An attempt to incorporate separate chemical and thermal freeze outs in hydrodynamics

From an analysis of various types of data obtained in relativistic nuclear collisions, the following picture has emerged in thermal and hydrodynamical descriptions: as the fluid expands and cools, particles first undergo a chemical freeze out at T_ch.~160-200 MeV then a thermal freeze out at T_th~100-140 MeV. In this paper we show how to incorporate these separate freeze outs consistently in a hydrodynamical code via a modified equation of state (general case) or via a modified Cooper-Frye formula (particular case of T_ch. close to T_th. or few particle species undergoing early chemical freeze-out). The modified equation of state causes faster cooling and may have sizable impact on the predicted values of observables.