Neutrino Opacity in Dense Matter

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Neutrino Opacity in Dense Matter
U. Lombardo, Orsay march 2004

• Outline
• effective interaction in dense matter
  three-body force
• two mechanisms of neutrino opacity in dense
  matter
• nuclear response to weak interaction in RPA
• RPA response function in termis of Landau
  parameters
• neutrino mean free path
• 3BF and superfluidity in dense matter

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• One of the main challanges of nuclear
  astrophysics is to try to trace
• the (time) evolution of the neutron star
  cooling.
• Starting from its birth the main steps are
  assumed
• to be
• 0 birth from supernova
  explosion
• 20s neutrino trapping gt rapid
  deleptonization
• 10-102 yrs thermal relaxation stage (?
  ? )
• 105-106yrs neutrino cooling stage L?gtgtL?
  ()
• T gt 106yrs photon cooling stage L? gtgtL?
• Recent exhaustive reviews are
• gtPrakash,Lattimer,Pons,Steiner and Reddy
• Lecture Notes in Physics, Springer Verlag
  (2001),
• gtYakovlev Pethick
• astro-ph/0402143 (2004)

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Cooling curves
Superfluid
Non superfluid
Yakovlev et al
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• dense-matter behaviour is mainly ruled by
  three-body forces
• due to
• NN virtual excitations via heavy meson fields
• (derived by
  GE Brown et al from DB)
• 2) Fujita-Miyazawa 3BF (with isobar,non
  isobar,...excitations)
• Nucleonic resonance N(1440)
• (introduced
  by Grange,Mathiot,...)

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NN virtual excitations
total
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Fujita Miyazawa (1957)
?,?
?
?,?


......
?,?
?,?
N N N
N N N
also N(1440) implicitly included
Chiral perturbation theory
Tucson-Melbourne
?,?
?,?
Lutz,Friman,Appel PLB 474 (2000) Kaiser,Fritsch,We
ise (2001)
Off-shell extension of N? scattering T
2?-3BF settled on QCD symmetry properties,but
expected negligible at high density?
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virtual nucleon excitations
N
N(1440)
from Tp750MeV pp?pp?? - (Patzold et al, PRC 67
(2003) decay widths
Grange,Lejeune,Martzolff,Mathiot PRC (1989)
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VV2V3
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• Along with the neutrino prodution rate a
• main property which determines cooling rate is
• the neutrino opacity
• (heat capacity,thermal conductivity)
• Recent contributions
• .........
• Burrow,Sawyer, PR C58 (1998)
• Reddy,Prakhash,Lattimer,Pons, PR C59 (1999)
• Bombaci, Margueron, Vidana, PR C68 (2004)
• Shen, Lombardo, Van Giai, PR C68 (2004)

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weak interaction coupling
dynamical structure fncts
lepton tensor (WS theory)
W
? absorption
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Dynamical structure function

• Free Fermi gas no correlations except for Pauli
  blocking
• Mean field model short range pp correlations
  incorporated
• Fermi liquid long range ph correlations

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RPA response function (Bethe-Salpeter Eq.)
scattering
absorption
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(No Transcript)
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Residual interaction in BHF
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Neutrino mean free pathin neutron matter
l(?,T,En)
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Spin Isospin Asymmetric NM
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two sets of calculation for n mean
free path 1) pure neutron matter (long-scale
epoch)
scattering
2) nuclear matter in beta-equilibrium
(short-scale deleptonization epoch)
scattering absorption
W
charge exchange with absorption
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Neutrino mean free pathin neutron matter
ferromagnetic instability
RPA from phenom. EOS
RPA from Brueckner EOS
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Predictions for neutrino mean free path
in several approximations
absorption mfp is much larger than scattering
i) coupling constant two times ii) ?abs
controled by ?? whereas ?scatt is controled
by ?e
RPA correlations reduce the phase space
available for scattering and absorption the
steep rise of absorption mean free path at very
high densityis due to the increase of Yp and
then ?p which make teh croos section smaller
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Temperature and energy dependence
Scattering
Absorption
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• Conclusions
• neutrino mean free path has been calculated from
  linear response
• theory in several approximations, including
  2bf and 2bf3bf
• gt neutrino absorption larger than scattering
• gt RPA neutrino opacity quite diferent from
  free-Fermi gas
• gt opacity extends to high density and should be
  taken into account
• in simulation even beyond the short-scale era
  
• gt A possible improvement Landau parameters at
  finite temperature

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Landau-Migdal Parameters T dependence
only 2BF
?(fm-3)
0.34
0.45
F0 F0 G0 G0
0.25
0.17
exponential T-dependence in Fermi functions
already included
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role of superfluid states
gtThre different superfluid states are supposed to
set on neutron stars nn 1S0, pp 1S0 and nn
3PF1 gtThe question is whether or not these
can explain the transition region where the
observation fall gtEmissivity reduction
QQoRpair with Rpair e-? / kT (the same
for opacity and heat capacity)
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SUPERFLUID STATES IN NEUTRON STARS
vortex creep model
pp- pairing in extended region would have a
drammatic effect suppression rapid urca processes
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Neutron 1S0 pairing rapidly disappears at high
density. Proton 1SO survives up to high density
for its modest contribution to asymmetric nuclear
matter in beta equilibrium Neutron pairing in PF
channel suffers from a large uncertainty But
anyhow it is expected to be suppressed
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proton 1S0 pairing
?URCA ? ?pair dURCA sligthly
affected by superfludity!
Zuo,Lombardo et al.,PP 2004
.Schulz et al.,2004
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End