1. 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

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

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

5. E sym      MeV)      1230 Asy-stiff Asy-soft Importance of the Nuclear Symmetry Energy in Nuclear and Astrophysics supernovae Heavy ion collisions in the Fermi energy regime; multifragmentation supernova simulations covers large range of thd. conditions Nuclear structure (neutron skin thickness, Pygmy DR, IAS ) Slope of Symm Energy Light cluster correlations at very low density

6. 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 r c ) and in-medium  mass scaling Different proton/neutron effective masses Isovector (Lane) potential: momentum dependence SE ist also momentum dependent  effective mass data m* n < m* p m* n > m* p

7. Heavy Ion Collisions pictorially: different behavior by varying system, asymmetry, incident energy, centrality, etc. examples: 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) 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) non-equlibrium also in dense phase  transport description

8. 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 T T TT QPA Spectral fcts, off-shell transport, quasi-particle approx. Transport equations Transport theory is on a well defined footing, in principle Boltzmann-Ühling-Uhlenbeck (BUU)

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

10. 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 Constraints on the Symmetry Energy from HIC in the range 50-200 AMeV

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

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

14. Y(n)/Y(p) son: asysoft, m n *>m p * stn: asystiff, m n *>m p * sop: asysoft, m n *<m p * stp: asystiff, m n *<m p * Asy-EOS dominates for slow particles; Effective mass dominates for fast particles,  separate density and momentum dependence Y(t)/Y(3He) 197 Au+ 197 Au 600 AMeV b=5 fm, |y 0 |  0.3 (V.Giordano, et al., PRC 81(2010)) effect of effective mass more prominent than that of asystiffness asy-stiff asy-soft m* n <m* p m* n >m* p crossing connected to crossing of Lane potentials Pre-Equilibrium Emission of Nucleons or Light Clusters 136Xe+124Sn, 150 MeV E transverse favors m n *<m p * (in contrast to optical model analyses)  more work required!

15. 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 K 0 /K + :  probe for symmetry energy 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 Important to fix the EOS of symm. nucl. matter Fuchs, et al., PRL 86 (01) NN NKNK KK NN N 

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

17. 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  Pion ratios in comparison to FOPI data Au+Au, semi-central Contradictory results, trend with asy-stiffness differs small dep. on SE J. Hong, P.Danielewicz FOPI exp (NPA 781, 459 (07))

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

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 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, K 0 and K + have large mean free path, small width: Larger (or equally large) effect for kaons, which come directly from high density region G.Ferini et al.,PRL 97 (2006) 202301 132Sn+124S n Au+Au, 1 AGeV, central Inclusive multiplicities 132Sn+124Sn Small effect for  ‘s more detailed analysis (Ferini, et al.,) Competing effects of asystiffness on  and K 0 /K + ratios from mean field (asystiff larger) and threshold (asystiff smaller) Single ratios are more sensitive! Comparision to FOPI data: Double ratio (Ru+Ru)/(Zr+Zr) finite nucleus Data (Fopi) X. Lopez, et al., PRC 75 (2007) G. Ferini, et al., NPA762(2005) 147 calculations infinite system (box)

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

22. Au+Au, 400AMeV, FOPI Fermi Energy HIC, MSU  +/  - ratio B.A. Li, et al.  +/  - ratio, Feng, et al. Present constraints on the symmetry energy S(  ) [MeV] - 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! neutron matter EoS mass-radius relation T. Fischer, M.Hempel, et al., EPJA50(14)46 Comparison to models for NS properties T. Fischer, M.Hempel, et al., EPJA50(14)46

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!

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

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

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

28. “Flow“, Momentum distribution of emitted particles Global momentum space Fourier analysis of momentum tensor : „flow“ v 2 : elliptic flowv 1 : sideward flow p n  stiff    Proton-neutron differential flow T. Gaitanos, M. Di Toro, et al., PLB562(2003) 132 Sn + 132 Sn @ 1.5 AGeV b=6fm   differential elliptic flow Elliptic flow more sensitive, since particles emitted perpendicular to reaction plane 

29. 1.„direct effects“: difference in proton and neutron (or light cluster) emission and flow 2.„secondary effects“: production of particles, isospin partners  -,+, K 0,+ NN NKNK KK NN N  in-medium inelastic  K and  potential (in- medium mass)  in-medium self-energies and width  potential, p, n Particle production as probe of symmetry energy box calculation Ferini et al., B.A.Li et al., PRL102 Two limits: 1.isobar model 2.chemical equilibrium ->  - /  + should be good probe!  Therefore consider ratios  - /  + ; K 0 /K + 1. Mean field effect: U sym more repulsive for neutrons, and more for asystiff 2. Threshold effect, in medium effective masses:  competing effects!  in HIC:

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

31. 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. further work required! Investigation with heavy ion collisions However, at high densities large differences. -- 3-body forces? (Baldo); scaling with density? -- short range tensor force (cut-off r c ) and in-medium mass scaling (parameter  ) (B.A.Li) J. Phys. G: Nucl. Part. Phys. 41 (2014) 093001

32. Momentum distributions, “Flow” - Directed flow not very sensitive to SE (involves many different densities) - Elliptic flow in this energy region probe of high density  =0.5  =1.5 neutron proton hydrog en Au+Au @ 400 AMeV, FOPI-LAND (Russotto, et al., PLB 697, 471 (11)) prediction p, n 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) not very precise (yet) but indicates rather stiff SE,  ~1

33. Determination of EOS at higher density: Flow: anisotropy of particle momentum distribution Stiff, more pressure Soft, less pressure Incompressibility K used as label Danielewicz, Lacey, Lynch,Science 298,1592(02) In-plane flow, v1 shadowing No more shadowing Squeeze-out, v2 y Au+Au, 2 AGeV Danielewicz, NPA673,375(00) 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)

34. Transport theory  Experiments (Observables) 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) To get information on the nuclear equation-of-state from HIC and transport theory v 2 : Elliptic flowv 1 : Sideward flow e.g. analysis of momentum distribution: „flow“: