High-energy neutrino emission from magnetised jets of rapidly rotating protomagnetars

Relativistic jets originating from protomagnetar central engines can lead to long duration gamma-ray bursts (GRBs) and are considered potential sources of ultrahigh-energy cosmic rays and secondary neutrinos. We explore the propagation of such jets through a broad range of progenitors, from stars which have shed their envelopes to supergiants which have not. We use a semi-analytical spindown model for the strongly magnetised and rapidly rotating PNS to investigate the role of central engine properties such as the surface dipole field strength, initial rotation period, and jet opening angle on the interactions and dynamical evolution of the jet-cocoon system. With this model, we determine the properties of the relativistic jet, the mildly-relativistic cocoon, and the collimation shock in terms of system parameters such as the time-dependent jet luminosity, injection angle and density profile of the stellar medium. We also analyse the criteria for a successful jet breakout, the maximum energy that can be deposited into the cocoon by the relativistic jet, and structural stability of the magnetised outflow relative to local instabilities. Lastly, we compute the high-energy neutrino emission as these magnetised outflows burrow through their progenitors. Precursor neutrinos from successful GRB jets are unlikely to be detected by IceCube, which is consistent with the results of previous works. On the other hand, we find high-energy neutrinos may be produced for extended progenitors like blue and red supergiants, and we estimate the detectability of neutrinos with next-generation detectors such as IceCube-Gen2.