The physics of supernovae and proto-neutron stars

G. J. Mathews - Univ. Notre Dame

Key Theme: What is the complex interplay between turbulent convection, neutrino interactions, nuclear reactions and the equatioin of state?

• Stages of a Supernova Explosion Progenitor evolution Collapse/Explosion Entropy Production

Proto-neutron star formation Nucleosynthesis

Progenitor Evolution

Progenitor models are based upon simple spherical models

(possibly with rotation) [e.g. Heger, Woosley, Weaver (2002)

12C(α,γ)16O reaction rate leads to some uncertainty in the final core composition and mass

Key Question for Progenitor Evolution: 1.  What is the complex interplay between the

nuclear reactions and turbulent convection in supernova progenitors?

•  Convective overshoot and nucleosynthesis? •  Effects of rotation/ magnetic field driven

convection on nucleosynthesis?

Precollapse Stars are not 1D objects

1D Models for Betelgeuse

Size of convective cell is consistent

with hot spot

Dolan, Mathews, Herczeg, Dearborn 2010

1D Nucleosynthesis

Need mixing below H-burning zone

This is not a 1D system

Freytag, et al. (2002)

Progenitor Evolution and Nucleosynthesis in 3D

D. Dearborn, P. Eggleton - LLNL J. Lattanzio - Monash U.

G. J. M., M. Dolan - U. Notre Dame

A Full Star 3D model for Stellar Evolution D. Dearborn, et al. (2005; 2006)

Mesh constructed of multi-block logically rectangular non-orthogonal hexahedrons.

Uses Arbitrary Lagrange-Eulerian method with a predictor-corrector Lagrange-Remap formalism. Second-order accurate in both time and space.

€

X1/ 2•

= X•

+ X••

δt1/ 2

X1/ 2 = X + X•

δt1/ 2

€

X•

= X•

1/ 2+ X••

δt

X = X + 0.5 X•

1/ 2+ X•

δt

} { Reevaluate force and source terms.

Decomposition for parallel operation, using MPI.

Hydrogen Helium, Carbon, and Oxygen Burning + NSE 7 element suite: 1H, 3He, 4He, 12C, 14N, 16O, 24Mg

21 element suite: 1H, 3He, 4He, 12C, 13C, 13N, 14N, 15N, 15O, 16O, 17O, 18O,17F, 18F, 19F, 20Ne, 22Ne, 24Mg, 28Si, 32S, 56Ni

In both element sets, the proton-proton chain is handled with the proton capture on Deuterium is assumed instant: p (p,β ν) D (p,γ) 3He 3He(3He,2p) 4He 3He(4He,γ) 7Be (p,4He)4He

The 21 element suite is suitable for the Hot CNO cycle, including leakage into 19F.

12C(p,γ)13N 13N(β, ν)13C 13C(p,γ)14N 14N(p,γ)15O 15O(β, ν)15N 15N(p,α)12C 15N(p,γ)16O 16O(p,γ)17F 17F(β, ν)17O 17O(p,α)14N 17O(p,γ)18F 18F(β, ν)18O 18O(p,α)15N 18O(p,γ)19F

The 7 element set includes only the slower rates. The beta decays on 13C, 15O, 17F, and 18F are assumed instantaneous, as are the proton captures on 15N and 17O:

In the 21 element set, reactions included;

4He(2α,γ)12C 12C(γ,2α)4He 12C(α,γ)16O 16O(γ,α)12C 16O(α,γ)20Ne 20Ne(γ,α)16O 20Ne(α,γ)24Mg 24Mg(γ,α)20Ne 24Mg(α,γ)28Si 28Si(γ,α)24Mg 28Si(α,γ)32S 32S(γ,α)28Si 14N(α,γ)18O 18O(α,γ)22Ne

The following reactions are included for beginning advanced stages of massive star evolution 12C(12C,γ)24Mg 12C(16O,γ)28Si 16O(16O,γ)32S

In the 7 element set, the 18O(α,γ)22Ne reaction is assumed to happen instantaneously, and the mass fraction change is places with all other heavy elements in 24Mg

NSE following Timmes, Hoffman, and Woosley, 2000, ApJ, 129, 377-398

€

dY(4He)dt

= −7Y(40Ca)Y (4He)λαγ (40Ca)+ 7Y (44Ti)λαγ (

44Ti)

dY(28Si)dt

= −Y (40Ca)Y (4He)λαγ (40Ca)+Y (44Ti)λαγ (

44Ti)

dY(56Ni)dt

= +Y (40Ca)Y (4He)λαγ (40Ca)− Y (44Ti)λαγ (44Ti)

This is a challenging problem

•  Code time ~ real time for stars to evolve •  Can only get snap shots of the true

evolution to be used to calibrate 1D codes. •  Even so, there are subtle effects in 3D that

can significantly alter the composition of a star (see Dearborn et al., 2006, ApJ)

Ingredients to a Supernova Model

Relativistic Hydrodynamics Equation of State Neutrino Transport

Key Question: What is the complex interplay between turbulent convection, neutrino interactions, nuclear reactions and the equation of state?

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Relativistic Hydrodynamics of a Spherical Supernova Model Metric

May & White (1967)

Mayle & Wilson (1988) ApJ Wilson & Mathews (2003)

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Energy Momentum Tensor

€

ρε = ρεM + EνP = PM + Pν

Wν =(Eν − 3Pν )

2

€

T µν =

ρ(1 +ε)a2

4πR 2ρΦν

a0 0

4πR2ρΦν

aP(4πR 2ρ)2 0 0

0 0 (P +Wν ) / R2 00 0 0 (P +Wν ) / R2 sin2θ

€

Eν = Fi∫1

6

∑ dEdΩν

Φν = Fi∫1

6

∑ cos(θ)dEdΩν

Pν = Fi∫1

6

∑ cos2(θ)dEdΩν

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Equation of State Must include: photons, neutrinos, electrons, pions, neutrons,

protons, atomic nuclei

e.g. nucleons & nuclei: Helmholtz free energy: F = -kT ln(Z)

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Neutrino Interactions

Internal Energy

Lepton Number conservation

Neutrino-nucleon scattering

Corrections - Horowitz

(2002)

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Neutrino Transport

Relativistic Boltzmann Equation

21

Flux-limited Diffusion

22

Steps to a Core Collapse Supernova: Part I What Happens at t = 0-100 ms

•  Stars with M ~ 10 - 40 M build up an Fe/Ni core •  Maximum core size Mch ~ 5 Ye

2 M ~ 1.3 M •  Collapse Separates

–  inner homologous (v ∝r) core ~ 1.1 M –  outer slowly collapsing core ~ 0.2 M

•  The central density increases till greater than nuclear matter density is reached –  ρnucl > 2x1014 g cm-3

•  An outward moving shock develops •  The shock dissociates the outer iron core into free

nucleons

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Collapse of the Core Prompt core bounce

E(iron core) ~ GM2/r ~ 1051 erg

E(neutron star) ~ GM2/r ~ 1053 erg

E(neutron star) - E(iron core) ~ 1053 erg

E(shock) ~ 1051 erg

E(outer core) ~ 1051 erg nuclear binding

Usually the shock is absorbed by Dissociating the iron core

Effects of a QGP

Equation of State

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2nd order

1st order

ρ/ρN

P = KρΓ

Γ = 1 + (P/ρε)

Gentile, et al. ApJ (1993)

Order of the QCD transition strongly affects the strength of the shock

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2nd order

2nd order

2nd order

1st order

t (sec)

1st order

1st order Shock velocity

Shock Energy

ρ/ρN

Two shocks form

26 t (sec)

ρ/ρN

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Steps to a Core Collapse Supernova: Part II What Happens at Later Times?

t = 100-500 ms •  Neutrinos diffuse out of the core after ~100 msec •  Neutrinos scatter off the heated material behind the

shock •  A gain radius develops above which net energy is

deposited by neutrinos •  A high entropy heated region forms above the gain

radius which begins to lift of the outer layers of the star

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Delayed Supernova Explosion Cooling = a c T4 σ(T)

p + e- → νe + n n + e+ → νe + p + νe e- + e+ → νe + νe

Heating = L / (4 π r2) σ (Tν) L ≈ a c π Rν

2 T4ν

σ(T) ≈ σ 0T2 dE/dt = {Heating - Cooling} = a c σ 0 [(Tν 6/4)(Rν/r)2 - T6] (Tν/T) (Rν /r)1/3 > 4 1/6

1D Models => Neutrino Heated Bubble Neutrino Luminosity ~1053 erg/sec

Neutrino Heating Produces a high entropy bubble

S = ∫dt (dQ/dt)/T Woosley, Wilson, GJM, Hoffman, Meyers (2004)

Key Issue:

•  The role of convection in the core is very important in the first 500 ms

•  Necessary to increase the neutrino luminosity and increase the shock heating

Enhanced early neutrino luminosity in first 0.5 sec

•  Very equation-of-state dependent in the region –  (T~5-10 MeV, ρ~1012-14 g cm-3, Ye~-0.1-0.2)

Hot heavier material

Cool lighter material

Neutron Finger

Instability

Neutrino Driven Heating & Convection in Core is Important

Enhanced Neutrino Luminosity •  Magnetic Convection/Rotation (MRI)

–  Wilson, Mathews & Dalhed ApJ (2005)

Neu

trino

Lum

inos

ity (

1053

erg

s-1 )

velocity

Neutrino luminosity

•  QGP forms at late times as central density increases

•  Late time Shock/neutrino emission from the second core collapse

•  Induces explosion!!

33 Sagert et al. PRL (2009); J. Phys. G (2009)

SASI: Standing Accretion Shock

Instability

Details of neutrino interactions and convection

are crucial

The region outside the core is also highly convective:

Murphy & Burrows ApJ (2008)

High entropy bubble is convective

Janka 2006

Janka et al. (2006)

Rotation/Convection Helps

There can be unexpected consequences when the full complex interplay between

turbulent convection, neutrinos and nuclear reactions is taken

into account

Convection + nuclear burn drives explosion Nuclear Statistical Equilibrium

Nuclear Reaction Network Included

S Bruenn et al. (2006) Inward mixing of nuclear fuel drives explosion?

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Steps to a Core Collapse Supernova: Part III What Happens at Later Times?

t = 1-15 sec •  Neutrinos continue to diffuse from the

proto-neutron star •  Neutron-rich matter is ablated from the

surface

Key Issue: What is the complex interplay between the neutrino and nuclear reactions and turbulent convection during late times?

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Material is ablated by neutrinos from the neutron-star surface

Woosley, Wilson, GJM, Hoffman, Meyers (2004)

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Material moving through the bubble achieves very

high entropy and is slightly neutron rich.

The r-Process

What we know from observations

Cowan et al. (2007)

Universality

Material moving through the bubble reassembles into alpha particles, neutrons, plus a few heavy

nuclei Free neutrons capture on heavy nuclei to form the r-process

Woosley et al. (1994)

Problems with the neutrino heated bubble r-process

•  Overproduction of intermediate mass A~ 90 elements • Neutrino-nucleus interactions diminish neutron/seed ratio • High enough entropy is difficult to achieve

Short timescales needed Otsuki et al (2000; 2003)

•  Jets? Nishimura et al (2005)

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Steps to a Core Collapse Supernova: Part IV What Happens at Later Times?

t > 15 sec •  The core slowly cools •  Neutrino luminosities and energy remain

large •  Neutrino Weak Magnetism helps to increase

the energy and luminosity of electron anti-neutrinos

Key Issue: What is the complex interplay between the nuclear reactions and turbulent convection at very late times?

Neutrino Luminosities Remain High

Neutrino Energies

Effect of higher anti-neutrino energy

•  Decreases Ye ~ Z/A •  p + νe → n + e+ faster than n + νe → p + e- •  Ye ~ [1 + (ενe/ ενe)2 ]-1

•  Increases neutrons /seed •  Improved r-process

The r-Process may continue at late times

35 sec

20 sec

15 sec

Conclusions There are still many questions

regarding core-collapse supernovae & the r-process

We still must unravel the complex interplay between turbulent convection, neutrino/nuclear

reactions, and energy transport in: Progenitor stars, collapse, and late

time evolution