Structure analysis of interstellar clouds. II. Applying the Δ-variance method to interstellar turbulence

Context: The Δ-variance analysis is an efficient tool for measuring the structural scaling behaviour of interstellar turbulence in astronomical maps. It has been applied both to simulations of interstellar turbulence and to observed molecular cloud maps. In Paper I we proposed essential improvements to the Δ-variance analysis and tested them on artificial structures with known characteristics.
Aims: In this paper we apply the improved Δ-variance analysis to simulations of interstellar turbulence and observations of molecular clouds. We tested the new capabilities in practical use and studied properties of interstellar turbulence that could not have been addressed before.
Methods: We selected three example data sets that profit in particular from the improved Δ-variance method: i) a hydrodynamic turbulence simulation with prominent density and velocity structures; ii) an observed intensity map of ρ Oph with irregular boundaries and variable uncertainties of the different data points; and iii) a map of the turbulent velocity structure in the Polaris Flare affected by the intensity dependence on the centroid velocity determination.
Results: The tests confirm the extended capabilities of the improved Δ-variance analysis. Prominent spatial scales were accurately identified and artifacts from a variable reliability of the data were removed. The analysis of the hydrodynamic simulations showed that the injection of a turbulent velocity structure creates the most prominent density structures are produced on a scale somewhat below the injection scale. The new analysis of a ρ Oph continuum map reveals an intermediate stage in the molecular cloud evolution showing both signatures of the typical molecular cloud scaling behaviour and the formation of condensed cores. When analysing the velocity structure of the Polaris Flare we show that a universal power law connects scales from 0.03 pc to 3 pc. However, a plateau in the Δ-variance spectrum around 5 pc indicates that the visible large-scale velocity gradient is not converted directly into a turbulent cascade here. It is obvious that, for any turbulent structure, effects of low-number statistics become important on the driving scale.