arXiv subjects

Lawrence E. Kidder

Publications and source records attributed to Lawrence E. Kidder.

At least 55 records · Page 3Linked to original sources

arXiv2025

Parameter control for eccentric, precessing binary black hole simulations with SpEC

Numerical relativity simulations of merging black holes provide the most accurate description of the binary dynamics and the emitted gravitational wave signal. However, practical considerations such as imperfect initial data and initial parameters mean that achieving target parameters, such as the orbital eccentricity or the black hole spin directions, at the beginning of the usable part of the simulation is challenging. In this paper, we devise a method to produce simulations with specific target parameters, namely the Keplerian orbital parameters-eccentricity, semimajor axis, mean anomaly-and the black hole spin vectors using SpEC. The method is an extension of the current process for achieving vanishing eccentricity and it is based on a parameter control loop that iteratively numerically evolves the system, fits the orbit with analytical post-Newtonian equations, and calculates updated input parameters. Through SpEC numerical simulations, we demonstrate $\lesssim 10^{-3}$ and $O(\rm degree)$ convergence for the orbital eccentricity and the spin directions respectively in $\leq7$ iterations. These tests extend to binaries with mass ratios $q \leq 3$, eccentricities $e \leq 0.65$, and spin magnitudes $|χ| \leq 0.75$. Our method for controlling the orbital and spin parameters of numerical simulations can be used to produce targeted simulations in sparsely covered regions of the parameter space or study the dynamics of relativistic binaries.

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arXiv2025

Simulating binary black hole mergers using discontinuous Galerkin methods

Binary black holes are the most abundant source of gravitational-wave observations. Gravitational-wave observatories in the next decade will require tremendous increases in the accuracy of numerical waveforms modeling binary black holes, compared to today's state of the art. One approach to achieving the required accuracy is using spectral-type methods that scale to many processors. Using the SpECTRE numerical-relativity code, we present the first simulations of a binary black hole inspiral, merger, and ringdown using discontinuous Galerkin methods. The efficiency of discontinuous Galerkin methods allows us to evolve the binary through ~18 orbits at reasonable computational cost. We then use SpECTRE's Cauchy Characteristic Evolution (CCE) code to extract the gravitational waves at future null infinity. The open-source nature of SpECTRE means this is the first time a spectral-type method for simulating binary black hole evolutions is available to the entire numerical-relativity community.

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arXiv2024

Late-time tails in nonlinear evolutions of merging black holes

We uncover late-time gravitational-wave tails in fully nonlinear 3+1 dimensional numerical relativity simulations of merging black holes, using the highly accurate SpEC code. We achieve this result by exploiting the strong magnification of late-time tails due to binary eccentricity, recently observed in perturbative evolutions, and showcase here the tail presence in head-on configurations for several mass ratios close to unity. We validate the result through a large battery of numerical tests and detailed comparison with perturbative evolutions, which display striking agreement with full nonlinear ones. Our results offer yet another confirmation of the highly predictive power of black hole perturbation theory in the presence of a source, even when applied to nonlinear solutions. The late-time tail signal is much more prominent than anticipated until recently, and possibly within reach of gravitational-wave detectors measurements, unlocking observational investigations of an additional set of general relativistic predictions on the long-range gravitational dynamics.

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arXiv2024

A Review of Gravitational Memory and BMS Frame Fixing in Numerical Relativity

Gravitational memory effects and the BMS freedoms exhibited at future null infinity have recently been resolved and utilized in numerical relativity simulations. With this, gravitational wave models and our understanding of the fundamental nature of general relativity have been vastly improved. In this paper, we review the history and intuition behind memory effects and BMS symmetries, how they manifest in gravitational waves, and how controlling the infinite number of BMS freedoms of numerical relativity simulations can crucially improve the waveform models that are used by gravitational wave detectors. We reiterate the fact that, with memory effects and BMS symmetries, not only can these next-generation numerical waveforms be used to observe never-before-seen physics, but they can also be used to test GR and learn new astrophysical information about our universe.

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arXiv2024

Binary neutron star mergers using a discontinuous Galerkin-finite difference hybrid method

We present a discontinuous Galerkin-finite difference hybrid scheme that allows high-order shock capturing with the discontinuous Galerkin method for general relativistic magnetohydrodynamics in dynamical spacetimes. We present several optimizations and stability improvements to our algorithm that allow the hybrid method to successfully simulate single, rotating, and binary neutron stars. The hybrid method achieves the efficiency of discontinuous Galerkin methods throughout almost the entire spacetime during the inspiral phase, while being able to robustly capture shocks and resolve the stellar surfaces. We also use Cauchy-Characteristic evolution to compute the first gravitational waveforms at future null infinity from binary neutron star mergers. The simulations presented here are the first successful binary neutron star inspiral and merger simulations using discontinuous Galerkin methods.

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arXiv2024

Robustness of neutron star merger simulations to changes in neutrino transport and neutrino-matter interactions

Binary neutron star mergers play an important role in nuclear astrophysics: their gravitational wave and electromagnetic signals carry information about the equation of state of cold matter above nuclear saturation density, and they may be one of the main sources of r-process elements in the Universe. Neutrino-matter interactions during and after merger impact the properties of these electromagnetic signals, and the relative abundances of the produced r-process elements. Existing merger simulations are however limited in their ability to realistically model neutrino transport and neutrino-matter interactions. Here, we perform a comparison of the impact of the use of state-of-the art two-moment or Monte-Carlo transport schemes on the outcome of merger simulations, for a single binary neutron star system with a short-lived neutron star remnant ($(5-10)\,{\rm ms}$). We also investigate the use of different reaction rates in the simulations. While the best transport schemes generally agree well on the qualitative impact of neutrinos on the system, differences in the behavior of the high-density regions can significantly impact the collapse time and the properties of the hot tidal arms in this metastable merger remnant. The chosen interaction rates, transport algorithm, as well as recent improvements by Radice et al to the two-moment algorithms can all contribute to changes at the $(10-30)\%$ level in the global properties of the merger remnant and outflows. The limitations of previous moment schemes fixed by Radice et al also appear sufficient to explain the large difference that we observed in the production of heavy-lepton neutrinos in a previous comparison of Monte-Carlo and moment schemes in the context of a low mass binary neutron star system.

astro-ph.HE↗

arXiv2024

High-Precision Ringdown Surrogate Model for Non-Precessing Binary Black Holes

Highly precise and robust waveform models are required as improvements in detector sensitivity enable us to test general relativity with more precision than ever before. In this work, we introduce a spin-aligned surrogate ringdown model. This ringdown surrogate, NRSur3dq8_RD, is built with numerical waveforms produced using Cauchy-characteristic evolution. In addition, these waveforms are in the superrest frame of the remnant black hole allowing us to do a correct analysis of the ringdown spectrum. The novel prediction of our surrogate model is complex-valued quasinormal mode (QNM) amplitudes, with median relative errors of $10^{-2}-10^{-3}$ over the parameter space. Like previous remnant surrogates, we also predict the remnant black hole's mass and spin. The QNM mode amplitude errors translate into median errors on ringdown waveforms of $10^{-4}$. The high accuracy and QNM mode content provided by our surrogate will enable high-precision ringdown analyses such as tests of general relativity. Our ringdown model is publicly available through the python package surfinBH.

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arXiv2024

High angular momentum hot differentially rotating equilibrium star evolutions in conformally flat spacetime

The conformal flatness approximation to the Einstein equations has been successfully used in many astrophysical applications such as initial data constructions and dynamical simulations. Although it has been shown that full general relativistic strongly differentially rotating equilibrium models deviate by at most a few percent from their conformally flat counterparts, whether those conformally flat solutions remain stable has not been fully addressed. To further understand the limitations of the conformal flatness approximation, in this work, we construct spatially-conformally-flat hot hypermassive neutron stars with post-merger-like rotation laws, and perform conformally flat evolutions and analysis over dynamical timescales. We find that enforcing conformally-flat spacetime could change the equilibrium of quasi-toroidal models with high angular momentum for $J \gtrsim 9 ~G M_{\odot}^2 / c$ compared to fully general relativistic cases. In contrast, all the quasi-spherical models considered in this work remain stable even with high angular momentum $J=9~G M_{\odot}^2 / c$. Our investigation suggests that the quasi-spherical models are suitable initial data for long-lived hypermassive neutron star modeling in conformally flat spacetime.

astro-ph.HE↗

arXiv2024

Striking the right tone: toward a self-consistent framework for measuring black hole ringdowns

The ringdown portion of a binary black hole merger consists of a sum of modes, each containing an infinite number of tones that are exponentially damped sinusoids. In principle, these can be measured as gravitational-waves with observatories like LIGO/Virgo/KAGRA, however in practice it is unclear how many tones can be meaningfully resolved. We investigate the consistency and resolvability of the overtones of the quadrupolar $\ell = m = 2$ mode by starting at late times when the gravitational waveform is expected to be well-approximated by the $\ell m n = 220$ tone alone. We present a Bayesian inference framework to measure the tones in numerical relativity data. We measure tones at different start times, checking for consistency: we classify a tone as stably recovered if and only if the 95\% credible intervals for amplitude and phase at time $t$ overlap with the credible intervals at all subsequent times. We test a set of tones including the first four overtones of the fundamental mode and the 320 tone and find that the 220 and 221 tones can be measured consistently with the inclusion of additional overtones. The 222 tone measurements can be stabilised when we include the 223 tone, but only in a narrow time window, after which it is too weak to measure. The 223 tone recovery appears to be unstable, and does not become stable with the introduction of the 224 tone. We find that $N=3$ tones can be stably recovered simultaneously. However, when analysing $N \geq 4$ tones, the amplitude of one tone is consistent with zero. Thus, within our framework, one can identify only $N=3$ tones with non-zero amplitude that are simultaneously stable.

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arXiv2024

Fully relativistic three-dimensional Cauchy-characteristic matching for physical degrees of freedom

A fully relativistic three-dimensional Cauchy-characteristic matching (CCM) algorithm is implemented for physical degrees of freedom in a numerical relativity code SpECTRE. The method is free of approximations and can be applied to any physical system. We test the algorithm with various scenarios involving smooth data, including the propagation of Teukolsky waves within a flat background, the perturbation of a Kerr black hole with a Teukolsky wave, and the injection of a gravitational-wave pulse from the characteristic grid. Our investigations reveal no numerical instabilities in the simulations. In addition, the tests indicate that the CCM algorithm effectively directs characteristic information into the inner Cauchy system, yielding higher precision in waveforms and smaller violations of Bondi-gauge constraints, especially when the outer boundary of the Cauchy evolution is at a smaller radius.

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arXiv2024

Improved frequency spectra of gravitational waves with memory in a binary-black-hole simulation

Numerical relativists can now produce gravitational waveforms with memory effects routinely and accurately. The gravitational-wave memory effect contains very low-frequency components, including a persistent offset. The presence of these components violates basic assumptions about time-shift behavior underpinning standard data-analysis techniques in gravitational-wave astronomy. This poses a challenge to the analysis of waveform spectra: How to preserve the low-frequency characteristics when transforming a time-domain waveform to the frequency domain. To tackle this challenge, we revisit the preprocessing procedures applied to the waveforms that contain memory effects. We find inconsistency between the zero-frequency limit of displacement memory and the low- frequency spectrum of the same memory preprocessed using the common scheme in literature. To resolve the inconsistency, we propose a new robust preprocessing scheme that produces the spectra of memory waveforms more faithfully. Using this new scheme, we inspect several characteristics of the spectrum of a memory waveform. In particular, we find a discernible beating pattern formed by the dominant oscillatory mode and the displacement memory. This pattern is absent in the spectrum of a waveform without memory. The difference between the memory and no-memory waveforms is too small to be observed by current-generation detectors in a single binary-black-hole event. Detecting the memory in a single event is likely to occur in the era of next-generation detectors.

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arXiv2024

Dynamical ejecta from binary neutron star mergers: Impact of residual eccentricity and equation of state implementation

Predicting the properties of the matter ejected during and after a neutron star merger is crucial to our ability to use electromagnetic observations of these mergers to constrain the masses of the neutron stars, the equation of state of dense matter, and the role of neutron star mergers in the enrichment of the Universe in heavy elements. Our ability to reliably provide such predictions is however limited by a broad range of factors, including the finite resolution of numerical simulations, their treatment of magnetic fields, neutrinos, and neutrino-matter interactions, and the approximate modeling of the equation of state of dense matter. In this manuscript, we study specifically the role that a small residual eccentricity and different implementations of the same equation of state have on the matter ejected during the merger of a $1.3M_\odot-1.4M_\odot$ binary neutron star system. We find that a residual eccentricity $e\sim 0.01$, as measured $\sim 4-6$ orbits before merger, causes $O(25\%-30\%)$ changes in the amount of ejected mass, mainly due to changes in the amount of matter ejected as a result of core bounces during merger. We note that $O(1\%)$ residual eccentricities have regularly been used in binary neutron star merger simulations as proxy for circular binaries, potentially creating an additional source of error in predictions for the mass of the dynamical ejecta.

astro-ph.HE↗

arXiv2024

Imprints of Changing Mass and Spin on Black Hole Ringdown

We numerically investigate the imprints of gravitational radiation-reaction driven changes to a black hole's mass and spin on the corresponding ringdown waveform. We do so by comparing the dynamics of a perturbed black hole evolved with the full (nonlinear) versus linearized Einstein equations. As expected, we find that the quasinormal mode amplitudes extracted from nonlinear evolution deviate from their linear counterparts at third order in initial perturbation amplitude. For perturbations leading to a change in the black hole mass and spin of $\sim 5\%$, which is reasonable for a remnant formed in an astrophysical merger, we find that nonlinear distortions to the complex amplitudes of some quasinormal modes can be as large as $\sim 50\%$ at the peak of the waveform. Furthermore, the change in the mass and spin results in a drift in the quasinormal mode frequencies, which for large amplitude perturbations causes the nonlinear waveform to rapidly dephase with respect to its linear counterpart. %These two nonlinear effects together create a large distortion in both the amplitude and phase of the ringdown gravitational waveform. Surprisingly, despite these nonlinear effects creating significant deviations in the nonlinear waveform, we show that a linear quasinormal mode model still performs quite well from close to the peak amplitude onwards.

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arXiv2024

Stability of hypermassive neutron stars with realistic rotation and entropy profiles

Binary neutron star mergers produce massive, hot, rapidly differentially rotating neutron star remnants; electromagnetic and gravitational wave signals associated with the subsequent evolution depend on the stability of these remnants. Stability of relativistic stars has previously been studied for uniform rotation and for a class of differential rotation with monotonic angular velocity profiles. Stability of those equilibria to axisymmetric perturbations was found to respect a turning point criterion: along a constant angular momentum sequence, the onset of unstable stars is found at maximum density less than but close to the density of maximum mass. In this paper, we test this turning point criterion for non-monotonic angular velocity profiles and non-isentropic entropy profiles, both chosen to more realistically model post-merger equilibria. Stability is assessed by evolving perturbed equilibria in 2D using the Spectral Einstein Code. We present tests of the code's new capability for axisymmetric metric evolution. We confirm the turning point theorem and determine the region of our rotation law parameter space that provides highest maximum mass for a given angular momentum.

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arXiv2024

Worldtube excision method for intermediate-mass-ratio inspirals: scalar-field model in 3+1 dimensions

Binary black hole simulations become increasingly more computationally expensive with smaller mass ratios, partly because of the longer evolution time, and partly because the lengthscale disparity dictates smaller time steps. The program initiated by Dhesi et al. (arXiv:2109.03531) explores a method for alleviating the scale disparity in simulations with mass ratios in the intermediate astrophysical range ($10^{-4} \lesssim q \lesssim 10^{-2}$), where purely perturbative methods may not be adequate. A region ("worldtube") much larger than the small black hole is excised from the numerical domain, and replaced with an analytical model approximating a tidally deformed black hole. Here we apply this idea to a toy model of a scalar charge in a fixed circular geodesic orbit around a Schwarzschild black hole, solving for the massless Klein-Gordon field. This is a first implementation of the worldtube excision method in full 3+1 dimensions. We demonstrate the accuracy and efficiency of the method, and discuss the steps towards applying it for evolving orbits and, ultimately, in the binary black-hole scenario. Our implementation is publicly accessible in the SpECTRE numerical relativity code.

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arXiv2024

A positivity-preserving adaptive-order finite-difference scheme for GRMHD

We present an adaptive-order positivity-preserving conservative finite-difference scheme that allows a high-order solution away from shocks and discontinuities while guaranteeing positivity and robustness at discontinuities. This is achieved by monitoring the relative power in the highest mode of the reconstructed polynomial and reducing the order when the polynomial series no longer converges. Our approach is similar to the multidimensional optimal order detection (MOOD) strategy, but differs in several ways. The approach is a priori and so does not require retaking a time step. It can also readily be combined with positivity-preserving flux limiters that have gained significant traction in computational astrophysics and numerical relativity. This combination ultimately guarantees a physical solution both during reconstruction and time stepping. We demonstrate the capabilities of the method using a standard suite of very challenging 1d, 2d, and 3d general relativistic magnetohydrodynamics test problems.

astro-ph.HE↗

arXiv2024

A high-order shock capturing discontinuous Galerkin-finite-difference hybrid method for GRMHD

We present a discontinuous Galerkin-finite-difference hybrid scheme that allows high-order shock capturing with the discontinuous Galerkin method for general relativistic magnetohydrodynamics. The hybrid method is conceptually quite simple. An unlimited discontinuous Galerkin candidate solution is computed for the next time step. If the candidate solution is inadmissible, the time step is retaken using robust finite-difference methods. Because of its a posteriori nature, the hybrid scheme inherits the best properties of both methods. It is high-order with exponential convergence in smooth regions, while robustly handling discontinuities. We give a detailed description of how we transfer the solution between the discontinuous Galerkin and finite-difference solvers, and the troubled-cell indicators necessary to robustly handle slow-moving discontinuities and simulate magnetized neutron stars. We demonstrate the efficacy of the proposed method using a suite of standard and very challenging 1d, 2d, and 3d relativistic magnetohydrodynamics test problems. The hybrid scheme is designed from the ground up to efficiently simulate astrophysical problems such as the inspiral, coalescence, and merger of two neutron stars.

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arXiv2024

Nonlinear Effects In Black Hole Ringdown From Scattering Experiments I: spin and initial data dependence of quadratic mode coupling

We investigate quadratic quasinormal mode coupling in black hole spacetime through numerical simulations of single perturbed black holes using both numerical relativity and second-order black hole perturbation theory. Focusing on the dominant $\ell=|m|=2$ quadrupolar modes, we find good agreement (within $\sim10\%$) between these approaches, with discrepancies attributed to truncation error and uncertainties from mode fitting. Our results align with earlier studies extracting the coupling coefficients from select binary black hole merger simulations, showing consistency for the same remnant spins. Notably, the coupling coefficient is insensitive to a diverse range of initial data, including configurations that led to a significant (up to $5\%$) increase in the remnant black hole mass. These findings present opportunities for testing the nonlinear dynamics of general relativity with ground-based gravitational wave observatories. Lastly, we provide evidence of a bifurcation in coupling coefficients between counter-rotating and co-rotating quasinormal modes as black hole spin increases.

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