Geometric and thermodynamic characterization of binary neutron star accretion discs

Accretion disks formed in binary neutron star mergers play a central role in many astrophysical processes of interest, including the launching of relativistic jets or the ejection of neutron-rich matter hosting heavy element nucleosynthesis. In this work we analyze in detail the properties of accretion disks from 44 ab initio binary neutron star merger simulations for a large set of nuclear equations of state, binary mass ratios, and remnant fates, with the aim of furnishing reliable initial conditions for disk simulations and a comprehensive characterization of their properties. We find that the disks have a significant thermal support, with an aspect ratio decreasing with the mass ratio of the binary from $\sim 0.7$ to 0.3. Even if the disk sample spans a broad range in mass and angular momentum, their ratio is independent from the equation of state and from the mass ratio. This can be traced back to the rotational profile of the disk, characterized by a constant specific angular momentum (as opposed to a Keplerian one) of $3-5\times {10}^{16}{\mathrm{cm}}^2{\mathrm{s}}^{-1}$. The profiles of the entropy per baryon and of the electron fraction depend on the mass ratio of the binary. For more symmetric binaries, they follow a sigmoidal distribution as a function of the rest mass density, for which we provide a detailed description and a fit. The disk properties discussed in this work can be used as a robust set of initial conditions for future long-term simulations of accretion disks from binary neutron star mergers, posing the basis for progress in the quantitative study of the outflow properties.

Figure 1

Isodensity surfaces for three representative simulations taken at $t_{\mathrm{end}}$. Left: disk from a long-lived BNS merger, as obtained from the equal mass, HR simulation with the BLh EOS (without turbulent viscosity). Center: disk from a short-lived BNS merger, as obtained from the equal mass, SR simulation with the LS220 EOS (without turbulent viscosity). Right: disk from a prompt-collapsed BNS merger, as obtained from the SR simulation with SFHo EOS (with turbulent viscosity).

Figure 2

Disk mass (left axis), radial extension, vertical extension, and aspect ratio in percentage (right axis) for a sample of SR simulations in each category. Left panel: long-lived BNS merger obtained from the $q=1$, simulation with the BLh EOS (without turbulent viscosity). Central panel: short-lived BNS merger obtained from the $q=1$ simulation with the LS220 EOS (without turbulent viscosity). Right panel: prompt-collapsed BNS merger obtained from the $q=1.66$ simulation with the SFHo EOS and turbulent viscosity.

Figure 3

Relation between the aspect ratio (top panel) and the half opening angle (bottom panel) with the mass ratio of the binary. Colors represent the EOS while markers label the fate of remnant. Values are taken at the last time step of the highest-resolution simulation available for each BNS model. Errors are estimated as the difference between the two higher resolutions available.

Figure 4

Mass fraction $\varphi$-averaged rest mass density distribution on the $rz$ plane for a $q=1.66$ long-lived BNS merger HR simulation with BLh EOS (without turbulent viscosity). The distribution is taken at the last available time step.

Figure 5

Disc mass $M_{\mathrm{disk}}$ and angular momentum $J_{\mathrm{disk}}$ as defined in Eqs. (1) and (2) and their ratio for each BNS merger model at the highest resolution available in our sample. Values are taken at the end of the simulation. Errors are estimated as the difference between the two higher resolutions available. Colors (markers) represent the EOS (fate of the remnant).

Figure 6

Mass weighted histogram of the angular momentum density and the rest mass density of the disk (top) and of the specific angular momentum (bottom), obtained from the long-lived equal mass merger HR simulation with BLh EOS (without turbulent viscosity). The color scale represents the fraction of $M_{\mathrm{disk}}$ in every bin. When the mass fraction is smaller than ${10}^{-5}$ the bin is gray. Bins related to fluid elements at radii smaller than 10 km are highlighted in light blue.

Figure 7

Specific angular momentum obtained from the linear fit of the angular momentum density as a function of the rest mass density (Eq. (6). Values are taken at $t_{\mathrm{end}}$ and for the simulation with highest resolution for each BNS merger model. Errors are estimated as the difference between the two highest resolutions available. The bottom panel shows the 1 standard deviation relative error on the fitted slope. Colors (markers) represent the EOS (the fate of the remnant).

Figure 8

$\varphi$-averaged flow lines of matter for the long-lived equal mass merger HR simulation with BLh EOS (without turbulent viscosity), taken at $\sim 52\mathrm{ms}$ postmerger. The green line is the disk border. The gray dashed circles represent spherical surfaces of 25, 50, and 100 km radius, on which the azimuthal distributions of $\dot{M}$ displayed in Fig. 10 are computed.

Figure 9

Time evolution of the total accretion/ejection rate across spherical surfaces of fixed coordinate radius $R$. From left to right: long-lived, short-lived, and prompt-collapsed BNS mergers chosen from the simulations sample, i.e., the equal mass merger HR simulation with BLh EOS (without turbulent viscosity), the equal mass merger SR simulation with LS220 EOS (without turbulent viscosity), and the SR simulation with SFHo EOS and $q=1.66$. The last plot on the right shows the total (i.e., time integrated) mass crossing each spherical surface for the three scenarios. The vertical dashed line in the short-lived plot indicates the BH formation time.

Figure 10

Time evolution of the angular distribution of the accretion/ejection rate across spherical surfaces of radii $R=25$, 50, 100 km (from left to right) for the same short-lived simulation of Fig. 9. The last plot on the right shows the total mass crossing each spherical surface at the various angles. The vertical dashed lines indicate the BH formation time. Note that the color coded scale is different with respect to Fig. 9.

Figure 11

Relative difference between the logarithms of the mass-weighted $\varphi$-average rest mass density and the fit discussed in Sec. 3b4, for the equal mass long-lived BNS merger HR simulation with BLh EOS (without turbulent viscosity), at the end of the simulation. The computation of the relative difference has been limited to the region occupied by the disk. Solid, dashed and dotted lines represent, respectively, the quantities $H(r)$, $z_0(r)$, and $z_{*}(r)$ obtained by fitting the parameters of Eq. (8) using Eq. (9).

Figure 12

Histogram of the distribution of the baryon mass vs rest mass density and entropy of the disk for the representative equal mass long-lived BNS merger HR simulation with BLh EOS (without turbulent viscosity), taken at the last available time step. The fit with Eq. (11) is shown using a green dashed line. The purple lines are the density-entropy distributions from the core-collapse supernova (CCSN) simulation discussed in IV at different postbounce time.

Figure 13

Rest mass density and entropy per baryon histogram for the prompt-collapsed BNS merger SR simulation with $q=1.66$ and SFHo EOS, at 11 ms after merger. The fluid elements in the low density ($\sim {10}^9–{10}^{11}\mathrm{g}{\mathrm{cm}}^{-3}$) and low entropy ($⪅5k_{\mathrm{B}}{\text{baryon}}^{-1}$) belong to the tidal component of the disk.

Figure 14

Equilibrium electron fraction for weak reaction in marginally optically thick conditions, i.e., for negligible neutrino fractions, as a function of the temperature and for different rest mass densities ranging between ${10}^{11}\mathrm{g}{\mathrm{cm}}^{-3}$ and ${10}^{13}\mathrm{g}{\mathrm{cm}}^{-3}$. The equilibrium is found by solving ${\mu }_e+{\mu }_p-{\mu }_n=0$ for the BLh EOS.

Figure 15

Mass weighted histograms of the rest mass density and electron fraction of the disk for the same representative simulation of Fig. 12 (top) and for the equal mass long-lived BNS merger SR simulation with BLh EOS (without turbulent viscosity) taken at the end the simulated time (bottom). The fit with Eq. (13) is shown using a green dashed line. The purple lines are the density vs. $Y_{\mathrm{e}}$ distributions from the CCSN simulation discussed in IV at a different postbounce time.

Figure 16

$\alpha$ vs the aspect ratio of the disks. Dotted, dashed, and dash-dotted horizontal lines represent the j const, Papaloizou and Pringle [98], and Keplerian values of $\alpha$.

Figure 17

Parameters obtained from the fit described in Par. 4 of Sec. B [Eq. (7)].

Figure 18

Parameters obtained from the fit described in Par. 4 of Sec. B [Eqs. (9)].