Turbulence in the Inter-galactic Medium: Solenoidal and Dilatational Motions, and the Impact of Numerical Viscosity

Abstract: We use a suite of cosmological hydrodynamic simulations, run by two fixed grid codes, to investigate the properties of solenoidal and dilatational motions of the intergalactic medium (IGM), and the impact of numerical viscosity on turbulence in a LCDM universe. The codes differ only in the spatial difference discretization. We find that (1) The vortical motion grows rapidly since $z=2$, and reaches $\sim 10 km/s -90 km/s$ at $z=0$. Meanwhile, the small-scale compressive ratio $r_{CS}$ drops from 0.84 to 0.47, indicating comparable vortical and compressive motions at present. (2) Power spectra of the solenoidal velocity possess two regimes, $\propto k^{-0.89}$ and $\propto k^{-2.02}$, while the total and dilatational velocity follow the scaling $k^{-1.88}$ and $k^{-2.20}$ respectively in the turbulent range. The IGM turbulence may contain two distinct phases, the supersonic and post-supersonic phases. (3) The non-thermal pressure support, measured by the vortical kinetic energy, is comparable with the thermal pressure for $\rho_b \simeq 10-100$, or $T <10^{5.5} K$ at $z=0.0$. The deviation of the baryon fraction from the cosmic mean shows a preliminary positive correlation with the turbulence pressure support. (4) A relatively higher numerical viscosity would dissipate both the compressive and vortical motions of the IGM into thermal energy more effectively, resulting in less developed vorticity, remarkably shortened inertial range, and leading to non-negligible uncertainty in the thermal history of gas accretion. Shocks in regions outside of clusters are significantly suppressed by numerical viscosity since $z=2$, which may directly cause the different levels of turbulence between two codes.