Thermal photons from fluctuating initial conditions
Rupa Chatterjee, Hannu Holopainen, Thorsten Renk, Kari J. Eskola
aa r X i v : . [ h e p - ph ] J un Thermal photons from fluctuating initial conditions
Rupa Chatterjee , Hannu Holopainen , , Thorsten Renk , , andKari J. Eskola , Department of Physics, P. O. Box 35, FI-40014 University of Jyv¨askyl¨a, Finland Helsinki Institute of Physics, P.O.Box 64, FI-00014 University of Helsinki, FinlandE-mail: [email protected]
Abstract.
Event-by-event fluctuations of initial QCD-matter density produced inheavy-ion collisions at RHIC enhance the production of thermal photons significantlyin the region 2 ≤ p T ≤ c compared to a smooth initial-state averaged profilein the ideal hydrodynamic calculation. This enhancement is a an early time effect dueto the presence of hotspots or over-dense regions in the fluctuating initial state. Theeffect of fluctuations is found to be stronger in peripheral than in central collisions.
1. Introduction
Photons have long been considered as one of the most powerful probes to characterizethe initial state of the system produced in ultra-relativistic heavy-ion collisions [1]. Thisis complementary to the p T spectra of bulk hadrons which reflect the late conditions closeto freeze-out. The thermal emission of photons shows a strong temperature dependence,high p T photons are mostly emitted from the hot and dense early stage of the systemevolution when the hydrodynamic flow is weak, whereas low p T photons are emitted fromthe flow boosted relatively cold later part of the system. Recent studies have shownthat event-by-event QCD-matter density fluctuations in the initial conditions (IC) areneeded (in addition to a correct reference plane definition) for reproducing the measuredcharged-particle elliptic flow even for most central collisions, which was underestimatedby all earlier hydrodynamic calculations using smooth IC [2].We show that fluctuations in the initial state enhance the production of thermalphotons significantly for p T > c compared to a smooth IC. This makes thethermal photons in that p T range especially suitable to probe the hotspots in the IC [3].
2. Event-by-event hydrodynamics and thermal photons
We use the event-by-event hydrodynamical model developed in [2] to calculate theproduction of thermal photons from fluctuating as well as from smooth IC. A MonteCarlo Glauber model with the standard two-parameter Woods-Saxon nuclear densityprofile is used to create the initial state nucleon configurations, and to compute the hermal photons from fluctuating initial conditions p T (GeV/c) -7 -5 -3 -1 d N / d p T d Y ( G e V - c ) PHENIX 0-20%PHENIX 0-10%PHENIX 10-20%Fluctuating IC (T f =160 MeV)Smooth IC (T f =160 MeV)Smooth IC (T f =120 MeV) Thermal Photons
Hadronic γ , T f =120 MeVHadronic γ , T f =160 MeV σ (fm) d N (f l u c t u a t i n g I C ) / d N ( s m oo t h I C ) p T =5 GeV/cp T =3 GeV/cp T =1 GeV/c Thermal Photons
Figure 1. (From [3]. Color online) [Left] Thermal photons from a smooth (longdashed blue line) and fluctuating (solid red line) IC along with PHENIX direct photondata [8, 9] for 0–20% centrality. [Right] σ dependence of the results. number of wounded nucleons. The initial density profile is taken to be proportional tothe number of wounded nucleons (WN), where entropy density s is distributed in the( x, y ) plane around the wounded nucleons using a 2D Gaussian smearing, s ( x, y ) = K πσ N WN X i =1 exp (cid:16) − ( x − x i ) + ( y − y i ) σ (cid:17) . (1)Here K is a fixed overall normalization constant and σ is a free parameter whichdetermines the size of the fluctuations. The initial formation time of the plasma istaken as τ = 0.17 fm/ c , motivated by the EKRT minijet saturation model [4]. Wechoose a default value for the size parameter as σ = 0.4 fm [2]. The equation of statewhich shows a sharp cross-over transition from the plasma phase to the hadronic phaseis from [5]. The temperature at freeze-out is taken as 160 MeV (see [2] and [3] for moredetails). This model has been applied successfully to reproduce both the measuredcentrality dependence as well as the p T dependence of charged particle elliptic flow upto p T ∼ c , and the pion p T spectra up to ∼ c [2].We use the complete leading order rates R = EdN/d pd x of [6] for the emissionfrom plasma and the parametrization given in [7] for the hadronic matter emissionwhich at present can be considered as the state of the art for photon production. Theswitching from the plasma rates to hadronic rates is done at a temperature 170 MeV.The total thermal emission from the produced QCD matter is obtained by integratingthe emission rates over the space-time history of the fireball as E dN/d p = Z d x R (cid:16) E ∗ ( x ) , T ( x ) (cid:17) , (2)with T ( x ) as the local temperature and E ∗ ( x ) = p µ u µ ( x ), where p µ is the four-momentum of the photon and u µ is the local four-velocity of the flow field.
3. Results and discussions
Figure 1 (left panel) shows our results for thermal photon spectra from a smooth andfrom fluctuating IC for 200A GeV Au+Au collisions at RHIC along with PHENIX hermal photons from fluctuating initial conditions -8 -6 -4 -2 d N / dp T d τ d Y | Y = ( c / G e V f m ) (a) (b) (c) τ (fm/c) Smooth ICFluctuating IC (hot events) p T =1 GeV/c p T =3 GeV/c p T =5 GeV/c Fluctuating IC (cold events)
Thermal photons, 0-20% Centrality
Figure 2. (From [3]. Color online) Time evolution of thermal photon yield for p T values of (a) 1, (b) 3, and (c) 5 GeV/ c . Results are compared with an initial stateaveraged event and four different random events from the fluctuating IC. data [8, 9] for the 0-20 % centrality bin. The result from the fluctuating IC scenariois obtained by averaging photon spectra from a sufficiently large number of randomevents. The smooth profile is obtained by taking an average of 1000 initial profileswhich is enough to remove essentially all the fluctuations [3]. We see that for both thesmooth and the fluctuating IC, the spectra are dominated by radiation from the QGPphase in the entire p T range shown in the figure. We further notice that even with amuch smaller freeze-out temperature ( ∼
120 MeV) we get significant contributions onlybelow p T ∼ c as shown by the brown dashed dotted line in Figure 1.The slope of the photon p T spectrum from the fluctuating IC is about 10% flattercompared to the slope from the smooth IC in the region 2 ≤ p T ≤ c . For p T < c , with the fluctuating IC we obtain 20-40% more photons than with the smoothprofile, whereas for p T > c the two results differ almost by a factor of 2. Weknow that the thermal emission of photons is exponential in temperature and linear inradiating volume. As a result, the hotspots in the fluctuating IC produce more high p T photons than the smooth profile and the difference between the two IC increasestowards higher values of transverse momentum. We find that the photon results fromthe fluctuating IC show a better agreement with the PHENIX experimental data for2 ≤ p T ≤ c leaving enough space for the other sources of direct photons besidesthe thermal contribution.The thermal photon production from the fluctuating IC is found to be quitesensitive to the value of the fluctuation size parameter σ , where the enhancement inthe production compared to a smooth IC is found to be maximal towards smaller valuesof σ and also for larger values of p T (see right panel of Figure 1).The time evolution of thermal photon yield for different values of p T is shown inFigure 2 which clearly explains the dynamics leading to the results presented in Figure 1.We see that most of the high p T photons are emitted from very early stage of the systemexpansion and their production drops by a few order of magnitude within a couple offm/ c . We further notice that the cold events (or events having less than average entropy)produce more high p T photons than the smooth IC for p T ≥ c . hermal photons from fluctuating initial conditions p T (GeV/ c ) -8 -7 -6 -5 -4 -3 -2 -1 d N / d p T d Y ( G e V - c ) Au+Au@200 GeV
Thermal Photons
Fluctuating ICSmooth IC p T (GeV/ c ) -6 -5 -4 -3 -2 -1 d N / d p T d Y ( G e V - c ) Fluctuating IC, LHCSmooth IC, LHCFluctuating IC, RHICSmooth IC, RHIC
Thermal Photons, 0-20% centrality bin
[email protected] ATeV, Au+Au@200 AGeV
Figure 3. (Color online) [Left] Centrality dependence of the thermal photon spectrafrom smooth and fluctuating IC. [Right] Results at RHIC and LHC are compared.
The centrality dependence of the results is shown in Figure 3 (left panel) wherethe difference between the smooth and fluctuating IC is found to increase from centralto peripheral collisions. The size of the produced system becomes smaller towardsperipheral collisions and the effect of the hot spots in the fluctuating IC becomes morepronounced, leading to the shown result. We have also noticed that the effect of initialstate fluctuations in the excess production of high p T photons is weaker at LHC thanat RHIC [10] (see right panel of Figure 3).In conclusion, we see that fluctuations in the initial density distribution enhancesignificantly the production of thermal photons compared to a smooth initial stateaveraged profile in ideal hydrodynamic calculation. This is an early time effect solelydue to the presence of hotspots in the fluctuating IC and this effect is found to bestronger towards peripheral collisions. This calls for a more detailed study of the effectsof fluctuations for lower beam energies and for smaller size systems. In addition to that,estimation of photon elliptic flow from the fluctuating IC will be very interesting.We are financially supported by the Academy of Finland (projects 130472 and133005), by the national Graduate School of Particle and Nuclear Physics, and by aMagnus Ehrnrooth Foundation travel grant. We acknowledge CSC-IT Center for Sciencein Espoo, Finland, for computational resources. References [1] P. V. Ruuskanen, Nucl. Phys. A , 169 (1992), and references therein.[2] H. Holopainen, H. Niemi, and K. Eskola, Phys. Rev. C , 034901 (2011); H. H. in these proc.[3] R. Chatterjee, H. Holopainen, T. Renk, and K. J. Eskola, Phys. Rev. C , 054908 (2011).[4] K. J. Eskola, K. Kajantie, P. V. Ruuskanen, and K. Tuominen, Nucl. Phys. B570 , 379 (2000).[5] M. Laine and Y. Schroder, Phys. Rev. D , 085009 (2006).[6] P. Arnold, G. D. Moore, and L. G. Yaffe, JHEP , 009 (2001).[7] S. Turbide, R. Rapp, and C. Gale, Phys. Rev. C , 014903 (2004).[8] A. Adare et al. [PHENIX Collaboration], Phys. Rev. Lett. , 132301 (2010).[9] S. S. Adler et al. [PHENIX Collaboration], Phys. Rev. Lett.94