Effects of chiral effective field theory equation of state on binary neutron star mergers

We present fully general relativistic simulations of binary neutron star mergers, employing a new zero-temperature chiral effective field theory equation of state (EOS), the BL EOS. We offer a comparison with respect to the older GM3 EOS, which is based on standard relativistic mean-field theory, and separately determine the impact of the mass. We provide a detailed analysis of the dynamics, with focus on the postmerger phase. For all models, we extract the gravitational wave strain and the postmerger frequency spectrum. Further, we determine the amount, velocity, and polar distribution of ejected matter and provide estimates for the resulting kilonova signals. We also study the evolution of the disk while it is interacting with the hypermassive remnant and discuss the merits of different disk mass definitions applicable before collapse, with regard to the mass remaining after black hole formation. Finally, we investigate the radial mass distribution and rotation profile of the remnants, which validate previous results and also corroborate a recently proposed stability criterion.

Figure 1

Baryonic mass as a function of central rest mass density of nonrotating (lower curves) and maximally uniformly rotating (upper curves) NSs for the two EOSs used in this paper (BL and GM3). The horizontal lines represent the masses of the BNS systems, while the markers on the curves represent the mass values for the single NSs in the binary.

Figure 2

Gravitational mass as a function of circumferential radius of NSs depending on the chosen EOS. Bottom panel: relation for nonrotating NSs. Top panel: relation for NSs rotating uniformly at mass shedding limit.

Figure 3

Proper separation between the NS barycenters during the inspiral as function of orbital phase. The separation is given in units of reduced mass $\mu =M_g^1{M}_g^2/(M_g^1+M_g^2)$. The barycenters and orbital phases are computed using simulation coordinates.

Figure 4

Rest-mass density evolution in the equatorial plane for the three simulations $BL-1.35$ (top), $GM3-1.31$ (middle) and $GM3-1.35$ (bottom). The yellow contour lines highlight the unbound ejected matter. The snapshots are taken at three different phases of the evolution: on the left at the time of merger, in the middle 2.5 ms after merger, and on the right 15 ms after merger. The apparent horizon of the newly formed BH for the $GM3-1.35$ model is highlighted with a red circle.

Figure 5

Same as Fig. 4, but showing a cut in the meridional plane.

Figure 6

Structure of the disk and embedded remnant for model $GM3-1.31$, at the end of the simulation. The mass density is shown as color plot. In order to remove contributions from oscillations, we average in time over the last 4 ms. The white circle marks the cutoff (coordinate) radius used to define the disk mass $M_{\mathrm{d}}$. The density cutoff $10^{13}{\mathrm{g}/\mathrm{cm}}^3$ used for the alternative definition $M_{\mathrm{d}}^{\mathrm{alt}}$ is marked by the blue contour. The other contours mark isodensity surfaces containing 90, 95, and 98% of the total baryonic mass, and those corresponding to remnant bulk and core (see text).

Figure 7

Time evolution of disk mass for our simulations. The solid thick lines show the disk mass measure $M_{\mathrm{d}}$, and the thin solid lines the alternative measure $M_{\mathrm{d}}^{\mathrm{alt}}$. After the BH formation for model $GM3-1.35$, we show the mass outside the apparent horizon instead (dashed line). The rapid initial decrease corresponds to the rapid initial growth of the apparent horizon. The horizontal lines mark a disk mass for which the remaining remnant mass is at the upper limit for a SMNS (the two GM3 models are indistinguishable due to almost identical total mass).

Figure 8

Rotation profile of the remnant for our models 11 ms after merger. $r_c$ is the circumferential radius, and $\nu$ the rotation frequency as observed from infinity. The dash-dotted curve represents the frequency for a test particle on a prograde circular orbit.

Figure 9

Time evolution of the TOV solutions equivalent to the remnant cores (see text) for our simulations. The curves show the bulk mass of the TOV solutions, and the horizontal lines mark the maximum bulk mass for TOV sequences of the given EOS. The vertical line marks the BH formation.

Figure 10

Average rest mass density along the rotation axis above the remnant. The average is taken between a distance 30 and 50 km from the origin. The density around $10^6\mathrm{g}/{\mathrm{cm}}^3$ during the inspiral is due to matter ejected by numerical artifacts at the NS surfaces. For comparison, the density of the artificial atmosphere used in our simulations is $6\times {10}^4\mathrm{g}/{\mathrm{cm}}^3$.

Figure 11

Radial distribution of unbound matter as a function of time. The logarithmic color scale corresponds to the unbound mass per coordinate radius. The black dashed line represents the trajectory of a radially outgoing test mass with velocity $v_{\infty }$ from Table 3. The trajectory has been estimated using the Newtonian potential of a mass equal to the ADM mass at the end of the simulation.

Figure 12

Time evolution of the unbound matter flux through a spherical surface at $r=148\mathrm{Km}$. Top panels: polar distribution of the flux reconstructed from the multipole moments up to $l=4$. The orbital plane corresponds to 0° and the orbital axis to 90°. The color scale is linear, ranging from zero (white) to the maximum flux for the given model (black). The horizontal line marks the angle below which 90% of the matter is ejected during the whole evolution. Bottom panels: total flux through the spherical surface, showing the contribution of the separate ejecta waves.

Figure 13

GW strain (top panel) and instantaneous frequency (bottom panel) for our simulations. We only show the main contribution to the strain, given by the $l=m=2$ mode. The signal is scaled to a nominal source distance of 100 Mpc. The gray curve is the GW strain coefficient $h_{22}^{+}$. The red curve is the generalized amplitude accounting for over-modulation (see text). The yellow curve shows the instantaneous frequency computed from the phase of the strain, while the blue line shows the frequency without the contribution of the phase jump. The vertical dashed lines mark the merger times. The dotted vertical lines in the right panels mark the formation of an apparent horizon.

Figure 14

Power spectrum of the GW strain for our simulations plotted together with the sensitivity curves for advanced LIGO and Virgo and the planned Einstein Telescope. The source is assumed at a distance 100 Mpc from the detector, oriented with orbital angular momentum along the line of sight. The symbols mark the frequencies of the main peak and combination frequencies $f_{\mathrm{pm}}+n{f}_{\rho }$, where $n=-1$, 1, 2 and $f_{\rho }=1.0\mathrm{kHz}$ is the quasiradial oscillation frequency.

Figure 15

Snapshots of the rest-mass density (top) and temperature (bottom) in the equatorial plane, for model BL-1.35 at merger time (left), 2.5 ms after merger (center), and 19 ms after merger (right).

Figure 16

Temperature inside the HMNS on the equatorial plane, 8.5 ms after merger, for model BL-1.35.