University of Ferrara Heavy ions collision evolution modeling with - PowerPoint PPT Presentation

University of Ferrara Heavy ions collision evolution modeling with ECHO-QGP Valentina Rolando May, 20th 2014 Valentina Rolando QM 2014

ECHO-QGP Tests Summary and Outlook ECHO-QGP Collaboration The ECHO-QGP collaboration involves the Universities of Ferrara, Firenze and Torino. ECHO-QGP L. Del Zanna, V. Chandra, G. Inghirami, V. Rolando, A. Beraudo, A. De Pace, G. Pagliara, and A. Drago, and F. Becattini. Relativistic viscous hydrodynamics for heavy-ion collisions with ECHO-QGP. Eur.Phys.J. ,C73:2524, 2013. arXiv(nucl-th):1305.7052 Valentina Rolando QM 2014

ECHO-QGP Tests Summary and Outlook Overwiew on ECHO-QGP ECHO-QGP is a development of ECHO ECHO L. Del Zanna, O. Zanotti, N. Bucciantini, and P. Londrillo. ECHO: an Eulerian Conservative High Order scheme for general relativistic magnetohydrodynamics and magnetodynamics Astron.Astrophys. , 473:11–30, 2007. arXiv(astro-ph):0704.3206 The original ECHO code can handle non-vanishing conserved-number currents as well as electromagnetic fields, which are essential for the astrophysical computations, in any (3+1)-D metric of General Relativity. Valentina Rolando QM 2014

ECHO-QGP Tests Summary and Outlook Setup Initial stage: Optical Glauber model (energy density/entropy density profile) or MC Glauber model Hydro stage: the evolution can be purely ideal or viscous can handle both Minkowski or Bjorken coordinates it is designed to use any EoS, tabulated or Analytical Decoupling stage: Cooper-Frye prescription (mean spectrum and event generation) Valentina Rolando QM 2014

ECHO-QGP Tests Summary and Outlook ECHO-QGP Features ECHO-QGP has been originally conceived to be publicly released user-friendly exhaustive documentation and tutorials Designed to perform serial or parallel simulations Built-in standard tests initialization ( e.g. shock tube, Bjorken expansion, Gubser’s solution . . . ) Highly Customizable at runtime ( e.g. output, end criterion, grid, collision parameters, . . . ) Several post-processing tools already included Valentina Rolando QM 2014

ECHO-QGP Tests Summary and Outlook The equations Set of equations � � − g µν = + +  d µ N µ = 0 , +   d µ T µν = 0   Orthogonal projector  EoS π µν evolution ∆ µν ≡ g µν + u µ u ν      Π evolution Covariant derivative Conservative form d µ = − u µ D + ∇ µ � �� � ���� ∂ 0 U + ∂ k F k = S D ≡ u α d α ∇ µ ≡ ∆ α µ d α N µ = nu µ + V µ T µν = eu µ u ν + ( P + Π)∆ µν + π µν + w µ u ν + w ν u µ Valentina Rolando QM 2014

ECHO-QGP Tests Summary and Outlook Test: (2+1)-D shock tubes 0.4 Inviscid 15 Inviscid η /s=0.01 3 ) 0.3 Energy density (GeV/fm η /s=0.01 η /s=0.1 η /s=0.1 v x (c units) 10 0.2 5 0.1 0.0 0 −4 −2 0 2 4 −4 −2 0 2 4 x (fm) x (fm) T L = 0 . 4 GeV ( P L = 5 . 40 GeV/fm 3 ) and T R = 0 . 2 GeV ( P = 0 . 34 GeV/fm 3 ) η/s = 0 , 0 . 01 , 0 . 1 at t = 4 fm/c. Valentina Rolando QM 2014

ECHO-QGP Tests Summary and Outlook The effect of viscosity Valentina Rolando QM 2014

ECHO-QGP Tests Summary and Outlook Test:(2+1)-D with azimuthal symmetry Ideal Gubser Test Analytic solution from symmetry consideration 1 : 1.0 1.0 τ =2.5 τ =2 0.8 0.8 4 ) τ =1.5 Energy density (1/fm 0.6 v r (c units) 0.6 ECHO−QGP τ =1 τ =1 Analytic 0.4 0.4 ECHO−QGP τ =1.5 0.2 0.2 Analytic τ =2 τ =2.5 0.0 0.0 0 1 2 3 4 0 1 2 3 4 r (fm) r (fm) 1S. S. Gubser. constraints on generalizations of Bjorken flow. PRD 82:085027, 2010. Valentina Rolando QM 2014

ECHO-QGP Tests Summary and Outlook Test: (2+1)-D with azimuthal symmetry Viscous Gubser Test Analytic solution from symmetry consideration in for the Israel-Stewart frame 2 : 0.20 τ =1.2 ECHO−QGP τ =1.2 fm/c MUSIC τ =1.2 fm/c 0.18 ECHO−QGP τ =1.5 fm/c MUSIC τ =1.5 fm/c τ =1.5 0.16 ECHO−QGP τ =2.0 fm/c MUSIC τ =2.0 fm/c 0.14 T (GeV) τ =2.0 0.12 0.10 0.08 0.06 0.04 0 1 2 3 4 5 radius (fm) 2H. Marrochio, et al. of Conformal Israel-Stewart Relativistic Viscous Fluid Dynamics. 2013.arXiv(nucl-th):1307.6130 Valentina Rolando QM 2014

ECHO-QGP Tests Summary and Outlook Decoupling fluid to particles Isothermal hypersuface: our implementation � � − 1 T ( u ν p ν + µ i ) ± 1 � e − 1 E d 3 N i g i f i ( x, p ) = − f i ( x, p ) p µ d 3 Σ µ d p 3 = (2 π ) 3 Σ   d V ⊥ τ d V ⊥ x   d 3 Σ µ =   d V ⊥ y   d V ⊥ η   τ ∆ x ∆ y ∆ η s s τ τ ∆ y ∆ η s ∆ τ s x   =   τ ∆ η s ∆ τ ∆ x s y   1 τ ∆ τ ∆ x ∆ y s η � ∂T � s µ = − sign ∂x µ Valentina Rolando QM 2014

ECHO-QGP Tests Summary and Outlook Freeze-out routine: tests with AZHYDRO 3 10 3 0.70 AZHYDRO b=12 AZHYDRO 10 2 ECHO-QGP-freezeout routine ECHO-QGP freezeout routine 0.60 10 1 b=9 (1/2 π )dN/dyp T dp T 0.50 10 0 0.40 10 -1 b=6 v 2 0.30 10 -2 10 -3 0.20 10 -4 b=3 0.10 10 -5 0.00 0 0.5 1 1.5 2 2.5 3 0 0.5 1 1.5 2 2.5 3 3.5 4 p T [GeV] p T [GeV] σ NN τ 0 e 0 α b µ π T freeze Gev fm − 3 mb fm fm GeV GeV 40 0.6 24.5 1 0,3,6,9,12 0.0622 0.120 Table : The grid spacing here used is: ∆ x = ∆ y = 0 . 4 fm ∆ τ = 0 . 16 fm. 3P. F. Kolb, J. Sollfrank and U. W. Heinz, transverse flow and the quark hadron phase transition PRC 62:054909, 2000 Valentina Rolando QM 2014

ECHO-QGP Tests Summary and Outlook The effect of viscosity 4 δf ( x, p ) = f 0 (1 ± f 0 ) p α p β π αβ 2 T 2 ( e + p ) 10 3 0.2 ideal hydro Ideal hydro 0.18 f 0 f 0 10 2 f 0 + δ f η 0.16 f 0 + δ f (1/2 π ) dN/dyp T dp T π 0.14 10 1 k 0.12 p 10 0 v 2 0.1 0.08 10 -1 0.06 0.04 10 -2 b=5 fm 0.02 b=5 fm 10 -3 0 0 0.5 1 1.5 2 2.5 3 0 0.5 1 1.5 2 2.5 3 p T [GeV] p T [GeV] 4D. Teaney. Effects of viscosity on spectra, elliptic flow, and HBT radii. PRC 68:034913, 2003. R. Baier et al. Dissipative hydrodynamics and heavy ion collisions PRC 73:064903, 2006. Valentina Rolando QM 2014

ECHO-QGP Tests Summary and Outlook The effect of viscosity 4 δf ( x, p ) = f 0 (1 ± f 0 ) p α p β π αβ 2 T 2 ( e + p ) 0.35 200 π 180 Ideal hydro 0.30 b=7 fm k f 0 + δ f 160 p π b=0 fm 0.25 140 b=3 fm k b=5 fm 0.20 p 120 dN/dy b=7 fm v 2 b=5 fm 100 0.15 80 0.10 60 b=3 fm 0.05 40 20 0.00 0 0.5 1 1.5 2 2.5 3 0 -6 -4 -2 0 2 4 6 p T [GeV] y 4D. Teaney. Effects of viscosity on spectra, elliptic flow, and HBT radii. PRC 68:034913, 2003. R. Baier et al. Dissipative hydrodynamics and heavy ion collisions PRC 73:064903, 2006. Valentina Rolando QM 2014

ECHO-QGP Tests Summary and Outlook Summary and Outlook summary ECHO-QGP is a robust high-order shock-capturing code, solving either ideal or viscous (Israel-Stewart) hydrodynamics Modules for 1D, 2D, and 3D Minkowsky and Bjorken available ECHO-QGP reproduces the standard analytic solutions ECHO-QGP is consistent with AZHYDRO, UVH2, MUSIC ECHO-QGP will be made available soon . . . stay tuned! More ongoing physics studies (vorticity, fluctuation propagations . . . ) Valentina Rolando QM 2014

ECHO-QGP Tests Summary and Outlook Summary and Outlook summary ECHO-QGP is a robust high-order shock-capturing code, solving either ideal or viscous (Israel-Stewart) hydrodynamics Modules for 1D, 2D, and 3D Minkowsky and Bjorken available ECHO-QGP reproduces the standard analytic solutions ECHO-QGP is consistent with AZHYDRO, UVH2, MUSIC ECHO-QGP will be made available soon . . . stay tuned! More ongoing physics studies (vorticity, fluctuation propagations . . . ) Valentina Rolando QM 2014

ECHO-QGP Tests Summary and Outlook Summary and Outlook summary ECHO-QGP is a robust high-order shock-capturing code, solving either ideal or viscous (Israel-Stewart) hydrodynamics Modules for 1D, 2D, and 3D Minkowsky and Bjorken available ECHO-QGP reproduces the standard analytic solutions ECHO-QGP is consistent with AZHYDRO, UVH2, MUSIC ECHO-QGP will be made available soon . . . stay tuned! More ongoing physics studies (vorticity, fluctuation propagations . . . ) Valentina Rolando QM 2014

ECHO-QGP Tests Summary and Outlook Summary and Outlook summary ECHO-QGP is a robust high-order shock-capturing code, solving either ideal or viscous (Israel-Stewart) hydrodynamics Modules for 1D, 2D, and 3D Minkowsky and Bjorken available ECHO-QGP reproduces the standard analytic solutions ECHO-QGP is consistent with AZHYDRO, UVH2, MUSIC ECHO-QGP will be made available soon . . . stay tuned! More ongoing physics studies (vorticity, fluctuation propagations . . . ) Valentina Rolando QM 2014

ECHO-QGP Tests Summary and Outlook Summary and Outlook summary ECHO-QGP is a robust high-order shock-capturing code, solving either ideal or viscous (Israel-Stewart) hydrodynamics Modules for 1D, 2D, and 3D Minkowsky and Bjorken available ECHO-QGP reproduces the standard analytic solutions ECHO-QGP is consistent with AZHYDRO, UVH2, MUSIC ECHO-QGP will be made available soon . . . stay tuned! More ongoing physics studies (vorticity, fluctuation propagations . . . ) Valentina Rolando QM 2014