Isovector Equation-of-State in Heavy Ion Collisions (and Neutron Stars)Collaborators:Theo Gaitanos, LMU Munich -> U. GiessenM. Di Toro, et al., LNS, CataniaC. Fuchs, U. TbingenS. Typel, GSID. Blaschke, et al., Univ. BreslauOutline:- Motivation: phase diagram of hadronic matter- the isovector EoS und its uncertainity, Lorentz structure- transport calculations of heavy ion collisions- low vs. high densities: fragmentation vs. flow, particle production- constraints from neutron star observables- deconfinement at large assymmetry?Virtual Institute Dense Hadronic Matter and QCD Phase Transitions, Workshop III, Rathen, Oct.15-17, 2006.Hermann WolterExzellenz(!) Universitt Mnchen

Schematic Phase Diagram of Strongly Interacting MatterLiquid-gas coexistenceSIS

Schematic Phase Diagram of Strongly Interacting MatterLiquid-gas coexistenceZ/N10SISneutron starsExotic nuclei

The nuclear EoS-UncertaintiesC. Fuchs, H.H. Wolter, WCI white book, EPJA in press, nucl-th/0511070the nuclear EoSEsymm [MeV]

Esym (r) (MeV) r/r0123The Elusive Symmetry EnergyNeutron Stars-formation-mass/radius-cooling-hybrid structure? ??Nuclear structureGiant Dipole Neutron skinLiquid-Gas P.T.Neutron star crust, mergingAsystiffAsysoft

RMF theory with scalar-isovector (d) field

Transport Description of Heavy Ion Collisions: BUU

HIC probing: - wide range of densities - high momenta - covariant structureAround normal density: I - Low to Fermi energies- Deep Inelastic dissipation, charge equilibration, neck dynamics Mass/Isospin vs Velocity correlations in fragment production Fast nucleon emission and Lane Potentials Isospin TransportHigh baryon density: II - Relativistic energies- n,p flows light ion flows Kaon/Pion production- Deconfinement Precursors?

Isospin Transport through Neck: Rami imbalance ratio:

Effect of momentum dependence on Isospin transportChen, Ko, B.A.Li, PRL94 (2005)

Some results of Transport Calc.Symmetric Nuclear MatterAsymmetric NMV2: Elliptic flowV1: Sideward flowT.Gaitanos, Chr. Fuchs, Nucl. Phys. 744 (2004)

Results from Flow Analysis(P. Danielewicz, R.Lacey, W. Lynch, Science)

Dynamical isovector effects: differential directed and elliptic flow132Sn + 132Sn @ 1.5 AGeV b=6fmr+drdifferential directed flowdifferential elliptic flowDynamical boosting of thevector contributionT. Gaitanos, M. Di Toro, et al., PLB562(2003)

Inelastic collisions: Production of particles and resonancesCoupled transport equations: Channels without strangenessElastic baryon-baryon collisions: NNNN (in-medium sNN), NDND, DDDDInelastic baryon-baryon collisions (hard D-production & absorption): NNND, NNDDInelastic baryon-meson collisions (soft D-production & absorption) NpDChannels with strangeness (perturbative kaon production)Baryon-Baryon : BBBYK (B=N,D,0,++, Y=L,S,0, K=K0,+)Pion-Baryon : pBYK (YKpB not included)Kaon-Baryon : BKBK (elastic, no isospin exchange)No channels with antistrangeness (K-)

Kaon Production:A good way to determine the symmetric EOS (C. Fuchs et al., PRL 86(01)1974)Also useful for Isovector EoS?charge dependent thresholds in-medium effective massesMean field effectsMain production mechanism:NNBYKpNYK

Pions: from entire evolutioncompensation Kaons: direct early production: high density phase isovector channel effects Pion and Kaon production in open systems (HIC)Au+Au@1AGeV

Strangeness ratio :Infinite Nuclear Matter vs. HICG. Ferini, et al., NPA762(2005) 147 and nucl-th/0607005

Kaon production as a probe for the isovector EoST. Gaitanos, G. Ferini, M. Di Toro, M. Colonna, H.H. Wolter, nucl-th/06

Au+Au central: Pi and K yield ratios vs. beam energyPions: less sensitivity ~10%, but larger yieldsNot sensitive to the K-potential(iso-dep.?)Kaons:~15% difference betweenDDF and NL132Sn+124Sn

K+ production and influence of kaon potentials: Ni+Ni, 1.93 AGeV

Consistency of Heavy Ion Resuts with Neutron Star DataMaximum masses and direct URCA cooling limit(see D.Blaschke,T. Klaehn)Lower boundary (LB) leads to too small NS masses!Flow constraint can be sharpened.T.Klhn, D. Blaschke, S.Typel, E.v.Dalen, A.Faessler, C.Fuchs, T.Gaitanos, H. Grigorian, A.Ho, E.Kolomeitsev, M.Miller, G.Rpke, J.Trmper, D.Voskresensky, F.Weber, H.H.Wolter,Phys.Rev.C, to appear, nucl-th/0602038

,Exotic matter over 10 fm/c ?In a C.M. cellbaryon densityquadrupole densityresonance densitytemperatureenergy densityasymmetrymore exoticphenomena?

Testing deconfinement with RIBs?(T,rB,rB3) binodal surfaceHadron-RMFQuark-bag modelrtrans onset of the mixed phase decreases with asymmetrySignatures?Di Toro, A. Drago, et al. nucl-th/0602052NPA775(2006)102-126Mixed Phase NLNLGM31 AGeV300 AMeV132Sn+124Sn, semicentralB1/4 =150 MeV

Transition to deconfined phase at high baryon densityH.Mueller NPA618(1997)Hadron EOS : QHDQuark EOS: MIT-Bag ModelSymmetricAsymmetric:I=0.4MixedPhaseReduced transition density1. earlier transition at high isospin density2. unfavorable model choice? Hadron: rho-meson only, Quark: B1/4=190MeV large Bag-Pressureliquid-gas P.T.

Lower Boundary of the Binodal Surface vs. NM Asymmetryvs. Bag-constant choiceProton-fractionsymmetricTemperature variationReduction of the crossing density vs. T: delta-meson very efficient!

Isospin content of the Quark Clusters in the Mixed PhaseHadronsMixedQuarksT=50 MeVLower boundarySignatures? Neutron migration to the quark clusters (instead of a fast emission) Di Toro,et al., NPA775(2006)102-126

Summary and Conclusions:While the Eos of symmetric NM is fairly well determined, the isovector EoS is still rather uncertain (but important for exotic nuclei, neutron stars and supernovae)Can be investigated in HIC both at low densities (Fermi energy regime, fragmentation) and high densities (relativistic collisions, flow, particle production). In particular Kaon ratios seem to be a sensitive observable.Data to compare with are still relatively scarce; it appears that the Iso-EoS is rather stiff. Effects scale with the asymmetry thus reactions with RB are very importantAdditional information can be obtained by cross comparison with neutron star observationsDeconfinement signals at high asymmetry??

closed (IHM) vs. open system (HIC)Consistency between IHM and HIC results (if fall of asymmetry in kaon source accounted for)

Astrophysical Implications of Iso-Vector EOSNeutron Star StructureConstraints on the Equation-of-state - from neutron stars: maximum mass gravitational mass vs. baryonic mass direct URCA process mass-radius relation - from heavy ion collisions: flow constraint kaon producton

Equations of State tested:

Neutron star masses and cooling and iso-vector EOSTolman-Oppenheimer-Volkov equation to determine mass of neutron starKlhn, Blaschke, Typel, v.Dalen, Faessler, Fuchs, Gaitanos, Gregorian, Wolter, submitted to Phys. Rev.Typical neutron starsHeaviest observed neutron star

Flow-Constraint from HIC:(P.Danielewicz, R. Lacey, W.G. Lynch, Science 298, 1592 (2002))

Heavy Ion Collisions and the Isovector Equation-of-Statep, K, Isospin dependence of mean field and threshhold conditionsFragmentation