Bjorken flow attractors with transverse dynamics

In the context of the longitudinally boost-invariant Bjorken flow with transverse expansion, we use three different numerical methods to analyze the emergence of attractor solutions in an ideal gas of massless particles exhibiting constant shear viscosity to entropy density ratio eta/s. The fluid energy density is initialized using a Gaussian profile in the transverse plane, while the ratio chi = P-L/P-T between the longitudinal and transverse pressures is set at initial time tau(0) to a constant value chi(0) throughout the system employing the Romatschke-Strickland distribution. We introduce the hydrodynamization time delta tau(H) = (tau(H) - tau(0))/tau(0) based on the time tau(H) when the standard deviation sigma(chi) of a family of solutions with different chi(0) reaches a minimum value at the point of maximum convergence of the solutions. In the 0 + 1D setup, delta tau(H) exhibits scale invariance, being a function only of (eta/s)/(tau T-0(0)). With transverse expansion, we find a similar delta tau(H) computed with respect to the local initial temperature, T-0(r). We highlight the transition between the regimes where the longitudinal and transverse expansions dominate. We find that the hydrodynamization time required for the attractor solution to be reached increases with the distance from the origin, as expected based on the properties of the 0 + 1D system defined by the local initial conditions. We argue that hydrodynamization is predominantly the effect of the longitudinal expansion, being significantly influenced by the transverse dynamics only for small systems or for large values of eta/s.