Teoria a molti-corpi della materia nucleare

1. Teoria a molti-corpi della materia nucleare

2. Lezione IV • Implicazioni per le stelle di neutroni • 2. Cenni sulla fase superfluida • 3. Indicazioni sulla EoS da dati osservativi e da • collisioni fra ioni pesanti • 4. Confronto con EoS fenomenologiche • 5. Formulazione relativistica, l’ approssimazione • Dirac-Brueckner • 6. Transizione alla fase di quark, modelli per la fase • deconfinata

3. Rappresentazione schematica di una stella massiva in condizioni pre-collasso

4. SN 1987a Exploding Beforeexplosion

5. La “nuvola” espulsa e il rimanente oggetto compatto

6. Abbondanza di oggetti compatti !

7. Visione schematica di una pulsar e del suo “faro”

8. “faro” in direzione della terra “faro” fuori direzione

9. Distribuzione delle pulsars in cielo rispetto al piano galattico

10. Asection(schematic) of a neutron star La parte piu’ interna di una Stella di neutroni “convenzionale” e’ dominata da materia nucleare omogenea e fortemente asimmetrica Piu’ avanti ci occuperemo della “crosta”

11. ThebaryonicEquationsofState HHJ : Astrophys. J. 525, L45 (1999 BBG : PRC 69 , 018801 (2004) AP : PRC 58, 1804 (1998)

12. Phenomenolocical area from Danielewicz et al., Science 298 (2002) 1592 Nonostante le incertezze dell’ analisi sembra esserci una ben definita discriminazione tra le diverse EOS Kh. Gad Nucl. Phys. 747 (2005) 655

13. Composition of asymmetric and beta-stable matter • Parabolic approximation • Composition of stellar matter i)Chemical equilibrium among the different baryonic species ii) Charge neutrality iii) Baryon number conservation

14. Symmetry energy as a function of density Proton fraction as a function of density in neutron stars AP becomes superluminal at high density and has no DU

16. Hyperon influence on hadronic EOS

17. Composition of asymmetric and beta-stable matterincludinghyperons • Parabolic approximation extended to hyperons • Composition of stellar matter i)Chemical equilibrium among the different baryonic species ii) Charge neutrality iii) Baryon number conservation

18. Including hyperons inside the neutron stars • Shift of the hyperon onset points • down to 2-3 times saturation density • At high densities N and Y present almost in the same percentage.

19. Mass-Radius relation • Inclusion of Y decreases the maximum mass value

20. H.J. Schulze et al., PRC 73, 058801 (2006)

23. IncludingQuarkmatter • Since we have no theory which describes both confined and • deconfined phases, we uses two separate EOS for baryon • and quark matter and assumes a first order phase transition. • Baryon EOS. BBG • AP • HHJ • Quark matter EOS. MIT bag model • Nambu-Jona Lasinio • Coloror dielectric model

24. The three baryon EOS for beta-stable neutron star matter in the pressure-chemical potential plane.

25. MIT bag model. “Naive version”

26. PRC , 025802 (2002)

27. Materia nucleare simmetrica Al decrescere del valore della bag constant la massa massima delle NS tende a crescere. Tuttavia B non puo’ essere troppo piccolo altrimenti lo stato fondamentale della materia nucleare all densita’ di saturazione e’ nella fase deconfinata !

28. Density dependent bag “constant”

29. Densityprofilesofdifferentphases MIT bag model

30. Evidence for “large” mass ? Nice et al. ApJ 634, 1242 (2005) PSR J0751+1807 M =2.1 +/- 0.2 Ozel, astro-ph /0605106 EXO 0748 – 676 M > 1.8 Quaintrell et al. A&A 401, 313 (2003) NS in VelaX-1 1.8 < M < 2

31. Alfordetal. , ApJ 629 (2005) 969 Non-perturbative corrections ; Strange quark mass corresponds to the usual MIT bag model Freedman & McLerran 1978

32. Maximum mass depends mainly on the parametrization and not on the transition point

33. BBG HHJ

34. The problem of nuclear matter ground state is solved. But, in any case one needs an additional repulsion in quark matter at high density

35. NJLModel The model is questionable at high density where the cutoff can be comparable with the Fermi momentum

36. IncludingColorSuperconductivityinNJL Steiner,ReddyandPrakash2002 Buballa&Oertel2002. ApplicationtoNS CT+ GSI,PLB562,,153(2003)

37. Massradiusrelationship Maximum mass

38. NJL , the quark current masses as a function of density

39. Equivalence between NJL and MIT bag model above chiral transition (two flavours). For NJL B = 170 MeV The pressure is zero at zero density ! (no confinement)

40. The CDM model : the equation of state for symmetric matter C. Maieron et al., PRD 70, 043010 (2004) The model is confining

41. The CDM model : maximum mass of neutron star

42. The effective Bag constsnt in the CDM model

43. Some (tentative) conclusions • The transition to quark matter in NS looks likely, • but the amount of quark matter depends on the quak • matter model. • If the “observed” high NS masses (about 2 solar mass) • have to be reproduced, additional repulsion is needed • with respect to “naive” quark models . • The situation resembles the one at the beginning of NS • physics with the TOV solution for the free neutron gas • The confirmation of a mass definitely larger than 2 • would be a major breakthrough 3. Further constraints can come from other observational data (cooling, glitches …….)

44. Comparison between phenomenological forces and microscopic calculations (BBG) at sub-saturation densities. M.Baldoetal..Nucl. Phys. A736,241(2004)

45. Asymmetry (isospin) dependence of EOS

46. Symmetry energy as a function of density. A comparison at low density. Microscopic results approximately fitted by

47. Trying connection with phenomenology : the case. Density functional from microscopic calculations rel. mean field Skyrme and Gogny microscopic functional The value of r_n - r_p from mic. fun. is consistent with data

48. Asection(schematic) of a neutron star

49. The structure of nuclei and Z/N ratio are dictated by beta equilibrium Negele & Vautherin classical paper. Simple functional, and no pairing.

50. Outer Crust Inner Crust No drip region Drip region Position of the neutron chemical potential