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Strangeness in Neutron Stars

Achievements and Perspectives in Low-Energy QCD with strangeness ECT*, Trento (Italy), 27 – 31 October 2014. Strangeness in Neutron Stars.

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Strangeness in Neutron Stars

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  1. Achievements and Perspectives in Low-Energy QCD with strangeness ECT*, Trento (Italy), 27 – 31 October 2014 Strangeness in Neutron Stars Ignazio BombaciDipartimento di Fisica “E. Fermi”, Università di Pisa INFN Sezione di Pisa

  2. Role of strangeness for the physics of Neutron Stars Strangeness in Neutron Stars Confined within hadrons (hyperons, strange mesons) Deconfined (Strange Quark Matter)

  3. “Neutron Stars” Nucleon Stars Hyperon Stars Hybrid Stars Strange Stars I. Bombaci, A. Drago, INFN Notizie, n. 13, 15 (2003)

  4. Relativistic equations for stellar structure Static and sphericaly symmetric self-gravitating mass distribution  = ( r), = ( r) metric functions for the present case the Einstein’sfield equations take the form called the Tolman – Oppenheimer – Volkov equations (TOV) One needs the equation of state (EOS) of dense matter, P = P(ρ), up tovery high densities

  5. The Oppenheimer-Volkoff maximum mass There is a maximum value for the gravitational mass of a Neutron Star that a given EOS can support. This mass is called the Oppenheimer-Volkoff mass Mmax = (1.4 – 2.5) M M “stiff” EOS “stiff” EOS Pressure “soft” “soft” R density The OV maximum mass represent the key physical quantity to separate (and distinguish) Neutrons Stars from Black Holes. Mmax(EOS)  all measured neutron star masses

  6. Measured Neutron Star masses in Relativistic binary systems Measuring post-Keplerian parameters: * very accurate NS mass measurements * model independent measuremets within GR PSR B1913+16 NS (radio PSR) + NS (“silent”)(Hulse and Taylor 1974) PPSR = 59 ms, Pb= 7 h 45 min (Mercury: ) Mp= 1.4408 ±0.0003 M Mc= 1.3873 ±0.0003 M Orbital period decay in agreement with GR predictions over about 40 yr → indirect evidence for gravitational waves emission PSR J0737-3039 NS(PSR) + NS(PSR) (Burgay, et al 2003) P1 = 22.7 ms, P2 = 2.77 s Pb= 2 h 24 min M1 = 1.34 M M2 = 1.25 M

  7. Two “heavy” Neutron Stars PSR J1614–2230MNS = 1.97 ± 0.04 MNS – WD binary system (He WD) MWD = 0.5 M (companion mass) Pb = 8.69 hr (orbital period) P = 3.15 ms (PSR spin period) i = 89.17  0.02 (inclination angle) P. Demorest et al., Nature 467 (2010) 1081 PSR J0348+0432 MNS = 2.01 ± 0.04 M NS – WD binary system MWD = 0.172 0.003 M (companion mass) Pb = 2.46 hr (orbital period) P = 39.12 ms (PSR spin period) i = 40.2  0.6 (inclination angle) Antoniadis et al., Science 340 (2013) 448

  8. Measured Neutron Star Masses Mmax Mmeasured Mmax 2 M Very stringent constraint on the EOS PSR J0737-3039 PSR J0737-3039 comp PSR J1614-2230 PSR J0348+0432

  9. Neutron star physics in a nutshell 1) Gravity compresses matter at very high density 2) Pauli priciple Stellar constituents are different species of identical fermions (n, p,….,e-, μ-) antisymmetric wave function for particle exchange Pauli principle Chemical potentialsrapidly increasing functions of density 3) Weak interactionschange the isospin and strangeness content of dense matter to minimize energy Cold catalyzed matter(Harrison, Wakano, Wheeler, 1958) The ground state (minimum energy per baryon) of a system of hadrons and leptons with respect to their mutual strong and weak interactions at a given total baryon density n and temperature T = 0.

  10. swiss cheeselasagne spaghetti meet-balls The internal structure of Neutron Stars

  11. Nucleon Stars -stable nuclear matter • Equilibrium with respect to the weak interaction processes neutrino-free matter • Charge neutrality To be solved for any given value of the total baryon number density nB

  12. Proton fraction in -stable nuclear matter and role of the nuclear symmetry energy  = (nn – np )/n = 1 – 2x n = nn + np x = np /nproton fraction Energy per nucleon for asymmetric nuclear matter Symmetry energy The “parabolic approximation” (*) β2 (*) Bombaci, Lombardo, Phys. Rev: C44 (1991)

  13. Proton fraction in -stable nuclear matter and role of the nuclear symmetry energy In the “parabolic approximation”:  = 0 symm nucl matter  = 1 pure neutron matter Chemical equil.+charge neutrality (no muons) if x<<1/2 Symmetry en. proton fraction The composition of -stable nuclear matter is strongly dependent on the nuclear symmetry energy. M. Baldo, I. Bombaci, G. Burgio, Astr. & Astrophys. 328 (1997)

  14. Microscopic approach to nuclear matter EOS input Two-body nuclear interactions:VNN“realistic” interactions: e.g. Argonne, Bonn, Nijmegen interactions. Parameters fitted to NN scatering data with χ2/datum ~1 • Three-body nuclear interactions: VNNNsemi-phenomenological. Parameters fitted to • binding energy of A = 3, 4 nuclei or • empirical saturation point of symmetric nuclear matter: n0= 0.16 fm-3 , E/A = -16 MeV AV18 AV18/UIXExp. B(3H)7.624 8.479 8.482 B(3He)6.925 7.750 7.718 B(4He) 24.21 28.46 28.30 Nuclear Matter at n = 0.16 fm-3 Epot(2BF)/A ~ -40 MeV Epot(3BF)/A ~ - 1 MeV Values in MeV A. Kievsky, S. Rosati, M.Viviani, L.E. Marcucci, L. Girlanda, Jour. Phys.G 35 (2008) 063101 A. Kievsky, M.Viviani, L. Girlanda, L.E. Marcucci, Phys. Rev. C 81 (2010) 044003 Z.H. Li, U. Lombardo, H.-J. Schulze, W. Zuo, Phys. Rev. C 77 (2008) 034316

  15. VNN + VNNN e.g. Brueckner-Hartree-Fock VNN GNN Quantum Many-Body Theory EOS β-stable matter TOV Neutron Star properties observational data (measured NS properties)

  16. Microscopic EOS for nuclear matter:Brueckner-Bethe-Goldstone theory

  17. Energy per baryon in the Brueckner-Hartree-Fock (BHF) approximation

  18. Mass-Radius relation for Nucleon Stars Maximum mass configuration for Nucleon Stars PSR J1614-2230 WFF: Wiringa-Ficks-Fabrocini, 1988. BPAL: Bombaci, 1995. BBB: Baldo-Bombaci-Burgio, 1997. APR: Akmal-Pandharipande-Ravenhall, 1988. KS: Krastev-Sammarruca, 2006 Mmax = (1.8  2.3) M

  19. Z.H. Li, H.-J. Schulze, NNN interction PSR J0348+0432 V18: Argonne V18 + mTBF BOB: Bonn B + mTBF N93: Nijmegen 93 + mTBF UIX: Argonne V18 + Urbana IX

  20. Message taken fromNucleon Stars(i.e. Neutron Stars with a pure nuclear matter core) NN interactions essential to have “large” stellar mass For a free neutron gas Mmax = 0.71 M (Oppenheimer and Volkoff, 1939) NNN interactions essential (i) to reproduce the correct empirical saturation point of nuclear matter (ii) to reproduce measured neutron star masses, i.e. to have Mmax > 2 M

  21. models ofNucleon Stars(i.e. Neutron Stars with a pure nuclear matter core) are able to explain measured Neutron Star masses as those of PSR J1614-2230 and PSR J0348+0432 MNS≈ 2 M Happy? Not the end of the story!

  22. Hyperon Stars Why is it very likely to have hyperons in the core of a Neutron Star? Pauli principle. Neutrons (protons) are identical Fermions, thus their chemical potentials (Fermi energies) increase very rapidly as a function of density. The central density of a Neutron Star is “high”:nc  (6 – 9) n0(n0 = 0.16 fm-3) above a threshold density,ncr  (2 – 3) n0 , weak interactions in dense matter can produce strange baryons (hyperons) n + e- -+ e p + e- + e etc. In Greek mythology Hyperion (Ὑπερίων) was one of the twelve Titan son of Gaia and Uranus A.V. Ambarsumyan, G.S. Saakyan, (1960) G.S. Saakyan, Y.L. Vartanian (1963) V.R. Pandharipande (1971)

  23. n + e-  -+ e p + e-  + e etc. Hyperons appear in the stellar core above a threshold density cr  (2 – 3) 0 I. Vidaña, Ph.D. Thesis (2001) Av18+TNF+NSC97e UΣ-(k=0, n0) = – 25 MeV

  24. Av18+TNF+ESC08b D. Logoteta, I. Bombaci (2014) TNF: Z H.. Li, U. Lombardo, H.-J. Schulze. W. Zuo, Phys. Rev. C 77 (2008)

  25. Microscopic approach to hyperonic matter EOS input 2BF:nucleon-nucleon (NN), nucleon-hyperon (NY), hyperon-hyperon (YY)e.g. Nijmegen, Julich models 3BF:NNN, NNY, NYY, YYY • Hyperonic sector: experimental data • YN scattering (very few data) • Hypernuclei Hypernuclear experiments FINUDA (LNF-INFN), PANDA and HypHI (FAIR/GSI), Jeff. Lab, J-PARC

  26. C. Curceanu, talk at INFN 2014, Padova 2014

  27. Microscopic EOS for hyperonic matter:extended Brueckner theory Vis the baryon -baryon interaction for the baryon octet ( n, p, , -, 0, +,  -,  0) Energy per baryon in the BHF approximation Baldo, Burgio, Schulze, Phys.Rev. C61 (2000) 055801; Vidaña, Polls, Ramos, Engvik, Hjorth-Jensen, Phys.Rev. C62 (2000) 035801; Vidaña, Bombaci, Polls, Ramos, Astron. Astrophys. 399, (2003) 687.

  28. The Equation of State of Hyperonic Matter Av18+TNF+ESC08b Av18+TNF+ESC08b Av18+TNF D. Logoteta, I. Bombaci (2014)

  29. Composition of hyperonic beta-stable matter Baryon number density b [fm-3] Particle fractions Av18+TNF+NSC97e Hyperonic Star MB = 1.34 M I. Vidaña, I. Bombaci, A. Polls, A. Ramos, Astron. and Astrophys. 399 (2003) 687 Radial coordinate [km ]

  30. Composition of hyperonic beta-stable matter Baryon number density b [fm-3] Particle fractions Av18+TNF+NSC97e Hyperonic Star MB = 1.34 M Hyperonic core NM shell crust I. Vidaña, I. Bombaci, A. Polls, A. Ramos, Astron. and Astrophys. 399 (2003) 687 Radial coordinate [km ]

  31. Composition of hyperonic beta-stable matter Av18+TNF+ESC08b D. Logoteta, I. Bombaci (2014)

  32. The stellar mass-radius relation Z.H. Li, H.-J. Schulze, interaction: NN + NY + YY + NNN PSR J0348+0432 PSR B1913+16 NY,YY: Nijmegen NSC89 potential (Maessen et al, Phys. Rev. C 40 (1989)

  33. The stellar mass-radius relation Av18+TNF+ESC08b D. Logoteta, I. Bombaci (2014) see also: H.-J. Schulze, T. Rijken, Phys. Rev. C 84 (2011) 035801

  34. Hyperons in Neutron Stars: implications for the stellar structure The presence of hyperons reduces the maximum mass of neutron stars:Mmax  (0.5 – 1.2) M Therefore, to neglect hyperons always leads to an overstimate of the maximum mass of neutron stars Improved NY, YY two-body interaction Three-body forces*: NNY, NYY, YYY Microscopic EOS for hyperonic matter: ”very soft” non compatible with measured NS masses Need for extra pressure at high density (*) A preliminary study: I. Vidana, D. Logoteta, C. Providencia, A. Polls, I. Bombaci, EPL 94 (2011) 11002

  35. Hyperons in Neutron Stars: implications for the stellar structure The presence of hyperons reduces the maximum mass of neutron stars:Mmax  (0.5 – 1.2) M Therefore, to neglect hyperons always leads to an overstimate of the maximum mass of neutron stars Improved NY, YY two-body interaction Three-body forces*: NNY, NYY, YYY Microscopic EOS for hyperonic matter: ”very soft” non compatible with measured NS masses Need for extra pressure at high density More experimental data from hypernuclear physics (*) A preliminary study: I. Vidana, D. Logoteta, C. Providencia, A. Polls, I. Bombaci, EPL 94 (2011) 11002

  36. Hyperons in Neutron Stars: implications for the stellar structure The presence of hyperons reduces the maximum mass of neutron stars:Mmax  (0.5 – 1.2) M Therefore, to neglect hyperons always leads to an overstimate of the maximum mass of neutron stars Improved NY, YY two-body interaction Three-body forces*: NNY, NYY, YYY Microscopic EOS for hyperonic matter: ”very soft” non compatible with measured NS masses Need for extra pressure at high density More experimental data from hypernuclear physics Theory: baryonic forces from SU(3) chiral effective theory (Petschauer’s talk, yesterday) (*) A preliminary study: I. Vidana, D. Logoteta, C. Providencia, A. Polls, I. Bombaci, EPL 94 (2011) 11002

  37. Estimation of the effect of hyperonic TBF on the maximum mass of neutron stars BHF calculations: NN (Av18) + NY (NSC89) TBF: phenomenological density dependent contact terms Energy density form inspired by S. Balberg, A. Gal, Nucl Phys. A 625, (1977) 435 I.Vidaña, D. Logoteta, C. Providencia, A. Polls, I. Bombaci, EPL 94 (2011) 11002

  38. we assume: empirical saturation point of symmetric NM Binding energy of Λ in NM

  39. effect of hyperonic TBF on the maximum mass of neutron stars I.Vidaña, D. Logoteta, C. Providencia, A. Polls, I. Bombaci, EPL 94 (2011) 11002

  40. Neutron Stars in the QCD phase diagram Lattice QCD at μb=0 and finite T ► The transition to Quark Gluon Plasma is a crossover Aoki et ,al., Nature, 443 (2006) 675 ► Deconfinement transition . temperature Tc HotQCD Collaboration Tc= 154 ± 9 MeVBazarov et al., Phys.Rev. D85 (2012) 054503 Wuppertal-Budapest Collab. Tc= 147 ± 5 MeVBorsanyi et al., J.H.E.P. 09 (2010) 073 Cristalline Color superconductor Neutron Stars: high μb and low T Quark deconfinement transition expected of the first orderZ. Fodor, S.D. Katz, Prog. Theor Suppl. 153 (2004) 86 Lattice QCD calculations are presently not possible

  41. 1st order phase transitions are triggered by thenucleationof acritical size dropof thenew (stable) phasein ametastablemother phase H  Q Virtual drops of the stable phase are created by small localized fluctuations in the state variables of the metastable phase P0 pressure H = Q  0 TH = TQ  T P(H) = P(Q)  P(0)  P0

  42. 1st order phase transitions are triggered by thenucleationof acritical size dropof thenew (stable) phasein ametastablemother phase H  Q Virtual drops of the stable phase are created by small localized fluctuations in the state variables of the metastable phase P0 pressure Astrophysical consequencesof thenucleation process of quark matter (QM)in the core of massive pure hadronic compact stars (“Hadronic Stars”, HS). Berezhiani, Bombaci, Drago, Frontera, Lavagno, Astrophys. Jour. 586 (2003) 1250 I. Bombaci, I. Parenti, I. Vidaña, Astrophys. Jour. 614 (2004) 314 I. Bombaci, G. Lugones, I. Vidaña, Astron. &Astrophys. 462 (2007) 1017

  43. Metastability of Hadronic Stars Hadronic Stars above a threshold value of their gravitational mass are metastable to the conversion to Quark Stars (QS) (hybrid stars or strange stars) M Hadronic Stars (no quark matter) Mmax(HS) (Oppenheimer-Volkoff mass) Quark Stars Mcr critical mass Metastable hadronic stars Mthr( = ) stable HSs R Berezhiani, Bombaci, Drago, Frontera, Lavagno, Astrophys. Jour. 586 (2003) 1250 I. Bombaci, I. Parenti, I. Vidaña, Astrophys. Jour. 614 (2004) 314 I. Bombaci, G. Lugones, I. Vidaña, Astron. &Astrophys. 462 (2007) 1017

  44. Metastability of Hadronic Stars M Hadronic Stars (no quark matter) Mcr , critical mass of hadronic stars. ..Two branches of compact stars . stellar conversion HSQS Econv  1053 erg (possible energy source for some GRBs) Mmax(HS) (Oppenheimer-Volkoff mass) Quark Stars Mcr critical mass Metastable hadronic stars Mthr( = ) stable HSs extension of the concept of limiting mass of compact stars with respect to the classical one given by Oppenheimer and Volkoff R Berezhiani, Bombaci, Drago, Frontera, Lavagno, Astrophys. Jour. 586 (2003) 1250 I. Bombaci, I. Parenti, I. Vidaña, Astrophys. Jour. 614 (2004) 314 I. Bombaci, G. Lugones, I. Vidaña, Astron. &Astrophys. 462 (2007) 1017

  45. Quantum nucleation theory I.M. Lifshitz and Y. Kagan, 1972; K. Iida and K. Sato, 1998 Quantum fluctuation of a virtual drop of QM in HM U(R) = (4/3) R3 nQ* (Q* - H ) + 4 R2  av R3 + as R2 QM drop R Hadronic Matter I. Bombaci, I. Parenti, I. Vidaña, Astrophys. Jour. 614 (2004) 314

  46. Hadronic Stars:nucleons + hyperons Bombaci, Parenti, Vidaña, Astrophys. Jour. 614 (2004) 314

  47. D. Logoteta, I. B. (2014) SQM EOS: Alford et al. Astrophys. J. 629 (2005); Fraga et al., Phys. Rev. D 63 (2001)

  48. Conclusions The presence of hyperons reduces the maximum mass of neutron stars, thus, to neglect hyperons always leads to an overstimate of the maximum mass of neutron stars. “Hyperon puzzle” in Neutron star physics Mmax < 2 M quest for extra pressure at high densities (i) ► strong short-range repulsion in NY, YY interactions ► repulsive NNY, NYY, YYY 3-baryon interactions (ii) or, the transition to Strange Quark Matter produce a stiffening of the EOS due to e.g. non-perturbative quark interactions NS → Quark Stars (hybrid or strange stars)

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