arXiv subjects

Saul A. Teukolsky

Publications and source records attributed to Saul A. Teukolsky.

At least 73 records · Page 4Linked to original sources

arXiv2015

Formulation of discontinuous Galerkin methods for relativistic astrophysics

The DG algorithm is a powerful method for solving pdes, especially for evolution equations in conservation form. Since the algorithm involves integration over volume elements, it is not immediately obvious that it will generalize easily to arbitrary time-dependent curved spacetimes. We show how to formulate the algorithm in such spacetimes for applications in relativistic astrophysics. We also show how to formulate the algorithm for equations in non-conservative form, such as Einstein's field equations themselves. We find two computationally distinct formulations in both cases, one of which has seldom been used before for flat space in curvilinear coordinates but which may be more efficient. We also give a new derivation of the ALE algorithm (Arbitrary Lagrangian-Eulerian) using 4-vector methods that is much simpler than the usual derivation and explains why the method preserves the conservation form of the equations. The various formulations are explored with some simple numerical experiments that also explore the effect of the metric identities on the results.

gr-qc↗

arXiv2015

The Kerr Metric

This review describes the events leading up to the discovery of the Kerr metric in 1963 and the enormous impact the discovery has had in the subsequent 50 years. The review discusses the Penrose process, the four laws of black hole mechanics, uniqueness of the solution, and the no-hair theorems. It also includes Kerr perturbation theory and its application to black hole stability and quasi-normal modes. The Kerr metric's importance in the astrophysics of quasars and accreting stellar-mass black hole systems is detailed. A theme of the review is the "miraculous" nature of the solution, both in describing in a simple analytic formula the most general rotating black hole, and in having unexpected mathematical properties that make many calculations tractable. Also included is a pedagogical derivation of the solution suitable for a first course in general relativity.

gr-qc↗

arXiv2014

Short note on the mass matrix for Gauss-Lobatto grid points

The mass matrix for Gauss-Lobatto grid points is usually approximated by Gauss-Lobatto quadrature because this leads to a diagonal matrix that is easy to invert. The exact mass matrix and its inverse are full. We show that the exact mass matrix \emph{and} its inverse differ from the approximate diagonal ones by a simple rank-1 update (outer product). They can thus be applied to an arbitrary vector in $O(N)$ operations instead of $O(N^2)$.

math.NA↗

arXiv2014

Initial data for high-compactness black hole-neutron star binaries

For highly compact neutron stars, constructing numerical initial data for black hole-neutron star binary evolutions is very difficult. We describe improvements to an earlier method that enable it to handle these more challenging cases. We examine the case of a 6:1 mass ratio system in inspiral close to merger, where the star is governed by a polytropic $Γ=2$, an SLy, or an LS220 equation of state. In particular, we are able to obtain a solution with a realistic LS220 equation of state for a star with compactness 0.26 and mass 1.98 $M_\odot$, which is representative of the highest reliably determined neutron star masses. For the SLy equation of state, we can obtain solutions with a comparable compactness of 0.25, while for a family of polytropic equations of state, we obtain solutions with compactness up to 0.21, the largest compactness that is stable in this family. These compactness values are significantly higher than any previously published results. We find that improvements in adapting the computational domain to the neutron star surface and in accounting for the center of mass drift of the system are the key ingredients allowing us to obtain these solutions.

gr-qc↗

arXiv2014

Magnetic effects on the low-T/|W| instability in differentially rotating neutron stars

Dynamical instabilities in protoneutron stars may produce gravitational waves whose observation could shed light on the physics of core-collapse supernovae. When born with sufficient differential rotation, these stars are susceptible to a shear instability (the "low-T/|W| instability"), but such rotation can also amplify magnetic fields to strengths where they have a considerable impact on the dynamics of the stellar matter. Using a new magnetohydrodynamics module for the Spectral Einstein Code, we have simulated a differentially-rotating neutron star in full 3D to study the effects of magnetic fields on this instability. Though strong toroidal fields were predicted to suppress the low-T/|W| instability, we find that they do so only in a small range of field strengths. Below 4e13 G, poloidal seed fields do not wind up fast enough to have an effect before the instability saturates, while above 5e14 G, magnetic instabilities can actually amplify a global quadrupole mode (this threshold may be even lower in reality, as small-scale magnetic instabilities remain difficult to resolve numerically). Thus, the prospects for observing gravitational waves from such systems are not in fact diminished over most of the magnetic parameter space. Additionally, we report that the detailed development of the low-T/|W| instability, including its growth rate, depends strongly on the particular numerical methods used. The high-order methods we employ suggest that growth might be considerably slower than found in some previous simulations.

astro-ph.HE↗

arXiv2013

A catalog of 174 binary black-hole simulations for gravitational-wave astronomy

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.

gr-qc↗

arXiv2013

Error-analysis and comparison to analytical models of numerical waveforms produced by the NRAR Collaboration

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 ~100-200 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.

gr-qc↗

arXiv2013

Periastron Advance in Spinning Black Hole Binaries: Gravitational Self-Force from Numerical Relativity

We study the general relativistic periastron advance in spinning black hole binaries on quasi-circular orbits, with spins aligned or anti-aligned with the orbital angular momentum, using numerical-relativity simulations, the post-Newtonian approximation, and black hole perturbation theory. By imposing a symmetry by exchange of the bodies' labels, we devise an improved version of the perturbative result, and use it as the leading term of a new type of expansion in powers of the symmetric mass ratio. This allows us to measure, for the first time, the gravitational self-force effect on the periastron advance of a non-spinning particle orbiting a Kerr black hole of mass M and spin S = -0.5 M^2, down to separations of order 9M. Comparing the predictions of our improved perturbative expansion with the exact results from numerical simulations of equal-mass and equal-spin binaries, we find a remarkable agreement over a wide range of spins and orbital separations.

gr-qc↗

arXiv2013

Periastron advance in spinning black hole binaries: comparing effective-one-body and Numerical Relativity

We compute the periastron advance using the effective-one-body formalism for binary black holes moving on quasi-circular orbits and having spins collinear with the orbital angular momentum. We compare the predictions with the periastron advance recently computed in accurate numerical-relativity simulations and find remarkable agreement for a wide range of spins and mass ratios. These results do not use any numerical-relativity calibration of the effective-one-body model, and stem from two key ingredients in the effective-one-body Hamiltonian: (i) the mapping of the two-body dynamics of spinning particles onto the dynamics of an effective spinning particle in a (deformed) Kerr spacetime, fully symmetrized with respect to the two-body masses and spins, and (ii) the resummation, in the test-particle limit, of all post-Newtonian (PN) corrections linear in the spin of the particle. In fact, even when only the leading spin PN corrections are included in the effective-one-body spinning Hamiltonian but all the test-particle corrections linear in the spin of the particle are resummed we find very good agreement with the numerical results (within the numerical error for equal-mass binaries and discrepancies of at most 1% for larger mass ratios). Furthermore, we specialize to the extreme mass-ratio limit and derive, using the equations of motion in the gravitational skeleton approach, analytical expressions for the periastron advance, the meridional Lense-Thirring precession and spin precession frequency in the case of a spinning particle on a nearly circular equatorial orbit in Kerr spacetime, including also terms quadratic in the spin.

gr-qc↗

arXiv2013

Final spin and radiated energy in numerical simulations of binary black holes with equal masses and equal, aligned or anti-aligned spins

The behavior of merging black holes (including the emitted gravitational waves and the properties of the remnant) can currently be computed only by numerical simulations. This paper introduces ten numerical relativity simulations of binary black holes with equal masses and equal spins aligned or anti-aligned with the orbital angular momentum. The initial spin magnitudes have $|χ_i| \lesssim 0.95$ and are more concentrated in the aligned direction because of the greater astrophysical interest of this case. We combine this data with five previously reported simulations of the same configuration, but with different spin magnitudes, including the highest spin simulated to date, $χ_i \approx 0.97$. This data set is sufficiently accurate to enable us to offer improved analytic fitting formulae for the final spin and for the energy radiated by gravitational waves as a function of initial spin. The improved fitting formulae can help to improve our understanding of the properties of binary black hole merger remnants and can be used to enhance future approximate waveforms for gravitational wave searches, such as Effective-One-Body waveforms.

gr-qc↗

arXiv2013

Dynamical Excision Boundaries in Spectral Evolutions of Binary Black Hole Spacetimes

Simulations of binary black hole systems using the Spectral Einstein Code (SpEC) are done on a computational domain that excises the regions inside the black holes. It is imperative that the excision boundaries are outflow boundaries with respect to the hyperbolic evolution equations used in the simulation. We employ a time-dependent mapping between the fixed computational frame and the inertial frame through which the black holes move. The time-dependent parameters of the mapping are adjusted throughout the simulation by a feedback control system in order to follow the motion of the black holes, to adjust the shape and size of the excision surfaces so that they remain outflow boundaries, and to prevent large distortions of the grid. We describe in detail the mappings and control systems that we use. We show how these techniques have been essential in the evolution of binary black hole systems with extreme configurations, such as large spin magnitudes and high mass ratios, especially during the merger, when apparent horizons are highly distorted and the computational domain becomes compressed. The techniques introduced here may be useful in other applications of partial differential equations that involve time-dependent mappings.

gr-qc↗

arXiv2013

Black hole-neutron star mergers at realistic mass ratios: Equation of state and spin orientation effects

Black hole-neutron star mergers resulting in the disruption of the neutron star and the formation of an accretion disk and/or the ejection of unbound material are prime candidates for the joint detection of gravitational-wave and electromagnetic signals when the next generation of gravitational-wave detectors comes online. However, the disruption of the neutron star and the properties of the post-merger remnant are very sensitive to the parameters of the binary. In this paper, we study the impact of the radius of the neutron star and the alignment of the black hole spin for systems within the range of mass ratio currently deemed most likely for field binaries (M_BH ~ 7 M_NS) and for black hole spins large enough for the neutron star to disrupt (J/M^2=0.9). We find that: (i) In this regime, the merger is particularly sensitive to the radius of the neutron star, with remnant masses varying from 0.3M_NS to 0.1M_NS for changes of only 2 km in the NS radius; (ii) 0.01-0.05M_sun of unbound material can be ejected with kinetic energy >10^51 ergs, a significant increase compared to low mass ratio, low spin binaries. This ejecta could power detectable optical and radio afterglows. (iii) Only a small fraction (<3%) of the Advanced LIGO events in this parameter range have gravitational-wave signals which could offer constraints on the equation of state of the neutron star. (iv) A misaligned black hole spin works against disk formation, with less neutron star material remaining outside of the black hole after merger, and a larger fraction of that material remaining in the tidal tail instead of the forming accretion disk. (v) Large kicks (v>300 km/s) can be given to the final black hole as a result of a precessing BHNS merger, when the disruption of the neutron star occurs just outside or within the innermost stable spherical orbit.

gr-qc↗

arXiv2012

Are different approaches to constructing initial data for binary black hole simulations of the same astrophysical situation equivalent?

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 \emph{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 $δϕ\lesssim 10^{-2}$ radians and the amplitudes agree to within $δA/A \lesssim 5 \times 10^{-3}$, 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}

gr-qc↗

arXiv2012

Black hole-neutron star mergers for 10 solar mass black holes

General relativistic simulations of black hole-neutron star mergers have currently been limited to low-mass black holes (less than 7 solar mass), even though population synthesis models indicate that a majority of mergers might involve more massive black holes (10 solar mass or more). We present the first general relativistic simulations of black hole-neutron star mergers with 10 solar mass black holes. 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 a/M = 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 a/M>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.

gr-qc↗

arXiv2011

Black hole-neutron star mergers: effects of the orientation of the black hole spin

The spin of black holes in black hole-neutron star (BHNS) binaries can have a strong influence on the merger dynamics and the postmerger state; a wide variety of spin magnitudes and orientations are expected to occur in nature. In this paper, we report the first simulations in full general relativity of BHNS mergers with misaligned black hole spin. We vary the spin magnitude from a/m=0 to a/m=0.9 for aligned cases, and we vary the misalignment angle from 0 to 80 degrees for a/m=0.5. We restrict our study to 3:1 mass ratio systems and use a simple Gamma-law equation of state. We find that the misalignment angle has a strong effect on the mass of the postmerger accretion disk, but only for angles greater than ~ 40 degrees. Although the disk mass varies significantly with spin magnitude and misalignment angle, we find that all disks have very similar lifetimes ~ 100ms. Their thermal and rotational profiles are also very similar. For a misaligned merger, the disk is tilted with respect to the final black hole's spin axis. This will cause the disk to precess, but on a timescale longer than the accretion time. In all cases, we find promising setups for gamma-ray burst production: the disks are hot, thick, and hyperaccreting, and a baryon-clear region exists above the black hole.

astro-ph.HE↗

arXiv2010

Spectral methods for the wave equation in second-order form

Current spectral simulations of Einstein's equations require writing the equations in first-order form, potentially introducing instabilities and inefficiencies. We present a new penalty method for pseudo-spectral evolutions of second order in space wave equations. The penalties are constructed as functions of Legendre polynomials and are added to the equations of motion everywhere, not only on the boundaries. Using energy methods, we prove semi-discrete stability of the new method for the scalar wave equation in flat space and show how it can be applied to the scalar wave on a curved background. Numerical results demonstrating stability and convergence for multi-domain second-order scalar wave evolutions are also presented. This work provides a foundation for treating Einstein's equations directly in second-order form by spectral methods.

gr-qc↗

arXiv2010

Measuring orbital eccentricity and periastron advance in quasi-circular black hole simulations

We compare different methods of computing the orbital eccentricity of quasi-circular binary black hole systems using the orbital variables and gravitational wave phase and frequency. For eccentricities of about a per cent, most methods work satisfactorily. For small eccentricity, however, the gravitational wave phase allows a particularly clean and reliable measurement of the eccentricity. Furthermore, we measure the decay of the orbital eccentricity during the inspiral and find reasonable agreement with post-Newtonian results. Finally, we measure the periastron advance of non-spinning binary black holes, and we compare them to post-Newtonian approximations. With the low uncertainty in the measurement of the periastron advance, we positively detect deviations between fully numerical simulations and post-Newtonian calculations.

gr-qc↗

arXiv2009

Equation of state effects in black hole-neutron star mergers

The merger dynamics of a black hole-neutron star (BHNS) binary is influenced by the neutron star equation of state (EoS) through the latter's effect on the neutron star's radius and on the character of the mass transfer onto the black hole. We study these effects by simulating a number of BHNS binaries in full general relativity using a mixed pseudospectral/finite difference code. We consider several models of the neutron star matter EoS, including Gamma=2 and Gamma=2.75 polytropes and the nuclear-theory based Shen EoS. For models using the Shen EoS, we consider two limits for the evolution of the composition: source-free advection and instantaneous beta-equilibrium. To focus on EoS effects, we fix the mass ratio to 3:1 and the initial aligned black hole spin to a/m=0.5 for all models. We confirm earlier studies which found that more compact stars create a stronger gravitational wave signal but a smaller postmerger accretion disk. We also vary the EoS while holding the compaction fixed. All mergers are qualitatively similar, but we find signatures of the EoS in the waveform and in the tail and disk structures.

astro-ph.HE↗