Transcript Bulk Viscous Effects on Relativistic Hydrodynamic Models

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,
arXiv:0903.4436; arXiv:0907.3078
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Outline

Introduction
Relativistic viscous hydrodynamics

Distortion of Distribution
How to express

Numerical Estimation
Effects of

in terms of dissipative currents
on observables
Summary and Outlook
Summary and constitutive equations
Bulk Viscous Effects on Relativistic Hydrodynamic Models of the Quark-Gluon Plasma, Hawaii, Oct. 15th 2009
Akihiko Monnai
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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
Bulk viscosity =
response of pressure
to volume change
Mizutani et al. (‘88)
Paech & Pratt (‘06)
Kharzeev & Tuchin (’08) …
Bulk Viscous Effects on Relativistic Hydrodynamic Models of the Quark-Gluon Plasma, Hawaii, Oct. 15th 2009
Akihiko Monnai
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Introduction

How does bulk viscosity affects observables?
One needs a translator of flow field into particles at freezeout
hydro result
observables
Cooper-Frye formula
particles
freezeout hypersurface Σ
variation of thehadron
flow/hypersurface
particles
hadron
resonance
gas
resonance
QGP
freezeout
gas hypersurface Σ
modification of the distribution
Express
with dissipative currents
in a multi-component system
QGP
Bulk Viscous Effects on Relativistic Hydrodynamic Models of the Quark-Gluon Plasma, Hawaii, Oct. 15th 2009
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Macroscopic to Microscopic

Generalization
Express
inof
terms
Israel-Stewart
of dissipative
method:
currents
Israel & Stewart (‘76)
Macroscopic quantities
,
,
Microscopic quantities
,
Dissipative currents
(given from hydro)
Distortion of distribution
(unknown)
14 “bridges” from Relativistic Kinetic Theory
Bulk Viscous Effects on Relativistic Hydrodynamic Models of the Quark-Gluon Plasma, Hawaii, Oct. 15th 2009
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in Multi-Component System

Grad’s 14-moment method
14 unknowns
,
No scalar, but non-zero trace tensor
: 2nd law of thermodynamics
+ constitutive equation

The distortion is uniquely obtained:
where
and
New tensor structure for
multi-component system
are calculated in kinetic theory.
Bulk Viscous Effects on Relativistic Hydrodynamic Models of the Quark-Gluon Plasma, Hawaii, Oct. 15th 2009
Akihiko Monnai
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Models Inputs

Estimation of particle spectra (with bulk viscosity in
Flow , freezeout hypersurface
:
(3+1)-D ideal hydrodynamic model
):
Bulk pressure:
Navier-Stokes limit
Hirano et al.(‘06)
Transport coefficients:
Equation of State: 16-component
hadron resonance gas
(hadrons up to
, under
,
)
where
: sound velocity
: entropy density
Freezeout temperature:
Weinberg (‘71)
Kovtun et al.(‘05)
Bulk Viscous Effects on Relativistic Hydrodynamic Models of the Quark-Gluon Plasma, Hawaii, Oct. 15th 2009
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Bulk Viscosity and Particle Spectra

Au+Au,
pT -spectra
, b = 7.2(fm), pT -spectra and v2(pT) of
suppressed
v2 (pT)
enhanced
*Possible overestimations due to... (i) Navier-Stokes limit (no relaxation effects)
(ii) ideal hydro flow (derivatives are larger)
Bulk Viscous Effects on Relativistic Hydrodynamic Models of the Quark-Gluon Plasma, Hawaii, Oct. 15th 2009
Akihiko Monnai
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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.
Bulk Viscous Effects on Relativistic Hydrodynamic Models of the Quark-Gluon Plasma, Hawaii, Oct. 15th 2009
Akihiko Monnai
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Estimation of Dissipative Currents
 2nd
order Israel-Stewart theory
AM and T. Hirano,
in preparation
Naïve generalization to a multi-component system
does NOT work

Constitutive equations in a multi-component system:
Bulk pressure
Navier-Stokes term
Israel-Stewart
2nd order terms
Post Israel-Stewart
2nd order terms
Shear tensor
in conformal limit reduces to AdS/CFT result (Baier et al. ‘08)
Bulk Viscous Effects on Relativistic Hydrodynamic Models of the Quark-Gluon Plasma, Hawaii, Oct. 15th 2009
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Thank You

The numerical code will become available at
http://tkynt2.phys.s.u-tokyo.ac.jp/~monnai/distributions.html
Bulk Viscous Effects on Relativistic Hydrodynamic Models of the Quark-Gluon Plasma, Hawaii, Oct. 15th 2009
Akihiko Monnai
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Appendix
Bulk Viscous Effects on Relativistic Hydrodynamic Models of the Quark-Gluon Plasma, Hawaii, Oct. 15th 2009
Akihiko Monnai
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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
Bulk Viscous Effects on Relativistic Hydrodynamic Models of the Quark-Gluon Plasma, Hawaii, Oct. 15th 2009
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Shear & Bulk Viscosity on Spectra

pT -spectra and v2(pT) of
bulk viscosity
with corrections from shear and
Accidental cancellation in viscous corrections in v2(pT)
Bulk Viscous Effects on Relativistic Hydrodynamic Models of the Quark-Gluon Plasma, Hawaii, Oct. 15th 2009
Akihiko Monnai
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Quadratic Ansatz

pT -spectra and v2(pT) of
when
Effects of the bulk viscosity is underestimated in the quadratic ansatz.
Bulk Viscous Effects on Relativistic Hydrodynamic Models of the Quark-Gluon Plasma, Hawaii, Oct. 15th 2009
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Bjorken Model

pT -spectra and v2(pT) of
geometry:
in Bjorken model with cylindrical
Bulk viscosity suppresses pT-spectra
Shear viscosity enhances pT-spectra
Bulk Viscous Effects on Relativistic Hydrodynamic Models of the Quark-Gluon Plasma, Hawaii, Oct. 15th 2009
Akihiko Monnai
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Blast wave model

pT -spectra and v2(pT) of
Shear viscosity enhances pT-spectra
and suppresses v2(pT).
Bulk Viscous Effects on Relativistic Hydrodynamic Models of the Quark-Gluon Plasma, Hawaii, Oct. 15th 2009
Akihiko Monnai