Temperature dependence of sound velocity and hydrodynamics of ultra-relativistic heavy-ion collisions

Abstract

The effects of different forms of the sound-velocity function c_s(T) on the hydrodynamic evolution of matter created in the central region of ultra-relativistic heavy-ion collisions are studied. At high temperatures (above the critical temperature T_c) we use the sound velocity function obtained from the recent lattice simulations of QCD, whereas at low temperatures we use the ideal hadron gas model. At moderate temperatures different interpolations between those two results are employed. They are characterized by different values of the local maximum (at T = 0.4 T_c) and local minimum (at T=T_c). The extreme values are chosen in such a way that at high temperature all considered sound-velocity functions yield the entropy density consistent with the lattice simulations of QCD. We find that the presence of a distinct minimum of the sound velocity leads to a very long (~ 20 fm/c) evolution time of the system. Since such long evolution times are not compatible with the recent estimates based on the HBT interferometry, we conclude that the hydrodynamic description becomes adequate if the QCD cross-over phase transition renders the smooth temperature variations of the sound velocity, with a possible shallow minimum at T_c where the values of c_s^2(T) remain well above 0.1.