source and its parameters. The data around the time of the event were analyzed coherently across the LIGO network using a suite of accurate waveform models that describe gravitational waves from a compact binary system in general relativity. GW150914 was produced by a nearly equal mass binary black hole of $36^{+5}_{-4} M_\odot$ and $29^{+4}_{-4} M_\odot$; for each parameter we report the median value and the range of the 90% credible interval. The dimensionless spin magnitude of the more massive black hole is bound to be $<0.7$ (at 90% probability). The luminosity distance to the source is $410^{+160}_{-180}$ Mpc, corresponding to a redshift $0.09^{+0.03}_{-0.04}$ assuming standard cosmology. The source location is constrained to an annulus section of $610$ deg$^2$, primarily in the southern hemisphere. The binary merges into a black hole of $62^{+4}_{-4} M_\odot$ and spin $0.67^{+0.05}_{-0.07}$. This black hole is significantly more massive than any other inferred from electromagnetic observations in the stellar-mass regime.
- We give a unified description of the flip-flop effect in spinning binary black holes and the anti-alignment instability in terms of real and imaginary flip-flop frequencies. We find that this instability is only effective for mass ratios $0.5<q<1$. We provide analytic expressions that determine the region of parameter space for which the instability occurs in terms of maps of the mass ratio and spin magnitudes $(q,\alpha_1,\alpha_2)$. This restricts the priors of parameter estimation techniques for the observation of gravitational waves from binary black holes and it is relevant for astrophysical modeling and final recoil computations of such binary systems.
- We use fully nonlinear numerical relativity techniques to study high energy head-on collision of nonspinning, equal-mass black holes to estimate the maximum gravitational radiation emitted by these systems. Our simulations include improvements in the construction of initial data, subsequent full numerical evolutions, and the computation of waveforms at infinity. The new initial data significantly reduces the spurious radiation content, allowing for initial speeds much closer to the speed of light, i.e. $v\sim0.99c$. Using these new techniques, We estimate the maximum radiated energy from head-on collisions to be $E_{\text{max}}/M_{\text{ADM}}=0.13\pm0.01$. This value differs from the second-order perturbative $(0.164)$ and zero-frequency-limit $(0.17)$ analytic computations, but is close to those obtained by thermodynamic arguments $(0.134)$ and by previous numerical estimates $(0.14\pm0.03)$.
- We study the spin dynamics of individual black holes in a binary system. In particular we focus on the polar precession of spins and the possibility of a complete flip of spins with respect to the orbital plane. We perform a full numerical simulation that displays these characteristics. We evolve equal mass binary spinning black holes for $t=20,000M$ from an initial proper separation of $d=25M$ down to merger after 48.5 orbits. We compute the gravitational radiation from this system and compare it to 3.5 post-Newtonian generated waveforms finding close agreement. We then further use 3.5 post-Newtonian evolutions to show the extension of this spin flip-flop phenomenon to unequal mass binaries. We also provide analytic expressions to approximate the maximum flip-flop angle and frequency in terms of the binary spins and mass ratio parameters at a given orbital radius. Finally we discuss the effect this spin flip-flop would have on accreting matter and other potential observational effects.
- We revisit the modeling of the properties of the remnant black hole resulting the merger of a black-hole binary as a function of the parameters of the binary. We provide a set of empirical formulas for the final mass, spin and recoil velocity of the final black hole as a function of the mass ratio and individual spins of the progenitor. In order to determine the fitting coefficients for these formulas, we perform a set of 128 new numerical evolutions of precessing, unequal-mass black-hole binaries, and fit to the resulting remnant mass, spin, and recoil. In order to reduce the complexity of the analysis, we chose configurations that have one of the black holes spinning, with dimensionless spin alpha=0.8, at different angles with respect to the orbital angular momentum, and the other non-spinning. In addition to evolving families of binaries with different spin-inclination angles, we also evolved binaries with mass ratios as small as q=1/6. We use the resulting empirical formulas to predict the probabilities of black hole mergers leading to a given recoil velocity, total radiated gravitational energy, and final black hole spin.
- We derive an analytical expression for extracting the gravitational waveforms at null infinity using the Weyl scalar $\psi_4$ measured at a finite radius. Our expression is based on a series solution in orders of 1/r to the equations for gravitational perturbations about a spinning black hole. We compute this expression to order $1/r^2$ and include the spin parameter $a$ of the Kerr background. We test the accuracy of this extraction procedure by measuring the waveform for a merging black-hole binary at ten different extraction radii (in the range r/M=75-190) and for three different resolutions in the convergence regime. We find that the extraction formula provides a set of values for the radiated energy and momenta that at finite extraction radii converges towards the expected values with increasing resolution, which is not the case for the `raw' waveform at finite radius. We also examine the phase and amplitude errors in the waveform as a function of observer location and again observe the benefits of using our extraction formula. The leading corrections to the phase are ${\cal O}(1/r)$ and to the amplitude are ${\cal O}(1/r^2)$. This method provides a simple and practical way of estimating the waveform at infinity, and may be especially useful for scenarios such as well separated binaries, where the radiation zone is far from the sources, that would otherwise require extended simulation grids in order to extrapolate the `raw' waveform to infinity. Thus this method saves important computational resources and provides an estimate of errors.
- Nov 03 2014 gr-qc arXiv:1410.8607v3We solve the Hamiltonian and momentum constraints of general relativity for two black holes with nearly extremal spins and relativistic boosts in the puncture formalism. We use a non-conformally-flat ansatz with an attenuated superposition of two Lorentz-boosted, conformally Kerr or conformally Schwarzschild 3-metrics and their corresponding extrinsic curvatures. We compare evolutions of these data with the standard Bowen-York conformally flat ansatz (technically limited to intrinsic spins $\chi=S/M^2_{\text{ADM}}=0.928$ and boosts $P/M_{\text{ADM}}=0.897$), finding, typically, an order of magnitude smaller burst of spurious radiation and agreement with inspiral and merger. As a first case study, we evolve two equal-mass black holes from rest with an initial separation of $d=12M$ and spins $\chi_i=S_i/m_i^2=0.99$, compute the waveforms produced by the collision, the energy and angular momentum radiated, and the recoil of the final remnant black hole. We find that the black-hole trajectories curve at close separations, leading to the radiation of angular momentum. We also study orbiting nonspinning and moderate-spin black-hole binaries and compare these with standard Bowen-York data. We find a substantial reduction in the nonphysical initial burst of radiation which leads to cleaner waveforms. Finally, we study the case of orbiting binary black-hole systems with spin magnitude $\chi_i=0.95$ in an aligned configuration and compare waveform and final remnant results with those of the SXS Collaboration, finding excellent agreement. This represents the first moving punctures evolution of orbiting and spinning black holes exceeding the Bowen-York limit. Finally, we study different choices of the initial lapse and lapse evolution equation in the moving punctures approach to improve the accuracy and efficiency of the simulations.
- We study binary spinning black holes to display the long term individual spin dynamics. We perform a full numerical simulation starting at an initial proper separation of $d\approx25M$ between equal mass holes and evolve them down to merger for nearly 48 orbits, 3 precession cycles, and half of a flip-flop cycle. The simulation lasts for $t=20000M$ and displays a total change in the orientation of the spin of one of the black holes from initially aligned with the orbital angular momentum to a complete anti-alignment after half of a flip-flop cycle. We compare this evolution with an integration of the 3.5 Post-Newtonian equations of motion and spin evolution to show that this process continuously flip-flops the spin during the lifetime of the binary until merger. We also provide lower order analytic expressions for the maximum flip-flop angle and frequency. We discuss the effects this dynamics may have on spin growth in accreting binaries and on the observational consequences for galactic and supermassive binary black holes.
- We perform a set of 36 nonprecessing black-hole binary simulations with spins either aligned or counteraligned with the orbital angular momentum in order to model the final mass, spin, and recoil of the merged black hole as a function of the individual black hole spin magnitudes and the mass ratio of the progenitors. We find that the maximum recoil for these configurations is $V_{max}=526\pm23\,km/s$, which occurs when the progenitor spins are maximal, the mass ratio is $q_{max}=m_1/m_2=0.623\pm0.038$, the smaller black-hole spin is aligned with the orbital angular momentum, and the larger black-hole spin is counteraligned ($\alpha_1=-\alpha_2=1$). This maximum recoil is about $80\,km/s$ larger than previous estimates, but most importantly, because the maximum occurs for smaller mass ratios, the probability for a merging binary to recoil faster than $400\,km/s$ can be as large as $17\%$, while the probability for recoils faster than $250\, km/s$ can be as large as $45\%$. We provide explicit phenomenological formulas for the final mass, spin, and recoil as a function of the individual BH spins and the mass difference between the two black holes. Here we include terms up through fourth-order in the initial spins and mass difference, and find excellent agreement (within a few percent) with independent results available in the literature. The maximum radiated energy is $E_{\rm rad}/m\approx11.3\%$ and final spin $\alpha_{\rm rem}^{\rm max}\approx0.952$ for equal mass, aligned maximally spinning binaries.
- Jan 07 2014 gr-qc astro-ph.CO arXiv:1401.0939v1The Numerical INJection Analysis (NINJA) project is a collaborative effort between members of the numerical relativity and gravitational-wave astrophysics communities. The purpose of NINJA is to study the ability to detect gravitational waves emitted from merging binary black holes and recover their parameters with next-generation gravitational-wave observatories. We report here on the results of the second NINJA project, NINJA-2, which employs 60 complete binary black hole hybrid waveforms consisting of a numerical portion modelling the late inspiral, merger, and ringdown stitched to a post-Newtonian portion modelling the early inspiral. In a "blind injection challenge" similar to that conducted in recent LIGO and Virgo science runs, we added 7 hybrid waveforms to two months of data recolored to predictions of Advanced LIGO and Advanced Virgo sensitivity curves during their first observing runs. The resulting data was analyzed by gravitational-wave detection algorithms and 6 of the waveforms were recovered with false alarm rates smaller than 1 in a thousand years. Parameter estimation algorithms were run on each of these waveforms to explore the ability to constrain the masses, component angular momenta and sky position of these waveforms. We also perform a large-scale monte-carlo study to assess the ability to recover each of the 60 hybrid waveforms with early Advanced LIGO and Advanced Virgo sensitivity curves. Our results predict that early Advanced LIGO and Advanced Virgo will have a volume-weighted average sensitive distance of 300Mpc (1Gpc) for $10M_{\odot}+10M_{\odot}$ ($50M_{\odot}+50M_{\odot}$) binary black hole coalescences. We demonstrate that neglecting the component angular momenta in the waveform models used in matched-filtering will result in a reduction in sensitivity for systems with large component angular momenta. [Abstract abridged for ArXiv, full version in PDF]
- We perform a set of 38 numerical simulations of equal-mass BH binaries in a configuration where the BH spins in the binary are equal in both magnitude and direction, to study precession effects. We vary the initial direction of the total spin S with respect to the orbital angular momentum L, covering the 2 dimensional space of orientation angles with 38 configurations consisting of 36 configurations distributed in the azimuthal angle phi and polar angle theta, and two configurations on the poles. In all cases, we set the initial dimensionless BH spins to 0.8. We observe that during the late-inspiral stage, the total angular momentum of the system J remains within 5 deg of its original direction, with the largest changes in direction occurring when the spins are nearly counter-aligned with the orbital angular momentum. We also observe that the angle between S and L is nearly conserved during the inspiral phase. These two dynamical properties allow us to propose a new phenomenological formula for the final mass and spin of merged BHs in terms of the individual masses and spins of the progenitor binary at far separations. We determine coefficients of this formula (in the equal-mass limit) using a least-squares fit to the results of this new set of 38 runs, an additional set of five new configurations with spins aligned/counteraligned with the orbital angular momentum, and over 100 recent simulations. We find that our formulas reproduce the remnant mass and spin of these simulations to within a relative error of 2.5%. We discuss the region of validity of this dynamical picture for precessing unequal-mass binaries. Finally, we perform a statistical study to see the consequence of this new formula for distributions of spin-magnitudes and remnant masses with applications to BH-spin distributions and gravitational radiation in cosmological scenarios involving several mergers.
- We evolve a set of 32 equal-mass black-hole binaries with collinear spins (with intrinsic spin magnitudes $|\vec{S}_{1,2}/m^2_{1,2}|=0.8$) to study the effects of precession in the highly nonlinear plunge and merger regimes. We compare the direction of the instantaneous radiated angular momentum, $\hat{\delta J}_{\rm rad}(t)$, to the directions of the total angular momentum, $\hat{J}(t)$, and the orbital angular momentum, $\hat{L}(t)$. We find that $\hat{\delta J}_{\rm rad}(t)$ approximately follows $\hat{L}$ throughout the evolution. During the orbital evolution and merger, we observe that the angle between $\vec{L}$ and total spin $\vec{S}$ is approximately conserved to within $1^\circ$, which allows us to propose and test models for the merger remnant's mass and spin. For instance, we verify that the \hangup effect is the dominant effect and largely explains the observed total energy and angular momentum radiated by these precessing systems. We also verify that the total angular momentum, which significantly decreases in magnitude during the inspiral, varies in direction by less than $\sim 5^\circ$. The maximum variation in the direction of $\vec J$ occurs when the spins are nearly antialigned with the orbital angular momentum. Based on our results, we conjecture that transitional precession, which would lead to large variations in the direction of $\vec J$, is not possible for similar-mass binaries and would require a mass ratio $m_1/m_2\lesssim1/4$.
- Jul 22 2013 gr-qc arXiv:1307.5307v3The Numerical-Relativity-Analytical-Relativity (NRAR) collaboration is a joint effort between members of the numerical relativity, analytical relativity and gravitational-wave data analysis communities. The goal of the NRAR collaboration is to produce numerical-relativity simulations of compact binaries and use them to develop accurate analytical templates for the LIGO/Virgo Collaboration to use in detecting gravitational-wave signals and extracting astrophysical information from them. We describe the results of the first stage of the NRAR project, which focused on producing an initial set of numerical waveforms from binary black holes with moderate mass ratios and spins, as well as one non-spinning binary configuration which has a mass ratio of 10. All of the numerical waveforms are analysed in a uniform and consistent manner, with numerical errors evaluated using an analysis code created by members of the NRAR collaboration. We compare previously-calibrated, non-precessing analytical waveforms, notably the effective-one-body (EOB) and phenomenological template families, to the newly-produced numerical waveforms. We find that when the binary's total mass is ~100-200 solar masses, current EOB and phenomenological models of spinning, non-precessing binary waveforms have overlaps above 99% (for advanced LIGO) with all of the non-precessing-binary numerical waveforms with mass ratios <= 4, when maximizing over binary parameters. This implies that the loss of event rate due to modelling error is below 3%. Moreover, the non-spinning EOB waveforms previously calibrated to five non-spinning waveforms with mass ratio smaller than 6 have overlaps above 99.7% with the numerical waveform with a mass ratio of 10, without even maximizing on the binary parameters.
- We perform several black-hole binary evolutions using fully nonlinear numerical relativity techniques at separations large enough that low-order post-Newtonian expansions are expected to be accurate. As a case study, we evolve an equal-mass nonspinning black-hole binary from a quasicircular orbit at an initial coordinate separation of D=100M for three different resolutions. We find that the orbital period of this binary (in the numerical coordinates) is T=6422M. The orbital motion agrees with post-Newtonian predictions to within 1%. Interestingly, we find that the time derivative of the coordinate separation is dominated by a purely gauge effect leading to an apparent contraction and expansion of the orbit at twice the orbital frequency. Based on these results, we improved our evolution techniques and studied a set of black hole binaries in quasi-circular orbits starting at D=20M, D=50M, and D=100M for ~ 5, 3, and 2 orbits, respectively. We find good agreement between the numerical results and post-Newtonian predictions for the orbital frequency and radial decay rate, radiated energy and angular momentum, and waveform amplitude and phases. The results are relevant for the future computation of long-term waveforms to assist in the detection and analysis of gravitational waves by the next generation of detectors as well as the long-term simulations of black-hole binaries required to accurately model astrophysically realistic circumbinary accretion disks.
- Apr 03 2013 gr-qc astro-ph.HE arXiv:1304.0670v4We present possible observing scenarios for the Advanced LIGO, Advanced Virgo and KAGRA gravitational-wave detectors over the next decade, with the intention of providing information to the astronomy community to facilitate planning for multi-messenger astronomy with gravitational waves. We estimate the sensitivity of the network to transient gravitational-wave signals, and study the capability of the network to determine the sky location of the source. We report our findings for gravitational-wave transients, with particular focus on gravitational-wave signals from the inspiral of binary neutron star systems, which are considered the most promising for multi-messenger astronomy. The ability to localize the sources of the detected signals depends on the geographical distribution of the detectors and their relative sensitivity, and 90% credible regions can be as large as thousands of square degrees when only two sensitive detectors are operational. Determining the sky position of a significant fraction of detected signals to areas of 5 square degrees to 20 square degees requires at least three detectors of sensitivity within a factor of ~2 of each other and with a broad frequency bandwidth. When all detectors, including KAGRA and the third LIGO detector in India, reach design sensitivity, a significant fraction of gravitational-wave signals will be localized to a few square degrees by gravitational-wave observations alone.
- We present results from an extensive study of 88 precessing, equal-mass black-hole binaries with large spins (83 with intrinsic spins of 0.8 and 5 with intrinsic spins of 0.9)and use these data to model new nonlinear contributions to the gravitational recoil imparted to the merged black hole. We find a new effect, the cross kick, that enhances the recoil for partially aligned binaries beyond the hangup kick effect. This has the consequence of increasing the probabilities of recoils larger than 2000 km/s by nearly a factor two, and, consequently, of black holes getting ejected from galaxies, as well as the observation of large differential redshifts/blueshifts in the cores of recently merged galaxies.
- We study the convergence properties of our implementation of the 'moving punctures' approach at very high resolutions for an equal-mass, non-spinning, black-hole binary. We find convergence of the Hamiltonian constraint on the horizons and the L2 norm of the Hamiltonian constraint in the bulk for sixth and eighth-order finite difference implementations. The momentum constraint is more sensitive, and its L2 norm shows clear convergence for a system with consistent sixth-order finite differencing, while the momentum and BSSN constraints on the horizons show convergence for both sixth and eighth-order systems. We analyze the gravitational waveform error from the late-inspiral, merger, and ringdown. We find that using several lower-order techniques for increasing the speed of numerical relativity simulations actually lead to apparently non-convergent errors. Even when using standard high-accuracy techniques, rather than seeing clean convergence, where the waveform phase is a monotonic function of grid resolution, we find that the phase tends to oscillate with resolution, possibly due to stochastic errors induced by grid refinement boundaries. Our results seem to indicate that one can obtain gravitational waveform phases to within 0.05 rad. (and possibly as small as 0.015 rad.), while the amplitude error can be reduced to 0.1%. We then compare with the waveforms obtained using the cZ4 formalism. We find that the cZ4 waveforms have larger truncation errors for a given resolution, but the Richardson extrapolation phase of the cZ4 and BSSN waveforms agree to within 0.01 rad., even during the ringdown.
- We study conformally-flat initial data for an arbitrary number of spinning black holes with exact analytic solutions to the momentum constraints constructed from a linear combination of the classical Bowen-York and conformal Kerr extrinsic curvatures. The solution leading to the largest intrinsic spin, relative to the ADM mass of the spacetime epsilon_S=S/M^2_ADM, is a superposition with relative weights of Lambda=0.783 for conformal Kerr and (1-Lambda)=0.217 for Bowen-York. In addition, we measure the spin relative to the initial horizon mass M_H_0, and find that the quantity chi=S/M_H_0^2 reaches a maximum of \chi^max=0.9856 for Lambda=0.753. After equilibration, the final black-hole spin should lie in the interval 0.9324<chi_final<0.9856. We perform full numerical evolutions to compute the energy radiated and the final horizon mass and spin. We find that the black hole settles to a final spin of chi_final^max=0.935 when Lambda=0.783. We also study the evolution of the apparent horizon structure of this "maximal" black hole in detail.
- Physics in curved spacetime describes a multitude of phenomena, ranging from astrophysics to high energy physics. The last few years have witnessed further progress on several fronts, including the accurate numerical evolution of the gravitational field equations, which now allows highly nonlinear phenomena to be tamed. Numerical relativity simulations, originally developed to understand strong field astrophysical processes, could prove extremely useful to understand high-energy physics processes like trans-Planckian scattering and gauge-gravity dualities. We present a concise and comprehensive overview of the state-of-the-art and important open problems in the field(s), along with guidelines for the next years. This writeup is a summary of the "NR/HEP Workshop" held in Madeira, Portugal from August 31st to September 3rd 2011.
- Jan 26 2012 gr-qc arXiv:1201.5319v1The Numerical INJection Analysis (NINJA) project is a collaborative effort between members of the numerical relativity and gravitational wave data analysis communities. The purpose of NINJA is to study the sensitivity of existing gravitational-wave search and parameter-estimation algorithms using numerically generated waveforms, and to foster closer collaboration between the numerical relativity and data analysis communities. The first NINJA project used only a small number of injections of short numerical-relativity waveforms, which limited its ability to draw quantitative conclusions. The goal of the NINJA-2 project is to overcome these limitations with long post-Newtonian - numerical relativity hybrid waveforms, large numbers of injections, and the use of real detector data. We report on the submission requirements for the NINJA-2 project and the construction of the waveform catalog. Eight numerical relativity groups have contributed 63 hybrid waveforms consisting of a numerical portion modelling the late inspiral, merger, and ringdown stitched to a post-Newtonian portion modelling the early inspiral. We summarize the techniques used by each group in constructing their submissions. We also report on the procedures used to validate these submissions, including examination in the time and frequency domains and comparisons of waveforms from different groups against each other. These procedures have so far considered only the $(\ell,m)=(2,2)$ mode. Based on these studies we judge that the hybrid waveforms are suitable for NINJA-2 studies. We note some of the plans for these investigations.
- We explore the newly discovered "hangup-kick" effect, which greatly amplifies the recoil for configuration with partial spin- orbital-angular momentum alignment, by studying a set of 48 new simulations of equal-mass, spinning black-hole binaries. We propose a phenomenological model for the recoil that takes this new effect into account and then use this model, in conjunction with statistical distributions for the spin magnitude and orientations, based on accretion simulations, to find the probabilities for observing recoils of several thousand km/s. In addition, we provide initial parameters, eccentricities, radiated linear and angular momentum, precession rates and remnant mass, spin, and recoils for all 48 configurations. Our results indicate that surveys exploring peculiar (redshifted or blueshifted) differential line-of-sight velocities should observe at least one case above 2000 km/s out of four thousand merged galaxies. The probability that a remnant BH receives a total recoil exceeding the ~2000 km/s escape velocity of large elliptical galaxies is ten times larger. Probabilities of recoils exceeding the escape velocity quickly rise to 5% for galaxies with escape velocities of 1000 km/s and nearly 20% for galaxies with escape velocities of 500 km/s. In addition the direction of these large recoils is strongly peaked toward the angular momentum axis, with very low probabilities of recoils exceeding 350 km/s for angles larger than 45 deg. with respect to the orbital angular momentum axis.
- We revisit the scenario of small-mass-ratio (q) black-hole binaries; performing new, more accurate, simulations of mass ratios 10:1 and 100:1 for initially nonspinning black holes. We propose fitting functions for the trajectories of the two black holes as a function of time and mass ratio (in the range 1/100 < q < 1/10$) that combine aspects of post-Newtonian trajectories at smaller orbital frequencies and plunging geodesics at larger frequencies. We then use these trajectories to compute waveforms via black hole perturbation theory. Using the advanced LIGO noise curve, we see a match of ~99.5% for the leading (l,m)=(2,2) mode between the numerical relativity and perturbative waveforms. Nonleading modes have similarly high matches. We thus prove the feasibility of efficiently generating a bank of gravitational waveforms in the intermediate-mass-ratio regime using only a sparse set of full numerical simulations.
- We revisit the scenario of the gravitational radiation recoil acquired by the final remnant of a black-hole-binary merger by studying a set of configurations that have components of the spin both aligned with the orbital angular momentum and in the orbital plane. We perform a series of 42 new full numerical simulations for equal-mass and equal-spin-magnitude binaries. We extend previous recoil fitting formulas to include nonlinear terms in the spins and successfully include both the new and known results. The new predicted maximum velocity approaches 5000km/s for spins partially aligned with the orbital angular momentum, which leads to an important increase of the probabilities of large recoils in generic astrophysical mergers. We find non-negligible probabilities for recoils of several thousand km/s from accretion-aligned binaries.
- Nov 13 2010 gr-qc arXiv:1011.2767v1Recently, we proposed an enhancement of the Regge-Wheeler-Zerilli formalism for first-order perturbations about a Schwarzschild background that includes first-order corrections due to the background black-hole spin. Using this formalism, we investigate gravitational wave recoil effects from a spinning black-hole binary system analytically. This allows us to better understand the origin of the large recoils observed in full numerical simulation of spinning black hole binaries.
- We review the developments in modeling gravitational recoil from merging black-hole binaries and introduce a new set of 20 simulations to test our previously proposed empirical formula for the recoil. The configurations are chosen to represent generic binaries with unequal masses and precessing spins. Results of these simulations indicate that the recoil formula is accurate to within a few km/s in the similar mass-ratio regime for the out-of-plane recoil.
- We measure the recoil velocity as a function of spin for equal-mass, highly-spinning black-hole binaries, with spins in the orbital plane, equal in magnitude and opposite in direction. We confirm that the leading-order effect is linear in the spin and the cosine of angle between the spin direction and the infall direction at merger. We find higher-order corrections that are proportional to the odd powers in both the spin and cosine of this angle. Taking these corrections into account, we predict that the maximum recoil will be 3680+-130 km/s.
- We perform the first fully nonlinear numerical simulations of black-hole binaries with mass ratios 100:1. Our technique for evolving such extreme mass ratios is based on the moving puncture approach with a new gauge condition and an optimal choice of the mesh refinement (plus large computational resources). We achieve a convergent set of results for simulations starting with a small nonspinning black hole just outside the ISCO that then performs over two orbits before plunging into the 100 times more massive black hole. We compute the gravitational energy and momenta radiated as well as the final remnant parameters and compare these quantities with the corresponding perturbative estimates. The results show a close agreement. We briefly discuss the relevance of this simulations for Advanced LIGO, third-generation ground based detectors, and LISA observations, and self-force computations.
- We describe in detail full numerical and perturbative techniques to compute the gravitational radiation from intermediate-mass-ratio black-hole-binary inspirals and mergers. We perform a series of full numerical simulations of nonspinning black holes with mass ratios q=1/10 and q=1/15 from different initial separations and for different finite-difference resolutions. In order to perform those full numerical runs, we adapt the gauge of the moving punctures approach with a variable damping term for the shift. We also derive an extrapolation (to infinite radius) formula for the waveform extracted at finite radius. For the perturbative evolutions we use the full numerical tracks, transformed into the Schwarzschild gauge, in the source terms of the Regge-Wheller-Zerilli Schwarzschild perturbations formalism. We then extend this perturbative formalism to take into account small intrinsic spins of the large black hole, and validate it by computing the quasinormal mode frequencies, where we find good agreement for spins |a/M|<0.3. Including the final spins improves the overlap functions when comparing full numerical and perturbative waveforms, reaching 99.5% for the leading (l,m)=(2,2) and (3,3) modes, and 98.3% for the nonleading (2,1) mode in the q=1/10 case, which includes 8 orbits before merger. For the q=1/15 case, we obtain overlaps near 99.7% for all three modes. We discuss the modeling of the full inspiral and merger based on a combined matching of post-Newtonian, full numerical, and geodesic trajectories.
- We construct and evolve non-rotating vacuum initial data with a ring singularity, based on a simple extension of the standard Brill-Lindquist multiple black-hole initial data, and search for event horizons with spatial slices that are toroidal when the ring radius is sufficiently large. While evolutions of the ring singularity are not numerically feasible for large radii, we find some evidence, based on configurations of multiple BHs arranged in a ring, that this configuration leads to singular limit where the horizon width has zero size, possibly indicating the presence of a naked singularity, when the radius of the ring is sufficiently large. This is in agreement with previous studies that have found that there is no apparent horizon surrounding the ring singularity when the ring's radius is larger than about twice its mass.
- We study critical black hole separations for the formation of a common apparent horizon in systems of $N$ - black holes in a time symmetric configuration. We study in detail the aligned equal mass cases for $N=2,3,4,5$, and relate them to the unequal mass binary black hole case. We then study the apparent horizon of the time symmetric initial geometry of a ring singularity of different radii. The apparent horizon is used as indicative of the location of the event horizon in an effort to predict a critical ring radius that would generate an event horizon of toroidal topology. We found that a good estimate for this ring critical radius is $20/(3\pi) M$. We briefly discuss the connection of this two cases through a discrete black hole 'necklace' configuration.
- Jan 22 2010 gr-qc arXiv:1001.3834v1We review some of the recent dramatic developments in the fully nonlinear simulation of generic, highly-precessing, black-hole binaries, and introduce a new approach for generating hybrid post-Newtonian / Numerical waveforms for these challenging systems.
- We study black-hole binaries in the intermediate-mass-ratio regime 0.01 < q < 0.1 with a new technique that makes use of nonlinear numerical trajectories and efficient perturbative evolutions to compute waveforms at large radii for the leading and nonleading modes. As a proof-of-concept, we compute waveforms for q=1/10. We discuss applications of these techniques for LIGO/VIRGO data analysis and the possibility that our technique can be extended to produce accurate waveform templates from a modest number of fully-nonlinear numerical simulations.
- We study the statistical distributions of the spins of generic black-hole binaries during the inspiral and merger, as well as the distributions of the remnant mass, spin, and recoil velocity. For the inspiral regime, we start with a random uniform distribution of spin directions S1 and S2 and magnitudes S1=S2=0.97 for different mass ratios. Starting from a fiducial initial separation of ri=50m, we perform 3.5PN evolutions down to rf=5m. At this final fiducial separation, we compute the angular distribution of the spins with respect to the final orbital angular momentum, L. We perform 16^4 simulations for six mass ratios between q=1 and q=1/16 and compute the distribution of the angles between L and Delta and L and S, directly related to recoil velocities and total angular momentum. We find a small but statistically significant bias of the distribution towards counter-alignment of both scalar products. To study the merger of black-hole binaries, we turn to full numerical techniques. We introduce empirical formulae to describe the final remnant black hole mass, spin, and recoil velocity for merging black-hole binaries with arbitrary mass ratios and spins. We then evaluate those formulae for randomly chosen directions of the individual spins and magnitudes as well as the binary's mass ratio. We found that the magnitude of the recoil velocity distribution decays as P(v) \exp(-v/2500km/s), <v>=630km/s, and sqrt<v^2> - <v>^2= 534km/s, leading to a 23% probability of recoils larger than 1000km/s, and a highly peaked angular distribution along the final orbital axis. The final black-hole spin magnitude show a universal distribution highly peaked at Sf/mf^2=0.73 and a 25 degrees misalignment with respect to the final orbital angular momentum.
- May 27 2009 gr-qc arXiv:0905.4227v1The 2008 NRDA conference introduced the Numerical INJection Analysis project (NINJA), a new collaborative effort between the numerical relativity community and the data analysis community. NINJA focuses on modeling and searching for gravitational wave signatures from the coalescence of binary system of compact objects. We review the scope of this collaboration and the components of the first NINJA project, where numerical relativity groups shared waveforms and data analysis teams applied various techniques to detect them when embedded in colored Gaussian noise.
- We obtain empirical formulae for the final remnant black hole mass, spin, and recoil velocity from merging black-hole binaries with arbitrary mass ratios and spins. Our formulae are based on the mass ratio and spin dependence of the post-Newtonian expressions for the instantaneous radiated energy, linear momentum, and angular momentum, as well as the ISCO binding energy and angular momentum. The relative weight between the different terms is fixed by amplitude parameters chosen through a least-squares fit of recently available fully nonlinear numerical simulations. These formulae can be used for statistical studies of N-body simulations of galaxy cores and clusters, and the cosmological growth of supermassive black holes. As an example, we use these formulae to obtain a universal spin magnitude distribution of merged black holes and recoil velocity distributions for dry and hot/cold wet mergers. We also revisit the long term orbital precession and resonances and discuss how they affect spin distributions before the merging regime.
- Jan 29 2009 gr-qc arXiv:0901.4399v2The Numerical INJection Analysis (NINJA) project is a collaborative effort between members of the numerical relativity and gravitational-wave data analysis communities. The purpose of NINJA is to study the sensitivity of existing gravitational-wave search algorithms using numerically generated waveforms and to foster closer collaboration between the numerical relativity and data analysis communities. We describe the results of the first NINJA analysis which focused on gravitational waveforms from binary black hole coalescence. Ten numerical relativity groups contributed numerical data which were used to generate a set of gravitational-wave signals. These signals were injected into a simulated data set, designed to mimic the response of the Initial LIGO and Virgo gravitational-wave detectors. Nine groups analysed this data using search and parameter-estimation pipelines. Matched filter algorithms, un-modelled-burst searches and Bayesian parameter-estimation and model-selection algorithms were applied to the data. We report the efficiency of these search methods in detecting the numerical waveforms and measuring their parameters. We describe preliminary comparisons between the different search methods and suggest improvements for future NINJA analyses.
- Jan 27 2009 gr-qc arXiv:0901.3861v1In this paper, we compare the waveforms from the post-Newtonian (PN) approach with the numerical simulations of generic black-hole binaries which have mass ratio $q\sim0.8$, arbitrarily oriented spins with magnitudes $S_1/m_1^2\sim0.6$ and $S_2/m_2^2\sim0.4$, and orbit 9 times from an initial orbital separation of $r\approx11M$ prior to merger. We observe a reasonably good agreement between the PN and numerical waveforms, with an overlap of over 98% for the first six cycles of the $(\ell=2,m=\pm2)$ mode and over 90% for the $(\ell=2,m=1)$ and $(\ell=3,m=3)$ modes.
- In this paper we develop a technique for determining the algebraic classification of a numerical spacetime, possibly resulting from a generic black-hole-binary merger, using the Newman-Penrose Weyl scalars. We demonstrate these techniques for a test case involving a close binary with arbitrarily oriented spins and unequal masses. We find that, post merger, the spacetime quickly approaches Petrov type II, and only approaches type D on much longer timescales. These techniques allow us to begin to explore the validity of the "no-hair theorem" for generic merging-black-hole spacetimes.
- We compare waveforms and orbital dynamics from the first long-term, fully non-linear, numerical simulations of a generic black-hole binary configuration with post-Newtonian predictions. The binary has mass ratio q~0.8 with arbitrarily oriented spins of magnitude S_1/m_1^2~0.6 and S_2/m_2^2~0.4 and orbits 9 times prior to merger. The numerical simulation starts with an initial separation of r~11M, with orbital parameters determined by initial 2.5PN and 3.5PN post-Newtonian evolutions of a quasi-circular binary with an initial separation of r=50M. The resulting binaries have very little eccentricity according to the 2.5PN and 3.5PN systems, but show significant eccentricities of e~0.01-0.02 and e~0.002-0.005 in the respective numerical simulations, thus demonstrating that 3.5PN significantly reduces the eccentricity of the binary compared to 2.5PN. We perform three numerical evolutions from r~11M with maximum resolutions of h=M/48,M/53.3,M/59.3, to verify numerical convergence. We observe a reasonably good agreement between the PN and numerical waveforms, with an overlap of nearly 99% for the first six cycles of the (l=2,m=+-2) modes, 91% for the (l=2,m=+-1) modes, and nearly 91% for the (l=3,m=+-3) modes. The phase differences between numerical and post-Newtonian approximations appear to be independent of the (l,m) modes considered and relatively small for the first 3-4 orbits. An advantage of the 3.5 PN model over the 2.5 PN one seems to be observed, which indicates that still higher PN order (perhaps even 4.0PN) may yield significantly better waveforms. In addition, we identify features in the waveforms likely related to precession and precession-induced eccentricity.
- We measure the gravitational recoil for unequal-mass-black- hole-binary mergers, with the larger BH having spin a/m^H=0.8, and the smaller BH non-spinning. We choose our configurations such that, initially, the spins lie on the orbital plane. The spin and orbital plane precess significantly, and we find that the out-of plane recoil (i.e. the recoil perpendicular to the orbital plane around merger) varies as \eta^2 / (1+q), in agreement with our previous prediction, based on the post-Newtonian scaling.
- In order to derive the precise gravitational waveforms for extreme mass ratio inspirals (EMRI), we develop a formulation for the second order metric perturbations produced by a point particle moving in the Schwarzschild spacetime. The second order waveforms satisfy a wave equation with an effective source build up from products of the first order perturbations and its derivatives. We have explicitly regularized this source at the horizon and at spatial infinity. We show that the effective source does not contain squares of the Dirac's delta and that perturbations are regular at the particle location. We introduce an asymptotically flat gauge for the radiation fields and the $\ell=0$ mode to compute explicitly the (leading) second order $\ell=2$ waveforms in the headon collision case. This case represents the first completion of the radiation reaction program self-consistently.
- We evolve equal-mass, equal-spin black-hole binaries with specific spins of a/mH 0.925, the highest spins simulated thus far and nearly the largest possible for Bowen-York black holes, in a set of configurations with the spins counter-aligned and pointing in the orbital plane, which maximizes the recoil velocities of the merger remnant, as well as a configuration where the two spins point in the same direction as the orbital angular momentum, which maximizes the orbital hang-up effect and remnant spin. The coordinate radii of the individual apparent horizons in these cases are very small and the simulations require very high central resolutions (h ~ M/320). We find that these highly spinning holes reach a maximum recoil velocity of ~3300 km/s (the largest simulated so far) and, for the hangup configuration, a remnant spin of a/mH 0.922. These results are consistent with our previous predictions for the maximum recoil velocity of ~4000 km/s and remnant spin; the latter reinforcing the prediction that cosmic censorship is not violated by merging highly-spinning black-hole binaries. We also numerically solve the initial data for, and evolve, a single maximal-Bowen-York-spin black hole, and confirm that the 3-metric has an O(1/r^2) singularity at the puncture, rather than the usual O(1/r^4) singularity seen for non-maximal spins.
- Unlike in the Schwarzschild black hole background, gravitational perturbations in a Kerr black hole background can not be decomposed into simple tensor harmonics in the time domain. Here, we make mode decompositions only in the azimuthal direction. As a first step, we discuss the resulting (2+1)-dimensional Klein-Gordon differential equation for scalar perturbations with a two dimensional Dirac's $\delta$-function as a source representing a point particle orbiting a much larger black hole. To make this equation amenable for numerical integrations we explicitly remove analytically the singular behavior of the source and compute a global, well bahaved, effective source for the corresponding waveform.
- Jan 18 2008 gr-qc arXiv:0801.2750v1Gravitational perturbations in a Kerr black hole background can not be decomposed into simple tensor harmonics in the time domain. Here, we make the mode decomposition only in the azimuthal direction and discuss the resulting (2+1)-dimensional Klein-Gordon differential equation for scalar perturbations with a two dimensional Dirac's $\delta$-function as a source representing a point particle orbiting a much larger black hole. To make this equation amenable for numerical integrations we explicitly remove analytically the singular behavior of the source and compute a global effective source for the corresponding waveform.
- We present techniques for long-term, stable, and accurate evolutions of multiple-black-hole spacetimes using the `moving puncture' approach with fourth- and eighth-order finite difference stencils. We use these techniques to explore configurations of three black holes in a hierarchical system consisting of a third black hole approaching a quasi-circular black-hole binary, and find that, depending on the size of the binary, the resulting encounter may lead to a prompt merger of all three black holes, production of a highly elliptical binary (with the third black hole remaining unbound), or disruption of the binary (leading to three free black holes). We also analyze the classical Burrau three-body problem using full numerical evolutions. In both cases, we find behaviors distinctly different from Newtonian predictions, which has important implications for N-body black-hole simulations. For our simulations we use analytic approximate data. We find that the eighth-order stencils significantly reduce the numerical errors for our choice of grid sizes, and that the approximate initial data produces the expected waveforms (after a rescaling of the puncture masses) for black-hole binaries with modest initial separations.
- There are periodic solutions to the equal-mass three-body (and N-body) problem in Newtonian gravity. The figure-eight solution is one of them. In this paper, we discuss its solution in the first and second post-Newtonian approximations to General Relativity. To do so we derive the canonical equations of motion in the ADM gauge from the three-body Hamiltonian. We then integrate those equations numerically, showing that quantities such as the energy, linear and angular momenta are conserved down to numerical error. We also study the scaling of the initial parameters with the physical size of the triple system. In this way we can assess when general relativistic results are important and we determine that this occur for distances of the order of 100M, with M the total mass of the system. For distances much closer than those, presumably the system would completely collapse due to gravitational radiation. This sets up a natural cut-off to Newtonian N-body simulations. The method can also be used to dynamically provide initial parameters for subsequent full nonlinear numerical simulations.