How Much Can ${}^{56}$Ni Be Synthesized by Magnetar Model for Long Gamma-ray Bursts and Hypernovae?

Abstract

A rapidly rotating neutron star with strong magnetic fields, called magnetar, is a possible candidate for the central engine of long gamma-ray bursts and hypernovae (HNe). We solve the evolution of a shock wave driven by the wind from magnetar and evaluate the temperature evolution, by which we estimate the amount of ${}^{56}$Ni that produces a bright emission of HNe. We obtain a constraint on the magnetar parameters, namely the poloidal magnetic field strength ($B_p$) and initial angular velocity (${\Omega }_i$), for synthesizing enough ${}^{56}$Ni mass to explain HNe ($M_{{}^{56}\mathrm{Ni}}\gtrsim 0.2M_{\odot }$), i.e. $(B_p/10^{16}\mathrm{G}{)}^{1/2}({\Omega }_i/10^4{\mathrm{rad}\mathrm{s}}^{-1})\gtrsim 0.7$.

6 pages, 4 figures; accepted for publication in MNRAS

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