3 rd Joint Meeting of the Nuclear Physics Divisions of the APS and the JPS October 15 th 2009, Hawaii USA Akihiko Monnai Department of Physics, The University of Tokyo Collaborator: Tetsufumi Hirano B ulk V iscous E ffects on R elativistic H ydrodynamic M odels of the Q uark- G luon P lasma AM and T. Hirano, arXiv: ; arXiv:

Akihiko MonnaiBulk Viscous Effects on Relativistic Hydrodynamic Models of the Quark-Gluon Plasma, Hawaii, Oct. 15 th 2009 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 Outline 2

Akihiko MonnaiBulk Viscous Effects on Relativistic Hydrodynamic Models of the Quark-Gluon Plasma, Hawaii, Oct. 15 th 2009 Introduction 3 Success of ideal hydrodynamic models Development of viscous hydrodynamic models at relativistic heavy ion collisions to correctly extract information from experimental data Paech & Pratt (‘06) Mizutani et al. (‘88) Kharzeev & Tuchin (’08) … How does bulk viscosity affects observables? It has almost been neglected, BUT bulk viscosity is not so small near Bulk viscosity = response of pressure to volume change

Akihiko MonnaiBulk Viscous Effects on Relativistic Hydrodynamic Models of the Quark-Gluon Plasma, Hawaii, Oct. 15 th 2009 One needs a translator of flow field into particles at freezeout Introduction 4 particles hadron resonance gas QGP freezeout hypersurface Σ particles hadron resonance gas QGP freezeout hypersurface Σ hydro resultobservables How does bulk viscosity affects observables? modification of the distributionvariation of the flow/hypersurface Express with dissipative currents in a multi-component system Cooper-Frye formula

Akihiko MonnaiBulk Viscous Effects on Relativistic Hydrodynamic Models of the Quark-Gluon Plasma, Hawaii, Oct. 15 th 2009 Generalization of Israel-Stewart method: Macroscopic to Microscopic Express in terms of dissipative currents 5,,, Dissipative currents (given from hydro) Distortion of distribution (unknown) Macroscopic quantitiesMicroscopic quantities 14 “bridges” from Relativistic Kinetic Theory Israel & Stewart (‘76)

Akihiko MonnaiBulk Viscous Effects on Relativistic Hydrodynamic Models of the Quark-Gluon Plasma, Hawaii, Oct. 15 th 2009 Grad’s 14-moment method 14 unknowns, in Multi-Component System 6 where and are calculated in kinetic theory. No scalar, but non-zero trace tensor The distortion is uniquely obtained: : 2 nd law of thermodynamics + constitutive equation New tensor structure for multi-component system

Akihiko MonnaiBulk Viscous Effects on Relativistic Hydrodynamic Models of the Quark-Gluon Plasma, Hawaii, Oct. 15 th 2009 Estimation of particle spectra (with bulk viscosity in ): Models Inputs 7 Flow, freezeout hypersurface : (3+1)-D ideal hydrodynamic model Hirano et al.(‘06) Bulk pressure: Navier-Stokes limit Transport coefficients:, where : sound velocity : entropy density Weinberg (‘71)Kovtun et al.(‘05) Equation of State: 16-component hadron resonance gas (hadrons up to, under ) Freezeout temperature:

Akihiko MonnaiBulk Viscous Effects on Relativistic Hydrodynamic Models of the Quark-Gluon Plasma, Hawaii, Oct. 15 th 2009 Au+Au,, b = 7.2(fm), p T -spectra and v 2 (p T ) of Bulk Viscosity and Particle Spectra 8 p T -spectra suppressed v 2 (p T )enhanced *Possible overestimations due to... (i) Navier-Stokes limit (no relaxation effects) (ii) ideal hydro flow (derivatives are larger)

Akihiko MonnaiBulk Viscous Effects on Relativistic Hydrodynamic Models of the Quark-Gluon Plasma, Hawaii, Oct. 15 th 2009 Determination of in a multi-component system - Viscous correction has non-zero trace. Visible effects of on particle spectra - p T -spectra is suppressed; v 2 (p T ) 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. Summary and Outlook 9

Akihiko MonnaiBulk Viscous Effects on Relativistic Hydrodynamic Models of the Quark-Gluon Plasma, Hawaii, Oct. 15 th nd order Israel-Stewart theory Estimation of Dissipative Currents 10 AM and T. Hirano, in preparation Naïve generalization to a multi-component system does NOT work Constitutive equations in a multi-component system: Bulk pressure Shear tensor in conformal limit reduces to AdS/CFT result (Baier et al. ‘08) Navier-Stokes term Israel-Stewart 2 nd order terms Post Israel-Stewart 2 nd order terms

Akihiko MonnaiBulk Viscous Effects on Relativistic Hydrodynamic Models of the Quark-Gluon Plasma, Hawaii, Oct. 15 th 2009 The numerical code will become available at Thank You 11

Akihiko MonnaiBulk Viscous Effects on Relativistic Hydrodynamic Models of the Quark-Gluon Plasma, Hawaii, Oct. 15 th 2009 Appendix 12

Akihiko MonnaiBulk Viscous Effects on Relativistic Hydrodynamic Models of the Quark-Gluon Plasma, Hawaii, Oct. 15 th 2009 p T -spectra and v 2 (p T ) of with shear viscous correction Shear Viscosity and Particle Spectra 13 Non-triviality of shear viscosity; both p T -spectra and v 2 (p T ) suppressed

Akihiko MonnaiBulk Viscous Effects on Relativistic Hydrodynamic Models of the Quark-Gluon Plasma, Hawaii, Oct. 15 th 2009 p T -spectra and v 2 (p T ) of with corrections from shear and bulk viscosity Shear & Bulk Viscosity on Spectra 14 Accidental cancellation in viscous corrections in v 2 (p T )

Akihiko MonnaiBulk Viscous Effects on Relativistic Hydrodynamic Models of the Quark-Gluon Plasma, Hawaii, Oct. 15 th 2009 p T -spectra and v 2 (p T ) of when Quadratic Ansatz 15 Effects of the bulk viscosity is underestimated in the quadratic ansatz.

Akihiko MonnaiBulk Viscous Effects on Relativistic Hydrodynamic Models of the Quark-Gluon Plasma, Hawaii, Oct. 15 th 2009 p T -spectra and v 2 (p T ) of in Bjorken model with cylindrical geometry: Bjorken Model 16 Bulk viscosity suppresses p T -spectra Shear viscosity enhances p T -spectra

Akihiko MonnaiBulk Viscous Effects on Relativistic Hydrodynamic Models of the Quark-Gluon Plasma, Hawaii, Oct. 15 th 2009 p T -spectra and v 2 (p T ) of Blast wave model 17 Shear viscosity enhances p T -spectra and suppresses v 2 (p T ).