Highly anisotropic and strongly dissipative hydrodynamics for early stages of relativistic heavy-ion collisions

Abstract

We introduce a new framework of highly-anisotropic hydrodynamics that includes dissipation effects. Dissipation is defined by the form of the entropy source that depends on the pressure anisotropy and vanishes for the isotropic fluid. With a simple ansatz for the entropy source obeying general physical requirements, we are led to a non-linear equation describing the time evolution of the anisotropy in purely-longitudinal boost-invariant systems. Matter that is initially highly anisotropic approaches naturally the regime of the perfect fluid. Thus, the resulting evolution agrees with the expectations about the behavior of matter produced at the early stages of relativistic heavy-ion collisions. The equilibration is identified with the processes of entropy production.

Second-order(2+1)-dimensional anisotropic hydrodynamics

“…Then the specific functional dependence of f 0 on the LRF energy is mostly irrelevant for our theory, since it enters only through the thermodynamic integrals (66) below whose actual values factors out in the present work. 9 Since we propose to incorporate bulk viscous corrections perturbatively, it is not necessary to incorporate them in the leading-order distribution function as originally proposed in [14]. As a result, we can take Φ in Sec.…”

“…This coordinate system is particularly well-adapted to longitudinally boost-invariant systems where ϑ = ς; the necessary differential operators then reduce to [9,14] …”

“…To account for these large early-time deviations from local momentum isotropy nonperturbatively, a framework called "anisotropic hydrodynamics" was developed [8][9][10][11][12][13][14][15][16][17].…”

Viscous hydrodynamics for strongly anisotropic expansion

“…These cause standard Israel-Stewart (second-order) viscous hydrodynamic theory (see [1] for a recent review) to break down. Anisotropic hydrodynamics [2,3,4] (aHydro) deals with the large longitudinal/transverse pressure anisotropy, P L −P T , "non-perturbatively", thereby avoiding the occurrence of negative longitudinal pressures and improving the performance of hydrodynamics at early times [2,3]. However, aHydro [2,3] accounts only for one (the largest) of the five independendent components of the shear stress tensor π µν .…”

“…Anisotropic hydrodynamics [2,3] is obtained from (5) by using in (3) the spheroidally deformed local momentum distribution…”