Published on *I. Physikalisches Institut* (https://www.astro.uni-koeln.de)

We develop and test measures to quantitatively describe the structure of turbulent interstellar clouds [1]. Main progress in the past was achived on three tools:

- Δ--variance analysis [2] introduced by Stutzki et al. (1998) and extended by Ossenkopf et al. (2008);
- Centroids velocity [3] studies of molecular lines;
- Scaling of velocity channel maps [4]

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).

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).

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.

**Links:**

[1] https://www.astro.uni-koeln.de/../../%7Eossk/ftpspace/preprints/zermatt2003.pdf

[2] https://www.astro.uni-koeln.de/node/426

[3] https://www.astro.uni-koeln.de/node/427

[4] https://www.astro.uni-koeln.de/node/428