The microphysics of neutrino transport at extreme density

1
The microphysics of neutrino transport at extreme
density

• .Understanding the temporal structure of a
  supernova neutrino signal
• Sanjay Reddy
• Theoretical Division, LANL

2
SN 1987a 20 events ..in support of supernova
theory

• 1057 neutrinos
• time scale 10 s
• neutrino energy
• total energy emitted in neutrinos 3 X 1053
  ergs 0.2 Msun c2

3
Core Collapse Supernova

• Fe core becomes unstable
• Collapse time scale 100 ms
• Nearly Adiabatic
• B.E. G Mcore/Rfinal 3 X 1053 ergs

4
Supernova Neutrinos - a (proto) neutron star is
born
1500 km
Core collapse tcollapse 100 ms
B. E. 2-3 X 1053 ergs
Shock wave Eshock1051ergs
3X107 km
10 km
Hot dense Proto-neutron Star t1-2 s
100 km
5
SN Neutrinos model predictions
Early time (t lt 1-2 s)
Temporal/spectral features set by explosion
details, accretion, convection and properties of
matter at sub-nuclear densities 1012-1013 g/cm3
R. Buras, M. Ramp, H-Th. Janka K. Kifonidis,
PRL 90, 241101 (2003)

• A. Mezzacappa et al., Phys. Rev. Lett. 86, 1935
  (2001)
• T. A. Thompson, A. Burrows, P. A. Pinto,
  astro-ph/0211194

6
Proto-neutron Star Phase late times (t gt 3-4 s)
Burrows Lattimer, Astrophys. J 307, 178
(1986) Kiel Janka, Astrnm. Astrophys. 296,
145 (1995) Pons, Reddy, Prakash, Lattimer,
Miralles,Astrophys. J. 513, 780 (1999)

• Neutrino diffusion dominates evolution
• Time scales set by neutrino mean free path and
  dense matter EoS

Reddy, Prakash, Lattimer, Pons Phys. Rev. C 59,
2888 (1999)
7
Proto-Neutron Star Evolution
Binding energy is stored in lepton degeneracy and
temperature
8
Microphysics of neutrino mean free paths
E
E
q
q
n,p,e-
target
9
Scattering off nucleons and nuclei
Low density (r lt1014g/cm3) nucleons are
non-relativistic p/M ltlt 1
Neutrinos couple to (fluctuations of) density and
spin
Spectrum of density and spin fluctuations
10
Correlation Functions/Dynamic Structure Factors

Need to evaluate in matter

• Exact Quantum calculations of real-time response
  difficult -
• variational/Monte Carlo
• methods can calculate moments ?S(q,w) wn dw
• Approximate methods include mean field theory,
  RPA, Fermi Liquid Theory.

11
1012 g/cm3

Nuclei (A50, Z25)(Tlt5 MeV),neutrons, protons
and electrons(degenerate) Classical gas (Tgt1
MeV)
Electrons degenerate and nearly free -gt e2/(d EF)
0 Debye screening length is large 80 fm
Coulomb and strong interaction correlations are
considered to be small but wplasmon 1 MeV and
ascatt/d 2 !
Coherent scattering Cross-section A2 Coulomb
correlations important Z2e2/d kT 10-50
Classical methods applicable
Dominant Reactions
Freedman. D. Z., Phys. Rev. D 9, (1974) Tubbs D.
L. Schramm D. N., Astrophys. J 201, 467 (1975)
12
1012 g/cm3

• Ion and electron correlations important
  (Horowitz, Phys. Rev. Lett. 66 , 272 (1991))
• Composition - abundance and properties of nuclei
  at T few MeV ?

Unpublished ongoing work Carlson Reddy, LANL
13
1013 g/cm3

• Pasta (A400, Z200) (for Tlt5 MeV), neutrons,
  protons and electrons(degenerate)
• Ground state is non-uniform with large structures
  ( r10 fm) exotic shapes very close in the energy
  

Response at q20 MeV is strongly modified by
clustering (large coherence) Spectrum of shape
fluctuations is soft - which neutrinos can
excite more on this from C. Horowitz soon -
priv. Comm.
sphere?rods ?slabs/slabs ?rods ?spheres
QMD simulations
Ravenhall, Pethick Wilson, Phys. Rev. Lett. 50,
2066 (1983)
Watanabe, Sato, Yasuoka, Ebisuzaki, Phys. Rev.
C 68, 035806 (2003)
14
1014 g/cm3

• Neutrons, protons and electrons(degenerate)
• Homogenous strongly coupled nuclear liquid
• Corrections to the EoS, static susceptibilities
  due to interactions are large factors of 2
• Nucleons non relativisitic and fairly degenerate
  (EF 50 MeV)

Carlson et. al, Phys. Rev. C68 025802 (2003)
15
1014 g/cm3
Random Phase Approximation



Horowitz Wehrberger, Phys. Lett. B 266, 236
(1991) Burrows Sawyer, Phys. Rev. C 58, 554
(1999) Reddy, Pons, Prakash, Lattimer, Phys. Rev.
C 59, 2888 (1999)
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Sum Rules
Thermodynamic (compressibility) Sum Rule
?Relates response to the Equation of State
F-Sum Rule
Spin/spin-isospin do not commute with tensor
interactions
Pethick Olsson, Phys. Rev. C 66, 065803
(2002) Cowell Pandharipande, Phys. Rev. C 67,
035504 (2003)
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1015 g/cm3

• Possible Phase Transitions
• Hyperons
• Pion/Kaon condensates
• Normal Quark Matter
• Superconducting Quark Matter

?
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Neutrino Propagation in Superconducting phases
pq
??
??
p

pq
??
??
Gap modifies excitation spectrum
p
Carter Reddy, Phys. Rev. D 62, 103002 (2000)
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Collective(Goldstone) modes
pq


q
??
??
??
p
Low energy response dominated by the Goldstone
(a.k.a. Bogoliubov-Anderson ) mode
Bogoliubov, Nuovo Cimento, 7, 6 (1958) Anderson,
Phys. Rev. 112, 1900 (1958) Nambu, Phys. Rev.
117, 648 (1960)
20
Color-Flavor Locked Phase
Alford, Rajagopal Wilczek, Nucl. Phys. B 558,
219 (1999)
BCS pairing of all 9 quarks ? ? 100 MeV !
Energy
Excitation Spectrum
21
Effective theory for Goldstone modes
Schafer Phys. Rev .D 65, 074006 (2002) Manuel
Tytgat, Phys. Lett. B 479, 190 (2000) Hong, Lee
Min, Phys. Lett. B 477, 137 (2000) Hong, Phys.
Lett. B 473, 118 (2000) Son Stephanov, Phys.
Rev. D 61, 074012 (2000)
22
Neutrino-Goldstone Boson Interactions
e-
W-
Z
?
?o
?-
?
?
W-
e-
?
Z
?
?
?
?
?
?
Reddy, Sadszikowski Tachibana, Nucl. Phys. A
714, 337 (2003) Jaikumar, Prakash Schafer,
Phys. Rev. D 66, 063003 (2002)
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Goldstone modes are space-like (? lt q)
?o
?
?
?e
GFf?
GFf?
?
e-
Neutrinos can Cerenkov radiate Goldstone modes
24
Neutrino-Goldstone Boson Interactions
Reddy, Sadszikowski Tachibana, Nucl. Phys. A
714, 337 (2003)
25
Neutrino processes in the CFLKo Phase
Excitation Spectrum
Bedaque Schafer, Nucl. Phys. A697, 802
(2002) Kaplan Reddy, Phys. Rev. D 65, 054042
(2002)
26
Dominant reactions in the CFLKo Phase
Reddy, Sadzikowski, Tachibana, Phys. Rev. D 68,
053010 (2003)

• U(1)B Goldstone still dominates response
• K plays a role - modest charged current opacity
• K dominates neutrino production at low T

27
Outlook (the glass is half full)

• Neutrino diffusion time scale is sensitive to
  properties of matter at supra-nuclear density
• Neutrinos (mean free path) probe the long
  wavelength response in density/spin/isospin
  spin-isospin
• Need neutrino rates at finite T in less
  symmetric quark phases (2SC, 2SC (with gapless
  modes), unpaired quark matter (UQM) etc)
• Need neutrino rates at high T (Tc) - GB
  effective theory fails - need microscopic
  approach (Kundu Reddy work in progress)
• Current estimates still preliminary warrants
  much further work

28
Outlook (the glass is half empty)

• New phases of matter may appear late
• (after most of the neutrinos are emitted)
• The nuclear outer shell of the proto-neutron star
  may be too opaque
• (damps out features of transport in the core)
• Convection and accretion may persist at late
  times
• influencing (and complicating) the ?-signal
• Galactic supernovae are rare

29
Additional slides
30
simulations with normal quark matter
Pons, Steiner, Prakash and Lattimer,
Phys.Rev.Lett. 86, 5223 (2001)