What does it mean to take the mean? The effect of the averaging scale on the characterization of interstellar turbulence

Abstract

In interstellar medium studies, separating ordered and random velocity or magnetic fields is essential for interpreting turbulence in both simulations and observations. We investigate how the choice of averaging scale affects the measurement and characterization of magnetic and kinetic turbulence in Milky Way-sized disk galaxies with different initial magnetic morphologies. We analyze two magnetohydrodynamic simulations of isolated disk galaxies, one initialized with a toroidal magnetic field (Model T) and the other with a random field (Model R). Using spherical filtering, we decompose the magnetic and velocity fields into mean and fluctuating components while varying the averaging scale, and examine their energy ratios and power spectra as functions of time and averaging radius. Both models develop ordered and turbulent magnetic structures, whose relative strengths vary strongly with the averaging radius. The power spectra of the velocity and magnetic mean fields steepen with increasing smoothing scale, tracing the transition from coherent to turbulent regimes. The turbulent kinetic energy dominates over the magnetic counterpart, though the latter remains dynamically significant. Very importantly, we find that these ratios depend more strongly on the averaging radius than on the initial conditions of the magnetic field. The characterization of turbulence as strong or weak, meaning whether or not fluctuations dominate over the mean depends sensitively on the chosen averaging scale, rather than being an intrinsic property of the system. The strong dependence of the turbulence fractions on the averaging scale has direct implications for magnetic field estimates obtained from observational methods such as the Davis-Chandrasekhar-Fermi technique emphasizing the need for careful scale selection when interpreting magnetic and kinetic turbulence in galaxies.

Figures (11)

• Figure 1: Face-on maps of the projected magnetic field vectors for the total field ($B_{tot}$), the mean field ($B_0$) and the turbulent component ($\delta B$) at 500 Myr. Model T and model R are shown on the left and right side, respectively.
• Figure 2: Face-on maps of the velocity field vectors for the total field ($v_{tot}$), the mean field ($v_0$) and the turbulent component ($\delta v$) at 500 Myr. Model T and model R are shown on the left and right side, respectively.
• Figure 3: Power spectra of the mean ($P_{B_0}$) (top panel) and turbulent magnetic field ($P_{\delta B}$) (bottom panel) for different averaging radii at 500 Myr. The orange, green and purple correspond to $R_{avg}$=0.1 kpc, $R_{avg}$=0.5 kpc and $R_{avg}$=1.0 kpc. The dashed blue line represents the power spectrum of the total magnetic field. Model T and model R are shown on the left and right side, respectively.
• Figure 4: Power spectra of the mean ($P_{v_0}$) (top panel) and turbulent velocity field ($P_{\delta v}$) (bottom panel) for different averaging radii at 500 Myr. The dotted, dashed and solid lines correspond to $R_{avg}$=0.1 kpc, $R_{avg}$=0.5 kpc and $R_{avg}$=1.0 kpc. The dashed blue line represents the power spectrum of the total velocity field. Model T and model R are shown on the left and right side, respectively.
• Figure 5: Power spectra of the residual energy density of the turbulent components ($P_{E_{r,turb}}$) for different averaging radii at 500 Myr. Model T and model R are shown on the left and right side, respectively.