$R$-process $\beta$-decay neutrino flux from binary neutron star mergers and collapsars

This study investigates the antineutrinos production by $\beta$-decay of $r$-process nuclei in two astrophysical sites that are capable of producing gamma-ray bursts (GRBs): binary neutron star mergers (BNSMs) and collapsars, which are promising sites for heavy element nucleosynthesis. We employ a simplified method to compute the $\beta$-decay ${\overline{\nu }}_e$ energy spectrum and consider a number of different representative thermodynamic trajectories for $r$-process simulations, each with four sets of $Y_e$ distribution. The time evolution of the ${\overline{\nu }}_e$ spectrum is derived for both the dynamical ejecta and the disk wind for BNSMs and collapsar outflow, based on approximated mass outflow rates. Our results show that the ${\overline{\nu }}_e$ has an average energy of approximately 3 to 9 MeV, with a high energy tail of up to 20 MeV. The ${\overline{\nu }}_e$ flux evolution is primarily determined by the outflow duration, and can thus remain large for $\mathcal{O}(10)\mathrm{s}$ and $\mathcal{O}(100)\mathrm{s}$ for BNSMs and collapsars, respectively. For a single merger or collapsar at 40 Mpc, the ${\overline{\nu }}_e$ flux is $\mathcal{O}(10-100){\mathrm{cm}}^{-2}{\mathrm{s}}^{-1}$, indicating a possible detection horizon up to 0.1–1 Mpc for Hyper-Kamiokande. We also estimate their contributions to the diffuse ${\overline{\nu }}_e$ background, and find that both sources should only contribute subdominantly to the diffuse background when compared to that expected from core-collapse supernovae.

Figure 1

Nuclear abundance, $Y(A)$ as a function of mass number $A$ at 1 Gyr for four different sets of $Y_e$ distributions with central value $Y_{e,c}=0.15$, 0.25, 0.35, and 0.45 described in the main text. The left, middle, and right panels show results obtained using trajectories with expansion dynamical timescale $\tau =0.2\mathrm{ms}$, $\tau =2\mathrm{ms}$ and $\tau =20\mathrm{ms}$, entropy $s=1$ $k_B$, $s=20$ $k_B$, and $s=15$ $k_B$ per nucleon, which are named as Case A, B, and C in the text, respectively. Also shown are the rescaled solar $r$-process abundances (black dots).

Figure 2

The $r$-process ${\overline{\nu }}_e$ energy spectrum ${\mathrm{\Phi }}_{{\overline{\nu }}_e}$ (top row), the time evolution of the ${\overline{\nu }}_e$ flux, $F_{{\overline{\nu }}_e}$ (middle row), and the time evolution of the ${\overline{\nu }}_e$ average energy, $⟨E_{{\overline{\nu }}_e}⟩$ (bottom row), from the model of BNSM-dyn. A (left column), BNSM-dyn. B (middle column), and BNSM-disk (right column), respectively. The ${\overline{\nu }}_e$ energy spectra shown in the top panels are taken at 0.03 s, 0.03 s, and 1.0 s, approximately at when the corresponding fluxes are near their peak values. Different lines in each panel represent cases with different $Y_{e,c}$ values of 0.15, 0.25, 0.35, and 0.45, whose $r$-process abundances are shown in Fig. 1. In the right middle panel, the BNSM-disk wind mass outflow rate is shown by the gray dashed-dotted line.

Figure 3

The $r$-process ${\overline{\nu }}_e$ energy spectrum ${\mathrm{\Phi }}_{{\overline{\nu }}_e}$ (left panel), the time evolution of the ${\overline{\nu }}_e$ flux, $F_{{\overline{\nu }}_e}$ (middle panel), and the time evolution of the ${\overline{\nu }}_e$ average energy, $⟨E_{{\overline{\nu }}_e}⟩$ (right panel) from the collapsar outflow model. The ${\overline{\nu }}_e$ energy spectrum is taken at 12.0 s. In the middle panel, the mass outflow rate is shown by the gray dashed-dotted line.

Figure 4

The adopted event rate per comoving volume $R(z)$ as a function of redshift $z$ for BNSM (the $\mathrm{CC}15\alpha 5$ model in [81], red dash-dotted line), CCSNe [83] (black solid line), and collapsars (blue shaded area). For the collapsar rate, we take the LGRB rate [82] (blue dash line) as the lower limit.

Figure 5

Diffuse $r$-process ${\beta }^{-}$-decay neutrino flux from BNSM (red dash-dotted line) and collapsars (blue shaded area). Also shown are the DSNB flux and diffuse thermal BNSM ${\overline{\nu }}_e$ flux (black solid line and black dash line) for comparison. The range of the collapsar flux is associated with the assumed uncertain event rate shown in Fig. 4. For the BNSM flux, it includes both the contribution from the dynamical ejecta (model BNSM-dyn. A) and the disk wind (model BNSM-disk). We use the $Y_e$ distribution with central value of $Y_{e,c}=0.25$ for both the BNSM and collapsar cases.

Figure 6

The comparison of the experimentally measured $\beta$-decay (normalized) spectrum for isotopes of Y, Ag, Ba, Dy, Au, U (crosses) with those computed based on the approximated formula Eq. (a1), which assumes ground state to ground state transition only. The solid (dashed) lines assume $P=1.0$ ($P=0.9$), where $P$ is an effective parameter taking into account energy loss to $\gamma$-ray emission from the decay to the excited state of the daughter nucleus.

Figure 7

Comparison of the time evolution of thermal ${\overline{\nu }}_e$ flux (black solid line) computed based on the model sym-n1-a6 from Ref [76] with the $r$-process ${\overline{\nu }}_e$ emitted by dynamical ejecta (red solid line) and disk outflow (blue solid line) with $Y_{e,c}=0.25$ evaluated in the main text.

Figure 8

The ${\overline{\nu }}_e$ emission energy spectrum $d{N}_{{\overline{\nu }}_e}/d{E}_{{\overline{\nu }}_e}$ from a single event used for the calculation of the diffuse flux for all the considered models.