numerical simulation of core- collapse supernovaekaroger/content/talks/... · 21.09.2011 r....
TRANSCRIPT
Numerical Simulation of Core-Collapse Supernovae
Roger Käppeli & Albino PeregoDepartment of Physics
Collaborators:Nicolas Vasset
Christian WintelerRuben Cabezon
Matthias LiebendörferThomas RauscherF.-K. Thielemann
John Biddiscombe
21.09.2011 R. Käppeli, CCCS2011, Basel 2
Outline● Core-collapse Supernova
● A quick introduction of the problem
● Numerical models and methods● Physics ingredients & mathematical model● Overview of solution algorithm
● Simulation of magneto-rotational core collapse
● Conclusions
21.09.2011 R. Käppeli, CCCS2011, Basel 3
Outline● Core-collapse Supernova
● A quick introduction of the problem
● Numerical models and methods● Physics ingredients & mathematical model● Overview of solution algorithm
● Simulation of magneto-rotational core collapse
● Conclusions
i) Core-Collapse Supernova Stellar life cycle
i) Core-Collapse Supernova Stellar life cycle
i) Stellar Explosions Stellar life cycle
21.09.2011 R. Käppeli, CCCS2011, Basel 7
Core-collapse supernova
● General idea:●
● Explosion powered by gravitational binding energy of forming compact remnant:
Mass of remnant
Radius of remnantGRAVITY BOMB!
i) Core-Collapse Supernova
21.09.2011 R. Käppeli, CCCS2011, Basel 8
Core-collapse supernova
i) Core-Collapse Supernova
21.09.2011 R. Käppeli, CCCS2011, Basel 9
CCSN Explosion Mechanism?● Discussed explosion mechanisms:
● “Enhanced” neutrino-driven explosion mechanism
Hydro. instabilities: convection, Standing Accretion Shock Instabilities (SASI)
● MHD mechanism
Rapid rotation + Magnetic field amplification (Flux compression, winding, MRI, dynamos)
● Acoustic mechanism
Excitation of ProtoNeutron Star (PNS) oscillations by accretion/SASI generating acoustic power to reheat the stalled shock
● Phase transition induced explosion mechanism
Additional compactification of PNS due to phase transition from hadronic matter to quark matter
Burrows et al. 2006,2007
e.g. Akiyama et al. 2003, Wilson et al. 2005, Kotake et al. 2006, Burrows et al. 2007, ...
e.g. Blondin et al. 2003, Blondin & Shaw 2007, Foglizzo et al. 2008, Iwakami et al. 2008, Marek & Janka 2009, ...
i) Core-Collapse Supernova
Migdal et al. 1971, … Sagert, Fischer et al. 2009
21.09.2011 R. Käppeli, CCCS2011, Basel 10
CCSN Explosion Mechanism?● Discussed explosion mechanisms:
● “Enhanced” neutrino-driven explosion mechanism
Hydro. instabilities: convection, Standing Accretion Shock Instabilities (SASI)
● MHD mechanism
Rapid rotation + Magnetic field amplification (Flux compression, winding, MRI, dynamos)
● Acoustic mechanism
Excitation of ProtoNeutron Star (PNS) oscillations by accretion/SASI generating acoustic power to reheat the stalled shock
● Phase transition induced explosion mechanism
Additional compactification of PNS due to phase transition from hadronic matter to quark matter
Burrows et al. 2006,2007
e.g. Akiyama et al. 2003, Wilson et al. 2005, Kotake et al. 2006, Burrows et al. 2007, ...
e.g. Blondin et al. 2003, Blondin & Shaw 2007, Foglizzo et al. 2008, Iwakami et al. 2008, Marek & Janka 2009, ...
i) Core-Collapse Supernova
Migdal et al. 1971, … Sagert, Fischer et al. 2009
21.09.2011 R. Käppeli, CCCS2011, Basel 11
Outline● Core-collapse Supernova
● A quick introduction of the problem
● Numerical models and methods● Physics ingredients & mathematical model● Overview of solution algorithm
● Simulation of magneto-rotational core collapse
● Conclusions
21.09.2011 R. Käppeli, CCCS2011, Basel 12
CCSN model
1)Multi-D hydro.
2)Plasma physics
3)Weak interactions
4)Neutrino transport
5)Nuclear physics
6)General relativity
7)“Accurate” initial conditions
Model's ingredients wish list:(no explosions generally in 1D, e.g. Thompson et al. (2003), Rampp & Janka (2002),Liebendoerfer et al. (2002/2005))
Stars have magnetic fields, e.g. Sun!
Most of the released gravitational binding energy “available” in form of neutrinos!
Equation of state describing matter at extreme conditions
Very compact and very massive objects!
ii) Numerical models & methods
21.09.2011 R. Käppeli, CCCS2011, Basel 13
MHD CCSN model
Parallel 3D ideal MHD code
Spectral leakage schemedeveloped by A. Perego
EoS Lattimer & Swesty 1991
Spherical effective GRpotential+2D axisymmetric Newtonpotential
Marek et al. 2006
Assume infinite conductivity
1)Multi-D hydro.
2)Plasma physics
3)Weak interactions
4)Neutrino transport
5)Nuclear physics
6)General relativity
7)“Accurate” initial conditions
“Not so bad”... 2D simulations shown thatcontribute only 10-25% to explosion energy
Actual model's ingredients list:
Rosswog & Liebendörfer 2003
ii) Numerical models & methods
21.09.2011 R. Käppeli, CCCS2011, Basel 14
MHD CCSN model
Parallel 3D ideal MHD code
Spectral leakage schemedeveloped by A. Perego
EoS Lattimer & Swesty 1991
Spherical effective GRpotential+2D axisymmetric Newtonpotential
Marek et al. 2006
Assume infinite conductivity
1)Multi-D hydro.
2)Plasma physics
3)Weak interactions
4)Neutrino transport
5)Nuclear physics
6)General relativity
7)“Accurate” initial conditions
“Not so bad”... 2D simulations shown thatcontribute only 10-25% to explosion energy
Actual model's ingredients list:
Rosswog & Liebendörfer 2003
ii) Numerical models & methods
21.09.2011 R. Käppeli, CCCS2011, Basel 15
The Radiation-MHD equations (2)
EoS:
ii) Numerical models & methods
21.09.2011 R. Käppeli, CCCS2011, Basel 16
Solution Algorithm: MHD● MHD (FISH)
● Split hydro. and magnetic variables update● Dimensional splitting: solves eqs in 1D ● Uses dim.-split constrained transport for● Well-balanced scheme for hydrostatic equilibrium
Käppeli et al. 2011
Käppeli et al. (in prep.)
ii) Numerical models & methods
Preserves discrete HSE exactly byreconstruction in equilibrium variables
21.09.2011 R. Käppeli, CCCS2011, Basel 17
MHD CCSN model
Parallel 3D ideal MHD code
Spectral leakage schemedeveloped by A. Perego
EoS Lattimer & Swesty 1991
Spherical effective GRpotential+2D axisymmetric Newtonpotential
Marek et al. 2006
Assume infinite conductivity
1)Multi-D hydro.
2)Plasma physics
3)Weak interactions
4)Neutrino transport
5)Nuclear physics
6)General relativity
7)“Accurate” initial conditions
“Not so bad”... 2D simulations shown thatcontribute only 10-25% to explosion energy
Actual model's ingredients list:
Rosswog & Liebendörfer 2003
ii) Numerical models & methods
21.09.2011 R. Käppeli, CCCS2011, Basel 18
Solution Algorithm: Neutrinos
● In principle, should solve the relativistic Boltzman eq
● Approximations:
● Isotropic Diffusion Source Approx. (IDSA)● Leakage scheme
Liebendörfer et al. 2009
Full transfer NOT feasible in 3D (3+3+1=7 dim. problem!)
ii) Numerical models & methods
ii) Numerical models & methods
ii) Numerical models & methods
ii) Numerical models & methods
ii) Numerical models & methods
21.09.2011 R. Käppeli, CCCS2011, Basel 23
Outline● Core-collapse Supernova
● A quick introduction of the problem
● Numerical models and methods● Physics ingredients & mathematical model● Overview of solution algorithm
● Simulation of magneto-rotational core collapse
● Conclusions
21.09.2011 R. Käppeli, CCCS2011, Basel 24
Role of Rotation & Magnetic Field
Pre-collapse
● Rotation (???)
● B (???)
Post-collapse
● Pulsar Magnetar
BANG!Rotation (???)
B (???)
● ObservableAsymmetries
SuccessfulExplosion...
Distributionin Fe core ???
Heger et al. 2005Hirschi et al. 2004 & 2005
Wang & Wheeler 2008Kjaer et al. 2010
Taylor et al. 1993Kouveliotou et al. 1998
iii) Simulation of MHD CCSN
21.09.2011 R. Käppeli, CCCS2011, Basel 25
Role of Rotation & Magnetic Field
Pre-collapse
● Rotation (???)
● B (???)
Post-collapse
● Pulsar Magnetar
BANG!Rotation (???)
B (???)
● ObservableAsymmetries
SuccessfulExplosion...
Distributionin Fe core ???
Heger et al. 2005Hirschi et al. 2004 & 2005
Wang & Wheeler 2008Kjaer et al. 2010
Taylor et al. 1993Kouveliotou et al. 1998
Rotation & Magnetic fields present before and after explosion
Influence of Rotation & B onexplosion???
If strong effects, is it commonor only (very) rare
iii) Simulation of MHD CCSN
21.09.2011 R. Käppeli, CCCS2011, Basel 26
A simulation example
●
●
●
Computations @
iii) Simulation of MHD CCSN
21.09.2011 R. Käppeli, CCCS2011, Basel 27
A simulation example
●
●
●
iii) Simulation of MHD CCSN
A simulation example
iii) Simulation of MHD CCSN
21.09.2011
MHD CCSN mechanism
iii) Simulation of MHD CCSN
21.09.2011
MHD CCSN mechanism
iii) Simulation of MHD CCSN
MHD CCSN mechanism
iii) Simulation of MHD CCSN
iii) Simulation of MHD CCSN
21.09.2011 R. Käppeli, CCCS2011, Basel 33
Conclusions
● Most MHD CCSN done in 2D axisymmetry...
extending to 3D
● Large initial magnetic field... physical?Realised in nature? But there are magnetars...
● Effective description of neutrinos by leakage scheme
● r-process nucleosynthesis?
See also Mikami et al. 2008, Kuroda & Umeda 2010
21.09.2011 R. Käppeli, CCCS2011, Basel 34
Core-collapse supernova
● Huge energy scales
● ~1e+53 erg neutrinos● ~1e+51 erg mechanical● ~1e+48 erg elm● ~1e+41 erg visible elm
● Observables
● Elm● Neutrinos● Gravitational waves
i) Core-Collapse Supernova
SN1987A
After Before
1 erg = 1e-7 Joule
Total worldwide energy consumption ~ 4.7e+27 erg/y
Sun radiation energy ~ 1.2e+41 erg/y
Elm = ELectroMagnetic
21.09.2011 R. Käppeli, CCCS2011, Basel 35
Well-balanced scheme for HSE● The problem: (in our simulations)
Ability to maintain near hydrostatic equilibrium for a long time!
ii) Numerical models & methods
21.09.2011 R. Käppeli, CCCS2011, Basel 36
MHD CCSN Mechanism
● Rotational energy of Proto-Neutron Star (PNS)
● Idea: Extract “free” energy stored in differential rotation with Magnetic Field
Typical explosion energy
iii) Simulation of MHD CCSN
21.09.2011 R. Käppeli, CCCS2011, Basel 37
MHD CCSN Mechanism
● Rotational energy of Proto-Neutron Star (PNS)
●
iii) Simulation of MHD CCSN
21.09.2011 R. Käppeli, CCCS2011, Basel 38
MHD CCSN Mechanism (2)
● How big must the magnetic field be to make a difference?● Gas pressure:● Magnetic pressure:
● How to amplify the magnetic field?
iii) Simulation of MHD CCSN
21.09.2011 R. Käppeli, CCCS2011, Basel 39
MHD CCSN Mechanism (2)
● How big must the magnetic field be to make a difference?● Gas pressure:● Magnetic pressure:
● How to amplify the magnetic field?
How to amplify the magnetic field?
●Flux compression
●Winding
●Magneto-Rotational Instability (MRI)
●Dynamo?
Works well during collapse!
With differential rotation, linear growth with time
With differential rotation, exponential growth with time, VERY smallwavelengths...
iii) Simulation of MHD CCSN