arXiv subjects

Nils L. Vu

Publications and source records attributed to Nils L. Vu.

44 records · Page 3Linked to original sources

arXiv2023

Numerical relativity surrogate model with memory effects and post-Newtonian hybridization

Numerical relativity simulations provide the most precise templates for the gravitational waves produced by binary black hole mergers. However, many of these simulations use an incomplete waveform extraction technique -- extrapolation -- that fails to capture important physics, such as gravitational memory effects. Cauchy-characteristic evolution (CCE), by contrast, is a much more physically accurate extraction procedure that fully evolves Einstein's equations to future null infinity and accurately captures the expected physics. In this work, we present a new surrogate model, NRHybSur3dq8$\_$CCE, built from CCE waveforms that have been mapped to the post-Newtonian (PN) BMS frame and then hybridized with PN and effective one-body (EOB) waveforms. This model is trained on 102 waveforms with mass ratios $q\leq8$ and aligned spins $χ_{1z}, \, χ_{2z} \in \left[-0.8, 0.8\right]$. The model spans the entire LIGO-Virgo-KAGRA (LVK) frequency band (with $f_{\text{low}}=20\text{Hz}$) for total masses $M\gtrsim2.25M_{\odot}$ and includes the $\ell\leq4$ and $(\ell,m)=(5,5)$ spin-weight $-2$ spherical harmonic modes, but not the $(3,1)$, $(4,2)$ or $(4,1)$ modes. We find that NRHybSur3dq8$\_$CCE can accurately reproduce the training waveforms with mismatches $\lesssim2\times10^{-4}$ for total masses $2.25M_{\odot}\leq M\leq300M_{\odot}$ and can, for a modest degree of extrapolation, capably model outside of its training region. Most importantly, unlike previous waveform models, the new surrogate model successfully captures memory effects.

gr-qc↗

arXiv2023

High-accuracy numerical models of Brownian thermal noise in thin mirror coatings

Brownian coating thermal noise in detector test masses is limiting the sensitivity of current gravitational-wave detectors on Earth. Therefore, accurate numerical models can inform the ongoing effort to minimize Brownian coating thermal noise in current and future gravitational-wave detectors. Such numerical models typically require significant computational resources and time, and often involve closed-source commercial codes. In contrast, open-source codes give complete visibility and control of the simulated physics, enable direct assessment of the numerical accuracy, and support the reproducibility of results. In this article, we use the open-source SpECTRE numerical relativity code and adopt a novel discontinuous Galerkin numerical method to model Brownian coating thermal noise. We demonstrate that SpECTRE achieves significantly higher accuracy than a previous approach at a fraction of the computational cost. Furthermore, we numerically model Brownian coating thermal noise in multiple sub-wavelength crystalline coating layers for the first time. Our new numerical method has the potential to enable fast exploration of realistic mirror configurations, and hence to guide the search for optimal mirror geometries, beam shapes and coating materials for gravitational-wave detectors.

astro-ph.IM↗

arXiv2023

Nonlinearities in Black Hole Ringdowns

The gravitational wave strain emitted by a perturbed black hole (BH) ringing down is typically modeled analytically using first-order BH perturbation theory. In this Letter we show that second-order effects are necessary for modeling ringdowns from BH merger simulations. Focusing on the strain's $(\ell,m)=(4,4)$ angular harmonic, we show the presence of a quadratic effect across a range of binary BH mass ratios that agrees with theoretical expectations. We find that the quadratic $(4,4)$ mode's amplitude exhibits quadratic scaling with the fundamental $(2,2)$ mode -- its parent mode. The nonlinear mode's amplitude is comparable to or even larger than that of the linear $(4,4)$ mode. Therefore, correctly modeling the ringdown of higher harmonics -- improving mode mismatches by up to 2 orders of magnitude -- requires the inclusion of nonlinear effects.

gr-qc↗

arXiv2022

Quasinormal-mode filters: a new approach to analyze the gravitational-wave ringdown of binary black-hole mergers

We propose two frequency-domain filters to analyze ringdown signals of binary black hole mergers. The first rational filter is constructed based on a set of (arbitrary) quasi-normal modes (QNMs) of the remnant black holes, whereas the second full filter comes from the transmissivity of the remnant black holes. The two filters can remove corresponding QNMs from original time-domain ringdowns, while changing early inspiral signals in a trivial way - merely a time and phase shift. After filtering out dominant QNMs, we can visualize the existence of various subdominant effects. For example, by applying our filters to a GW150914-like numerical relativity (NR) waveform, we find second-order effects in the (l = 4, m = 4), (l = 5, m = 4) and (l = 5, m = 5) harmonics; the spherical-spheroidal mixing mode in the (l = 2,m = 2) harmonic; and a mixing mode in the (l = 2,m = 1) harmonic due to a gravitational recoil. In another NR simulation where two component spins are anti-aligned with the orbital angular momentum, we also find retrograde modes. The filters are sensitive to the remnant properties (i.e., mass and spin) and thus have a potential application to future data analyses and parameter estimations. We also investigate the stability of the full filter. Its connection to the instability of QNM spectra is discussed.

gr-qc↗

arXiv2022

Fixing the BMS frame of numerical relativity waveforms with BMS charges

The Bondi-van der Burg-Metzner-Sachs (BMS) group, which uniquely describes the symmetries of asymptotic infinity and therefore of the gravitational waves that propagate there, has become increasingly important for accurate modeling of waveforms. In particular, waveform models, such as post-Newtonian (PN) expressions, numerical relativity (NR), and black hole perturbation theory, produce results that are in different BMS frames. Consequently, to build a model for the waveforms produced during the merging of compact objects, which ideally would be a hybridization of PN, NR, and black hole perturbation theory, one needs a fast and robust method for fixing the BMS freedoms. In this work, we present the first means of fixing the entire BMS freedom of NR waveforms to match the frame of either PN waveforms or black hole perturbation theory. We achieve this by finding the BMS transformations that change certain charges in a prescribed way -- e.g., finding the center-of-mass transformation that maps the center-of-mass charge to a mean of zero. We find that this new method is 20 times faster, and more correct when mapping to the superrest frame, than previous methods that relied on optimization algorithms. Furthermore, in the course of developing this charge-based frame fixing method, we compute the PN expression for the Moreschi supermomentum to 3PN order without spins and 2PN order with spins. This Moreschi supermomentum is effectively equivalent to the energy flux or the null memory contribution at future null infinity $\mathscr{I}^{+}$. From this PN calculation, we also compute oscillatory ($m\not=0$ modes) and spin-dependent memory terms that have not been identified previously or have been missing from strain expressions in the post-Newtonian literature.

gr-qc↗

arXiv2022

Simulating magnetized neutron stars with discontinuous Galerkin methods

Discontinuous Galerkin methods are popular because they can achieve high order where the solution is smooth, because they can capture shocks while needing only nearest-neighbor communication, and because they are relatively easy to formulate on complex meshes. We perform a detailed comparison of various limiting strategies presented in the literature applied to the equations of general relativistic magnetohydrodynamics. We compare the standard minmod/$ΛΠ^N$ limiter, the hierarchical limiter of Krivodonova, the simple WENO limiter, the HWENO limiter, and a discontinuous Galerkin-finite-difference hybrid method. The ultimate goal is to understand what limiting strategies are able to robustly simulate magnetized TOV stars without any fine-tuning of parameters. Among the limiters explored here, the only limiting strategy we can endorse is a discontinuous Galerkin-finite-difference hybrid method.

gr-qc↗

arXiv2022

Gravitational-wave echoes from numerical-relativity waveforms via space-time construction near merging compact objects

We propose a new approach toward reconstructing the late-time near-horizon geometry of merging binary black holes, and toward computing gravitational-wave echoes from exotic compact objects. A binary black-hole merger spacetime can be divided by a time-like hypersurface into a Black-Hole Perturbation (BHP) region, in which the space-time geometry can be approximated by homogeneous linear perturbations of the final Kerr black hole, and a nonlinear region. At late times, the boundary between the two regions is an infalling shell. The BHP region contains late-time gravitational-waves emitted toward the future horizon, as well as those emitted toward future null infinity. In this region, by imposing no-ingoing wave conditions at past null infinity, and matching out-going waves at future null infinity with waveforms computed from numerical relativity, we can obtain waves that travel toward the future horizon. In particular, the Newman-Penrose $ψ_0$ associated with the in-going wave on the horizon is related to tidal deformations measured by fiducial observers floating above the horizon. We further determine the boundary of the BHP region on the future horizon by imposing that $ψ_0$ inside the BHP region can be faithfully represented by quasi-normal modes. Using a physically-motivated way to impose boundary conditions near the horizon, and applying the so-called Boltzmann reflectivity, we compute the quasi-normal modes of non-rotating ECOs, as well as gravitational-wave echoes. We also investigate the detectability of these echoes in current and future detectors, and prospects for parameter estimation.

gr-qc↗

arXiv2022

A scalable elliptic solver with task-based parallelism for the SpECTRE numerical relativity code

Elliptic partial differential equations must be solved numerically for many problems in numerical relativity, such as initial data for every simulation of merging black holes and neutron stars. Existing elliptic solvers can take multiple days to solve these problems at high resolution and when matter is involved, because they are either hard to parallelize or require a large amount of computational resources. Here we present a new solver for linear and nonlinear elliptic problems that is designed to scale with resolution and to parallelize on computing clusters. To achieve this we employ a discontinuous Galerkin discretization, an iterative multigrid-Schwarz preconditioned Newton-Krylov algorithm, and a task-based parallelism paradigm. To accelerate convergence of the elliptic solver we have developed novel subdomain-preconditioning techniques. We find that our multigrid-Schwarz preconditioned elliptic solves achieve iteration counts that are independent of resolution, and our task-based parallel programs scale over 200 million degrees of freedom to at least a few thousand cores. Our new code solves a classic initial data problem for binary black holes faster than the spectral code SpEC when distributed to only eight cores, and in a fraction of the time on more cores. It is publicly accessible in the next-generation SpECTRE numerical relativity code. Our results pave the way for highly parallel elliptic solves in numerical relativity and beyond.

gr-qc↗