New exact solutions of relativistic hydrodynamics for longitudinally expanding fireballs

TL;DR

This paper introduces new exact solutions to relativistic hydrodynamics equations for expanding fireballs, applicable to high-energy collisions, with analytical formulas for observable distributions that match experimental data.

Contribution

It generalizes previous solutions by incorporating a realistic, temperature-independent speed of sound, providing more accurate models for fireball expansion in collisions.

Findings

Derived analytical formulas for rapidity and pseudorapidity densities.

Solutions approach the Hwa-Bjorken model in the boost-invariant limit.

Applicable to high-energy proton-proton and heavy ion collision data.

Abstract

We present new, exact, finite solutions of relativistic hydrodynamics for longitudinally expanding fireballs for arbitrary constant value of the speed of sound. These new solutions generalize earlier, longitudinally finite, exact solutions, from an unrealistic to a reasonable equation of state, characterized by a temperature independent (average) value of the speed of sound. Observables like the rapidity density and the pseudorapidity density are evaluated analytically, resulting in simple and easy to fit formulae that can be matched to the high energy proton-proton and heavy ion collision data at RHIC and LHC. In the longitudinally boost-invariant limit, these new solutions approach the Hwa-Bjorken solution and the corresponding rapidity distributions approach a rapidity plateaux.