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Viscous hydrodynamics

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.

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Viscous hydrodynamics

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  1. 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

  2. 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 has been studied in ideal hydro -non-equilibrium chemistry in HG -bulk viscosity ? 5 -Present conservative upper limit:

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

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

  5. 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: deceleratecooling process

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

  7. Shear viscosity vs. bulk viscosity (III) Same Initial & final conditions ideal hydro viscous hydro-shear only viscous hydro-bulk only Elliptical flow v2 -v2 is sensitive to both shear and bulk viscosity

  8. Viscous v2 suppression: shearandbulk viscosity ideal hydro visc. hydro: 30% 20% -at RHIC, 2 x min. bulk viscositycould result in ~50% additional v2 suppression -when extracting the from RHIC data, bulk viscous effects cannot be neglected

  9. Viscous v2 suppression: shearandbulk viscosity ideal hydro visc. hydro: 30% 20% -at RHIC, 2 x min. bulk viscositycould result in ~50% additional v2 suppression -when extracting the from RHIC data, bulk viscous effects cannot be neglected (a) Change the flow profile during hydro evolution bulk viscosity effects: (b) Additional spectra correction along freeze-out surface Song & Heinz: v2 will decrease, flow corrections only (a),, at freeze-out Monnai& Hirano: v2 will increase,spectra corrections only(b), ideal hydro for evolution

  10. Bulk Viscosity -relaxation time effects

  11. Bulk viscous v2 suppression: -- Smaller vs.largerrelaxation time -viscous effects from bulk viscosity strongly depend on relaxation time and the initialization for bulk pressure

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

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

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

  15. 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 pressure - bulk viscosity of hadronic phase, etc

  16. Thank You

  17. --shear viscosity only Viscous hydro: a short summary for shear viscosity -2+1-d viscous hydro code individually developed by different groups: Romatsche & Romatschke (INT), Song & Heinz (OSU), Dusling & Teaney (Stony) Huovinen & Molnar (Purdue), Chaudhuri (Kolkata, India) -v2 at RHIC is sensitive to even the minimum shear viscosity entropy ratio -v2 suppression from different groups ranges from 20% to 70% -the above discrepancy was largely resolved by investigating effects from system size, EoS 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 data: Luzum & Romatschke, PRC 78 (2008)

  18. Viscous hydro in 2+1-dimension 3+1 2+1 coordinates Bjorken 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 EoS near the QCD phase transition)

  19. Shear viscosity vs. bulk viscosity (I) The same Initial & final conditions: ideal hydro viscous hydro-shear only viscous hydro-bulk only Local temperature 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

  20. - is insensitive to different initializations of Effects from initialization of Song & Heinz, PLB08 & PRC 77(2008) vs. -after ~1fm/c (several relaxation times), viscous pressure loses memory of initial cond. -Effects on entropy production: ~20%

  21. EOS EOS

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