Simulation of Core Collapse Supernovae Tony Li Cornell University Shizuka Akiyama Stanford Linear Accelerator Center Kavli Institute for Particle Astrophysics and Cosmology August 14, 2008

Big star go boom Cassiopeia A Source: NASA

Core Collapse Supernovae Occurs in stars greater than ~8 solar masses Stellar core Source: http://cse.ssl.berkeley.edu/bmendez/ay10/2000/cycle/massive.html

Core Collapse Supernovae Animation on this page, show each layer of star down to Fe core (Not to scale) Source: http://commons.wikimedia.org/wiki/Image:Evolved_star_fusion_shells.svg

Core Collapse Supernovae No fusion in iron core – supported against collapse by: Electron degeneracy pressure Thermal pressure …until mass is ~1.4 solar masses (close to Chandrasekhar limit) Gravity becomes the dominant force, and the core implodes

Core Collapse Supernovae Gravity takes over, core collapses Source: http://commons.wikimedia.org/wiki/Image:Core_collapse_scenario.png

Core Collapse Supernovae Center reaches nuclear density, forms proto-neutron star Source: http://commons.wikimedia.org/wiki/Image:Core_collapse_scenario.png

Core Collapse Supernovae Collapsing material “bounces” to form an outward shockwave Source: http://commons.wikimedia.org/wiki/Image:Core_collapse_scenario.png

Core Collapse Supernovae Shock stalls, somehow gets re-energized ? Source: http://commons.wikimedia.org/wiki/Image:Core_collapse_scenario.png

Core Collapse Supernovae Proto-neutron star remains, shock blows away stellar envelope Source: http://commons.wikimedia.org/wiki/Image:Core_collapse_scenario.png

Core Collapse Supernovae Simulations of core-collapse supernovae currently fail to yield explosions for very massive stars Problem: shock stalls within the star, so how does it get re-energized? Conventional explanation relies on neutrino heating, which only produces explosions for small mass stars (~9 solar masses) Effect of strong magnetic fields? Mention: reason to believe important physics missing (neutrino heating works, but not full picture)

Why magnetic fields? Magneto-rotational instability (MRI) Differential rotation + Initial magnetic field = Exponential amplification According to some studies, MRI can potentially beef up the magnetic field to > 1015 G within tens of milliseconds Good motivation to study effect of very strong magnetic fields

Why magnetic fields? Strong magnetic fields: Can drive explosion via magnetic pressure Can account for asymmetries in observed supernovae (jets, counterjets) Aid in angular momentum transport Also motivated by possible observation of magnetars: neutron stars with extreme magnetic fields Source: http://en.wikipedia.org/wiki/Image:Magnetar-3b-450x580.gif

A closer look Point out aspherical features – jetlike (jet + weaker counterjet) – not explained by spherical model Cassiopeia A Source: NASA

The code: COSMOS++ General Relativistic Magnetohydrodynamic (GRMHD) code Massively parallel Set up the grid and all initial conditions Physics code (advection, equations of state) determines time evolution

Limitations Not enough computational power to resolve MRI Neutrino heating not included – simulation ends before neutrinos become important However, simulations in 3D are important: Relatively new Need 3D for asymmetric features (magnetic field, hydrodynamic instabilities)

Computational Mesh Simulation is carried out on a mesh in spherical coordinates 300 zones in , 60 zones in , 120 zones in Mention adding ratio-grid feature in 3D

Computational Mesh Added a 3D ratio grid feature to code – already in place for 2D grids, but now extended to 3D Needed to resolve: Pre-collapse core: radius ~ 1700 km Proto-neutron star: radius ~ 50 km

Initial Model Core modeled as a polytrope – i.e. a self-gravitating sphere of gas Added a routine in the code to numerically solve for the initial density distribution of the core, through the Lane-Emden equation:

Initial Model

Initial Model Rotation profile: used the “j-constant” model Also added to code: option of “v-constant” or rigid rotation models For our purposes, all are very nearly rigid rotation (aka almost constant) Mention adding solid-body and constant v profiles as well, as options, mention being able to change degree of differential rotation with “a” parameter “v-constant” rigid rotation

Initial Model Magnetic field Initial magnetic field calculated from an imaginary current loop inside the stellar core Remind: tilted field inherently a 3D feature, show images of tilted / untilted field, show pole issue/no pole issue figures Source: http://hermital.org/images/CrrntLpMgFlx2.gif

Initial Model Magnetic field Modified program to set up a tilted initial magnetic field Magnetic field calculations are sensitive to coordinate singularities (origin, z-axis) – special steps taken to ensure correct magnetic field Remind: tilted field inherently a 3D feature, show images of tilted / untilted field, show pole issue/no pole issue figures

Remind: tilted field inherently a 3D feature, show images of tilted / untilted field, show pole issue/no pole issue figures

Current and Future Work Still awaiting a full core-collapse simulation with magnetic fields and rotation Possible necessity of running job on a more powerful computer cluster

Summary 3D simulations are important for understanding core collapse supernovae, and especially for studying magnetic field effects Laid groundwork for 3D simulation Implemented spherical ratio mesh in 3D Set up initial density and rotation profiles Implemented tilted magnetic field Awaiting results of a full simulation

Acknowledgments Shizuka Akiyama Stuart Marshall and Ken Zhou Department of Energy Farah Rahbar, Steve Rock, Susan Schultz