Neutrinos from supernovae and failed supernovae

Neutrinos from supernovae and failed supernovae
2010.12.14 NNN10@Toyama
Hideyuki Suzuki, Tokyo Univ. of Science
H
He CO ONeMg Fe Si
Main Sequence
Mass Loss
Collapse
M>8M
Companion
Neutron Star
Black Hole
Binary
White Dwarf
Type Ia Supernova
Collapse-driven Supernova

1 Collapse-Driven Supernova Explosion
SN Core (T ∼ 10MeV, ρ > ∼ 10 14 g/cm 3 )
• τ weak ≪ τ dyn Neutrino Trapping
⇒ Neutrinos are also in thermal equilibrium and in chemical equilibrium
n ν ∼ n γ ∼ n e
• mean free path length λ ν ≫ λ γ , λ e , λ N
⇒ Neutrinos carry the energy and drive the evolution of the core
⇒ SN core can be seen by neutrinos (neutrinosphere)
SN as a neutrino source
• source of all species (ν e ,¯ν e ,ν µ ,¯ν µ ,ν τ ,¯ν τ )
• T < O(100MeV) = m µ ⇒ n e −
≫ n µ , n τ : ν x ≡ ν µ , ¯ν µ , ν τ , ¯ν τ
• ∫ L ν dt ∼ O(10 53 )erg ∼ 10 4 L ν⊙ τ ⊙ ∼ 10 2 L γ⊙ τ ⊙
τ ∼ O(10)sec, d > O(10 18 )cm
• Spectral difference: hierarchy of average energy(O(10)MeV)
σ νe > σ¯νe > σ νx ⇒ 〈ω νe 〉

H
He
CO
ONeMg
Si
νe
Fe
Fe core
9−10
ρ 3
c =10 g/cm
Neutrinosphere
11
ρ >10 g/cm
c
3
ν trapping (ρ > 10 10 − 10 12 g/cm 3 )
ν e from e − A −→ ν e A ′ and e − p −→ ν e n
main opacity source: coherent scattering ν e A −→ ν e A
cross section σ ∝ A 2 ων: 2 λ νA < λ νN
(ν wave length ¯hc
E
E ν
∼ 20fm( ν
10MeV )−1 ≫ nuclear size 1.2A 1 3 fm ∼ 5fm( A 56 ) 1 3 )
collapse
σ∼E^2
increase
opaque
ν
trapping
ν
degenerate
µ(ν) increase
coherent
scattering
nuclei survive
e capture suppress
not so n−rich
Positive feedback (Sato 1975)

νeneutronization
burst
shock stall
ν(all)
ρ c
bounce
14
>10 g/cm
3
Proto
Neutron
Star
shock wave
τ(collapse)~O(10−100)ms
τ (neutronization burst)

Prompt explosion (Hillebrandt, Nomoto and Wolff 1984). M MS = 9M ⊙
Failed Prompt explosion (Hillebrandt 1987). M MS = 20M ⊙

Wilson’s Delayed explosion model (Colgate 1989).

shock revival
νwind
PNS cooling
ν heating
Hot Bubble
t(core exp.)=O(1)s
τ(PNS cooling)=O(10)s
Supernova
Explosion
Neutron Star
t(SNE)=hours−day
SN1987A
Crab nebula (remnant of
SN1054)

Classical Simulations
Totani et al., 1998
early phase: hierarchy of average energy
late phase: n-rich matter interacts ¯ν e and
ν x almost equally. degeneracy prohibits
ν e interactions, too.
neutrinos from protoneutron star cooling phase
(Suzuki 2002)

Energetics
• ∆E G =
(
GM
2
core
R Fe core
− GM 2 core
R NS
)
∼ O(10 53 )erg
• E kin (obs.)∼O(10 51 )erg, E rad (obs.)∼O(10 49 )erg, E GW (sim.)∼O(10 51 )erg
• rest O(10 53 )erg ∼ E ν
cf. E ν (SNIa) < 10 49 erg
ν e ’s from neutronization of all protons
26 M Fe core
〈E νe 〉 ∼ 1.2 · 10 52 erg M Fe core 〈E νe 〉
m Fe
1.4M ⊙ 10MeV ∼ O(0.1) × E ν tot
=⇒ thermal ν ≫ neutronization ν e =⇒ ν e , ¯ν e , ν x : roughly equipartiton

Neutrino Transfer
distibution function f νi (t, ⃗r, ⃗p ν ) (7 independent variables)
∂f ν
+ d⃗r ∂f ν
∂t p dt p ∂⃗r + d⃗p (
ν ∂f ν ∂fν
=
dt p ∂⃗p ν
∂t p
)ν int.
• Spherically symmetric case:
f νi (t, r, ω ν = p ν c, µ = cos θ) (4 independent variables)
⇒ Fully general relativistic Boltzmann solver
(Mezzacappa, Burrows, Janka, Sumiyoshi+Yamada > ∼ 2000)
• Non-spherical case: 2D/3D ν transfer in progress
Neutrino Interactions (minimal standard: Bruenn’85)
e − p ←→ ν e n e + n ←→ ¯ν e p e − A −→ ν e A ′ e + A −→ ¯ν e A ′
e − e + ←→ ν¯ν plasmon ←→ ν¯ν NN −→ NNν¯ν ν e¯ν e ←→ ν x¯ν x
νN −→ νN νA −→ νA νe ± −→ νe ± νν ′ −→ νν ′

Equation of States (EOS) for high density matter (T ≠ 0)
• Lattimer-Swesty 1991: FORTRAN code
Liquid Drop model: K s = 180, 220, 375MeV, S v = 29.3MeV
E/n ∼ −B + K s (1 − n/n s ) 2 /18 + S v (1 − 2Y e ) 2 + · · ·
• Shen’s EOS table (Shen et al., 1998)
RMF (n,p,σ, ρ, ω) with TM1 parameter set(g ρ , · · ·) ⇐ Nuclear data including
unstable nuclei
ρ B , n B , Y e , T , F , U, P , S, A, Z, M ∗ , X n , X p , X α , X A , µ n , µ p
grids: wide range T = 0, 0.1 ∼ 100MeV ∆ log T = 0.1
Y e = 0, 0.01 ∼ 0.56 ∆ log Y e = 0.025
ρ B = 10 5.1 ∼ 10 15.4 g/cm 3 ∆ log ρ B = 0.1
Extension with hyperons (Ishizuka, Ohnishi), quarks (Nakazato)

Modern Simulations
Light ONeMg core + CO shell(1.38M ⊙ ): weak explosion (O(10 50 )erg)
(Progenitor: Nomoto 8-10M ⊙ )
ν-heating + nuclear reaction ⇒ weak explosion
res (prompt explosions,
ups (Fryer et al. 1999).
ional
Fig. 1. Mass trajectories for the simulation with the W&H EoS as a
function of post-bounce time (t pb ). Also plotted: shock position (thick
solid line starting at time zero and rising to the upper right corner),
gain radius (thin dashed line), and neutrinospheres (ν e : thick solid;
¯ν e : thick dashed;ν µ , ¯ν µ ,ν τ , ¯ν τ : thick dash-dotted). In addition, the
composition interfaces are plotted with different bold, labelled lines:
the inner boundaries of the O-Ne-Mg layer at∼0.77 M ⊙ , of the C-O
layer at∼1.26 M ⊙ , and of the He layer at 1.3769 M ⊙ . The two dotted
lines represent the mass shells where the mass spacing between
the plotted trajectories changes. An equidistant spacing of 5×10 −2 M ⊙
was chosen up to 1.3579M ⊙ , between that value and 1.3765M ⊙ it was
1.3×10 −3 M ⊙ , and 8×10 −5 M ⊙ outside.
Fig. 3. Velocity profiles as functions of radius for different postbounce
times for the simulation with the W&H EoS. The insert shows
the velocity profile vs. enclosed mass at the end of our simulation.
Kitaura et al., AAp 450(2006)345
(Mezzacappa’07: 11.2M ⊙ model explodes, too)

L [10 52 erg s -1 ]
4
3
2
1
L/10
Accretion Phase
Cooling Phase
ν e
ν e
ν µ/τ
10 0
10 -1
0
10 -2
[MeV]
12
10
10
8
5
0 0.05 0.1 0.15 0.2 2 4 6 8
4
Time after bounce [s]
Neutrino luminosities and average energies at infinity for 8.8M ⊙
L. Hüdepohl et al., PRL104 (2010) 251101
progenitor.

Phase transition into quark matter
Luminosity [10 53 erg/s]
1
0
Luminosity [10 53 erg/s]
1
0
0.255 0.26 0.265
Time after bounce [s]
rms Energy [MeV]
30
25
20
15
10
0 0.1 0.2 0.3 0.4 0.5
Time after bounce [s]
FIG. 1: Neutrino luminosities and rms neutrino energies as
functions of time after bounce, sampled at 500 km radius in
the comoving frame, for a 10 M ⊙ progenitor star as modeled
in [17]: ν e in solid (blue), ¯ν e in dashed (red), and ν µ/τ in
dot-dashed (green). In contrast to the deleptonization burst
just after bounce (t ∼ 5 ms) the second burst at t ∼ 257−261
ms is associated with the QCD phase transition. The inset
shows the second burst blown up.
Dasgupta et al., PRD81 (2010) 103005
The second shock wave merges the first shock wave leading to explosion.
¯ν e > ν e in the second burst (protonization)

Modern simulations with GR 1D Boltzmann ν-transfer
canonical models: no explosion
Newton+O(v/c)
Relativistic
10 3 Time After Bounce [s]
Radius [km]
10 2
10 1
0 0.1 0.2 0.3 0.4 0.5
NH 13M ⊙ , GR Boltzman, LS EOS+Si burning
Liebendörfer et al., Phys.Rev. D63 (2001) 103004
(astro-ph/0006418 v2) Fig.6
10 4
Fig. 1.—Trajectories of selected mass shells vs. time from the start of the
simulation. The shells are equidistantly spaced in steps of 0.02 M ,, and the
trajectories of the outer boundaries of the iron core (at 1.28 M ,) and of the
silicon shell (at 1.77 M ,) are indicated by thick lines. The shock is formed
at 211 ms. Its position is also marked by a thick line. The dashed curve shows
the position of the gain radius.
WW 15M ⊙ , M Fe = 1.28M ⊙ , NR Boltzmann
(tangent-ray method), only ν e ,¯ν e , without
e − e + ↔ ν ¯ν, LS EOS, Rampp et al., ApJ 539
(2000) L33 Fig.1
10 3
radius [km]
10 2
10 1
10 0
0.0
0.2
0.4
time [sec]
15M ⊙ , Shen EOS, Sumiyoshi et al., 2005.
0.6
0.8
1.0
Fig. 5.—Radial position (in km) of selected mass shells as a function of
time in our fiducial 11 M model.
NR 1D Boltzmann ν-transfer, Thompson et al.,
ApJ 592 (2003) 434 Fig.5

Comparison between Boltzmann solvers
Fig. 5.—(a) Shock position as a function of time for model N13. The shock in VERTEX (thin line) propagates initially faster and nicely converges after its maximum
expansion to the position of the shock in AGILE-BOLTZTRAN (thick line). (b) Neutrino luminosities and rms energies for model N13 are presented as functions of
time. The values are sampled at a radius of 500 km in the comoving frame. The solid lines belong to electron neutrinos and the dashed lines to electron antineutrinos. The
line width distinguishes between the results from AGILE-BOLTZTRAN and VERTEX in the same way as in (a). The luminosity peaks are nearly identical; the rms
energies have the tendency to be larger in AGILE-BOLTZTRAN.
Liebendörfer et al., ApJ620(2005)840 Fig.5

2 Failed supernovae
implicit GR hydrodynamics + Boltzmann ν transfer code
Sumiyoshi, Yamada, Suzuki, Chiba PRL97(2006) 091101
Fig. 1.—Radial trajectories of mass elements of the core of a 40 M star as a
function of time after bounce in the SH model. The location of the shock wave is
shown by a thick dashed line.
Fig. 2.—Radial trajectories of mass elements of the core of a 40 M star as a
function of time after bounce in the LS model. The location of the shock wave is
shown by a thick dashed line.
luminosity [erg/s]
2x10 53 1
0
0.0
0.5
1.0
1.5
time after bounce [sec]
luminosity [erg/s]
2x10 53 1
0
0.0
0.5
1.0
time after bounce [sec]
Progenitor 40M ⊙ , left: Shen EOS, right: Lattimer-Swesty EOS 180
1.5
L ν increases due to
matter accretion
ν x < ν e , ¯ν e from accreted
matter
Burst duration time
strongly depends on
EOS!

(a)
Luminosity [10 53 erg/s]
rms Energy [MeV]
6
5
4
3
2
1
0
40
35
30
25
20
15
10
5
e Neutrino
e Antineutrino
µ/τ Neutrinos
0 0.2 0.4 0.6 0.8 1 1.2 1.4
Time After Bounce [s]
(b)
0 0.2 0.4 0.6 0.8 1 1.2 1.4
Time After Bounce [s]
Figure 2. Luminosities and mean energies during the post bounce phase
of a core collapse simulation of a 40 M ⊙ progenitor model from
Woosley and Weaver (1995). Comparing eos1 (thick lines) and eos2
(thin lines).
Fischer et al., 2008

Failed supernova neutrinos: expected observation by SK
Nakazato et al., PRD78 (2008) 083014
FIG. 5: Time-integrated spectra before the neutrino oscillation for models W40S (left) and W40L (right). Solid, dashed and
dot-dashed lines represent the spectra of νe, ¯νe and νx, respectively.
FIG. 8: Time-integrated total event number of failed supernova neutrinos for the normal mass hierarchy (left) and the inverted
mass hierarchy (right). Error bars represents the upper and lower limits owing to the different nadir angles. The upper and
lower sets represent models W40S and W40L, respectively.
θ 13 dependence for W40S vs. W40L
FIG. 9 (color online). Time-integrated spectra for the total event number of failed supernova neutrinos for the normal mass hierarchy
with sin 2 13 ¼ 10 8 (upper left), the normal mass hierarchy with sin 2 13 ¼ 10 2 (upper right), the inverted mass hierarchy with
sin 2 13 ¼ 10 5 (lower left), and the inverted mass hierarchy with sin 2 13 ¼ 10 2 (lower right). Results obtained without the Earth
effects are shown. Solid, long-dashed, short-dashed, dot-dashed, and dotted lines represent models W40S, W40L, T50S, T50L, and
H40L, respectively.
EOS (S,L), Progenitors (W40, T50, H40)

hyperon EOS vs. soft nucleon EOS
50
40
10 -1
10 -2
Λ
Σ 0
n
p
α
10 -1
10 -2
Λ
Ξ −
Σ −
n
p
α
< E ν > [MeV]
30
20
10
0
10 -3
10 -4
Ξ −
10 -3
10 -4
Ξ 0
L ν [erg/s]
2x10 53 1
10 -5
0
10 0 20x10 5
Σ − Ξ 0
Σ + 10
20
radius [km]
10 -5
0
10 0 20x10 5
Σ 0 Σ + 10
20
radius [km]
0
0.0
0.5
1.0
time after bounce [sec]
1.5
Fig. 2.— Mass fractions of hyperons in model IS are shown as a function of radius at t pb =500
(left) and 680 ms (right).
Sumiyoshi et al., Astrophys. J. 690 (2009) L43-L46
Fig. 3.— Average energies and luminosities of ν e (solid), ¯ν e (dashed) and ν µ/τ (dash-dotted)
for model IS are shown as a function of time after bounce. The results for model SH and LS
are shown by thin lines with the same notation.
increase of degree of freedom
→ Soft EOS
Hyperon EOS vs. Lattimer-Swesty EOSs
(LS180/220)(Nakazato et al., 2010)
might be distinguishable by the time profile
Good probe to properties of high density matter

3 Non-spherial explosion
SN1987A observations
• polarization
• material mixing (large v Fe > 3000km/sec(Fe II IR line), early detection of
X-ray, 847keV/1238keV 60 Co line), slow H velocity (∼ 800km/sec)
• asymmetric image
⇒ fluid instability, rotation, magnet field: multi-dimensional simulation
HST image of SN1987A on 1994.2 and 2003.11.28

Nomoto et al., astro-ph/0308136

2D/3D Hydrodynamics + simplified ν-transfer + full/approximated GR
At present, evolution of f ν (t, ⃗r, ⃗p ν ) cannot be calculated.
SASI: Standing Accretion Shock Instability Blondin et al., 2003
Instability modes with l = 1, 2 grow between stalled shock wave and protoneutron
star
(amplifying advective-accoustic cycle)
It helps neutrino heating (longer advection time) ? ⇒ successful explosion
Accoustic Explosion? Burrows et al., 2006
accretion → excitation of g-mode in PNS → sound wave
→ dissipation behind the shock front ? → robust explosion
rotation/magnetic field?
Angular momentum of core might be small (Heger et al., 2005)
jet-like explosion by non-spherical neutrino heating?
suppresion of instability due to rotation?
practically strong magnetic field ? → Magnetar (B = 10 15 G)
Many groups are at work.
Garching, LANL, ORNL, Basel, Princeton/Caltech,
NAOJ/Waseda, Kyoto ...

Janka et al.., 2006, non-rotating 11.2M ⊙ 2D simulation
⇒ weak explosion due to SASI+ν-heating
Simulation for π 4 ≤ θ ≤ 3π 4
does not explode, 0 ≤ θ ≤ π: explodes
instability modes with l = 1, 2(SASI) evolve → kick velocity?
entropy profiles: Janka et al., astro-ph/0612072
Figure 4: Four stages (at postbounce times of 141.1ms, 175.2ms, 200.1ms, and 225.7ms) during the evolution
of a (non-rotating), exploding two-dimensional 11.2M ⊙ model [12], visualized in terms of the entropy. The scale
is in km and the entropies per nucleon vary from about 5k B (deep blue), to 10 (green), 15 (red and orange),
up to more than 25k B (bright yellow). The dense neutron star is visible as low-entropy (< ∼
5k B per nucleon)
circle at the center. The computation was performed in spherical coordinates, assuming axial symmetry, and
employing the “ray-by-ray plus” variable Eddington factor technique of Refs. [41, 11] for treating ν transport in
multi-dimensional supernova simulations. Equatorial symmetry is broken on large scales soon after bounce, and
low-mode hydrodynamic instabilities (convective overturn in combination with the SASI) begin to dominate the
τ adv ↗> τ heat , wider heating region: SASI helps ν-heating

Marek et al., Astron. Astrophys. 496 (2009) 475
20
2•10 9
20
2•10 9
s[kB/baryon]
15
10
0
-2•10 9
vr [cm/s]
s[kB/baryon]
15
10
0
-2•10 9
vr [cm/s]
5
-4•10 9
5
-4•10 9
180 120 60 0
60 120 180
r [km]
180 120 60 0
60 120 180
r [km]
s[kB/baryon]
20
15
10
5
180 120 60 0
60 120 180
r [km]
2•10 9
0
-2•10 9
-4•10 9
vr [cm/s]
s[kB/baryon]
25
20
15
10
5
180 120 60 0
60 120 180
r [km]
Fig. 3. Four representative snapshots from the 2D simulation with the L&S EoS at post-bounce times of 247 ms (top left), 255 ms (top right),
322 ms (bottom left), and 375 ms (bottom right). The lefthand panel of each figure shows color-coded the entropy distribution, the righthand
panel the radial velocity component with white and whitish hues denoting matter at or near rest; black arrows in the righthand panel indicate the
direction of the velocity field in the post-shock region (arrows were plotted only in regions where the absolute values of the velocities were less
than 2×10 9 cm s −1 ). The vertical axis is the symmetry axis of the 2D simulation. The plots visualize the accretion funnels and expansion flows in
the SASI layer, but the chosen color maps are unable to resolve the convective shell inside the nascent neutron star.
4•10 9
2•10 9
0
-2•10 9
-4•10 9
vr [cm/s]
Rs,max [km], Rns [km]
250
200
150
100
50
L&S-EoS
H&W-EoS
0
0 100 200
t pb [ms]
300 400
Rs [km]
L&S-EoS
248 ms
270 ms
300 ms
H&W-EoS
-250 -150 50 50 150 250
R s [km]
Fig. 4. Left: maximum shock radii (solid lines) and proto-neutron star radii (dashed lines) as functions of post-bounce time for the 2D simulations
with different nuclear equations of state. The neutron star radii are determined as the locations where the rest-mass density is equal to 10 11 g cm −3 .
Right: shock contours at the different post-bounce times listed in the figure. The vertical axis of the plot is the symmetry axis of the simulation.
319 ms
380 ms
200
100
0
-100
-200
Rs [km]

Marek et al., Astron. Astrophys. 496 (2009) 475
100
ν e
100
ν e
L [10 51 erg/s]
80
60
40
L&S-EoS
H&W-EoS
L [10 51 erg/s]
80
60
40
L&S-EoS
H&W-EoS
20
1D
2D
0
0 100 200
t pb [ms]
300 400
20
1D
2D
0
0 100 200
t pb [ms]
300 400
L [10 51 erg/s]
L [10 51 erg/s]
80
60
40
L&S-EoS
H&W-EoS
20
1D
2D
0
0 100 200
t pb [ms]
300 400
50
40
30
20
10
L&S-EoS
H&W-EoS
1D
2D
0
0 100 200
t pb [ms]
300 400
¯ν e
ν x
L [10 51 erg/s]
L [10 51 erg/s]
80
60
40
20
L&S-EoS
H&W-EoS
1D
2D
0
0 100 200
t pb [ms]
300 400
50
40
30
20
10
L&S-EoS
H&W-EoS
1D
2D
0
0 100 200
t pb [ms]
300 400
Fig. 6. Isotropic equivalent luminosities of electron neutrinos (top), electron antineutrinos (middle), and one kind of heavy-lepton neutrinos (ν µ,
¯ν µ,ν τ, or ¯ν τ; bottom) versus time after core bounce as measurable for a distant observer located along the polar axis of the 2D spherical coordinate
grid (solid lines). The dashed lines display the radiated luminosities of the corresponding spherically symmetric (1D) simulations. The evaluation
was performed at a radius of 400 km (from there the remaining gravitational redshifting to infinity is negligible) and the results are given for an
observer at rest relative to the stellar center. While the left column shows the (isotropic equivalent) luminosities computed from the flux that is
radiated away in an angular grid bin very close to the north pole, the right column displays the emitted (isotropic equivalent) luminosities when
the neutrino fluxes are integrated over the whole northern hemisphere of the grid (see Eqs. (2) and (4), respectively).
¯ν e
ν x
〈ǫν〉 [MeV]
〈ǫν〉 [MeV]
〈ǫν〉 [MeV]
18
16
14
12
10
L&S-EoS
ν e
¯ν e
ν x
8
0 100 200
t pb [ms]
300 400
18
16
14
12
10
ν e
¯ν e
ν x
8
0 100 200
t pb [ms]
300 400
18
16
14
12
10
L&S-EoS
L&S-EoS
ν e
¯ν e
ν x
8
0 100 200
t pb [ms]
300 400
〈ǫν〉 [MeV]
〈ǫν〉 [MeV]
〈ǫν〉 [MeV]
18
16
14
12
10
H&W-EoS
ν e
¯ν e
ν x
8
0 100 200
t pb [ms]
300 400
18
16
14
12
10
H&W-EoS
ν e
¯ν e
ν x
8
0 100 200
t pb [ms]
300 400
18
16
14
12
10
H&W-EoS
ν e
¯ν e
ν x
8
0 100 200
t pb [ms]
300 400
Fig. 7. Mean energies of radiated neutrinos as functions of post-bounce time for our 1D simulations (top) and 2D models (middle and bottom) with
both equations of state (the lefthand panels are for the L&S EoS, the right ones for the H&W EoS). The displayed data are defined as ratios of
the energy flux to the number flux and correspond to the luminosities plotted with dashed and solid lines in Fig. 6. The panels in the middle show
results for a lateral grid zone near the north polar axis, the bottom panels provide results that are averaged over the whole northern hemisphere of
the computational grid. In all cases the evaluation has been performed in the laboratory frame at a distance of 400 km from the stellar center.
〈ω¯νe 〉 > 〈ω νx 〉 but 〈ω¯νe 〉 rms < 〈ω νx 〉 rms

Summary
• state-of-the-art 1D simulation
light core explodes weakly
canonical cores do not explode
black hole formation? explode with non-sphericity?/unknown EOS?
• 2D/3D simulations are still in progress
• Neutrinos from failed supernovae are good probe to high density matter
Today’s Lesson:
Supernova neutrinos will come to us suddenly, we must be always ready.