Quasiparticle equation of state for anisotropic hydrodynamics

We present a new method for imposing a realistic equation of state in anisotropic hydrodynamics. The method relies on the introduction of a single finite-temperature quasiparticle mass which is fit to lattice data. By taking moments of the Boltzmann equation, we obtain a set of coupled partial differential equations which can be used to describe the 3+1-dimensional (3+1d) spacetime evolution of an anisotropic relativistic system. We then specialize to the case of a 0+1d system undergoing boost-invariant Bjorken expansion and subject to the relaxation-time approximation collisional kernel. Using this setup, we compare results obtained using the new quasiparticle equation of state method with those obtained using the standard method for imposing the equation of state in anisotropic hydrodynamics. We demonstrate that the temperature evolution obtained using the two methods is nearly identical and that there are only small differences in the pressure anisotropy. However, we find that there are significant differences in the evolution of the bulk pressure correction.

Figure 1

Panel (a) shows the energy density and pressure scaled by their respective Stefan-Boltzmann limits as a function of temperature. Panel (b) shows the speed of sound squared as a function of temperature.

Figure 2

In panel (a) we plot the temperature dependence of the quasiparticle mass scaled by the temperature obtained using Eq. (26). In panel (b) we plot the temperature dependence of the background term $B_{\mathrm{eq}}$ scaled by the temperature obtained using (25).

Figure 3

The four panels show (a) the effective temperature scaled by $T_0$, (b) ${(\tau /{\tau }_0)}^{4/3}$ times the energy density scaled by the initial energy density, ${\mathcal{E}}_0$, (c) the pressure anisotropy, and (d) the bulk correction to the pressure scaled by ${\mathcal{P}}_{\mathrm{eq}}$. For this figure we took $4\pi \eta /s=1$.

Figure 4

Same as Fig. 3 except here we take $4\pi \eta /s=3$.

Figure 5

Same as Fig. 3 except here we take $4\pi \eta /s=10$.

Figure 6

Same as Fig. 4 except here we take anisotropic initial conditions.