Physics of Physics of SupernovaeSupernovaeKonstantin Postnov, Konstantin Postnov,

Sternberg Astronomical Sternberg Astronomical Institute, Moscow, RussiaInstitute, Moscow, Russia

Erice 2004, July 3Erice 2004, July 3

Outlook

• Introduction• Core collapse supernovae (SN II, Ib, Ic). • Asymmetry: magnetorotational explosion• Thermonuclear supernovae (SN Ia). • SN Ia light curve modeling • Conclusions

Pre-SN: eta Carinae (LBV-star)M~100 M, L~106L

Pre-SN: rho Cassiopeae

3 AU

SN 1987A in LMC

SNR Cas A in X-ray (Chandra)

I. Core collapse supernovae (SNII, Ib, Ic)

• Hydrogen lines in spectra, variety of light curves

• End products of evolution of stars with M>8 M

• Core collapse Proto neutron star formation @ ρ~2x1014g/cm3

• Bounce shock (Colgate & White 1965) stalls @ R~150-200 km above neutrinosphere and does not lead to explosion due to

• A) electron deleptonization • B) kinetic bounce shock energy spending to

nuclear dissociation • Need for additional heating (Wilson & Bethe

1985) – neutrino convection (delayed explosion)

Delayed SN explosion. Basic picture

Proto NST~10 MeV

RPNS~50-80 kmτν~ 2/3neutrinosphere

Neutrinocooling layer

(Gain region):Q+ ~(Lv/r2)ε2

v

ΔM~0.01-0.1M

Stalled bounce shockRs~150-200 km

Rg~100 km

MassaccretionNeutrino

heating layer

Q-~T6 ~1/r6

Initial energy of explosion: ΔE~(ΔM/mb) Q+ Δth

heating time: Δth~(GMmb/rQ+)~ 40 ms

This energy triggers outward explosion

After shock revival, most additional energy comes from nuclear recombination from nucleons (~8 MeV per nucleon that recombines)

Heating ΔM~0.01-0.1 M yields correct energy of SN explosion!

The only problem is how to heat this mass

One-dimensional models with detailed neutrino physics fail to

explode!

Further modifications

• Accurate treatment of neutrino transport

• 1D 2D3D

• Inclusion of rotation • Inclusion of magnetic fields

EOS effects (1D calculations)

(Janka, Buras, Kifonidis, Marek, Rampp 2004)

Comparison of models with Boltzmann neutrino transport (in 1D, 15 M with relativistic gravity,

no explosion)(Liebendoerfer et al. 2004)

Multidimensional calculations

a) Grid effects

Janka et al. 2004

90o wedge, no explosion180owedge, weak explosion

1200 km

11.2M:1017flopseveral monthsweak explosion…

15M ,simplifiedneutrino transp.:ΔE~6x1050erg

b) 2D models are about to make explosion…

c) 2D recovers high NS kicks(Scheck et al.2004)

NS acceleration bygravitational and hydroforces in direction opposite to low-mode (l=1,2) large-scale convection bubbles

First 3D calculations (Scheck et al. 2004)

Surf. of const. mass accretion rate per unit area

2D, time-dependent, multi-group, multi-angle radiation hydrodynamics

(VULCAN/2D code)(Livne, Burrows, Walder, Lichtenstadt,

Thompson 2004). • Solves 2D Boltzmann transport equation for neutrino

using multi-group energy method along discrete set of representative angular directions

• Couples radiation field to matter through emission, absorption, scattering and radiation pressure

• Limitations: no energy redistribution, no velocity-dependence terms

• Test simulations (only electron neutrinos): 22ms post-bounce,11 M progenitor (Woosley & Weaver 1995) (no explosion…)

• Important finding: emergent neutrino spectrum should be angle-dpendent

T=10.2 msVelocity vectorsLepton number

420 km

T=10.2 msNeutrino fluxvectors

T=10.2 msVelocityvectors.Neutrino energy density map240x240 km

T=22ms

Velocity vec.

T=22 msVelocityvectors.Neutrino energy density map 420 km

T=22 msNeutrino flux vectorsEntropy map420x420 km

T=22 msNeutrino fluxVectorsEnergy density map

Simple physical conditions for thermal SN explosion

1. Advective timescale across pressure scale: τAdv=H/Vr

2. Net neutrino heating: τqν=(P/ρ)/(dqν/dt), dqν/dt=Hν-Cν

Necessary condition for explosion: matter is heated in the gain region faster than is advected from the accreting envelop

Sufficient condition for explosion:net heating holds enough time to deposit the binding energy of the overlying mantle (~1051ergs)

bindE q dVdt

Adv q

In pure thermal neutrino-driven 1D-models explosions fail because necessary condition τAdv > τqv is violated (fresh matter is advected more rapidly than is neutrino-heated). To make an explosion, moderate 25% to 50% increase in the energy deposition rate in the gain region is required

No MRI heating

(Thompson, Quataert andBurrows 2004)

τadv< τqv

Rotation and viscosity (Thompson, Quataert, Burrows 2004)

• Rotation is naturally amplified during core collapse• Differential rotation may store substantial fraction of

gravitational energy released

• Viscosity in the region of differential rotation (1) transports angular momentum (2) dissipate energy stored in shear on viscous timescale

• Sources of viscosity: (1) neutrino (found ineffective) (2) turbulence (induced by (a) MRI and (b) hydrodynamic convection )

2 252

3~10

1 50 10 /PNS

shear

M RE erg

M km rad s

Role of instabilities

Main goal: to increase effective neutrino heating

• Double-diffusion instability inside neutrinosphere (Bruenn et al. 2004)

• Magneto-rotational instability (MRI) exterior to proto-neutron star (Thomson et al. 2004)

q

Double-diffusion instability: a) Neutron fingers

• “salt” gradient, destabilizing, slow diffusion

• “heat” gradient, stabilizing, rapid duffusion

• In PNS: “salt”neutron richness (Ye)

“heat” entropy• Unlikely to occur below

ν-sphere

Gravity gradient

Double-diffusion instability: b) lepton semi-convection

Gravity gradient

• “salt” gradient, destabilizing, slow diffusion

• “heat” gradient, stabilizing, rapid duffusion

• In PNS: “salt”neutron richness (Ye)

“heat” entropy

• Can produce convection in PNS, increase neutrino luminosity and help explosion

Magneto-rotational instability

• Idea: Velikhov (1959), Chandrasekhar (1960)

• Applied to accretion disk turbulence by Balbus & Howley (1991-1998)

• Condition: dΩ2/d(lnr) < 0 (ignoring • Increment: ΓMRI~Ω

• Turbulent viscosity (α-prescription, Shakura & Sunyaev 1973):

ηMRI=α Vt Lt =α (ΩH) H = αΩH2 ,(α~0.1)

• Heat generation rate: qMRI=ηMRI(r(dΩ/dr))2

MRI heating included, stalledshock revived

Possible signatures of rotation in post-bounce neutrino spectra

Asymmetric explosions• Evidence: a) strong

polarisation of SN emission (esp. type Ib/c without hydrogen shell, e.g 1997X)b) high space velocity (up to 1000 km/s) of young pulsars

c) SN1987A: substantial mixing of Ni56, line profiles asymmetry, light polarisation, direct HST picturesd) young SNR Cas A: asymmetric motion of O-rich clouds, iron-rich layers external to silicon-rich (Chandra), peculiar velocity wrt local ISM (also in other young SNR N132D, E0102.2-7219 etc.)

• Mechanisms: a) neutrino asymmetry (parity violation in strong magnetic fields ~1014 -1016 G (Chugai 1984). Reproduces pulsar kicks 100-150 km/s b) magnetorotational explosion (Bisnovaty-Kogan 1970)c) SN explosions in binary systems (Blinnikov et al. 1984). Imshennik (1992): rotational instability of rapidly rotating core binary NS coalescence explosion of light NS large kick velocity of 2d NS

Asymmetric models: magnetorotational SN explosion

• Idea: G.S.Bisnovatyj-Kogan 1970• First successful 2D-calculations (B-K,

Moiseenko, Ardeljan 2003-2004)• Differential rotation increases toroidal

magnetic field compression MHD wave forms and moves through envelope with steeply decreasing density

• Initial poloidal magnetic field: Emag~10-6Egrav

• Initial NS spin period: P~0.001 s

Velocity field @ t=0.191 safter mag.field turn-on

Specific ang. momentum j=vφr

MHD-shock

Ejected/rotational energy(~1.12x1051ergs)

Ejected/total mass(~0.11 M)

II. Thermonuclear supernovae (SNIa)

• No hydrogen in spectra; similar light curves• Rate: 1/100 yrs both in spiral and elliptic galaxies• Progenitors: C+O white dwarf with M~MCh~1.4 M

(Hoyle & Fowler 1960)• “Standard candles” in cosmology (Riess et

al.1999,2004)• Main problem (until recently): how to obtain

explosion and correct nucleosynthetic products? prompt detonation (Arnett 1969) incinerates carbon to iron, deflagration (flame) is too slow (in 1D and 2D), Machflame~0.01, star expands and cools

• How to speed up deflagration? Blinnikov & Sasorov (1996) – Landau-Darrieus flame instability fractalization of flame front wrinkles and folds increases front area

3D calculations (Hillebrandt et al.2002-2004, MPA group) of turbulent deflagration, no deflagration-detonation transition is required for successful explosion

Ignition conditions: density 2-9x109g/cm3, temperature >1.5x109K

a) 3D model c3_3d_256 (Travaglio et al. 2004)(256x256x256 cells), central ignition; Minit(C12)=0.475 M, O16=0.5 M, Ne22=0.025 M

T=0s

107cm

Initial frontfrom 2D

T=0.2s

T=0.4s

T=0.6s

b) Model b30_3d_768 (Travaglio et al. 2004)(768x768x768 cells), ignition in bubbles within ~100 km (Woosley et al. 2004)

T=0s

T=0.1s

T=0.14s

T=0.2s

40% remainsunburned

Total energy increases in 3D models!

Nucleosynthesis yields

III. SNIa light curves

• Form: Radioactive decay of Ni56

• Empirical relation max. brightness – decay rate (Pskovsky 1968)

• Used in modern cosmology as “standard candles”

• Sensitive to how degenerate core ignites, Ni56 yield, rotation, mass …

• Can probe explosion models! (Sorokina, Blinnikov et al. 2002-2005, multi-group radiation hydrocode STELLA)

2D-models

Model: c3_2d_256, Ni56 mass dependence

MB

Comparison of 2D – 3D models

Sorokina, Blinnikov, Hillebrandt et al. 2004

Conclusions

• Core collapse SN: about to explode in 2D. • Neutrino-driven convection models:

(a) increase in neutrino luminosity by 20-30% due to accurate neutrino transport (Janka et al. 2004)(b) differential rotation and viscosity (convective + MRI turbulence) (Thompson et al.2004)(c) 3D?

• Magnetorotational mechanism is shown to work in 2D (Bisnovaty-Kogan & Moiseenko 2004)

• Thermonuclear SN: (a) Turbulent deflagration in 3D produces

explosion and correct nucleosynthetic yields (Travaglio et al. 2004). No transition to detonation is required.

(b) Light curves (in different colors) are successfully reproduced (STELLA code, Sorokina et al 2004)

• Neutrino spectra are sensitive to rotation, EOS… and will be invaluable for SN physics