Post-merger evolution of a neutron star-black hole binary with neutrino transport

We present a first simulation of the post-merger evolution of a black hole-neutron star binary in full general relativity using an energy-integrated general-relativistic truncated moment formalism for neutrino transport. We describe our implementation of the moment formalism and important tests of our code, before studying the formation phase of an accretion disk after a black hole-neutron star merger. We use as initial data an existing general-relativistic simulation of the merger of a neutron star of mass $1.4M_{\odot }$ with a black hole of mass $7M_{\odot }$ and dimensionless spin ${\chi }_{\mathrm{BH}}=0.8$. Comparing with a simpler leakage scheme for the treatment of the neutrinos, we find noticeable differences in the neutron-to-proton ratio in and around the disk, and in the neutrino luminosity. We find that the electron neutrino luminosity is much lower in the transport simulations, and that both the disk and the disk outflows are less neutron rich. The spatial distribution of the neutrinos is significantly affected by relativistic effects, due to large velocities and curvature in the regions of strongest emission. Over the short time scale evolved, we do not observe purely neutrino-driven outflows. However, a small amount of material ($3\times {10}^{-4}{M}_{\odot }$) is ejected in the polar region during the circularization of the disk. Most of that material is ejected early in the formation of the disk, and is fairly neutron rich (electron fraction $Y_e\sim 0.15–0.25$). Through r-process nucleosynthesis, that material should produce high-opacity lanthanides in the polar region, and could thus affect the light curve of radioactively powered electromagnetic transients. We also show that by the end of the simulation, while the bulk of the disk remains neutron rich ($Y_e\sim 0.15–0.2$ and decreasing), its outer layers have a higher electron fraction: 10% of the remaining mass has $Y_e>0.3$. As that material would be the first to be unbound by disk outflows on longer time scales, and as composition evolution is slower at later times, the changes in $Y_e$ experienced during the formation phase of the disk could have an impact on nucleosynthesis outputs from neutrino-driven and viscously driven outflows. Finally, we find that the effective viscosity due to momentum transport by neutrinos is unlikely to have a strong effect on the growth of the magnetorotational instability in the post-merger accretion disk.

Figure 1

Density and velocity field in the equatorial plane of the black hole at the initial time $t_0\sim t_{\text{merge}}+6.1\mathrm{ms}$. For reference, the velocity at the peak of the density distribution is about $0.6c$.

Figure 2

Radial distribution of the material outside of the black hole. We plot the fraction of the total mass within bins of width $\mathrm{\Delta }r\approx 3\mathrm{km}$ at four representative times of the simulation. Most of the matter is initially near the black hole ($r\lesssim 60\mathrm{km}$) and close to periastron. The disk then expands, and later circularizes.

Figure 3

Fraction of the total mass within temperature bins of width $\mathrm{\Delta }T=0.5\mathrm{MeV}$, plotted at four representative times of the simulation. Within 10 ms, the temperature of the disk becomes very homogeneous.

Figure 4

Fraction of the total mass within electron fraction bins of width $\mathrm{\Delta }{Y}_e=0.01$, plotted at four representative times of the simulation. Within 10 ms, the electron fraction of the disk becomes very homogeneous. The tail of higher-$Y_e$ material is due to lower-density regions around the disk.

Figure 5

Fraction of the baryon mass with $Y_e$ below a given value, at four representative times of the simulation. We note the slowly growing tail of high-$Y_e$ material even after the average $Y_e$ begins to decrease.

Figure 6

Density and velocity field in the equatorial plane of the black hole at the end of the simulation, 20 ms after merger. For scale, the velocities at the peak of the density distribution are $v\sim 0.5c$.

Figure 7

Density (in $\mathrm{g}/{\mathrm{cm}}^3$) and velocity field in the $y=y_{\mathrm{BH}}$ plane at the end of the simulation, 20 ms after merger. For reference, the largest poloidal velocities are about $0.6c$. In the core of the disk, the velocities are mostly directed out of the plane of the visualization.

Figure 8

Temperature in the equatorial plane of the black hole at the end of the simulation, 20 ms after merger. Density contours are shown as thick black lines for ${\rho }_0=({10}^9,{10}^{10},{10}^{11})\mathrm{g}/{\mathrm{cm}}^3$.

Figure 9

Temperature in a plane orthogonal to the equatorial plane of the disk the at the end of the simulation, 20 ms after merger. Density contours are shown as thick black lines for ${\rho }_0=({10}^9,{10}^{10},{10}^{11})\mathrm{g}/{\mathrm{cm}}^3$.

Figure 10

Electron fraction $Y_e$ in the equatorial plane of the black hole at the end of the simulation, 20 ms after merger. Density contours are shown as thick black lines for ${\rho }_0=({10}^9,{10}^{10},{10}^{11})\mathrm{g}/{\mathrm{cm}}^3$.

Figure 11

Electron fraction $Y_e$ in a plane orthogonal to the equatorial plane of the disk at the end of the simulation, 20 ms after merger. Density contours are shown as thick black lines for ${\rho }_0=({10}^9,{10}^{10},{10}^{11})\mathrm{g}/{\mathrm{cm}}^3$.

Figure 12

Neutrinospheres $\tau =2/3$ at the end of the simulation, 20 ms after merger. We show the vertical plane $y=y_{\mathrm{BH}}$. The three contours are, from the outside to the inside, the neutrinospheres for ${\nu }_e$ (outer solid line), ${\overline{\nu }}_e$ (dashed line) and ${\nu }_x$ (inner solid line). The disk is colored according to its baryon density ${\rho }_0$.

Figure 13

Energy density and normalized flux ($\alpha F^i/E-{\beta }^i$) of the electron neutrinos at the end of the simulation, 20 ms after merger. We show the vertical plane $y=y_{\mathrm{BH}}$.

Figure 14

Energy density and normalized flux ($\alpha F^i/E-{\beta }^i$) of the electron neutrinos at the end of the simulation (20 ms after merger), in the equatorial plane of the disk.

Figure 15

Energy density and normalized fluxes of the electron neutrinos on the ${\tau }_{{\nu }_e}=0.1$ surface.

Figure 16

Luminosities for the different neutrino species as a function of time. Solid curves show the M1 results. Dashed curves show results using a leakage scheme. Thin dot-dashed curves show the prediction of the leakage scheme, but for the value of the hydrodynamic variables obtained by evolving the disk with the M1 scheme. Heavy-lepton neutrino luminosities ${\nu }_x$ are for all four species combined.

Figure 17

Average neutrino energy for the different neutrino species as a function of time. Solid curves show the results from the M1 simulation. Dashed curves show results using a leakage scheme. Heavy-lepton neutrino energies (${\nu }_x$) are for all four species combined. Note that for both simulations, the energy is computed using the number and energy source terms from the leakage scheme, as the gray M1 scheme does not contain information about the neutrino spectrum.

Figure 18

Energy density for the single beam test, after $\mathrm{\Delta }t=0.4$. The black arrows show the flux $F_i$.

Figure 19

Energy density for the oblique beam test, after $\mathrm{\Delta }t=0.2$. The arrows show the flux $F_i$.

Figure 20

Energy density for the shadow test after $\mathrm{\Delta }t=1$. The arrows show the flux $F_i$.

Figure 21

Energy density in steady state for a two-dimensional beam in a Kerr-like spacetime, with the beam emitted from $r=7M-8M$ where $M$ is the mass of the nonspinning central black hole. The solid lines show null geodesics bounding the expected location of the beam. The simulation is performed in full three dimensions, but the metric and beam are independent of $z$.

Figure 22

Same as in Fig. 21, but with the beam emitted from $r=3M-4M$. As before, the solid lines trace null geodesics.

Figure 23

Same as Fig. 22, but using the full three-dimensional Kerr metric and a beam of finite transverse size.

Figure 24

Contours of constant energy density for the crossing beams test. The contours are for 10, 1 and 0.1% of the original energy density of the beams.

Figure 25

Energy density of neutrinos at $t=2$ for the emitting sphere tests with $\overline{\kappa }=5$ and $\overline{\kappa }={10}^{10}$. The numerical results are shown by circles/squares while the solid lines are the analytical predictions.

Figure 26

Temperature after 8 ms of evolution for the evolution of a post-bounce configuration, in the region in which the temperature evolution is most affected by the gray approximation.

Figure 27

Electron fraction $Y_e$ after 8 ms of evolution for the evolution of a post-bounce configuration.