Thinking Outside the Box: Numerical Relativity with Particles

Abstract

The observation of gravitational waves from compact objects has now become an active part of observational astronomy. For a sound interpretation, one needs to compare such observations against detailed Numerical Relativity simulations, which are essential tools to explore the dynamics and physics of compact binary mergers. To date, essentially all simulation codes that solve the full set of Einstein’s equations are performed in the framework of Eulerian hydrodynamics. The exception is our recently developed Numerical Relativity code SPHINCS_BSSN which solves the commonly used BSSN formulation of the Einstein equations on a structured mesh and the matter equations via Lagrangian particles. We show here, for the first time, SPHINCS_BSSN neutron star merger simulations with piecewise polytropic approximations to four nuclear matter equations of state. In this set of neutron star merger simulations, we focus on perfectly symmetric binary systems that are irrotational and have 1.3 M⊙ masses. We introduce some further methodological refinements (a new way of steering dissipation, an improved particle–mesh mapping), and we explore the impact of the exponent that enters in the calculation of the thermal pressure contribution. We find that it leaves a noticeable imprint on the gravitational wave amplitude (calculated via both quadrupole approximation and the Ψ4 formalism) and has a noticeable impact on the amount of dynamic ejecta. Consistent with earlier findings, we only find a few times 10−3M⊙ as dynamic ejecta in the studied equal mass binary systems, with softer equations of state (which are more prone to shock formation) ejecting larger amounts of matter. In all of the cases, we see a credible high-velocity (∼0.5…0.7c) ejecta component of ∼10−4M⊙ that is launched at contact from the interface between the two neutron stars. Such a high-velocity component has been suggested to produce an early, blue precursor to the main kilonova emission, and it could also potentially cause a kilonova afterglow.

GRMHD Simulations of Neutron-star Mergers with Weak Interactions: r-process Nucleosynthesis and Electromagnetic Signatures of Dynamical Ejecta

“…Previous analyses of fast ejecta with GRHD simulations using neutrino transport (Radice et al 2018;Nedora et al 2021a) and Newtonian simulations at ultra-high resolution in axisymmetry (Dean et al 2021) report fast-ejecta masses within factors of 5−10 higher than those found here. SPH simulations find even higher masses than grid-based simulations, of the order of 10 −4 -10 −5 M e (Metzger et al 2015;Kullmann et al 2022;Rosswog et al 2022). Our default mass estimates are similar to the ones obtained in the grid-based ultra-highresolution simulations (purely hydrodynamic, without weak interactions) of Kiuchi et al (2017), specifically, their HB EOS case, which leads to a similar NS compactness to APR (see Figure 7 in Hotokezaka et al 2018).…”

“…Differences to other gridbased merger simulations (Nedora et al 2021a) can be understood in terms of the definition of asymptotic velocity (see above), while the higher level of ejecta in grid-based convergence studies (Dean et al 2021) may be attributable to differences in the overall setup (such as, e.g., Newtonian versus general-relativistic dynamics and geometric effects due to assumed symmetries), since ejecta masses are expected to be roughly converged according to these studies at our present resolution (at least up to a factor of a few). Fast ejecta tails are resolved by tens of SPH particles in present SPH simulations (Kullmann et al 2022;Rosswog et al 2022), and details about the dependence of fast ejecta masses with resolution (number of particles) have been reported only recently (Rosswog et al 2022). Rosswog et al (2022) showed that the mass of fast ejecta decreases by a factor of ≈10 when the resolution is increased from 10 6 to 5 × 10 6 SPH particles used in the simulation.…”

“…Fast ejecta tails are resolved by tens of SPH particles in present SPH simulations (Kullmann et al 2022;Rosswog et al 2022), and details about the dependence of fast ejecta masses with resolution (number of particles) have been reported only recently (Rosswog et al 2022). Rosswog et al (2022) showed that the mass of fast ejecta decreases by a factor of ≈10 when the resolution is increased from 10 6 to 5 × 10 6 SPH particles used in the simulation. The total fast ejecta mass in the latter paperestimated using the relativistic asymptotic velocity similar to our work-is still a factor of ≈2 higher than the value we find for a BNS merger with a similar setup and using the APR3 EOS, but much closer than previous SPH simulations.…”

“…We conjecture that based on these results and convergence studies (Dean et al 2021), the amount of fast ejecta should be roughly converged at our grid resolution and atmosphere level. Remaining differences to Newtonian setups and SPH simulations (Dean et al 2021;Kullmann et al 2022;Rosswog et al 2022) remain an open question, but may likely be attributable to differences in the overall setup, such as Newtonian dynamics, velocity extraction, geometric effects due to assumed symmetries, and insufficiently converged ejecta tails in SPH simulations with  tens of particles (see the discussion in Section 3.2).…”

Neutrino transport in general relativistic neutron star merger simulations

“…This allows for the use of the single unknown c to represent the function f tr m . The ASL scheme has been adapted for use in merger simulations within a smoothed particle hydrodynamics (SPH) code (Gizzi et al 2021), which in conjunction with the development of a first general relativistic SPH code (Rosswog et al 2022) should allow for the use of ASL in general relativsitic merger simulations in the near future. We note that the general relativistic algorithm of Sekiguchi ( 2010) also keeps track of the energy density of trapped neutrinos when, in the notation of Perego et al (2016), t diff t prod .…”