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Jianwei Li, Yugang Ma and Guoliang Ma Shanghai Institute of Applied Physics, CAS

Effects of bulk viscosity in causal viscous hydrodynamics. Jianwei Li, Yugang Ma and Guoliang Ma Shanghai Institute of Applied Physics, CAS. 1. Motivation

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Jianwei Li, Yugang Ma and Guoliang Ma Shanghai Institute of Applied Physics, CAS

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  1. Effects of bulk viscosity in causal viscous hydrodynamics Jianwei Li, Yugang Ma and Guoliang Ma Shanghai Institute of Applied Physics, CAS 1. Motivation 2. Central collisions 3. Noncentral collisions 4. Summary

  2. 1. Motivation Ideal hydrodynamics can not describe particle spectral and elliptic flow at large transverse momentum. P.F. Kolb and U. Heinz nucl-th/0305084 PRL 92 (2004) 052302 Can not fit HBT results. viscous effects? P.F. Kolb

  3. Effects of shear viscosity Decrease elliptic flow. : 0—0.16 M. Luzum and P. Romatschke, PRC 78 (2008) 034915 bulk viscosity? P. Romatschke, EPJC 52 (2007), 203

  4. Theoretical calculations for bulk viscosity -weakly coupled QCD prediction: P. Arnold etal, PRD, 74 (2006), 085021 -lattice SU(3) gluon dynamics: Harvey B. Meyer, PRL, 100 (2008), 162001 -strongly coupled AdS/CFT prediction:‏ A. Buchel, PLB, 663 (2008), 286 reaches a peak near phase transition, people need to investigate the influence of the bulk viscosity!

  5. Equations in viscous hydrodynamics Conservation law: shear pressure tensor bulk viscous pressure Evolution equations for bulk viscous pressure and shear pressure tensor: Numerical codes are based on: R. Baier and P. Romatschke, EPJC 51 (2007), 667 P. Romatschke, EPJC 52 (2007), 203 Central collision: Noncentral collision: P. Romatschke and U. Romatschke, PRL 99 (2007)172301

  6. Input parameters -Initial condition for energy density: Glauber model -Equation of state: M. Laine and Y. Schroder PRD 73 (2006) 085009 -Freeze-out mechanism: The correction for distribution function due to bulk viscosity is not included.

  7. A linear plane wave perturbation propagate in a static homogeneous equilibrium fluid background.

  8. The determinant of the matrix vanishes 1. small k limit:

  9. 2. large k limit:

  10. 2. Central collisions Shear viscosity: Bulk viscosity: Relaxation times: or

  11. (a) shear viscosity only Efficient large peak leads to instability? (b) with bulk viscosity, larger peak, smaller width (c) with bulk viscosity, smaller peak, larger width -decelerate cooling process -dissipate to other places at late time -time averaged bulk viscosity is more important -smaller relaxation time, larger effects

  12. (a) shear viscosity only (b) with bulk viscosity, larger peak, smaller width (c) with bulk viscosity, smaller peak, larger width -decrease transverse flow, results in steeper particle spectral -the ratio of HBT radius are not so sensitive to bulk viscosity

  13. 3. Noncentral collisions -preliminary results Shear viscosity: Bulk viscosity: Min. AdS/CFT prediction Relaxation times:

  14. (a) shear viscosity only (b) Min. bulk viscosity (c) larger bulk viscosity -decelerate cooling process -decrease transverse flow, results in steeper particle spectral -larger effects at larger impact parameter

  15. Viscous v2 suppression: -At low transverse momentum, bulk viscosity will result in about 40% additional suppression. This suppression is enhanced at larger impact parameter. -bulk viscosity can not be neglected especially at large impact parameter.

  16. 4. Summary -bulk viscosity will decrease the cooling process in hydrodynamics -the ratio of HBT radius is not sensitive to bulk viscosity in central collision -the elliptic flow is sensitive to bulk viscosity, especially at large impact parameters.

  17. Thank You 17

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