From Choked to Successful: The Role of Black Hole Spin in Collapsar Jet Breakout
Long gamma-ray bursts (LGRBs) are believed to originate from the core collapse of massive Wolf-Rayet (WR) stars, leading to the formation of a spinning black hole that powers a relativistic jet. The prompt emission is produced once the jet emerges from the stellar envelope. We perform 2D axisymmetric RHD simulations using the PLUTO code to model semi-self-consistent, accretion-powered jets launched by Kerr black holes. For the two progenitor models, we adopt black hole masses of $4 M_{\odot}$ and $5 M_{\odot}$ corresponding to WR stars of $10 M_{\odot}$ and $25 M_{\odot}$, respectively. Unlike previous studies, our simulations employ continuous jet injection, with the injected power linked to black hole spin and accretion through an empirical relation motivated by GRMHD simulations, enabling a controlled exploration of jet energetics over $10^{48}$-$10^{52}\,\mathrm{erg\,s^{-1}}$. We investigate jet breakout for WR progenitors of $10\,M_{\odot}$ and $25\,M_{\odot}$ and identify a critical spin threshold: jets are choked for $a \leq 0.001$ and successfully break out for $a > 0.001$. The breakout time ($t_B$) shows a correlation with jet luminosity ($L_{\rm jet}$) and spin ($a$), revealing three regimes: Newtonian ($a \lesssim 0.03$), relativistic ($a \gtrsim 0.3$), and intermediate. A dichotomy is observed in jet head velocity at breakout, with $β_h \gtrsim 0.8$ for high-spin and $β_h \sim 0.35$-$0.8$ for lower spins. In the Newtonian regime, simulations yield $t_B \propto L_{\rm jet}^{-0.48}$, steeper than analytical predictions, with systematically longer breakout times indicating modified jet-head scaling. In the relativistic regime, calibrated analytical models show improved agreement, with simulations indicating efficient jet propagation.