Angular Energy Distribution of Collapsar-Jets

Abstract

Collapsars are fast-spinning, massive stars, whose core collapse liberates an energy, that can be channeled in the form of ultrarelativistic jets. These jets transport the energy from the collapsed core to large distances, where it is dissipated in the form of long-duration gamma-ray bursts. In this paper we study the dynamics of ultrarelativistic jets produced in collapsars. Also we extrapolate our results to infer the angular energy distribution of the produced outflows in the afterglow phase. Our main focus is to look for global energetical properties which can be imprinted by the different structure of different progenitor stars. Thus, we employ a number of pre-supernova, stellar models (with distinct masses and metallicities), and inject in all of them jets with fixed initial conditions. We assume that at the injection nozzle, the jet is mildly relativistic (Lorentz factor $\sim 5$), has a finite half-opening angle ($5^\circ$), and carries a power of $10^{51} $erg s$^{-1}$. These jets arrive intact to the stellar surface and break out of it. A large Lorentz factor region $Γ\simmore 100$ develops well before the jet reaches the surface of the star, in the unshocked part of the beam, located between the injection nozzle and the first recollimation shock. These high values of $Γ$ are possible because the finite opening angle of the jet allows for free expansion towards the radial direction. We find a strong correlation between the angular energy distribution of the jet, after its eruption from the progenitor surface, and the mass of the progenitors. The angular energy distribution of the jets from light progenitor models is steeper than that of the jets injected in more massive progenitor stars. This trend is also imprinted in the angular distribution of isotropic equivalent energy.