First minutes of a binary-driven hypernova

We simulate the first minutes of the evolution of a binary-driven hypernova event, with a special focus on the associated accretion processes of supernova ejecta onto the newborn neutron star ($\nu \mathrm{NS}$) and the NS companion. We calculate the rotational evolution of the $\nu \mathrm{NS}$ and the NS under the torques exerted by the accreted matter and the magnetic field. We take into account general relativistic effects through effective models for the NSs binding energy and the specific angular momentum transferred by the accreted matter. We use realistic hypercritical accretion rates obtained from three-dimensional smoothed-particle-hydrodynamics numerical simulations of the binary-driven hypernova event for a variety of orbital periods. We show that the rotation power of the $\nu \mathrm{NS}$ has a unique double-peak structure while that of the NS has a single peak. These peaks are of comparable intensity and can occur very close in time or even simultaneously depending on the orbital period and the initial angular momentum of the stars. We outline the consequences of the above features in the early emission and their consequent observation in long gamma-ray bursts.

Figure 1

SPH simulation of a BDHN I: model “30m1p1eb” of Table 2 in [49]. The binary progenitor is composed of a CO star of $\approx 9M_{\odot }$, produced by a ZAMS star of $30M_{\odot }$, and a $2M_{\odot }$ NS companion. The orbital period is $\approx 6$ minutes. Each frame, from left to right, corresponds to selected increasing times with $t=0\mathrm{s}$ the instant of the SN shock breakout. The upper panel shows the mass density on the equatorial plane and the lower panel the plane orthogonal to the equatorial one. The reference system is rotated and translated to align the $x$ axis with the line joining the binary components. The origin of the reference system is located at the NS companion position. The first frame corresponds to $t=40\mathrm{s}$, and it shows that the particles entering the NS capture region form a tail behind the star. These particles then circularize around the NS, forming a thick disk that is already visible in the second frame at $t=80\mathrm{s}$. Part of the SN ejecta is also accreted by the $\nu \mathrm{NS}$ as is appreciable in the third frame at $t=171\mathrm{s}$. At $t=337\mathrm{s}$ (about one orbital period), a disk structure has been formed around the $\nu \mathrm{NS}$ and the NS companion. This figure has been produced with the SNsplash visualization program [56].

Figure 2

Accretion rate onto the $\nu \mathrm{NS}$ (left) and onto the NS companion (right) as a function of time, obtained from SPH simulations of BDHNe with different orbital periods.

Figure 3

Evolution of the $\nu \mathrm{NS}$ (left panel) and the NS companion (right panel) rotation period starting from a nonrotating star, i.e., $j(0)=0$. The $\nu \mathrm{NS}$ and the NS companion initial mass are $1.8M_{\odot }$ and $2M_{\odot }$, respectively. For both stars the radius is ${10}^6\mathrm{cm}$, the magnetic dipole field strength is $B_{\mathrm{dip}}={10}^{13}\mathrm{G}$, and the quadrupole to dipole strength ratio is varied from 0 (pure dipole) to 1000. The quadrupole field is set in the $m=1$ mode, i.e., $({\theta }_1,{\theta }_2)=(\pi /2,0)$. The plot shows the phases of spinup and spindown of the $\nu \mathrm{NS}$. The spindown phase is enhanced by the presence of the quadrupole component. The black curves correspond to the case of a pure dipole magnetic field.

Figure 4

Evolution with time of $\dot{E}$, given by Eq. (14), for the $\nu \mathrm{NS}$ and the NS companion. We set the $\nu \mathrm{NS}$ initially as nonrotating (i.e., $J(0)=0$), and explore the effects of a nonzero initial value of the NS companion angular momentum. In this example, we have initial values of the NS dimensionless angular momentum from $j(0)=0$ (first curve in blue from bottom to top), to $j(0)=1$ (last curve in orange from top to bottom). Each plot corresponds to a binary with a different orbital period (see also Fig. 2). In this example, for simplicity, we set the same initial mass and magnetic dipole moment for both stars, respectively, $1.8M_{\odot }$, radius $R={10}^6\mathrm{cm}$, and a pure dipole ($\eta =0$) with magnetic field strength $B_{\mathrm{dip}}={10}^{13}\mathrm{G}$.

Figure 5

Time separation between the peak of $\dot{E}$ of the NS companion and the second peak of $\dot{E}$ of the $\nu \mathrm{NS}$ (see Fig. 4).