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

Nagy, Márton and Csörgő, Tamás (2016) Simple solutions of fireball hydrodynamics for rotating and expanding triaxial ellipsoids and final state observables. PHYSICAL REVIEW C, 94 (6). ISSN 2469-9985

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Abstract

We present a class of analytic solutions of non-relativistic fireball hydrodynamics for a fairly gen- eral class of equation of state. The presented solution describes the expansion of a triaxial ellipsoid that rotates around one of its 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 corre- sponding radius parameters, utilizing simple analytic formulas. The final tilt angle of the fireball, an important observable quantity, is shown to be not independent of its exact definition: one gets different tilt angles from the geometrical anisotropies, from the single-particle spectra, and from HBT measurements. Taken together, the tilt angle in the momentum space and in the relative momentum or HBT variable may be sufficient for the determination of the magnitude of the rota- tion of the fireball. We argue that observing this rotation and its dependence on collision energy could characterize the softest point 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.

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