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

Akihiko MonnaiDepartment of Physics, The University of Tokyo

Collaborator: Tetsufumi Hirano

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

AM and T. Hirano, arXiv:0903.4436; arXiv:0907.3078

Akihiko MonnaiBulk Viscous Effects on Relativistic Hydrodynamic Models of the Quark-Gluon Plasma, Hawaii, Oct. 15 th 2009

IntroductionRelativistic viscous hydrodynamics

Distortion of DistributionHow to express in terms of dissipative currents

Numerical EstimationEffects of on observables

Summary and OutlookSummary and constitutive equations

Outline2

Akihiko MonnaiBulk Viscous Effects on Relativistic Hydrodynamic Models of the Quark-Gluon Plasma, Hawaii, Oct. 15 th 2009

Introduction3

Success of ideal hydrodynamic models

Development of viscous hydrodynamic models

at relativistic heavy ion collisions

to correctly extract information from experimental data

Paech & Pratt (‘06)Mizutani et al. (‘88)

Kharzeev & Tuchin (’08) …

How does bulk viscosity affects observables? It has almost been neglected, BUT bulk viscosity is not so small near

Bulk viscosity = response of pressure to volume change

Akihiko MonnaiBulk Viscous Effects on Relativistic Hydrodynamic Models of the Quark-Gluon Plasma, Hawaii, Oct. 15 th 2009

One needs a translator of flow field into particles at freezeout

Introduction4

particles

hadron resonancegas

QGP

freezeout hypersurface Σ

particles

hadronresonancegas

QGP

freezeout hypersurface Σ

hydro result observables

How does bulk viscosity affects observables?

modification of the distributionvariation of the flow/hypersurface

Express with dissipative currentsin a multi-component system

Cooper-Frye formula

Akihiko MonnaiBulk Viscous Effects on Relativistic Hydrodynamic Models of the Quark-Gluon Plasma, Hawaii, Oct. 15 th 2009

Generalization of Israel-Stewart method:

Macroscopic to MicroscopicExpress in terms of dissipative currents

5

, , , Dissipative currents(given from hydro)

Distortion of distribution(unknown)

Macroscopic quantities Microscopic quantities

14 “bridges” from Relativistic Kinetic Theory

Israel & Stewart (‘76)

Akihiko MonnaiBulk Viscous Effects on Relativistic Hydrodynamic Models of the Quark-Gluon Plasma, Hawaii, Oct. 15 th 2009

Grad’s 14-moment method 14 unknowns ,

in Multi-Component System6

where and are calculated in kinetic theory.

No scalar, but non-zero trace tensor

The distortion is uniquely obtained:

: 2nd law of thermodynamics

+ constitutive equation

New tensor structure for multi-component system

Akihiko MonnaiBulk Viscous Effects on Relativistic Hydrodynamic Models of the Quark-Gluon Plasma, Hawaii, Oct. 15 th 2009

Estimation of particle spectra (with bulk viscosity in ):

Models Inputs7

Flow , freezeout hypersurface : (3+1)-D ideal hydrodynamic modelHirano et al.(‘06)

Bulk pressure: Navier-Stokes limit

Transport coefficients:

,

where : sound velocity

: entropy

densityWeinberg (‘71) Kovtun et al.(‘05)

Equation of State: 16-component hadron resonance gas (hadrons up to , under )

Freezeout temperature:

Akihiko MonnaiBulk Viscous Effects on Relativistic Hydrodynamic Models of the Quark-Gluon Plasma, Hawaii, Oct. 15 th 2009

Au+Au, , b = 7.2(fm), pT -spectra and v2(pT) of

Bulk Viscosity and Particle Spectra8

pT -spectra　

suppressed　

v2 (pT) enhanced　

*Possible overestimations due to... (i) Navier-Stokes limit (no relaxation effects) (ii) ideal hydro flow (derivatives are larger)

Akihiko MonnaiBulk Viscous Effects on Relativistic Hydrodynamic Models of the Quark-Gluon Plasma, Hawaii, Oct. 15 th 2009

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.

Summary and Outlook9

Akihiko MonnaiBulk Viscous Effects on Relativistic Hydrodynamic Models of the Quark-Gluon Plasma, Hawaii, Oct. 15 th 2009

2nd order Israel-Stewart theory

Estimation of Dissipative Currents10

AM and T. Hirano, in

preparationNaïve 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

Akihiko MonnaiBulk Viscous Effects on Relativistic Hydrodynamic Models of the Quark-Gluon Plasma, Hawaii, Oct. 15 th 2009

The numerical code will become available athttp://tkynt2.phys.s.u-tokyo.ac.jp/~monnai/distributions.html

Thank You11

Akihiko MonnaiBulk Viscous Effects on Relativistic Hydrodynamic Models of the Quark-Gluon Plasma, Hawaii, Oct. 15 th 2009

Appendix

12

Akihiko MonnaiBulk Viscous Effects on Relativistic Hydrodynamic Models of the Quark-Gluon Plasma, Hawaii, Oct. 15 th 2009

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

Shear Viscosity and Particle Spectra13

Non-triviality of shear viscosity; both pT -spectra and v2(pT) suppressed

Akihiko MonnaiBulk Viscous Effects on Relativistic Hydrodynamic Models of the Quark-Gluon Plasma, Hawaii, Oct. 15 th 2009

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

Shear & Bulk Viscosity on Spectra14

Accidental cancellation in viscous corrections in v2(pT)

Akihiko MonnaiBulk Viscous Effects on Relativistic Hydrodynamic Models of the Quark-Gluon Plasma, Hawaii, Oct. 15 th 2009

pT -spectra and v2(pT) of when

Quadratic Ansatz15

Effects of the bulk viscosity is underestimated in the quadratic ansatz.

Akihiko MonnaiBulk Viscous Effects on Relativistic Hydrodynamic Models of the Quark-Gluon Plasma, Hawaii, Oct. 15 th 2009

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

Bjorken Model16

Bulk viscosity suppresses pT-spectraShear viscosity enhances pT-spectra

Akihiko MonnaiBulk Viscous Effects on Relativistic Hydrodynamic Models of the Quark-Gluon Plasma, Hawaii, Oct. 15 th 2009

pT -spectra and v2(pT) of

Blast wave model17

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