supernova collapse dynamics

W. Bauer, Breckenridge 03 1

Supernova Collapse DynamicsSupernova Collapse Dynamics

Wolfgang BauerWolfgang BauerMichigan State UniversityMichigan State University

• Pre-collapse dynamicsPre-collapse dynamics• Kinetic theory for collapseKinetic theory for collapse• Similarities to nuclear dynamics simulation Similarities to nuclear dynamics simulation


NassauNassau• Declared victory in search for fragmentation Declared victory in search for fragmentation

critical point propertiescritical point properties


Supernova ExplosionSupernova Explosion

• Galaxy NGC3310Galaxy NGC3310

Supernova 1991N Supernova 1991N

N.A.Sharp, G.J.Jacoby/NOAO/AURA/NSF

After

Before

Typical light curve


Supernova RemnantsSupernova Remnants

• Cassiopeia supernova remnant observed Cassiopeia supernova remnant observed in X-rays (Chandra), 10,000 light years in X-rays (Chandra), 10,000 light years from Earthfrom Earth

• Color composite of supernova remnant Color composite of supernova remnant E0102-72: X-ray (blue), optical (green), E0102-72: X-ray (blue), optical (green),

and radio (red)and radio (red)


Crab NebulaCrab Nebula

– 6500 light years from 6500 light years from herehere

– Supernova in 1054Supernova in 1054– Visible in broad daylight Visible in broad daylight

for several weeksfor several weeks– Left behind neutron star Left behind neutron star

the size of Manhattanthe size of Manhattan

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HubbleHubble

HubbleHubble

Chandra / HubbleChandra / Hubble


SupernovaeSupernovae

• Type 1Type 1– White dwarf exceeds its Chandrasekhar Mass White dwarf exceeds its Chandrasekhar Mass

(~1.4 M(~1.4 M) due to accretion and collapses) due to accretion and collapses

• Type 2Type 2– Powered by gravitational energy released during Powered by gravitational energy released during

star’s late stage iron core collapsestar’s late stage iron core collapse– Mass range 11 MMass range 11 M to 40 M to 40 M at ZAMS (zero age main at ZAMS (zero age main

sequence; mass of star at start of its evolution)sequence; mass of star at start of its evolution)

• Type 2 has hydrogen lines, type 1 does notType 2 has hydrogen lines, type 1 does not

• Here: focus on type 2 and use M=15 MHere: focus on type 2 and use M=15 M


Stellar EvolutionStellar Evolution• Conventional stellar energy production via Conventional stellar energy production via

hydrogen fusion (t~10hydrogen fusion (t~1077y for 20 My for 20 M))

• Late stages of evolutionLate stages of evolution– Triple alpha process (t~ 10Triple alpha process (t~ 1066y)y)

– Burning of C (t~300y), Ne, O (t~6months), Si Burning of C (t~300y), Ne, O (t~6months), Si (2days) occurs successively in the center of the (2days) occurs successively in the center of the star (higher and higher T) star (higher and higher T)

– Final products: Final products: 5656Ni, Ni, 5656Fe or Fe or 5454Fe (iron core mass Fe (iron core mass typically 10%)typically 10%)

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411H→2

4 He + 2e+ + 2ν e + 2γ

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24 He+2

4 He↔48 Be; 2

4He+48 Be→ 6

12 C +γ


Initial Conditions for Core CollapseInitial Conditions for Core Collapse

Woosley, Weaver 86Iron CoreIron Core


Instabilities and Instabilities and Onset of CollapseOnset of Collapse

• Electron Capture (dominant for ZAMS < 20 MElectron Capture (dominant for ZAMS < 20 M))– ReactionReaction

– Reduced electron fraction and therefore decrease stabilizing Reduced electron fraction and therefore decrease stabilizing electron pressureelectron pressure

– Neutrinos carry entropy and energy out of starNeutrinos carry entropy and energy out of star

• Photodisintegration (dominant for ZAMS > 20 MPhotodisintegration (dominant for ZAMS > 20 M))– ReactionsReactions

– Also reduce temperature and therefore pressureAlso reduce temperature and therefore pressure

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p+ + e− → n+ν e

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2656 Fe +γ →13 2

4He + 4n

24 He +γ → 2p+ 2n


Supernova NucleosythesisSupernova Nucleosythesis

Mezzacappa


2D Hydro Simulations2D Hydro Simulations

• Strong convection effectsStrong convection effects• TurbulenceTurbulence

Mezzacappa et al. (98)


3d3d

Fryer, Warren, ApJ 02Fryer, Warren, ApJ 02

•Very preliminaryVery preliminary

•Similar convection Similar convection as seen in their 2d as seen in their 2d workwork

• Explosion energy 3foeExplosion energy 3foe• ttexplexpl = 0.1 - 0.2 s = 0.1 - 0.2 s


Hydro SimulationsHydro Simulations

• Tough problem for hydroTough problem for hydro– Length scales vary drastically in timeLength scales vary drastically in time– Multiple fluidsMultiple fluids– Strongly time dependent viscosityStrongly time dependent viscosity– Very large number of time stepsVery large number of time steps

• Special relativity, causality, …Special relativity, causality, …• Huge magnetic fieldsHuge magnetic fields• 3D simulations needed3D simulations needed

– Giant gridsGiant grids


Simulations of Nuclear CollisionsSimulations of Nuclear Collisions

• Hydro, mean field, cascadesHydro, mean field, cascades• Numerical solution of transport theories Numerical solution of transport theories

– Need to work in 6d phase space => prohibitively Need to work in 6d phase space => prohibitively large grids (20large grids (2033x40x4022x80~10x80~109 9 lattice sites)lattice sites)

– Idea: Only follow initially occupied phase space Idea: Only follow initially occupied phase space cells in time and represent them by test particlescells in time and represent them by test particles

– One-body mean-field potentials (One-body mean-field potentials ( , , pp, , ) via local ) via local averaging proceduresaveraging procedures

– Test particles scatter with realistic cross sections Test particles scatter with realistic cross sections => (exact) solution of Boltzmann equation => (exact) solution of Boltzmann equation (+Pauli, Bose)(+Pauli, Bose)

– Very small cross sections via perturbative Very small cross sections via perturbative approachapproach

– Coupled equations for many species no problemCoupled equations for many species no problem– Typically 100-1000 test particles/nucleonTypically 100-1000 test particles/nucleon


ExampleExample

• Density in Density in reaction reaction planeplane

• Integration Integration over over momentum momentum spacespace

• Cut for Cut for z=0+-0.5 z=0+-0.5 fmfm

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Momentum SpaceMomentum Space• Output quantities (not input!)Output quantities (not input!)• Momentum space information onMomentum space information on

– Thermalization & equilibration Thermalization & equilibration – FlowFlow– ParticleParticle

productionproduction

• Shown here:Shown here:locallocaltemperaturetemperature QuickTime™ and aSorenson Video 3 decompressorare needed to see this picture.


Try this for Supernovae!Try this for Supernovae!

• 2 M2 M in iron core = 2x10 in iron core = 2x105757 baryons baryons• 101077 test particles => 2x10 test particles => 2x105050 baryons/test baryons/test

particle particle • Need time-varying grid for (non-gravity) Need time-varying grid for (non-gravity)

potentials, because whole system collapsespotentials, because whole system collapses• Need to think about internal excitation of test Need to think about internal excitation of test

particlesparticles• Can create Can create -test particles and give them -test particles and give them

finite mean free path => Boltzmann solution finite mean free path => Boltzmann solution for for -transport problem-transport problem

• Can address angular momentum questionCan address angular momentum question


NumericsNumerics

• Test particle equations of motionTest particle equations of motion

• Nuclear EoS evaluated on spherical gridNuclear EoS evaluated on spherical grid• Newtonian monopole approximation for Newtonian monopole approximation for

gravitygravity


Equation of StateEquation of State

• Low density:Low density:– Degenerate e-gasDegenerate e-gas

• High densityHigh density– Dominated by Dominated by

nuclear EoSnuclear EoS– Isospin term in Isospin term in

nuclear EoS nuclear EoS becomes becomes dominant, Ydominant, Yee~0.4~0.4

• High density neutron rich EoS can be High density neutron rich EoS can be explored by GSI upgrade and/or RIAexplored by GSI upgrade and/or RIA


Electron Fraction, YElectron Fraction, Yee

• Strongly density dependentStrongly density dependent• Neutrino coolingNeutrino cooling


Internal Heating of Test ParticlesInternal Heating of Test Particles

• Test particles Test particles represent mass represent mass of order Mof order Mearthearth..

• Internal Internal excitation of test excitation of test particles particles becomes becomes important for important for energy balanceenergy balance


NeutrinosNeutrinos

• Neutrinos similar to pions at RHICNeutrinos similar to pions at RHIC– Not present in entrance channelNot present in entrance channel– Produced in very large numbers (RHIC: 10Produced in very large numbers (RHIC: 1033, here , here

10105656))– Essential for reaction dynamicsEssential for reaction dynamics

• Different: No formation time or off -shell Different: No formation time or off -shell effectseffects

• Represent 10Represent 10NN neutrinos by one test particle neutrinos by one test particle– Populate initial neutrino phase space uniformlyPopulate initial neutrino phase space uniformly– Sample test particle momenta from a thermal dist.Sample test particle momenta from a thermal dist.

• Neutrino test particles represent “2Neutrino test particles represent “2ndnd fluid”, fluid”, do do NOTNOT escape freely (neutrino trapping), and escape freely (neutrino trapping), and need to be followed in time.need to be followed in time.


Neutrino Test particlesNeutrino Test particles

• Move on straight lines (no mean field)Move on straight lines (no mean field)• Scattering with hadronsScattering with hadrons

– NOT negligible!NOT negligible!– Convolution over all Convolution over all AAAA22 (weak neutral (weak neutral

current)current)– Resulting test particle cross section angular Resulting test particle cross section angular

distrib.:distrib.: cmcm ff ff -- ii

– Center of mass picture:Center of mass picture:Pi pN,i

Pf pN,f=> Internal excitation


Effects of Angular MomentumEffects of Angular Momentum

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ResultsResults

• ““mean field” mean field” levellevel

• 1 fluid: hadrons 1 fluid: hadrons


0(a)(a) Initial conditionsInitial conditions(b)(b) After 2 msAfter 2 ms(c)(c) After 3 msAfter 3 ms(d)(d) Core bounceCore bounce(e)(e) 1 ms after core bounce1 ms after core bounce

120 km


Vortex FormationVortex Formation


Some Supernovae are Not Spherical!Some Supernovae are Not Spherical!

• 1987A remnant shows “smoke rings”1987A remnant shows “smoke rings”• Cylinder symmetry, but not sphericalCylinder symmetry, but not spherical• Consequence of high angular momentum Consequence of high angular momentum

collapsecollapse HST Wide Field Planetary Camera 2


More QualitativeMore Qualitative

• Neutrino focusing along poles gives preferred Neutrino focusing along poles gives preferred direction for neutrino fluxdirection for neutrino flux

• Neutrinos have finite mass, helicityNeutrinos have finite mass, helicity• Parity violation on the largest scaleParity violation on the largest scale• Net excess of neutrinos emitted along “North Net excess of neutrinos emitted along “North

Pole”Pole”• => Strong recoil kick for neutron star => Strong recoil kick for neutron star

supernova remnantsupernova remnant• => Non-thermal contribution to neutron star => Non-thermal contribution to neutron star

velocity distributionvelocity distribution


The Man who did the WorkThe Man who did the Work

Tobias BollenbachTobias Bollenbach(M.S. Thesis, MSU, 2002)(M.S. Thesis, MSU, 2002)

Funding from NSF, Studienstiftung des Deutschen Funding from NSF, Studienstiftung des Deutschen Volkes, and Alexander von Humboldt FoundationVolkes, and Alexander von Humboldt Foundation

supernova collapse dynamics

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