Nuclear Composition of Magnetized GRB Jets

We investigate the fraction of metal nuclei in the relativistic jets of gamma-ray bursts associated with core-collapse supernovae. We simulate the fallback in jet-induced explosions with two-dimensional relativistic hydrodynamics calculations and the jet acceleration with steady, radial, relativistic magnetohydrodynamics calculations, and derive detail nuclear composition of the jet by postprocessing calculation. We found that if the temperature at the jet launch site is above $4.7\times 10^9$K, quasi-statistical equilibrium (QSE) is established and heavy nuclei are dissociated to light particles such as $^4$He during the acceleration of the jets. The criterion for the survival of metal nuclei is written in terms of the isotropic jet luminosity as $L_{\rm j}^{\rm iso} \lesssim 3.9\times 10^{50}(R_{\rm i}/10^7{\rm cm})^2 (1+\sigma_{\rm i})~{\rm erg~s^{-1}}$, where $R_{\rm i}$ and $\sigma_{\rm i}$ are the initial radius of the jets and the initial magnetization parameter, respectively. If the jet is initially dominated by radiation field (i.e., $\sigma_{\rm i} \ll 1$) and the isotropic luminosity is relatively high ($L_{\rm j}^{\rm iso}\gtrsim 4\times 10^{52}~{\rm erg s^{-1}}$), the metal nuclei cannot survive in the jet. On the other hand, if the jet is mainly accelerated by magnetic field (i.e., $\sigma_{\rm i} \gg1$), metal nuclei initially contained in the jet can survive without serious dissociation even for the case of high luminosity jet. If the jet contains metal nuclei, the dominant nuclei are $^{28}$Si, $^{16}$O, and $^{32}$S and the mean mass number can be $\langle$A$\rangle\sim25$.