Simulating the Magnetorotational Collapse of Supermassive Stars: Incorporating Gas Pressure Perturbations and Different Rotation Profiles

Collapsing supermassive stars (SMSs) with masses $M \gtrsim 10^{4-6}M_\odot$ have long been speculated to be the seeds that can grow and become supermassive black holes (SMBHs). We previously performed GRMHD simulations of marginally stable magnetized $Γ= 4/3$ polytropes uniformly rotating at the mass-shedding limit to model the direct collapse of SMSs. These configurations are supported entirely by thermal radiation pressure and model SMSs with $M \gtrsim 10^{6}M_\odot$. We found that around $90\%$ of the initial stellar mass forms a spinning black hole (BH) surrounded by a massive, hot, magnetized torus, which eventually launches an incipient jet. Here we perform GRMHD simulations of $Γ\gtrsim 4/3$, polytropes to account for the perturbative role of gas pressure in SMSs with $M \lesssim 10^{6}M_\odot$. We also consider different initial stellar rotation profiles. The stars are initially seeded with a dynamically weak dipole magnetic field that is either confined to the stellar interior or extended from its interior into the stellar exterior. We find that the mass of the BH remnant is $90\%-99\%$ of the initial stellar mass, depending sharply on $Γ-4/3$ as well as on the initial stellar rotation profile. After $t\sim 250-550M\approx 1-2\times 10^3(M/10^6M_\odot)$s following the BH formation, a jet is launched and it lasts for $\sim 10^4-10^5(M/10^6M_\odot)$s, consistent with the duration of long gamma-ray bursts. Our results suggest that the Blandford-Znajek mechanism powers the jet. They are also in agreement with our proposed universal model that estimates accretion rates and luminosities that characterize magnetized BH-disk remnant systems that launch a jet. This model helps explain why the outgoing luminosities for vastly different BH-disk formation scenarios all reside within a narrow range ($\sim 10^{52 \pm 1} \rm erg/s$), roughly independent of $M$.