Challenges of Modeling Stellar Explosions

Summary

• Focus: efficient simulation of stellar dynamics

• Stars 101:

  • Fuse Hydrogen to Helium

    • Process is very Temperature sensitive

    • Internal Pressure/Temperature pushing against Gravitational collapse

    • More massive stars are hotter, fuse faster

    • Usually in thermal equilibrium

  • Once Hydrogen is used up, fuse Helium into heavier elements until Iron is reached

    • Iron can’t be fused by stars so that’s the end of a star’s life

  • Low mass stars end their lives as white dwarfs

  • High mass stars reach Iron, collapse and undergo collapse, then supernova

  • Most stars are in binary systems and if they interact and transfer mass they can re-energize and ultimately explode in other ways

• Simulation challenges:

  • Physical processes”

    • Hydrodynamics of moving gas (conservation of mass, momentum, energy)

    • Combustion / nuclear reactions (similar to chemical reaction)

    • Self-gravity

    • Radiation/diffusion

    • Magnetic fields

  • Mostly modeled in 1D

  • However, convection and binary interactions, magnetic fields, etc. are 3D

• Modeling conservation laws:

  • Discretize star in space on a grid (regular or adaptively refined)

  • Update state of each cell based on its neighbor

  • Complexity is computing mass/energy fluxes through cell boundaries

  • Mesh parallelized onto a parallel computer

• Time step:

  • Mesh resolution constrained by the speed at which information is transmitted

  • Must be fine enough that information can’t propagate through more than one mesh cell in one time step

    • There are some techniques to get around this…

  • More complex with multi-physics

    • E.g. Reaction + hydrodynamics

    • Reactions change composition + inject energy

    • Change the material that is moving

    • This can destabilize the simulation because the reaction model and hydrodynamics push the simulation in different directions, so they must be kept tightly coupled

    • Approach: modify the time step based on the rate of the reactions

• AMReX astrophysics suite: https://github.com/amrex-astro

  • MAESTROeX: https://amrex-astro.github.io/MAESTROeX: massively parallel low Mach number stellar hydrodynamics code

  • Castro: https://amrex-astro.github.io/Castro: adaptive mesh, astrophysical radiation/MHD/hydrodynamics simulation code

  • Nyx: https://amrex-astro.github.io/Nyx: adaptive mesh, cosmological hydrodynamics simulation code

  • Pynucastro: https://github.com/pynucastro/pynucastro: framework for working with reaction databases

    • Outputs code that simulates known reactions

• Computers

  • OLCF Frontier

    • 9408 nodes

      • 1 AMD CPU (64 cores)

      • 4 AMD GPUs (x2 dies)

    • 1 exaflop

  • Conversion of Castro to GPUs started in 2018

    • Moved from Fortran to C++ (preferred by GPU software stacks) since 2020

    • Move all data to GPU and do all computation there

    • CPU not used except for IO

    • Achieves good parallelism on large clusters

• Approaches for coupling multi-physics

  • Operator (Strang) Splitting:

    • Alternate reactions and hydro steps

    • Model reactions with old hydro for half time step

    • Then update hydro based on that

    • Then model reaction on updated hydro

  • Simplified-SDC

    • Model hydro advections using reactions from last time step

    • Then recompute the hydro and reactions based on just-computed advection and current time step reaction

    • This does more work per time step but with larger time steps, so less work overall

• Example: Type Ia supernovae

  • No H, strong Si, Ca, Fe lines

  • Very rare, very dim beforehand, brighter than a whole galaxy afterwards

  • Consensus: thermonuclear explosion of carbon/oxygen white dwarf

    • Don’t know what type of white dwarf configuration is exploding

  • Modeling one scenario:

    • Small white dwarf pulling He from a companion

    • He forms a layer, gets very hot, explodes around the star

    • Creates a compression wave from outside in, compresses the C inside, causing it to burn, exploding it

  • Challenge: shock wave fronts are supersonic, normally require small time steps

  • Evaluation:

    • Simplified SDC reproduces the solution from operator splitting with much larger time step, less compute time

  • Now running 3D model of binary system

• Example: massive stars

  • Burn through H -> He -> O ->....-> Iron core that can’t be fused

  • Iron core needs to support to pressure of star’s mass but without the energy output from fusion

  • This pressure can be resisted by electrons but only up to a point

  • At the high temperature inside the iron core, 

    • High energy photons inside the core can break up nuclei into protons, neutrons and neutrinos

    • This leaks out neutrinos, making the core cooler

    • This process is often omitted in simulations

  • Improved operator coupling approach allows simulation of this process, including the core dynamics, without shrinking the time step too much

• Resources

  • Pyro: hydro by example

    • Hydro code design with clarify to teach students about simulation techniques

    • 2D solvers for major physical dynamics

  • Open astrophysics bookshelf: https://github.com/Open-Astrophysics-Bookshelf

  • Virtual Astronomy Software talks: https://vast-seminars.github.io