Ellipsoidal Flows in Relativistic Hydrodynamics of Finite Systems

Abstract

Abstract. A new class of 3D anisotropic analytic solutions of relativistic hydrodynamics with constant pressure is found. We analyse, in particular, solutions corresponding to ellipsoidally symmetric expansion of finite systems into vacuum. They can be utilized for relativistic description of the system evolution in thermodynamic region near the softest point and at the final stage of the hydrodynamic expansion in A+A collisions. The solutions can be used also for testing of numerical hydrodynamic codes solving relativistic hydrodynamic equations for anisotropic expansion of finite systems.

Uniform description of bulk observables in the hydrokinetic model ofA+Acollisions at the BNL Relativistic Heavy Ion Collider and the CERN Large Hadron Collider

“…At this moment the system gains anisotropic prethermal transverse flow that is caused by the transverse finiteness of the system [7,9]. Typically the flow is almost nonrelativistic, v T ≈ y T , and for the Gaussian initial profile for freely expanding fields or partons, which are suddenly thermalized at the time τ i , is proportional to the transverse coordinate r and inversely proportional to the homogeneity lengths squared [9]. If the homogeneity length is directed along an axis that is tilted by angular φ to the in-plane axis x, then one can write it in the form…”

“…Only in recent years have the main factors that make it possible to describe simultaneously the spectra and femtoscopic scales become clear. They are [7][8][9][10][11]: a relatively hard EoS because of a crossover transition (instead of the 1st order one) between quark-gluon and hadron phases, the presence of the prethermal anisotropic transverse flow developed to thermalization time, an "additional portion" of the transverse flow caused by the shear viscosity effect and fluctuations of the initial conditions. An account of these factors gives the possibility to describe well the pion and kaon spectra together with the femtoscopy RHIC data within a realistic freeze-out picture with a gradual decay of the fluid into observed particles [12].…”

HBT and initial conditions for hydrodynamic expansion in A+A collisions

“…It is possible to examine the anisotropy of the momentum distribution in different co-moving reference frames associated with different spacial points, where the 3-momentum p * determines p in accordance with Eq. (8).…”

New exact solutions of relativistic hydrodynamics

“…Although the renowned Hwa-Bjorken solution [6] lacks acceleration and yields a too perfectly flat rapidity distribution, it yields a key estimate of the initial energy density in high energy reactions. Other families of exact solutions were born from the desire of understanding the dynamics of high-energy heavy reactions [7,8,9,10,11,12,13,14]. Here we present a new, accelerating, analytic, exact and explicit solution of relativistic hydrodynamics, which fits dn/dy data at RHIC and allows for an advanced estimate of initial energy density and life-time of the reaction.…”