Modeling GW170817 based on numerical relativity and its implications

Gravitational-wave observation together with a large number of electromagnetic observations shows that the source of the latest gravitational-wave event, GW170817, detected primarily by advanced LIGO, is the merger of a binary neutron star. We attempt to interpret this observational event based on our results of numerical-relativity simulations performed so far, paying particular attention to the optical and infrared observations. We finally reach a conclusion that this event is described consistently by the presence of a long-lived hypermassive or supramassive neutron star as the merger remnant because (i) significant contamination by lanthanide elements along our line of sight to this source can be avoided by the strong neutrino irradiation from it and (ii) it could play a crucial role in producing an ejecta component of appreciable mass with fast motion in the postmerger phase. We also point out that (I) the neutron-star equation of state has to be sufficiently stiff (i.e., the maximum mass of cold spherical neutron stars, $M_{\max }$, has to be appreciably higher than $2M_{\odot }$) in order for a long-lived massive neutron star to be formed as the merger remnant for the binary systems of GW170817, for which the initial total mass is $\gtrsim 2.73M_{\odot }$, and (II) the absence of optical counterparts associated with relativistic ejecta suggests a not-extremely-high value of $M_{\max }$ approximately as $2.15–2.25M_{\odot }$.

Figure 1

Merger remnant for the SFHo EOS with $(m_1,m_2)=(1.4M_{\odot },1.3M_{\odot })$. The upper left and right panels show the profiles of the rest-mass density and electron fraction for the merger remnant, i.e., a black hole surrounded by a torus, respectively. The lower left and middle panels show the profiles of the rest-mass density and electron fraction for the dynamical ejecta component, respectively. The white region in these panels indicates that no ejecta component is present in the inner region. These snapshots are generated at $\approx 40\mathrm{ms}$ after the onset of merger. The lower right panel shows the mass histogram of the ejecta component as a function of $Y_e$ for the regions of $z>x(\theta <45°)$ and $z<x(\theta >45°)$.

Figure 2

The same as Fig. 1 but for the merger remnant for the DD2 EOS with $(m_1,m_2)=(1.4M_{\odot },1.3M_{\odot })$. The snapshots are generated at $\approx 80\mathrm{ms}$ after the onset of merger. For this case, a massive neutron star is located at the center (compare the upper panels of Figs. 1 and 2).

Figure 3

The upper panels: The profiles of the rest-mass density (left) and electron fraction (middle) for the early viscosity-driven ejecta component at $t=100\mathrm{ms}$ after the evolution of the massive neutron star–torus system. The white region indicates that no ejecta component is present in the inner region. The right panel shows the mass histogram of the accumulated ejecta component as a function of $Y_e$ for the regions of $z>x(\theta <45°)$ and $z<x(\theta >45°)$. The middle panels: The same as the upper panels but at $t=500\mathrm{ms}$ after the evolution of the system at which only the viscosity-driven ejecta from the torus with neutrino irradiation is dominant in the computational region. The bottom panels: The same as the upper panels but at $t=1500\mathrm{ms}$ after the evolution of the system at which the late-time viscosity-driven ejecta from the torus are driven, increasing the ejecta of $0.3\lesssim Y_e\lesssim 0.4$. For all the panels, the results with ${\alpha }_{\mathrm{vis}}=0.04$ for the DD2 model are shown.

Figure 4

Observational light curves (in terms of the data taken from Ref. [82]) and a light curve model [3] of the electromagnetic counterparts of GW170817. Plotted are the absolute AB magnitudes for the $r$, $i$, $z$, $J$, $H$, and $K_s$ bands. The horizontal axis shows the day spent after merger of the binary neutron stars. Here, we assume that the distance to the source is 40 Mpc.

Figure 5

Schematic picture of the ejecta profile for the case of a soft EOS in which a black hole is formed in $\sim 10\mathrm{ms}$ after the onset of merger. The largest anisotropic-shell component (red color) denotes the dynamical ejecta. The smaller anisotropic-shell (red) and polar components (ocher) denote the viscous and MHD ejecta from the torus, respectively. “Low $Y_e$” implies that it contains neutron-rich matter with $Y_e\lesssim 0.2$, which synthesizes an appreciable amount of lanthanide elements and contributes to enhancing the opacity to $\kappa \sim 10{\mathrm{cm}}^2/\mathrm{g}$. The polar component could have ejecta of $Y_e=0.3–0.4$, but it is a minor component in mass. The black filled circle and neighboring (orange) ellipsoids in the central region denote a spinning black hole and accretion torus surrounding the black hole, respectively. Since the opacity is entirely high for all the major ejecta components, it is difficult to describe the observational results (in particular. early peak time) for the electromagnetic counterparts of GW170817 by this model.

Figure 6

Schematic picture of the ejecta profile for the case of a stiff EOS in which a long-lived massive neutron star is formed as a remnant. The largest anisotropic-shell component (red color) denotes the neutron-rich dynamical ejecta. The smaller anisotropic-shell component (blue color) denotes the early viscosity-driven ejecta and long-term viscosity-driven ejecta from the torus. The polar spheroid component (dark blue color) denotes the viscosity-driven ejecta from the torus influenced by neutrino irradiation from the massive neutron star. Low $Y_e$ implies that it contains neutron-rich matter with $Y_e\lesssim 0.2$, which contributes to enhancing the opacity through the nucleosynthesis of lanthanide elements. “Medium $Y_e$” and “high $Y_e$” imply that it does not contain such neutron-rich matter because $Y_e\gtrsim 0.25$ and $Y_e\gtrsim 0.35$, respectively. The filled (purple) circle and neighboring small (orange) ellipsoids in the central region denote a massive neutron star and accretion torus surrounding it. We note that the low-$Y_e$ component has a high average expansion velocity of ${\overline{v}}_{\mathrm{ej}}\sim 0.2c$, while the medium and high components have slower velocity, $0.1–0.2c$. Note that the gravitational-wave observation indicates that we observe the merger remnant of GW170817 along the direction of $\theta \le 28°$ from the rotation axis.