Hybrid equation of state approach in binary neutron-star merger simulations

We investigate the use of hybrid equations of state in binary neutron-star simulations in full general relativity, where thermal effects are included in an approximate way through the adiabatic index ${\mathrm{\Gamma }}_{\mathrm{th}}$. We employ a newly developed finite-temperature equation of state derived in the Brueckner-Hartree-Fock approach and carry out comparisons with the corresponding hybrid versions of the same equation of state, investigating how different choices of ${\mathrm{\Gamma }}_{\mathrm{th}}$ affect the gravitational-wave signal and the hydrodynamical properties of the remnant. We also perform comparisons with the widely used Steiner-Fischer-Hempel equation of state, detailing the differences between the two cases. Overall, we determine that when using a hybrid equation of state in binary neutron-star simulations, the value of the thermal adiabatic index ${\mathrm{\Gamma }}_{\mathrm{th}}\approx 1.7$ best approximates the dynamical and thermodynamical behavior of matter computed using complete, finite-temperature equations of state.

Figure 1

Left panel: pressure $p$ and energy density $e$ of betastable matter at $T=0$ as a function of the baryon number density. Right panel: thermal pressure and internal energy density, Eqs. (9), (10) at different temperatures. Results with V18 and SFHo EOSs are compared.

Figure 2

Adiabatic index of betastable matter, Eq. (12), as a function of density at different temperatures. Dashed curves show results obtained from betastable hot and cold matter, while for the solid (dash-dotted) curves the proton fraction is fixed to the one of betastable hot (cold) matter (see discussion in the text).

Figure 3

Gravitational mass as a function of the central rest-mass density for $T=0$ and $T=50\mathrm{MeV}$ with full temperature treatment, and different choices of constant ${\mathrm{\Gamma }}_{\mathrm{th}}=1.1$, 1.5, 1.75 at $T=50\mathrm{MeV}$. Dashed orange and green lines, together with the shaded regions of the same color, refer to the observational constraints of Refs. [36, 61], respectively.

Figure 4

Maximum values of rest-mass density (upper panels) and temperature (third and fourth panels from the top, only for the simulations using the FT EOSs) as a function of time. The evolution of the average temperature $⟨T⟩$, Eq. (15), is also displayed. A lighter color is chosen for the inspiral phase, where such temperatures are meant as representative only and do not reflect an accurate description of the thermodynamics of the matter. The average deviation from betastability, Eq. (16), is also represented in the lowest panel for both FT EOSs.

Figure 5

Gravitational waveforms over a timescale of about 20 ms after the merger for the V18 and SFHo EOSs obtained for gravitational masses $2\times 1.35M_{\odot }$, comparing different choices of constant ${\mathrm{\Gamma }}_{\mathrm{th}}=1.1$, 1.5, 1.7, 1.75 and the FT EOSs.

Figure 6

PSDs of the simulations with the V18 and SFHo EOSs, at a distance of 100 Mpc. Vertical dashed lines of different colors indicate the frequency $f_2$. The sensitivity curve (magenta color) of Advanced LIGO is displayed for reference.

Figure 7

Average rest-mass density and angular velocity for the different V18-based EOSs as a function of the radial coordinate $r$ ($z=0$) at $t=14\mathrm{ms}$.

Figure 8

Distributions of ${\mathrm{\Gamma }}_{\mathrm{th}}$, Eq. (12), (upper-left side of the figures), rest-mass density (upper right), temperature (lower right), and deviation from betastability (lower left), in the $z=0$ plane at $t\approx 9\mathrm{ms}$ after the merger.

Figure 9

The average ${\mathrm{\Gamma }}_{\mathrm{th}}$, Eq. (19), as a function of time for the FT V18 and SFHo simulations. Time averages related to the total time interval considered here are represented as arrows in the plot. Dot-dashed curves represent the average values of ${\mathrm{\Gamma }}_{\mathrm{th}}$ calculated using Eq. (12) with $x_p=x_{\beta }(\rho ,T=0)$, as described in the text.

Figure 10

Isocontours of ${\mathrm{\Gamma }}_{\mathrm{th}}$ as a function of cylindrical radius $r$ and time $t$ for the V18 and SFHo FT simulations.