A Comparative Study of Isothermal Turbulence Statistics: Fourier Space Driving vs. Point Source Driving

Abstract

The turbulence driving parameter ($b \equiv \sigma_{\rho/\langle \rho \rangle}/\mathcal{M}$; the ratio of the density to velocity fluctuations) is widely used to infer the dominant mode of energy injection in interstellar turbulence. Numerical simulations of turbulence using Fourier Space Driving (FSD) establish a mapping from $b\approx 1/3$ for purely solenoidal to $b\approx 1$ for purely compressive driving. We test the robustness of this calibration by comparing FSD against Point Source Driving (PSD), which stochastically injects radial momentum at random locations mimicking supernovae. Using isothermal hydrodynamic simulations in a periodic box with AthenaK, we run a suite of carefully curated simulations to match Mach numbers between the two driving methods and compare morphology, probability density functions, and power spectra of density and velocity. Despite injecting purely compressive motions, the PSD models yield $b=0.33$ to $0.49$, values that the FSD calibration would associate with more solenoidal driving. With mass-weighted mean Mach number, excluding high-velocity bubble interiors, $b_M=0.74$ to $0.79$ still does not recover the expected $b\approx 1$ for volume-filling, purely compressive driving. More broadly, the PSD models show density and velocity statistics closer to solenoidal and compressive FSD models, respectively, and exhibit unique features, including non-Gaussian velocity tails and a positive density-Mach number correlation at high densities. Within the FSD framework itself, varying the forcing correlation time changes $b$ by a factor of more than 3 for compressive driving. These results demonstrate that $b$ is degenerate with both the spatial locality and the temporal correlation of the driving, limiting its utility as a standalone diagnostic of the energy injection mode.