Structure analysis

Measuring the turbulent and fractal structure of interstellar clouds

We develop and test measures to quantitatively describe the structure of turbulent interstellar clouds. Main progress in the past was achived on three tools:

Δ--variance analysis introduced by Stutzki et al. (1998) and extended by Ossenkopf et al. (2008);
Centroids velocity studies of molecular lines;
Scaling of velocity channel maps

Applying the Δ-variance analysis to observations of the Galactic Ring (Brüll et al. 2004) and in the Perseus molecular cloud (Sun et al. 2006), we were able to identify characteristic length scales and signatures of dynamic interaction. Studying the Δ-variance spectra of synthetic velocity structures allowed to calibrate these tools to allow a one-by-one comparison between models and observations (Mac Low & Ossenkopf 2000, Ossenkopf et al. 2001, 2006). An application of this tool to large scale mapping data sets (extinction maps and molecular line surveys) was recently published in collaboration with the CEA Saclay and Heidelberg groups (Schneider et al. 2011a,b).

13CO over 8µm for Cygnus cloud

¹³CO 1–0 integrated intensity map of Cygnus-X (contours) overlaid on colors of MSX 8µm emission (left) and resulting ¹³CO 1–0 Δ-variance spectrum of the entire complex tracing the characteristic scales of the molecular cloud formation (Schneider et al.2011).

Current studies cover:

PDFs of intensities and velocities
PDFs of spatial increments
Structure functions of variable order
Principal component analysis
Δ-variance spectra and spatial correlation analysis
Clump decomposition
Tsallis statistics
Bispectrum

During the first period of the ISM-SPP project, we will concentrate on the ability of the different tools to quantify the spatial correlation and systematic variation between different observational tracers. In this way we want to measure the physical scales of the different chemical phase transitions in the interstellar medium. First attempts have been performed by studying the mutual correlation in the distribution of different tracers in molecular clouds (Sun et al. 2006, Schuster et al. 2007).

IC348: Colors: CI, Contours: 13CO 1-0

¹³CO in IC348. The left panel shows CI in colors and¹³CO 1-0 in contours (Sun et al. 2006). The right panel contains theΔ-variance spectra of the two maps and the cross correlation spectrum indicating a characteristic chemical correlation scale of 2-3' where the spectrum saturates.

More valuable additional information is hidden in the map anisotropy as measured by an adapted version of the Δ-variance analysis and the velocity structure as measured by a generalized Larson relation. A combination of the investigation of the general map appearance, the Δ-variance, the determination of the smoothness and wing behaviour of line profiles and the investigation of single channel maps is necessary to obtain a reliable cloud modeling.