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The Physics of Stellar Collapse and Core-Collapse...
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The Physics of Stellar Collapse and Core-Collapse Supernovae
Christian David Ott
Niels Bohr International Academyand California Institute of Technology
C. D. Ott - The Physics of Stellar Collapse and Core-Collapse Supernovae
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• Onset of Collapse, Hydrodynamics, and Homologous Collapse.
• Collapse Microphysics and Neutrino Trapping.
• Core Bounce and Shock Formation.
• The Supernova Problem and its Energetics.
• Supernova simulations: 1D, 2D, and 3D and their ingredients.
• Candidate supernova mechanisms.
C. D. Ott - The Physics of Stellar Collapse and Core-Collapse Supernovae 2
Outline
Outline
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Situation at the Onset of Collapse
HydrostaticEquilibrium
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The General Picture
M ≈ 1.3 – 2.2 MSUN
M = MCH,0 + corrections (thermal, GR, etc.)
“Core Bounce” atnuclear density.
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The General Picture
M ≈ 1.3 – 2.2 MSUN
M = MCH,0 + corrections (thermal, GR, etc.)
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Hydrostatics of the Iron Core and the Onset of Collapse
Blackboard/Lecture Notes
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Stellar Collapse
Studying Stellar Collapse: Essential Ingredients
Hydrodynamics
Microphysics: Nuclear & Neutrino Physics
Gravity: Newton / General Relativity
Transport Theory: Neutrino TransportFully
co
up
led
!
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Stellar Collapse: Hydrodynamics
HydrodynamicsConservation Laws: Mass, Momentum, Energy(Ideal fluid approximation -> No viscosity, radiation)
• Mass Conservation -> Equation of Continuity
Using Gauss’s theorem, we can rewrite this to:
Since this must hold for any volume V, the continuity equation follows:
• Same approach: momentum and energy equations
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Stellar Collapse: Hydrodynamics
The Equations of Newtonian Hydrodynamics
Continuity
• Alternative: Lagrangian formulation (“comoving frame”).Transformation:
Momentum
Energy
(Eulerian Formulation -> “laboratory frame”)
NewtonianGravity
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Stellar Collapse: Self Similarity
Self-Similarity in Stellar Collapse
• Separation into homologously (vr) collapsing inner coreand supersonically collapsing outer core.
Schematic View of Spherical Collapse
Analytic similarity solutions:Goldreich & Weber 1980Yahil & Lattimer 1982Yahil 1983
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More Collapse Physics
Important Collapse MicrophysicsIn collapse, pressure support is reduced by
• Photodissociation of heavy nuclei: 125 MeV/reaction
Capture rates:
• Electron Capture
• Neutrinos stream off freely at densities below 1012 g/cm3.-> core “deleptonizes” during collapse.
• Net entropy change very small, -> collapse proceeds practically adiabatic.
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Stellar Collapse: Nuclear EOS
Neutrino Trapping• Collapse phase: Neutrino opacity dominated by coherent
neutrino-nucleus scattering:
Neutrinomean-free path:
• For ρ 3 x 1012 g/cm3, diffusion time τdiff >> time between collisions τcoll -> neutrinos become trapped in the collapsing core.
• Consequences:
Beta Equilibrium
Deleptonizationstopped
Detailed simulations:
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Nuclear EOS
The Nuclear Equation of State (EOS)Nuclear Statistical Equilibrium (ρ > 107 g/cm3, T > 0.5 MeV)
-> P = P(ρ,T,Ye)
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Nuclear EOS
The Nuclear Equation of State (EOS)Nuclear Statistical Equilibrium (ρ > 107 g/cm3, T > 0.5 MeV)
-> P = P(ρ,T,Ye)
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Nuclear EOS
The Nuclear Equation of State (EOS)Nuclear Statistical Equilibrium (ρ > 107 g/cm3, T > 0.5 MeV)
-> P = P(ρ,T,Ye)
Something happensnear 1014 g/cm3 !
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Nuclear EOS
The Nuclear Equation of State (EOS)Nuclear Physics:
recall:
“Stiffening”of the EOS
Nuclear Density:
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Nuclear EOS
Nuclear EOS: What happens near ρnuc?Nuclear Physics:
recall:
“Stiffening”of the EOS
Nuclear Density:
Phase transition frominhomogeneous to homogeneous nuclear matter
nucleons, alphas, nuclei
pure nucleons
• Above ≈ρnuc n,p are so closethat “repulsive core” of the strong force kicks in and leads to the stiffening of the EOS
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Stellar Collapse: Nuclear EOS
Collapse and Bounce
• Inner Core reaches ρnuc, rebounds (“bounces”) into stillinfalling outer core.
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Stellar Collapse: Bounce
Shock Formation
• Stiffening of EOS leads to sound wave that propagates through the inner core and steepens to a shock at the sonic point.
Credit: E. MüllerSaas-Fee Lectures 1998
InnerCore
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Stellar Collapse: Universality of Collapse
Universality of Core Collapse
The Mass Mic of the inner core at bounce is determined by nuclear physics and weak interactions, is 0.5 MSUN , and is
practically independent of progenitor star mass and structure.
Credit: E. MüllerSaas-Fee Lectures 1998
InnerCore
Mic (Ylep)2
+ GR correction (-)+ thermal correction (+)+ rotation (+)
Mic
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Stellar Collapse: Inner Core Mass
Why worry about Mic?
Mic
• Mic is the amount of matter dynamically relevant in bounce.
• Mic sets kinetic energy imparted to the shock.
• Mic (and IC radius) sets the angular momentum that can be dynamically relevant.
• Sets mass cut for material that the shock needs to go through.
• Mic0.5 MSUN can easily stabilized by nuclear EOS. No “prompt” Black Hole formation.
• Mic sets the mass that must be accreted (before explosion?) to makea canonical 1.4 MSUN neutron star.
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Stellar Collapse: Getting into trouble
The Supernova Problem
Radius (km)
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Stellar Collapse: Getting into trouble.
Why Does the Shock Stall
Janka et al. 2007
• Shock loses energy to:
– Dissociation of infallingheavy nuclei: 8.8 MeV/baryon
– Neutrinos that streamaway from behind the shock.
Inner core -> Core of the proto-neutron star (PNS)
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Stellar Collapse: Neutrinos
Neutrino Burst
Trapping
• Optical depth
• Neutrinosphere:
Depends on (єν)2
• Postbounce neutrino burst:Release of neutrinos created by e- capture on free protons in shocked region when shock ‘breaks out’ of the νe
neutrinospheres.Thompson et al. 2003
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Stellar Collapse: Neutrinos, Neutrinos, Neutrinos
Postbounce Neutrino Emission• Neutrinos and Anti-
neutrinos of ALL species:Thompson et al. 2003
Don’t participate in charged-currentreactions. Can be treated as ‘one’.
• Emission:
• Accretion luminosity and diffusive luminosity.
Pair processes:hot & denseenvironmentneeded
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Stellar Collapse: The Quantitative Picture
Putting Things Together: Supernova Energetics• Supernova problem: What revives the shock?
• Precollapse iron core gravitational energy:
-> Shock stalls “after” 0.1 MSUN.
(Shock formation at 0.55 MSUN, v 0.05 c )
• Binding energy of a cold 1.5 MSUN NS, R=12.5 km -> Energy Reservoir
• Initial shock energy:
• Dissociation:
• Neutrinos: initially up to
• Binding energy of the mantle (12-MSUN star):
-> need multiple Bethes to blow up the star!
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The General Picture
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The General Picture
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The General Picture
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The General Picture
What is the Mechanism of shock revival?
The Supernova Problem
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Stellar Collapse: Supernova Mechansims
The Essence of any Supernova Mechanism
Explosion mechanism must tap the gravitational energy reservoir and convert the necessary
fraction into energy of the explosion.
• Collapse to neutron star: 3 x 1053 erg = 300 Bethe [B] gravitational energy.
• 1051 erg = 1 B kinetic and internal energy of the ejecta. (Extreme cases: 1052 erg; “hypernova”)
• 99% of the energy is radiated as neutrinos over hundreds of seconds as the protoneutron star (PNS) cools.
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Stellar Collapse: Supernova Mechansims
Supernova Mechanism: First Simulations
HansDave ArnettSterling Colgate Jim Wilson
Colgate & White 1966 Arnett 1966 Bethe & Wilson 1985
• No supercomputers yet (Cray-I only in 1976!): Limited to spherical symmetry, low resolution, poor neutrino transport.
• Nevertheless: Very important discovery ->Energy deposition by neutrinos may revive/drive the shock.
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Stellar Collapse: Supernova Mechansims
The Neutrino MechanismNeutrino cooling:
Neutrino heating:
[Ott et al. 2008]
Gain Radius
• Neutrino-driven mechanism:Based on subtle imbalance between neutrino heating and cooling in postshock region.
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Stellar Collapse: Neutrino Mechanism
Does it work?• Yes!
BUT: Only for lowest-massmassive stars.
• FAILS in spherical symmetry (1D) for garden-variety massivestars (15 MSUN) in simulations with bestneutrino physics andneutrino transport
Kitaura et al. 2006
8.8 MSUN
progenitor
(Kitaura et al. 2006, Burrows 1988, Burrows, Livne, Dessart 2007)
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Stellar Collapse: Neutrino Mechanism
Failure of the Neutrino Mechanism in 1D
Marek & Janka 2009
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Stellar Collapse: Neutrino Mechanism
A few Words on Neutrino Transport
• 6D problem: 3D space, 3D (є, θ, φ) momentum space.
• Limiting cases – easy to handle:(1) Diffusion (isotropic radiation field)(2) Free streaming
(“forward-peaked” radiation field)
30 km 60 km 120 km 240 km
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Stellar Collapse: Neutrino Mechanism
Neutrino Transport in Core-Collapse SNe• Main complication: Need to track radiation field from complete
isotropy to full free streaming over many orders of magnitude of τ.
• Neutrino heating depends on details of the radiation field:
• Inverse Flux factor:
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Stellar Collapse: Neutrino Mechanism
Anyway... What next?
• Why does the neutrino mechanism fail in 1D?
• Is dimensionality an issue? What is 1D missing?
– Rotation and magnetohydrodynamics (MHD)
– Convection/Turbulence
– Other multi-D processes; e.g., pulsations
• First multi-D radiation-hydrodynamics simulations:
– early to mid 1990s: Herant et al. 1994, Burrows et al. 1995, Janka & Müller 1996.
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C. D. Ott @ NAOJ Mitaka, Tokyo 2009/05/24 39
[Ott
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A Look at the Beast:
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C. D. Ott - The Physics of Stellar Collapse and Core-Collapse Supernovae 40
Convection
Convection• Ledoux criterion for instability:
< 0 < 0
• CL > 0 -> convective instability.
• Postbounce supernova cores:
• Negative entropy gradient in postshock region -> convection
• Negative entropy region inside the neutrinosphere in the PNS -> convection
• Important effect of convection:
• “Dwell time” of material in the heating (“gain”)region is increased -> leads to more favorableratio advect / heat .
Lepton Gradient
Entropy Gradient
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C. D. Ott - The Physics of Stellar Collapse and Core-Collapse Supernovae 41
SASI
Standing Accretion Shock Instability[Blondin et al. ‘03,’06; Foglizzo et al. ‘06, Scheck et al. ‘06, ‘07, Burrows et al. ‘06, ’07]
Advective-acoustic cycle drives shock instability.
Seen in simulations byall groups!
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C. D. Ott - The Physics of Stellar Collapse and Core-Collapse Supernovae 42
Status of the Neutrino Mechanism
Status of the Neutrino Mechanism
• Best simulations are still in 2D.
• Things look better in 2D, somemodels explode under specialcircumstances.
• No robust explosions.
• Crucial conditions (?):General relativitySoft nuclear EOS
• Robust explosions in 3D?-> ongoing research!
Marek & Janka 2009
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C. D. Ott - The Physics of Stellar Collapse and Core-Collapse Supernovae 43
Alternatives
Alternatives to the Neutrino Mechanism
MagnetorotationalMechanism
Acoustic Mechanism
[LeBlanc & Wilson 1970, Bisnovatyi-Kogan et al. 1976, Meier et al. 1976,
Symbalisty 1984]
[proposed by Burrows et al. 2006, 2007; not (yet?) confirmed by other
groups/codes]
(qualitative discussion!)
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C. D. Ott - The Physics of Stellar Collapse and Core-Collapse Supernovae 44
Alternatives
Alternatives to the Neutrino Mechanism
MagnetorotationalMechanism
Acoustic Mechanism
[LeBlanc & Wilson 1970, Bisnovatyi-Kogan et al. 1976, Meier et al. 1976,
Symbalisty 1984]
[proposed by Burrows et al. 2006, 2007; not (yet?) confirmed by other
groups/codes]
(qualitative discussion!)
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MHD-driven Explosions
45
[e.g., Burrows et al. 2007, Dessart et al. 2008, Kotake et al. 2004, Yamada & Sawai 2004, Sawai et al. 2008, Takiwaki et al. 2009]
VULCAN 2D R-MHD code, Livne et al. 2007, Burrows et al. 2007.
• Rapid rotation: P0 < 4-6 s-> millisecond PNS
• PNS rotational energy:10 B
• Amplification of B fields up to equipartition:
• compression
• dynamos
• magneto-rotational instability (MRI)
• Jet-driven outflows.
• MHD-driven explosionmay be GRB precursor.
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46
MHD jet/explosion launched when Pmag / Pgas 1
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C. D. Ott @ NAOJ Mitaka, Tokyo 2009/05/24 47
Magnetic field lines inM15B11UP2A1H of Burrows, Dessart, Livne, Ott, Murphy ‘07.
NewtonianRadiation-MHDSimulations withVULCAN/2D
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C. D. Ott - The Physics of Stellar Collapse and Core-Collapse Supernovae 48
Alternatives
Features/Limitations of the Magnetorotational Mechanism
• Jet powers up to 10 B/s (1052 erg/s).
• Simultaneous explosion and accretion.
• Hypernova energies (> 10 B) attainable.
• MHD mechanism inefficient for cores with precollapse P0 > 4 s, but stellar evolution + NS birth spin estimates: P0 > 30 s in most cores.
• MHD explosion — a GRB precursor?
• Limitations: Resolution does not allow to capture Magnetorotational Instability; Simulations 2D and Newtonian.
[Heger et al. 2005, Ott et al. 2006]
[Burrows et al. 2007]
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C. D. Ott - The Physics of Stellar Collapse and Core-Collapse Supernovae 49
Alternatives
Alternatives to the Neutrino Mechanism
MagnetorotationalMechanism
Acoustic Mechanism
[LeBlanc & Wilson 1970, Bisnovatyi-Kogan et al. 1976, Meier et al. 1976,
Symbalisty 1984]
[proposed by Burrows et al. 2006, 2007; not (yet?) confirmed by other
groups/codes]
(qualitative discussion!)
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C. D. Ott - The Physics of Stellar Collapse and Core-Collapse Supernovae 50
Alternatives: The Acoustic Mechanism
Setting the Stage: SASI[e.g., Burrows et al. 2006, 2007bc, Ott et al. 2006]
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C. D. Ott - The Physics of Stellar Collapse and Core-Collapse Supernovae 51
Alternatives: The Acoustic Mechanism
The Acoustic Mechanism
SASI-modulated supersonic accretion streams and SASI generated turbulence excite lowest-order (l=1) buoyancy mode in the PNS.
[e.g., Burrows et al. 2006, 2007bc, Ott et al. 2006]
• g-modes reach large amplitudes 800—1000 ms after bounce.
• Damping by strong sound waves that steepen into shocks; deposit energy in the stalled shock.
• Drive 1 B explosions at late times.
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PNS core oscillations, Burrows et al. 2006, 2007; Ott et al. 2006
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C. D. Ott - The Physics of Stellar Collapse and Core-Collapse Supernovae 53
Alternatives: The Acoustic Mechanism
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C. D. Ott - The Physics of Stellar Collapse and Core-Collapse Supernovae 54
Alternatives: The Acoustic Mechanism
SASI-modulated supersonic accretion streams and SASI generated turbulence excite lowest-order (l=1) g-mode in the PNS. f 300 Hz.
• g-modes reach large amplitudes500 ms —1 s after bounce.
• Damping by strong sound wavesthat steepen into shocks; depositenergy in the stalled shock.
• 1 B explosions at late times.
• (1) hard to simulate; unconfirmed, (2) possible parametric instability, limiting mode amplitudes.
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C. D. Ott - The Physics of Stellar Collapse and Core-Collapse Supernovae 55
Summary
Summary• Core-Collapse Supernovae are “Gravity Bombs”.
• The Supernova Problem:The supernova shock always stalls and must be revived.
• There are multiple possible supernova mechanisms:Neutrino, magnetorotational, and acoustic mechanism.
• None of the mechanisms is robust (generic & reproducible)
• Current best simulations in 2D, work towards 3D underway. But will 3D provide the solution to the supernova problem?
• How can we gain observational insight? -> neutrinos and gravitational waves! (see Ott 2009b)