Numerical Relativity Research Articles

Inconsistent black hole kick estimates from gravitational-wave models

The accuracy of gravitational-wave (GW) models of compact binaries has traditionally been addressed by the mismatch between the model and numerical-relativity (NR) simulations. This is a measure of the overall agreement between the two waveforms. However, the largest modelling error typically appears in the strong-field merger regime and may affect subdominant signal harmonics more strongly. These inaccuracies are often not well characterised by the mismatch. We explore the use of a complementary, physically motivated tool to investigate the accuracy of GW harmonics in waveform models: the remnant’s recoil, or kick velocity. Asymmetric binary mergers produce remnants with significant recoil, encoded by subtle imprints in the GW signal. The kick estimate is highly sensitive to the intrinsic inaccuracies of the modelled GW harmonics during the strongly relativistic merger regime. Here we investigate the accuracy of the higher harmonics in four state-of-the-art waveform models of binary black holes. We find that the SEOBNRv4HM_ROM, IMRPhenomHM, IMRPhenomXHM and NRHybSur3dq8 models are not consistent in their kick predictions. Our results enable us to identify regions in the parameter space where the models require further improvement and support the use of the kick estimate to investigate waveform systematics. We discuss how NR kick estimates could be used to calibrate waveform models further, proposing the first steps towards kick-based gravitational-wave tuning.

Using rational filters to uncover the first ringdown overtone in GW150914

There have been debates in the literature about the existence of the first overtone in the ringdown of GW150914. We develop a novel Bayesian framework to reanalyze the data of this event, by incorporating a new technique, the ``rational filter'' that can clean particular modes from the ringdown signal. We examine the existence of the first overtone in GW150914 from multiple novel perspectives. First, we confirm that the estimates of the remnant black hole mass and spin are more consistent with those obtained from the full inspiral-merger-ringdown signal when including the first overtone at an early stage of the ringdown (right after the inferred signal peak); such improvement fades away at later times. Second, we formulate a new way to compare the ringdown models with and without the first overtone by calculating the Bayes factor at different times during the ringdown. We obtain a Bayes factor of 600 at the time when the signal amplitude reaches its peak. The Bayes factor decreases sharply when moving away from the peak time and eventually oscillates around a small value when the overtone signal is expected to have decayed. Third, we clean the fundamental mode from the ringdown of GW150914 and estimate the amplitudes of the modes using the filtered data with Markov chain Monte Carlo (MCMC). The inferred amplitude of the fundamental mode is $\ensuremath{\sim}0$ whereas the amplitude of the first overtone remains almost unchanged, implying that the filtered data is consistent with a first-overtone-only template. Similarly, if we remove the first overtone from the GW150914 data, the filtered data are consistent with a fundamental-mode-only template. Finally, after removing the fundamental mode, we use MCMC to infer the remnant black hole mass and spin from the first overtone alone. We find the posteriors are still informative and consistent with those inferred from the fundamental mode. The conclusions are also verified through simulations in Gaussian noise using a GW150914-like numerical relativity waveform.

Study of the intermediate mass ratio black hole binary merger up to 1000:1 with numerical relativity

We explicitly demonstrate that current numerical relativity techniques are able to accurately evolve black hole binaries with mass ratios of the order of 1000:1. This proof of principle is relevant for future third generation gravitational wave detectors and space mission LISA, as by purely numerical methods we would be able to accurately compute gravitational waves from the last stages of black hole mergers, as directly predicted by general relativity. We perform a sequence of simulations in the intermediate to small mass ratio regime, , with the small hole starting from rest at a proper distance . We compare these headon full numerical evolutions with the corresponding semianalytic point particle perturbative results finding an impressive agreement for the total gravitational radiated energy and linear momentum as well as for the waveform spectra. We display numerical convergence of the results and identify the minimal numerical resolutions required to accurately solve for these very low amplitude gravitational waves. This work represents a first step towards the considerable challenge of applying numerical-relativity waveforms to interpreting gravitational-wave observations by LISA and next-generation ground-based gravitational-wave detectors.

Muons in the aftermath of neutron star mergers and their impact on trapped neutrinos

Context. In the upcoming years, present and next-generation gravitational wave observatories will detect a larger number of binary neutron star (BNS) mergers with increasing accuracy. In this context, improving BNS merger numerical simulations is crucial to correctly interpret the data and constrain the equation of state (EOS) of neutron stars (NSs). Aims. State-of-the-art simulations of BNS mergers do not include muons. However, muons are known to be relevant in the microphysics of cold NSs and are expected to have a significant role in mergers, where the typical thermodynamic conditions favour their production. Our work is aimed at investigating the impact of muons on the merger remnant. Methods. We post-process the outcome of four numerical relativity simulations of BNS mergers performed with three different baryonic EOSs and two mass ratios considering the first 15 milliseconds after merger. We compute the abundance of muons in the remnant and analyse how muons affect the trapped neutrino component and the fluid pressure. Results. We find that depending on the baryonic EOS, the net fraction of muons is between 30% and 70% the net fraction of electrons. Muons change the flavour hierarchy of trapped (anti-)neutrinos such that deep inside the remnant, muon anti-neutrinos are the most abundant, followed by electron anti-neutrinos. Finally, muons and trapped neutrinos modify the neutron-to-proton ratio, affecting the remnant pressure by up to 7% when compared with calculations neglecting them. Conclusions. This work demonstrates that muons have a non-negligible effect on the outcome of BNS merger simulations, and they should be included to improve the accuracy of a simulation.

Self-interacting gravitational atoms in the strong-gravity regime

We numerically investigate free and self-interacting ultralight scalar fields around black holes in General Relativity. We focus on complex scalar fields Φ whose self-interactions are described by the quartic potential V ∝ λ |Φ|4, and ignore the black hole spin in order to disentangle the effects of self interactions on the boson cloud. Using the spectral solver Kadath, we compute quasi-equilibrium configurations of the dominant eigenstates, including their backreaction on the spacetime metric. For scenarios with -10-2 ≲ λ ≲ 10-2 we find the mass of the self-interacting scalar cloud to be up to ∼ 70% larger than that of a free scalar cloud, though the additional backreaction effect on the spacetime metric is only up to ∼ 1% due to the low-density nature of the bosonic configurations. In this region of parameter space we observe approximate quadratic scalings between the mass of the cloud with λ, the scalar field amplitude, and the couplings between these two parameters. For systems with λ beyond this range, the eigenfrequencies differ sufficiently from the known free-test-field values used as inputs in our numerical setupto make the results, though convergent, physically unreliable.This bounds the range of λ in which the free scalar field solution remains a good approximation to self-interacting scalar field configurations. Our work is among the first nonperturbative explorations of self-interacting bosonic clouds around black holes, yielding detailed new insights into such systems in the nonlinear regime, while also overcoming technical challenges and quantifying limitations. Additionally, our results provide useful inputsfor fully dynamical numerical relativity simulations and for future explorations of spinning black holes and real scalar fields.

Flares, Jets, and Quasiperiodic Outbursts from Neutron Star Merger Remnants

Using numerical relativity simulations with a subgrid dynamo prescription to generate strong initial magnetic fields, we investigate the possibility of launching a jet-like outflow from the hypermassive neutron star (HMNS) during the early stages of the merger, prior to the remnant’s collapse to a black hole. We demonstrate that buoyant instabilities in the strongly magnetized HMNS can lead to a periodic emission of powerful electromagnetic flares shortly after the merger. These are followed by a collimated mildly relativistic outflow. Both types of outflows feature quasiperiodic kilohertz substructure. These early-time outflows may power precursors to short-duration gamma-ray bursts (sGRBs) or in some cases the entire sGRB. While the overall temporal power spectrum we find broadly agrees with the one recently reported for quasiperiodic oscillations in the sGRB GRB910711, our simulations suggest that the periodic electromagnetic substructure is dominated by magnetohydrodynamic shearing processes rather than correlating with the corresponding postmerger gravitational-wave signal.

COMPUTATIONAL DESIGN FOR FUTURISTIC ENVIRONMENTALLY ADAPTIVE BUILDING FORMS AND STRUCTURES

Introduction: With the rapid development in computational design, both architectural design and representation processes have witnessed a revolutionary change from the analog to the digital medium, opening new doors for adaptability in the architectural design process by leveraging nature concepts in design. The computational design approach starts with the mathematical model definition based on numerical relations and equations, thus, replacing the standard visual representation. Purpose of the study: We aimed to integrate computational design technologies to create self-learning buildings that could adapt to environmental challenges and adjust accordingly by collecting data from the surrounding environment via the implementation of sensors. Methods: We started with extensive research on state-of-the-art computational design in architecture, followed by the design implementation and the implementation of the architectural design of a building. The design followed a parametric approach to design and strategies. An algorithm was developed with Grasshopper Scripting to generate documents that mimic the growth process of cellular bone structures and adapt that form to a selected project site. To ensure that the generated form is adaptable, we performed multiple analyses, such as sunlight, radiation, and shadow analysis, before selecting the form and finishing its development. The results show that an environmentally responsive form that extends from the surrounding environment is characterized by high levels of adaptability. Results: In the course of the study, the effectiveness of computational design technologies in architecture was established.

Study of the agreement between binary neutron star ejecta models derived from numerical relativity simulations

Neutron star mergers have recently become a tool to study extreme gravity, nucleosynthesis, and the chemical composition of the Universe. To date, there has been one joint gravitational and electromagnetic observation of a binary neutron star merger, GW170817, as well as a solely gravitational observation, GW190425. In order to accurately identify and interpret electromagnetic signals of neutron star mergers, better models of the matter outflows generated by these mergers are required. We compare a series of ejecta models to see where they provide strong constraints on the amount of ejected mass expected from a system, and where systematic uncertainties in current models prevent us from reliably extracting information from observed events. We also examine 2396 neutron star equations of state compatible with GW170817 to see whether a given ejecta mass could be reasonably produced with a neutron star of said equation of state, and whether different ejecta models provide consistent predictions. We find that the difference between models is often comparable to or larger than the error generally assumed for these models, implying better constraints on the models are needed. We also note that the extrapolation of outflow models outside of their calibration window, while commonly needed to analyze gravitational wave events, is extremely unreliable and occasionally leads to completely unphysical results.

Strong-field scattering of two black holes: Numerical relativity meets post-Minkowskian gravity

We compare numerical relativity (NR) data on the scattering of equal-mass, nonspinning binary black holes to various analytical predictions based on post-Minkowskian (PM) results. While the usual sequence of PM-expanded scattering angles shows a rather poor convergence towards NR data, we find that a reformulation of PM information in terms of effective-one-body radial potentials leads to remarkable agreement with NR data, especially when using the radiation-reacted 4PM information. Using Firsov's inversion formula we directly extract, for the first time, from NR simulations a (radiation-reacted) gravitational potential describing the scattering of equal-mass, nonspinning binary black holes. We urge the NR community to compute more sequences of scattering simulations, so as to extend this knowledge to a wider region of parameter space.

Numerical relativity higher order gravitational waveforms of eccentric, spinning, nonprecessing binary black hole mergers

We use the open source, community-driven, numerical relativity software, the Einstein Toolkit to study the physics of eccentric, spinning, nonprecessing binary black hole mergers with mass-ratios $q=\{2, 4, 6\}$, individual dimensionless spin parameters $\chi_{1z}=\pm0.6$, $\chi_{2z}=\pm0.3$, that include higher order gravitational wave modes $\ell\leq4$, except for memory modes. Assuming stellar mass binary black hole mergers that may be detectable by the advanced LIGO detectors, we find that including modes up to $\ell=4$ increases the signal-to-noise of compact binaries between $3.5\%$ to $35\%$, compared to signals that only include the $\ell=|m|=2$ mode. We use two waveform models, TEOBResumS and SEOBNRE, which incorporate spin and eccentricity corrections in the waveform dynamics, to quantify the orbital eccentricity of our numerical relativity catalog in a gauge-invariant manner through fitting factor calculations. Our findings indicate that the inclusion of higher order wave modes has a measurable effect in the recovery of moderately and highly eccentric black hole mergers, and thus it is essential to develop waveform models and signal processing tools that accurately describe the physics of these astrophysical sources.

Surrogate light curve models for kilonovae with comprehensive wind ejecta outflows and parameter estimation for AT2017gfo

The electromagnetic emission resulting from neutron star mergers have been shown to encode properties of the ejected material in their light curves. The ejecta properties inferred from the kilonova emission has been in tension with those calculated based on the gravitational wave signal and numerical relativity models. Motivated by this tension, we construct a broad set of surrogate light curve models derived for kilonova ejecta. The four-parameter family of two-dimensional anisotropic simulations and its associated surrogate explore different assumptions about the wind outflow morphology and outflow composition, keeping the dynamical ejecta component consistent. We present the capabilities of these surrogate models in interpolating kilonova light curves across various ejecta parameters and perform parameter estimation for AT2017gfo both without any assumptions on the outflow and under the assumption that the outflow must be representative of solar r-process abundance patterns. Our parameter estimation for AT2017gfo shows these surrogate models help alleviate the ejecta property discrepancy while also illustrating the impact of systematic modeling uncertainties on these properties, urging further investigation.

Conserved currents for a Kerr black hole and orthogonality of quasinormal modes

Using a symmetry of the Kerr spacetime, the authors determine an original bilinear form for perturbations of the Weyl scalars. They show that upon choosing appropriate integration contours, this form can also be used on quasi-normal mode data. This manuscript provides a formalism for studying ringdown beyond the leading order, with potential application to numerical relativity and gravitational wave observation.

Extreme gravitational interactions in the problem of three black holes in general relativity

We study the three-body problem going from Newtonian mechanics to general relativity. In the classical case, we model the interactions in a typical chaotic configuration, identifying extreme gravitational interactions (EGIs), namely transients in which the system manifests complex, highly-energetic dynamics. We then concentrate on the main part of the work, by selecting these EGIs as initial data for the general relativistic case, and performing a campaign of numerical relativity simulations. To provide a comprehensive menu of cases, we investigate different global configurations. By comparing with the more ‘quiet’ two-body inspiral, we observe strong nonlinear emission of gravitational waves. The multi-body signals have been inspected by employing both Fourier and wavelet analyses, showing net differences among the global configurations. The wavelet analysis reveals the reminiscence of the EGIs in the three black holes problem. Such a survey of simulations might be a guide for future observations.

CTTK: a new method to solve the initial data constraints in numerical relativity

In numerical relativity simulations with non-trivial matter configurations, one must solve the Hamiltonian and momentum constraints of the ADM formulation for the metric variables in the initial data. We introduce a new scheme based on the standard conformal transverse-traceless decomposition, in which instead of solving the Hamiltonian constraint as a 2nd order elliptic equation for a choice of mean curvature K, we solve an algebraic equation for K for a choice of conformal factor. By doing so, we evade the existence and uniqueness problem of solutions of the Hamiltonian constraint without using the usual conformal rescaling of the source terms. This is particularly important when the sources are fundamental fields, as reconstructing the fields’ configurations from the rescaled quantities is potentially problematic. Using an iterative multigrid solver, we show that this method provides rapid convergent solutions for several initial conditions that have not yet been studied in numerical relativity; namely (a) periodic inhomogeneous spacetimes with large random Gaussian scalar field perturbations and (b) asymptotically flat black hole spacetimes with rotating scalar clouds.

The polymorphism of HLA class I and II alleles in Indian patient with thalassemia

Numerous HLA allele relations with various diseases have been observed all over the world, including leukemia, aplastic anemia, and thalassemia. The current study looked at the frequency of HLA A, B, C, DRB1, and DQB1 loci with thalassemia to see if there was a correlation between the HLA allele and the disease. The study involved a total of 200 patients (cases) and 200 healthy people (controls). Using a polymerase chain reaction sequence-specific oligonucleotide probe technique, all of these samples were HLA typed for HLA class I (A, B, C loci) and class II (DRB1 and DQB1 loci). HLA-DRB1*15:02 (p = 0.0395400, OR = 2.288) and DQB1*06:01 (p = 0.00056000, OR = 2.248911) were found to have a positive connection with thalassemia. Whereas, HLA-A*31:01 (p = 0.0361200, OR = 0.202), B*07:02 (p 0.0358530, OR = 0.296), B*08:01 (p = 0.04595400, OR = 0.476), C*07:02 (p = 0.000240000, OR = 0.00001,) and HLA-DQB1*06:03 (p = 0.007966000, OR = 0.395) were seen to be negatively associated. Our findings are the first to indicate an association between thalassemia and HLA alleles (A, B, C, DRB1, and DQB1 alleles) in the Indian population, and they can be used to strengthen thalassemia studies.

A scale-aware dispersion-relation-preserving finite difference scheme for computational aeroacoustics

The numerical schemes for computational aeroacoustics (CAA) should have minimal dispersion and proper dissipation in order to accurately capture the amplitude and phase of waves. In this paper, we propose a scale-aware dispersion-relation-preserving (SA-DRP) finite difference scheme based on an improved scale sensor and a new dispersion control strategy. The scale sensor quantifies the local length scale of the solution in the form of the effective scaled wavenumber. The new feature of this scale sensor is the accurate prediction of the wavenumber for a pure sine wave. The new dispersion control strategy determines the dispersion parameter of the scheme in terms of the scale sensor. In contrast to the traditional dispersion-relation-preserving (DRP) scheme that minimizes the integral dispersion error, the new strategy directly solves the dispersion parameter by requiring the numerical dispersion relation to be equal to the exact one. As a result, precise dispersion relation can be realized within a very broad wavenumber range. The approximate dispersion relation analysis shows that the SA-DRP scheme maintains an accurate dispersion relation up to the scaled wavenumber k = 2.5. Moreover, the overshoot in the dispersion relation of the DRP scheme is not presented in that of the SA-DRP scheme. To suppress nonphysical oscillations, we also add proper dissipation that is adjusted automatically according to the effective scaled wavenumber. Several CAA benchmark test cases are presented to demonstrate the higher resolution and higher efficiency achieved by the proposed scheme compared with the conventional spectrally optimized schemes.

Cosmological distances with general-relativistic ray tracing: framework and comparison to cosmographic predictions

In this work we present the first results from a new ray-tracing tool to calculate cosmological distances in the context of fully nonlinear general relativity. We use this tool to study the ability of the general cosmographic representation of luminosity distance, as truncated at third order in redshift, to accurately capture anisotropies in the “true” luminosity distance. We use numerical relativity simulations of cosmological large-scale structure formation which are free from common simplifying assumptions in cosmology. We find the general, third-order cosmography is accurate to within 1% for redshifts to z ≈ 0.034 when sampling scales strictly above 100 h -1 Mpc, which is in agreement with an earlier prediction. We find the inclusion of small-scale structure generally spoils the ability of the third-order cosmography to accurately reproduce the full luminosity distance for wide redshift intervals, as might be expected. For a simulation sampling small-scale structures, we find a ∼ ±5% variance in the monopole of the ray-traced luminosity distance at z ≈ 0.02. Further, all 25 observers we study here see a 9–20% variance in the luminosity distance across their sky at z ≈ 0.03, which reduces to 2–5% by z ≈ 0.1. These calculations are based on simulations and ray tracing which adopt fully nonlinear general relativity, and highlight the potential importance of fair sky-sampling in low-redshift isotropic cosmological analysis.

Hierarchical Bayesian method for constraining the neutron star equation of state with an ensemble of binary neutron star postmerger remnants

Binary neutron star (BNS) post-merger gravitational-wave emission can occur in the aftermath of a BNS merger -- provided the system avoids prompt collapse to a black hole -- as a quasistable hypermassive remnant experiences quadrupolar oscillations and non-axisymmetric deformations. The post-merger gravitational-wave spectrum possesses a characteristic peak frequency that has been shown to be dependent on the binary chirp mass and the neutron star equation of state (EoS), rendering post-merger gravitational waves a powerful tool for constraining neutron star composition. Unfortunately, the BNS post-merger signal is emitted at high ($\gtrsim 1.5$ kHz) frequencies, where ground-based gravitational wave detectors suffer from reduced sensitivity. It is therefore unlikely that post-merger signals will be detected with sufficient signal-to-noise ratio (SNR) until the advent of next-generation detectors. However, by employing empirical relations derived from numerical relativity simulations, we can combine information across an ensemble of BNS mergers, allowing us to obtain EoS constraints with many low-SNR signals. We present a hierarchical Bayesian method for deriving constraints on $R_{1.6}$, the radius of a 1.6$\mathrm{M_{\odot}}$ neutron star, through an ensemble analysis of binary neutron star mergers. We apply this method to simulations of the next two LIGO-Virgo-KAGRA observing runs, O4 and O5, as well as an extended 4-year run at A+ sensitivity, demonstrating the potential of our approach to yield EoS information from the post-merger signal with current-generation detectors. The A+ 4-year scenario is predicted to improve the constraint on $R_{1.6}$ from the currently available multimessenger-based 95\% credible interval (C.I.) uncertainty of $R_{1.6}=12.07^{+0.98}_{-0.77}$ km to $R_{1.6}=11.91^{+0.80}_{-0.56}$ km, a 22% reduction of the 95% C.I. width.

Peridynamic elastic waves in two-dimensional unbounded domains: Construction of nonlocal Dirichlet-type absorbing boundary conditions

The focus of this paper is on application of peridynamics (PD) to propagation of elastic waves in unbounded domains. We construct absorbing boundary conditions (ABCs) derived from a semi-analytical solution of the PD governing equation at the exterior region. This solution is made up of a finite series of plane waves, as fundamental solutions (modes), which satisfy the PD dispersion relations. The modes are adjusted to transmit the energy from the interior region (near field) to the exterior region (far field). The corresponding unknown coefficients of the series are found in terms of the displacement field at a layer of points adjacent to the absorbing boundary. This is accomplished through a collocation procedure at subregions (clouds) around each absorbing point. The proposed ABCs offer appealing advantages, which facilitate their application to PD. They are of Dirichlet-type, hence their implementation is relatively simple as no derivatives of the field variables are required. They are constructed in the time and space domains and thus application of Fourier and Laplace transforms, cumbersome for nonlocal models, is not required. At the discrete level, the modes satisfy the same numerical dispersion relations of the near field, which makes the far-field solution compatible with that of the near field. We scrutinize the performance of the proposed ABCs through several examples. Our investigation shows that the proposed ABCs perform stably in time with an appropriate level of accuracy even in problems characterized by highly-dispersive propagating waves, including crack propagation in semi-unbounded brittle solids.

Linear response, Hamiltonian, and radiative spinning two-body dynamics

Using the spinning, supersymmetric worldline quantum field theory formalism we compute the momentum impulse and spin kick from a scattering of two spinning black holes or neutron stars up to quadratic order in spin at third post-Minkowskian (PM) order, including radiation-reaction effects and with arbitrarily misaligned spin directions. Parts of these observables, both conservative and radiative, are also inferred from lower-PM scattering data by extending Bini and Damour's linear response formula to include misaligned spins. By solving Hamilton's equations of motion we also use a conservative scattering angle to infer a complete 3PM two-body Hamiltonian including finite-size corrections and misaligned spin-spin interactions. Finally, we describe mappings to the bound two-body dynamics for aligned spin vectors: including a numerical plot of the binding energy for circular orbits compared with numerical relativity, analytic confirmation of the NNLO PN binding energy, and the energy loss over successive orbits.