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Bulk Viscous Effects on Relativistic Hydrodynamic Models of the

VIEWS: 2 PAGES: 17

									Bulk Viscous Effects on Relativistic Hydrodynamic
       Models of the Quark-Gluon Plasma
                          Akihiko Monnai
         Department of Physics, The University of Tokyo
                Collaborator: Tetsufumi Hirano

 3rd Joint Meeting of the Nuclear Physics Divisions of the APS and the JPS
                       October 15th 2009, Hawaii USA
                                            AM and T. Hirano,
                                            arXiv:0903.4436; arXiv:0907.3078
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                                                    Outline
        Introduction
        Relativistic viscous hydrodynamics

        Distortion of Distribution
        How to express                  in terms of dissipative currents

        Numerical Estimation
        Effects of            on observables

        Summary and Outlook
        Summary and constitutive equations




Bulk Viscous Effects on Relativistic Hydrodynamic Models of the Quark-Gluon Plasma, Hawaii, Oct. 15th 2009   Akihiko Monnai
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                                           Introduction
        Success of ideal hydrodynamic models
       at relativistic heavy ion collisions


        Development of viscous hydrodynamic models
       to correctly extract information from experimental data


        How does bulk viscosity affects observables?
       It has almost been neglected, BUT bulk viscosity is not so small near
                                                                                         Mizutani et al. (‘88)
          Bulk viscosity =                                                               Paech & Pratt (‘06)
          response of pressure
                                                                                         Kharzeev & Tuchin (’08) …
          to volume change


Bulk Viscous Effects on Relativistic Hydrodynamic Models of the Quark-Gluon Plasma, Hawaii, Oct. 15th 2009     Akihiko Monnai
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                                           Introduction
      How does bulk viscosity affects observables?
     One needs a translator of flow field into particles at freezeout
                                                         hydro result                 observables
                           Cooper-Frye formula
                                     particles          freezeout hypersurface Σ



                      hadron
      variation of the flow/hypersurface                              modification of the distribution
                              resonance              QGP
         particles          freezeout hypersurface Σ
                              gas
                                                                    Express      with dissipative currents
       hadron                                                       in a multi-component system
       resonance             QGP
       gas




Bulk Viscous Effects on Relativistic Hydrodynamic Models of the Quark-Gluon Plasma, Hawaii, Oct. 15th 2009   Akihiko Monnai
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               Macroscopic to Microscopic
      Express      in terms of dissipative currents
       Generalization of Israel-Stewart method:
                                                                                             Israel & Stewart (‘76)

         Macroscopic quantities                                                 Microscopic quantities

                     ,      ,       ,
              Dissipative currents                                              Distortion of distribution
              (given from hydro)                                                       (unknown)

                                14 “bridges” from Relativistic Kinetic Theory




Bulk Viscous Effects on Relativistic Hydrodynamic Models of the Quark-Gluon Plasma, Hawaii, Oct. 15th 2009    Akihiko Monnai
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                      in Multi-Component System
      Grad’s 14-moment method                                          14 unknowns                     ,


       No scalar, but non-zero trace tensor
                                                            : 2nd law of thermodynamics
          + constitutive equation

                                                                                      New tensor structure for
      The distortion is uniquely obtained:                                           multi-component system




      where               and           are calculated in kinetic theory.

Bulk Viscous Effects on Relativistic Hydrodynamic Models of the Quark-Gluon Plasma, Hawaii, Oct. 15th 2009   Akihiko Monnai
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                                        Models Inputs
      Estimation of particle spectra (with bulk viscosity in                                                    ):



  Flow , freezeout hypersurface    :                                      Bulk pressure:
  (3+1)-D ideal hydrodynamic model                                         Navier-Stokes limit
                                   Hirano et al.(‘06)
                                                                          Transport coefficients:
  Equation of State: 16-component                                                                            ,
  hadron resonance gas
  (hadrons up to         , under                              )           where                       : sound velocity
                                                                                                     : entropy density
  Freezeout temperature:                                                    Weinberg (‘71)            Kovtun et al.(‘05)



Bulk Viscous Effects on Relativistic Hydrodynamic Models of the Quark-Gluon Plasma, Hawaii, Oct. 15th 2009            Akihiko Monnai
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      Bulk Viscosity and Particle Spectra
      Au+Au,                                        , b = 7.2(fm), pT -spectra and v2(pT) of




           pT -spectra                   suppressed                              v2 (pT)                     enhanced
 *Possible overestimations due to... (i) Navier-Stokes limit (no relaxation effects)
                                     (ii) ideal hydro flow (derivatives are larger)

Bulk Viscous Effects on Relativistic Hydrodynamic Models of the Quark-Gluon Plasma, Hawaii, Oct. 15th 2009       Akihiko Monnai
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                         Summary and Outlook
      Determination of     in a multi-component system
       - Viscous correction     has non-zero trace.
      Visible effects of      on particle spectra
       - pT-spectra is suppressed; v2(pT) is enhanced


      Bulk viscosity can be important in extracting information
       (e.g. transport coefficients) from experimental data.
      Full Viscous hydrodynamic models need to be developed to
       see more realistic behavior of the particle spectra.



Bulk Viscous Effects on Relativistic Hydrodynamic Models of the Quark-Gluon Plasma, Hawaii, Oct. 15th 2009   Akihiko Monnai
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      Estimation of Dissipative Currents
                                                                                                     AM and T. Hirano,
   2nd       order Israel-Stewart theory                                                             in preparation
             Naïve generalization to a multi-component system
             does NOT work
      Constitutive equations in a multi-component system:
  Bulk pressure
                                                                                  Navier-Stokes term
                                                                                  Israel-Stewart
                                                                                  2nd order terms

                                                                                  Post Israel-Stewart
                                                                                  2nd order terms

  Shear tensor                  in conformal limit reduces to AdS/CFT result (Baier et al. ‘08)

Bulk Viscous Effects on Relativistic Hydrodynamic Models of the Quark-Gluon Plasma, Hawaii, Oct. 15th 2009     Akihiko Monnai
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                                               Thank You
      The numerical code will become available at
               http://tkynt2.phys.s.u-tokyo.ac.jp/~monnai/distributions.html




Bulk Viscous Effects on Relativistic Hydrodynamic Models of the Quark-Gluon Plasma, Hawaii, Oct. 15th 2009   Akihiko Monnai
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Appendix

Bulk Viscous Effects on Relativistic Hydrodynamic Models of the Quark-Gluon Plasma, Hawaii, Oct. 15th 2009   Akihiko Monnai
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  Shear Viscosity and Particle Spectra
      pT -spectra and v2(pT) of                              with shear viscous correction




         Non-triviality of shear viscosity; both pT -spectra and v2(pT) suppressed


Bulk Viscous Effects on Relativistic Hydrodynamic Models of the Quark-Gluon Plasma, Hawaii, Oct. 15th 2009   Akihiko Monnai
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      Shear & Bulk Viscosity on Spectra
      pT -spectra and v2(pT) of                              with corrections from shear and
       bulk viscosity




                      Accidental cancellation in viscous corrections in v2(pT)

Bulk Viscous Effects on Relativistic Hydrodynamic Models of the Quark-Gluon Plasma, Hawaii, Oct. 15th 2009   Akihiko Monnai
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                                   Quadratic Ansatz
      pT -spectra and v2(pT) of                     when




           Effects of the bulk viscosity is underestimated in the quadratic ansatz.


Bulk Viscous Effects on Relativistic Hydrodynamic Models of the Quark-Gluon Plasma, Hawaii, Oct. 15th 2009   Akihiko Monnai
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                                       Bjorken Model
      pT -spectra and v2(pT) of                              in Bjorken model with cylindrical
       geometry:




                                                                      Bulk viscosity suppresses pT-spectra
                                                                      Shear viscosity enhances pT-spectra




Bulk Viscous Effects on Relativistic Hydrodynamic Models of the Quark-Gluon Plasma, Hawaii, Oct. 15th 2009   Akihiko Monnai
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                                  Blast wave model
      pT -spectra and v2(pT) of

                                                                       Shear viscosity enhances pT-spectra
                                                                       and suppresses v2(pT).




Bulk Viscous Effects on Relativistic Hydrodynamic Models of the Quark-Gluon Plasma, Hawaii, Oct. 15th 2009   Akihiko Monnai

								
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