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Hydrodynamical modeling of heavy ion

Estructura and Constituents de la Materia. Volodymyr Magas. Hydrodynamical modeling of heavy ion. collisions and freeze out. Feb 22, 2006. Jan 98 - Aug 01. Simulations of the relativistic heavy ion collisions. M Sc, Jan 99 "Freeze out in hydrodynamical models".

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Hydrodynamical modeling of heavy ion

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  1. Estructura and Constituents de la Materia Volodymyr Magas Hydrodynamical modeling of heavy ion collisions and freeze out Feb 22, 2006

  2. Jan 98 - Aug 01 Simulations of the relativistic heavy ion collisions MSc,Jan 99 "Freeze out in hydrodynamical models" PhD, Aug 01 "Multi Module Model for Ultra-Relativistic Heavy Ion Collisions" Supervisor: Laszlo P. Csernai

  3. Why to do relativistic heavy ion collisions? Primary goal – to observe and study the properties of the Quark-Gluon Plasma and Phase Transition But also to study the modifications of the hadron properties at high T and n Requires more runs at intermediate energies Coming back nowadays

  4. Nuclear Matter Phase diagram What can we learn from Lattice QCD?

  5. Lattice results Critical Temperature is about 170-180 MeV Deconfinement and Chiral Symmetry restoration

  6. What is the order of the Phase Transition? How to go to the final baryon chemical potential? Works of Fodor, Katz, Karsch, Redlich Works of Karsch, Moscy, Heinz, Braun-Munzinger, Redlich Lattice provides guidance, but many ambiguities remain

  7. QGP: A new state of Matter CERN, 2000 “The combined data coming from the seven experiments on CERN's Heavy Ion programme have given a clear picture of a new state of matter. . . . We nowhave evidence of a new state of matter where quarks and gluons are not confined. There is still an entirely new territory to be exploredconcerning the physical properties of quark-gluon matter.” [ L. Maiani]

  8. Simulations of the relativistic heavy ion collisions Animation by Jeffery Mitchell. VNI model by Klaus Kinder-Geiger and RonLongacre, BNL

  9. Simulations of the relativistic heavy ion collisions Relativistic heavy ion collision goes through three main different stages: Initial stage – before local equilibrium is achieved Intermediate stage - EoS, collective flow Final stage – interaction breaks down, freeze out Each stage requires a suitable theoretical approach !

  10. Multi Module Modeling Initial stage –parton cascade (e. g. MPC) or effective string models Additional Input: EoS Intermediate stage - hydrodynamics Additional Input: FO condition and scenario Final stages –freeze out (sudden or gradual) or hadron cascade (e. g. UrQMD)

  11. How to combine Modules together? • Conservation laws • Nondecreasing entropy ! Will be discussed later in more details for the Freeze Out

  12. Multi Module Model is required for a realistic simulation of a heavy ion reaction

  13. Multi Module Modeling – Collaboration: Dr V. Magas–U. of Barcelona, Spain Prof. D. Strottman– U. of Valencia, ES / LANL, USA Prof. B. Schlei - LANL, USA/ Germany Prof. L. Csernai, PhD students E. Molnar, A. Nyiriand K. Tamosiunas U. of Bergen, Norway PhD student J. Manninen –Oulu U., Finland/U. of Bergen, NO

  14. [Heinz–SQM2004] 1st order

  15. Success of Hydrodynamics Relativistic fluid dynamics has been demonstrated to be extremely useful in describing heavy ion collisions at all energies Basically the only predictions which worked well for RHIC were predictions from hydro models

  16. pT dependence for p,p • Hydro calculations: P. Huovinen, P. Kolb and U. Heinz Presented at QM'2001

  17. Success of Hydrodynamics Relativistic fluid dynamics has been demonstrated to be extremely useful in describing heavy ion collisions at all energies Basically the only predictions which worked well for RHIC were predictions from hydro models Strong elliptic flow at RHIC, which is in a good agreement with hydro predictions A strong argument that we really produce “matter”– system in equilibrium, characterized by the EoS

  18. The most problematic is the initial state Module Can not be calculated completely from the first principles Phenomenological parameterizations to be fitted to the data Two basic scenarios for the initial stages of the reaction:

  19. Landau initial state – complete stopping Works well at low energies

  20. Bjorken initial state – complete transparency Initial state is boost invariant – all quantities depent only on t, not on y give rise to 2+1D simple hydro models Very popular at ultra-relativistic energies Does not conserve energy and momentum!!!

  21. How to conserve momentum? At low energies – fire streak picture [Myers, Gosset, Kapusta, Westfall] Tilted initial state

  22. Initial condition Simple 2+1 dim. FD models can fit data quite well ! But in most FD model calculations initial state is fitted: [Heinz–SQM2004] These parameters are fitted to the measured data! Not to the initial parameters of the collision. (except the EoS)

  23. The most problematic is the Initial state Module Can not be calculated completely from the first principles Phenomenological parameterizations to be fitted to the data • Alternative (more demanding) approach: all (or part) of parameters are calculated from the principal collisionparameters in an INITIAL STATE MODEL: • Nexus in NexSpherio • Parton Cascade • Color Glass Condensate • Effective string rope model Magas, Csernai, Strottman, PRC 64 (2001) 014901, NPA 712 (2002) 167

  24. Effective string rope model Transparency in the first moment + stretching chromoelectric field + energy-momentum conservation  deceleration of the colliding partons

  25. String ropes In heavy reaction modeling all string models had to introduce new, more energetic than ordinary hadronic strings, objects like string ropes [Biro’84, Sorge’95], quark clusters [Werner’96], fuser strings [Amelin, Pajares’93,94] in order to describe formation of massive particles, like strange antibaryons. Our string tension s= 4-10 GeV/fm for 65+65 GeV/nucl collisions s= 6-15 GeV/fm for 100+100 GeV/nucl collisions String ropes

  26. Initial state from effective string rope model Tilted ! Au+Au at 100+100 GeV/nucl, b=0.25*2R

  27. Au+Au ECM=65 GeV/nucl. b=0.5 bmax Aσ=0.08 => σ~10 GeV/fm e [ GeV / fm3 ] T [ MeV] . . t=0.0 fm/c, Tmax= 420 MeV, emax= 20.0 GeV/fm3, Lx,y= 1.45 fm, Lz=0.145 fm EoS: p= e/3 - 4B/3 B = 397 MeV/fm3 8.7 x 4.4 fm

  28. Au+Au ECM=65 GeV/nucl. b=0.5 bmax Aσ=0.08 => σ~10 GeV/fm e [ GeV / fm3 ] T [ MeV] . . t=4.6 fm/c, Tmax= 419 MeV, emax= 19.9 GeV/fm3, Lx,y= 1.45 fm, Lz=0.145 fm 14.5 x 4.9 fm

  29. Au+Au ECM=65 GeV/nucl. b=0.5 bmax Aσ=0.08 => σ~10 GeV/fm e [ GeV / fm3 ] T [ MeV] . . t=9.1 fm/c, Tmax= 417 MeV, emax= 19.6 GeV/fm3, Lx,y= 1.45 fm, Lz=0.145 fm 20.3 x 5.8 fm

  30. Phobos Coll. nucl-ex/0405029 Recent results from RHIC Strong antiflow in v is observed 1

  31. 3rd Module Chemical Freeze Out Chemical freeze out describesmany hadron ratios with only three parameters T, m and g s Experimental point of view Becattini, Florkowski, Keranen, Manninen, Tawfik, Redlich…

  32. From theoretical point of view FO is frequently considered • as a discontinuity in the relativistic flow: • - FO happens on some closed FO hypersurface in space-time • on the pre-FO side we have an interacting matter • on the post-FO side we have non-interacting matter: mixture • of ideal gases of different hadron species

  33. From theoretical point of view FO is frequently considered • as a discontinuity in the relativistic flow: • - FO happens on some closed FO hypersurface in space-time • on the pre-FO side we have an interacting matter • on the post-FO side we have non-interacting matter: mixture • of ideal gases of different hadron species How to find this FO hypersurface? Typical ways are T(r,t)=Tcrit or n(r,T)=ncrit Or simply you run your hydro code until it gives reasonable results and then stop FO hypersurface is t=tfinal

  34. Consequences of conservation laws –Problem I • Non-decreasing entropy current across front! PRC 59 (99) 3308

  35. Anchishkin, nucl-th/9904061; Ukr. Jour. of Phys. 47 (02) 451

  36. Space-like hypersurface -Problem II

  37. Kinetic Freeze Out Is there a sharp FO hypersurface? [L Bravina et al. (1995), UrQMD simulations]

  38. Simple phenomenological FO model

  39. Simple phenomenological FO model PLB 459 (99) 33 PRC 59 (99) 388 NPA 661 (99) 596 HIP 9 (99) 193

  40. Model leads to a cut off asymmetric non-equilibrated post FO distribution Same modeling should be applied for the time-like Freeze Out surface ! vo=0 EPJ C30 (03) 255 x= 0.02, 3, 100 X [l] vo=0.5

  41. Freeze out in the layer L-x Cos q

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