Akihiko Monnai

1
Bulk Viscous Effects on Relativistic Hydrodynamic
Models of the Quark-Gluon Plasma

• Akihiko Monnai
• Department of Physics, The University of Tokyo
• Collaborator Tetsufumi Hirano

• 3rd Joint Meeting of the Nuclear Physics
  Divisions of the APS and the JPS
• October 15th 2009, Hawaii USA

AM and T. Hirano, arXiv0903.4436
arXiv0907.3078
2
Outline

• Introduction
• Relativistic viscous hydrodynamics
• Distortion of Distribution
• How to express in terms of dissipative
  currents
• Numerical Estimation
• Effects of on observables
• Summary and Outlook
• Summary and constitutive equations

3
Introduction

Success of ideal hydrodynamic models
at relativistic heavy ion collisions
Development of viscous hydrodynamic models
to correctly extract information from
experimental data
How does bulk viscosity affects observables?
It has almost been neglected, BUT bulk viscosity
is not so small near
Mizutani et al. (88)
Bulk viscosity response of pressure to volume
change
Paech Pratt (06)

Kharzeev Tuchin (08)
4
Introduction

• One needs a translator of flow field into
  particles at freezeout

How does bulk viscosity affects observables?
hydro result
observables
Cooper-Frye formula
particles
freezeout hypersurface S
hadron resonance gas
modification of the distribution
variation of the flow/hypersurface
QGP
Express with dissipative currents in a
multi-component system
5
Macroscopic to Microscopic

• Generalization of Israel-Stewart method

Express in terms of dissipative currents
Israel Stewart (76)
Macroscopic quantities
Microscopic quantities
, , ,
Distortion of distribution (unknown)
Dissipative currents (given from hydro)
14 bridges from Relativistic Kinetic Theory
6
in Multi-Component System

• Grads 14-moment method 14 unknowns
  ,

No scalar, but non-zero trace tensor
2nd law of thermodynamics
constitutive equation
New tensor structure for multi-component system

• The distortion is uniquely obtained

7
Models Inputs

• Estimation of particle spectra (with bulk
  viscosity in )

Flow , freezeout hypersurface
(31)-D ideal hydrodynamic model
Bulk pressure
Navier-Stokes limit
Hirano et al.(06)
Transport coefficients
, where sound
velocity entropy
density
Equation of State 16-component hadron resonance
gas (hadrons up to , under
)
Freezeout temperature
Weinberg (71)
Kovtun et al.(05)
8
Bulk Viscosity and Particle Spectra

• AuAu, , b
  7.2(fm), pT -spectra and v2(pT) of

pT -spectra
suppressed
v2 (pT)
enhanced
Possible overestimations due to... (i)
Navier-Stokes limit (no relaxation effects)

(ii) ideal hydro flow (derivatives are
larger)
9
Summary and Outlook

• Determination of in a multi-component
  system
• - Viscous correction has non-zero
  trace.
• Visible effects of on particle spectra
• - pT-spectra is suppressed v2(pT) is
  enhanced
• Bulk viscosity can be important in extracting
  information (e.g. transport coefficients) from
  experimental data.
• Full Viscous hydrodynamic models need to be
  developed to see more realistic behavior of the
  particle spectra.

10
Estimation of Dissipative Currents
AM and T. Hirano, in preparation

• 2nd order Israel-Stewart theory

Naïve generalization to a multi-component system
does NOT work

• Constitutive equations in a multi-component
  system
• Bulk pressure
• Shear tensor in conformal limit reduces
  to AdS/CFT result (Baier et al. 08)

Navier-Stokes term
Israel-Stewart 2nd order terms
Post Israel-Stewart 2nd order terms
11
Thank You

• The numerical code will become available at
• http//tkynt2.phys.s.u-tokyo.ac.jp/monnai/distrib
  utions.html

12
Appendix
13
Shear Viscosity and Particle Spectra

• pT -spectra and v2(pT) of with shear
  viscous correction

Non-triviality of shear viscosity both pT
-spectra and v2(pT) suppressed
14
Shear Bulk Viscosity on Spectra

• pT -spectra and v2(pT) of with corrections
  from shear and bulk viscosity

Accidental cancellation in viscous corrections in
v2(pT)
15
Quadratic Ansatz

• pT -spectra and v2(pT) of when

Effects of the bulk viscosity is underestimated
in the quadratic ansatz.
16
Bjorken Model

• pT -spectra and v2(pT) of in Bjorken model
  with cylindrical geometry

Bulk viscosity suppresses pT-spectra Shear
viscosity enhances pT-spectra
17
Blast wave model

• pT -spectra and v2(pT) of

Shear viscosity enhances pT-spectra and
suppresses v2(pT).