Simple solutions of fireball hydrodynamics for rotating and expanding triaxial ellipsoids and final state observables

TL;DR

This paper provides analytic solutions for rotating, expanding triaxial ellipsoids in fireball hydrodynamics and explores how final state observables can reveal the fireball's rotation and the equation of state, aiding the search for the critical point.

Contribution

It introduces new analytic solutions for rotating, expanding triaxial ellipsoids in non-relativistic hydrodynamics and connects observables to the fireball's rotation and equation of state.

Findings

Final tilt angle depends on measurement method.

Observables can determine the fireball's rotation.

Rotation dependence on collision energy indicates equation of state softness.

Abstract

We present a class of analytic solutions of non-relativistic fireball hydrodynamics for a fairly general class of equation of state. The presented solution describes the expansion of a triaxial ellipsoid that rotates around one of the principal axes. We calculate the hadronic final state observables such as single-particle spectra, directed, elliptic and third flows, as well as HBT correlations and corresponding radius parameters, utilizing simple analytic formulas. We call attention to the fact that the final tilt angle of the fireball, an important observable quantity, is not independent on the exact definition of it: one gets different angles from the single-particle spectra and from HBT measurements. Taken together, it is pointed out that these observables may be sufficient for the determination of the magnitude of the rotation of the fireball. We argue that observing this rotation and its dependence on collision energy would reveal the softness of the equation of state. Thus determining the rotation may be a powerful tool for the experimental search for the critical point in the phase diagram of strongly interacting matter.