Introduction
The discovery of quasars at high cosmological redshifts strongly supports the idea that supermassive black holes (SMBHs) with masses $M \gtrsim 10^9M_\odot$ exist in the early universe. At the same time, these observations raise questions about how SMBHs could be formed in less than a billion years after the Big Bang, as well as about their growth processes. A possible scenario to explain the origin of SMBHs is provided by the collapse of supermassive stars (SMSs) with masses $\gtrsim 10^{4}M_{\odot}$ to black holes (BHs) following their quasistationary cooling and contraction evolution epochs. These seed BHs could grow through accretion and mergers to become SMBHs. An alternative scenario is the collapse of Population III (Pop III) stars with $M \sim 100-500 M_{\odot}$ at $z \sim 20$. For less massive Pop III stars ($140M_{\odot} \lesssim M \lesssim 260M_{\odot}$), the electron-positron pair instability would cause rapid stellar contraction and oxygen and silicon burning would produce sufficient energy to reverse the collapse and form pair-instability supernovae. However, it is believed that with $M > 260 M_{\odot}$, nuclear burning is not powerful enough to overcome the implosion by the pair instability and the star would collapse to a BH.
Idealized SMSs are objects supported dominantly by radiation pressure $P_r$, which can be well described by a $\Gamma \approx 4/3$ adiabatic index, or an $n = 3$ polytropic equation of state. SMSs are likely to be highly spinning and turbulent viscosity induced by magnetic fields would keep them in uniform rotation. The critical configuration of a SMS at the mass-shedding limit along a quasistationary evolution sequence is set by the onset of a relativistic radial instability, leading to collapse. Previous studies have shown that the SMS remnant is a BH surrounded by a massive, hot accretion torus. The remnant BH has a mass $M_{BH}$ of about $\sim 90\%$ of the initial stellar mass $M$ and spin $a_{BH}/M_{BH}$ $\sim 0.70-0.75$. GRMHD simulations in which the SMS is threaded initially by a dynamically weak dipole magnetic field, either confined or not to the stellar interior, have shown that the above parameters remain basically unchanged. In the magnetized case, however, following the gravitational wave (GW) burst at collapse, the BH-accretion disk remnant gives rise to a magnetically confined jet with an outgoing electromagnetic Poynting luminosity $L_{EM} \sim 10^{52\pm1}\rm erg/s$, consistent with typical GRB luminosities. This feature may explain the recent detection of high redshift GRBs reported from the Burst Alert Telescope (BAT) on Swift. It may indicate that some metal-free Pop III stars could also be the engines that power long GRBs, as they are at the epoch when Pop III stars reached peak formation.
Although numerical calculations obtained from strictly radiation-dominated $n = 3$ SMS models provide promising observational suggestions, the simplification of the model may neither accurately describe a realistic progenitor, nor sufficiently display some physical characteristics during the evolution. For example, SMSs also contain gas pressure $P_g \ll P_r$, which becomes increasingly important as the mass of the star decreases. This importance is reflected in the adiabatic index and polytropic index of the star. For a SMS with $M \sim 10^5M_{\odot}$ the effective adiabatic index is $\Gamma = 1.339$ or $n = 2.95$ while for $M \sim 10^4 M_{\odot}$ these parameters are $\Gamma = 1.345$ or $n = 2.9$. Both the critical configuration at the onset of collapse and the final BH-disk system following collapse are extremely sensitive functions of $\Gamma -4/3 \ll 1$ or $3 - n \ll 1$. On the other hand, if the initial angular momentum is not sufficient prior to stellar contraction, then it is possible that SMSs do not spin-up sufficiently to reach the mass-shedding limit when the radial-instability is triggered. Moreover, if magnetic effects are greatly suppressed, then uniform rotation would not be sustained by turbulent processes during the contraction phase and instead angular momentum would be conserved on each concentric cylindrical shell. As a result, the SMSs would become differentially rotating, even if uniformly rotating initially.
Here, we extend our previous GRMHD calculations of collapsing SMSs described by $\Gamma = 4/3$, $n=3$ polytropes to $\Gamma \gtrsim 4/3$, $n \lesssim 3$ polytropes to treat lower mass models with gas pressure perturbations. We also consider the evolution of SMS models with different initial stellar rotation profiles. Our simulations might be useful for interpreting future coincident detections of GW bursts with electromagnetic (EM) counterpart radiation (multimessenger observations). Multimessenger signatures from the direct collapse of a SMS and the subsequent accretion epoch have not been explored to a great extent. The future detection of GW signals by detectors such as LISA, in coincident with GRBs at very high redshift, would provide evidence for the direct-collapse massive-star model for the seed SMBHs.
Simulations were performed on the Blue Waters supercomputer at UIUC. The Illinois GRMHD code, which implements the BSSN formulation of GR with moving box adaptive mesh refinement, was used for all simulations.
