Teoria a molti-corpi della materia nucleare

Transcription

1 Teoria a molti-corpi della materia nucleare

2 Lezione IV 1. 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 Before explosion

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 A section (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 The baryonic Equations of State HHJ : Astrophys. J. 525, L45 (1999 BBG : PRC 69, (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 Composition of of asymmetric asymmetric and and beta beta-stable stable matter matter Parabolic approximation ) 0,, ( ) 1,, ( ), ( ), ( ) 0,, ( ),, ( 2x 1- parameter Asymmetry 2 p Y Y Y sym Y sym Y Y p n x A B x A B x E x E x A B x A B = = = + = = = β β β β β β Composition of stellar matter i) Chemical equilibrium among the different baryonic species ii) Charge neutrality iii) Baryon number conservation n p e p e e p n µ µ µ µ µ µ µ + = + = = + =

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

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16 Hyperon influence on hadronic EOS

17 Composition Composition of of asymmetric asymmetric and and beta beta-stable stable matter matter including including hyperons hyperons Parabolic approximation ) 0,, ( ) 1,, ( ), ( ), ( ) 0,, ( ),, ( 2x 1- parameter Asymmetry 2 p Y Y Y sym Y sym Y Y p n x A B x A B x E x E x A B x A B = = = + = = = β β β β β β Composition of stellar matter i) Chemical equilibrium among the different baryonic species ii) Charge neutrality iii) Baryon number conservation Λ Σ Σ Λ Σ = + + = = + = = + = µ µ µ µ µ µ µ µ µ µ µ µ n p e p n p n e e p n 2 extended to hyperons

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, (2006)

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23 Including Quark matter 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. a) Baryon EOS. BBG AP HHJ b) 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, (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 εq =1.1 GeV 3 fm

29 Density profiles of different phases MIT bag model

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

31 Alford et al., ApJ 629 (2005) 969 a4 = 3 3 Ω µ 4π 4π a a QM = a 2 4 µ + a Non-perturbative corrections ; Strange quark mass corresponds to the usual MIT bag model B eff 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 NJL Model The model is questionable at high density where the cutoff can be comparable with the Fermi momentum

36 Including Color Superconductivity in NJL Steiner,Reddy and Prakash 2002 Buballa & Oertel Application to NS CT + GSI, PLB 562,,153 (2003)

37 Mass radius relationship 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, (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 1. The transition to quark matter in NS looks likely, but the amount of quark matter depends on the quak matter model. 2. 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.Baldo et al.. 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 31.3 ( / ) 0.6 0

47 Trying connection with phenomenology : the case. Density functional from microscopic calculations 208 Pb rel. mean field Skyrme and Gogny microscopic functional The value of r_n - r_p from mic. fun. is consistent with data

48 A section (schematic) of a neutron star

49 The structure of nuclei and Z/N ratio are dictated by beta equilibrium µ = µ + n p µ e 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

51 Looking for the energy minimum at a fixed baryon density Density = 1/30 saturation density Wigner-Seitz approximation

52 The neutron matter EOS Solid line : Fayans functional ; Dashes : SLy4 Dotted line : microscopic (Av-18)

53 Including pairing in crust structure calculations M.B., E. Saperstein et al., Nucl. Phys. A750, 409 (2005)

54 Dependence on the functionals

55 In search of the energy minimum as a function of the Z value inside the WS cell

56 Neutron density profile at different Fermi momenta

57 Proton density profile at different Fermi momenta

58 Negele & Vautherin 2 Uniform nuclear matter (M.B.,Maieron,Schuck,Vinas NPA 736, 241 (2004))

59 Comparing different Equations of State for low density Despite the quite different lattice structure, the EoS appears stable.