We present the first attempt at calibrating the effective-one-body (EOB) model to accurate numeri... more We present the first attempt at calibrating the effective-one-body (EOB) model to accurate numerical-relativity simulations of spinning, non-precessing black-hole binaries. Aligning the EOB and numerical waveforms at low frequency over a time interval of 1000M , we first estimate the phase and amplitude errors in the numerical waveforms and then minimize the difference between numerical and EOB waveforms by calibrating a handful of EOB-adjustable parameters. In the equal-mass, spin aligned case, we find that phase and fractional amplitude differences between the numerical and EOB (2,2) mode can be reduced to 0.01 radians and 1%, respectively, over the entire inspiral waveforms. In the equal-mass, spin anti-aligned case, these differences can be reduced to 0.13 radians and 1% during inspiral and plunge, and to 0.4 radians and 10% during merger and ringdown. The waveform agreement is within numerical errors in the spin aligned case while slightly over numerical errors in the spin anti-aligned case. Using Enhanced LIGO and Advanced LIGO noise curves, we find that the overlap between the EOB and the numerical (2,2) mode, maximized over the initial phase and time of arrival, is larger than 0.999 for binaries with total mass 30-200M⊙. In addition to the leading (2,2) mode, we compare four subleading modes. We find good amplitude and frequency agreements between the EOB and numerical modes for both spin configurations considered, except for the (3,2) mode in the spin anti-aligned case. We believe that the larger difference in the (3,2) mode is due to the lack of knowledge of post-Newtonian spin effects in the higher modes.
We calibrate the effective-one-body (EOB) model to an accurate numerical simulation of an equalma... more We calibrate the effective-one-body (EOB) model to an accurate numerical simulation of an equalmass, nonspinning binary black-hole coalescence produced by the Caltech-Cornell Collaboration. Aligning the EOB and numerical waveforms at low frequency over a time interval of $1000M, and taking into account the uncertainties in the numerical simulation, we investigate the significance and degeneracy of the EOB-adjustable parameters during inspiral, plunge, and merger, and determine the minimum number of EOB-adjustable parameters that achieves phase and amplitude agreements on the order of the numerical error. We find that phase and fractional amplitude differences between the numerical and EOB values of the dominant gravitational-wave mode h 22 can be reduced to 0.02 radians and 2%, respectively, until a time 20M before merger, and to 0.04 radians and 7%, respectively, at a time 20M after merger (during ringdown). Using LIGO, Enhanced LIGO, and Advanced LIGO noise curves, we find that the overlap between the EOB and the numerical h 22 , maximized only over the initial phase and time of arrival, is larger than 0.999 for equal-mass binary black holes with total mass 30-150M. In addition to the leading gravitational mode (2, 2), we compare the dominant subleading modes (4, 4) and (3, 2) for the inspiral and find phase and amplitude differences on the order of the numerical error. We also determine the mass-ratio dependence of one of the EOB-adjustable parameters by calibrating to numerical inspiral waveforms for black-hole binaries with mass ratios 2:1 and 3:1. The results presented in this paper improve and extend recent successful attempts aimed at providing gravitational-wave data analysts the best analytical EOB model capable of interpolating accurate numerical simulations.
Based on a recent study of the linearized Bianchi equations by Buchman and Sarbach, we construct ... more Based on a recent study of the linearized Bianchi equations by Buchman and Sarbach, we construct and implement a hierarchy of absorbing boundary conditions for the Einstein equations in generalized harmonic gauge. As a test problem, we demonstrate that we can evolve multipolar gravitational waves without any spurious reflections at linear order in perturbation theory.
Coalescing binary black holes are a primary science target of ground-based gravitational-wave det... more Coalescing binary black holes are a primary science target of ground-based gravitational-wave detectors. Detecting gravitational waves from these binaries and understanding the properties of the waves' sources require detailed knowledge of the expected waveforms. This paper presents a catalog of numerical binary black-hole simulations that represents a major advance toward the application of numerical relativity to gravitational-wave data analysis. The 171 simulations in the catalog include 90 precessing binaries, mass ratios up to 8:1, orbital eccentricities from a few percent to 1e-5, and black-hole spins up to 97% of the theoretical maximum. The simulations follow more orbits (up to 34) than previous simulations, allowing a more reliable connection to approximate analytical waveforms, which are used to extend numerical waveforms to span the entire frequency range of a detector. The expanded parameter-space coverage of this catalog, together with the length and accuracy of the included waveforms, will facilitate the development of new (and improvement of existing) gravitational-wave template families, the study of detection efficiency of gravitational-wave searches, and the understanding of systematic biases in parameter estimation of detected gravitational waves. Formidable challenges remain; for example, precession complicates the connection of numerical and approximate analytical waveforms, and vast regions of the parameter space remain unexplored.
The 2008 NRDA conference introduced the Numerical INJection Analysis project (NINJA), a new colla... more The 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.
The tetrad-based equations for vacuum gravity published by Estabrook, Robinson, and Wahlquist are... more The tetrad-based equations for vacuum gravity published by Estabrook, Robinson, and Wahlquist are simplified and adapted for numerical relativity. We show that the evolution equations as partial differential equations for the Ricci rotation coefficients constitute a rather simple first-order symmetrizable hyperbolic system, not only for the Nester gauge condition on the acceleration and angular velocity of the tetrad frames considered by Estabrook et al., but also for the Lorentz gauge condition of van Putten and Eardley and for a fixed gauge condition. We introduce a lapse function and a shift vector to allow general coordinate evolution relative to the timelike congruence defined by the tetrad vector field.
The numerical computation of gravitational radiation emitted from binary black hole systems has b... more The numerical computation of gravitational radiation emitted from binary black hole systems has been pivotal in the detection and characterization of 10 binary black hole astrophysical events since Sept. 14, 2015. However, the drive for more accurate waveforms remains, especially when computing higher-order spherical harmonic modes. The numerical relativity simulations currently used for LIGO / VIRGO detections solve Einsteinâ s field equations on a finite computational domain with an outer boundary. In order to obtain a unique Cauchy evolution, it is necessary to impose boundary conditions which should yield a well posed problem and ideally, be completely transparent to the physical problem on the unbounded domain. Short of achieving this ideal, one can try to develop so-called absorbing boundary conditions which form a well-posed problem and insure that only a very small amount of spurious gravitational radiation is reflected from the outer boundary into the computational domain. In this talk, I discuss the implementation of a hierarchy of such boundary conditions which hopefully will improve the accuracy of binary black hole numerical simulations.
The Numerical INJection Analysis (NINJA) project is a collaborative effort between members of the... more The 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 gravitationalwave detectors. Nine groups analysed this data using search and parameterestimation 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.
The Numerical INJection Analysis (NINJA) project is a collaborative effort between members of the... more The 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 gravitationalwave detectors. Nine groups analysed this data using search and parameterestimation 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.
The Numerical INJection Analysis (NINJA) project is a collaborative effort between members of the... more The 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
We calibrate an effective-one-body (EOB) model to numerical-relativity simulations of mass ratios... more We calibrate an effective-one-body (EOB) model to numerical-relativity simulations of mass ratios 1, 2, 3, 4, and 6, by maximizing phase and amplitude agreement of the leading (2, 2) mode and of the subleading modes (2, 1), (3, 3), (4, 4) and (5, 5). Aligning the calibrated EOB waveforms and the numerical waveforms at low frequency, the phase difference of the (2, 2) mode between model and numerical simulation remains below ∼ 0.1 rad throughout the evolution for all mass ratios considered. The fractional amplitude difference at peak amplitude of the (2, 2) mode is 2% and grows to 12% during the ringdown. Using the Advanced LIGO noise curve we study the effectualness and measurement accuracy of the EOB model, and stress the relevance of modeling the higher-order modes for parameter estimation. We find that the effectualness, measured by the mismatch, between the EOB and numerical-relativity polarizations which include only the (2, 2) mode is smaller than 0.2% for binaries with total mass 20-200M⊙ and mass ratios 1, 2, 3, 4, and 6. When numericalrelativity polarizations contain the strongest seven modes, and stellar-mass black holes with masses less than 50M⊙ are considered, the mismatch for mass ratio 6 (1) can be as high as 7% (0.2%) when only the EOB (2, 2) mode is included, and an upper bound of the mismatch is 0.5% (0.07%) when all the four subleading EOB modes calibrated in this paper are taken into account. For binaries with intermediate-mass black holes with masses greater than 50M⊙ the mismatches are larger. We also determine for which signal-to-noise ratios the EOB model developed here can be used to measure binary parameters with systematic biases smaller than statistical errors due to detector noise.
We present the first attempt at calibrating the effective-one-body (EOB) model to accurate numeri... more We present the first attempt at calibrating the effective-one-body (EOB) model to accurate numerical-relativity simulations of spinning, non-precessing black-hole binaries. Aligning the EOB and numerical waveforms at low frequency over a time interval of 1000M , we first estimate the phase and amplitude errors in the numerical waveforms and then minimize the difference between numerical and EOB waveforms by calibrating a handful of EOB-adjustable parameters. In the equal-mass, spin aligned case, we find that phase and fractional amplitude differences between the numerical and EOB (2,2) mode can be reduced to 0.01 radians and 1%, respectively, over the entire inspiral waveforms. In the equal-mass, spin anti-aligned case, these differences can be reduced to 0.13 radians and 1% during inspiral and plunge, and to 0.4 radians and 10% during merger and ringdown. The waveform agreement is within numerical errors in the spin aligned case while slightly over numerical errors in the spin anti-aligned case. Using Enhanced LIGO and Advanced LIGO noise curves, we find that the overlap between the EOB and the numerical (2,2) mode, maximized over the initial phase and time of arrival, is larger than 0.999 for binaries with total mass 30-200M⊙. In addition to the leading (2,2) mode, we compare four subleading modes. We find good amplitude and frequency agreements between the EOB and numerical modes for both spin configurations considered, except for the (3,2) mode in the spin anti-aligned case. We believe that the larger difference in the (3,2) mode is due to the lack of knowledge of post-Newtonian spin effects in the higher modes.
The Numerical-Relativity-Analytical-Relativity (NRAR) collaboration is a joint effort between mem... more The 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 ∼ 100-200M , 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.
this paper, we present the results on our preliminary study and of on the based 31) graphics Spec... more this paper, we present the results on our preliminary study and of on the based 31) graphics Specifically, a computer-generated topographical model of is used since the photometry of have been studied in great details, photometric function derived is mapped onto the computer-generated topographic model. Using the model and specific camera parameters, accurate CC]) pixel response to target then be calculated. This pixel can be used by the feature tracking algorithm, and sensitivity to signal-to-noise ratio can then be determined. topography) photometric modeling, camera, feature tracking images of small bodies are essential to the dcr ivation of J1'1,-developed Autonomous Feature And Star (A to permit visually-guided, autonomous Actual images of bodies are rare compared to of and icy Only comet and have been captured by planetary spacecraft, the only data available for a complete and photometric characterization is that of computer-generated images of small bodies accurately pre...
Developing image acquisition requirements is a major part of the Autonomous Feature and Star Trac... more Developing image acquisition requirements is a major part of the Autonomous Feature and Star Tracking (AFAST) project's work in advancing sensor technologies for planetary exploration. Sensing and detecting desired planetary features also involve topographic and photometric characterization of celestial bodies. The photometric study can provide felicitous designs of optics, focal plane array, and processing pertaining to feature extraction and tracking.
We generalize Bowen-York black hole initial data to hyperboloidal constant mean curvature slices ... more We generalize Bowen-York black hole initial data to hyperboloidal constant mean curvature slices which extend to future null infinity. We solve this initial value problem numerically for several cases, including unequal mass binary black holes with spins and boosts. The singularity at null infinity in the Hamiltonian constraint associated with a constant mean curvature hypersurface does not pose any particular difficulties. The inner boundaries of our slices are minimal surfaces. Trumpet configurations are explored both analytically and numerically.
We present the first attempt at calibrating the effective-one-body (EOB) model to accurate numeri... more We present the first attempt at calibrating the effective-one-body (EOB) model to accurate numerical-relativity simulations of spinning, non-precessing black-hole binaries. Aligning the EOB and numerical waveforms at low frequency over a time interval of 1000M , we first estimate the phase and amplitude errors in the numerical waveforms and then minimize the difference between numerical and EOB waveforms by calibrating a handful of EOB-adjustable parameters. In the equal-mass, spin aligned case, we find that phase and fractional amplitude differences between the numerical and EOB (2,2) mode can be reduced to 0.01 radians and 1%, respectively, over the entire inspiral waveforms. In the equal-mass, spin anti-aligned case, these differences can be reduced to 0.13 radians and 1% during inspiral and plunge, and to 0.4 radians and 10% during merger and ringdown. The waveform agreement is within numerical errors in the spin aligned case while slightly over numerical errors in the spin anti-aligned case. Using Enhanced LIGO and Advanced LIGO noise curves, we find that the overlap between the EOB and the numerical (2,2) mode, maximized over the initial phase and time of arrival, is larger than 0.999 for binaries with total mass 30-200M⊙. In addition to the leading (2,2) mode, we compare four subleading modes. We find good amplitude and frequency agreements between the EOB and numerical modes for both spin configurations considered, except for the (3,2) mode in the spin anti-aligned case. We believe that the larger difference in the (3,2) mode is due to the lack of knowledge of post-Newtonian spin effects in the higher modes.
We calibrate the effective-one-body (EOB) model to an accurate numerical simulation of an equalma... more We calibrate the effective-one-body (EOB) model to an accurate numerical simulation of an equalmass, nonspinning binary black-hole coalescence produced by the Caltech-Cornell Collaboration. Aligning the EOB and numerical waveforms at low frequency over a time interval of $1000M, and taking into account the uncertainties in the numerical simulation, we investigate the significance and degeneracy of the EOB-adjustable parameters during inspiral, plunge, and merger, and determine the minimum number of EOB-adjustable parameters that achieves phase and amplitude agreements on the order of the numerical error. We find that phase and fractional amplitude differences between the numerical and EOB values of the dominant gravitational-wave mode h 22 can be reduced to 0.02 radians and 2%, respectively, until a time 20M before merger, and to 0.04 radians and 7%, respectively, at a time 20M after merger (during ringdown). Using LIGO, Enhanced LIGO, and Advanced LIGO noise curves, we find that the overlap between the EOB and the numerical h 22 , maximized only over the initial phase and time of arrival, is larger than 0.999 for equal-mass binary black holes with total mass 30-150M. In addition to the leading gravitational mode (2, 2), we compare the dominant subleading modes (4, 4) and (3, 2) for the inspiral and find phase and amplitude differences on the order of the numerical error. We also determine the mass-ratio dependence of one of the EOB-adjustable parameters by calibrating to numerical inspiral waveforms for black-hole binaries with mass ratios 2:1 and 3:1. The results presented in this paper improve and extend recent successful attempts aimed at providing gravitational-wave data analysts the best analytical EOB model capable of interpolating accurate numerical simulations.
Based on a recent study of the linearized Bianchi equations by Buchman and Sarbach, we construct ... more Based on a recent study of the linearized Bianchi equations by Buchman and Sarbach, we construct and implement a hierarchy of absorbing boundary conditions for the Einstein equations in generalized harmonic gauge. As a test problem, we demonstrate that we can evolve multipolar gravitational waves without any spurious reflections at linear order in perturbation theory.
Coalescing binary black holes are a primary science target of ground-based gravitational-wave det... more Coalescing binary black holes are a primary science target of ground-based gravitational-wave detectors. Detecting gravitational waves from these binaries and understanding the properties of the waves' sources require detailed knowledge of the expected waveforms. This paper presents a catalog of numerical binary black-hole simulations that represents a major advance toward the application of numerical relativity to gravitational-wave data analysis. The 171 simulations in the catalog include 90 precessing binaries, mass ratios up to 8:1, orbital eccentricities from a few percent to 1e-5, and black-hole spins up to 97% of the theoretical maximum. The simulations follow more orbits (up to 34) than previous simulations, allowing a more reliable connection to approximate analytical waveforms, which are used to extend numerical waveforms to span the entire frequency range of a detector. The expanded parameter-space coverage of this catalog, together with the length and accuracy of the included waveforms, will facilitate the development of new (and improvement of existing) gravitational-wave template families, the study of detection efficiency of gravitational-wave searches, and the understanding of systematic biases in parameter estimation of detected gravitational waves. Formidable challenges remain; for example, precession complicates the connection of numerical and approximate analytical waveforms, and vast regions of the parameter space remain unexplored.
The 2008 NRDA conference introduced the Numerical INJection Analysis project (NINJA), a new colla... more The 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.
The tetrad-based equations for vacuum gravity published by Estabrook, Robinson, and Wahlquist are... more The tetrad-based equations for vacuum gravity published by Estabrook, Robinson, and Wahlquist are simplified and adapted for numerical relativity. We show that the evolution equations as partial differential equations for the Ricci rotation coefficients constitute a rather simple first-order symmetrizable hyperbolic system, not only for the Nester gauge condition on the acceleration and angular velocity of the tetrad frames considered by Estabrook et al., but also for the Lorentz gauge condition of van Putten and Eardley and for a fixed gauge condition. We introduce a lapse function and a shift vector to allow general coordinate evolution relative to the timelike congruence defined by the tetrad vector field.
The numerical computation of gravitational radiation emitted from binary black hole systems has b... more The numerical computation of gravitational radiation emitted from binary black hole systems has been pivotal in the detection and characterization of 10 binary black hole astrophysical events since Sept. 14, 2015. However, the drive for more accurate waveforms remains, especially when computing higher-order spherical harmonic modes. The numerical relativity simulations currently used for LIGO / VIRGO detections solve Einsteinâ s field equations on a finite computational domain with an outer boundary. In order to obtain a unique Cauchy evolution, it is necessary to impose boundary conditions which should yield a well posed problem and ideally, be completely transparent to the physical problem on the unbounded domain. Short of achieving this ideal, one can try to develop so-called absorbing boundary conditions which form a well-posed problem and insure that only a very small amount of spurious gravitational radiation is reflected from the outer boundary into the computational domain. In this talk, I discuss the implementation of a hierarchy of such boundary conditions which hopefully will improve the accuracy of binary black hole numerical simulations.
The Numerical INJection Analysis (NINJA) project is a collaborative effort between members of the... more The 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 gravitationalwave detectors. Nine groups analysed this data using search and parameterestimation 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.
The Numerical INJection Analysis (NINJA) project is a collaborative effort between members of the... more The 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 gravitationalwave detectors. Nine groups analysed this data using search and parameterestimation 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.
The Numerical INJection Analysis (NINJA) project is a collaborative effort between members of the... more The 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
We calibrate an effective-one-body (EOB) model to numerical-relativity simulations of mass ratios... more We calibrate an effective-one-body (EOB) model to numerical-relativity simulations of mass ratios 1, 2, 3, 4, and 6, by maximizing phase and amplitude agreement of the leading (2, 2) mode and of the subleading modes (2, 1), (3, 3), (4, 4) and (5, 5). Aligning the calibrated EOB waveforms and the numerical waveforms at low frequency, the phase difference of the (2, 2) mode between model and numerical simulation remains below ∼ 0.1 rad throughout the evolution for all mass ratios considered. The fractional amplitude difference at peak amplitude of the (2, 2) mode is 2% and grows to 12% during the ringdown. Using the Advanced LIGO noise curve we study the effectualness and measurement accuracy of the EOB model, and stress the relevance of modeling the higher-order modes for parameter estimation. We find that the effectualness, measured by the mismatch, between the EOB and numerical-relativity polarizations which include only the (2, 2) mode is smaller than 0.2% for binaries with total mass 20-200M⊙ and mass ratios 1, 2, 3, 4, and 6. When numericalrelativity polarizations contain the strongest seven modes, and stellar-mass black holes with masses less than 50M⊙ are considered, the mismatch for mass ratio 6 (1) can be as high as 7% (0.2%) when only the EOB (2, 2) mode is included, and an upper bound of the mismatch is 0.5% (0.07%) when all the four subleading EOB modes calibrated in this paper are taken into account. For binaries with intermediate-mass black holes with masses greater than 50M⊙ the mismatches are larger. We also determine for which signal-to-noise ratios the EOB model developed here can be used to measure binary parameters with systematic biases smaller than statistical errors due to detector noise.
We present the first attempt at calibrating the effective-one-body (EOB) model to accurate numeri... more We present the first attempt at calibrating the effective-one-body (EOB) model to accurate numerical-relativity simulations of spinning, non-precessing black-hole binaries. Aligning the EOB and numerical waveforms at low frequency over a time interval of 1000M , we first estimate the phase and amplitude errors in the numerical waveforms and then minimize the difference between numerical and EOB waveforms by calibrating a handful of EOB-adjustable parameters. In the equal-mass, spin aligned case, we find that phase and fractional amplitude differences between the numerical and EOB (2,2) mode can be reduced to 0.01 radians and 1%, respectively, over the entire inspiral waveforms. In the equal-mass, spin anti-aligned case, these differences can be reduced to 0.13 radians and 1% during inspiral and plunge, and to 0.4 radians and 10% during merger and ringdown. The waveform agreement is within numerical errors in the spin aligned case while slightly over numerical errors in the spin anti-aligned case. Using Enhanced LIGO and Advanced LIGO noise curves, we find that the overlap between the EOB and the numerical (2,2) mode, maximized over the initial phase and time of arrival, is larger than 0.999 for binaries with total mass 30-200M⊙. In addition to the leading (2,2) mode, we compare four subleading modes. We find good amplitude and frequency agreements between the EOB and numerical modes for both spin configurations considered, except for the (3,2) mode in the spin anti-aligned case. We believe that the larger difference in the (3,2) mode is due to the lack of knowledge of post-Newtonian spin effects in the higher modes.
The Numerical-Relativity-Analytical-Relativity (NRAR) collaboration is a joint effort between mem... more The 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 ∼ 100-200M , 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.
this paper, we present the results on our preliminary study and of on the based 31) graphics Spec... more this paper, we present the results on our preliminary study and of on the based 31) graphics Specifically, a computer-generated topographical model of is used since the photometry of have been studied in great details, photometric function derived is mapped onto the computer-generated topographic model. Using the model and specific camera parameters, accurate CC]) pixel response to target then be calculated. This pixel can be used by the feature tracking algorithm, and sensitivity to signal-to-noise ratio can then be determined. topography) photometric modeling, camera, feature tracking images of small bodies are essential to the dcr ivation of J1'1,-developed Autonomous Feature And Star (A to permit visually-guided, autonomous Actual images of bodies are rare compared to of and icy Only comet and have been captured by planetary spacecraft, the only data available for a complete and photometric characterization is that of computer-generated images of small bodies accurately pre...
Developing image acquisition requirements is a major part of the Autonomous Feature and Star Trac... more Developing image acquisition requirements is a major part of the Autonomous Feature and Star Tracking (AFAST) project's work in advancing sensor technologies for planetary exploration. Sensing and detecting desired planetary features also involve topographic and photometric characterization of celestial bodies. The photometric study can provide felicitous designs of optics, focal plane array, and processing pertaining to feature extraction and tracking.
We generalize Bowen-York black hole initial data to hyperboloidal constant mean curvature slices ... more We generalize Bowen-York black hole initial data to hyperboloidal constant mean curvature slices which extend to future null infinity. We solve this initial value problem numerically for several cases, including unequal mass binary black holes with spins and boosts. The singularity at null infinity in the Hamiltonian constraint associated with a constant mean curvature hypersurface does not pose any particular difficulties. The inner boundaries of our slices are minimal surfaces. Trumpet configurations are explored both analytically and numerically.
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Papers by Luisa Buchman