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Universität zu Köln
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Mathematisch-Naturwissenschaftliche Fakultät
Fachgruppe Physik

I. Physikalisches Institut

Analysis of velocity channel maps

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Structure of star-formation in the Galactic Molecular Ring

We have systematically applied the Delta-variance analysis to observed maps of different CO transitions in the Galactic Ring. We find that the extended material seen in CO 1-0 and CO 2-1 shows a significantly higher degree of fragmentation in comparison to high-contrast molecular clumps as seen in 13CO. The 13CO emission shows a similar structure to the CO 3-2 maps tracing warm gas heated by active star formation. The diffuse foreground material shows the same Delta-variance slope as the extended material in the Galactic Ring in all tracers.

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3-D color plot of the Delta-variance as a function of structure size and velocity for the CO 3-2 data of the G30-31 field in the Galatic Ring. The figure at the left bottom shows the line integrated map, the figure on the right bottom indicates the single Delta-variance spectrum for the velocity channel at 90 km/s (Brüll et al. 2004).

By applying the Delta-variance analysis to individual channel maps we find that the corresponding maps of structure contrast as a function of structure size and velocity provide a very good indicator for prominent scales of star-formation both in terms of length and velocity scales. Comparing the Delta-variance spectra of maps taken in different tracers helps to study the effect of star-formation on the general structure formation in the Galactic ring. If we compute the ratio between the Delta-variance plots as function of lag and velocity for the 12CO and the 13CO maps, we find an extremely sensitive indicator for sizes and velocities of column density enhancements tracable by the relative change of the optical depth in the two transitions.

The "velocity channel analysis"

Lazarian & Pogosyan (2000) have introduced an analytic relation for the change of the spectral index of maps taken in velocity channels of different widths as a function of the bin size, provided that the underlying density and velocity structure is given by a Gaussian field of fluctuations. The method opens in principle a way to simultaneously determine the scaling behaviour of the density and the velocity fields from a single analysis of a data cube of lines. This method was called velocity channel analysis (VCA).

We have re-implemented the method by combining it with the advantages of the Delta-variance analysis. This was applied to observational data obtained in Perseus (Sun et al. 2005) and to cloud models given by fractal descriptions and hydrodynamic simulations. For fractal clouds we were able to confirm that the method allows to deduce the spectral indices of density and velocity structure. A different picture arises, however, in the application to observed CO data from Perseus and Serpens and to hydrodynamic simulations demonstrated in next Figure:

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Spectral indices of channel maps with varying width for a self-similar hydrodynamic cloud model combined with molecular line radiative transfer. The second panel shows the dependence of the average channel index as a function of the channel width.

The numerical experiments using hydrodynamic simulations with a self-similar behaviour over a long but limited range of scales have proven that the VCA is no longer able to derive the spectral indices there. We can trace this back to the basic assumption of the VCA that it is only justified if the data represent a completely sampled structure with Gaussian statistics (Esquivel et al. 2003). In contrast, molecular cloud observations often show indications of low-number statistics or intermittency, visible as non-Gaussian average line profiles. Thus the applicability of the method has to be tested for every set of observational data. Further systematic experiments covering a wider range of possible cloud behaviours have to be performed to provide a general criterion.

Contact: Volker Ossenkopf