Testing influence of tides on gravitational wave emission with SPH code PHANTOM

Abstract

In this article, we demonstrate how a Newtonian SPH (Smoothed Particle Hydrodynamics) code PHANTOM can be used to estimate the tidal contribution to gravitational wave (GW) waveforms. Using a binary neutron star (NS+NS) system with typical masses of 1.5 + 1.5 Msun as an example, we show - by comparing our results with waveforms calibrated against full numerical General Relativity (GR) simulations - that the tidal contribution to GWs can be reliably extracted using as few as about 10$^4$ smoothed particles. Naturally, one must account for the difference in neutron star compactness between Newtonian gravity and general relativity. At separations greater than 100 km, the relative tidal contribution falls below the level of numerical noise inherent in SPH; however, at such distances, GW waveforms for point-like sources are sufficient for detection purposes. For a white dwarf-neutron star (WD+NS) binary with typical masses of 0.6 Msun and 1.5 Msun respectively, a much larger number of smoothed particles is required, along with a separation on the order of tens of thousands of kilometers, as tidal mass transfer and the disruption of the white dwarf begin quite rapidly. Nevertheless, these challenges can be overcome, but the approach is not capable of yielding useful results due to the richness of Newtonian effects. In all cases, it is crucial to perform a hydrostatic/hydrodynamic relaxation (HPR) of the initial models; otherwise, the entire GW signal is lost in the numerical noise.