1. 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

2. Big star go boom
Cassiopeia A
Source: NASA

3. Core Collapse Supernovae
Occurs in stars greater than ~8 solar masses
Stellar core
Source:

4. Core Collapse Supernovae
Animation on this page, show each layer of star down to Fe core
(Not to scale)
Source:

5. 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

6. Core Collapse Supernovae
Gravity takes over, core collapses
Source:

7. Core Collapse Supernovae
Center reaches nuclear density, forms proto-neutron star
Source:

8. Core Collapse Supernovae
Collapsing material “bounces” to form an outward shockwave
Source:

9. Core Collapse Supernovae
Shock stalls, somehow gets re-energized ?
Source:

10. Core Collapse Supernovae
Proto-neutron star remains, shock blows away stellar envelope
Source:

11. 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)

12. 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

13. 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:

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

15. 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

16. 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)

17. 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

18. 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

19. 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:

20. Initial Model

21. 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

22. 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:

23. 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

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

25. 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

26. 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

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