Upload
keefe
View
40
Download
0
Embed Size (px)
DESCRIPTION
B ulk V iscous E ffects on R elativistic H ydrodynamic M odels of the Q uark- G luon P lasma. Akihiko Monnai Department of Physics, The University of Tokyo Collaborator: Tetsufumi Hirano. 3 rd Joint Meeting of the Nuclear Physics Divisions of the APS and the JPS - PowerPoint PPT Presentation
Citation preview
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).