Introduction to core-collapse
supernova simulation
Roger Käppeli
Department of Physics
Collaborators:
Simon Scheidegger
Tobias Fischer
Stuart Whitehouse
Matthias Liebendörfer
Urs Frischknecht
Christian Winteler
Thomas Rauscher
F.-K. Thielemann
Outline
i) Stellar evolution
Stellar cycle: birth, life, death and nucleosynthesis
ii)Core-collapse supernova
Phenomenological description and stress
consequences for numerical simulation
iii)Numerical simulation
Summarize what is important from comp. view
1D simulation exploring possibility of QCD phase transition (T.
Fischer)
3D MHD simulation and GW (S. Scheidegger)
3D MHD code improvements
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i) Stellar evolution
Stellar evolution
●
Where do the elements come from?
Iron peak
Peaks
Asplund 2005
From primordial abundances of roughly H (75%), He (25%),
(very) small amount of Li
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i) Stellar evolution
Energy production in stars
●
●
Energy generated via nuclear fusion and
gravitational contraction
Energy continuously transported away (lost!) by
photon and neutrino emission
Energy generation
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Fusion
Fission
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i) Stellar evolution
Nucleosynthesis processes
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i) Stellar evolution
Stellar life cycle
Evolution as a function of mass
chandra.harvard.edu
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Birth
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Life
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Death
i) Stellar evolution
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...
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Tarutto 2003
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i) Stellar evolution
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...
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Tarutto 2003
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ii) Core-collapse supernova
Core-collapse supernova
●
●
Huge energy scales
●
~1e+53 erg neutrinos
●
~1e+51 erg mechanical
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~1e+48 erg elm
●
~1e+41 erg visible elm
SN1987A
Observables
●
Elm
●
Neutrinos
●
Gravitational waves
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After
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Before
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ii) Core-collapse supernova
Core-collapse supernova (2)
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General idea:
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●
Implosion of iron core of massive
end of thermonuclear evolution
at the
Explosion powered by gravitational binding energy
of forming compact remnant:
Mass of remnant
Radius of remnant
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ii) Core-collapse supernova
Conditions at onset of core-collapse
●
Onion like structure: history of nuclear burning
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Central density
●
Central temperature
●
Core mainly iron group nuclei
“Iron core”
Radius ~ 3000 km
●
Dynamical or free fall time scale
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Average density
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ii) Core-collapse supernova
Conditions at onset of core-collapse
●
Onion like structure: history of nuclear burning
●
Central density
●
Central temperature
At
Core
suchmainly
high densities
iron group
and temperatures
nuclei
the strong
and elm interactions are in equilibrium
“Iron core”
Composition
givenkm
by Nuclear Statistical Equilibrium
Radius ~ 3000
(NSE)
Independent
of reaction
● Dynamical or
free fall time
scale rates
●
No nuclear network needed
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Average density
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ii) Core-collapse supernova
Conditions at onset of core-collapse (2)
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Energy transport & dissipative processes
●
Diffusion of photons & electrons
●
Heat conduction of degenerate electrons or ions
●
Viscosity of core matter
●
Neutrinos
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ii) Core-collapse supernova
Conditions at onset of core-collapse (2)
●
Energy transport & dissipative processes
●
Diffusion of photons & electrons
●
Heat conduction of degenerate electrons or ions
●
Viscosity of core matter
●
Neutrinos
The mean free path is so small, that a
considerable amount of energy can only be
transported on time scales much larger than
the dynamical time scale
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ii) Core-collapse supernova
Conditions at onset of core-collapse (2)
●
Energy transport & dissipative processes
●
Diffusion of photons & electrons
●
Heat conduction of degenerate electrons or ions
●
Viscosity of core matter
●
Neutrinos
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Flowers & Itoh (1976)
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ii) Core-collapse supernova
Conditions at onset of core-collapse (2)
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Energy transport & dissipative processes
●
Diffusion of photons & electrons
●
Heat conduction of degenerate electrons or ions
●
Viscosity of core matter
●
Neutrinos
Only dissipative/transport effects from
● Shock waves
● Energy transport by neutrinos (weak
interaction NOT in equilibrium)
Flowers & Itoh (1976)
Iron core matter treated as ideal fluid!
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ii) Core-collapse supernova
Conditions at onset of core-collapse (3)
●
Iron core stabilized against gravity by relativistic
and degenerate electrons
Adiabatic index
●
Stability against collapse only for
Polytropic EoS
Stable up to Chandrasekhar
mass
Average grav. force
Av. pressure gradient
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ii) Core-collapse supernova
Conditions at onset of core-collapse (3)
●
●
Iron core stabilized against gravity by relativistic
electrons
Stability against collapse only for
Polytropic EoS
Stable up to Chandrasekhar
mass
Average grav. force
Av. pressure gradient
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ii) Core-collapse supernova
Collapse
●
Iron core collapses due to
1)Mass grows due to accreting Si burning ashes
Ultimately reaching
2)Electron captures reduce lepton number and
neutrinos escape
Escapes freely
3)Pressure reduced due to endothermic photodisintegration of nuclei by energetic photons
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ii) Core-collapse supernova
Collapse (2)
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Iron core collapses due to
1)Mass grows due to accreting Si burning ashes
Ultimately reaching
2)Electron captures reduce lepton number and
neutrinos escape
Escapes freely
3)Pressure reduced due to endothermic photodisintegration of nuclei by energetic photons
Janka et al. 2007
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ii) Core-collapse supernova
Collapse (3)
●
As soon as
become trapped
exceeded neutrinos
Neutrino diffusion time scale
Accurate neutrino
transport important!
As for stellar
atmospheres
one can define
neutrino spheres
Janka et al. 2007
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ii) Core-collapse supernova
Bounce & Shock formation
●
●
●
As central exceeds
nuclear matter
density the EoS
stiffens
Collapse halted
Shock wave
propagating outward
formed
Hydrodynamics must be shock proof!
Strong gravitational fields → GR
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Janka et al. 2007
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ii) Core-collapse supernova
Shock propagation
●
Shock looses energy
due to dissociation of
iron nuclei
~8.8 MeV/nucleon
~
Nuclear Physics (EoS)
●
Neutrino losses
Electron captures on free
protons
Weak interaction rates and neutrino transport
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Janka et al. 2007
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ii) Core-collapse supernova
Explosion
●
Shock strong enough
to “survive” energy
looses in iron core
Weak interaction rates and neutrino transport
Prompt mechanism
Works only for special conditions
●
Shock stalls and
becomes a standing
accretion shock
Shock reheated by
neutrinos Delayed mechanism
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Janka et al. 2007
Colgate & White 1966, Wilson 1985, Bethe & Wilson 1985
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ii) Core-collapse supernova
Explosion (2)
●
Alternative explosion mechanisms:
●
“Enhanced” delayed explosion mechanism
Hydro. instabilities: convection, Standing Accretion Shock
Instabilities (SASI) Blondin et al. 2003, Blondin & Shaw 2007, Marek & Janka 2008
●
MHD-Jet mechanism
Rapid rotation + Magnetic field amplification (winding, MRI)
●
Akiyama 2003, Wilson 2005, Kotake 2006, Burrows 2007
Acoustic mechanism
Excitation of ProtoNeutron Star (PNS) oscillations by
accretion/SASI generating acoustic power to reheat the
stalled shock Burrows et al. 2006,2007
MultiD Hydro & plasma physics
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iii) Numerical simulation
Numerical simulation
●
What is needed
1)Multi-Dimensional hydrodynamics
2)Plasma physics
3)Weak interactions
4)Neutrino transport
5)Nuclear physics
6)General relativity
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iii) Numerical simulation
Approximation: spherical symmetry
1)Multi-D hydro.
1D spherical symmetry
2)Plasma physics
Multi-D effect
3)Weak interactions
Coherent scattering of neutrinos on nuclei, neutrino absorption
on nuclei, neutrino absorption on nucleon, neutrino-nucleon
scattering, neutrino-electron scattering, neutrino production
from pair annihilation Bruenn 1985
4)Neutrino transport
Boltzmann equation
5)Nuclear physics
EoS
Lattimer & Swesty 1991
6)General relativity
NO explosions for
Thompson et al. 2003, Rampp & Janka 2002, Liebendörfer et al. 2002/2005
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iii) Numerical simulation
Exploring QCD phase transition
From Tobias Fischer
●
After bounce matter continues to accrete on PNS
●
Density may rise above nuclear saturation density
●
Temperature ~30 MeV
●
Highly asymmetric matter
Conditions favourable for phase
transition from hadronic matter to
quark mater
●
Due to phase transition PNS further collapses
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iii) Numerical simulation
Exploring QCD phase transition
From Tobias Fischer
●
After bounce matter continues to accrete on PNS
●
Density may rise above nuclear saturation density
●
Temperature ~30 MeV
●
Highly asymmetric matter
Conditions favourable for phase
transition from hadronic matter to
quark mater
●
Due to phase transition PNS further collapses
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iii) Numerical simulation
Exploring QCD phase transition
From Tobias Fischer
●
After bounce matter continues to accrete on PNS
●
Density may rise above nuclear saturation density
●
Temperature ~30 MeV
●
Highly asymmetric matter
Conditions favourable for phase
transition from hadronic matter to
quark mater
●
Due to phase transition PNS further collapses
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iii) Numerical simulation
Exploring QCD phase transition
From Tobias Fischer
●
After bounce matter continues to accrete on PNS
●
Density may rise above nuclear saturation density
●
Temperature ~30 MeV
●
Highly asymmetric matter
Conditions favourable for phase
transition from hadronic matter to
quark mater
●
Due to phase transition PNS further collapses
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iii) Numerical simulation
Exploring QCD phase transition
From Tobias Fischer
●
After bounce matter continues to accrete on PNS
●
Density may rise above nuclear saturation density
●
Temperature ~30 MeV
●
Highly asymmetric matter
Conditions favourable for phase
transition from hadronic matter to
quark mater
●
Due to phase transition PNS further collapses
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iii) Numerical simulation
Exploring QCD phase transition
From Tobias Fischer
●
After bounce matter continues to accrete on PNS
●
Density may rise above nuclear saturation density
●
Temperature ~30 MeV
●
Highly asymmetric matter
Conditions favourable for phase
transition from hadronic matter to
quark mater
●
Due to phase transition PNS further collapses
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iii) Numerical simulation
Exploring QCD phase transition
From Tobias Fischer
●
After bounce matter continues to accrete on PNS
●
Density may rise above nuclear saturation density
●
Temperature ~30 MeV
●
Highly asymmetric matter
Conditions favourable for phase
transition from hadronic matter to
quark mater
●
Due to phase transition PNS further collapses
01.10.08
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iii) Numerical simulation
Exploring QCD phase transition
From Tobias Fischer
●
After bounce matter continues to accrete on PNS
●
Density may rise above nuclear saturation density
●
Temperature ~30 MeV
●
Highly asymmetric matter
Conditions favourable for phase
transition from hadronic matter to
quark mater
●
Due to phase transition PNS further collapses
01.10.08
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iii) Numerical simulation
Exploring QCD phase transition
From Tobias Fischer
●
After bounce matter continues to accrete on PNS
●
Density may rise above nuclear saturation density
●
Temperature ~30 MeV
●
Highly asymmetric matter
Conditions favourable for phase
transition from hadronic matter to
quark mater
●
Due to phase transition PNS further collapses
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iii) Numerical simulation
Exploring QCD phase transition
From Tobias Fischer
●
After bounce matter continues to accrete on PNS
●
●
●
Density may rise above nuclear saturation density
Temperature ~30 MeV
Explosions for
Highly asymmetric
matter
astro-ph/0809.4225
Conditions favourable for phase
transition from hadronic matter to
quark mater
●
Due to phase transition PNS further collapses
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iii) Numerical simulation
Approximation 2: 3D with simplifications
Assume infinite conductivity
1)Multi-D hydro.
2)Plasma physics
3)Weak interactions
4)Neutrino transport
5)Nuclear physics
6)General relativity
Parallel 3D ideal MHD code
Pen et al. 2003, Käppeli et al. (in prep.)
Parametrised
Liebendörfer 2005
EoS Lattimer & Swesty 1991
Spherical effective GR
potential
Marek et al. 2006
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iii) Numerical simulation
The MHD equations
Mass
Momentum
Energy
Magnetic flux
No monopoles
EoS:
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iii) Numerical simulation
Solution Algorithm: An Overview
●
●
●
●
●
Algorithm from Pen et al. 2003, Liebendörfer et al.
2005
Uses operator splitting:
●
Dimensional splitting: solves eqs in 1D
●
Split hydro and magnetic variables update
Uses 2nd order TVD finite volume method for
hydrodynamic and magnetic variables
Uses constrained transport for
Correct operator ordering gives 2nd order accuracy
in time
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iii) Numerical simulation
Simulation s15g
From Simon Scheidegger 2008
●
●
●
Inner 600km cube followed
by 3D MHD
Outside followed by 1D
spherical symmetric code
Progenitor: 15
Woosley & Weaver 1995
●
●
Magnetic field as suggested
by Heger et al. 2005
Rotation
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iii) Numerical simulation
Simulation s15g
From Simon Scheidegger 2008
●
●
●
●
●
Inner 600km cube followed
by 3D MHD
Movie
s15g
Outside followed by 1D
spherical symmetric
code
Left entropy
colour coded
Progenitor: Right
15 absolute magnetic field
Density contours
Woosley & Weaver 1995
Magnetic field as suggested
by Heger et al. 2005
Super Computing Center
RotationSwiss
(CSCS)
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iii) Numerical simulation
Gravitational wave signature
From Simon Scheidegger 2008
●
●
●
Emission of gravitational waves possible due to
large “mass movements”
GW come directly from the innermost regions
Observation of GW could:
●
Constrain nuclear physics (compressibility of matter)
●
Explosion mechanism
●
Constraints on hydro. instabilities (convection/SASI...)
Detectors build over the world
Important to provide signal patterns, so that they
no roughly what should be seen
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LIGO, Advanced LIGO, TAMA 300, AIGO, GEO 600, VIRGO
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iii) Numerical simulation
Gravitational wave signature
From Simon Scheidegger 2008
●
●
●
Emission of gravitational waves possible due to
Spectral energy distribution at 10kpc
large “mass movements”
Rotating (s15g)
Non-Rotating (s15h)
GW come directly from the innermost regions
Observation of GW could:
●
Constrain nuclear physics (compressibility
of matter)
Difference bewteen
●
Explosion mechanism
●
Constraints on hydro. instabilities (convection/SASI...)
rot. and non-rot.
Detectors build overLigothe world
Important to provide
signal patterns, so that they
Advanced Ligo
no roughly what should be seen
01.10.08
LIGO, Advanced LIGO, TAMA 300, AIGO, GEO 600, VIRGO
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iii) Numerical simulation
Improvements: Adapting the mesh
Assume infinite conductivity
1)Multi-D hydro.
2)Plasma physics
3)Weak interactions
4)Neutrino transport
5)Nuclear physics
6)General relativity
Parallel 3D ideal MHD code
Pen et al. 2003, Käppeli et al. (in prep.)
Parametrised
Liebendörfer 2005
EoS Lattimer & Swesty 1991
Spherical effective GR
potential
Marek et al. 2006
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iii) Numerical simulation
Adapting the mesh
●
Motivation
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iii) Numerical simulation
Adapting the mesh (2)
●
Simplest approach
–
●
Use non-equidistant Cartesian mesh
Better:
–
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Adaptive Mesh Refinement (AMR)
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iii) Numerical simulation
Adapting the mesh (3)
●
Simplest approach
–
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Use non-equidistant Cartesian mesh
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iii) Numerical simulation
Adapting the mesh (4)
●
Sedov-Taylor blast wave (point explosion)
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Uniform mesh
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Gaussian mesh
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iii) Numerical simulation
Adapting the mesh (5)
●
Magnetic explosion (Sedov-Taylor + Magnetic field)
Abs. Magnitude of velocity
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iii) Numerical simulation
Improvements: Weak int. & neutrino transport
Assume infinite conductivity
1)Multi-D hydro.
2)Plasma physics
3)Weak interactions
4)Neutrino transport
5)Nuclear physics
6)General relativity
Parallel 3D ideal MHD code
Pen et al. 2003, Käppeli et al. (in prep.)
Parametrised
Liebendörfer 2005
EoS Lattimer & Swesty 1991
Spherical effective GR
potential
Marek et al. 2006
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iii) Numerical simulation
Weak interactions & neutrino transport
●
Full Boltzmann transport
●
1 fluid element contains
4
●
types x 20 energies x 100 angles = 8000 Variables
For 3D domain with ~1000^3 cells
64 TB per time step
●
Parametrisation, but only good before bounce
Does not include heating (delayed mechanism)
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iii) Numerical simulation
Weak interactions & neutrino transport
●
Full Boltzmann transport
●
1 fluid element contains
4
types x 20 energies x 100 angles = 8000 Variables
Parametrised 3D 5ms after bounce
●
For 3D domain with ~1000^3 cells
64 TB per time step
Full transport 1D 5ms after bounce
●
Parametrisation, but only good before bounce
Does not include heating (delayed mechanism)
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iii) Numerical simulation
Weak interactions & neutrino transport (2)
●
●
Find way of approximating dominant features of
full Boltzmann transport
Currently under development:
Isotropic Diffusion Source Approximation (IDSA)
Liebendörfer et al. 2007
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iii) Numerical simulation
Weak interactions & neutrino transport (2)
●
●
1Dway
full Boltzmann
vs IDSA (1ms
& 3msfeatures
a.b.)
Find
of approximating
dominant
of
full Boltzmann transport
Currently under development:
Isotropic Diffusion Source Approximation (IDSA)
Liebendörfer et al. 2007
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Summary
●
Supernova complex dynamic system
●
●
Explosion mechanism not fully understood
●
●
All 4 nature forces are involved
(weak,strong,elm,gravity)
Exploring possibility QCD phase transition
3D simulations only possible with
approximations so far
Thank you for your attention!
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