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Compact Stars in the QCD Phase Diagram IV, Prerow, Germany, Sept. 26-30, 2014

The Symmetry Energy at Supersaturation Densities from Heavy Ion Collisions. Hermann Wolter University of Munich, Germany. Compact Stars in the QCD Phase Diagram IV, Prerow, Germany, Sept. 26-30, 2014. Outline: 1. Nuclear Symmetry Energy and ist uncertainities

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Compact Stars in the QCD Phase Diagram IV, Prerow, Germany, Sept. 26-30, 2014

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  1. The Symmetry Energy at Supersaturation Densities from Heavy Ion Collisions Hermann Wolter University of Munich, Germany Compact Stars in the QCD Phase Diagram IV, Prerow, Germany, Sept. 26-30, 2014

  2. Outline: 1. Nuclear Symmetry Energy and ist uncertainities 2. Investigation in heavy ion collisions: low density <~0: (multi)fragmentation, isospin transport supersaturation density >0: flow, particle emission and production 3. Status of knowledge of symmetry energy Implication for compact stars Acknowledgement to my collaborators: M. Colonna, M. Di Toro, V. Greco (Lab. Naz. del Sud, INFN, Catania) T. Gaitanos (U. Giessen  U. Thessaloniki, Greece) D. Blaschke, T. Klähn (U. Wroclav), G. Röpke (U. Rostock), S.Typel (GSI)

  3. Quark-hadron coexistence 1 Supernovae IIa neutron stars 0 Z/N Isospin degree of freedom Our general aim in Heavy Ion Reactions: The Phase Diagram of Strongly Interacting Matter heavy ion collisions (HIC) Caveat: HIC trajectories are non-equilibrium processes, and are not in the plane of the diagram  transport theory is necessary SIS18 Liquid-gas coexistence FAIR, NICA

  4. neutron matter EOS Symmetry energy: neutron - symm matter, rather unknown, e.g. Skyrme-like param.,B.A.Li EOS of symmetric nuclear matter asy-stiff stiff asy-soft soft Parametrizations around 0 :  Esympot() often parametrized as saturation point Fairly well fixed! Soft! Equation-of-State and Symmetry Energy symmetry energy BW mass formula density-asymmetry dep. of nucl.matt. density  asymmetry

  5. Heavy ion collisions in the Fermi energy regime; multifragmentation Asy-stiff EsymMeV) Asy-soft supernovae 0 1  2 3 Nuclear structure (neutron skin thickness, Pygmy DR, IAS) Slope of Symm Energy Importance of the Nuclear Symmetry Energy in Nuclear and Astrophysics Light cluster correlations at very low density supernova simulations covers large range of thd. conditions

  6. Different proton/neutron effective masses m*n < m*p Isovector (Lane) potential: momentum dependence m*n > m*p data Microscopic many-body calculations for the symmetry energy: Marcello Baldo, NuSYM14 Low density symmetry energy behave similarly and are consistent with analyses from nuclear structure and HIC. However, at high densities large differences. -- 3-body forces? (Baldo); scaling with density? -- short range tensor force (cut-off rc) and in-medium  mass scaling SE ist also momentum dependent  effective mass

  7. Heavy Ion Collisions pictorially: different behavior by varying system, asymmetry, incident energy, centrality, etc. examples: Collision at relativistic energies of ~600 MeV/A to several GeV/A: Compression to several times saturation density, non-spherical momentum distributions („flow“), particle production (pions, strangeness (kaons),etc.) (GSI, FAIR, NICA,HIAF) Collisions at Fermi energies in nuclei, about 35 to several hundred MeV/A: Moderate compression, multifragmentation, phase transitions of the liquid-gas type (NSCL, GANIL, Texas A&M, HIRFL, RIKEN, future FRIB) non-equlibrium also in dense phase transport description

  8. T T T T QPA Transport equations Boltzmann-Ühling-Uhlenbeck (BUU) Can be derived:  Classically from the Liouville theorem collision term added  Semiclassically from THDF (and fluctuations)  From non-equilibrium theory (Kadanoff-Baym) collision term included mean field and in-medium cross sections consistent, e.g. from BHF Spectral fcts, off-shell transport, quasi-particle approx. Transport theory is on a well defined footing, in principle

  9. Dynamical Interpretations of Low Energy Heavy Ion Collisions central Coulomb barrier to Fermi energies peripheral Isospin migration Isospin fractionation, multifragmentation deep-inelastic pre-equil. light particles pre-equil. dipole N/Z of PLF residue = isospin diffusion N/Z ratio of IMF‘s N/Z of neck fragment and velocity correlations Information on symmetry energy for densities of below to about 20% above . not discuss here

  10. Constraints on the Symmetry Energy from HIC in the range 50-200 AMeV C.J.Horowitz, et al., „A way forward in the study of the symmetry energy: experiment, theory, observations“, arxiv 1401.5839, J. Phys. G: Nucl. Part. Phys. 41 (2014) 093001

  11. -- e.g. SE that fit nuclear masses cross below saturation density, (some average densitiy of a finite nucleus) -- induces a correlation between value and slope at  within the model., eg. in lin. approx. Correlations between model parameters, e.g. --different observables are sensitive to different densities (or ranges of densities) and thus induce different correlations -- crossing point will hopefully fix S and L, which are independent -- Represents an extrapolation using a model with different density dependences in some cases a wide extrapolation, eg. for neutron star J. Lattimer, A.W.Steiner, Eur. Phys. J. A (2014) 50: 40

  12. n  K N t N  p N N  Inel.collisions Particle product. NN->NNK N Flow, In-plane, transverse Squeeze-out, elliptic disintegration Asy-stiff Asy-soft Y 132Sn + 132Sn, 1.5 AGeV n neutron nn -> - p n- pp -> ++ n  p+ (asystiff) p stiff  n n proton p <px> Differential p/n flow (or t/3He) diff # p,n (asymmetry of system) diff. force on n,p e.g.asy-stiff n preferential n/p y/yproj Sketch of reaction mechanism at intermediate energies and observables Pre-equilibr emiss. (first chance, high momenta) Reaction mechanism can be tested with several observables: Consistency required!

  13. Momentum distributions, “Flow” Au+Au @ 400 AMeV, FOPI-LAND neutron proton hydrogen p, n =0.5 (Russotto, et al., PLB 697, 471 (11)) =1.5 preliminary result from new experiment ASY-EOS (Russotto, IWM_EC workshop, Catania 2014) prediction - Directed flow not very sensitive to SE (involves many different densities) - Elliptic flow in this energy region probe of high density not very precise (yet) but indicates rather stiff SE, ~1

  14. 197Au+197Au 600 AMeV b=5 fm, |y0|0.3 asy-stiff • m*n<m*p • m*n>m*p Etransverse asy-soft crossing connected to crossing of Lane potentials effect of effective mass more prominent than that of asystiffness (V.Giordano, et al., PRC 81(2010)) Etransverse son: asysoft, mn*>mp* stn: asystiff, mn*>mp* sop: asysoft, mn*<mp* stp: asystiff, mn*<mp* Pre-Equilibrium Emission of Nucleons or Light Clusters 136Xe+124Sn, 150 MeV Y(n)/Y(p) Asy-EOS dominates for slow particles; Effective mass dominates for fast particles, separate density and momentum dependence favors mn*<mp* (in contrast to optical model analyses)  more work required! Y(t)/Y(3He)

  15. NN N N K NK Important to fix the EOS of symm. nucl. matter Fuchs, et al., PRL 86 (01) Particle Production Inelastic collisions: Production of particles and resonances: Coupled transport equations e.g. pion and kaon production; coupling of  and strange-ness channels. Many new potentials, elastic and inelastic cross sections needed, dynamics in medium What can one learn from different species? • pions: production at all stages of the evolution via the -resonace • kaons (strange mesons with high mass): subthreshold production, probe of high density phase • ratios of and K0/K+: probe for symmetry energy

  16. soft Esym stiff Esym Dynamics of particle production (,K) in heavy ion collisions Au+Au@1AGeV Central density  and K: production in high density phase Pions: low and high density phase Sensitivity to asy-stiffness  and multiplicity K0,+ multiplicity Dependence of ratios on asy-stiffness n/p 0,-/+,++ -/+, K0/K+  n/p ratio governs particle ratios  time [fm/c] G.Ferini et al.,PRL 97 (2006) 202301

  17. Pion ratios in comparison to FOPI data Au+Au, semi-central MDI, x=0, mod. soft Xiao,.. B.A.Li, PRL 102 (09) MDI, x=1, very soft NL, stiff Ferini, Gaitanos,.. NPA 762 (05) NLlinear =2, stiff Feng,… PLB 683 (10) SIII, very soft small dep. on SE J. Hong, P.Danielewicz FOPI exp (NPA 781, 459 (07)) Contradictory results, trend with asy-stiffness differs

  18. in-medium threshold effect in-medium  production Possible reasons: dynamics, medium effects: potentials, effetive cross sections, spectral fcts (C.M. Ko)  Spectral function transport theory of particles with finite width, „off-shell“ transport, see Mosel (GiBUU) and Cassing (HSE) groups not systematically investigated

  19. Planned experiment at Srit (MSU, Riken) 300 MeV: R. Shane, J. Estee calculations with pBUU (P. Danielewicz) new sugg. observable

  20. Strangeness production in HIC: Kaons Au+Au, 1 AGeV, central 132Sn+124Sn 132Sn+124Sn Inclusive multiplicities G.Ferini et al.,PRL 97 (2006) 202301 Small effect for ‘s Comparision to FOPI data: Double ratio (Ru+Ru)/(Zr+Zr) calculations Data (Fopi) X. Lopez, et al., PRC 75 (2007) infinite system (box) finite nucleus G. Ferini, et al., NPA762(2005) 147 Kaons were a decisive observable to determine the symmetric EOS; perhaps also useful for SE? Kaons are closer to threshold, come only from high density, K0 and K+ have large mean free path, small width: Larger (or equally large) effect for kaons, which come directly from high density region Single ratios are more sensitive! more detailed analysis (Ferini, et al.,) Competing effects of asystiffness on  and K0/K+ ratios from mean field (asystiff larger) and threshold (asystiff smaller)

  21. pion, kaon,.. production collective flow around , masses, collective excitations very low density, clusterization fragmentation, liquid-gas PT Present constraints on the symmetry energy from HIC in different density regions

  22. Au+Au, 400AMeV, FOPI +/- ratio, Feng, et al. Fermi Energy HIC, MSU +/- ratio B.A. Li, et al. Comparison to models for NS properties T. Fischer, M.Hempel, et al., EPJA50(14)46 mass-radius relation neutron matter EoS T. Fischer, M.Hempel, et al., EPJA50(14)46 Present constraints on the symmetry energy - Moving towards a determination of the symmetry energy from HIC - Large uncertainties at higher density - Conflicting conclusions for pion observables need to be clarified - kaon observables promising - Work in experiment and theory necessary! S() [MeV]

  23. Summary and Outlook: 1. Transport approaches are essential to obtain information on the equation of state of nuclear matter in the laboratory. but also open problems: - role of fluctuations and correlations - consistency of different implementations - treatment of particles with finite width (off-shell transport) 2. Constraints on the nuclear symmetry energy from HIC: - around and below saturation energy they are converging and are consistent with theory - at high densities the situation is less satisfactory and more work experimentally and theoretically is necessary 3. Consequences for Compact stars Thank you!

  24. Au+Au, 0.6AGeV  soft Esym NL NL NL stiff Esym time [fm/c] Dynamics of particle production (,K) in heavy ion collisions Au+Au@1AGeV Central density Dependence of ratios on asy-stiffness n/p 0,-/+,++ -/+  and multiplicity  and K: production in high density phase Pions: low and high density phase Sensitivity to asy-stiffness K0,+ multiplicity  time [fm/c] G.Ferini et al.,PRL 97 (2006) 202301

  25. NN N K N NK Important to fix the EOS of symm. nucl. matter M(K+) ~ (Apart) >1: evidence of two-step process Fuchs, et al., PRL 86 (01) Kaon production as a probe for the EOS Subthreshold, Eth=1.58 MeV Two-step process dominant In havier systems. Collective effect

  26. Trümper Constraints (Universe Cluster, Irsee 2012) Constraints on EoS from Astrophysical Observation Observations of: masses radii (X-ray bursts) rotation periods Increasingly stringent constraint on many EoS models

  27. Global momentum space v1: sideward flow v2: elliptic flow 132Sn + 132Sn @ 1.5 AGeV b=6fm stiff   n p differential elliptic flow Proton-neutron differential flow Elliptic flow more sensitive, since particles emitted perpendicular to reaction plane     T. Gaitanos, M. Di Toro, et al., PLB562(2003) “Flow“, Momentum distribution of emitted particles Fourier analysis of momentum tensor : „flow“

  28. Particle production as probe of symmetry energy p, n NN N B.A.Li et al., PRL102 N K NK in-medium inelastic   in-medium self-energies and width  potential , K and  potential (in-medium mass) Therefore consider ratios -/+; K0/K+ Two limits: • isobar model 2. chemical equilibrium -> -/+should be good probe! box calculation Ferini et al.,  in HIC: 1. Mean field effect: Usym more repulsive for neutrons, and more for asystiff 2. Threshold effect, in medium effective masses:  competing effects! „direct effects“: difference in proton and neutron (or light cluster) emission and flow „secondary effects“: production of particles, isospin partners -,+, K0,+

  29. O.1 Deconfinement transition with large asymmetry 1 neutron stars 0 B1/4 =150 MeV NLρ Z/N NLρδ GM3 Transition density/0 1 AGeV 300 AMeV 132Sn+124Sn, semicentral DiToro,Drago,Gaitanos,Greco,Lavagno, NPA775(2006)102 Di Toro: NICA Round Table Quark-hadron coexistence

  30. Microscopic many-body calculations for the symmetry energy: Marcello Baldo, NuSYM14 J. Phys. G: Nucl. Part. Phys. 41 (2014) 093001 Low density symmetry energy behave similarly and are consistent with analyses from nuclear structure and HIC. However, at high densities large differences. -- 3-body forces? (Baldo); scaling with density? -- short range tensor force (cut-off rc) and in-medium mass scaling (parameter ) (B.A.Li) further work required! Investigation with heavy ion collisions

  31. Momentum distributions, “Flow” Au+Au @ 400 AMeV, FOPI-LAND neutron proton hydrogen p, n =0.5 (Russotto, et al., PLB 697, 471 (11)) =1.5 Each band: soft vs. stiff eos of symmetric matter, (Cozma, arXiv 1102.2728)  robust probe preliminary result from new experiment ASY-EOS (Russotto, IWM_EC workshop, Catania 2014) prediction - Directed flow not very sensitive to SE (involves many different densities) - Elliptic flow in this energy region probe of high density not very precise (yet) but indicates rather stiff SE, ~1

  32. Au+Au, 2 AGeV Stiff, more pressure y Soft, less pressure In-plane flow, v1 Squeeze-out, v2 No more shadowing shadowing Danielewicz, Lacey, Lynch,Science 298,1592(02) Determination of EOS at higher density: Flow: anisotropy of particle momentum distribution Danielewicz, NPA673,375(00) Incompressibility K used as label Constraint area for symmetric EoS Similar approach to determine symmetry energy but now for differences or ratios of flow and production of n-like and p-like species (isospin partners)

  33. Transport theory  Experiments (Observables) e.g. analysis of momentum distribution: „flow“: v1: Sideward flow v2: Elliptic flow To get information on the nuclear equation-of-state from HIC and transport theory Transport theory calculates , i.e. full information about the complete evolution, but only (!) of single particle observables. Experiment measures , i.e. asymptotic momentum distribution, of nucleons, and also of newly produced particles (, K, …) (inelastic cross sections)  and of clusters (in principle many-body observables) Comparison conclusion on employed physical input (EOS, elastic and inel. cross sect., etc)

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