Numerical scalar curvature deformation and a gluing construction

In this work a new numerical technique to prepare Cauchy data for the initial value problem (IVP) formulation of Einstein's field equations (EFE) is presented. Our method is directly inspired by the exterior asymptotic gluing (EAG) result of Corvino (2000). The argument assumes a moment in time symmetry and allows for a composite, initial data set to be assembled from (a finite subdomain of) a known asymptotically Euclidean initial data set which is glued (in a controlled manner) over a compact spatial region to an exterior Schwarzschildean representative. We demonstrate how (Corvino, 2000) may be directly adapted to a numerical scheme and under the assumption of axisymmetry construct composite Hamiltonian constraint satisfying initial data featuring internal binary black holes (BBH) glued to exterior Schwarzschild initial data in isotropic form. The generality of the method is shown in a comparison of properties of EAG composite initial data sets featuring internal BBHs as modelled by Brill-Lindquist and Misner data. The underlying geometric analysis character of gluing methods requires work within suitably weighted function spaces, which, together with a technical impediment preventing (Corvino, 2000) from being fully constructive, is the principal difficulty in devising a numerical technique. Thus the single previous attempt by Giulini and Holzegel (2005) (recently implemented by Doulis and Rinne (2016)) sought to avoid this by embedding the result within the well known Lichnerowicz-York conformal framework which required ad-hoc assumptions on solution form and a formal perturbative argument to show that EAG may proceed. In (Giulini and Holzegel, 2005) it was further claimed that judicious engineering of EAG can serve to reduce the presence of spurious gravitational radiation - unfortunately, in line with the general conclusion of (Doulis and Rinne, 2016) our numerical investigation does not appear to indicate that this is the case. Concretising the sought initial data to be specified with respect to a spatial manifold with underlying topology R×S² our method exploits a variety of pseudo-spectral (PS) techniques. A combination of the eth-formalism and spin-weighted spherical harmonics together with a novel complex-analytic based numerical approach is utilised. This is enabled by our Python 3 based numerical toolkit allowing for unified just-in-time compiled, distributed calculations with seamless extension to arbitrary precision for problems involving generic, geometric partial differential equations (PDE) as specified by tensorial expressions. Additional features include a layer of abstraction that allows for automatic reduction of indicial (i.e., tensorial) expressions together with grid remapping based on chart specification - hence straight-forward implementation of IVP formulations of the EFE such as ADM-York or ADM-York-NOR is possible. Code-base verification is performed by evolving the polarised Gowdy T³ space-time with the above formulations utilising high order, explicit time-integrators in the method of lines approach as combined with PS techniques. As the initial data we prepare has a precise (Schwarzschild) exterior this may be of interest to global evolution schemes that incorporate information from spatial-infinity. Furthermore, our approach may shed light on how more general gluing techniques could potentially be adapted for numerical work. The code-base we have developed may also be of interest in application to other problems involving geometric PDEs

GRAthena++: puncture evolutions on vertex-centered oct-tree AMR

Numerical relativity is central to the investigation of astrophysical sources in the dynamical and strong-field gravity regime, such as binary black hole and neutron star coalescences. Current challenges set by gravitational-wave and multi-messenger astronomy call for highly performant and scalable codes on modern massively-parallel architectures. We present GR-Athena++, a general-relativistic, high-order, vertex-centered solver that extends the oct-tree, adaptive mesh refinement capabilities of the astrophysical (radiation) magnetohydrodynamics code Athena++. To simulate dynamical space-times GR-Athena++ uses the Z4c evolution scheme of numerical relativity coupled to the moving puncture gauge. We demonstrate stable and accurate binary black hole merger evolutions via extensive convergence testing, cross-code validation, and verification against state-of-the-art effective-one-body waveforms. GR-Athena++ leverages the task-based parallelism paradigm of Athena++ to achieve excellent scalability. We measure strong scaling efficiencies above $95\%$ for up to $\sim 1.2\times10^4$ CPUs and excellent weak scaling is shown up to $\sim 10^5$ CPUs in a production binary black hole setup with adaptive mesh refinement. GR-Athena++ thus allows for the robust simulation of compact binary coalescences and offers a viable path towards numerical relativity at exascale

Numerical Relativity Simulations of the Neutron Star Merger GW170817: Long-Term Remnant Evolutions, Winds, Remnant Disks, and Nucleosynthesis

We present a systematic numerical-relativity study of the dynamical ejecta, winds and nucleosynthesis in neutron star merger remnants. Binaries with the chirp mass compatible with GW170817, different mass ratios, and five microphysical equations of state (EOS) are simulated with an approximate neutrino transport and a subgrid model for magnetohydrodynamics turbulence up to 100 milliseconds postmerger. Spiral density waves propagating from the neutron star remnant to the disk trigger a wind with mass flux ${\sim}0.1{-}0.5\,{\rm M_\odot/s}$ persisting for the entire simulation as long as the remnant does not collapse to black hole. This wind has average electron fraction $\gtrsim 0.3$ and average velocity ${\sim}0.1-0.17\,$c and thus is a site for the production of weak $r$-process elements (mass number $A<195$). Disks around long-lived remnants have masses ${\sim}0.1{-}0.2\,{\rm M_\odot}$, temperatures peaking at $\lesssim10\,$MeV near the inner edge, and a characteristic double-peak distribution in entropy resulting from shocks propagating through the disk. The dynamical and spiral-wave ejecta computed in our targeted simulations are not compatible with those inferred from AT2017gfo using two-components kilonova models. Rather, they indicate that multi-component kilonova models including disk winds are necessary to interpret AT2017gfo. The nucleosynthesis in the combined dynamical ejecta and spiral-wave wind in the comparable-mass long-lived mergers robustly accounts for all the $r$-process peaks, from mass number ${\sim}75$ to actinides in terms of solar abundances. Total abundandes are weakly dependent on the EOS, while the mass ratio affect the production of first peak elements.Comment: 20 pages, 13 figures, 3 table

Accretion-induced prompt black hole formation in asymmetric neutron star mergers, dynamical ejecta and kilonova signals

We present new numerical relativity results of neutron star mergers with chirp mass $1.188M_\odot$ and mass ratios $q=1.67$ and $q=1.8$ using finite-temperature equations of state (EOS), approximate neutrino transport and a subgrid model for magnetohydrodynamics-induced turbulent viscosity. The EOS are compatible with nuclear and astrophysical constraints and include a new microphysical model derived from ab-initio calculations based on the Brueckner-Hartree-Fock approach. We report for the first time evidence for accretion-induced prompt collapse in high-mass-ratio mergers, in which the tidal disruption of the companion and its accretion onto the primary star determine prompt black hole formation. As a result of the tidal disruption, an accretion disc of neutron-rich and cold matter forms with baryon masses ${\sim}0.15M_\odot$, and it is significantly heavier than the remnant discs in equal-masses prompt collapse mergers. Massive dynamical ejecta of order ${\sim}0.01M_\odot$ also originate from the tidal disruption. They are neutron rich and expand from the orbital plane with a crescent-like geometry. Consequently, bright, red and temporally extended kilonova emission is predicted from these mergers. Our results show that prompt black hole mergers can power bright electromagnetic counterparts for high-mass-ratio binaries, and that the binary mass ratio can be in principle constrained from multimessenger observations.Comment: 20 pages, 21 figures, 4 table