My two cents on strangeness production

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My two cents on strangeness production
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• Firestreak model
• Includes all of the thermal physics
• Plus realistic reaction geometry in coordinate
  space, nuclear transparency effects, all strange
  and non-strange baryons and mesons up to mass 1.3
  GeV, resonance decays, temperature is calculated
  and not a fit parameter

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Cathy Mader

• 14.6 A GeV Si Al, y1.5

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Supernova-Physics
Wolfgang Bauer Michigan State University
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Whats our Goal?

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

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Supernova Explosion
After

• Galaxy NGC3310 Supernova
  1991N

Before
Typical light curve
N.A.Sharp, G.J.Jacoby/NOAO/AURA/NSF
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Supernova Remnants

• Cassiopeia supernova remnant observed in X-rays
  (Chandra), 10,000 light years from Earth
• Color composite of supernova remnant E0102-72 
  X-ray (blue), optical (green), and radio (red)

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Supernovae

• Type 1
• White dwarf exceeds its Chandrasekhar Mass (1.4
  M?) due to accretion and collapses
• Type 2
• Powered by gravitational energy released during
  stars late stage iron core collapse
• Mass range 11 M? to 40 M? at ZAMS (zero age main
  sequence mass of star at start of its evolution)
• Type 2 has hydrogen lines, type 1 does not
• Here focus on type 2 and use M15 M?

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Stellar Evolution

• Conventional stellar energy production via
  hydrogen fusion (t107y for 20 M?)
• Late stages of evolution
• Triple alpha process (t 106y)
• Burning of C (t300y), Ne, O (t6months), Si
  (2days) occurs successively in the center of the
  star (higher and higher T)
• Final products 56Ni, 56Fe or 54Fe (iron core
  mass typically 10)

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Initial Conditions for Core Collapse
Woosley, Weaver 86
Iron Core
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Instabilities and Onset of Collapse

• Electron Capture (dominant for ZAMS lt 20 M?)
• Reaction
• Reduced electron fraction and therefore decrease
  stabilizing electron pressure
• Neutrinos carry entropy and energy out of star
• Photodisintegration (dominant for ZAMS gt 20 M?)
• Reactions
• Also reduce temperature and therefore pressure

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Supernova Nucleosythesis
Mezzacappa
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12D Hydro Simulations

• Strong convection effects
• Turbulence

Mezzacappa et al. (98)
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3d

• Explosion energy 3foe
• texpl 0.1 - 0.2 s

• Fryer, Warren, ApJ 02
• Very preliminary
• Similar convection as seen in their 2d work

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Hydro Simulations

• Tough problem for hydro
• Length scales vary drastically in time
• Multiple fluids
• Strongly time dependent viscosity
• Very large number of time steps
• Special relativity, causality,
• Huge magnetic fields
• 3D simulations needed
• Giant grids

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Simulations of Nuclear Collisions

• Hydro, mean field, cascades
• Numerical solution of transport theories
• Need to work in 6d phase space gt prohibitively
  large grids (203x402x80109 lattice sites)
• Idea Only follow initially occupied phase space
  cells in time and represent them by test
  particles
• One-body mean-field potentials (r, p, t) via
  local averaging procedures
• Test particles scatter with realistic cross
  sections gt (exact) solution of Boltzmann
  equation (Pauli, Bose)
• Very small cross sections via perturbative
  approach
• Coupled equations for many species no problem
• Typically 100-1000 test particles/nucleon

G.F. Bertsch, H. Kruse und S. Das Gupta, PRC
(1984) H. Kruse, B.V. Jacak und H. Stöcker, PRL
(1985) W. Bauer, G.F. Bertsch, W. Cassing und U.
Mosel, PRC (1986) H. Stöcker und W. Greiner,
PhysRep (1986)
1st Developed _at_ MSU FFM
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Transport Equations
Mean field EoS 2-body scattering
f phase space density for baryons
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Test Particle Equations of Motion
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Try this for Supernovae!

• 2 M? in iron core 2x1057 baryons
• 107 test particles gt 2x1050 baryons/test
  particle ?
• Need time-varying grid for (non-gravity)
  potentials, because whole system collapses
• Need to think about internal excitation of test
  particles
• Can create n-test particles and give them finite
  mean free path gt Boltzmann solution for
  n-transport problem
• Can address angular momentum question

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Numerical Realization

• Test particle equations of motion
• Nuclear EoS evaluated on spherical grid
• Newtonian monopole approximation for gravity

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Equation of State

• Low density
• Degenerate e-gas
• High density
• Dominated by nuclear EoS
• Isospin term in nuclear EoS becomes dominant
• For now

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

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Electron Fraction, Ye

• Strongly density dependent
• Neutrino cooling

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Internal Heating of Test Particles

• Test particles represent mass of order Mearth.
• Internal excitation of test particles becomes
  important for energy balance

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Test Particle Scattering

• Nuclear case test particles scatter with
  (reduced) nucleon-nucleon cross sections
• Elastic and inelastic

Elastic

• Similar rules apply for astro test particles
• Scale invariance
• Shock formation
• Internal heating

cm frame
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Excluded Volume

• Collision term simulation via stochastic
  scattering (Direct Simulation Monte Carlo)
• Additional advection contribution
• Modification to collision probability

2nd Enskogvirial coefficient
Alexander, Garcia, Alder, PRL 95 Kortemeyer,
Daffin, Bauer, PRB 96
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Neutrinos

• Neutrinos similar to pions at RHIC
• Not present in entrance channel
• Produced in very large numbers (RHIC 103, here
  1056)
• Essential for reaction dynamics
• Different No formation time or off -shell
  effects
• Represent 10N neutrinos by one test particle
• Populate initial neutrino phase space uniformly
• Sample test particle momenta from a thermal dist.
• Neutrino test particles represent 2nd fluid, do
  NOT escape freely (neutrino trapping), and need
  to be followed in time.
• Neutrinos created in center and are light fluid
  on which heavy baryon fluid rests
• Inversion problem
• Rayleigh-Taylor instability
• turbulence

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Neutrino Test particles

• Move on straight lines (no mean field)
• Scattering with hadrons
• NOT negligible!
• Convolution over all sAn?A2 (weak neutral
  current)
• Resulting test particle cross section angular
  distrib.scm(qf) d(qf -qi)
• Center of mass picture

Pn,i
pN,i
Pn,f
pN,f
gt Internal excitation
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Neutrino Scattering Off Protons
P. Vogl, nucl-th/0305003
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First Results

• Mean field level
• Only nuclear and electron gas EoS, gravity
• No collisions yet
• Exploratory role of collective rotation

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Global Angular Momentum
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Energy of Baryons
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Results

• mean field level
• 1 fluid hadrons

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Max. Density vs. Angular Momentum

• Mean field only!!!

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• Initial conditions
• After 2 ms
• After 3 ms
• Core bounce
• 1 ms after core bounce

120 km
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Vortex Formation
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Some Supernovae are Not Spherical!

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

HST Wide Field Planetary Camera 2
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More Qualitative

• Neutrino focusing along poles gives preferred
  direction for neutrino flux
• Neutrinos have finite mass, helicity
• Parity violation on the largest scale
• Net excess of neutrinos emitted along North
  Pole
• gt Strong recoil kick for neutron star supernova
  remnant
• gt Non-thermal contribution to neutron star
  velocity distribution
• Horrowitz et al.

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The People who did the Work

• Tobias Bollenbach
• Terrance Strother
• Funding from NSF, Studienstiftung des Deutschen
  Volkes, and Alexander von Humboldt Foundation