General relativistic hydrodynamics code for dynamical spacetimes with curvilinear coordinates, tabulated equations of state, and neutrino physics

TL;DR

GRoovy addresses the need for efficient, accurate GRHD simulations of near-axisymmetric compact-object systems by solving GRHD in full GR using curvilinear and Cartesian coordinates. The code integrates a reference-metric BSSN spacetime evolution with GRHayL's GRMHD algorithms, including finite-temperature EOSs and a neutrino-leakage scheme, and leverages an orthonormal basis to stabilize tensor evolution in curvilinear coordinates. Through a comprehensive suite of flat, curved, and dynamical spacetime tests, GRoovy demonstrates robust shock capturing, stable neutron-star evolutions, and consistent neutrino physics, enabling long-term post-merger remnant studies. The work lays the groundwork for future MHD, multi-patch, and Charm++-based 3D simulations, potentially advancing our understanding of gamma-ray bursts, nucleosynthesis, and remnant evolution in BNS/BHNS systems.

Abstract

Many astrophysical systems of interest to numerical relativity-such as rapidly rotating stars, black hole accretion disks, and core-collapse supernovae-exhibit near-symmetries. These systems generally consist of a strongly gravitating central object surrounded by an accretion disk, debris, and ejecta. Simulations can efficiently exploit the near-axisymmetry of these systems by reducing the number of points in the angular direction around the near-symmetry axis, enabling efficient simulations over seconds-long timescales with minimal computational expense. In this paper, we introduce GRoovy, a novel code capable of modeling astrophysical systems containing compact objects by solving the equations of general relativistic hydrodynamics (GRHD) in full general relativity using singular curvilinear (spherical-like and cylindrical-like) and Cartesian coordinates. We demonstrate the code's robustness through a battery of challenging GRHD tests, ranging from flat, static spacetimes to curved, dynamical spacetimes. These tests further showcase the code's capabilities in modeling systems with realistic, finite-temperature equations of state and neutrino cooling via a leakage scheme. GRoovy extensively leverages GRHayL, an open-source, modular, and infrastructure-agnostic general relativistic magnetohydrodynamics library built from the highly robust algorithms of IllinoisGRMHD. Long-term simulations of binary neutron star and black hole-neutron star post-merger remnants will benefit greatly from using a future Charm++-parallelized version of GRoovy to study phenomena such as remnant stability, gamma-ray bursts, and nucleosynthesis.

Figures (11)

• Figure 1: Density profile at time $t=1.0$ from the evolution of the Balsara 0 initial data.
• Figure 2: Pressure profiles from the spherical explosion test, at $t=0$ and $t=4.0$.
• Figure 3: Left: Radial profile of optical depth from the initialization procedure for an optically thick gas. Right: Time evolution of the electron fraction $Y_\mathrm{e}\xspace$ and temperature $T$ for an optically thin gas.
• Figure 4: Static-spacetime TOV evolution in spherical coordinates: central density drift. Left: Convergence study showing approximately third-order convergence, with radial resolutions $N_r = \left(100, 200, 400\right)$ and angular resolutions fixed at $N_\theta = N_\phi = 2$. The high-resolution run captures more power in the high-frequency overtones, as illustrated in the right panel. Right: Power spectrum of the central density for $N_r=400$. Dashed vertical lines mark the fundamental mode (F) and overtones (H1--H6) from Font_2002. A Hann window is applied to the time series before performing the Fourier transform.
• Figure 5: Luminosities computed using the neutrino leakage module of GRHayL, from evolving a hot TOV model using the SHT Shen_2011 EoS in a static spacetime. Left: Time evolution of neutrino luminosities, using spherical coordinates with a radial resolution of $25\,\mathrm{m}$. Right: Normalized power spectrum for all three neutrino species, showing the fundamental mode and overtones. Reference frequencies taken from Galeazzi:2013mia.