Multipole solution of hydrodynamics and higher order harmonics

Abstract

The time evolution of the medium created in heavy ion collisions can be described by hydrodynamical models. After expansion and cooling, the hadrons are created in a freeze-out. Their distribution describes the final state of this medium. In particular their azimuthal asymmetry, characterized by the elliptic flow coefficient $v_2$, is one of the most important observables in heavy ion physics. In recent years it has been revealed that if measuring relative to higher order event planes ${\Psi }_n$, higher order flow coefficients $v_n$ for $n>2$ can be measured. This is due to initial state fluctuations, previously not described by analytic solutions of relativistic hydrodynamics. In this paper we show the first solutions that utilize higher order asymmetries and thus yield realistic $v_n$ flow coefficients. It is a clear consequence of this that different flow patterns may lead to the same observed flow coefficients. We also compare our results to PHENIX measurements and determine a possible parameter set corresponding to these data.

7 pages, 6 figures, accepted in Phys. Rev. C

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• Initial energy density of $\sqrt{s}=$ 7 and 8 TeV p+p collisions at the LHC
• New exact solutions of relativistic hydrodynamics for longitudinally expanding fireballs
• The "ripples" on relativistically expanding fluid
• Higher order anisotropies in the Buda-Lund model: Disentangling flow and density field anisotropies
• Simple solutions of fireball hydrodynamics for rotating and expanding triaxial ellipsoids and final state observables
• Early time behavior of spatial and momentum anisotropies in kinetic theory across different Knudsen numbers
• A non-boost-invariant solution of relativistic hydrodynamics in 1+3 dimensions
• Analytic approaches to relativistic hydrodynamics
• Polarized baryon production in heavy ion collisions: an analytic hydrodynamical study
• Higher order anisotropies in hydrodynamics
• New solutions of viscous relativistic hydrodynamics
• A Particle Emitting Source From an Accelerating, Perturbative Solution of Relativistic Hydrodynamics
• Perturbative accelerating solutions of relativistic hydrodynamics