<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>R</mml:mi></mml:math> -process <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>β</mml:mi></mml:math> -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 $\bar\nu_e$ 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 $\bar\nu_e$ 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 $\bar\nu_e$ has an average energy of approximately 3 to 9~MeV, with a high energy tail of up to 20 MeV. The $\bar\nu_e$ flux evolution is primarily determined by the outflow duration, and can thus remain large for $\mathcal{O}(10)$~s and $\mathcal{O}(100)$~s for BNSMs and collapsars, respectively. For a single merger or collapsar at 40~Mpc, the $\bar\nu_e$ flux is $\mathcal{O}(10-100)$~cm$^{-2}$~s$^{-1}$, indicating a possible detection horizon up to $0.1-1$~Mpc for Hyper-Kamiokande. We also estimate their contributions to the diffuse $\bar\nu_e$ background, and find that both sources should only contribute subdominantly to the diffuse background when compared to that expected from core-collapse supernovae.