Computational astrophysics The explosion mechanism of massive Roger Käppeli Outline

● Introduction

– A brief introduction of the problem

● Physical model, numerical & computational aspects

– Physics ingredients & mathematical model

● Simulation of magneto-rotational core-collapse

– MHD CCSN mechanism – Magnetic field amplification, formation and driving mechanism of bipolar outflow – Explosion energy, ejected mass and its composition

● Conclusion Outline

● Introduction

– A brief introduction of the problem

● Physical model, numerical & computational aspects

– Physics ingredients & mathematical model

● Simulation of magneto-rotational core-collapse

– MHD CCSN mechanism – Magnetic field amplification, formation and driving mechanism of bipolar outflow – Explosion energy, ejected mass and its composition

● Conclusion i) Introduction Stellar life cycle Evolution as a function of mass

09.10.14 Roger Käppeli, CSE Case Studies, ETHZ 4 i) Introduction Stellar life cycle Evolution as a function of mass

09.10.14 Roger Käppeli, CSE Case Studies, ETHZ 5 i) Introduction Stellar life cycle Evolution as a function of mass

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09.10.14 Roger Käppeli, CSE Case Studies, ETHZ 7 i) Introduction Supernovae classification

● Taxonomical/Morphological approach Like botanists and zoologists, find observable characteristics that eventually provide a deeper physical understanding. However, not all necessarily meaning full...

Tarutto 2003 09.10.14 Roger Käppeli, CSE Case Studies, ETHZ 8 i) Introduction Core-collapse

● Huge energy scales SN1987A – ~1e+53 erg neutrinos – ~1e+51 erg mechanical – ~1e+48 erg elm – ~1e+41 erg visible elm

● Observables – Elm – Neutrinos After Before – Gravitational waves Neutrino & GW astronomy!!!

09.10.14 Roger Käppeli, CSE Case Studies, ETHZ 9 SN1987A in the Large Magellanic Cloud (a nearby ) ~ 163'000 light-years away! i) Introduction Core-collapse supernova

● General idea: – Implosion of iron core of massive at the end of thermonuclear evolution – Explosion powered by gravitational binding energy of forming compact remnant:

Mass of remnant Radius of remnant

GRAVITY BOMB!

09.10.14 Roger Käppeli, CSE Case Studies, ETHZ 10 i) Introduction Conditions at onset of collapse

H Evolved massive star He prior to collapse C Onion-like structure O due to nuclear burning stages E.g.: Mass ~ Age ~ Si 09.10.14 Size ~ Roger Käppeli, CSE Case Studies, ETHZ 11 Shells not at scale! Fe i) Introduction Conditions at onset of collapse

H Evolved massive star He prior to collapse C Onion-like structure O due to nuclear burning stages ZOOM E.g.: Mass ~ Age ~ Si 09.10.14 Size ~ Roger Käppeli, CSE Case Studies, ETHZ 12 Shells not at scale! Fe i) Introduction Conditions at onset of collapse Ten thousand tons per cubic centimeter!!! Core made of ashes Si from Silicone burning... Mainly iron group nuclei Fe

IRON CORE

Iron core stabilized against by relativistic and degenerate electrons

09.10.14 Roger Käppeli, CSE Case Studies, ETHZ 13 Electron Ion Photon pressure i) Introduction Conditions at onset of collapse Ten thousand tons per cubic centimeter!!! Core made of ashes Si from Silicone burning... Mainly iron group nuclei Fe

IRON CORE

Iron core stabilized against gravity by relativistic and degenerate electrons UPPER STABILITY LIMIT 09.10.14 Roger Käppeli, CSECHANDRASEKHAR Case Studies, ETHZ MASS 14 Electron Ion Photon pressure i) Introduction Collapse Iron core collapse due: Si Mass grows due to accreting Si 1 burning ashes ultimately reaching Fe

Electron captures reduce 2 lepton number and neutrinos escape freely

Pressure reduced due to 3 endothermic photo-disintegration of nuclei by energetic photons

09.10.14 Roger Käppeli, CSE Case Studies, ETHZ 17 i) Introduction Collapse: trapping Neutrino trapping: Si

Fe The outward “diffusion speed” equals or is less than the infall speed

The collapse proceeds adiabatically

Neutrinos as still copiously produced and a large fraction09.10.14 of the liberated gravitationalRoger binding Käppeli, energy CSE Case is Studies, ETHZ 18 accumulated in the neutrinos i) Introduction Bounce At densities exceeding the nuclei phase transition into nucleons Si that at such high Fe densities experience strong nuclear repulsion

This halts and reverses the collapse: bounce!

09.10.14This happens within less thanRoger a millisecond!!! Käppeli, CSE Case Studies, ETHZ 19 i) Introduction Shock i) Introduction Shock i) Introduction Shock stalling i) Introduction Shock “revival” i) Introduction Shock “revival” i) Introduction CCSN Explosion Mechanism?

● Discussed explosion mechanisms:

– “Enhanced” neutrino-driven explosion mechanism Hydro. instabilities: convection, Standing Shock Instabilities (SASI) e.g. Blondin et al. 2003, Blondin & Shaw 2007, Foglizzo et al. 2008, Iwakami et al. 2008, Marek & Janka 2009, Suwa et al. 2010, 2012, Takiwaki et al. 2013, Bruenn et al. 2013... – MHD mechanism Rapid rotation + Magnetic field amplification (Flux compression, winding, MRI, dynamos) e.g. Akiyama et al. 2003, Wilson et al. 2005, Kotake et al. 2006, Burrows et al. 2007, Winteler et al. 2012, ... – Acoustic mechanism Excitation of ProtoNeutron Star (PNS) oscillations by accretion/SASI generating acoustic power to reheat the stalled shock Burrows et al. 2006,2007 – Phase transition induced explosion mechanism Additional compactification of PNS due to phase transition from hadronic matter to quark matter Migdal et al. 1971, … Sagert, Fischer et al. 2009, Fischer et al. 2011, ...

09.10.14 Roger Käppeli, CSE Case Studies, ETHZ 25 Outline

● Introduction

– A brief introduction of the problem

● Physical model, numerical & computational aspects

– Physics ingredients & mathematical model

● Simulation of magneto-rotational core-collapse

– MHD CCSN mechanism – Magnetic field amplification, formation and driving mechanism of bipolar outflow – Explosion energy, ejected mass and its composition

● Conclusion ii) Physical model, numerical & computational aspects The overall challenge

General relativity Hydrodynamics of stellar plasma Progenitor conditions

Neutrino physics & transport

Nuclear EoS

CCSN explosion models

Neutrino signal Nucleosynthesis

Gravitational waves signal Explosion morphology ( kicks!)

Explosion energies & remnant masses

ELM waves signal (light curve & spectra) ii) Physical model, numerical & computational aspects CCSN model Model's ingredients wish list:

1)Multi-D hydro. It's a 3D problem

2)Plasma physics Stars have magnetic fields, e.g. , ... & !

3)Weak interactions Most of the released gravitational binding energy “available” in form of 4)Neutrino transport neutrinos!

5)Nuclear physics Equation of state describing matter at extreme conditions

6)General relativity Very compact and very massive objects!

7)“Accurate” initial conditions

DOABLE DIFFICULT VERY DIFFICULT ii) Physical model, numerical & computational aspects CCSN model: 1D (spherical symm.) Model's ingredients list:

1)Multi-D hydro. It's a 3D problem

2)Plasma physics Stars have magnetic fields, e.g. Sun, ... pulsars & magnetars!

3)Weak interactions Most of the released gravitational binding energy “available” in form of 4)Neutrino transport neutrinos!

5)Nuclear physics Equation of state describing matter at extreme conditions

6)General relativity Very compact and very massive objects!

7)“Accurate” initial conditions

DOABLE NO explosions for DIFFICULT

Thompson et al. 2003, Rampp & Janka 2002, Liebendörfer et al. 2002/2005 VERY DIFFICULT ii) Physical model, numerical & computational aspects CCSN Explosion Mechanism?

● Discussed explosion mechanisms:

– “Enhanced” neutrino-driven explosion mechanism Hydro. instabilities: convection, Standing Accretion Shock Instabilities (SASI) e.g. Blondin et al. 2003, Blondin & Shaw 2007, Foglizzo et al. 2008, Iwakami et al. 2008, Marek & Janka 2009, Suwa et al. 2010, 2012, Takiwaki et al. 2013, Bruenn et al. 2013... – MHD mechanism Rapid rotation + Magnetic field amplification (Flux compression, winding, MRI, dynamos) e.g. Akiyama et al. 2003, Wilson et al. 2005, Kotake et al. 2006, Burrows et al. 2007, Winteler et al. 2012, ... – Acoustic mechanism Excitation of ProtoNeutron Star (PNS) oscillations by accretion/SASI generating acoustic power to reheat the stalled shock Burrows et al. 2006,2007 – Phase transition induced explosion mechanism Additional compactification of PNS due to phase transition from hadronic matter to quark matter Migdal et al. 1971, … Sagert, Fischer et al. 2009, Fischer et al. 2011, ...

09.10.14 Roger Käppeli, CSE Case Studies, ETHZ 30 ii) Physical model, numerical & computational aspects CCSN model: 2D (axisymmetry) Model's ingredients list:

1)Multi-D hydro. It's a 3D problem

2)Plasma physics Stars have magnetic fields, e.g. Sun, ... pulsars & magnetars!

3)Weak interactions Most of the released gravitational binding energy “available” in form of 4)Neutrino transport neutrinos!

5)Nuclear physics Equation of state describing matter at extreme conditions

6)General relativity Very compact and very massive objects!

7)“Accurate” initial conditions

DOABLE Some explosions... DIFFICULT VERY DIFFICULT ii) Physical model, numerical & computational aspects CCSN Explosion Mechanism?

● Discussed explosion mechanisms:

– “Enhanced” neutrino-driven explosion mechanism Hydro. instabilities: convection, Standing Accretion Shock Instabilities (SASI) e.g. Blondin et al. 2003, Blondin & Shaw 2007, Foglizzo et al. 2008, Iwakami et al. 2008, Marek & Janka 2009, Suwa et al. 2010, 2012, Takiwaki et al. 2013, Bruenn et al. 2013... – MHD mechanism Rapid rotation + Magnetic field amplification (Flux compression, winding, MRI, dynamos) e.g. Akiyama et al. 2003, Wilson et al. 2005, Kotake et al. 2006, Burrows et al. 2007, Winteler et al. 2012, ... – Acoustic mechanism Excitation of ProtoNeutron Star (PNS) oscillations by accretion/SASI generating acoustic power to reheat the stalled shock Burrows et al. 2006,2007 – Phase transition induced explosion mechanism Additional compactification of PNS due to phase transition from hadronic matter to quark matter Migdal et al. 1971, … Sagert, Fischer et al. 2009, Fischer et al. 2011, ...

09.10.14 Roger Käppeli, CSE Case Studies, ETHZ 32 ii) Physical model, numerical & computational aspects CCSN model: 3D Model's ingredients list:

1)Multi-D hydro. It's a 3D problem

2)Plasma physics Stars have magnetic fields, e.g. Sun, ... pulsars & magnetars!

3)Weak interactions Most of the released gravitational binding energy “available” in form of 4)Neutrino transport neutrinos!

5)Nuclear physics Equation of state describing matter at extreme conditions

6)General relativity Very compact and very massive objects!

7)“Accurate” initial conditions

DOABLE DIFFICULT VERY DIFFICULT ii) Physical model, numerical & computational aspects CCSN Explosion Mechanism?

● Discussed explosion mechanisms:

– “Enhanced” neutrino-driven explosion mechanism Hydro. instabilities: convection, Standing Accretion Shock Instabilities (SASI) e.g. Blondin et al. 2003, Blondin & Shaw 2007, Foglizzo et al. 2008, Iwakami et al. 2008, Marek & Janka 2009, Suwa et al. 2010, 2012, Takiwaki et al. 2013, Bruenn et al. 2013... – MHD mechanism Rapid rotation + Magnetic field amplification (Flux compression, winding, MRI, dynamos) e.g. Akiyama et al. 2003, Wilson et al. 2005, Kotake et al. 2006, Burrows et al. 2007, Winteler et al. 2012, ... – Acoustic mechanism Excitation of ProtoNeutron Star (PNS) oscillations by accretion/SASI generating acoustic power to reheat the stalled shock Burrows et al. 2006,2007 – Phase transition induced explosion mechanism Additional compactification of PNS due to phase transition from hadronic matter to quark matter Migdal et al. 1971, … Sagert, Fischer et al. 2009, Fischer et al. 2011, ...

09.10.14 Roger Käppeli, CSE Case Studies, ETHZ 34 ii) Physical model, numerical & computational aspects Enhanced-nu-CCSN model 3D Actual model's ingredients list: Assume infinite conductivity 1)Multi-D hydro. Parallel 3D ideal MHD code 2)Plasma physics 3)Weak interactions 4)Neutrino transport IDSA Liebendörfer et al. 2009

5)Nuclear physics EoS e.g. Lattimer & Swesty 1991, 6)General relativity Shen et al. 1998, Hempel et al. 2011 Spherical effective GR potential Marek et al. 2006 7)“Accurate” initial conditions + 2D axisymmetric Newton potential ii) Physical model, numerical & computational aspects The Radiation-MHD equations (2)

Mass

Momentum

Energy

Electron #

Magnetic flux

No monopoles

EoS: ii) Physical model, numerical & computational aspects Solution Algorithm: MHD

● MHD (FISH) Käppeli et al. 2011 – Split hydro. and magnetic variables update – Dimensional splitting: solves eqs in 1D – Uses dim.-split constrained transport for – Well-balanced scheme for hydrostatic equilibrium Preserves discrete HSE exactly by reconstruction in equilibrium variables Käppeli & Mishra, 2014

– Hybrid MPI/OpenMP parallelisation for distributed/shared memory architectures ii) Physical model, numerical & computational aspects Solution Algorithm: Neutrinos

● In principle, should solve the relativistic Boltzmann eq

4-vector 4-momentum Distribution function

e.g. Cercignani & Kremer 2002 Proper time Absorption, emission, scattering in medium

Full transfer NOT feasible in 3D (3+3+1=7 dim. problem!)

● Approximations: t s o

c – Liebendörfer 2005

Parametrisation scheme: only collapse phase l a

n – o Spectral Leakage scheme: only cooling Perego et al. in prep. i t a

t Epstein & Pethick 1981, van Riper & Lattimer 1981, ..., Ruffert et al. 1996, Rosswog & Liebendörfer 2003 u p –

m Isotropic Diffusion Source Approx. (IDSA)

o Liebendörfer et al. 2009 C ii) Physical model, numerical & computational aspects Enhanced-nu-CCSN model 3D

Computations @ By M. Liebendoerfer ii) Physical model, numerical & computational aspects Implementation details

● Directional operator splitting

Write only 1D update routines

● Data rotated so that stencil OPs along contiguous memory direction

● Distributed memory parallelisation with MPI

● Overlap communication/computation with non-blocking communication

● Shared memory parallelisation with OpenMP ii) Physical model, numerical & computational aspects Parallelisation: MPI

● Domain decomposition

Domain

Physical boundary ii) Physical model, numerical & computational aspects Parallelisation: MPI

● Domain decomposition

Physical boundary Artificial boundary ii) Physical model, numerical & computational aspects Parallelisation: MPI

● Domain decomposition

Direction of update Artificial boundary ii) Physical model, numerical & computational aspects Parallelisation: MPI

● Overlapping communication/computation

u_left u u_right !sweep in x-direction !copy data from center to left and right data u_left = u(...) u_right = u(...) !copy data into sending buffer and initiate comm call comm_mpistartall(nx%requests) !perform computation on center call update(u,nx,ny,nz) !wait for communication to complete call comm_waitall(nx%requests)

z !copy received data and perform update on boundary y !left 3 xb call update(u_left,nx_left,ny,nz) x !right call update(u_right,nx_right,ny,nz) solution u at !copy left and right data to center u(...) = u_left Stencil of update u(...) = u_right

empty data ii) Physical model, numerical & computational aspects Parallelisation: MPI

● Overlapping communication/computation

u_left u u_right !sweep in x-direction !copy data from center to left and right data u_left = u(...) u_right = u(...) !copy data into sending buffer and initiate comm call comm_mpistartall(nx%requests) !perform computation on center call update(u,nx,ny,nz) !wait for communication to complete call comm_waitall(nx%requests)

z !copy received data and perform update on boundary y !left 2 xb 3 xb call update(u_left,nx_left,ny,nz) x !right call update(u_right,nx_right,ny,nz) solution u at !copy left and right data to center u(...) = u_left Stencil of update u(...) = u_right

empty data ii) Physical model, numerical & computational aspects Parallelisation: MPI

● Overlapping communication/computation

u_left u u_right !sweep in x-direction !copy data from center to left and right data u_left = u(...) u_right = u(...) !copy data into sending buffer and initiate comm call comm_mpistartall(nx%requests) !perform computation on center call update(u,nx,ny,nz) !wait for communication to complete call comm_waitall(nx%requests)

z !copy received data and perform update on boundary y !left 2 xb 3 xb call update(u_left,nx_left,ny,nz) x !right call update(u_right,nx_right,ny,nz) solution u at !copy left and right data to center u(...) = u_left Stencil of update u(...) = u_right

empty data ii) Physical model, numerical & computational aspects Parallelisation: MPI

● Overlapping communication/computation ii) Physical model, numerical & computational aspects Parallelisation: MPI

● Overlapping communication/computation ii) Physical model, numerical & computational aspects Parallelisation: MPI

● Overlapping communication/computation ii) Physical model, numerical & computational aspects Parallelisation: MPI

● Overlapping communication/computation ii) Physical model, numerical & computational aspects Parallelisation: MPI

● Overlapping communication/computation ii) Physical model, numerical & computational aspects Parallelisation: MPI

● Overlapping communication/computation ii) Physical model, numerical & computational aspects Parallelisation: MPI

● Overlapping communication/computation ii) Physical model, numerical & computational aspects Parallelisation: MPI

● Overlapping communication/computation ii) Physical model, numerical & computational aspects Parallelisation: MPI

● Overlapping communication/computation ii) Physical model, numerical & computational aspects Parallelisation: MPI

● Overlapping communication/computation ii) Physical model, numerical & computational aspects Parallelisation: MPI

● Overlapping communication/computation ii) Physical model, numerical & computational aspects (Strong) Scaling: MPI (2)

FISH+ELEPHANT (Radiation+MHD): 600x600x600 zones

Performed on Cray XT5 @ CSCS ii) Physical model, numerical & computational aspects Parallelisation: MPI+OpenMP

● Overlapping communication/computation

empty data ii) Physical model, numerical & computational aspects Parallelisation: MPI+OpenMP

● Overlapping communication/computation

empty data ii) Physical model, numerical & computational aspects Parallelisation: MPI+OpenMP

● Overlapping communication/computation

empty data ii) Physical model, numerical & computational aspects (Strong) Scaling: MPI+OpenMP (2)

FISH+ELEPHANT (Radiation+MHD): 600x600x600 zones

MPI+OpenMP 12 threads/MPI Pure MPI

Performed on Cray XT5 @ CSCS Outline

● Introduction

– A brief introduction of the problem

● Physical model, numerical & computational aspects

– Physics ingredients & mathematical model

● Simulation of magneto-rotational core-collapse

– MHD CCSN mechanism – Magnetic field amplification, formation and driving mechanism of bipolar outflow – Explosion energy, ejected mass and its composition

● Conclusion iii) Simulation of MHD CCSN MHD-CCSN model Actual model's ingredients list: Assume infinite conductivity 1)Multi-D hydro. Parallel 3D ideal MHD code 2)Plasma physics 3)Weak interactions Spectral leakage scheme 4)Neutrino transport developed by A. Perego Rosswog & Liebendörfer 2003 “Not so bad”... 2D simulations shown that 5)Nuclear physics contribute only 10-25% to explosion energy EoS e.g. Lattimer & Swesty 1991, 6)General relativity Shen et al. 1998, Hempel et al. 2011 Spherical effective GR potential Marek et al. 2006 7)“Accurate” initial conditions + 2D axisymmetric Newton potential iii) Simulation of MHD CCSN The Radiation-MHD equations (2)

Mass

Momentum

Energy

Electron #

Magnetic flux

No monopoles

EoS: iii) Simulation of MHD CCSN Solution Algorithm: MHD

● MHD (FISH) Käppeli et al. 2011 – Split hydro. and magnetic variables update – Dimensional splitting: solves eqs in 1D – Uses dim.-split constrained transport for – Well-balanced scheme for hydrostatic equilibrium Preserves discrete HSE exactly by reconstruction in equilibrium variables Käppeli & Mishra, 2014

– Hybrid MPI/OpenMP parallelisation for distributed/shared memory architectures iii) Simulation of MHD CCSN Solution Algorithm: Neutrinos

● In principle, should solve the relativistic Boltzmann eq

4-vector 4-momentum Distribution function

e.g. Cercignani & Kremer 2002 Proper time Absorption, emission, scattering in medium

Full transfer NOT feasible in 3D (3+3+1=7 dim. problem!)

● Approximations: t s o

c – Liebendörfer 2005

Parametrisation scheme: only collapse phase l a

n – o Spectral Leakage scheme: only cooling Perego et al. in prep. i t a

t Epstein & Pethick 1981, van Riper & Lattimer 1981, ..., Ruffert et al. 1996, Rosswog & Liebendörfer 2003 u p –

m Isotropic Diffusion Source Approx. (IDSA)

o Liebendörfer et al. 2009 C iii) Simulation of MHD CCSN Role of Rotation & Magnetic Field

Pre-collapse Post-collapse Successful ● Rotation (???) Explosion... ● Pulsar ● B (???) Rotation (???) Distribution ! B (???) in Fe core ??? G Taylor et al. 1993 N Kouveliotou et al. 1998 Observations: e.g. A Mereghetti 2008 Thompson et al. 2003 B Donati & Landstreet 2009 ● Observable models: Asymmetries Heger et al. 2005 Wang & Wheeler 2008 Hirschi et al. 2004 & 2005 Kjaer et al. 2010 09.10.14 Roger Käppeli, CSE Case Studies, ETHZ 68 iii) Simulation of MHD CCSN Role of Rotation & Magnetic Field

Pre-collapse Post-collapse Rotation &Successful Magnetic fields present ● Rotation (???) Explosion... ● Pulsar before and after explosion! Magnetar ● B (???) Rotation (???) DistributionInfluence of Rotation & B on explosion??? ! B (???) in Fe core ??? G Taylor et al. 1993 N Kouveliotou et al. 1998 ObservationsIf strong: e.g. effects, is Ait common Mereghetti 2008 Thompson et al. 2003 B Donati & Landstreetor only 2009 (very) rare? ● Observable Stellar evolution models: Asymmetries Heger et al. 2005 Wang & Wheeler 2008 Hirschi et al. 2004 & 2005 Kjaer et al. 2010 09.10.14 Roger Käppeli, CSE Case Studies, ETHZ 69 iii) Simulation of MHD CCSN MHD CCSN Mechanism

● Rotational energy of Proto- (PNS)

Requires fast rotation!

● Idea: Extract “free” energy stored in differential rotation with ● Viscosity Thompson et al. 2005 ● Magnetic Field

09.10.14 Roger Käppeli, CSE Case Studies, ETHZ 70 Typical CCSN explosion energy iii) Simulation of MHD CCSN MHD CCSN Mechanism

● Rotational energy of Proto-Neutron Star (PNS)

“Free” energy in differential rotation?

Requires fast rotation! Angular momentum Appreciable fraction of energy can be ● Idea: Extractextracted “free” by magnetic energy field stored and inmaybe differential rotationtrigger an with explosion● Viscosity Thompson et al. 2005 ● Note: Structure assumed constant Magneticfor the two realisations Field Only approx.!

09.10.14 Roger Käppeli, CSE Case Studies, ETHZ 71 Typical CCSN explosion energy iii) Simulation of MHD CCSN Simulation of MHD CCSN

● Simulation parameters – L&S EoS K=180 MeV

– Rotation laws: 1) Solid body

2) Shellular

Popular in axisym. 3) Cylindrical I

Popular in Japan 4) Cylindrical II

Degree of diff. rotation – Magnetic field: 1) Uniform poloidal 2) Dipole-like poloidal

09.10.14 Roger Käppeli, CSE Case Studies, ETHZ 72 iii) Simulation of MHD CCSN Simulation of MHD CCSN

● Simulation parameters – L&S EoS K=180 MeV

– Rotation laws: 1) Solid body

2) Shellular

Popular in axisym. 3) Cylindrical I

Popular in Japan 4) Cylindrical II

Degree of diff. rotation – Magnetic field: 1) Uniform poloidal 2) Dipole-like poloidal

09.10.14 Roger Käppeli, CSE Case Studies, ETHZ 73 iii) Simulation of MHD CCSN Simulation of MHD CCSN

● Simulation parameters Computations @ – L&S EoS K=180 MeV

– Rotation laws: 1) Solid body

Initial conditions: 2) Shellular

Popular in axisym. 3) Cylindrical I

Popular in Japan 4) Cylindrical II

Degree of diff. rotation – Magnetic field: Constant 1 km 1) Uniform poloidal

resolution! 2) Dipole-like poloidal MOVIE

09.10.14 Roger Käppeli, CSE Case Studies, ETHZ 74 iii) Simulation of MHD CCSN Magnetic field amplification

● Flux compression Factor Works well during collapse... Actually the main amplification

● Winding

With differential rotation, linear growth with time

● Magneto-Rotational Instability (MRI)

With differential rotation, exponential growth with time, VERY small wavelengths... ● Dynamo? 09.10.14 Roger Käppeli, CSE Case Studies, ETHZ 75 iii) Simulation of MHD CCSN

Formation and driving mechanism of bipolar outflow

● Differential rotation winds poloidal magnetic field into toroidal field increasing the magnetic energy and pressure

● Strongly magnetised regions appear along the rotational axis

● Magnetic pressure quickly reaches and exceeds the gas pressure

● Consider the equation of motion

Pressure force Lorentz force 09.10.14 Roger Käppeli,Gravity CSE Case force Studies, ETHZ 76 iii) Simulation of MHD CCSN

Formation and driving mechanism of bipolar outflow

● Differential rotation winds poloidal magnetic field into toroidal field increasing the magnetic energy and pressure

● Strongly magnetised regions appear along the rotational axis

● Magnetic pressure quickly reaches and exceeds the gas pressure

● Consider the equation of motion Angular velocity [rad/s]

Pressure force Lorentz force 09.10.14 Roger Käppeli,Gravity CSE Case force Studies, ETHZ 77 iii) Simulation of MHD CCSN

Formation and driving mechanism of bipolar outflow

● Differential rotation winds poloidal magnetic field into toroidal field increasing the magnetic energy and pressure

● Strongly magnetised regions appear along the rotational axis

● Magnetic pressure quickly reaches and exceeds the gas pressure

● Consider the equation of motion

Pressure force Lorentz force 09.10.14 Roger Käppeli,Gravity CSE Case force Studies, ETHZ 78 iii) Simulation of MHD CCSN

Formation and driving mechanism of bipolar outflow

● Differential rotation winds poloidal magnetic field toroidal field increasing the magnetic energy and pressure

● Strongly magnetised regions appear along the rotational axis

● Magnetic pressure quickly reaches and exceeds the gas pressure

● Consider the equation of motion

Pressure force Lorentz force 09.10.14 Roger Käppeli,Gravity CSE Case force Studies, ETHZ 79 iii) Simulation of MHD CCSN

Formation and driving mechanism of bipolar outflow

● Differential rotation winds poloidal magnetic field toroidal field increasing the magnetic energy and pressure

● Strongly magnetised regions appear along the rotational axis

● Magnetic pressure quickly reaches and exceeds the gas pressure

● Consider the equation of motion

Pressure force Lorentz force 09.10.14 Roger Käppeli,Gravity CSE Case force Studies, ETHZ 80 iii) Simulation of MHD CCSN

Explosion energy, ejected mass and its composition

● Bipolar jets quickly expand & transport energy and stellar material outward against the gravitational attraction of the PNS

● Very neutron rich matter is lifted... r-process?

● Approximately determine explosion energy and ejected mass

Specific total energy

when shock reaches upper boundary of 3D domain 700 x 700 x 1400 km

Still growing! Prompt time ! scale...

09.10.14 Roger Käppeli, CSE Case Studies, ETHZ 81 iii) Simulation of MHD CCSN

Explosion energy, ejected mass and its composition

● Bipolar jets quickly expand & transport energy and stellar material outward against theExtracting gravitational attraction of the PNS “free” rotational ● Very neutron rich energymatter by is fieldlifted... r-process? winding ● Approximately determine explosion energy and ejected mass

VERY neutron rich Specific total energy PNS

when shock reaches upper boundary of 3D domain 700 x 700 x 1400 km

r-process? Still growing! Prompt time ! scale...

09.10.14 Roger Käppeli, CSE Case Studies, ETHZ 82 iii) Simulation of MHD CCSN

Explosion energy, ejected mass and its composition

● Bipolar jets quickly expand & transport energy and stellar material outward against theExtracting gravitational attraction of the PNS “free” rotational ● Very neutron rich energymatter by is fieldlifted... r-process? winding ● Approximately determine explosion energy and ejected mass

VERY neutron rich Specific total energy PNS

when shock reaches upper boundary of 3D domain 700 x 700 x 1400 km

r-process? Still growing! Prompt time ! scale...

09.10.14 Roger Käppeli, CSE Case Studies, ETHZ 83 iii) Simulation of MHD CCSN Composition of the ejecta

● Included tracer particles to track the evolution of thermodynamic conditions in a Lagrangian manner

● Electron fraction is a key input for the nucleosynthesis and strongly depends on the challenging transport ! ! ! Evolve the electron Analytic G

fraction with integrated N expansion I neutrino S outside of the neutrino S E

spheres using approx. C

emission/absorption on O WITH neutrino reactions R nucleons Janka 2001 P - T S

NO neutrino reactions O

Inlcuding neutrino reactions P

!

09.10.14 Roger Käppeli, CSE Case Studies, ETHZin network (Fröhlich et al. 2006)84 ! ! Winteler et al. 2012 iii) Simulation of MHD CCSN Composition of the ejecta

● Included tracer particles to track the evolution of thermodynamic conditions in a Lagrangian manner

● Electron fraction is a key input for the nucleosynthesis and strongly depends on the challenging transport ! ! !

WITH neutrino reactions G N NO neutrino reactions I S S

Including neutrino E

interactions shifts the peak C and broadens the O R

distribution of electron P -

fraction to the right T S O P

!

09.10.14 Roger Käppeli, CSE Case Studies, ETHZ 85 ! ! NO neutrino reactions Winteler et al. 2012 iii) Simulation of MHD CCSN Composition of the ejecta

● Included tracer particles to track the evolution of thermodynamic conditions in a Lagrangian manner

● Electron fraction is a key input for the nucleosynthesis and strongly depends on the challenging transport ! ! !

WITH neutrino reactions G N NO neutrino reactions I S S E

Mass integrated C O

abundances R P - T S O P

!

09.10.14 Roger Käppeli, CSE Case Studies, ETHZ 86 ! ! NO neutrino reactions Winteler et al. 2012 iii) Simulation of MHD CCSN Discussion of MHD-CCSN

● (Too) Fast initial rotation rate? MHD CCSN Stellar evolution with magnetic fields only Heger et al. 2005 rare event Stellar evolution without magnetic fields with special conditions e.g. Heger et al. 2000, Hirschi et al. 2004 Woosley & Heger 2006 ● (Too) much r-process matter ejected? Consistent with Eject of r-process material... large star-to-star But: if all CCSN exploded with the MHD mechanism, scatter of r-process then r-process overproduced by factor abundances at low e.g. Cowan & Sneden 2006 ● (Too) strong initial magnetic field Some stars may have large field strengths... e.g. magnetars Numerical issues... strong magnetic white dwarfs Angular momentum e.g. Wickramasinghe & Ferrario 2000 conservation ● (Very) Short simulation time? Currently working on angular momentum preserving schemes 09.10.14Only 33 ms !!! Roger Käppeli, CSE Case Studies, ETHZ 87 Resolution of MRI... Conclusion

● A brief introduction to the problem of CCSN

● Simulation of CCSN a challenging field for physics/computational science/numerics

● Highly sophisticated 1D models do not explode 2D & ultimately 3D models with comparable sophistication are needed (what is important?)

● New physics?

● MHD mechanism works and performs a strong r- process nucleosynthesis BUT: it s probably not the standard explosion mechanism!

09.10.14 Roger Käppeli, CSE Case Studies, ETHZ 88 The End, Thanks! Early galactic r-process nucleosythesis