1. PhD student at the International PhD Studies Institute of Nuclear Physics PAN Institute of Nuclear Physics PAN Department of Theory of Structure of Matter Hydrodynamic evolution of matter in ultra-relativistic heavy-ion collisions Mikołaj Chojnacki

2. 2 Physics News Update April 20, 2005 At... (RHIC)..., the four large detector groups agreed,..., on a consensus interpretation of … high-energy ion collisions: the fireball made in these collisions … was not a gas of weakly interacting quarks and gluons as earlier expected, but... a liquid of strongly interacting quarks and gluons. Motivation – discovery of perfect fluid at RHIC Our achievement: Development of new approach to relativistic hydrodynamics where the temperature-dependent sound velocity is the only thermodynamic input characterizing matter. Perfect fluid, 1000 times less viscous than water.

3. 3  freeze-out  free hadrons streaming to detectors Time evolution of matter in heavy-ion collisions  nuclei before collision  moving close to the speed of light  collision, production of particles  interactions  thermalization  rapid expansion  temperature decreases Hydrodynamic evolution quarks, gluons  hadrons

4. 4 Energy and momentum conservation law  Energy and momentum conservation law  energy-momentum tensor of the perfect fluid energy density, - pressure, - energy density, - pressure, - four-velocity of the fluid element  at midrapidity (y = 0) for RHIC energies Equations of relativistic hydrodynamics

5. 5 In our approach 2+1 hydrodynamic expansion is described by two coupled partial differential equations for auxiliary function a and  Boost-invariant and cylindrically asymmetric hydrodynamic equations  Physical input

6. 6 Initial temperature profiles  Initial temperature is connected with the density of wounded nucleons the density of wounded nucleons xyAB b Transverse plane

7. 7 Results  centrality classes 0 – 20 %0 ≤ b ≤ 6 [fm] 0 – 20 %0 ≤ b ≤ 6 [fm] 40 – 60 %8 [fm] ≤ b ≤ 10 [fm 40 – 60 %8 [fm] ≤ b ≤ 10 [fm]  starting time of hydrodynamic evolutiont 0 = 1 [fm]  initial central temperatureT 0 = 2 T C = 340 [MeV]

8. 8 Centrality class 0 – 20%

9. 9

10. 10 Centrality class 40 – 60%

11. 11 Centrality class 40 – 60%

12. 12 Asymmetry parameter v 2  Cooper-Frye formula

13. 13 Comput. Phys. Commun. 167 : 229, 2005 Future extensions: connection to codes describing the hadronic phase

14. 14 Comput. Phys. Commun. 174 : 669, 2006

15. 15 Conclusions  We have developed a new and efficient method of solving relativistic hydrodynamics, reformulating the appropriate partial differential equations in such a way that the sound velocity in medium is the only input characterizing the properties of matter.  We have solved the problem of evolution of matter created in relativistic heavy collisions for the case of azimuthally asymmetric and boost-invariant expansion, which allowed us to make predictions for the elliptic flow of hadrons which is a signature of the creation of the strongly coupled system.  Our successful description of v 2 supports: - early thermal equilibrium, - strong collective expansion.

16. 16 M. Ch. Cylindrically asymmetric hydrodynamic equations Acta Phys. Pol. B37 : 3391, 2006 M. Ch., W. Florkowski Characteristic form of boost-invariant and cylindrically non-symmetric hydrodynamic equations Phys. Rev. C74 : 034905, 2006 M. Ch. Hubble-like flows in relativistic heavy-ion collisions Acta Phys. Hung. A27 : 331, 2006 M. Ch., W. Florkowski, T. Csorgo On the formation of Hubble flow in little bangs Phys. Rev. C71 : 044902, 2005. References