Neutrinos from supernovae and failed supernovae2010.12.14 NNN10@Toyama

Hideyuki Suzuki, Tokyo Univ. of Science

H

M>8MMass Loss

Collapse

He CO ONeMg FeSi

Neutron StarBlack Hole

Main Sequence

Type Ia Supernova Collapse-driven Supernova

White Dwarf

Companion

Binary

0-0

1 Collapse-Driven Supernova Explosion

SN Core (T ∼ 10MeV, ρ >∼ 1014g/cm3)• τweak ¿ τdyn Neutrino Trapping⇒ Neutrinos are also in thermal equilibrium and in chemical equilibriumnν ∼ nγ ∼ ne

• mean free path length λν À λγ , λe, λN

⇒ 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 (νe,νe,νµ,νµ,ντ ,ντ )

• T < O(100MeV) = mµ ⇒ ne− À nµ, nτ : νx ≡ νµ, νµ, ντ , ντ

•∫

Lνdt ∼ O(1053)erg ∼ 104Lν¯τ¯ ∼ 102Lγ¯τ¯τ ∼ O(10)sec, d > O(1018)cm

• Spectral difference: hierarchy of average energy(O(10)MeV)σνe > σνe > σνx ⇒ 〈ωνe〉<〈ωνe〉<〈ωνx〉

• Neutrinos pass through high density (matter and neutrinos) region(ρ = 0 ∼1015g/cm3): High density MSW resonance, collective oscillation due to ν-νinteractions

0-1

Neutrinosphere

ρ >10 g/cm11 3

c

Fe

HHeCO

SiONeMg

Fe core

ρc=10 g/cm9−10 3

νe

ν trapping (ρ > 1010 − 1012g/cm3)νe from e−A −→ νeA′ and e−p −→ νenmain opacity source: coherent scattering νeA −→ νeA

cross section σ ∝ A2ω2ν : λνA < λνN

(ν wave length hcEν

∼ 20fm( Eν

10MeV )−1 À nuclear size 1.2A13 fm ∼ 5fm( A

56 )13 )

coherentscattering

collapse

opaque trapping

σ∼ E^2

ν µ(ν) increase

increase

e capture suppressnuclei survive

degenerateν

not so n−rich

Positive feedback (Sato 1975)

0-2

bounce

>10 g/cm14 3

cρ

shock wave

ν neutronizationburst

shock stall

e ν(all)

(collapse)~O(10−100)msτ t(stall)=O(100ms)τ (neutronization burst)<O(10)ms

ProtoNeutron

Star

Neutronization burst. Thompson et al., ApJ 592 (2003) 434

Fig.6 (failed explosion)

Shocked regionA → np, e−p → nνe

σ(e−A → νeA′) < σ(e−p → νen)

0-3

Prompt explosion (Hillebrandt, Nomoto and Wolff 1984). MMS = 9M¯

Failed Prompt explosion (Hillebrandt 1987). MMS = 20M¯

0-4

Wilson’s Delayed explosion model (Colgate 1989).

0-5

PNS cooling

(PNS cooling)=O(10)sτ

shock revival

heatingνHot Bubble

νwind

t(core exp.)=O(1)s

SupernovaExplosion

t(SNE)=hours−day

Neutron Star

SN1987A

Crab nebula (remnant of

SN1054)

0-6

Classical Simulations

Totani et al., 1998

early phase: hierarchy of average energylate phase: n-rich matter interacts νe andνx almost equally. degeneracy prohibitsνe interactions, too. neutrinos from protoneutron star cooling phase

(Suzuki 2002)

0-7

Energetics• ∆EG =

(GM2

coreRFe core

− GM2core

RNS

)∼ O(1053)erg

• Ekin(obs.)∼O(1051)erg, Erad(obs.)∼O(1049)erg, EGW(sim.)∼O(1051)erg• rest O(1053)erg ∼ Eν cf. Eν(SNIa) < 1049erg

νe’s from neutronization of all protons

26MFe core

mFe〈Eνe〉 ∼ 1.2 · 1052erg

MFe core

1.4M¯

〈Eνe〉10MeV

∼ O(0.1) × Eν tot

=⇒ thermal ν À neutronization νe =⇒ νe, νe, νx: roughly equipartiton

0-8

Neutrino Transferdistibution function fνi(t, ~r, ~pν) (7 independent variables)

∂fν

∂tp+

d~r

dtp

∂fν

∂~r+

d~pν

dtp

∂fν

∂~pν=

(∂fν

∂tp

)ν int.

• Spherically symmetric case:fνi(t, r, ων = pνc, 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 ←→ νen e+n ←→ νep e−A −→ νeA′ e+A −→ νeA′

e−e+ ←→ νν plasmon ←→ νν NN −→ NNνν νeνe ←→ νxνx

νN −→ νN νA −→ νA νe± −→ νe± νν′ −→ νν′

0-9

Equation of States (EOS) for high density matter (T 6= 0)• Lattimer-Swesty 1991: FORTRAN code

Liquid Drop model: Ks = 180, 220, 375MeV, Sv = 29.3MeVE/n ∼ −B + Ks(1 − n/ns)2/18 + Sv(1 − 2Ye)2 + · · ·

• Shen’s EOS table (Shen et al., 1998)RMF (n,p,σ, ρ, ω) with TM1 parameter set(gρ, · · ·) ⇐ Nuclear data includ-ing unstable nucleiρB , nB , Ye, T , F , U , P , S, A, Z, M∗, Xn, Xp, Xα, XA, µn, µp

grids: wide range T = 0, 0.1 ∼ 100MeV ∆ log T = 0.1Ye = 0, 0.01 ∼ 0.56 ∆ log Ye = 0.025ρB = 105.1 ∼ 1015.4g/cm3 ∆log ρB = 0.1

Extension with hyperons (Ishizuka, Ohnishi), quarks (Nakazato)

0-10

Modern SimulationsLight ONeMg core + CO shell(1.38M¯): weak explosion (O(1050)erg)

(Progenitor: Nomoto 8-10M¯)ν-heating + nuclear reaction ⇒ weak explosion

in the SN simulations of O-Ne-Mg cores (prompt explosions,

erent nuclear EoSs used by the groups (Fryer et al. 1999).

ional

Fig. 1. Mass trajectories for the simulation with the W&H EoS as afunction of post-bounce time (tpb). Also plotted: shock position (thicksolid line starting at time zero and rising to the upper rightcorner),gain radius (thin dashed line), and neutrinospheres (νe: thick solid;νe: thick dashed;νµ, νµ, ντ, ντ: thick dash-dotted). In addition, thecomposition interfaces are plotted with different bold, labelled lines:the inner boundaries of the O-Ne-Mg layer at∼0.77 M⊙, of the C-Olayer at∼1.26 M⊙, and of the He layer at 1.3769M⊙. The two dot-ted lines represent the mass shells where the mass spacing betweenthe plotted trajectories changes. An equidistant spacing of 5×10−2M⊙was chosen up to 1.3579M⊙, between that value and 1.3765M⊙ it was1.3× 10−3M⊙, and 8× 10−5M⊙ outside.

Fig. 3. Velocity profiles as functions of radius for different post-bounce times for the simulation with the W&H EoS. The insert showsthe 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)

0-11

0

1

2

3

4

L [

10

52 e

rg s

-1]

10-2

10-1

100

0 0.05 0.1 0.15 0.28

10

12

<ε>

[M

eV]

2 4 6 85

10

νe

νe

νµ/τ

L/10

Time after bounce [s]

Accretion Phase Cooling Phase

4Neutrino luminosities and average energies at infinity for 8.8M¯ progenitor.L. Hudepohl et al., PRL104 (2010) 251101

0-12

Phase transition into quark matter

0 0.1 0.2 0.3 0.4 0.5Time after bounce [s]

10

15

20

25

30

rms

Ene

rgy

[MeV

]

0

1

Lum

inos

ity [1

053 e

rg/s

]

0.255 0.26 0.265Time after bounce [s]

0

1

Lum

inos

ity [1

053 e

rg/s

]

FIG. 1: Neutrino luminosities and rms neutrino energies asfunctions of time after bounce, sampled at 500 km radius inthe comoving frame, for a 10 M⊙ progenitor star as modeledin [17]: νe in solid (blue), νe in dashed (red), and νµ/τ indot-dashed (green). In contrast to the deleptonization burstjust after bounce (t ∼ 5 ms) the second burst at t ∼ 257−261ms is associated with the QCD phase transition. The insetshows the second burst blown up.

Dasgupta et al., PRD81 (2010) 103005

The second shock wave merges the first shock wave leading to explosion.νe > νe in the second burst (protonization)

0-13

Modern simulations with GR 1D Boltzmann ν-transfercanonical models: no explosion

0 0.1 0.2 0.3 0.4 0.510

1

102

103

Time After Bounce [s]

Rad

ius

[km

]Newton+O(v/c)Relativistic

NH 13M¯, GR Boltzman, LS EOS+Si burningLiebendorfer et al., Phys.Rev. D63 (2001) 103004

(astro-ph/0006418 v2) Fig.6

100

101

102

103

104

radi

us [

km]

1.00.80.60.40.20.0

time [sec]

15M¯, Shen EOS, Sumiyoshi et al., 2005.

Fig. 1.—Trajectories of selected mass shells vs. time from the start of thesimulation. The shells are equidistantly spaced in steps of 0.02 M,, and thetrajectories of the outer boundaries of the iron core (at 1.28 M,) and of thesilicon shell (at 1.77 M,) are indicated by thick lines. The shock is formedat 211 ms. Its position is also marked by a thick line. The dashed curve showsthe position of the gain radius.

WW 15M¯, MFe = 1.28M¯, NR Boltzmann(tangent-ray method), only νe,νe, without

e−e+ ↔ νν, LS EOS, Rampp et al., ApJ 539(2000) L33 Fig.1

Fig. 5.—Radial position (in km) of selected mass shells as a function oftime in our fiducial 11M�model.

NR 1D Boltzmann ν-transfer, Thompson et al.,ApJ 592 (2003) 434 Fig.5

0-14

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 maximumexpansion to the position of the shock in AGILE-BOLTZTRAN (thick line). (b) Neutrino luminosities and rms energies for model N13 are presented as functions oftime. 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. Theline width distinguishes between the results from AGILE-BOLTZTRAN and VERTEX in the same way as in (a). The luminosity peaks are nearly identical; the rmsenergies have the tendency to be larger in AGILE-BOLTZTRAN.

Liebendorfer et al., ApJ620(2005)840 Fig.5

0-15

2 Failed supernovaeimplicit 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 40M� star as afunction of time after bounce in the SHmodel. The location of the shock wave isshown by a thick dashed line.

Fig. 2.—Radial trajectories of mass elements of the core of a 40M� star as afunction of time after bounce in the LSmodel. The location of the shock wave isshown by a thick dashed line.

2x1053

1

0

lum

inos

ity [

erg/

s]

1.51.00.50.0

time after bounce [sec]

2x1053

1

0

lum

inos

ity [

erg/

s]

1.51.00.50.0

time after bounce [sec]

Lν increases due tomatter accretionνx < νe, νe from ac-creted matterBurst duration timestrongly depends onEOS!

Progenitor 40M¯, left: Shen EOS, right: Lattimer-Swesty EOS 180

0-16

0 0.2 0.4 0.6 0.8 1 1.2 1.40

1

2

3

4

5

6

(a)

Time After Bounce [s]Lu

min

osity

[1053

erg

/s]

0 0.2 0.4 0.6 0.8 1 1.2 1.45

10152025303540

(b)

Time After Bounce [s]

rms

Ene

rgy

[MeV

]

e Neutrinoe Antineutrinoµ/τ Neutrinos

Figure 2. Luminosities and mean energies during the post bounce phaseof a core collapse simulation of a 40 M⊙ progenitor model fromWoosley and Weaver (1995). Comparing eos1 (thick lines) and eos2(thin lines).

Fischer et al., 2008

0-17

Failed supernova neutrinos: expected observation by SKNakazato et al., PRD78 (2008) 083014

FIG. 5: Time-integrated spectra before the neutrino oscillation for models W40S (left) and W40L (right). Solid, dashed anddot-dashed lines represent the spectra of νe, νe and νx, respectively.

FIG. 9 (color online). Time-integrated spectra for the total event number of failed supernova neutrinos for the normal mass hierarchy

with sin2 13 ¼ 10

!8 (upper left), the normal mass hierarchy with sin2 13 ¼ 10

!2 (upper right), the inverted mass hierarchy with

sin2 13 ¼ 10!5 (lower left), and the inverted mass hierarchy with sin2

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)

FIG. 8: Time-integrated total event number of failed supernova neutrinos for the normal mass hierarchy (left) and the invertedmass hierarchy (right). Error bars represents the upper and lower limits owing to the different nadir angles. The upper andlower sets represent models W40S and W40L, respectively.

θ13 dependence for W40S vs. W40L

0-18

hyperon EOS vs. soft nucleon EOS

10-5

10-4

10-3

10-2

10-1

100

20x105

100

radius [km]

Λ

Ξ−

n

p

αΣ−

Ξ0

Σ0

Σ+

2010

-5

10-4

10-3

10-2

10-1

100

20x105

100

radius [km]

Λ

Ξ−

n

p

αΣ−

Ξ0

Σ0

Σ+

20

Fig. 2.— Mass fractions of hyperons in model IS are shown as a function of radius at tpb=500

(left) and 680 ms (right).

50

40

30

20

10

0

< E

ν >

[M

eV]

2x1053

1

0

Lν

[erg

/s]

1.51.00.50.0

time after bounce [sec]

Fig. 3.— Average energies and luminosities of νe (solid), νe (dashed) and νµ/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.

Sumiyoshi et al., Astrophys. J. 690 (2009) L43-L46

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 pro-file

FIG. 2: Un-normalized time profiles of cumulative event numbers for two mixing parameter sets and

two total event numbers. The observational data are shown by solid lines whereas the theoretical

estimations are displayed by dash-dotted lines for LS180-EOS and dashed lines for LS220-EOS.

The error bars are corresponding to 99% C.L. in the KS test.

Good probe to properties of high density matter

0-19

3 Non-spherial explosion

SN1987A observations• polarization• material mixing (large vFe > 3000km/sec(Fe II IR line), early detection of

X-ray, 847keV/1238keV 60Co 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

0-20

Nomoto et al., astro-ph/0308136

0-21

2D/3D Hydrodynamics + simplified ν-transfer + full/approximated GRAt present, evolution of fν(t, ~r, ~pν) cannot be calculated.SASI: Standing Accretion Shock Instability Blondin et al., 2003

Instability modes with ` = 1, 2 grow between stalled shock wave and pro-toneutron star(amplifying advective-accoustic cycle)It helps neutrino heating (longer advection time) ?⇒ successful explosion

Accoustic Explosion? Burrows et al., 2006accretion → 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 = 1015G)

Many groups are at work.Garching, LANL, ORNL, Basel, Prince-ton/Caltech, NAOJ/Waseda, Kyoto ...

0-22

Janka et al.., 2006, non-rotating 11.2M¯ 2D simulation⇒ weak explosion due to SASI+ν-heating

Simulation for π4 ≤ θ ≤ 3π

4 does not explode, 0 ≤ θ ≤ π: explodesinstability modes with l = 1, 2(SASI) evolve → kick velocity?

Figure 4: Four stages (at postbounce times of 141.1ms, 175.2ms, 200.1ms, and 225.7ms) during the evolutionof a (non-rotating), exploding two-dimensional 11.2M⊙ model [12], visualized in terms of the entropy. The scaleis in km and the entropies per nucleon vary from about 5kB (deep blue), to 10 (green), 15 (red and orange),up to more than 25 kB (bright yellow). The dense neutron star is visible as low-entropy (<

∼5 kB per nucleon)

circle at the center. The computation was performed in spherical coordinates, assuming axial symmetry, andemploying the “ray-by-ray plus” variable Eddington factor technique of Refs. [41, 11] for treating ν transport inmulti-dimensional supernova simulations. Equatorial symmetry is broken on large scales soon after bounce, andlow-mode hydrodynamic instabilities (convective overturn in combination with the SASI) begin to dominate theflow between the neutron star and the strongly deformed supernova shock. The model develops a — probablyrather weak — explosion, the energy of which was not determined before the simulation had to be stoppedbecause of CPU time limitations.

entropy profiles: Janka et al., astro-ph/0612072

τadv ↗> τheat, wider heating region: SASI helps ν-heating

0-23

Marek et al., Astron. Astrophys. 496 (2009) 475

0 60 120 180

-4•109

-2•109

0

2•109

180 120 60 0

5

10

15

20

s[k

B/b

ary

on

]

vr

[cm/s

]

r [km]0 60 120 180

-4•109

-2•109

0

2•109

180 120 60 0

5

10

15

20

s[k

B/b

ary

on

]

vr

[cm/s

]

r [km]

0 60 120 180

-4•109

-2•109

0

2•109

180 120 60 0

5

10

15

20

s[k

B/b

ary

on

]

vr

[cm/s

]

r [km]0 60 120 180

-4•109

-2•109

0

2•109

4•109

180 120 60 0

5

10

15

20

25

s[k

B/b

ary

on

]

vr

[cm/s

]

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 righthandpanel the radial velocity component with white and whitish hues denoting matter at or near rest; black arrows in the righthand panel indicate thedirection of the velocity field in the post-shock region (arrows were plotted only in regions where the absolute values of the velocities were lessthan 2 × 109 cm s−1). The vertical axis is the symmetry axis of the 2D simulation. The plots visualize the accretion funnels and expansion flows inthe SASI layer, but the chosen color maps are unable to resolve the convective shell inside the nascent neutron star.

0 100 200 300 400

0

50

100

150

200

250

Rs,

max

[km

],R

ns

[km

]

tpb [ms]

L&S-EoS

H&W-EoS

-250 -150 50

50 150 250

-200

-100

0

100

200

Rs

[km

]

Rs

[km

]

Rs [km]

L&S-EoS H&W-EoS

248 ms

270 ms

300 ms

319 ms

380 ms

Fig. 4. Left: maximum shock radii (solid lines) and proto-neutron star radii (dashed lines) as functions of post-bounce time for the 2D simulationswith different nuclear equations of state. The neutron star radii are determined as the locations where the rest-mass density is equal to 1011 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.

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Marek et al., Astron. Astrophys. 496 (2009) 475

0 100 200 300 400

0

20

40

60

80

100

νe

L[1

05

1er

g/s]

tpb [ms]

L&S-EoS

H&W-EoS

1D

2D

0 100 200 300 400

0

20

40

60

80

100

νe

L[1

05

1er

g/s]

tpb [ms]

L&S-EoS

H&W-EoS

1D

2D

0 100 200 300 400

0

20

40

60

80

νe

L[1

05

1er

g/s]

tpb [ms]

L&S-EoS

H&W-EoS

1D

2D

0 100 200 300 400

0

20

40

60

80

νeL

[10

51

erg/s]

tpb [ms]

L&S-EoS

H&W-EoS

1D

2D

0 100 200 300 400

0

10

20

30

40

50

νx

L[1

05

1er

g/s]

tpb [ms]

L&S-EoS

H&W-EoS

1D

2D

0 100 200 300 400

0

10

20

30

40

50

νx

L[1

05

1er

g/s]

tpb [ms]

L&S-EoS

H&W-EoS

1D

2D

Fig. 6. Isotropic equivalent luminosities of electron neutrinos (top), electron antineutrinos (middle), and one kind of heavy-lepton neutrinos (νµ,νµ, ντ, or ντ; bottom) versus time after core bounce as measurable for a distant observer located along the polar axis of the 2D spherical coordinategrid (solid lines). The dashed lines display the radiated luminosities of the corresponding spherically symmetric (1D) simulations. The evaluationwas performed at a radius of 400 km (from there the remaining gravitational redshifting to infinity is negligible) and the results are given for anobserver at rest relative to the stellar center. While the left column shows the (isotropic equivalent) luminosities computed from the flux that isradiated away in an angular grid bin very close to the north pole, the right column displays the emitted (isotropic equivalent) luminosities whenthe neutrino fluxes are integrated over the whole northern hemisphere of the grid (see Eqs. (2) and (4), respectively).

0 100 200 300 400

8

10

12

14

16

18

νeνeνx

〈ǫν〉

[MeV

]

tpb [ms]

L&S-EoS

0 100 200 300 400

8

10

12

14

16

18

νeνeνx

〈ǫν〉

[MeV

]

tpb [ms]

H&W-EoS

0 100 200 300 400

8

10

12

14

16

18

νeνeνx

〈ǫν〉

[MeV

]

tpb [ms]

L&S-EoS

0 100 200 300 400

8

10

12

14

16

18

νeνeνx

〈ǫν〉

[MeV

]

tpb [ms]

H&W-EoS

0 100 200 300 400

8

10

12

14

16

18

νeνeνx

〈ǫν〉

[MeV

]

tpb [ms]

L&S-EoS

0 100 200 300 400

8

10

12

14

16

18

νeνeνx

〈ǫν〉

[MeV

]

tpb [ms]

H&W-EoS

Fig. 7. Mean energies of radiated neutrinos as functions of post-bounce time for our 1D simulations (top) and 2D models (middle and bottom) withboth 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 ofthe 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 showresults for a lateral grid zone near the north polar axis, the bottom panels provide results that are averaged over the whole northern hemisphere ofthe computational grid. In all cases the evaluation has been performed in the laboratory frame at a distance of 400 km from the stellar center.

〈ωνe〉 > 〈ωνx〉 but 〈ωνe〉rms < 〈ωνx〉rms

0-25

Summary• state-of-the-art 1D simulation

light core explodes weaklycanonical cores do not explodeblack 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.

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