Fully Dynamical General Relativistic SPH: Progress and Challenges

The method of Smoothed Particle Hydrodynamics (SPH) has a lot of appeal for simulating variety of catastrophic astrophysical scenarios, such as mergers of compact objects, tidal disruptions, etc. Conservation of angular momentum in particular is crucial in various scenarios involving stellar binaries. SPH naturally refines dense areas and avoids vacuum without need for a "density floor". With the recent detections of binary neutron star mergers GW 170817 and GW 190425 by the LIGO/Virgo collaboration, there is an increasing demand to better understand the mechanics of such mergers. Of particlar interest is the amount and composition of the neutron-rich matter ejected during the merger, as it harbors robust rapid neutron capture nucleosynthesis.

Several previous works explored SPH in fixed curved geometries, or with limited relativistic approximations, and only one pioneered study with fully relativistic SPH (Rosswog & Diener 2021). Here, we present another SPH approach to fully general relativistic dynamical geometry with a new code SPaRTA (= Smoothed Particles for Relativistic Theoretical Astrophysics). It uses our own implementation of the Generalized Harmonic formulation of Einstein's equations for evolving the dynamical metric, featuring damping of constraint violations and rigorous stability proof in its first-order form. On the hydrodynamics side, SPaRTA builds upon the novel fixed-metric SPH approach of Tejeda et al. (2017), generalizing it to time-dependent curvilinear geometries. We will discuss progress and challenges in construction of the initial data for such setup using effective potentials, and present code tests.