SFB-TR7

Quarks to Universe in Computational Science (QUCS 2012)
Nara, Japan, December 13–16

Core-Collapse Supernovae
Unravelling the Explosion Mechanism byComputational Models
Hans-Thomas JankaMax Planck Institute for Astrophysics, Garching

For concise reviews of most of what I will say, see
ARNPS 62 (2012) 407, arXiv:1206.2503
andPTEP 2012, 01A309, arXiv:1211.1378

Supernova and neutron star merger research is team effort

Students & postdocs:
Robert Bollig
Thomas Ertl
Tobias Melson
Andreas Voth
Florian Hanke
Lorenz Hüdepohl
Janina von GrooteElse Pllumbi
Tomasz Rembiasz
Andreas Bauswein
Oliver Just
Pedro Montero
Bernhard Müller
Marcella Ugliano
Annop Wongwathanarat

Collaborators:
Ewald Müller
Martin Obergaulinger
Andreas Marek
Stephane Goriely
Nick Stergioulas
Thomas Baumgarte
Georg Raffelt
Victor Utrobin
Shinya Wanajo

Outline●Introduction to core-collapse supernova dynamics●The neutrino-driven mechanism●Status of self-consistent models in two dimensions●The dimension conundrum: How does 3D differ from 2D?

Explosion Mechanism
byNeutrino Heating

Evolved massive starprior to its collapse:
Star develops onion-shellstructure in sequence ofnuclear burning stages
over millions of years

HHeCOSiFe(layers not drawn to scale)Evolved massive starprior to its collapse:
Star develops onion-shellstructure in sequence ofnuclear burning stages
over millions of years

HHeCO

SiFe
(layers not drawn to scale)Gravitational
instability of thestellar core:OStellar iron core
begins collapse
when it reaches
a mass near thecritical
Chandrasekhar
mass limit

SiFeCollapse
becomes
dynamical
because ofelectron capturesand photodisintegration ofFe-group nuclei

Core bounce at
nuclear density:
Inner corebounces when
nuclear matter
density isreached andincompressibility
increases
Shock wave
forms

Shock wave

Proto-neutron star

SiOAccretion
FeShock stagnation:
Shock wave
loses hugeamounts ofenergy by photodisintegration of
Fe-group nuclei.
Shock stagnatesstill inside Fecore

Shock wave

Proto-neutron star

SiAccretion
Fen, pShock “revival”:
Stalled shock
wave mustreceive energy tostart reexpansion
against ram
pressure of
infalling stellarcore.

OAccretionSiν

Shock canreceive freshenergy fromneutrinos!

νn, pShock wave
SiProto-neutron starννExplosion:

O

Shock wave
expands into
outer stellar
layers, heats
and ejects
them.
Creation ofradioactive
nickel inshock-heatedSi-layer.

Shock wave
Proto-neutronstar (PNS)OOννn, p, αν

Nin, pν

Nucleosynthesis
during theexplosion:O
Ni

Shock-heatedand neutrinoheated outflows
are sites forelement
formation

Shock wave

Neutrinodriven “wind”

Oν

νn, p

ν

n, p, α,(Zk,Nk)

νNeutrinos &SN Explosion
Mechanism
Paradigm: Explosions by theneutrino-heating mechanism,supported by hydrodynamic
instabilities in the postshock layer

Rs ~ 200 km●“Neutrino-heating mechanism”: Neutrinos `revive' stalled shock by energy deposition(Colgate & White 1966, Wilson 1982, Bethe & Wilson 1985);●

Convective processes & hydrodynamic instabilities support the heating mechanism(Herant et al. 1992, 1994; Burrows et al. 1995, Janka & Müller 1994, 1996;
Fryer & Warren 2002, 2004; Blondin et al. 2003; Scheck et al. 2004,06,08,
Iwakami et al. 2008, 2009, Ohnishi et al. 2006).

●Neutrino heating:●

Neutrino cooling:See, e.g., Janka, ARNPS 62 (2012) 407

Neutrino Heating and Cooling

Hydrodynamicinstabilities

Supernova Explosion Energy●

Neutrino-energy deposition until onset of explosion makes postshock
layer only marginally unbound: Eexp(texp) ~ 0

Additional energy by
●

●

●

●

Recombination of nucleons to alpha particles and heavy nuclei inpostshock matter (“recombination energy”)
Power of neutrino-driven wind on timescale of 1–2 seconds.
Nuclear burning of shock-heated matter: Only small energy
contribution because 0.1 Msun of C+O —> Si, Ni yields ~0.1*1051 erg

Negative energy contribution from gravitational binding energy of matterahead of shock (and possible energy subtraction by fallback)For a discussion, see Ugliano et al., ApJ 757 (2012) 69, and Scheck et al., A&A 457 (2006) 963.

Scheck et al., A&A 457 (2006) 963

Supernova Explosion Energy

Possible additional evidence forneutrino-driven mechanism:* Neutron star kicks* Large-scale mixing instabilities

Neutron Star Kicks
in 3D SN Explosions
●●●

●

●

Parametric —not fully self-consistent— explosion simulations:
Neutrino core luminosity of proto-NS chosen;
Accretion luminosity calculated with simple (grey) transport scheme

Neutron Star Recoil in 3D Explosion Models(Wongwathanarat, Janka, Müller, ApJL 725 (2010) 106; A&A, submitted, arXiv:1210.8148)

Neutron Star Recoil by"Gravitational Tug-Boat" Mechanism@ t = 1.4 s@ t = 3.3 s(Wongwathanarat, Janka, Müller, ApJL 725 (2010) 106; A&A, to be submitted)

Neutron Star Recoil by"Gravitational Tug-Boat" Mechanism@ t = 1.4 s@ t = 3.3 s(Wongwathanarat, Janka, Müller, ApJL 725 (2010) 106; A&A, to be submitted)

Neutron Star Recoil by"Gravitational Tug-Boat"
Mechanism(Wongwathanarat, Janka, Müller, ApJL 725 (2010) 106;
A&A, submitted, arXiv:1210.8148)

3D Explosions
andSupernova Asymmetries

Mixing Instabilities in 3D SN Models
0.5 s

5*1011 cm

green: carbon
red: oxygen
blue: nickel

350 s

9000 s
7.5*1012 cm(Hammer, Janka, Müller, ApJ 2010)

Asymmetry of Supernova 1987A(Wongwathanarat, Janka,Müller, in preparation)

contours: oxygenblue & green: nickel

1.4 s●11000 sRelatively small convective asymmetries of early explosion can grow into largescale asymmetry of the nickel and heavy-elements distributions!

Supernova
1987A
as aTeenager

Supernova 1987A

Observational consequences and indirect evidence ofneutrino heating and hydrodynamic instabilities at theonset of stellar explosions:●

Neutron star kicks●

Asymmetric mass ejection & large-scale radial mixing(Scheck et al. 2004, 2006; Wongwathanat et al. 2010, 2012)(Kifonidis et al. 2005, Hammer er al. 2010)●

Characteristic neutrino-signal modulations(Marek et al. 2009; Müller et al. 2011, Lund et al. 2011, 2012)●Gravitational-wave signals

But: Is neutrino heating strong
enough to initiate the explosion?
Most sophisticated, self-consistent numericalsimulations of the explosion mechanism in 2D
and 3D are necessary!

Predictions of Signals from SN Corehydrodynamics of stellar plasma

Relativistic gravity(nuclear) EoS

progenitor conditions

neutrino physics

SN explosion models

neutrinosLC, spectra

gravitational waves
explosion energies, remnant masses

nucleosynthesis

explosion asymmetries,
pulsar kicks

General-Relativistic 2D
Supernova Models of theGarching Group(Müller B., PhD Thesis (2009);
Müller et al., ApJS, (2010))

GR hydrodynamics (CoCoNuT)

CFC metric equations

Neutrino transport (VERTEX)Neutrino Reactions in Supernovae
Beta processes:

Neutrino scattering:
Thermal pair
processes:
Neutrino-neutrino
reactions:

The Curse and Challenge of theDimensions
Φ–Boltzmann equation determines neutrino
distribution function in 6D phase space and time

Θϵf (r , θ , ϕ ,Θ , Φ , ϵ ,t )–

θIntegration over 3D momentum space yields
source terms for hydrodynamicsr

ϕQ (r , θ , ϕ , t) , Y˙ e ( r ,θ , ϕ , t)
Solution approach
●

●

●

●

3D hydro + 6D direct discretization of Boltzmann Eq.
(code development by Sumiyoshi & Yamada '12)
3D hydro + two-moment closure of Boltzmann Eq.
(next feasible step to full 3D; cf. Kuroda et al. 2012)
3D hydro + ''ray-by-ray-plus'' variable Eddington factor
method (method used at MPA/Garching)
2D hydro + ''ray-by-ray-plus'' variable Eddington factor
method (method used at MPA/Garching)Required resources●≥ 10–100 PFlops/s (sustained!)●≥ 1–10 Pflops/s, TBytes●≥ 0.1–1 PFlops/s, Tbytes●≥ 0.1–1 Tflops/s, < 1 TByte

"Ray-by-Ray" Approximation for Neutrino
Transport in 2D and 3D Geometry
Solve large numberof sphericaltransport problems
on radial “rays”
associated withangular zones ofpolar coordinate grid
Suggests efficientparallization over the“rays”
radial “ray”

Performance and Portability of ourSupernova Code Prometheus-Vertex

Code has been ported to different
computer platforms by AndreasMarek, High Level Application
Support, Rechenzentrum
Garching (RZG).
Code shows excellent parallel
efficiency, which will be fully
exploited in 3D.

Strong Scaling

Andreas Marek, RZG (2012)

Code employs hybrid
MPI/OpenMP programming
model (collaborativedevelopment with Katharina
Benkert, HLRS).

Computing Requirements for
2D & 3D Supernova ModelingTime-dependent simulations: t ~ 1 second, ~ 106 time steps!
––

CPU-time requirements for one model run:
In 2D with 600 radial zones, 1 degree lateral resolution:––~ 3*1018 Flops, need ~106 processor-core hours.
In 3D with 600 radial zones, 1.5 degrees angular resolution:–––~ 3*1020 Flops, need ~108 processor-core hours.

Explosion Mechanism:
Most Sophisticated CurrentModels

Relativistic 2D CCSN Explosion Models
8.8 Msun

8.1 Msun

9.6 Msun

11.2 Msun

15 Msun27 MsunradiusNorth

Color coded:
entropytime after bounceSouth

25 MsunBernhard Müller, THJ, etal. (ApJ 756, ApJ 761,
arXiv:1210.6984
Basic confirmation ofprevious explosion models
for 11.2 and 15 Msun stars byMarek & THJ (2009)

Relativistic 2D CCSN Explosion Models"Diagnostic energy" of explosion

Maximum shock radius

2D explosions for 11.2 and 15 Msun progenitors of Woosley et al. (2002, 1995)

Suwa et al., arXiv:1206.6101

2D explosions for 13 Msun progenitor of Nomoto & Hashimoto (1988)

Suwa et al. (PASJ 62 (2010) L49

Support for 2D CCSN Explosion Models

Support for 2D CCSN Explosion Models
2D explosions for 12, 15, 20, 25 Msun progenitors of Woosley & Heger (2007)

Bruenn et al., arXiv:1212.1747

2D SN Explosion Models●●Basic confirmation of the neutrino-driven mechanism
Confirm reduction of the critical neutrino luminosity that enables an
explosion in self-consistent 2D treatments compared to 1D

However, many aspects are different:●

Different codes, EoS treatment, neutrino transport and reactions●

Different progenitor sets●

Different explosion energies

Comparisons are urgently needed!

One more caveat:
2D explosions depend on the employedneutron-star equation of stateNeutron Star Equations of State
Neutron star EoS is crucial ingredient but incompletely known!

(Source: F. Weber)Neutron Star Equations of State●●●Lattimer & Prakash, Phys. Rep. 442 (2007)

Collapse and bounce
show dependences on
the EoS properties
below and aroundnuclear saturation
density ρ0SN explosion andprotoneutron starcooling are sensitive tothe high-density EoS
above ρ0 through thecompactness of the
proto-neutron star
Neutrino signal
contains information
about the nuclear EoS!

2D Explosions of 11.2 Msunstar : Test of EoS Influence●

Simulations for 3 different nuclear EoSs:–Lattimer & Swesty (L&S), Hillebrandt & Wolff(H&W), Shen et al.
●●Neutron-star radii“Softer” (L&S) EoS and thus more compact PNS
leads to earlier explosion.
Reasons: more neutrino heating, more violent
convective activity.

–Shock radii–Explosion energy(Andreas Marek 2010, unpublished)2D Explosions of 11.2 Msunstar : Test of EoS Influence

L&S EoS, t ~ 400 ms p.b.

Shen EoS,t ~ 470 ms p.b.

H&W EoS, t ~ 460 ms p.b.

(Andreas Marek 2010,unpublished)Support for 2D CCSN Explosion Models
Suwa et al. (2012) also found that 2D explosions for 11.2 and 15 Msun progenitorsof Woosley et al. (2002, 1995) depend on the employed nuclear EoS.

Suwa et al., arXiv:1206.6101

Problems & Challenges
●

●

●

●

●

2D explosions seem to be “marginal”, at least for some progenitor
models and in some (the most?) sophisticated simulations.
Nature is three dimensional, but 2D models impose the constraint ofaxisymmetry on the flow!
Turbulent cascade in 3D transports energy from large to small scales,
which is opposite to 2D.
Is 3D turbulence more supportive to an explosion?
Is the third dimension the key to the neutrino mechanism?
3D models are needed to confirm explosion mechanism suggested by
2D simulations!

3D vs. 2D Differences:The Dimension Conundrum

2D-3D Differences in Parametric
Explosion Models●Nordhaus et al. (ApJ 720 (2010) 694) performed 2D & 3D simulations with simple
neutrino- heating and cooling terms (no neutrino transport but lightbulb) and found
15‒25% improvement in 3D for 15 Msun progenitor star
(ApJ 720 (2010) 694)

2D-3D Differences in Parametric
Explosion Models●F. Hanke (Diploma Thesis, MPA, 2010) in agreement with L. Scheck (PhD Thesis,MPA, 2007) could not confirm the findings by Nordhaus et al. (2010) ! 2D and 3D
simulations for 11.2 Msun and 15 Msun progenitors are very similar but results
depend on numerical grid resolution: 2D with higher resolution explodes easier,
3D shows opposite trend!

Hanke et al., ApJ 755 (2012) 138,
arXiv:1108.4355

2D & 3D slices for 11.2 Msun model, L = 1.0*1052 erg/s

2D-3D Differences in ParametricExplosion Models●F. Hanke (Diploma Thesis, MPA, 2010) in agreement with L. Scheck (PhD Thesis,MPA, 2007) could not confirm the findings by Nordhaus et al. (2010) ! 2D and 3D
simulations for 11.2 Msun and 15 Msun progenitors are very similar but results
depend on numerical grid resolution: 2D with higher resolution explodes easier,
3D shows opposite trend!

Hanke et al., ApJ 755 (2012) 138,
arXiv:1108.4355

2D & 3D slices for 11.2 Msun model, L = 1.0*1052 erg/s

2D-3D Differences
Average entropy of gas in gain layer
is not good diagnostic quantity forproximity to explosionNordhaus et al., ApJ 720 (2010) 694

Hanke et al., ApJ 755 (2012) 138,
arXiv:1108.4355

Growing "Diversity" of 3D Results
●

●

●

●

●

Dolence et al. (arXiv:1210.5241) find much smaller 2D/3D difference of
critical luminosity but still somewhat earlier explosion in 3D. Confirm thatentropy does not indicate readiness to explosion and deny importance ofSASI in 3D. Is longer dwell time of mass in gain layer cause for result?
Takiwaki et al. (ApJ 749:98, 2012) obtain explosion for an 11.2 Msun
progenitor in 3D later than in 2D. See differences in convection inside theproto-NS and slightly faster 3D explosions with higher resolution.
Couch (arXiv:1212.0010) finds also faster explosions in 2D than in 3D
and somewhat higher critical luminosity in 3D ! But critical luminosity
increases in 2D with higher resolution, but no high-resolution 3D case!
Ott et al. (arXiv:1210.6674) reject relevance of SASI in 3D but diagnose
dominance of neutrino-driven convection. Yet, they confess that result
may be affected by large perturbations associated with cartesian grid.
Kuroda et al. (ApJ 755: 11, 2012) confirm relevance of general relativistic
gravity in 3D, supporting previous results in 1D and 2D; however, nocomparison of 2D vs. 3D was made.

Growing "Diversity" of 3D Results●

These results do not yield a clear picture of 3D effects.

But:
●

●

●

●

The simulations were performed with different grids (cartesian+AMR,polar), different codes (CASTRO, ZEUS, FLASH, Cactus,
Prometheus), and different treatments of input physics for EOS andneutrinos, some with simplified, not fully self-consistent set-ups.
Resolution differences are difficult to assess and are likely to strongly
depend on spatial region and coordinate direction.
Partially compensating effects of opposite influence might beresponsible for the seemingly conflicting results.
Convergence tests with much higher resolution and detailed code
comparisons for “clean”, well defined problems are urgently needed,
but both will be ambitious!

A Comment on SASI in SN Cores
●

●

●

●

●

●

SASI growth is well understood, analytically, numerically, andexperimentally (see SWASI analog).
SASI triggers convection and SASI amplitudes saturate by parasitic
instabilities
Neutrino-driven convection affects SASI, whether supportive (bypumping energy) or suppressive (by destroying mode coherence) ispresently not clear.
SASI grows preferentially in fast accretion flows, in which neutrinodriven convection is hampered (tadv/tconv < 3 ===> growth ofneutrino-driven convection is suppressed; Foglizzo et al. ApJ 2006).
Dominance of SASI or convection is likely to depend on progenitor
and phase of post-bounce evolution.
SASI might play important role in 3D despite potentially smaller
amplitude. What is role of spiral SASI in rotating stellar cores?

Laboratory Astrophysics"SWASI" Instability as an analogue of SASI in the supernova core
Foglizzo et al., PRL 108 (2012) 051103

Constraint of experiment:
No convective activity

Summary●●

Modelling of SN explosion mechanism has made considerable
progress in 1D and multi-D.
2D relativistic models yield explosions for “soft” EoSs. Explosion
energy tends to be on low side (except, maybe, recent models byBruenn et al., arXiv:1212.1747).

●

●

●

●

3D modeling has only begun. No clear picture of 3D effects yet.
3D SN modeling is extremely challenging and variety of approaches
for neutrino transport and hydrodynamics/grid choices will be andneed to be used.
Numerical effects (and artifacts) and resolution dependencies in 2D
and 3D models must still be understood.
Bigger computations on faster computers are indispensable, buthigher complexity of highly-coupled multi-component problem will
demand special care and quality control.