Although numerical simulations of transsonic and supersonic turbulence appropriate to interstellar gas have been carried out for several years now (Porter et al. 1992, 1994; Padoan & Nordlund 1999; Mac Low et al. 1998; Stone et al. 1998) there are only a few direct comparisons between numerical results and astrophysical observations (e.g. Falgarone et al. 1994; Padoan et al. 1999; Rosolowsky et al. 1999). This is mainly due to the lack of appropriate measures applicable both to simulated and observed structures. Measures common for turbulence studies like the power spectrum of spatial or velocity fluctuations or the probability distribution of velocity increments are not easily applied to observations where their use is greatly impaired by the limitations due to finite signal to noise ratio and limited telescope resolution.
To obtain clues to the true physical nature of interstellar turbulence, characteristic scales and any inherent scaling laws have to be measured and modelled. A major problem with characterizing both the observations and the models is to determine what scaling behaviour, if any, is present in complex turbulent structures. Both the velocity and density fields need to be considered, but only the radial velocity and column densities can be observed.
One measure useful for characterizing structure and scaling in observed maps of molecular clouds is the -variance, , introduced by Stutzki et al. (1998). It can better separate observational effects from the real cloud structure than e.g. the power spectrum or fractal dimensions. The -variance spectrum clearly shows characteristic scales and scaling relations, and its logarithmic slope can be analytically related to the spectral index of the corresponding power spectrum.
Stutzki et al. (1998) and Bensch et al. (1999) have applied the -variance analysis to observations of the Polaris Flare and the FCRAO survey of the outer galaxy. They found a relatively universal law describing these clouds, with a power law structure at scales below the cloud size and the general cloud size as the only characteristic scale within the resolution limit. Given the limited number of samples, however, it is not yet possible to draw conclusions on the scaling of turbulence in molecular clouds in general. To study the common behaviour and differences between several clouds and interstellar regions the analysis of more and larger maps obtained with a good signal-to-noise ratio is required.
In order to understand the physical significance of the characterization of the observational maps by -variance spectra, we apply here the same analysis to simulated gas distributions resulting from MHD models. In this first paper, we try to get a general feeling for the scaling behaviour in different models, and for the influence of the different parameters and numerical approaches on the produced structures. We only perform a qualitative comparison to the observations here. In a subsequent paper we will attempt to make a detailed fit of several observed regions using MHD models including the solution of the radiative transfer problem.
© European Southern Observatory (ESO) 2000
Online publication: December 8, 1999