1. 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

2. 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, (2009)
is expected to be non-zero for heavy ion collision

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

4. 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: v2 [nucl-th]
Add acausal slide in the backup, why the shear stress is traceless?
Convective derivative
Symmetric traceless tensor

5. 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

6. 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.

7. 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

8. 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 :

9. 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

10. 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 for
freeze-out temperature ~ MeV.
Connect the second point to third and 4th point to the 5th

11. Extra Slides