Viscous hydrodynamics with shear and bulk viscosity Huichao

Viscous hydrodynamics with shear and bulk viscosity Huichao Song and Ulrich Heinz The Ohio State University Supported by DOE Quark Matter 2009 March 30 -April 4, Knoxville, TN 04/02/2009

Glauber Luzum & Romatschke, PRC 2008 CGC -Glauber vs. CGC ~100% effect on the extracted value of -A detailed extraction of shear viscosity entropy ratio also requires: -viscous late hadronic stage -non-equilibrium chemistry in HG -bulk viscosity ? -Present conservative upper has been studied in ideal hydro 5

Viscous hydro with shear & bulk viscosity shear viscosity bulk viscosity Conservation laws: Evolution equations for shear pressure tensor and bulk presurre: (2 nd order shear-bulk -mixing term (Muronga, Rischke) not included. )

Numerical Results Shear viscosity: Bulk viscosity: HRG QGP Min. Ad. S/CFT prediction Relaxation times: (see later)

Shear viscosity vs. bulk viscosity (I) Same initial & final conditions ideal hydro viscous hydro-shear only viscous hydro-bulk only Local temperature -Shear viscosity: decelerate cooling process in early stage accelerate cooling process in middle and late stages -Bulk viscosity: decelerate cooling process

Shear viscosity vs. bulk viscosity (II) Same Initial & final conditions ideal hydro viscous hydro-shear only radial flow viscous hydro-bulk only spectra -shear viscosity: increases radial flow, results in flatter spectra -bulk viscosity: decreases radial flow, results in steeper spectra

Shear viscosity vs. bulk viscosity (III) Same Initial & final conditions ideal hydro viscous hydro-shear only Elliptical flow v 2 -v 2 is sensitive to both shear and bulk viscosity viscous hydro-bulk only

Viscous v 2 suppression: shear and bulk viscosity ideal hydro visc. hydro: 30% 20% -at RHIC, 2 x min. bulk viscosity could result in ~50% additional v 2 suppression -when extracting the from RHIC data, bulk viscous effects cannot be neglected

Viscous v 2 suppression: shear and bulk viscosity ideal hydro visc. hydro: 30% 20% -at RHIC, 2 x min. bulk viscosity could result in ~50% additional v 2 suppression -when extracting the bulk viscosity effects: from RHIC data, bulk viscous effects cannot be neglected (a) Change the flow profile during hydro evolution (b) Additional spectra correction along freeze-out surface Song & Heinz: v 2 will decrease, flow corrections only (a), , at freeze-out Monnai & Hirano: v 2 will increase, spectra corrections only(b), ideal hydro for evolution

Bulk Viscosity -relaxation time effects

Bulk viscous v 2 suppression: -- Smaller vs. larger relaxation time -viscous effects from bulk viscosity strongly depend on relaxation time and the initialization for bulk pressure

Effects from initialization of (I) Smaller relaxation time -When is small , is insensitive to different initializations of -after (several relaxation times), viscous pressure loses memory of initial cond.

Effects from initialization of (II) larger relaxation time -When is larger , is sensitive to different initializations of -after (several relaxation times), viscous pressure loses memory of initial cond.

Effects from initialization of (III) Smaller vs. larger relaxation time -viscous effects from bulk viscosity strongly depend on relaxation time and the initialization for bulk pressure

A Short Summary -first attempts to constrain from RHIC data indicate No consistent simultaneous treatment yet of: a realistic EOS, initialization, bulk viscosity, highly viscous hadronic stage -When extracting QGP viscosity from experimental data, bulk viscosity effects should not be neglected -More theoretical inputs are needed for bulk viscosity: - relaxation time - initialization for bulk - bulk viscosity of hadronic phase, etc pressure

Thank You 16

Viscous hydro: a short summary for shear viscosity --shear viscosity -2+1 -d viscous hydro code individually developed onlyby different Romatsche & Romatschke (INT), groups: Huovinen & Molnar (Purdue), Song & Heinz (OSU), Dusling & Teaney (Stony) Chaudhuri (Kolkata, India) -v 2 at RHIC is sensitive to even the minimum shear viscosity entropy -v 2 suppression from different groups ranges from 20% to ratio 70% -the above discrepancy was largely resolved by investigating effects from system size, Eo. S and different forms of I-S eqns. used Song & Heinz, PRC 78 (2008) 20% 70% -Code checking within the TECHQM collaboration: TECHQM webpage -The first attempt to extract QGP shear viscosity from RHIC Luzum & Romatschke, PRC 78 (2008) data:

Viscous hydro in 2+1 -dimension Bjorken coordinates 3+1 2+1 approximation: --the transport equations for energy momentum tensor are explicit written as: -shear tensor decelerate longitudinal expansion, but accelerate transverse expansion -bulk pressure decelerates both longitudinal & transverse expansion (bulk pressure effectively softens the Eo. S near the QCD phase transition)

Shear viscosity vs. bulk viscosity (I) The same Initial & final conditions: ideal hydro viscous hydro-shear only Local temperature viscous hydro-bulk only Local temperature -Shear viscosity: slowing down of cooling process due to decelerated longitudinal expansion initially, but faster cooling in middle and late stages due to stronger transverse expansion -Bulk viscosity: slowing down of cooling process, since it decelerate longitudinal and transverse expansion; most of the effects in mixed phase region

Effects from initialization of Song & Heinz, PLB 08 & PRC 77(2008) vs. -after ~1 fm/c (several relaxation times), viscous pressure loses memory of initial cond. is insensitive to different initializations of -Effects on entropy production: ~20%

EOS