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

1. Motivation

PRL 92 (2004) 052302P.F. Kolb and U. Heinz nucl-th/0305084

viscous effects?

P.F. Kolb

Ideal hydrodynamics can not describe particle spectral and elliptic flow at large transverse momentum.

Can not fit HBT results.

bulk viscosity?

M. Luzum and P. Romatschke, PRC 78 (2008) 034915

P. Romatschke, EPJC 52 (2007), 203

Effects of shear viscosity

Decrease elliptic flow.

: 0—0.16

Theoretical calculations for bulk viscosity

-lattice SU(3) gluon dynamics:

Harvey B. Meyer, PRL, 100 (2008), 162001

-strongly coupled AdS/CFT prediction:

A. Buchel, PLB, 663 (2008), 286

-weakly coupled QCD prediction:

P. Arnold etal, PRD, 74 (2006), 085021

reaches a peak near phase transition, people need to investigate the influence of the bulk viscosity!

Equations in viscous hydrodynamicsConservation law:

Evolution equations for bulk viscous pressure and shear pressure tensor:

Numerical codes are based on:

bulk viscous pressure

shear pressure tensor

R. Baier and P. Romatschke, EPJC 51 (2007), 667 P. Romatschke, EPJC 52 (2007), 203

P. Romatschke and U. Romatschke, PRL 99 (2007)172301

Central collision:

Noncentral collision:

Input parameters

-Initial condition for energy density:Glauber model

-Equation of state:

-Freeze-out mechanism:

The correction for distribution function due to bulk viscosity is not included.

M. Laine and Y. Schroder

PRD 73 (2006) 085009

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

The determinant of the matrix vanishes

1. small k limit:

2. large k limit:

2. Central collisionsShear viscosity:

Bulk viscosity:

Relaxation times:

or

-dissipate to other places at late time

-smaller relaxation time, larger effects

-time averaged bulk viscosity is more important

Efficient large peak leads to instability?

(a) shear viscosity only

(b) with bulk viscosity, larger peak, smaller width(c) with bulk viscosity, smaller peak, larger width

-decelerate cooling process

-the ratio of HBT radius are not so sensitive to bulk viscosity

-decrease transverse flow, results in steeper particle spectral

(a) shear viscosity only

(b) with bulk viscosity, larger peak, smaller width(c) with bulk viscosity, smaller peak, larger width

3. Noncentral collisions

Shear viscosity:

Bulk viscosity:

Min. AdS/CFT prediction

Relaxation times:

-preliminary results

(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

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.

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.

Thank You

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