Int. Workshop on Nuclear Dynamics in HIR and Neutron Stars Beijing Normal University, 9-14 July 2007 outline: observational data of neutron stars microscopic hadron EoS from pure baryon to composite matter (leptons,Y,K ¯) onset of transition to quark phase confinement models of quarks M-R diagram of NS from general relativity (TOV) EoS of Nuclear Matter and Structure of Neutron Stars

preliminary remarks: nuclear matter is an homogeneous system made of rigid nucleons interacting via the nuclear force (surface and coulomb effects are neglected). neutron stars are compact astrophysical objects, mostly born after the explosion of supernovae. They are supposed to be made of nuclear matter in their interior. But, the way they were born, the neutron stars in the inner core are not simply made of nucleons, but of neutrons and protons in equilibrium with leptons (electrons and muons), and we should assume that, at increasing density, the threshold for the production of new particles is reached hyperons, kaons, and quarks. Therefore we will deal with asymmetric nuclear matter  beta-equilibrium with electrons and muons : p + e¯  n +  hyperonized matter: n + n  n +  ( p +  ¯) at  > 2  o  kaon condensation n  p + K¯ at  > 2-3  o  transition to quark matter HP  QP (u,d,s) at  ~ 6  o

view of a neutron star Crust : pinning,thermal emission,… ( Cao talk) Interior

N.K. Glendenning, Compact Stars, Nuclear Physics, Particle Physics, Springer, 2000 Facts about Neutron Stars : M ~ 1 to 2M 0 ( M 0 =1.998·10 33 g) R ~ 10 Km N obs. Pulsars P > 1.58 ms (630 Hz) B = 10 8 ÷ Gauss

Observed Masses: three main families PSR J M > 2.1±0.3 M © PSR M = 1.44 M © J. Lattimer

Yakovlev et al Non superfluid Superfluid Thermal evolution (n,p) + p + e -  (n,p) + n + e (n,p) + n  (n,p) + p + e - + e direct URCA : Y p > modified URCA p + e -  n + e n  p + e - + e

due to the poor information from NS we need to make theoretical predictions as much accurate as possible. for the EoS of nuclear matter the state of art is quite reasonable since the theory of nuclear matter has undergone a long term development reaching a high Degree of sophistication. The description yperon matter is also satisfactory since we know the N-Y force, even we still don’t know the Y-Y force. ( see Dang and Takatsuka talks ) the interaction N-K is less known, and all predictions for the k condensation are still model-dependent. ( see Sun talk ) for the quark phase we have many theories still waiting constraints ( Gao, Liu,Maruyama, Huang, Di Toro,...talks)

Hadron EoS from the NN experimental phase shifts  two-body realistic interactions from B-W nuclear mass formula  saturation properties EA = -16 MeV  =.17 fm -3 K A = 220 MeV (monopole) E sym =30 MeV --empirical constrains --

SP Coester et al., Phys. Rev. C1, 769 (1970) Saturation curve within the BBG “gap choice” (U(k)=0 if k≥k F ), and Av14 BBG “continuous choice”  Similar results within the Variational Method  Possible corrections : many-body forces and/or relativistic effects

Nucleon-Nucleon Interaction: Argonne v18 (Wiringa, Stoks & Schiavilla, Phys. Rev. C51, 38 (1995)) Neutron Matter Symmetric Matter ? Dependence on the many-body scheme APR : Variational (Akmal, Pandharipande & Ravenhall, PRC 58, 1804 (1998)) Catania group : BHF (Akmal, Pandharipande & Ravenhall, PRC 58, 1804 (1998))

Three Body Force TBF provides the repulsion necessary for 1) saturation properties 2) stiff EoS  massive NS

3bf is poorly known :  A phenomenological model is built up from the saturation energy of nuclear matter (or density) and the binding energy of the triton  A microscopic model is based on a meson exchange model coupled with nucleonic excitations: (  (1232),N*(1440),…) consistent with two body interaction  Chiral perturbation theory

Carlson et al., NP A401,(1983) 59 P. Grange’ et al, PR C40, (1989) 1040 Microscopic model : (a) : excitation of a Δ resonance (attractive) (b) : Roper R resonance (repulsive) (a) : excitation of (Δ,R) resonances (b) : excitation of a nucleon-antinucleon pair (relativistic effect on the EOS, repulsive) Zuo, Lombardo,Lejeune,Mathiot, N P A706, 418 (2002) Effects of TBF

   + + N    + + N     ,N* + (  -  ) Meson-exchange Model of the two and three body Interaction baryon exc ph exc from Dirac sea

  + +  +  N*   N +     N     N +   + (-)(-)

BHF vs Dirac-BHF relativistic effects but DB misses other TBF effects impressive overlap!   N BHF + ( ) = DBHF

EoS Symmetry energy  Improved saturation point  ≈ 0.18 fm-3  Symmetry energy at saturation S v ≈ 32 MeV  Incompressibility at saturation K ≈ 210 MeV

Science 298, 1592 (2002) Transverse Flow Measurements in Au + Au collisions at E/A=0.5 to 10 GeV Pressure determined from simulations based on the Boltzmann-Uehling-Uhlenbeck transport theory EoS of dense matter from HIC

from pure baryon to composite matter

Composition of Neutron Stars  -equilibrium neutral matter

Neutron Stars : Asymmetric and charge neutral beta-stable matter Zhou, Burgio,Lombardo,Zuo. PR. C69, (2004) Compact Stars in GTR : Tolman-Oppenheimer-Volkoff Equations M theor  M obs Only stiff EoS is compatible with massive NS (2.1 M © )

Yperons

INCLUDING HYPERONS  Possible extension of the BBG theory.  Few experimental data on NH interaction. Nijmegen interaction (NSC89) (Maessen et al., Phys. Rev. C40, 2226 (1989))  Unknown HH interaction.  Strong consequences for NS structure. See F. Burgio et al., Phys. Rev. C58,3688 (1998), ibid. 61, (2000)

Hyperon onset at density close to 2-3 times the saturation value. Weak dependence on the adopted 3BF. Strong softening of the EoS, no matter the nucleonic TBF’s. Hyperon-hyperon interaction ?

Same results by the Barcelona group: I. Vidana et al., Phys. Rev. C73, (2006) with NSC97 Nijmegen potential (NH + HH inter. (Stoks & Riken,1999) ) Appearance of baryonic strange matter not compatible with any NS mass data It demands for a stiffening of the Equation of State!!

K condensation Bethe-Brown, ApJ 1995

K¯ - condensation Proton strangeness content: a 3 m s [MeV] (a)=-310 (b)=-230 (c)=-134 Chemical equilibrium: n ↔ p + l + l n ↔ p + K¯ l ↔ l + K¯ nuclear matter: n.p,e, ,K,… K= eK= e TBF Zuo,A.Li,ZH Li, Lombardo, PRC 2004 Thorsson,Lattimer, Prakash NPA 1994

Chemical composition of NS with K-condensation p p K-K- K-K- e-e- e-e- Av 18 ( thin ) Av 18 +TBF ( thick ) Zuo,A.Li,ZH Li, Lombardo, PRC 2004 ‘nuclear matter’ star Bethe & Brown,ApJ 1995

Critical density  c /  0 2bf 2bf+3bf a 3 m s = in competitiowith Yperons = = model parameter dependence

Critical density (u=  /  0 ): 2bf 2bf+3bf a 3 m s =-310 u c = =-222 = =-134 = K-condensation vs hyperonization V 18 (or Paris)+ TBF the two critical density could be comparable!

Kaon condensantion - neutrino trapping - -trapping free K threshold model dependent no kaons with kaons

EoS with phase transition to K-condensation Thorsson,Lattimer, Prakash NPA 1994 Zuo,A.Li,ZH Li, F. Burgio, Lombardo, PRC 2006

K-condensation in NS: Mass-Radius plot neutrino trapping

Quark phase

Structure of Hybrid Stars  at large  (  1 fm -3 ) hadron phase can coexist with deconfined quark phase, and, eventually, completely dissolve into a pure quark core ( hybrid star ).  after the recent discovery of massive stars, with M>2M © (2005) study of hybrid stars it has been addreesed to the evolutionary scenarios of NS birth  the low mass and high mass NS could belong to two different evolutionary scenarios outlook: :

transition from Hadron to Quark Phase  ~1/fm 3  d NN ~ 1 fm Since we have no unified theory which describes both confined and deconfined phases, we use two separate EOS: one with hadronic degrees of freedom (HP) one with quark degrees of freedom (QP)

Which model for Quark Matter ? Constraints from phenomenology on the general quark EOS : i) In symmetric nuclear matter one can expect a transition to quark matter at some density, but it must be larger than at least 2-3 times normal nuclear matter density (no evidence from heavy ion reactions at intermediate energy) ii) Strongly asymmetric nuclear matter would favour the appearance of quark phase at lower density (no experiments so far at (N-Z)/A >> 0.3) iii) Strange matter stable against two-flavor matter iv) The maximum mass of neutron stars must be larger than 1.44 solar mass (not true after 2005 new data with M/M © > 2: PSR J !) Baym & Chin, PLB62 (1976)241 Chapline and Nauenberg, Nature 264 (1976) Keister & Kisslinger, PLB64(1976)117 c60c60

Quark matter models : MIT Bag Model, Quark matter models : MIT Bag Model, Nambu-Jona—Lasinio (NJL) Nambu-Jona—Lasinio (NJL) Color Dielectric (CDM) Color Dielectric (CDM) DDM Model DDM Model

DDM: model from deconfined phase to asymptotic freedom

QM vs HM EoS in  -equilibrium - crosspoints - quark matter n b =(N u +N d +N s )/3V nuclear matter  = (N+Z)/ V Maieron,Baldo,Burgio,Schulze,Phys.Rev. D70 (2004) Yperonized NM Peng and Lombardo, PP 2007 ● d → u + e + s → u + e + u + s ↔ d + u Baryonic NM Three flavor QM p + e → n + n + n → n +  n + n ↔ p +  ¯

hadron-to-quark phase transition Gibbs equilibrium condition p HP (  n,  e ) = p QP (  n,  e )  HP =  QP T HP = T QP under the total charge neutrality condition  line p HP under H-charge neutrality is the EoS of pure hadron phase  line p QP under Q-charge neutrality is the EoS of pure quark phase  line intersecting the two pressure surfaces is the EoS of Hadron-Quark mixed phase  n =  u + 2  d in he quark phase hadron-to-quark phase transition

NP and QP charge neutrality gives a curve Peng and Lombardo, 2007

 The value of the maximum mass lies in the range between 1.5 and 1.9 solar masses (>1.44 M 0 ).  The value of the maximum mass is mainly determined by the quark component of the neutron star and by the corresponding EOS. MIT, DDM : stable stars are in a quark + mixed + hadronic phase. CDM : stable stars are only in pure quark phase. NJL : instability at the quark onset (hadron + mixed phase) “Hybrid” stars C. Maieron et al., Phys. Rev. D70, (2004) F. Burgio et al., Phys. Rev. C66, (2002) M. Buballa et al., PLB 562, 153 (2003) GX Peng and U. Lombardo PP 2007 Quark Phase Hadronic Phase The structure of neutron star is strongly dependent on the EoS used for describing the quark phase. MDD

Two evolutionary scenarios for NS Haensel, exoct 2007 (Catania, June 11-15)  NS born in core-collapse of massive stars (20-30 M © ) are sufficiently dense and hot to produce eos-softening quark core resulting in M max = 1.5 M ©  NS coupled to a white dwarf companion could increase their mass by accretion in a long-lived binary sistem up to M max  2. M © (no quark core)

PSR J M  2.1  0.2 M  Two evolutionary branches of NS pure hadron matter hybrid neutron star PSR M  144  0.2 M 

Final comments NS mass is a robust constraint of the nuclear matter EoS: the range solar masses predicted by solving theTOV eqs is not trivial.  But there are other constraints of the EoS to be investigated:  Superfluidity of the crust (pinning) and of the interior (cooling)  Cooling mechanisms: URCA, opacity, pairing  Magnetic field

Conclusions:  The EoS of nuclear matter is stiff according to a microscopic theory constrained by the experimental NN cross section.  A stiff EoS is also supported by the NS observed masses (and other observables not discussed here).  EoS of hadron phase, including yperons, is reasonably described  EoS of quark phase requires additional study (improving NJL model)  the low mass (M<1.5M © ) stars can be interpreted as hybrid stars if the critical density of deconfined phase is so low to hinder both yperons and kaons  the high mass (M>2.0M © ) is interpreted as pure hadron phase  anyhow the existence of two classes of neutron stars demands for the study of the evolution of neutron stars

Thank you!

under charge neutrality condition for the two phases - Maxwell construction - hadron-to-quark phase transition no Coulomb, no surface Gibbs equilibrium condition p HP (  n,  e ) = p QP (  n,  e )  HP =  QP T HP = T QP

hadron phase p + e → n + n → p + e + n ↔ p + K  P +  e =  n  N +  P =  K no trapping quark phase  u +  e =  d  d =  s d → u + e + s → u + e + u + s ↔ d + u one (two) independent variables in each phase, if charge neutrality is (not) required. d → u + e + s → u + e + u + s ↔ d + u

Isospin dependence of critical density no charge neutrality Skyrme-like EoS

Kaon condensation in pure hadron phase with Skirme-like EoS ( the scenario will not significantly change with the BHF+TBF EoS)

supernovae explosions (high temperature and isospin and density)

205 MeV is the threshold for hadron stability against two flavor quark matter

M-R plot for Hybrid Stars

Sensitivity of M/M Θ to constant B M/M   Alford & Reddy,2003

quark phase in beta-equilibrium u,d,s,e -  u +  e =  d  d =  s

DDM vs MIT-B models

conservation charge conservation  hadron phase  mixed phase  quark phase

Phase transition from nuclear matter to SQM (skyrme-like EoS)

DDM vs MIT: P minimum in DDM E=0 in the vacumm Q matter in beta-equilibrium (charge neutrality) Quark matter hadronization(no quarks) If D1/2 decreases the crosspoint Moves to lower density.

Baldo,Burgio,Schulze, PRC 61 (2000) Yperon-rich NS

MIT bag vs Color Dielectric Model Yperonized Nuclear Matter Maieron,Baldo,Burgio,Schulze, Phys.Rev. D70 (2004)

Neutron Star Structure Clusters and light particle condensates Superfluid states Coexisting liquid-gas phase Nuclei far from stability line Hypernuclear matter K condensation Quark matter Hadron-to quark mixed phase Color superconductivity Collective excitations ……… extraordinary laboratory for studying states of nuclear matter

Table of Isotopes Neutron skin GR in neutron-rich nuclei Spin-isospin modes (GT) Super-heavy elements nuclear compressibility, symmetry energy, spin-isospin from exotic nuclei Di Toro et al. Exotic HIC at intermediate energy Light fragment production at Fermi energy Unstable nucleus-nucleus systems Isospin distillation

Mass-Radius Plot for a NS from Tolman-Oppenheimer-Volkov Eq. + EoS: =P(  ) mass-radius plot all EoS are consistent with the observed max mass of NS and the central densities are also quite large,but we need a very large max mass, when including hyperons

NS cooling via neutrino emission p + e -  n + e n  p + e - + e (n,p) + p + e -  (n,p) + n + e (n,p) + n  (n,p) + p + e - + e direct URCA : Y p > modified URCA The EoS predicts: Yp>Yp>  > 0.28 fm -3  central = 6.24 fm -3 Direct URCA processes are allowed to occur!