Simple solutions of fireball hydrodynamics for self-similar elliptic flows

Abstract

Simple, self-similar, elliptic solutions of non-relativistic fireball hydrodynamics are presented, generalizing earlier results for spherically symmetric fireballs with Hubble flows and homogeneous temperature profiles. The transition from one dimensional to three dimensional expansions is investigated in an efficient manner.

Rotation in an exact hydrodynamical model

“…We now assume that the temperature profile is flat, and consequently the density profiles are Gaussian and separable [17]. With this approximation the different integrated energies are calculated.…”

“…In the main steps we followed Ref. [17]; however it turned out that the modified last step of the method provides a more straightforward solution. We show that the model provides an excellent and simple semianalytic tool to study the effects and consequences of an expanding and rotating system.…”

Ellipsoidal Flows in Relativistic Hydrodynamics of Finite Systems

“…[ 11] as the elliptic solutions of the non-relativistic hydrodynamics equations. In this sense the solution proposed could be considered as the generalization (at vanishing pressure) of the corresponding non-relativistic solutions allowing one to describe relativistic expansion of the finite system into vacuum.…”

Quark recombination and elliptic flow

“…Blast wave descriptions [10,11,12,13], provide a simple means by which one can test thermal concepts along with those for collective flow. Typically, a blast-wave model requires four parameters: a temperature T , a breakup time τ , a transverse radius R and a maximum transverse collective rapidity, ρ 0 .…”

“…(2) is valid. For blast-wave models of the emitting state [10,11,12,13], we will show that the validity is sensitive to seemingly arcane choices of how to parameterize the model. Boltzmann equations are also solved for the partonic evolution where validity of Eq.…”