1. INFN Sezione di Catania
Hyperonic PNS’s in the Brueckner theory
F.Burgio
INFN Sezione di Catania
with H.-J. Schulze (INFN CT),
A. Li ( Xiamen Univ., China) & N. Yasutake (Tokyo Univ., Japan)
EoS in Brueckner-Hartree-Fock theory at finite temperature.
Hot hyperons. Effects of the nucleon-hyperon interaction
Composition of PNS matter
Structure properties of PNS.
MODE-SNR-PWN Workshop in Bordeaux, November 2010

2. EoS of nuclear matter at finite T (Microscopic approaches)
Variational method
B. Friedman & V. R. Pandharipande,
Nucl. Phys. A361, 502 (1981)‏
BHF
A. Lejeune et al., NP A453, 189 (1986)‏
M. Baldo & L. Ferreira, PRC 59, 682 (1999)‏
Van der Waals behavior.
Liquid-gas phase transition with
Tc~18-20 MeV.
Chiral Perturbation Theory
S.Fritsch, N.Kaiser, W.Weise, PLB 545, 73 (2002)‏
B. Ter Haar & R. Malfliet , Phys. Rep. 149, 207 (1987)
DBHF
H.Huber, F.Weber, M.K.Weigel , PRC 57, 3484,(1998)‏

3. Expanding the arctan function (up to the first term ) :
Bloch & De Dominicis
NP 10, 509 (1959)‏
Brueckner-Hartree-Fock theory at finite T
k2/2m+U(k)
Grand-canonical potential density ω
Expanding the arctan function (up to the first term ) :

4. Argonne v18 as bare nucleon-nucleon interaction
Frozen Correlations Approximation (FCA) :
U(k) independent of T
Equation of state :
Argonne v18 as bare nucleon-nucleon interaction
Nucleonic three-body forces. Urbana IX model.
(…practically an effective two-body force …)
Nijmegen soft-core nucleon-hyperon interaction NSC89
No available hyperon-hyperon scattering data !

5. 104 BHF calculations in the (ρn, ρp, ρΣ, ρΛ, T )-space
Functional forms easy to implement numerically
Example : the nucleonic contribution
β : asymmetry parameter, t = T/100

6. Composition (beta-equilibrium + charge cons. + lepton number cons.)
Hot ν -free matter
Hot ν-trapped matter
N,l
N, free Y,l
N, interacting Y,l
N, interacting Y,l
Onset densities shifted by the NY interaction
Absence of thresholds at finite entropy.
Stellar core mainly populated by N + 40% hyp.
More symmetric matter.
Hyperon onset shifted by ν trapping.
Strong Σ suppression.
Smaller hyperon fraction , about 20%.

7. PNS structure Equation of state Softening in purely N matter
Stiffening in hyperon matter
Large increase of P due to NY interaction
Slight thermal effects, trapping more important
PNS structure

8. 2) Hadron-Quark phase transition
Check of different microscopic TBF’s
Check of a different parametrization of
NY interaction
Concluding remarks
1) Repulsive YY interaction (J-PARC data)
2) Hadron-Quark phase transition

9. COMPSTAR 2011 School & Workshop
“Gravitational waves and Electromagnetic Radiation
from Compact Stars”
Catania, May 3-12, 2011