The role of neutrinos in core collapse Supernova explosion - LUTh ...

The role of neutrinos in core collapse
Supernova explosion
Albino Perego
albino.perego@unibas.ch
University of Basel
Department of Physics
Seminar talk at LUTH, Observatoire de Paris, Meudon
10 December 2009
Neutrinos in core collapse SN explosion - Paris, 10 September 2009 – p. 1/48

Outline
Introduction: core collapse SN explosion paradigm
neutrinos in core collapse SN explosion
Neutrino transport: the Boltzmann equation
results from 1D General Relativistic (GR) simulations
Neutrino transport: approximation methods for higher
dimensions
state-of-art of 2D simulations
Isotropic Diffusion Source Approximation (IDSA)
leakage scheme
Conclusion and outlook
Neutrinos in core collapse SN explosion - Paris, 10 September 2009 – p. 2/48

Introduction:
core collapse Supernova
explosion paradigm
Neutrinos in core collapse SN explosion - Paris, 10 September 2009 – p. 3/48

SNe history
Before telescope introduction (before 1885), naked-eye
observations of some Galactic SNe
Anasazi (American indian people) SN
1054 observation
Kepler SN 1572 observation in Europe
Neutrinos in core collapse SN explosion - Paris, 10 September 2009 – p. 4/48

SNe history
Before telescope introduction (before 1885), naked-eye
observations of some Galactic SNe
after telescope introduction (since 1885), . . .
. . . search for previous SNe remnants
. . . discovery of extra-galactic SNe
Remnant of SN 1054: Crab Nebula,
www.hubblesite.org
Remnant of SN 1572,
www.chandra.harvard.edu
Neutrinos in core collapse SN explosion - Paris, 10 September 2009 – p. 4/48

SNe history
Before telescope introduction (before 1885), naked-eye
observations of some Galactic SNe
after telescope introduction (since 1885), . . .
. . . search for previous SNe remnants
. . . discovery of extra-galactic SNe
Optical image of SN 2001du in NGC
1365, www.supernovae.net
X-ray image of SN 2006gy in NGC 1260,
www.chandra.harvard.edu
Neutrinos in core collapse SN explosion - Paris, 10 September 2009 – p. 4/48

SNe history
Before telescope introduction (before 1885), naked-eye
observations of some Galactic SNe
after telescope introduction (since 1885), . . .
. . . search for previous SNe remnants
. . . discovery of extra-galactic SNe
since 1941, spectral analysis led to SNe classification
type I → without H lines
type II → with H lines
Neutrinos in core collapse SN explosion - Paris, 10 September 2009 – p. 4/48

SNe history
Before telescope introduction (before 1885), naked-eye
observations of some Galactic SNe
after telescope introduction (since 1885), . . .
. . . search for previous SNe remnants
. . . discovery of extra-galactic SNe
since 1941, spectral analysis led to SNe classification
type I → without H lines
type II → with H lines
after 60’s, quantitative models for SN explosion
SN Ia → thermonuclear explosion of a white dwarf
(WD) or a neutron star (NS) in stellar binary systems
SN II, Ib, Ic, . . . → core collapse SN explosion of a
massive star
Neutrinos in core collapse SN explosion - Paris, 10 September 2009 – p. 4/48

SNe history
Before telescope introduction (before 1885), naked-eye
observations of some Galactic SNe
after telescope introduction (since 1885), . . .
. . . search for previous SNe remnants
. . . discovery of extra-galactic SNe
since 1941, spectral analysis led to SNe classification
type I → without H lines
type II → with H lines
after 60’s, quantitative models for SN explosion
SN Ia → thermonuclear explosion of a white dwarf
(WD) or a neutron star (NS) in stellar binary systems
SN II, Ib, Ic, . . . → core collapse SN explosion of a
massive star
Neutrinos in core collapse SN explosion - Paris, 10 September 2009 – p. 4/48

Life of a star
www.chandra.harvard.edu
Neutrinos in core collapse SN explosion - Paris, 10 September 2009 – p. 5/48

Core collapse SN: energetics
SN energy comes from gravitational energy released by compact
remnant formation
(e.g. NS of MNS ∼ 1.5 M⊙ and RNS ∼ 10 km)
Egrav ∼ GM2 NS
RNS
− GM2 NS
Rcore
∼ 6 × 10 53 ergs
Is all this energy necessary to explode the star? No . . .
Egrav ≫ Ekin matter ∼ 10 51 ergs ≫ Eγ ∼ 10 48 ergs
Most of Egrav is released by neutrinos, which escape from the star on
long timescales (10 s) (estimated neutronization energy for 1.5M⊙:
Eneut ∼ few 10 53 ergs)
Deposition of ∼ 1% of Eν can produce explosion (Colgate & White (1966))
⇒ ν driven explosion mechanism
Neutrinos in core collapse SN explosion - Paris, 10 September 2009 – p. 6/48

Neutrinos in SN explosion
Neutrinos (of all flavours) are fundamental ingredients in
core collapse SN (Bethe (1990), Burrows (1990), Raffelt (2001));
they . . .
exchange energy with matter (heating and cooling)
release energy out of the system
influence explosive nucleosynthesis
give us important informations about dense matter
νe and ¯νe differ from νµ,τ and ¯νµ,τ
origin of the
difference:
me ≪ mµ ≪ mτ
⇒ at the on-set of the collapse, Ye = 0
while Yµ = Yτ ≈ 0
Neutrinos in core collapse SN explosion - Paris, 10 September 2009 – p. 7/48

Neutrino-matter interaction
Neutrinos interact significantly by charged (CC) or neutral
(NC) current reactions with matter at high ρ and T
Major consequences:
Neutrinos in core collapse SN explosion - Paris, 10 September 2009 – p. 8/48

Neutrino-matter interaction
Neutrinos interact significantly by charged (CC) or neutral
(NC) current reactions with matter at high ρ and T
Major consequences:
opacity a
κ ∼ 5 × 10−20 2 Eν 2 −1
MeV cm g ⇒ 0 τν 103 for Eν ≈ 20MeV
a κ → opacity, λν → ν mean free path, τν → ν optical depth
Neutrinos in core collapse SN explosion - Paris, 10 September 2009 – p. 8/48

Neutrino-matter interaction
Neutrinos interact significantly by charged (CC) or neutral
(NC) current reactions with matter at high ρ and T
Major consequences:
opacity
κ ∼ 5 × 10 −20 Eν
MeV
energy exchange
2 cm 2 g −1 ⇒ 0 τν 10 3 for Eν ≈ 20MeV
Neutrinos in core collapse SN explosion - Paris, 10 September 2009 – p. 8/48

Neutrino-matter interaction
Neutrinos interact significantly by charged (CC) or neutral
(NC) current reactions with matter at high ρ and T
Major consequences:
opacity
κ ∼ 5 × 10 −20 Eν
MeV
energy exchange
particle number variation
2 cm 2 g −1 ⇒ 0 τν 10 3 for Eν ≈ 20MeV
Neutrinos in core collapse SN explosion - Paris, 10 September 2009 – p. 8/48

Electron neutrinos reactions
Reaction Current Important for . . .
e − + p ↔ n + νe CC νe production, opacity and energy exchange
e + + n ↔ p + ¯νe CC ¯νe production, opacity and energy exchange
e − + A ↔ A ′ + νe CC νe production, opacity and energy exchange
ν + N → ν ′ + N ′ NC opacity
ν + A → ν ′ + A ′ NC opacity
ν + e ± → ν ′ + e ±′
CC&NC energy exchange
e + + e − ↔ νe + ¯νe CC&NC ν production
N + N ↔ N ′ + N ′ + νe + ¯νe NC secondary importance
N + N + ν → N ′ + N ′ + ν ′ NC secondary importance
ν stands for both νe and ¯νe
Bruenn 1985, Hannestad & Raffelt 1998, Buras et al. 2002, Marek et al. 2005, Buras et al.
2006
Neutrinos in core collapse SN explosion - Paris, 10 September 2009 – p. 9/48

µ and τ neutrinos reactions
Reaction Current Important for . . .
ν + N → ν ′ + N ′ NC opacity
ν + A → ν ′ + A ′ NC opacity
ν + e ± → ν ′ + e ±′
NC energy exchange
e + + e − ↔ νx + ¯νx NC ν production
N + N ↔ N ′ + N ′ + νx + ¯νx NC ν production and energy exchange
N + N + ν → N ′ + N ′ + ν ′ NC energy exchange
νe + ¯νe ↔ νx + ¯νx NC ν production
νe + ν → ν ′ e + ν ′ NC secondary importance
¯νe + ν → ¯ν ′ e + ν ′ NC secondary importance
νx stands for both νµ and ντ
ν stands for both νx and ¯νx
Bruenn 1985, Hannestad & Raffelt 1998, Buras et al. 2002, Marek et al. 2005, Buras et al.
2006
Neutrinos in core collapse SN explosion - Paris, 10 September 2009 – p. 10/48

Raffelt (2001)
Expected neutrinos behaviour
for τ ≫ 1, νe and ¯νe mainly
interact by weak reactions →
thermal equilibrium with matter
and diffusive transport;
when τ ∼ 1 (ν sphere), νe and
¯νe stream out
Raffelt (2001)
for τ ≫ 1 and high
temperature, termal processes
provide νµ,τ − ¯νµ,τ production,
thermalization and diffusion
when thermal processes freeze
out but τ ≫ 1, isoenergetic
diffusion
for τ ∼ 1, νµ,τ and ¯νµ,τ stream
out Neutrinos in core collapse SN explosion - Paris, 10 September 2009 – p. 11/48

Neutrino transport:
the Boltzmann equation for
1D simulations
Neutrinos in core collapse SN explosion - Paris, 10 September 2009 – p. 12/48

Core collapse SN simulations
CCSN is a complex, dynamics process, which involves
many physical topics and large calculations capabilities
⇓
good implementation of the fundamental physics in
sophisticated numerical simulations is required
Neutrinos in core collapse SN explosion - Paris, 10 September 2009 – p. 13/48

AGILE-BOLTZTRAN
AGILE-BOLTZTRAN: 1D GR ν radiation hydrodynamics
parallelized code
AGILE
implicit GR hydrodynamics code
adaptive grid technique (103 zones)
BOLTZTRAN
implicit 3 flavours, multigroup GR Boltzmann ν transport solver
20 energy bins (3MeV ≤ Eν ≤ 300MeV)
8 ν directions
actually, only 2 independent flavours (µ = τ)
Lattimer-Swesty EOS
several progenitor models tested
Liebendorfer et al. 2000,2001,2004,2005 and references therein
Neutrinos in core collapse SN explosion - Paris, 10 September 2009 – p. 14/48

Problem formulation
symmetry: General Relativity (GR) + spherical symmetry (1D)
coordinates: (t, a, θ, φ)
ds 2 = −α 2 dt 2 ′ r
+
Γ
2
da 2 +r 2 dΩ 2
a enclosed rest mass
r = r(t, a) radial radius
r ′ = dr
da
α = α(t, a) lapse function
reference frame: comoving reference frame (Lagrangian)
u = ˙r/a comoving observer 4-velocity
gravitational field source: fluid + neutrino stress-energy tensor
(fluid = baryons + γ + electrons & positrons )
T tt = ρ(1 + e + J)
T ta = H
T aa = p + ρK
T θθ = T φφ = p + 1
2ρ(J − K)
ρ rest mass density
e specific internal energy
J specific ν energy
p isotropic fluid pressure
H and K specific ν stresses
Neutrinos in core collapse SN explosion - Paris, 10 September 2009 – p. 15/48

Boltzmann transport equation
Distribution functions, f(t,a,µ,E)
dN = gsf(t, a, µ, E)E2 dE dµ dV
µ = cos θp
θp angle between p and r, mea-
Γ
sured by comoving observer
Boltztrann transport equation (BTE): evolution of the distribution
function in phase space
D[f] = C[f]
D[f] → Liouville operator: directional derivative of f along
trajectories of free particles propagation
α ∂
D[ ] = p
∂xα − Γα βγp β γ ∂
p
∂pα C[f] → collision integral: changes in f due to collision and
reactions
Neutrinos in core collapse SN explosion - Paris, 10 September 2009 – p. 16/48

C[f] = j(1 − f) − χf +
+ X
» Z
(1 − f)
scat
+ X
pair prod
Collision integral
» Z
(1 − f)
R in
s f ′ E ′2 dE ′ dµ ′ − f
R in TP (1 − ¯ f ′ )E ′2 dE ′ dµ ′ − f
Z
R out
s (1 − f ′ ) E ′2
–
′ ′
dE dµ +
Z
R out
TP ¯ f ′ E ′2
–
′ ′
dE dµ
Neutrinos in core collapse SN explosion - Paris, 10 September 2009 – p. 17/48

C[f] = j(1 − f) − χf +
+ X
» Z
(1 − f)
scat
+ X
pair prod
Collision integral
» Z
(1 − f)
R in
s f ′ E ′2 dE ′ dµ ′ − f
particle emissivity and absorptivity
R in TP (1 − ¯ f ′ )E ′2 dE ′ dµ ′ − f
Z
R out
s (1 − f ′ ) E ′2
–
′ ′
dE dµ +
Z
R out
TP ¯ f ′ E ′2
–
′ ′
dE dµ
j(E, µ)(1 − f(E, µ)) ∝ amount of neutrinos with energy E and
direction µ emitted by electron (positron) capture
χ(E, µ)f(E, µ) ∝ amount of neutrinos with energy E and
direction µ absorbed by inverse electron (positron) capture
Neutrinos in core collapse SN explosion - Paris, 10 September 2009 – p. 17/48

C[f] = j(1 − f) − χf +
+ X
» Z
(1 − f)
scat
+ X
pair prod
Collision integral
» Z
(1 − f)
R in
s f ′ E ′2 dE ′ dµ ′ − f
particle emissivity and absorptivity
in-scattering contribution
R in TP (1 − ¯ f ′ )E ′2 dE ′ dµ ′ − f
Z
R out
s (1 − f ′ ) E ′2
–
′ ′
dE dµ +
Z
R out
TP ¯ f ′ E ′2
–
′ ′
dE dµ
(1 − f(E, µ)) Rs in (E, E ′ , µ, µ ′ )f(E ′ , µ ′ )E ′2 dE ′ dµ ′ ∝ amount of
particles which, from any initial configuration (E ′ , µ ′ ), goes into
(E, µ) configuration
Neutrinos in core collapse SN explosion - Paris, 10 September 2009 – p. 17/48

C[f] = j(1 − f) − χf +
+ X
» Z
(1 − f)
scat
+ X
pair prod
Collision integral
» Z
(1 − f)
R in
s f ′ E ′2 dE ′ dµ ′ − f
particle emissivity and absorptivity
in-scattering contribution
out-scattering contribution
R in TP (1 − ¯ f ′ )E ′2 dE ′ dµ ′ − f
Z
R out
s (1 − f ′ ) E ′2
–
′ ′
dE dµ +
Z
R out
TP ¯ f ′ E ′2
–
′ ′
dE dµ
f(E, µ)) Rs out (E, E ′ , µ, µ ′ )(1 − f(E ′ , µ ′ ))E ′2 dE ′ dµ ′ ∝ amount of
particles which, from the initial configuration (E, µ), goes into any
(E ′ , µ ′ ) configuration
Neutrinos in core collapse SN explosion - Paris, 10 September 2009 – p. 17/48

C[f] = j(1 − f) − χf +
+ X
» Z
(1 − f)
scat
+ X
pair prod
Collision integral
» Z
(1 − f)
R in
s f ′ E ′2 dE ′ dµ ′ − f
particle emissivity and absorptivity
in-scattering contribution
out-scattering contribution
in-coming pair contribution
R in TP (1 − ¯ f ′ )E ′2 dE ′ dµ ′ − f
Z
R out
s (1 − f ′ ) E ′2
–
′ ′
dE dµ +
Z
R out
TP ¯ f ′ E ′2
–
′ ′
dE dµ
(1 − f(E, µ)) R in TP (E, E′ , µ, µ ′ )(1 − ¯ f ′ (E ′ , µ ′ ))E ′2 dE ′ dµ ′ ∝
amount of particles with configuration (E, µ) and anti-particles ( ¯ f)
with any configuration (E ′ , µ ′ ), created by pair processes
Neutrinos in core collapse SN explosion - Paris, 10 September 2009 – p. 17/48

C[f] = j(1 − f) − χf +
+ X
» Z
(1 − f)
scat
+ X
pair prod
Collision integral
» Z
(1 − f)
R in
s f ′ E ′2 dE ′ dµ ′ − f
particle emissivity and absorptivity
in-scattering contribution
out-scattering contribution
in-coming pair contribution
out-coming pair contribution
R in TP (1 − ¯ f ′ )E ′2 dE ′ dµ ′ − f
Z
R out
s (1 − f ′ ) E ′2
–
′ ′
dE dµ +
Z
R out
TP ¯ f ′ E ′2
–
′ ′
dE dµ
f(E, µ) R out
TP (E, E′ , µ, µ ′ ) ¯ f ′ (E ′ , µ ′ )E ′2 dE ′ dµ ′ ∝ amount of
particles with configuration (E, µ) and anti-particles ( ¯ f) with any
configuration (E ′ , µ ′ ), absorbed by pair processes
Neutrinos in core collapse SN explosion - Paris, 10 September 2009 – p. 17/48

Results: "cold" collapse phase
homologous collapse and shock formation
Neutrinos in core collapse SN explosion - Paris, 10 September 2009 – p. 18/48

Results: "cold" collapse phase
homologous collapse and shock formation
Neutrinos in core collapse SN explosion - Paris, 10 September 2009 – p. 18/48

Results: "cold" collapse phase
homologous collapse and shock formation
deleptonization and ν trapping
T 2MeV: low pair
production
for 10 9 g/cm 3 → 10 12 g/cm 3 ,
high e − capture and νe’s
production, which escape
almost freely
⇒ Yl : 0.42 → 0.3
for ρ 10 12 g/cm 3 , ν diffuses
and tdiff > tdyn: ˙ Yl ≈ 0 ≈ ˙ S
Martinez-Pinedo et al. (2006)
Neutrinos in core collapse SN explosion - Paris, 10 September 2009 – p. 18/48

Results: "cold" collapse phase
homologous collapse and shock formation
deleptonization and ν trapping
T 2MeV: low pair
production
for 10 9 g/cm 3 → 10 12 g/cm 3 ,
high e − capture and νe’s
production, which escape
almost freely
⇒ Yl : 0.42 → 0.3
for ρ 10 12 g/cm 3 , ν diffuses
and tdiff > tdyn: ˙ Yl ≈ 0 ≈ ˙ S
Martinez-Pinedo et al. (2006)
Neutrinos in core collapse SN explosion - Paris, 10 September 2009 – p. 18/48

Results: "cold" collapse phase
homologous collapse and shock formation
deleptonization and ν trapping
T 2MeV: low pair
production
for 10 9 g/cm 3 → 10 12 g/cm 3 ,
high e − capture and νe’s
production, which escape
almost freely
⇒ Yl : 0.42 → 0.3
for ρ 10 12 g/cm 3 , ν diffuses
and tdiff > tdyn: ˙ Yl ≈ 0 ≈ ˙ S
Martinez-Pinedo et al. (2006)
Neutrinos in core collapse SN explosion - Paris, 10 September 2009 – p. 18/48

Results: "cold" collapse phase
homologous collapse and shock formation
deleptonization and ν trapping
T 2MeV: low pair
production
for 10 9 g/cm 3 → 10 12 g/cm 3 ,
high e − capture and νe’s
production, which escape
almost freely
⇒ Yl : 0.42 → 0.3
for ρ 10 12 g/cm 3 , ν diffuses
and tdiff > tdyn: ˙ Yl ≈ 0 ≈ ˙ S
Martinez-Pinedo et al. (2006)
Neutrinos in core collapse SN explosion - Paris, 10 September 2009 – p. 18/48

Results: 100ms after bounce
Mprog = 13M⊙: no prompt explosion! Maybe delayed . . .
Liebendorfer et al. (2001)
Neutrinos in core collapse SN explosion - Paris, 10 September 2009 – p. 19/48

ν’s can cool and heat matter,
according to radial location:
cooling region, close to
PNS surface
heating region, between
Rgain and Rshock
The gain radius
Neutrinos in core collapse SN explosion - Paris, 10 September 2009 – p. 20/48

Results:ν luminosity after bounce
νe burst close to bounce
(t ∼ 5 ms after bounce)
¯νe and µ and τ ν’s
luminosities rise behind
the shock (high T )
spectra comparison at
t = 100 ms after bounce:
νe’s interact more →
lower energy
Liebendorfer et al. (2001)
Neutrinos in core collapse SN explosion - Paris, 10 September 2009 – p. 21/48

Results: 500ms after bounce
Mprog = 13M⊙
Shock recession: no delayed explosion!
Liebendorfer et al. (2001) Neutrinos in core collapse SN explosion - Paris, 10 September 2009 – p. 22/48

Neutrino transport:
approximation methods for
higher dimensions
Neutrinos in core collapse SN explosion - Paris, 10 September 2009 – p. 23/48

Motivations: climbing up dimensions
Results from 1D GR simulations with detailed Boltzmann transport:
in general, no SN explosion!
Suggestion:
high dimensions can provide new macrophysics (convection, rotation,
magnetic fields . . . ) which can help stars to explode!
Problem:
full Boltzmann ν transport is memory and CPU-time too expensive
Avaiable solution:
development of approximated methods to model ν transport
computationally simpler and cheaper
physically motivated and effective
Neutrinos in core collapse SN explosion - Paris, 10 September 2009 – p. 24/48

Present state-of-art
Axisymmetric (2D) hydrodynamic simulation
GR effective gravitational potential
GR corrections (like time dilation)
approx ν transport
ray by ray method
multigroup flux limited diffusion (MGFLD)
multi-angle, multi-group ν transport
O(v/c) Boltzmann equation, GR corrections
Lattimer-Swesty EOS and Shen EOS
updated ν opacities and emissivities
nuclear network
Neutrinos in core collapse SN explosion - Paris, 10 September 2009 – p. 25/48

Present state-of-art
Axisymmetric (2D) hydrodynamic simulation
GR effective gravitational potential
GR corrections (like time dilation)
approx ν transport
ray by ray method
multigroup flux limited diffusion (MGFLD)
multi-angle, multi-group ν transport
O(v/c) Boltzmann equation, GR corrections
Lattimer-Swesty EOS and Shen EOS
updated ν opacities and emissivities
nuclear network
Neutrinos in core collapse SN explosion - Paris, 10 September 2009 – p. 25/48

2D ν transport approximations
ray by ray
solution of several 1D ν transport problems, in angular wedges with
periodic boundary conditions
Neutrinos in core collapse SN explosion - Paris, 10 September 2009 – p. 26/48

2D ν transport approximations
ray by ray
solution of several 1D ν transport problems, in angular wedges with
periodic boundary conditions
MGFLD
solution of diffusion equations for different neutrino species and
different energy bins; ν flux is limited in order to give consistent
results in the free streaming regime
Neutrinos in core collapse SN explosion - Paris, 10 September 2009 – p. 26/48

2D ν transport approximations
ray by ray
solution of several 1D ν transport problems, in angular wedges with
periodic boundary conditions
MGFLD
solution of diffusion equations for different neutrino species and
different energy bins; ν flux is limited in order to give consistent
results in the free streaming regime
multi-angle, multi-group ν transport
solution of discretized and simplified (no special and general
relativistic corrections) 2D Boltzmann equation for each ν species,
with several energy bins, with standard ν-matter interactions
Neutrinos in core collapse SN explosion - Paris, 10 September 2009 – p. 26/48

2D simulations results: new features
Convection
overturn behind the stalling shock
ν heating → dS/dr < 0
effect: more efficient ν heating
Neutrinos in core collapse SN explosion - Paris, 10 September 2009 – p. 27/48

2D simulations results: new features
Convection
overturn behind the stalling shock
ν heating → dS/dr < 0
effect: more efficient ν heating
Standing Accretion Shock Instability (SASI)
hydro instability of shocked accretion
flows to non-radial deformation modes
effect: large shock oscillations and
convection
effect: increase tadvection: more time for
ν heating!
Foglizzo et al (2007), Blondin et al. (2003)
Neutrinos in core collapse SN explosion - Paris, 10 September 2009 – p. 27/48

2D simulations results: new features
Convection
overturn behind the stalling shock
ν heating → dS/dr < 0
effect: more efficient ν heating
Standing Accretion Shock Instability (SASI)
hydro instability of shocked accretion
flows to non-radial deformation modes
effect: large shock oscillations and
convection
effect: increase tadvection: more time for
ν heating!
Foglizzo et al (2007), Blondin et al. (2003)
Marek & Janka 2008
Neutrinos in core collapse SN explosion - Paris, 10 September 2009 – p. 27/48

2D simulations results: comparison
MPA-Garching group
PROMETHEUS-VERTEX code
2D effective GR gravitational potential
ray-by-ray O(v/c) ν transport, with GR correction
Neutrinos in core collapse SN explosion - Paris, 10 September 2009 – p. 28/48

2D simulations results: comparison
MPA-Garching group
PROMETHEUS-VERTEX code
Results:
2D effective GR gravitational potential
ray-by-ray O(v/c) ν transport, with GR correction
1. ν driven, SASI aided explosion
for Mprog = 11.2M⊙ , texp ≈
200ms
2. ν driven, SASI aided explosion
for Mprog = 15M⊙
texp ≈ 600ms
Neutrinos in core collapse SN explosion - Paris, 10 September 2009 – p. 28/48

2D simulations results: comparison
MPA-Garching group
PROMETHEUS-VERTEX code
Results:
2D effective GR gravitational potential
ray-by-ray O(v/c) ν transport, with GR correction
1. ν driven, SASI aided explosion
for Mprog = 11.2M⊙ , texp ≈
200ms
2. ν driven, SASI aided explosion
for Mprog = 15M⊙
texp ≈ 600ms
Marek & Janka 2008
Neutrinos in core collapse SN explosion - Paris, 10 September 2009 – p. 28/48

2D simulations results: comparison
Oak Ridge-Florida group
CHIMERA code
2D effective GR gravitational potential
ray-by-ray O(v/c) ν transport, with GR correction + MGFLD
Neutrinos in core collapse SN explosion - Paris, 10 September 2009 – p. 29/48

2D simulations results: comparison
Oak Ridge-Florida group
CHIMERA code
Results:
2D effective GR gravitational potential
ray-by-ray O(v/c) ν transport, with GR correction + MGFLD
ν driven, SASI aided explosion
Mprog = 12, 15, 20, 25M⊙
texp ≈ 300 − 400ms
Eexp ≈ 1 × 10 51 ergs
Bruenn (2009)
Neutrinos in core collapse SN explosion - Paris, 10 September 2009 – p. 29/48

2D simulations results: comparison
Oak Ridge-Florida group
CHIMERA code
Results:
2D effective GR gravitational potential
ray-by-ray O(v/c) ν transport, with GR correction + MGFLD
ν driven, SASI aided explosion
Mprog = 12, 15, 20, 25M⊙
texp ≈ 300 − 400ms
Eexp ≈ 1 × 10 51 ergs
Bruenn (2009)
Neutrinos in core collapse SN explosion - Paris, 10 September 2009 – p. 29/48

2D simulations results: comparison
Princeton-Tucson group
VULCAN code
2D Newtonian gravitation potential
2D multi-angle, multi-group ν transport + MGFLD
Neutrinos in core collapse SN explosion - Paris, 10 September 2009 – p. 30/48

2D simulations results: comparison
Princeton-Tucson group
VULCAN code
Results:
2D Newtonian gravitation potential
2D multi-angle, multi-group ν transport + MGFLD
1. no ν driven, SASI aided explosion!
Mprog = 20M⊙
vrot = 0 and vrot = π rad/s
2. acoustic mechanism explosion
texp ∼ 1.5 s after bounce
Ott et al. (2008)
Neutrinos in core collapse SN explosion - Paris, 10 September 2009 – p. 30/48

2D simulations results: comparison
Princeton-Tucson group
VULCAN code
Results:
2D Newtonian gravitation potential
2D multi-angle, multi-group ν transport + MGFLD
1. no ν driven, SASI aided explosion!
Mprog = 20M⊙
vrot = 0 and vrot = π rad/s
2. acoustic mechanism explosion
texp ∼ 1.5s after bounce Ott et al. (2008)
Neutrinos in core collapse SN explosion - Paris, 10 September 2009 – p. 30/48

IDSA: motivations
IDSA = Isotropic Diffuson Source Approximation
Approx ν transport for 3D simulations: accuracy . . .
thermodynamics of trapped particles
accurate diffusion limit
explicit ν spectral dependence
non local (geometric) ν propagation directions
Neutrinos in core collapse SN explosion - Paris, 10 September 2009 – p. 31/48

IDSA: motivations
IDSA = Isotropic Diffuson Source Approximation
Approx ν transport for 3D simulations: accuracy . . .
thermodynamics of trapped particles
accurate diffusion limit
explicit ν spectral dependence
non local (geometric) ν propagation directions
. . . and efficiency
distinction between trapped and streaming particles
Neutrinos in core collapse SN explosion - Paris, 10 September 2009 – p. 31/48

IDSA: motivations
IDSA = Isotropic Diffuson Source Approximation
Approx ν transport for 3D simulations: accuracy . . .
thermodynamics of trapped particles
accurate diffusion limit
explicit ν spectral dependence
non local (geometric) ν propagation directions
. . . and efficiency
distinction between trapped and streaming particles
adaptive and flexible algorithom: evolution of ν distributions are
guided by diffusion limit at high opacity and free streaming limit at low
opacity
Liebendorfer, Whitehouse, Kappeli (2009)
Neutrinos in core collapse SN explosion - Paris, 10 September 2009 – p. 31/48

f → D[f] = C[f]
IDSA: basic ideas
Neutrinos in core collapse SN explosion - Paris, 10 September 2009 – p. 32/48

IDSA: basic ideas
f → D[f] = C[f] ⇒ f = ftrapped + fstreaming
D[ftrapped] = C[ftrapped] − Σ (1)
D[fstreaming] = C[fstreaming] + Σ (2)
Σ: Diffusion source → conversion
between streaming
and trapped part
Neutrinos in core collapse SN explosion - Paris, 10 September 2009 – p. 32/48

IDSA: basic ideas
f → D[f] = C[f] ⇒ f = ftrapped + fstreaming
D[ftrapped] = C[ftrapped] − Σ (1)
D[fstreaming] = C[fstreaming] + Σ (2)
Σ: Diffusion source → conversion
between streaming
and trapped part
different approximation for the 2 components:
Σ is determined by solving (1) in the
diffusion limit
(2) is solved assuming stationary-state
approx to calculate streaming particle
flux (Poisson equation)
Neutrinos in core collapse SN explosion - Paris, 10 September 2009 – p. 32/48

IDSA →
IDSA: ingredients
primarily implemented for νe and ¯νe
first tested in core collapse SN model
dominant production and absorption mechanisms
p + e − ↔ n + νe
n + e + ↔ p + ¯νe
diffusion mechanism: isoenergetic scattering on nucleons and nuclei
N + ν → N ′ + ν ′
A + ν → A ′ + ν ′
when treac ≪ tdiff, local thermodynamical equilibrium applies ⇒
reduction of independent variables number
details of implementations depend on the hydro code
Neutrinos in core collapse SN explosion - Paris, 10 September 2009 – p. 33/48

dY/dE [MeV −1 ]
dY/dE [MeV −1 ]
dY/dE [MeV −1 ]
x (a)
10−4
5
4
3
2
1
0
0 20 40 60
E [MeV]
x (c)
10−3
1
0.8
0.6
0.4
0.2
0
0 10 20 30
E [MeV]
x (e)
10−3
3.5
3
2.5
2
1.5
1
0.5
0
0 10 20 30
E [MeV]
IDSA: spectral results
dY/dE [MeV −1 ]
dY/dE [MeV −1 ]
dY/dE [MeV −1 ]
x (b)
10−4
5
4
3
2
1
Boltzmann
Approx.
Trapped
Streaming
0
0 20 40 60
E [MeV]
x (d)
10−3
1
0.8
0.6
0.4
0.2
0
0 10 20 30
E [MeV]
x (f)
10−3
3.5
3
2.5
2
1.5
1
0.5
0
0 10 20 30
E [MeV]
Comparison between Boltztran and
IDSA spectra (left-νe, right-¯νe)
Hydro: AGILE (1D, GR)
t = 150ms after bounce
progenitor M = 13M⊙ (Nomoto 88)
EOS: Lattimer-Swesty
1. R = 40km, trapped regime
trapped particles dominate
2. R = 80km, semi-trasparent
both trapped and streaming particles
3. R = 160km, transparent regime
streaming particles dominate
Neutrinos in core collapse SN explosion - Paris, 10 September 2009 – p. 34/48

Density, log 10 (ρ [g/cm 3 ])
Entropy per Baryon [k B ])
Electron Fraction
Velocity [km/s]
14
12
10
8
6
10
8
6
4
2
0
0.5
0.4
0.3
0.2
1
0
−1
−2
−3
−4
IDSA: hydrodynamical evolution
x 10 4 0.1
Boltzmann
Approx.
Spectral
−5
0 50 100 150 200 250 300
Radius [km]
Comparison between Boltztran and
IDSA post-bounce evolution
Hydro: AGILE (1D, GR)
1. t = 30ms after bounce, where
Rshock ∼ 150km
2. t = 100ms after bounce, where
Rshock ∼ 250km
progenitor M = 13M⊙ (Nomoto 88)
EOS: Lattimer-Swesty
Very good agreement in the shock
expanding phase
Neutrinos in core collapse SN explosion - Paris, 10 September 2009 – p. 35/48

Leakage scheme: motivations
Present day state-of-art of core collapse SN modelling is not the whole
story; open tasks:
exploration of large parameter space for initial conditions (rotation,
magnetic field,. . . )
comparison of different explosion mechanisms (quark phase
transition, acustic mechanism, magneto-rotational instabilities, . . . )
improvement of hydrodynamics (GR, MHD, 3D, . . . )
other astrophysical contexts, where neutrinos play a major role
(cosmology, NS merger, BH formation . . . )
Neutrinos in core collapse SN explosion - Paris, 10 September 2009 – p. 36/48

Leakage scheme: motivations
Present day state-of-art of core collapse SN modelling is not the whole
story; open tasks:
exploration of large parameter space for initial conditions (rotation,
magnetic field,. . . )
comparison of different explosion mechanisms (quark phase
transition, acustic mechanism, magneto-rotational instabilities, . . . )
improvement of hydrodynamics (GR, MHD, 3D, . . . )
other astrophysical contexts, where neutrinos play a major role
(cosmology, NS merger, BH formation . . . )
For those, approx ν (at least, for µ and τ flavours) treatment which
catchs the very essential physics (conservative approach: mainly, ν
cooling effect)
does not impact on the computational efficiency
Ruffert et al. (1996), Rosswog & Liebendorfer (2003)
Neutrinos in core collapse SN explosion - Paris, 10 September 2009 – p. 36/48

Leakage scheme: basic idea
Transparent regime (τ 1)
tdiff ≈ tfree stream
all the produced ν can stream
out freely (label: fs)
Qfs ≈ Qprod
Rfs ≈ Rprod
where Q → energy rate, R → particle rate
How to put them togheter? interpolation
Qeff = QtrQfs
Qtr + Qfs
Opaque regime (τ ≫ 1)
tdiff ≫ tfree stream
ν’s form a Fermi gas in
equilibrium with matter and
leak out on tdiff (label: tr)
Qtr ≈ Qdiff+Qeq ∼ Eν gas
tdiff
Rtr ≈ Rdiff +Req ∼ Nν gas
tdiff
+ δEint
δt
+ δNeq
δt
Neutrinos in core collapse SN explosion - Paris, 10 September 2009 – p. 37/48

Leakage scheme: testing µ and τ cooling
Velocity, u [km/s]
Entropy per Baryon, s [k B ])
1
0
−1
−2
−3
−4
−5
−6
6
4
2
0
x 10 4
10 1
10 1
227ms After Bounce
10 2
Radius, r [km]
10 2
Radius, r [km]
(c)
grid points
10 3
10 3
Baryon Density, log 10 (ρ [g/cm 3 ])
Electron Fraction, Y e
14
12
10
8
6
0.5
0.4
0.3
0.2
0.1
10 1
10 1
10 2
Radius, r [km]
s15s7b2
10 2
Radius, r [km]
(d)
Boltztran
leakage
10 3
10 3
Hydro: AGILE (1D GR)
νe transport: BOLTZTRAN
t = 10ms post bounce
νµ and ντ cooling: Boltztran
results VS leakage results
Quantitatively good
agreement
. . . but probably because
too close to bounce!
Neutrinos in core collapse SN explosion - Paris, 10 September 2009 – p. 38/48

Leakage scheme: testing µ and τ cooling
Velocity, u [km/s]
Entropy per Baryon, s [k B ])
1
0
−1
−2
−3
−4
−5
−6
10
8
6
4
2
0
x 10 4
10 1
10 1
269ms After Bounce
10 2
Radius, r [km]
10 2
Radius, r [km]
(c)
grid points
10 3
10 3
Baryon Density, log 10 (ρ [g/cm 3 ])
Electron Fraction, Y e
14
12
10
8
6
0.5
0.4
0.3
0.2
0.1
10 1
10 1
10 2
Radius, r [km]
s15s7b2
10 2
Radius, r [km]
(d)
Boltztran
leakage
10 3
10 3
Hydro: AGILE (1D GR)
νe transport: BOLTZTRAN
t = 50ms post bounce
νµ and ντ cooling: Boltztran
results VS leakage results
Qualitatively good
agreement,
entropy shows some
different features
Neutrinos in core collapse SN explosion - Paris, 10 September 2009 – p. 38/48

Leakage scheme: testing µ and τ cooling
Velocity, u [km/s]
Entropy per Baryon, s [k B ])
1
0
−1
−2
−3
−4
−5
−6
12
10
8
6
4
2
0
x 10 4
10 1
10 1
317ms After Bounce
10 2
Radius, r [km]
10 2
Radius, r [km]
(c)
grid points
10 3
10 3
Baryon Density, log 10 (ρ [g/cm 3 ])
Electron Fraction, Y e
14
12
10
8
6
0.5
0.4
0.3
0.2
0.1
10 1
10 1
10 2
Radius, r [km]
s15s7b2
10 2
Radius, r [km]
(d)
Boltztran
leakage
10 3
10 3
Hydro: AGILE (1D GR)
νe transport: BOLTZTRAN
t = 100ms post bounce
νµ and ντ cooling: Boltztran
results VS leakage results
Qualitatively good
agreement,
entropy shows some
different features
shock position slightly different
Neutrinos in core collapse SN explosion - Paris, 10 September 2009 – p. 38/48

Leakage scheme: testing µ and τ cooling
Velocity, u [km/s]
Entropy per Baryon, s [k B ])
1
0
−1
−2
−3
−4
−5
−6
18
16
14
12
10
8
6
4
2
0
x 10 4
10 1
10 1
417ms After Bounce
10 2
Radius, r [km]
10 2
Radius, r [km]
(c)
grid points
10 3
10 3
Baryon Density, log 10 (ρ [g/cm 3 ])
Electron Fraction, Y e
14
12
10
8
6
0.5
0.4
0.3
0.2
0.1
10 1
10 1
10 2
Radius, r [km]
s15s7b2
10 2
Radius, r [km]
(d)
Boltztran
leakage
10 3
10 3
Hydro: AGILE (1D GR)
νe transport: BOLTZTRAN
t = 200ms post bounce
νµ and ντ cooling: Boltztran
results VS leakage results
Qualitatively good
agreement,
entropy shows some
different features
shock position slightly different
Neutrinos in core collapse SN explosion - Paris, 10 September 2009 – p. 38/48

Leakage scheme: testing µ and τ cooling
Velocity, u [km/s]
Entropy per Baryon, s [k B ])
1
0
−1
−2
−3
−4
−5
−6
26
24
22
20
18
16
14
12
10
8
6
4
2
0
x 10 4
10 1
10 1
717ms After Bounce
10 2
Radius, r [km]
10 2
Radius, r [km]
(c)
grid points
10 3
10 3
Baryon Density, log 10 (ρ [g/cm 3 ])
Electron Fraction, Y e
14
12
10
8
6
0.5
0.4
0.3
0.2
0.1
10 1
10 1
10 2
Radius, r [km]
s15s7b2
10 2
Radius, r [km]
(d)
Boltztran
leakage
10 3
10 3
Hydro: AGILE (1D GR)
νe transport: BOLTZTRAN
t = 500ms post bounce
νµ and ντ cooling: Boltztran
results VS leakage results
Qualitatively good
agreement,
entropy shows some
different features
shock position slightly different
Neutrinos in core collapse SN explosion - Paris, 10 September 2009 – p. 38/48

Work in progress @ unibas . . .
ELEPHANT
ELEgant Parallel Hydrodynamics with Approximate Neutrino
Transport
Fusion between . . .
. . . FISH: 3D MHD code for magneto-hydrodynamics
Lattimer-Swesty EOS and Shen EOS available
. . . IDSA: detailed approx νe and ¯νe transport
. . . leakage scheme: approx νµ, ντ, ¯νµ and ¯ντ cooling
extention of leakage scheme to νe flavour
Testing phase! But . . . let’s have a look!
Neutrinos in core collapse SN explosion - Paris, 10 September 2009 – p. 39/48

Conclusions and outlook
Neutrinos in core collapse SN explosion - Paris, 10 September 2009 – p. 40/48

Conclusions
Core collapse SN is a very interesting topic, which involves deeply
many different physics subjects and computational tools
neutrinos play a major role in core collapse SN, where they interact
significantly with matter in extreme conditions
after almost 50 years of quantitative modeling, core collapse SN
explosion is not yet understood; many different mechanism have
been proposed and most of them are under investigation
multi-dimensional effects, improved neutrino-matter interactions,
detailed nuclear physics seem to be all necessary to model core
collapse SN correctly
approximated, but enough detailed neutrino transport (with spectral
analysis) is required
Neutrinos in core collapse SN explosion - Paris, 10 September 2009 – p. 41/48

Outlook
Development of approximated ν transport:
investigation of wide parameter space in core collapse SN theory
(rotation, magnetic field, . . . ) and prediction of their GW signatures
(S. Sheidegger)
verification of neutrino driven explosion in 3D model, with reasonable
computational time (M. Liebendorfer, S. Whitehouse)
application of leakage schemes to other explosion mechanism
quark phase transition (T. Fisher)
jets formation in highly rotating, highly magnetized stars (R.
Kappeli)
investigation of ν transport in different astrophysics contexts (like
neutron star merger, A. Perego)
Neutrinos in core collapse SN explosion - Paris, 10 September 2009 – p. 42/48

Neutrinos in core collapse SN explosion - Paris, 10 September 2009 – p. 43/48

Neutrinos in core collapse SN explosion - Paris, 10 September 2009 – p. 44/48

Core collapse SN in a nutshell I
Core collapse SN explosion is the fate of a massive star
(8M⊙ M∗ 90M⊙) before becoming a NS or a BH
Neutrinos in core collapse SN explosion - Paris, 10 September 2009 – p. 45/48

Core collapse SN in a nutshell I
Core collapse SN explosion is the fate of a massive star
(8M⊙ M∗ 90M⊙) before becoming a NS or a BH
dynamics:
Collapse phase at the end of the nuclear burning
phases, Fe core of a star collapses due to gravity
initial Fe core properties for Mprog = 15M⊙:
Rc ∼ 3000 km & M(Rc) ∼ MCh 106 ρ(g/cm3 ) 10 10
0.2 kBT(MeV) 0.7 0.42 Ye 0.5
Pressure: relativistic degenerate e − gas
tcol ∼ tff ∼ 1/ √ G¯ρ ∼ 200ms
Neutrinos in core collapse SN explosion - Paris, 10 September 2009 – p. 45/48

Core collapse SN in a nutshell I
Core collapse SN explosion is the fate of a massive star
(8M⊙ M∗ 90M⊙) before becoming a NS or a BH
dynamics:
Collapse phase
Bounce phase when ρ(R = 0) ∼ ρnucl, the core
bounces because of nuclear short range repulsive
interaction;
core properties at bounce:
10 6 ρ(g/cm 3 ) 5 × 10 14 0.2 kBT(MeV) 13.7
0.32 Ye 0.5
shock wave formation at the sonic point
Neutrinos in core collapse SN explosion - Paris, 10 September 2009 – p. 45/48

Core collapse SN in a nutshell I
Core collapse SN explosion is the fate of a massive star
(8M⊙ M∗ 90M⊙) before becoming a NS or a BH
dynamics:
Collapse phase
Bounce phase
Post-bounce phase the outgoing shock wave expands
and stops, because it loses energy dissociating Fe
matter and emitting ν’s; later, the wave is somehow
revived and the star is destroyed
several proposed mechanisms: neutrino heating, sound
mechanism, 3D MHD effects, jets, neutrino oscillations . . .
texpl ∼ 300ms − 1.5s
Neutrinos in core collapse SN explosion - Paris, 10 September 2009 – p. 45/48

Simulation building blocks
Computational domain
EOS
symmetry degree of the system and domain extension
for every point of the domain, a vector with hydrodynamics,
thermodynamics and neutrino variables is defined
it describes the termodynamics state of baryonic matter and
electromagnetic radiation
whenever hydrodynamics or neutrino transport change one of the
thermodynamics variables, the EOS accunts for all the other
variables changes, assuming equilibrium
Hydrodynamics (HD)
Solution of hydrodynamics equations, with Newtonian gravity (NR) or
in General Relativity (GR), eventually including magnetic field (MHD).
Neutrinos in core collapse SN explosion - Paris, 10 September 2009 – p. 46/48

Mass and spin coevolution during the alignment of a BH]Mass
and spin coevolution during the alignment of a black hole in a
warped accretion disc A. Perego et al.]A. Perego 11 , M. Dotti 2 ,
M. Colpi 3 , M. Volonteri 2
1 Department of Physics, University of Basel, Klingerbergstr.
82, 4056 Basel, Switzerland
2 Department of Astronomy, University of Michigan, Ann Arbor,
MI 48109, USA
3 Dipartimento di Fisica, Università degli Studi di Milano-Bicocca,
Piazza Della Scienza 3, 20126 Milano, Italy
46-1

ILE-BOLTZTRAN fundamental equatio
Einstein eqs (conservative formulation) + Boltzmann eqs
∇νT µν = 0 D[fi] = C[fi] with i = νe, νµ, ντ, ¯νe, . . .
Einstein eqs. and conservation eqs. give evolution equations for
global quantities (total energy, total momentum, total internal energy,
. . . )
integration of Boltzmann equations over momentum space (E, µ)
gives local conservation laws for neutrino numbers and neutrino
energies, and neutrino contributions to general equations
consistent equations for hydrodynamical evolution can be found by
subtraction of neutrino contributions from global equations
Neutrinos in core collapse SN explosion - Paris, 10 September 2009 – p. 47/48

Leakage scheme: ingredients
Production mechanisms: pair production, e ± capture
e + + e − ↔ ν + ¯ν p + e − ↔ n + νe n + e + ↔ p + ¯νe
Rprod = Rprod(ρ, T, Ye) Qprod = Qprod(ρ, T, Ye) ⇒ local
Diffusion mechanism: elastic scattering on nucleons and nuclei
N + ν → N ′ + ν ′ A + ν → A ′ + ν ′
Rdiff = Rdiff(T, λν, τν) Qdiff = Qdiff(T, λν, τν) ⇒ local + global
Equilibrium conditions: local thermodynamical equilibrium
for ρ 10 13 g/cm 3 , local equilibrium conditions apply
for 10 11 g/cm 3 ρ 10 13 g/cm 3 , smooth approach to equilibrium
Neutrinos in core collapse SN explosion - Paris, 10 September 2009 – p. 48/48