Mechanism of CollapseMechanism of Collapse--driven Supernovaedriven Supernovae

ShoichiShoichi YamadaYamada

Science & EngineeringScience & EngineeringWasedaWaseda UniversityUniversity

Scenario of CollapseScenario of Collapse--driven Supernovaedriven Supernovae

core collapse

H

HeC+O

Si

Fe

ν ν

ν

ν

ν trapping core bounce

ν

νν

ν

ν

νν

ν

NS

shock propagation in coreshock in envelopeSN explosion

Evolutions and Instabilities of Evolutions and Instabilities of Massive StarsMassive Stars

4 6 8 10 12 14 16

9

10

11

12

7

8

Log ρc [g/cm ]

Log

T [

K]

3

GR

e-capture

Fe, He dissociation

+

15Msolar140

40260

e+e ->γ

Massive stars become gravitationally unstabledue to some processes.— electron captures— photo-dissociations of He, Fe— annihilation of electron – positron— general relativity

Gravitational collapse is followed by the formation ofneutron stars, black holes or nothing.

Physics involved in Physics involved in CollapseCollapse--driven Supernovaedriven Supernovae

Macro Physics• hydrodynamics

— rotation— convection

• radiative transport• general relativity

— gravitational waves• magnetic field

Micro Physics• weak interactions

— neutrino interaction rateswith matter

— neutrino oscillations• nuclear physics

— equation of state— many body effects on

neutrino reaction rates

• how the explosion occurs and what is the neutron star mass, • what is the mass range of progenitor for NS/BH formations,• chemmical evolution of the universe

— explosive nucleosynthesis, r-process• relations with other high energy objects such as GRB and magnetar

— hypernovae ?

Supernova theory must address following issues :

Nuclear Physics in Nuclear Physics in CollapseCollapse--driven Supernovaedriven Supernovae

Nucleosynthesis : explosive nucleosynthesis, r-process, neutrino-process

― nuclear masses, reaction rates ― weak interaction rates

Dynamics of collapse and explosion― nuclear EOS― weak interactions rates

Detections of supernova neutrinos― neutrino-nucles interaction rates

Failure of Prompt ExplosionFailure of Prompt Explosion

Sumiyoshi, Suzuki, Yamada, Toki 01

20MsolarThe shock wave stalls in the core by energy loss due to

(1) photo-dissociations of nuclei,

(2) neutrino emissions.

Meridian Section of Core

Heating Rate of these Reactions

Gravitational Binding Energy

Quantitative evaluation is required.

NeutrinoNeutrino--heating Mechanismheating Mechanism

Unsuccessful 1D ModelsUnsuccessful 1D Modelsspherically symmetricfully general relativisticBoltzmann transport15Msolar model by WoosleyEOS’s by Lattimer & Swesty and Shen et al.

Sumiyoshi et al. ‘05

Trajectories

Shock Radii

Shen EOS

LS EOS

Failed 1D SimulationsFailed 1D Simulations

Liebendoerfer et al. ‘01

Rampp et al. ‘00

No Explosion found !

Burrows et al. ‘02

good agreement among these models

Crucial Role of NeutrinosCrucial Role of Neutrinos

Janka & Mueller ‘95

There is a critical luminosity!

confirmed by analytic models— Burrows & Ghoshy ‘93— Janka ‘01— Yamasaki & Yamada ‘05

Accurate treatment of neutrino transport is mandatory !

Explosion Energy vs Neutrino Luminosity

ν luminosity in 1052 erg/s

Critical Neutrino LuminosityCritical Neutrino LuminosityBurrows & Ghoshy ’93 : ― For a given mass accretion rate, there is a

critical neutrino luminosity, above which no steady accretion flow exists.

― This may indicate the revival of shock wave.

Standard Neutrino Reactions Standard Neutrino Reactions implemented in Supernova Simulationsimplemented in Supernova Simulations

neutrino-nucleon reactions are energy-dependent: ∝Eνelectron scattering is neither isoenergetic nor isotropic.coherent scattering is forward-peaked : ∝(1+cos θ)pair processes are sources of νμ

2

Ref. S.W. Bruenn ’85 ApJS 58, 771 A. Burrows et al. ’05 NPA in press

Effective mass and correlations of nucleons due to nuclear forces

Ref. Burrows et al. 99 Reddy et al. 98Raffelt et al. 96Yamada et al. 99Carter & Prakash 02

See, however, Mornas et al. 02

recoil & weak magnetism of nucleons,

Ref. Horowitz 01Liebendoerfer et al. 02 Rampp et al. 02

More about Reaction RatesMore about Reaction Rates

νe + νe νμ + νμ

Density & Temperature of Relevance

Correlations of NucleonsCorrelations of Nucleons

Typical Scales

Nucleons are not free but correlated.

interaction Lagrangian density

NeutrinoNeutrino--nucleon Reaction Ratesnucleon Reaction Rates

Formulae of Reaction Rates

ν-nucleon scattering rates in RPA

• vector current contribution • axial vector current contribution

Yamada & Toki ‘99

Reductions of Neutrino Reaction RatesReductions of Neutrino Reaction Rates

Convections in ProtoConvections in Proto--neutron Starsneutron Stars

convections might occur in proto-neutron stars due to lepton-and entropy-gradient.

convections enhance bothluminosity and energy of neutrinos.

Ledoux criterion

Keil 97

Keil 97 : • 2D proto-neutron star cooling• flux-limited diffusion in each

radial direction

1D standard

2D standard

1D RPA

2D RPA

1D

2D

Janka, Keil & Yamada unpublished

2D PNS cooling ν-luminosity increases by ~ ４０％.

Possible Increase of Neutrino Luminosity ?Possible Increase of Neutrino Luminosity ?

These effects are almost nullified by the time neutrinos reach the neutrino sphere.

Failure of 2D simulations Failure of 2D simulations Ray by ray radial transport neglecting lateral transferRay by ray radial transport neglecting lateral transfer

inappropriate for global asymmetric explosioninappropriate for global asymmetric explosionConvections both in PNS and heating regionConvections both in PNS and heating regionNo explosionNo explosion

but may be very close to successbut may be very close to success

Janka et al. 02

NucleiNuclei--related Issuesrelated Issues

Low density regions might be important.

Nuclei-related reactions will then be important.

Nuclei exist before bounce and outside shock after bounce.

— electron captures on nuclei before bouncesubstantial improvement in the last years

— pre-heating of nucleinot very important : Bruenn & Haxton ’91 ApJ

Electron Captures on NucleiElectron Captures on NucleiHix et al. ’03 PRL 91, 201102

Large-scale shell model + RPANuclei are more important than nucleons.

Finite temperature effect and forbidden transitions are important.

Ye and the inner core get smaller.

Inner Core

Population of NucleiPopulation of Nuclei

Hix et al. ‘03

Population of different nuclei should be taken into account.

EOS should be consistent.

Before collapse

ν-trapping

Obstacles for Shock— photodissociation of Fe— neutrino cooling— ram pressure

core bounce

ν

νν

innercore

outer core

Yamada & Sato ‘94

YlYl

EnergeticsEnergetics of Prompt Explosionof Prompt Explosion

Generic Asymmetry of Generic Asymmetry of CollapseCollapse--driven Supernovaedriven Supernovae

collapse-driven supernovae showa percent of polarization in general

– corresponding to an aspect ratio of ~2

type Ic > type Ib > typeIIb > type IIP

<~0.5% for Hypernovae― SN1998bw, SN2003dh, SN1997ef― exception : SN2002ap

Leonard et al. ‘99

Schematic picture of asymmetric scattering envelope

Polarizations Filippenko et al. ‘03

Asymmetry of SNAsymmetry of SN１９８７１９８７AA

spectropolarimetry and speckle observations suggest a prolate ejecta.

— consistent with the HST image— more asymmetric deeper inside

Wheeler 02

HST image on Nov. 03

Rotational Steady Accretion FlowsRotational Steady Accretion Flows

Flow Pattern

j = 4x1015cm2/s

Radial Velocities

Critical Luminosity

j = 4x1015cm2/s

Yamasaki & Yamada ’05 ApJ in press

Rotational Effect on the Critical Rotational Effect on the Critical νν-- LuminosityLuminosityThe critical luminosity is reduced by rotation.The critical luminosity is reduced by rotation.The shock may be revived at the rotation axis.The shock may be revived at the rotation axis.

Critical Luminosity

j = 4x1015cm2/s

Critical Luminosities Radial Velocities

no rotation

j = 4x1015cm2/s

j = 1.3x1015cm2/s

Anisotropy of Neutrino FluxAnisotropy of Neutrino Fluxνν--luminosity is increased toward the rotation axis.luminosity is increased toward the rotation axis.The critical luminosities are further reduced.The critical luminosities are further reduced.

isotropic

10% anisotropy30% anisotropy

100% anisotropy

No Rotation

Critical Luminosities

j = 4x1015cm2/sisotropicno ratation

10% anisotropy30% anisotropy

100% anisotropy

Convections in Supernova CoresConvections in Supernova Cores

convection in heating regions— neutrino heating— entropy-driven— between shock and gain radius

convection in proto-neutron stars— neutrino diffusion— lepton-driven — around and inside ν-sphere

ν

ν

ν

• convectively unstable regions

Shock Wave

Gain Radius

PNS

Instability of Standing Accretion ShockInstability of Standing Accretion ShockStable for radial perturbations but unstable for nonStable for radial perturbations but unstable for non--radial perturbationsradial perturbationsNot sufficient for explosionNot sufficient for explosionMay be partially responsible for asymmetryMay be partially responsible for asymmetry

Blondin et al. 02 Plewa et al. 02

AcoustoAcousto--vortex Instabilityvortex Instability

Interplay of vortices and pressure waves

Blondin et al. ‘02Foglizzo et al. ‘02

Nuclear Population behind ShockNuclear Population behind Shockr=200km mass fraction時間発展

0

0.2

0.4

0.6

0.8

1

0 0.5 1 1.5 2

time (s)

mas

s fr

acti

on X

Xa

Xα

Ｘｐ

Xn

1sec1sec 200km200km 500km500km 1000km1000km

XaXa 00 0.240.24 0.850.85XXαα 0.380.38 0.680.68 0.100.10XpXp 0.310.31 0.050.05 0.040.04XnXn 0.310.31 0.030.03 0.010.01

● Time Evolutionα : decreased

p, n : increased

● Dependence on Shock Pos.200km :α, p, n, no nuclei

1000km : mostly nuclei

◎αalways abundant !

Watanabe & Yamada ‘04

SummarySummary

Despite almost 40 years of intensive and extensive studies, bothanalytical and numerical, we still do NOT figure out how the collapse-driven supernova occurs.

Combination of multi-dimensional dynamics and microphysics should be studied further. In particular,— convections in supernova cores & instability of SAS,— anisotropic neutrino heating,together with— neutrino-nucleus reactions in lower density regions,— neutrino reaction rates in hot and dense hadronic matter.

Self-consistent multi-dimensional numerical simulations with an appropriate neutrino transfer are also required.

CollaboratorsCollaborators

H. Suzuki (Tokyo University of Science)

K. Sumiyoshi (Numazu College of Technology)

N. Ohnishi (Tohoku University)

K. Kotake (University of Tokyo)

M. Watanabe (Waseda University)

A. Ohnishi (Hokkaido University)

C. Ishizuka (Hokkaido University)