Bulk viscosity in heavy ion collisions Victor Roy Variable Energy Cyclotron Centre, Kolkata, India. In collaboration with Dr. A.K. Chaudhuri OUTLINE: Motivation Viscous Hydrodynamics Results Conclusions

Non zero bulk viscosity D. Kharzeev, K Tuchin pQCD JHEP0809:093,2008 Lattice input S. Weinberg, AstroPhys. J. 168,175(1971) AdS-CFT P. Benicasa et. al. NPB733,160 (2006) HRG J Noronha-Hostler et al. PRL 103,172302 (2009) is expected to be non-zero for heavy ion collision

Temperature dependence of z/s Roy & Chaudhuri G.S. Denicol et al. PRC 80,064901 (2009) arXiv:0801.3180v2 [nucl-th] Form 1 Form 2 Lattice data F karsch et al. Phys. Lett.B663, 217-221(2008) QGP Phase : QGP Phase : HRG Phase : J Noronha-Hostler et al. PRL 103,172302 (2009)

Israel-Stewart 2nd order causal viscous hydro W. Israel & J.M. Stewart Ann. Phys. 118,341 (1979) non-zero trace traceless Recently added to AZHYDRO-KOLKATA arXiv:0801.3180v2 [nucl-th] Add acausal slide in the backup, why the shear stress is traceless? Convective derivative Symmetric traceless tensor

Input to Viscous Hydrodynamics Parameters Value Thermalization time : 0.6 fm/c Initial central energy density: ~30 GeV/fm3 Initial transverse velocity : Freeze-out temperature 130 MeV Relaxation time 2η/3p Initial shear stress Initial bulk stress Initial energy density : EoS: Lattice+HRG Tc=175 MeV Au+Au Collision Impact Parameter, b=7.4 fm b=3.2 fm Borsanyi et al JHEP 11(2010)077

Transverse velocity & pT spectra of p- VTshear>Vtideal~VTbulk VTform1>VTform2 Form 1 Form 2 z/sform1<z/sform2 Spectra: Form1- <10% change Form2- <20% change Tell the change in slope of the pT spectra Shear viscous correction to freezeout distribution only.

Momentum anisotropy & Elliptic flow of p- At freeze-out Form 1 Form 2 epideal>epshear,epbulk epform1>epform2 Elliptic Flow: Form1- <5% change Form2- <10% change

Correction to freezeout distribution function The invariant yield: Correction to the ideal distribution function in Grad 14 moment : The energy momentum tensor and net baryon number current : Akihiko Monnai et al. PRC 80,054906 Tell about delta_epsilon and p_mu Landau matching condition :

Applicability: Grad’s 14 moment method Temperature B0 D0 130 MeV 1.12×105 - 3.27×104 9.1×104 140 MeV 5.60×104 - 1.98×104 5.31×104 Tell about our condition of 50% correction Akihiko Monnai et al. PRC 80,054906 Methods applicable if <0.1 z/s for Tf=130 MeV <0.05 z/s for Tf=140 MeV

Conclusions The effect of two different temperature dependent form of z/s on pion spectra and elliptic flow was studied. Reduced transverse flow velocity in bulk viscous evolution compared to both ideal and shear viscous evolution. Change in particle spectra due to bulk viscosity is ~10-20% Momentum anisotropy at freezeout reduced in both shear and bulk viscous evolution compared to ideal case. Change in elliptic flow is ~5-10%. Applicability of Grad 14 moment method for correction to freeze-out distribution function is valid only if z/s is reduced by a factor 10-20 for freeze-out temperature ~130-140 MeV. Connect the second point to third and 4th point to the 5th

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