Simulation Parameters and Results

1. Simulations of Accretion Powered Supernovae in the Progenitors of Gamma Ray Bursts Christopher C. Lindner1,2, Milos Milosavljevic1,3, Rongfeng Shen4, and Pawan Kumar1 1The University of Texas at Austin, USA 2NSF Research Fellow 3Texas Cosmology Center, USA 4University of Toronto, Canada Texas Advanced Computing Center Abstract Observational evidence suggests a link between long duration gamma ray bursts (LGRBs) and Type Ic supernovae. In Milosavljevic et al. 2010, we proposed a potential mechanism for Type Ic supernovae in GRB progenitors powered solely by accretion energy. Here, we present spherically-symmetric hydrodynamic simulations of the long-term accretion of a rotating gamma-ray burst progenitor star, a “collapsar,'' onto the central compact object, which we take to be a black hole. The simulations were carried out with the adaptive mesh refinement code FLASH in one spatial dimension and with rotation, an explicit shear viscosity, and a mixing length theory convection prescription. If an accretion disk forms outside of the black hole, a shockwave will form at the outer edge of the disk, and move outward through the stellar envelope. Energy is carried from the central accretion disk to the stellar envelope via convection. Our simulations track the formation of the accretion shock through its subsequent expansion and breakout through the stellar exterior. We treat the region ~1.5 gravitational radii from the final, ~5 Mblack hole, to beyond the stellar exterior for 100 s. Energy losses through neutrinos and nuclear processes are considered in our calculations. We find that the shock velocity, energy, and unbound mass are sensitive to convective efficiency, effective viscosity, and initial stellar angular momentum. Our simulations show that given the appropriate combinations of stellar and physical parameters, explosions with energies ~5 x 1050 ergs, velocities ~3,000 km s-1, and unbound material masses >5 Mare possible for a 16 Mmain sequence progenitor star. Further work is needed to constrain the values of these parameters and explore likely outcomes for other progenitors. Accretion Powered Supernovae The collapse of the core of a massive star will be followed by a core bounce and possible reinvigoration from neutrino heating. If this mechanism fails to unbind the star, material will fall back onto the central object, which we assume to be a black hole. If some of this material has sufficient angular momentum, it will circularize outside of this black hole. When the first piece of material becomes rotationally supported, infalling material will encounter an angular momentum barrier and form an accretion shock. Inside of this accretion shock, an accretion disk will form and generate heat via viscous dissipation. Much of the energy released in the disk will fall directly in the black hole. However, the negative specific entropy gradient of the system will drive the disk to become convectively unstable. Through convection, this energy can be carried from the accretion disk to the post-shock material. This will invigorate the accretion shock and may ultimately deposit enough energy into the stellar envelope to generate a supernova. Simulation Parameters and Results We performed nine simulations to test the sensitivity of our results to resolution, viscous stress-to-pressure ratio (α), the initial rotation parameter (ξl), convective energy transport efficiency (ξC), and convective mixing efficiency (ξC,mix). The values of the parameters and some of the key results are shown in the table above. We found that capabilities for explosion were most closely tied to the value of our convective efficiency parameter, ξC.. All simulations except for that with the lowest convective efficiency had unbound stellar material by t=100 s. The total masses of unbound material in each simulation are shown above (Munbound). The total mechanical (kinetic + gravitational potential + thermal, Etot) energies along with the kinetic energies Ekinat t=100 s are shown as well. In simulations with favorable parameters, ~5Mof material was unbound by t=100 s, with ~0.5 Bethes of total mechanical energy present in the star. Our simulations included time-relaxed NSE calculates into our model to capture photodisintegration effects and some nuclear fusion. Below, we describe the nucleosynthetic processes in more detail. In the table above, we show the total mass of Fe-group elements present at t=100 s in our simulations. This may be used as an indicator of the lower limit of potential 56Fe production in our models, although this needs to be verified with more accurate nucleosynthesis networks. We find (0.02 – 0.09) M of Fe-group elements are produced. Mass Accretion and Shock Propagation Before the formation of the accretion shock, matter accretes onto the central black hole in a quasi-spherical nearly-unabated accretion. After the formation of the accretion shock at t~20 s, the mass accretion rate quickly declines, and further accretion is determined by accretion disk dynamics. Above, on the left, we show the evolution of the mass of the star and black hole, the mass of material significantly supported by rotation, and the mass accretion rate for Run 1. In the figure on the right, we show the location of the accretion shock (white, solid) and the outer edge of the accretion disk (blue, dashed), and the velocity of the accretion shock for Run 1. After its formation, the accretion shock achieves a velocity ~3,000 km s-1. Nucleosynthesis Above, we show the total mass-weighted abundance of all of the isotopes of each of the most abundant elements carried in our code at (left to right) t = 0,15,25,50 s in Run 1. In the innermost hottest regions of the collapsing star, hydrostatic heavy elements are photodisintegrated into free protons and neutrons. After the formation of the accretion shock, convection carries these lighter elements further out into the stellar envelope where they can be reprocessed into heavier elements once again. Convective mixing also carries heavier elements inwards, where they will be broken down. Thus, we predict well mixed hydrostatic and explosively produced elements to be present in the unbound material. Summary and Conclusions We have conducted a series of hydrodynamic simulations of the viscous post-core-collapse accretion of a rapidly rotating ~14 M Wolf-Rayet(Woosley & Heger 2006) star onto the central black hole. The spherically-symmetric simulations with rotation were carried out for up to 100 s and resolved the radii down to 2.5 x 106 cm where the collapsing stellar material circularizes around the black hole. We included neutrino cooling, nuclear statistical equilibrium, convective mixing length, and Navier-Stokes viscous fluid dynamics calculations. In these simulations, we varied the initial angular momentum profile, convective energy transport and compositional mixing efficiency, and the viscous stress-to-pressure ratio. Initially, the stellar envelope is essentially in free fall, as the initial material near the central black hole does not have enough angular momentum to form a rotationally supported disk. At t~20 s, the first material able to circularize outside of the black hole becomes centrifugally supported. An accretion shock forms and moves outwards. In the innermost regions of the shocked bubble energy and mass transport are now dominated by accretion disk physics. Between the thick disk and the outward moving shock, there is a CDAF region, where energy generated by viscous dissipation may be carried to the post-shock stellar atmosphere. We found that the final energy deposited into the envelope strongly depended on the efficiency of convective energy transport and the viscous stress-to-pressure ratio. These two parameters greatly influence the location of the ADAF/CDAF transition, as we described in Milosavljevicet al. 2010. The point of this transition ultimately determines how much energy may be extracted from viscous processes and be injected into outer layers of the star, possibly contributing to a supernova. Our simulations showed that for favorable values of convective efficiency, the stellar envelope was capable of obtaining positive total mechanical energies (kinetic + internal + gravitational potential) in the range of ~(0.04 - 0.5) Bethes, with shock velocities of ~(2,000 - 5,000) km s-1, and unbound masses of ~(1 - 5) M. We suggest this may be a plausible mechanism for low luminosity Type Ic supernovae, but further study is needed to investigate convective efficiency and the effect of using different stellar progenitors. Acknowledgements The software used in this work was in part developed by the DOE-supported ASC/Alliance Center for Astrophysical Thermonuclear Flashes at the University of Chicago. The authors acknowledge the Texas Advanced Computing Center (TACC) at the University of Texas at Austin for providing high-performance computing resources that have contributed to this research. This material is based upon work supported under a National Science Foundation Graduate Research Fellowship awarded to C. C. L. M. M. acknowledges support from NSF grant AST-0708795 and P. K. acknowledges support from NSF grant AST-0909110. Background image: Supernova remnant N49, courtesy chandra.harvard.edu REFERENCES: Milosavljevic, Milos, Lindner, Christopher C., Shen, Rongfeng, & Kumar, P. 2011, Submitted to ApJ Woosley, S. E., & Heger, A. 2006, ApJ, 637, 914