Event-by-event distribution of azimuthal asymmetries in ultrarelativistic heavy-ion collisions Hannu Holopainen Frankfurt Institute for Advanced Studies in collaboration with G. S. Denicol, P. Huovinen, H. Niemi and D. H. Rischke VIII Workshop on Particle Correlations and Femtoscopy Frankfurt am Main 12.9.2012 WPCF 2012 12.9.2012 H. Holopainen (FIAS) 1/21
Event-by-event hydrodynamics Why are we interested in ebye hydrodynamics? We can get correct v 2 in central collisions. Triangular flow! Fluctuations of v n. Higher harmonics and correlation between different harmonics. v 2 0.1 (a) 0-5% charged v2{ep} v2{pp} v2{rp} v2{smooth} 0.0 0.0 0.5 1.0 1.5 p T [GeV] HH, Niemi, Eskola PRC83 (2011) 034901 WPCF 2012 12.9.2012 H. Holopainen (FIAS) 2/21
Event-by-event hydrodynamics Viscous ebye reproduces the data pretty well. v n 0.15 0.1 0.05 v 2 v 3 v 4 v 5 PHENIX v 2 PHENIX v 3 PHENIX v 4 η/s=0.08 0-10% 0.3 5 0.15 0.1 v 2 20-30% v 3 20-30% v 4 20-30% v 5 20-30% PHENIX v 2 PHENIX v 3 PHENIX v 4 η/s=0.08 0.05 0 0 0.5 1 1.5 2 2.5 3 p T [GeV] 0 0 0.5 1 1.5 2 2.5 3 p T [GeV] Schenke, Jeon, Gale, Phys. Rev. C85, 024901 (2012) If ebye hydro really works, one can apply hydro in each event we should be able to reproduce the v n distributions! WPCF 2012 12.9.2012 H. Holopainen (FIAS) 3/21
Hydrodynamical model WPCF 2012 12.9.2012 H. Holopainen (FIAS) 4/21
Our model Hydrodynamical model previously employed in Niemi, Denicol, Huovinen, Molnar, Rischke, Phys. Rev. Lett. 106, 212302 (2011) Niemi, Denicol, Huovinen, Molnar, Rischke, Phys. Rev. C86, 014909 (2012) 2+1D viscous hydrodynamics, Bjorken in beam direction No net-baryon number EoS: s95p-pce-v1 Huovinen, Petreczky, NPA837 (2010) 26-53 Chemical freeze-out T c = 150 MeV Kinetical decoupling T f = 100 MeV Hadrons only up to mass 1.1 GeV, 2- and 3-particle decays Initial state from Monte Carlo Glauber Velocities and shear-stress tensor initialized to zero WPCF 2012 12.9.2012 H. Holopainen (FIAS) 5/21
Initial states Nucleons are distributed into nuclei using Woods-Saxon. No finite size or NN-correlation effects included. Random impact parameter from dn/db b. Nucleons collide if (x i x j ) 2 +(y i y j ) 2 σ NN π σ NN = 42 mb for RHIC. 10 8 6 4 2 y [fm] -10-8 -6-4 -2 2 4 6 8 10-2 -4-6 -8-10 HH, Niemi, Eskola PRC83 (2011) 034901 HH PhD thesis x [fm] WPCF 2012 12.9.2012 H. Holopainen (FIAS) 6/21
Initial profiles from MCG We use sbc and swn profiles with Gaussian smearing, i.e s(x, y) = const. wn,bc where σ = 0.8 fm. We choose τ 0 = 1 fm. y [fm] T [MeV] 10 8 6 4 2 0-2 -4-6 -8-10 -10-8 -6-4 -2 0 2 4 6 8 10 x [fm] σ = 0.4 fm 1 [ 2πσ 2 exp (x x i) 2 +(y y i ) 2 ] 2σ 2, 500 450 400 350 300 250 200 150 100 50 0 y [fm] T [MeV] 10 8 6 4 2 0-2 -4-6 -8-10 -10-8 -6-4 -2 0 2 4 6 8 10 x [fm] σ = 0.8 fm WPCF 2012 12.9.2012 H. Holopainen (FIAS) 7/21 500 450 400 350 300 250 200 150 100 50 0
Centrality classes Let s use the number of BC/WN to define the centrality classes. Impact parameter varies freely in each centrality class. N/N tot 10-1 10-2 10-3 10-4 10-5 30-40% Au+Au snn = 200 GeV 20-30% 10-20% 5-10% 0-5% 0 100 200 300 400 N part Centrality N part range N part b [fm] 0-5 % 325-394 352 2.25 5-10 % 276-324 299 4.07 10-20 % 197-275 234 5.72 20-30 % 138-196 166 7.40 30-40 % 93-137 114 8.76 Centrality N bin range N part b [fm] 0-5 % 1405-951 351 2.27 5-10 % 950-752 299 4.04 10-20 % 752-471 234 5.71 20-30 % 470-284 166 7.38 30-40 % 283-161 114 8.74 HH, Niemi, Eskola PRC83 (2011) 034901 WPCF 2012 12.9.2012 H. Holopainen (FIAS) 8/21
v n determination We use event plane method v n = dφ cos[n(φ ψn )] dn dydφ dφ dn dydφ = cos[n(φ ψ n )] ψ n = (1/n) arctan ( p Ty / ptx ) We know the orientation of the event plane exactly! Remember this if comparing with the data. (e.g. Luzum, Ollitrault, The event-plane method is obsolete, arxiv:1209.2323 [nucl-ex]) WPCF 2012 12.9.2012 H. Holopainen (FIAS) 9/21
Results WPCF 2012 12.9.2012 H. Holopainen (FIAS) 10/21
Correlations v 2, ǫ 2 v 2 0.14 0.12 0.10 0.08 0.06 c( 2,v 2) =0.979 C 2 =07 (a) v 2 0.10 0.08 0.06 0.04 c( 2,v 2) =0.989 C 2 =0.147 (b) 0.04 0.02 sbc /s =0 0.02 sbc /s =0.16 20 30 % 20 30 % 0.1 0.3 0.4 0.5 0.6 2 0.1 0.3 0.4 0.5 0.6 2 Clear linear correlation between ǫ 2 and v 2. c(a, b) = ( )( ) a a ev b b ev σ a σ b ev WPCF 2012 12.9.2012 H. Holopainen (FIAS) 11/21
Correlations v 3, ǫ 3 0.06 0.05 0.04 c( 3,v 3) =0.893 C 3 =0.176 (a) 0.030 0.025 0.020 c( 3,v 3) =0.954 C 3 =0.087 (b) v 3 0.03 v 3 0.015 0.02 0.010 0.01 sbc /s =0 0.005 sbc /s =0.16 2030 % 2030 % 0.05 0.10 0.15 0 5 0.30 0.35 3 0.05 0.10 0.15 0 5 0.30 0.35 3 Clear linear correlation between ǫ 3 and v 3. c(a, b) = ( )( ) a a ev b b ev σ a σ b ev WPCF 2012 12.9.2012 H. Holopainen (FIAS) 12/21
Correlations v 4, ǫ 4 0.04 0.03 c( 4,v 4) =0.199 C 4 =0.109 (a) 0.016 0.014 0.012 0.010 c( 4,v 4) =0.199 C 4 =0.032 (b) v 4 v 4 0.008 0.02 0.006 0.01 sbc /s =0 2030 % 0.004 0.002 sbc /s =0.16 2030 % 0.05 0.10 0.15 0 5 0.30 0.35 4 0.05 0.10 0.15 0 5 0.30 0.35 4 For n = 4 there is basically no correlation. c(a, b) = ( )( ) a a ev b b ev σ a σ b ev WPCF 2012 12.9.2012 H. Holopainen (FIAS) 13/21
Correlations v 4, ǫ 4 v 4 0.010 0.008 0.006 0.004 c( 4,v 4) =0.511 C 4 =0.039 (b) v 4 0.016 0.014 0.012 0.010 0.008 0.006 c( 4,v 4) =0.199 C 4 =0.032 (b) 0.002 sbc /s =0.16 05 % 0.004 0.002 sbc /s =0.16 2030 % 0.05 0.10 0.15 0 4 0.05 0.10 0.15 0 5 0.30 0.35 4 However, in central collisions we can see the correlation, why? WPCF 2012 12.9.2012 H. Holopainen (FIAS) 14/21
Correlations v 4, ǫ 4 best est. v 4 rms 1 0.8 0.6 0.4 0 Ε 4 Ε 6,4 Ε 2,4 2 Ε 4 andε 2 2 Ε 2 0 10 20 30 40 50 60 centrality Gardim, Grassi, Luzum, Ollitrault Phys. Rev. C85, 024908 (2012) v 4 comes from ǫ 4 and ǫ 2 2. In central collisions contribution from ǫ 2 2 is weak we see ǫ 4, v 4 correlation In more peripheral collisions ǫ 2 2 is more important no ǫ 4, v 4 correlation WPCF 2012 12.9.2012 H. Holopainen (FIAS) 15/21
v 2 distributions 1.2 <v 2 <v 2 > =0.061 ('/s =0.0) > =0.043 ('/s =0.16) sbc %/s =0.0 sbc %/s =0.16 1.2 <v 2 <v 2 > =0.039 (swn) > =0.043 (sbc) swn -/s =0.16 sbc -/s =0.16 1.0 sbc & 2 1.0 swn. 2 sbc. 2 2) $##v2 ), P( 0.8 (a) 2),++v2 ), P( 0.8 (a) 0.6 0.6 P( 0.4 P( 0.4 0.0 1.0 0.5 0.0 0.5 1.0 1.5 2.0 2.5 (v 2! <v 2 >)/ <v 2 >, (" 2! <" 2 >)/ <" 2 > 0.0 (1.0 (0.5 0.0 0.5 1.0 1.5 2.0 2.5 (v 2 ) <v 2 >)/ <v 2 >, (* 2 ) <* 2 >)/ <* 2 > Distributions are not sensitive to transport properties! sbc and swn initial states are similar since they come from the same Glauber model. WPCF 2012 12.9.2012 H. Holopainen (FIAS) 16/21
v 3 distributions 1.2 <v 3 <v 3 > =0.023 (6/s =0.0) > =0.011 (6/s =0.16) sbc 4/s =0.0 sbc 4/s =0.16 1.2 <v 3 <v 3 > =0.012 (swn) > =0.011 (sbc) swn </s =0.16 sbc </s =0.16 1.0 sbc 5 3 1.0 swn = 3 sbc = 3 3) 322v3 ), P( 0.8 (b) 3) ;::v3 ), P( 0.8 (b) 0.6 0.6 P( 0.4 P( 0.4 0.0 /1.0 /0.5 0.0 0.5 1.0 1.5 2.0 2.5 (v 3 0 <v 3 >)/ <v 3 >, (1 3 0 <1 3 >)/ <1 3 > 0.0 71.0 70.5 0.0 0.5 1.0 1.5 2.0 2.5 (v 3 8 <v 3 >)/ <v 3 >, (9 3 8 <9 3 >)/ <9 3 > Distributions are not sensitive to transport properties! sbc and swn initial states are similar since they come from the same Glauber model. WPCF 2012 12.9.2012 H. Holopainen (FIAS) 17/21
v 4 distributions 1.2 <v 4 <v 4 > =0.013 (E/s =0.0) > =0.004 (E/s =0.16) sbc C/s =0.0 sbc C/s =0.16 1.2 <v 4 <v 4 > =0.003 (swn) > =0.004 (sbc) swn K/s =0.16 sbc K/s =0.16 1.0 sbc D 4 1.0 swn L 4 sbc L 4 4) BAAv4 ), P( 0.8 (c) 4) JIIv4 ), P( 0.8 (c) 0.6 0.6 P( 0.4 P( 0.4 0.0 >1.0 >0.5 0.0 0.5 1.0 1.5 2.0 2.5 (v 4? <v 4 >)/ <v 4 >, (@ 4? <@ 4 >)/ <@ 4 > 0.0 F1.0 F0.5 0.0 0.5 1.0 1.5 2.0 2.5 (v 4 G <v 4 >)/ <v 4 >, (H 4 G <H 4 >)/ <H 4 > Distributions are not sensitive to transport properties! Direct probe of the initial state fluctuations! WPCF 2012 12.9.2012 H. Holopainen (FIAS) 18/21
Correlations between different harmonics sbc N/s =0.0 sbc Q/s =0.0 0.9 sbc S/s =0.0 (a) sbc N/s =0.16 swn N/s =0.16 (b) sbc Q/s =0.16 swn Q/s =0.16 0.8 (c) sbc S/s =0.16 swn S/s =0.16 20R30 % 0.7 20T30 % c(v 2,v 3 ) 0.1 0.0 20O30 % c(v 3,v 4 ) 0.1 0.0 c(v 2,v 4 ) 0.6 0.5 0.4 0.3 M0.1 P0.1 0.0 0.5 1.0 1.5 2.0 p T [GeV] 0.0 0.5 1.0 1.5 2.0 p T [GeV] 0.1 0.0 0.5 1.0 1.5 2.0 p T [GeV] Only v 2 and v 4 have a linear correlation. This correlation is sensitive to initial conditions and transport properties. WPCF 2012 12.9.2012 H. Holopainen (FIAS) 19/21
Correlations between different harmonics c(ǫ 2,ǫ 3 ) c(v 2, v 3 ) c(ǫ 2,ǫ 4 ) c(v 2, v 4 ) c(ǫ 3,ǫ 4 ) c(v 3, v 4 ) sbc η/s = 0.0 0.09 0.11 6 0.32 0.03 0.11 sbc η/s = 0.16 0.09 0.09 4 0.61 0.02 0.06 swn η/s = 0.16 0.15 0.14 0.04 0.42 0.03 0.11 In the initial state the anisotropies are not correlated. Correlation between v 2 and v 4 builds up during the evolution. WPCF 2012 12.9.2012 H. Holopainen (FIAS) 20/21
Summary There is a linear correlation between ǫ 2, v 2 and ǫ 3, v 3, but for ǫ 4, v 4 the correlation is weak. v n distributions probe the initial state fluctuations! Only the correlation between v 2 and v 4 probes both initial conditions and transport properties use this to study ebye hydrodynamics? WPCF 2012 12.9.2012 H. Holopainen (FIAS) 21/21
Backup slides WPCF 2012 12.9.2012 H. Holopainen (FIAS) 22/21
Viscous hydrodynamics Time evolution of the shear-stress tensor µν αβ τ π π αβ + π µν = 2ησ µν 4 3 πµν θ 10 7 µν αβ σα λ πβλ + 74 315η µν αβ πα λ πβλ, Transport coefficients taken from massless limit, 14-moment approximation and relaxation time was assumed to be τ π = 5η/(ε+P) Denicol, Niemi, Molnar, Rischke, Phys. Rev. D85, 114047 (2012) Denicol, Koide, Rischke, Phys. Rev. Lett. 105, 162501 (2010) WPCF 2012 12.9.2012 H. Holopainen (FIAS) 23/21