We present a detailed investigation into the properties of GW170729, the gravitational wave with ... more We present a detailed investigation into the properties of GW170729, the gravitational wave with the most massive and distant source confirmed to date. We employ an extensive set of waveform models, including new improved models that incorporate the effect of higher-order waveform modes which are particularly important for massive systems. We find no indication of spin-precession, but the inclusion of higher-order modes in the models results in an improved estimate for the mass ratio of (0.3 − 0.8) at the 90% credible level. Our updated measurement excludes equal masses at that level. We also find that models with higher-order modes lead to the data being more consistent with a smaller effective spin, with the probability that the effective spin is greater than zero being reduced from 99% to 94%. The 90% credible interval for the effective spin parameter is now (−0.01 − 0.50). Additionally, the recovered signal-to-noise ratio increases by ∼ 0.3 units compared to analyses without higher-order modes. We study the effect of common spin priors on the derived spin and mass measurements, and observe small shifts in the spins, while the masses remain unaffected. We argue that our conclusions are robust against systematic errors in the waveform models. We also
Simulating a binary black hole (BBH) coalescence by solving Einstein's equations is computational... more Simulating a binary black hole (BBH) coalescence by solving Einstein's equations is computationally expensive, requiring days to months of supercomputing time. Using reduced order modeling techniques, we construct an accurate surrogate model, which is evaluated in a millisecond to a second, for numerical relativity (NR) waveforms from non-spinning BBH coalescences with mass ratios in [1, 10] and durations corresponding to about 15 orbits before merger. We assess the model's uncertainty and show that our modeling strategy predicts NR waveforms not used for the surrogate's training with errors nearly as small as the numerical error of the NR code. Our model includes all spherical-harmonic −2Y m waveform modes resolved by the NR code up to = 8. We compare our surrogate model to Effective One Body waveforms from 50-300M for advanced LIGO detectors and find that the surrogate is always more faithful (by at least an order of magnitude in most cases).
The Caltech-Cornell spectral Einstein Code (SpEC) is now able to robustly and accurately evolve b... more The Caltech-Cornell spectral Einstein Code (SpEC) is now able to robustly and accurately evolve binary black hole systems through the inspiral, merger and ringdown phases. This is attributed to new gauge conditions as well as a robustly stable numerical algorithm. The talk will highlight the key new elements of our algorithm. )
General relativistic simulations of black hole-neutron star mergers have currently been limited t... more General relativistic simulations of black hole-neutron star mergers have currently been limited to low-mass black holes (MBH ≤ 7M⊙), even though population synthesis models indicate that a majority of mergers might involve more massive black holes (MBH ≥ 10M⊙). We present the first general relativistic simulations of black hole-neutron star mergers with MBH ∼ 10M⊙. For massive black holes, the tidal forces acting on the neutron star are usually too weak to disrupt the star before it reaches the innermost stable circular orbit of the black hole. Varying the spin of the black hole in the range aBH/MBH = 0.5-0.9, we find that mergers result in the disruption of the star and the formation of a massive accretion disk only for large spins aBH/MBH ≥ 0.7-0.9. From these results, we obtain updated constraints on the ability of BHNS mergers to be the progenitors of short gamma-ray bursts as a function of the mass and spin of the black hole. We also discuss the dependence of the gravitational wave signal on the black hole parameters, and provide waveforms and spectra from simulations beginning 7-8 orbits before merger.
Many relevant applications in gravitational wave physics share a significant common problem: the ... more Many relevant applications in gravitational wave physics share a significant common problem: the seven-dimensional parameter space of gravitational waveforms from precessing compact binary inspirals and coalescences is large enough to prohibit covering the space of waveforms with sufficient density. We find that by using the reduced basis method together with a parametrization of waveforms based on their phase and precession, we can construct ultracompact yet high-accuracy representations of this large space. As a demonstration, we show that less than 100 judiciously chosen precessing inspiral waveforms are needed for 200 cycles, mass ratios from 1 to 10, and spin magnitudes ≤ 0.9. In fact, using only the first 10 reduced basis waveforms yields a maximum mismatch of 0.016 over the whole range of considered parameters. We test whether the parameters selected from the inspiral regime result in an accurate reduced basis when including merger and ringdown; we find that this is indeed the case in the context of a nonprecessing effective-one-body model. This evidence suggests that as few as ∼100 numerical simulations of binary black hole coalescences may accurately represent the seven-dimensional parameter space of precession waveforms for the considered ranges.
We develop, test, and compare new numerical and geometrical methods for improving the accuracy of... more We develop, test, and compare new numerical and geometrical methods for improving the accuracy of extracting waveforms using characteristic evolution. The new numerical method involves use of circular boundaries to the stereographic grid patches which cover the spherical cross sections of the outgoing null cones. We show how an angular version of numerical dissipation can be introduced into the characteristic code to damp the high frequency error arising form the irregular way the circular patch boundary cuts through the grid. The new geometric method involves use of the Weyl tensor component É 4 to extract the waveform as opposed to the original approach via the Bondi news function. We develop the necessary analytic and computational formula to compute the Oð1=rÞ radiative part of É 4 in terms of a conformally compactified treatment of null infinity. These methods are compared and calibrated in test problems based upon linearized waves.
We present a first exploration of the results of neutron star-black hole mergers using black hole... more We present a first exploration of the results of neutron star-black hole mergers using black hole masses in the most likely range of 7M⊙-10M⊙, a neutrino leakage scheme, and a modeling of the neutron star material through a finite-temperature nuclear-theory based equation of state. In the range of black hole spins in which the neutron star is tidally disrupted (χBH > ∼ 0.7), we show that the merger consistently produces large amounts of cool (T < ∼ 1 MeV), unbound, neutron-rich material (Mej ∼ 0.05M⊙-0.20M⊙). A comparable amount of bound matter is initially divided between a hot disk (Tmax ∼ 15 MeV) with typical neutrino luminosity Lν ∼ 10 53 erg/s, and a cooler tidal tail. After a short period of rapid protonization of the disk lasting ∼ 10 ms, the accretion disk cools down under the combined effects of the fall-back of cool material from the tail, continued accretion of the hottest material onto the black hole, and neutrino emission. As the temperature decreases, the disk progressively becomes more neutron-rich, with dimmer neutrino emission. This cooling process should stop once the viscous heating in the disk (not included in our simulations) balances the cooling. These mergers of neutron star-black hole binaries with black hole masses MBH ∼ 7M⊙-10M⊙ and black hole spins high enough for the neutron star to disrupt provide promising candidates for the production of short gamma-ray bursts, of bright infrared post-merger signals due to the radioactive decay of unbound material, and of large amounts of r-process nuclei.
Black Holes, Gravitational Radiation and the Universe, 1999
This paper gives a detailed pedagogic presentation of the central concepts underlying a new algor... more This paper gives a detailed pedagogic presentation of the central concepts underlying a new algorithm for the numerical solution of Einstein's equations for gravitation. This approach incorporates the best features of the two leading approaches to computational gravitation, carving up spacetime via Cauchy hypersurfaces within a central worldtube, and using characteristic hypersurfaces in its exterior to connect this region with null infinity and study gravitational radiation. It has worked well in simplified test problems, and is currently being used to build computer codes to simulate black hole collisions in 3-D.
Gravitational radiation is properly defined only at future null infinity (J +), but in practice i... more Gravitational radiation is properly defined only at future null infinity (J +), but in practice it is estimated from data calculated at a finite radius. We have used characteristic extraction to calculate gravitational radiation at J + for the inspiral and merger of two equal mass non-spinning black holes. Thus we have determined the first unambiguous merger waveforms for this problem. The implementation is general purpose, and can be applied to calculate the gravitational radiation, at J + , given data at a finite radius calculated in another computation.
This paper presents a publicly available catalog of 174 numerical binary black-hole simulations f... more This paper presents a publicly available catalog of 174 numerical binary black-hole simulations following up to 35 orbits. The catalog includes 91 precessing binaries, mass ratios up to 8:1, orbital eccentricities from a few percent to 10 −5 , black-hole spins up to 98% of the theoretical maximum, and radiated energies up to 11.1% of the initial mass. We establish remarkably good agreement with post-Newtonian precession of orbital and spin directions for two new precessing simulations, and we discuss other applications of this catalog. Formidable challenges remain: e.g., precession complicates the connection of numerical and approximate analytical waveforms, and vast regions of the parameter space remain unexplored.
Several improvements in numerical methods and gauge choice are presented that make it possible no... more Several improvements in numerical methods and gauge choice are presented that make it possible now to perform simulations of the merger and ringdown phases of "generic" binary black-hole evolutions using the pseudo-spectral evolution code SpEC. These improvements include the use of a new damped-wave gauge condition, a new grid structure with appropriate filtering that improves stability, and better adaptivity in conforming the grid structures to the shapes and sizes of the black holes. Simulations illustrating the success of these new methods are presented for a variety of binary black-hole systems. These include fairly "generic" systems with unequal masses (up to 2:1 mass ratios), and spins (with magnitudes up to 0.4M 2) pointing in various directions.
Gravitational waves emitted by black-hole binary systems have the highest signal-to-noise ratio i... more Gravitational waves emitted by black-hole binary systems have the highest signal-to-noise ratio in LIGO and Virgo detectors when black-hole spins are aligned with the orbital angular momentum and extremal. For such systems, we extend the effective-one-body inspiral-merger-ringdown waveforms to generic mass ratios and spins calibrating them to 38 numerical-relativity nonprecessing waveforms produced by the SXS Collaboration. The numerical-relativity simulations span mass ratios from 1 to 8, spin magnitudes up to 98% of extremality, and last for 40 to 60 gravitational-wave cycles. When the total mass of the binary is between 20 and 200M ⊙ , the effective-one-body nonprecessing (dominant mode) waveforms have overlap above 99% (using the advanced-LIGO design noise spectral density) with all of the 38 nonprecessing numerical waveforms, when maximizing only on initial phase and time. This implies a negligible loss in event rate due to modeling. We also show that-without further calibration-the precessing effective-onebody (dominant mode) waveforms have overlap above 97% with two very long, strongly precessing numerical-relativity waveforms, when maximizing only on the initial phase and time.
A new gauge driver is introduced for the generalized harmonic (GH) representation of Einstein's e... more A new gauge driver is introduced for the generalized harmonic (GH) representation of Einstein's equation. This new driver allows a rather general class of gauge conditions to be implemented in a way that maintains the hyperbolicity of the combined evolution system. This driver is more stable and effective and, unlike previous drivers, allows stable evolutions using the dual-frame evolution technique. Appropriate boundary conditions for this new gauge driver are constructed, and a new boundary condition for the ''gauge'' components of the spacetime metric in the GH Einstein system is introduced. The stability and effectiveness of this new gauge driver are demonstrated through numerical tests, which impose a new damped-wave gauge condition on the evolutions of single black-hole spacetimes.
Initial data for numerical evolutions of binary-black holes have been dominated by "conformally f... more Initial data for numerical evolutions of binary-black holes have been dominated by "conformally flat" (CF) data (i.e., initial data where the conformal background metric is chosen to be flat) because they are easy to construct. However, CF initial data cannot simulate nearly extremal spins, while more complicated "conformally curved" initial data (i.e., initial data in which the background metric is not explicitly chosen to be flat), such as initial data where the spatial metric is chosen to be proportional to a weighted superposition of two Kerr-Schild (SKS) black holes can. Here we establish the consistency between the astrophysical results of these two initial data schemes for nonspinning binary systems. We evolve the inspiral, merger, and ringdown of two equal-mass, nonspinning black holes using SKS initial data and compare with an analogous simulation using CF initial data. We find that the resultant gravitational-waveform phases agree to within δφ 10 −2 radians and the amplitudes agree to within δA/A 5 × 10 −3 , which are within the numerical errors of the simulations. Furthermore, we find that the final mass and spin of the remnant black hole agree to one part in 10 5 .
We present a detailed investigation into the properties of GW170729, the gravitational wave with ... more We present a detailed investigation into the properties of GW170729, the gravitational wave with the most massive and distant source confirmed to date. We employ an extensive set of waveform models, including new improved models that incorporate the effect of higher-order waveform modes which are particularly important for massive systems. We find no indication of spin-precession, but the inclusion of higher-order modes in the models results in an improved estimate for the mass ratio of (0.3 − 0.8) at the 90% credible level. Our updated measurement excludes equal masses at that level. We also find that models with higher-order modes lead to the data being more consistent with a smaller effective spin, with the probability that the effective spin is greater than zero being reduced from 99% to 94%. The 90% credible interval for the effective spin parameter is now (−0.01 − 0.50). Additionally, the recovered signal-to-noise ratio increases by ∼ 0.3 units compared to analyses without higher-order modes. We study the effect of common spin priors on the derived spin and mass measurements, and observe small shifts in the spins, while the masses remain unaffected. We argue that our conclusions are robust against systematic errors in the waveform models. We also
Simulating a binary black hole (BBH) coalescence by solving Einstein's equations is computational... more Simulating a binary black hole (BBH) coalescence by solving Einstein's equations is computationally expensive, requiring days to months of supercomputing time. Using reduced order modeling techniques, we construct an accurate surrogate model, which is evaluated in a millisecond to a second, for numerical relativity (NR) waveforms from non-spinning BBH coalescences with mass ratios in [1, 10] and durations corresponding to about 15 orbits before merger. We assess the model's uncertainty and show that our modeling strategy predicts NR waveforms not used for the surrogate's training with errors nearly as small as the numerical error of the NR code. Our model includes all spherical-harmonic −2Y m waveform modes resolved by the NR code up to = 8. We compare our surrogate model to Effective One Body waveforms from 50-300M for advanced LIGO detectors and find that the surrogate is always more faithful (by at least an order of magnitude in most cases).
The Caltech-Cornell spectral Einstein Code (SpEC) is now able to robustly and accurately evolve b... more The Caltech-Cornell spectral Einstein Code (SpEC) is now able to robustly and accurately evolve binary black hole systems through the inspiral, merger and ringdown phases. This is attributed to new gauge conditions as well as a robustly stable numerical algorithm. The talk will highlight the key new elements of our algorithm. )
General relativistic simulations of black hole-neutron star mergers have currently been limited t... more General relativistic simulations of black hole-neutron star mergers have currently been limited to low-mass black holes (MBH ≤ 7M⊙), even though population synthesis models indicate that a majority of mergers might involve more massive black holes (MBH ≥ 10M⊙). We present the first general relativistic simulations of black hole-neutron star mergers with MBH ∼ 10M⊙. For massive black holes, the tidal forces acting on the neutron star are usually too weak to disrupt the star before it reaches the innermost stable circular orbit of the black hole. Varying the spin of the black hole in the range aBH/MBH = 0.5-0.9, we find that mergers result in the disruption of the star and the formation of a massive accretion disk only for large spins aBH/MBH ≥ 0.7-0.9. From these results, we obtain updated constraints on the ability of BHNS mergers to be the progenitors of short gamma-ray bursts as a function of the mass and spin of the black hole. We also discuss the dependence of the gravitational wave signal on the black hole parameters, and provide waveforms and spectra from simulations beginning 7-8 orbits before merger.
Many relevant applications in gravitational wave physics share a significant common problem: the ... more Many relevant applications in gravitational wave physics share a significant common problem: the seven-dimensional parameter space of gravitational waveforms from precessing compact binary inspirals and coalescences is large enough to prohibit covering the space of waveforms with sufficient density. We find that by using the reduced basis method together with a parametrization of waveforms based on their phase and precession, we can construct ultracompact yet high-accuracy representations of this large space. As a demonstration, we show that less than 100 judiciously chosen precessing inspiral waveforms are needed for 200 cycles, mass ratios from 1 to 10, and spin magnitudes ≤ 0.9. In fact, using only the first 10 reduced basis waveforms yields a maximum mismatch of 0.016 over the whole range of considered parameters. We test whether the parameters selected from the inspiral regime result in an accurate reduced basis when including merger and ringdown; we find that this is indeed the case in the context of a nonprecessing effective-one-body model. This evidence suggests that as few as ∼100 numerical simulations of binary black hole coalescences may accurately represent the seven-dimensional parameter space of precession waveforms for the considered ranges.
We develop, test, and compare new numerical and geometrical methods for improving the accuracy of... more We develop, test, and compare new numerical and geometrical methods for improving the accuracy of extracting waveforms using characteristic evolution. The new numerical method involves use of circular boundaries to the stereographic grid patches which cover the spherical cross sections of the outgoing null cones. We show how an angular version of numerical dissipation can be introduced into the characteristic code to damp the high frequency error arising form the irregular way the circular patch boundary cuts through the grid. The new geometric method involves use of the Weyl tensor component É 4 to extract the waveform as opposed to the original approach via the Bondi news function. We develop the necessary analytic and computational formula to compute the Oð1=rÞ radiative part of É 4 in terms of a conformally compactified treatment of null infinity. These methods are compared and calibrated in test problems based upon linearized waves.
We present a first exploration of the results of neutron star-black hole mergers using black hole... more We present a first exploration of the results of neutron star-black hole mergers using black hole masses in the most likely range of 7M⊙-10M⊙, a neutrino leakage scheme, and a modeling of the neutron star material through a finite-temperature nuclear-theory based equation of state. In the range of black hole spins in which the neutron star is tidally disrupted (χBH > ∼ 0.7), we show that the merger consistently produces large amounts of cool (T < ∼ 1 MeV), unbound, neutron-rich material (Mej ∼ 0.05M⊙-0.20M⊙). A comparable amount of bound matter is initially divided between a hot disk (Tmax ∼ 15 MeV) with typical neutrino luminosity Lν ∼ 10 53 erg/s, and a cooler tidal tail. After a short period of rapid protonization of the disk lasting ∼ 10 ms, the accretion disk cools down under the combined effects of the fall-back of cool material from the tail, continued accretion of the hottest material onto the black hole, and neutrino emission. As the temperature decreases, the disk progressively becomes more neutron-rich, with dimmer neutrino emission. This cooling process should stop once the viscous heating in the disk (not included in our simulations) balances the cooling. These mergers of neutron star-black hole binaries with black hole masses MBH ∼ 7M⊙-10M⊙ and black hole spins high enough for the neutron star to disrupt provide promising candidates for the production of short gamma-ray bursts, of bright infrared post-merger signals due to the radioactive decay of unbound material, and of large amounts of r-process nuclei.
Black Holes, Gravitational Radiation and the Universe, 1999
This paper gives a detailed pedagogic presentation of the central concepts underlying a new algor... more This paper gives a detailed pedagogic presentation of the central concepts underlying a new algorithm for the numerical solution of Einstein's equations for gravitation. This approach incorporates the best features of the two leading approaches to computational gravitation, carving up spacetime via Cauchy hypersurfaces within a central worldtube, and using characteristic hypersurfaces in its exterior to connect this region with null infinity and study gravitational radiation. It has worked well in simplified test problems, and is currently being used to build computer codes to simulate black hole collisions in 3-D.
Gravitational radiation is properly defined only at future null infinity (J +), but in practice i... more Gravitational radiation is properly defined only at future null infinity (J +), but in practice it is estimated from data calculated at a finite radius. We have used characteristic extraction to calculate gravitational radiation at J + for the inspiral and merger of two equal mass non-spinning black holes. Thus we have determined the first unambiguous merger waveforms for this problem. The implementation is general purpose, and can be applied to calculate the gravitational radiation, at J + , given data at a finite radius calculated in another computation.
This paper presents a publicly available catalog of 174 numerical binary black-hole simulations f... more This paper presents a publicly available catalog of 174 numerical binary black-hole simulations following up to 35 orbits. The catalog includes 91 precessing binaries, mass ratios up to 8:1, orbital eccentricities from a few percent to 10 −5 , black-hole spins up to 98% of the theoretical maximum, and radiated energies up to 11.1% of the initial mass. We establish remarkably good agreement with post-Newtonian precession of orbital and spin directions for two new precessing simulations, and we discuss other applications of this catalog. Formidable challenges remain: e.g., precession complicates the connection of numerical and approximate analytical waveforms, and vast regions of the parameter space remain unexplored.
Several improvements in numerical methods and gauge choice are presented that make it possible no... more Several improvements in numerical methods and gauge choice are presented that make it possible now to perform simulations of the merger and ringdown phases of "generic" binary black-hole evolutions using the pseudo-spectral evolution code SpEC. These improvements include the use of a new damped-wave gauge condition, a new grid structure with appropriate filtering that improves stability, and better adaptivity in conforming the grid structures to the shapes and sizes of the black holes. Simulations illustrating the success of these new methods are presented for a variety of binary black-hole systems. These include fairly "generic" systems with unequal masses (up to 2:1 mass ratios), and spins (with magnitudes up to 0.4M 2) pointing in various directions.
Gravitational waves emitted by black-hole binary systems have the highest signal-to-noise ratio i... more Gravitational waves emitted by black-hole binary systems have the highest signal-to-noise ratio in LIGO and Virgo detectors when black-hole spins are aligned with the orbital angular momentum and extremal. For such systems, we extend the effective-one-body inspiral-merger-ringdown waveforms to generic mass ratios and spins calibrating them to 38 numerical-relativity nonprecessing waveforms produced by the SXS Collaboration. The numerical-relativity simulations span mass ratios from 1 to 8, spin magnitudes up to 98% of extremality, and last for 40 to 60 gravitational-wave cycles. When the total mass of the binary is between 20 and 200M ⊙ , the effective-one-body nonprecessing (dominant mode) waveforms have overlap above 99% (using the advanced-LIGO design noise spectral density) with all of the 38 nonprecessing numerical waveforms, when maximizing only on initial phase and time. This implies a negligible loss in event rate due to modeling. We also show that-without further calibration-the precessing effective-onebody (dominant mode) waveforms have overlap above 97% with two very long, strongly precessing numerical-relativity waveforms, when maximizing only on the initial phase and time.
A new gauge driver is introduced for the generalized harmonic (GH) representation of Einstein's e... more A new gauge driver is introduced for the generalized harmonic (GH) representation of Einstein's equation. This new driver allows a rather general class of gauge conditions to be implemented in a way that maintains the hyperbolicity of the combined evolution system. This driver is more stable and effective and, unlike previous drivers, allows stable evolutions using the dual-frame evolution technique. Appropriate boundary conditions for this new gauge driver are constructed, and a new boundary condition for the ''gauge'' components of the spacetime metric in the GH Einstein system is introduced. The stability and effectiveness of this new gauge driver are demonstrated through numerical tests, which impose a new damped-wave gauge condition on the evolutions of single black-hole spacetimes.
Initial data for numerical evolutions of binary-black holes have been dominated by "conformally f... more Initial data for numerical evolutions of binary-black holes have been dominated by "conformally flat" (CF) data (i.e., initial data where the conformal background metric is chosen to be flat) because they are easy to construct. However, CF initial data cannot simulate nearly extremal spins, while more complicated "conformally curved" initial data (i.e., initial data in which the background metric is not explicitly chosen to be flat), such as initial data where the spatial metric is chosen to be proportional to a weighted superposition of two Kerr-Schild (SKS) black holes can. Here we establish the consistency between the astrophysical results of these two initial data schemes for nonspinning binary systems. We evolve the inspiral, merger, and ringdown of two equal-mass, nonspinning black holes using SKS initial data and compare with an analogous simulation using CF initial data. We find that the resultant gravitational-waveform phases agree to within δφ 10 −2 radians and the amplitudes agree to within δA/A 5 × 10 −3 , which are within the numerical errors of the simulations. Furthermore, we find that the final mass and spin of the remnant black hole agree to one part in 10 5 .
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Papers by Bela Szilagyi