Realistic Equations of State Informing Neutron Star Post-Merger Gravitational-Wave Frequencies

Abstract

Binary neutron star mergers are thought to produce hot, rapidly rotating neutron stars with masses that can far exceed their Tolman-Oppenheimer-Volkoff mass. The gravitational-wave emission from such remnants provides a unique opportunity to measure the nuclear equation of state at densities and temperatures not available to terrestrial experiments. Current detector design is informed by gravitational-wave signals from general relativistic hydrodynamics simulations of neutron star mergers, typically with hybrid thermal treatments for the equation of state, where a cold equation of state is modified by adding a thermal component. We use realistic equations of state based on the relativistic mean field model with consistent treatment of thermal effects to compute the distribution of expected peak gravitational-wave frequencies. Marginalising over equation of state and progenitor neutron star masses, we show the peak frequency of emission ranges from $\sim2.5$ to 4 kHz. The width of this distribution suggests the need for broadband observatories with kHz sensitivity, and calls into question some of the so-called post-merger optimised configurations. We show the proposed KAGRA high-frequency design is well-suited to measuring post-merger remnants when compared to the KAGRA broadband design.

Figures (6)

• Figure 1: Temperature as a function of baryon density for nucleonic matter for warm ($S/A=1$) and hot ($S/A=2$) neutron star configurations.
• Figure 2: Peak GW frequency as a function of mass of post-merger remnant at Kepler rotation for cold ($T=0$; grey), warm ($S/A=1$; green) and hot ($S/A=2$; red) EoSs.
• Figure 3: Peak GW frequency distributions with zero and finite temperature EoSs for all post-merger remnant masses. Shown are results for cold ($T=0$; grey), warm ($S/A=1$; green) and hot ($S/A=2$; red) remnants.
• Figure 4: Distributions for the peak frequency of a post-merger remnant of a binary neutron star merger for cold (grey), warm (green) and hot (red) EoSs compared to the sensitivity curves of a 20 km Cosmic Explorer (blue), LIGO at A$\sharp$ sensitivity (orange), and various configurations of NEMO (blue, green) and a high frequency KAGRA detector (red, brown, purple).
• Figure 5: Violin plots of expected signal-to-noise ratios of post-merger remnants for our EoSs. The signal-to-noise ratios for the post-merger optimised detectors are normalised against the standard or 'broadband' configuration of the detector. The top panel corresponds to a 2 kHz configuration of the KAGRA HF detector whereas the bottom panel corresponds to a 3 kHz configuration of the KAGRA HF detector. Each panel contains three violin plots representing (from left to right) the hot ($S/A=2$),warm ($S/A=1$), and cold ($S/A=0$) equations of state. The black dashed line represents a signal-to-noise ratio of 1, i.e, exactly the same detector response from the broadband and optimised detectors.