Bulk viscous evolution within anisotropic hydrodynamics

Abstract

We derive a system of moment-based dynamical equations that describe the $1+1d$ space-time evolution of a cylindrically symmetric massive gas undergoing boost-invariant longitudinal expansion. Extending previous work, we introduce an explicit degree of freedom associated with the bulk pressure of the system. The resulting form generalizes the ellipsoidal one-particle distribution function appropriate for massless particles to massive particles. Using this generalized form, we obtain a system of partial differential equations that can be solved numerically. In order to assess the performance of this scheme, we compare the resulting anisotropic hydrodynamics solutions with the exact solution of the $0+1d$ Boltzmann equation in the relaxation-time approximation. We find that the inclusion of the bulk degree of freedom improves the agreement between anisotropic hydrodynamics and the exact solution for a massive gas.