Core-Collapse Supernova
Explosions: The Theoretical
Challenge

Adam Burrows, Josh Dolence,
Jeremiah Murphy, Jason Nordhaus,
Christian Ott, John Bell, Ann
Almgren, Luc Dessart, Eli Livne, Tim
BrandtSupported by:
SciDAC,NSF/PetaApps/JINAMechanisms of Explosion
 Direct Hydrodynamic Mechanism: always fails
 Neutrino-Driven Wind Mechanism, ~1D; Low-mass progenitors
 2D Convection Neutrino-driven (circa 1995-2009)(“SASI” not a mechanism, but a shock instability) Neutrino-Driven Jet/Wind Mechanism, Rapidly rotating AIC of White
Dwarf
 MHD/Rapid Rotation - “Hypernovae”?
 Acoustic Power/Core-oscillation Mechanism? (Aborted if neutrinomechanism works earlier; Weinberg & Quataert ?) 3D “Convection” Neutrino-driven Mechanism

Important Ingredients/Physics
 Progenitor Models (and initial perturbations?) Multi-D Hydrodynamics (3D) Multi-D Neutrino Transport (multi-D) (most challenging aspect) Instabilities - Neutrino-Driven Convection (+ SASI?) Neutrino Processes - Cross sections, emissivities, etc. (at high densities?) General Relativity (May & White; Schwartz; Bruenn et al.; Mueller et al.;
Kotake et al.)
 Rotation!

Density Profiles of Supernova Progenitor Cores
Progenitors (density profiles) Make a Big Difference!
Mechanism? 3D
Neutrino; MHD Jet?

Neutrino-driven Wind Explosions?

Convection-aided,Neutrino-DrivenExplosion?

Neutrino Mechanism Confusion?
 2D explosions compromised by Axial
Sloshing (“SASI”), which is not much inevidence in (non-rotating) 3D simulations
 2D: Groups do not agree qualitatively orquantitatively
 When models explode, explosion is marginaland get very different energies
 Compromised by “ray-by-ray” approximations
employed by some?
 3D not reproducing explosions seen in 2D
 Is something missing?

VULCAN/2D Multi-Group,Multi-Angle,Time-dependent Boltzmann/Hydro (6D)
 Only code with multi-D transport used in supernova theory
 Arbitrary Lagrangian-Eulerian (ALE); remapping
 6 - dimensional (1(time) + 2(space) + 2(angles) + 1(energy-group)) Moving Mesh, Arbitrary Grid; Core motion (kicks?)
 2D multi-group, multi-angle, Sn (~150 angles), time-dependent,
implicit transport - Ott et al. 2009 2D MGFLD, rotating version (quite fast) Poisson gravity solver
 Axially-symmetric; Rotation
 MHD version (“2.5D”) - div B = 0 to machine accuracy; torques
 Flux-conservative; smooth matching to diffusion limit Parallelized in energy groups; almost perfect parallelism
 Livne, Burrows et al. (2004,2007a)
 Burrows et al. (2006,2007b), Ott et al. (2005,2008); Dessart et al.
2005ab,2006

CASTRO - 3D AMR, Multi-Group
Radiation-Hydrodynamic Supernova Code

2nd-order, Eulerian, unsplit, compressible hydroPPM and piecewise-linear methodologies
Multi-grid Poisson solver for gravity
Multi-component advection scheme with reactions
Adaptive Mesh Refinement (AMR) - flow control, memory management, gridgeneration
Block-structured hierarchical grids
Subcycles in time (multiple timestepping - coarse, fine)
Sophisticated synchronization algorithm
BoxLib software infrastructure, with functionality for serial distributed and sharedmemory architectures
1D (cartestian, cylindrical, spherical); 2D (Cartesian, cylindrical); 3D (Cartesian)Transport is a conservative implementation of mixed-frame method of Hubeny &Burrows (2007), with v/c terms and inelastic scattering
Uses scalable linear solvers (e.g., hypre) with high-performance preconditioners thatfeature parallel multi-grid and Krylov-based iterative methods - challenging!
Developers: John Bell, Ann Almgren, Weiqun Zhang, Louis Howell, Adam Burrows,
Jason Nordhaus - LBNL, LLNL, Princeton

8.8-Solar mass Progenitor of Nomoto: Neutrino-driven Wind Explosion
First shownby Kitaura etal. 2006
Burrows,Dessart, &Livne 2007

SN 2009md;
SN 1997D:Low EnergyExplosion
NOTEWINDTHATFOLLOWS

The Generic Neutrino
Heating Mechanism - Multi-D
CrucialThe Pause that Refreshes?

Burrows & Goshy ‘93; Murphy & Burrows 2008
Critical Condition for Neutrino Mechanism:
Dimension-dependent

Explosions!
(No Solution)

Lνe
Critical Curve
Steady-state accretion(Solution). “equivalent” to τ ~ τ conditionMLν vs. Accretion Rate Parameter Studyadv

heatSimple Dynamical model for Shock Radius Evolution:
Intersection of Critical CurveCritical Curve Intersection by Abrupt Change in Accretion Rate?

Simplified Dynamical Model of Shock Evolution with Abrupt Change inAccretion Rate

Comparison of Dynamical Model Results with Hydrodynamic Models

How do the criticalluminosities differ between
1D, 2D, and 3D?

Critical Curve for Neutrino Mechanism: 1D versus 2D
Different mass cores
1D

2D

3D??

1D no; 2D Marginal?
Murphy & Burrows 2008

Critical Curve for Neutrino Mechanism: Dimensional
Dependence??

??

Nordhaus et al. 2010

Critical Curve(s)Mean Radius Evolution in 3D and 2D

Explosions are Earlier in 3D

Mean Radius Evolution in 3D and 2D: 10.8 Solar Mass

Explosions are Earlier in 3DA Tale of Two Instabilities:
Neutrino-driven Convection(Buoyancy) versus the Sanding
Accretion-Shock Instability (“SASI”)

CASTRO - 1D, 2D, 3D
Hydro, plus simple transport Results

2D:2.3“Inverse” Energy
Cascade in 2D BuoyancyDriven
Convection has(anomalously) a
lot of large-scale
power - Often
confused for theSASIComparison - with and without Neutrinos
Neutrino-driven (Buoyancy) Convection - Crucial
SASI generally SubdominantDipolar Amplitudes versus Driving Luminosity

Burrows, et al. 2012; See also Couch & O’Connor 2013SASI is subdominant for all neutrino-driven explosions

Shock Surface Power Spectrum versus Driving Luminosity
SASI tonex100

Buoyant Plumes!

Neutrino-driven Buoyancy, not SASI See also Fernandez et al. 2013)

“When Neutrinos Drive theExplosion, Neutrinos Drive
the Turbulence”
The “SASI” is Less Relevant(or is Sub-Dominant) in
Neutrino-Driven SupernovaeConfusing in 2D Buoyancy-Driven
Convection with the SASI
 In 2D, convection (inverse) cascades to large scales and small sphericalharmonic order (l) The SASI favors small angular orders l (=1 (dipolar), 2)
Confusion Misled by the notion that convection is a small-scale, large-l phenomenon,
some said large-scale, small l, motions couldn’t be convection - small ΔR/R
 However, large ΔR/R convection favors small l, larger scales Computationally limited to 2D, the wrong intuitions were developed Nature is 3D - cascade is to small scales, but SASI is still large scale (as in2D) - not much in evidence in 3D

Character of 3D Turbulence
Qualitatively Different than thatin 2DAmplitudes of Dipolar(“Sloshing”) Modes much
Smallerin 3D

Comparison of 2D with 3D

3DCouch 20122D

Character of 3D turbulence and Explosion VeryDifferent from those in 2D

Buoyancy-driven Bubbles!

Bubble(s) lead (and lead to)
Explosion(Dolence et al. 2013)

L=2.2

Dimensional Dependence of:1) Dwell time in Gain region2) Turbulent Pressures (!)3) Cooling rate interior toGain Radius
4) Unstable Mode order (l)5) Delay to Explosion (!)

Possible Problems with
“Ray-by-ray” PseudoTransport

Ray-by-ray May Exaggerate Angular and Temporal Variation in
Neutrino Fluxes and Heatingo In 2D, the artificial sloshing along the axis (identified by somewith the SASI) might facilitate explosion
o “Ray-by-ray” heating rate correlates too strongly with axial
motiono Real Multi-D transport smoothes angular variation of mattersourceso Needs to be tested (but has not been)Brandt et al. 2011 - Multi-Angle, MultiGroup, 2D Transport

2D (Castro): MGFLD with multi-D Transport (no ray-by-ray)

2D, 1D (CASTRO): MGFLD with multi-DTransport (no ray-by-ray)

Burrows et al. 2013; Dolence et al. 2013

Shock Radii 1D-2D Comparison (Castro): MGFLD with multi-DTransport (no ray-by-ray)
Burrows et al. 2013; Dolence et al. 2013

Neutrino Luminosities - 1D (Castro): MGFLD Transport
Burrows et al. 2013; Dolence et al. 2013

Neutrino Luminosities, Average Energies for 12, 15, 20, 25 Solar
Mass Models- 1D (Castro): MGFLD with Transport
Burrows et al. 2013; Dolence et al. 2013

12 solar mass (WH 2007) 2D (Castro): MGFLD with multi-D Transport

25 solar mass (WH 2007) 2D (Castro): MGFLD with multi-D TransportDifferent EOSsDifferent Equations of State: 1D Examples

Shen versus LS 220: 1D Example

The Effects of Drastic Changes in Neutrino
Opacities - FEEDBACKSGross Changes in Neutrino Opacities: Examples

Drastic Changes in Neutrino Opacities: 1D Examples

Severe Feedbacks in Core-Collapse

Pre-Collapse Perturbations

See also Couch & Ott 2013

Perturbations: 2D (VULCAN) - Spikes - 2008 tests

Perturbations: 2D (VULCAN): l = 2

25 solar mass (WH 2007) 2D (Castro): MGFLD with multi-D Transport, with Shelf (!)

Core-Collapse Theory: A Status Summary “SASI” is not a mechanism Neutrino-driven convection > SASI (when object explodes to yield SN)
 “Ray-by-ray” may be problematic
 3D different from 2D
 Multi-D is Key Enabler of explosion for (almost) all viable mechanisms
 Progenitor structure crucial (initial perturbations? -Density shelfs?)
 Whatever increases the steady-state post-bounce shock radius large isconducive to explosion
 Critical condition Input physics feedbacks can be severe - details?
 Neutrino Mechanism marginal/ambiguous in 2D; Need to go to 3D, butdefault 3D not exploding (Hanke et al. 2013)!?
 Rotation!!
 Is something missing?