Hydrodynamic attractor in the non-conformal Bjorken flow

TL;DR

This paper investigates the emergence of hydrodynamic attractors in non-conformal plasmas, revealing late-time universal behavior and proposing methods to restore early-time attractors for better simulation accuracy.

Contribution

It demonstrates the existence of non-conformal hydrodynamic attractors and explores conditions to recover early-time attractor behavior in non-conformal fluids.

Findings

Non-conformal attractors exhibit universal late-time patterns.

Early-time attractors are absent due to unstable modes.

Mixtures of viscous corrections can restore early-time attractors.

Abstract

Non-conformal attractor behavior is studied by solving non-conformal 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 non-conformal hydrodynamic attractor. However, as a generic feature, the non-conformal 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 non-conformal fluids is a consequence of the early-time instable mode, which arises from a positive-valued eigen-mode associated with the free-streaming dynamics. To support practical simulations of hydrodynamics in high-energy heavy-ion collisions, early-time attractor can be restored in a mixture of the shear and the bulk viscous corrections, in which early-time instable modes cancel approximately. Early-time non-conformal attractor is also approachable, if the quadratic coupling between the bulk pressure and the expansion rate is enhanced by at least a factor of two through the transport coefficient $\delta_{\Pi\Pi}$.