Relativistic viscous hydrodynamics for heavy-ion collisions: A comparison between the Chapman-Enskog and Grad methods

Abstract

Derivations of relativistic second-order dissipative hydrodynamic equations have relied almost exclusively on the use of Grad's 14-moment approximation to write f (x, p), the nonequilibrium distribution function in the phase space. Here we consider an alternative Chapman-Enskog-like method, which, unlike Grad's, involves a small expansion parameter. We derive an expression for f (x, p) to second order in this parameter. We show analytically that while Grad's method leads to the violation of the experimentally observed 1/ √ mT scaling of the longitudinal femtoscopic radii, the alternative method does not exhibit such an unphysical behavior. We compare numerical results for hadron transverse-momentum spectra and femtoscopic radii obtained in these two methods, within the one-dimensional scaling expansion scenario. Moreover, we demonstrate a rapid convergence of the Chapman-Enskog-like expansion up to second order. This leads to an expression for δf (x, p) which provides a better alternative to Grad's approximation for hydrodynamic modeling of relativistic heavy-ion collisions.

Thermodynamically Consistent Formulation of Quasiparticle Viscous Hydrodynamics

“…The equations of motion for the dissipative quantities may be obtained using the Chapman-Enskog-like iterative solution [16,17,18,19] of the effective Boltzmann equation for quasiparticles with T -dependent mass [11,20] …”

Relativistic quantum transport coefficients for second-order viscous hydrodynamics

“…Two most extensively used methods to determine f (x, p) for a system which is close to local thermodynamic equilibrium are (1) the Grad's 14-moment approximation [34] and (2) the ChapmanEnskog method [35]. Note that while Grad's 14-moment approximation has been widely employed in the formulation of a causal theory of relativistic dissipative hydrodynamics [4][5][6][7][8][9][10][11][12][13][14], the Chapman-Enskog method remains less explored [15][16][17][18][19]. On the other hand, the ChapmanEnskog formalism has been often used to extract various transport coefficients of hot hadronic matter [20][21][22][23][24] Although in both methods the distribution function is expanded around its equilibrium value f 0 (x, p), it has been demonstrated that the Chapman-Enskog method in the relaxation-time approximation (RTA) leads to better agreement with both microscopic Boltzmann simulations as well as exact solutions of the relativistic RTA Boltzmann equation [16][17][18][19].…”

Transport coefficients for bulk viscous evolution in the relaxation-time approximation

“…On the other hand, the derivations based on kinetic theory require the non-equilibrium phase-space distribution function, f (x, p), to be specified. Consistent and accurate determination of the form of the dissipative equations and the associated transport coefficients is currently an active research area [6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24].…”