Hydrodynamic attractor in the nonconformal Bjorken flow

Abstract

Nonconformal attractor behavior is studied by solving nonconformal second-order viscous hydrodynamics with respect to boost-invariant plasmas. Numerical solutions of the relative decay rate of the enthalpy density, the inverse shear and bulk Reynolds numbers all exhibit universal patterns towards an ideal fluid description at late stages, demonstrating the existence of a nonconformal hydrodynamic attractor. However, as a generic feature, the nonconformal hydrodynamic attractor emerges only at late times, which differs drastically from the behavior observed in conformal systems. The absence of the early-time attractor in nonconformal fluids is a consequence of the early-time unstable mode, which arises from a positive-valued eigenmode associated with the free-streaming dynamics. The early-time attractor can be restored in a mixture of the shear and bulk viscous corrections, in which early-time unstable modes cancel approximately. However, to support practical simulations of hydrodynamics in high-energy heavy-ion collisions, for which the early-time nonconformal attractor is approachable in all independent modes, the quadratic coupling between the bulk pressure and the expansion rate should be enhanced by at least a factor of two through the transport coefficient ${\ensuremath{\delta}}_{\mathrm{\ensuremath{\Pi}}\mathrm{\ensuremath{\Pi}}}$.