Low mass binary neutron star mergers: Gravitational waves and neutrino emission

Neutron star mergers are among the most promising sources of gravitational waves for advanced ground-based detectors. These mergers are also expected to power bright electromagnetic signals, in the form of short gamma-ray bursts, infrared/optical transients powered by r-process nucleosynthesis in neutron-rich material ejected by the merger, and radio emission from the interaction of that ejecta with the interstellar medium. Simulations of these mergers with fully general relativistic codes are critical to understand the merger and postmerger gravitational wave signals and their neutrinos and electromagnetic counterparts. In this paper, we employ the Spectral Einstein Code to simulate the merger of low mass neutron star binaries (two $1.2M_{\odot }$ neutron stars) for a set of three nuclear-theory-based, finite temperature equations of state. We show that the frequency peaks of the postmerger gravitational wave signal are in good agreement with predictions obtained from recent simulations using a simpler treatment of gravity. We find, however, that only the fundamental mode of the remnant is excited for long periods of time: emission at the secondary peaks is damped on a millisecond time scale in the simulated binaries. For such low mass systems, the remnant is a massive neutron star which, depending on the equation of state, is either permanently stable or long lived (i.e. rapid uniform rotation is sufficient to prevent its collapse). We observe strong excitations of $l=2$, $m=2$ modes, both in the massive neutron star and in the form of hot, shocked tidal arms in the surrounding accretion torus. We estimate the neutrino emission of the remnant using a neutrino leakage scheme and, in one case, compare these results with a gray two-moment neutrino transport scheme. We confirm the complex geometry of the neutrino emission, also observed in previous simulations with neutrino leakage, and show explicitly the presence of important differences in the neutrino luminosity, disk composition, and outflow properties between the neutrino leakage and transport schemes.

Figure 1

Equatorial cut of the pseudospectral grid just before the two neutron stars get into contact. The color scale shows the baryon density (logarithmic scale).

Figure 2

Equatorial cut of the pseudospectral grid just after the change to a grid centered on the postmerger neutron star remnant. The color scale shows the baryon density (logarithmic scale).

Figure 3

Mass-radius relationships for the three equations of state considered here, for cold neutron stars in neutrinoless $\beta$ equilibrium. Horizontal dashed lines are provided at the initial mass of the individual neutron stars ($1.2M_{\odot }$) and total mass of the binaries ($2.4M_{\odot }$) considered here.

Figure 4

Dominant (2,2) mode of the gravitational wave strain for all three configurations, at 100 Mpc from the source. The simulation with the stiffest equation of state (DD2) shows the fastest inspiral. As opposed to other figures in this paper, we show the waveforms extrapolated to infinity, which explains the short length of the postmerger waveform.

Figure 5

Power spectrum of the merger and postmerger gravitational wave signal for optimally oriented mergers at a distance of 100 Mpc, multiplied by $f^{1/2}$. For reference, we also plot the design sensitivity of advanced LIGO (zero-detuned high power detector strain noise spectrum, dashed blue curve) [98]. Note the clear dominant peaks at $(2.3–3)\mathrm{kHz}$. All spectra are Fourier transforms of the dominant (2,2) mode of the merger waveform in the time interval $[t_{\text{peak}}-2\mathrm{ms},t_{\text{peak}}+6\mathrm{ms}]$, with a tapering window of width 0.8 ms used at the beginning and end of the interval.

Figure 6

Spectrograms of the gravitational wave signal for the simulations using the SFHo (left), LS220 (middle) and DD2 (right) equations of state, for an optimally oriented binary at 100 Mpc. The dashed horizontal black curves show the location of the peaks predicted in [42]. The time is calculated as the difference between the center of the window function used to compute the spectrogram (see text) and the peak of the gravitational wave amplitude. The dominant peak is clearly visible at (2.3–3) kHz. Secondary peaks in the (1.3–2.1) kHz range are poorly resolved, and quickly damped. The strong emission at frequencies $f\lesssim 1.3\mathrm{kHz}$ is the merger signal itself.

Figure 7

Dominant (2,2) mode of the gravitational wave strain for the LS220 waveform at the standard and high resolution, at 100 Mpc from the source. We find excellent agreement even in the postmerger signal.

Figure 8

Density in the equatorial plane of the postmerger remnant at three characteristic times: 0.5 ms after the peak of the gravitational wave emission (top), 3 ms after the peak (middle), and 10 ms after the peak (bottom). We show results for the SFHo (left), LS220 (center) and DD2 (right) equations of state. In each of those plots, we show density contours at $(1,3,5,7,9)\times {10}^{14}\mathrm{g}{\mathrm{cm}}^{-3}$ (solid blue lines). Here and in subsequent figures, the coordinates are those of the simulation, as evolved in the generalized harmonic formulation of Einstein’s equations.

Figure 9

Maximum value of the baryon density on the grid as a function of time for all three equations of state. $t_{\text{peak}}$ is the time at which the amplitude of the gravitational wave signal is maximal.

Figure 10

Density and velocity in the equatorial plane for the simulation with the LS220 equation of state, 10 ms after merger. The excited quadrupole mode is still clearly visible at that time.

Figure 11

Instantaneous orbital frequency of the fluid, in the coordinates of the simulation and 10 ms after merrger, in a slice orthogonal to the orbital plane and along the major axis of the bar in the postmerger neutron star. The black lines are density contours at ${\rho }_0=({10}^{12},{10}^{13},{10}^{14})\mathrm{g}/{\mathrm{cm}}^3$.

Figure 12

Hydrodynamic variables (in the equatorial plane) 10 ms after the peak of the gravitational wave signal. From top to bottom, we show the density, temperature, and electron fraction for the four simulations considered in this paper—from left to right, SFHo, LS220 with neutrino leakage, LS220 with neutrino transport, and DD2.

Figure 13

Hydrodynamic variables 10 ms after the peak of the gravitational wave signal in a slice along the major axis of the remnant and orthogonal to the equatorial plane. From top to bottom, we show the density, entropy per baryon, temperature, and electron fraction for the four simulations considered in this paper—from left to right, SFHo, LS220 with neutrino leakage, LS220 with neutrino transport, and DD2.

Figure 14

Density (left) and temperature (right) profiles in the equatorial plane along the major axis of the merger remnant. We show results for the merger using the LS220 equation of state and the neutrino transport (solid lines) or neutrino leakage (dashed line) scheme. The two simulations are very similar, with a slightly smoother temperature profile and hotter outer disk when using neutrino transport. The hot shocked tidal arms are clearly visible around 40 km from the center in both plots.

Figure 15

Total neutrino luminosity for the three simulations using the leakage scheme and the LS220, SFHo, and DD2 equations of state (solid curves) as well as the simulation using the LS220 equation of state and neutrino transport (dashed red curve).

Figure 16

Density (color scale) and location of the surfaces of optical depth $\tau \sim 1$ for ${\nu }_e$ (solid black line), ${\overline{\nu }}_e$ (dashed red line), and ${\nu }_x$ (dot-dashed black line) at the end of the simulation using the LS220 equation of state and a neutrino transport scheme.

Figure 17

Energy density (color scale) and normalized flux $\alpha F_{\nu }^i/E_{\nu }-{\beta }^i$ (black arrows) of the electron neutrinos on the density isosurface with ${\rho }_0={10}^{11}\mathrm{g}/{\mathrm{cm}}^3$. The region of brightest ${\nu }_e$ emission, at the center of the plot, coincides with the polar region of the neutron star remnant.

Figure 18

Energy density (color scale) and normalized flux $\alpha F_{\nu }^i/E_{\nu }-{\beta }^i$ (black arrows) of the electron antineutrinos on the density isosurface with ${\rho }_0={10}^{11}\mathrm{g}/{\mathrm{cm}}^3$. The regions of brightest ${\overline{\nu }}_e$ emission (dark blue) are in the hot, shocked tidal arms.

Figure 19

Energy density and normalized flux $\alpha F_{\nu }^i/E_{\nu }-{\beta }^i$ of the electron neutrinos in the same vertical slice as in Fig. 13. The vertical stripes with higher neutrino energy in the polar regions are an artifact of the M1 closure.

Figure 20

Energy density and normalized flux $\alpha F_{\nu }^i/E_{\nu }-{\beta }^i$ of the electron antineutrinos in the same vertical slice as in Fig. 13. The vertical stripes with higher neutrino energy in the polar regions are an artifact of the M1 closure.

Figure 21

Energy density and normalized flux $\alpha F_{\nu }^i/E_{\nu }-{\beta }^i$ of the heavy-lepton neutrinos in the same vertical slice as in Fig. 13.

Figure 22

Expected equilibrium electron fraction of the fluid $Y_e^{\mathrm{irr}}$ if the composition was set solely by neutrino absorption. The white region has $Y_e^{\mathrm{irr}}>0.4$.

Figure 23

Neutrino luminosities for the simulations using the LS220 equation of state and the neutrino leakage scheme (solid curves), or the neutrino transport scheme (dashed curves). We show the luminosity in electron neutrinos (black), electron antineutrinos (red), and all heavy-lepton neutrinos and antineutrinos combined (green).

Figure 24

Rate at which material flagged as unbound leaves the computational grid in the simulation using the LS220 equation of state and the neutrino leakage scheme. We also show the flow of unbound material at the same location in the simulation using the transport scheme. Note that due to neutrino absorptions at larger distances (the transport simulation uses a larger numerical grid), the true mass outflows in the simulation using a transport scheme are higher at late times, with $\dot{M}\sim 0.04M_{\odot }{s}^{-1}$. The oscillations in the outflow rates are largely due to the use of a rectangular outer boundary and the asymmetry of the outflows.