1. Clump decomposition methods and the DQS Tony Wong University of Illinois

2. Interstellar Turbulence Fourier transform power spectra (Lazarian & Pogosyan 2000) Wavelets (including ∆-variance) Spectral correlation function (Rosolowsky et al. 1999) Principal component analysis (Brunt & Heyer 2002) Clumpfind (Williams et al. 1994) Gaussclumps (Stutzki & Güsten 1990) CPROPS (Rosolowsky & Leroy 2006) Statistical methods: Structural decomposition:

3. NANTEN 12 CO

4. Mopra 13 CO

5. Mopra C 18 O

6. SEST 1.2 mm

7. Column density and 13 CO opacity

8. 8 Highest opacity regions G333.6-0.2 “Ring” radius ~10 pc; consistent with 10 km s -1 expansion for 1 Myr

9. τ -corrected total cloud mass is only slightly (~10%) larger than would be derived from the optically thin assumption with T ex =20 K. However, distribution of column densities differs significantly on the high end. Column density PDF τ -corrected

10. Comparison with Ridge et al. (2006) Extinction (2MASS) CO emission (FCRAO)

11. Ostriker, Stone, Gammie 2001 A log-normal volume density distribution is expected from isothermal turbulence The column density PDF should transition from log-normal to Gaussian as more independent zones along the line of sight are integrated. Comparison with simulations high B low B

12. CLUMPFIND: Use a hierarchy of contour levels to identify emission maxima. ‣ Clumps are identified as closed contours in contour plot ‣ Contested emission assigned to nearest clump using “friends of friends” algorithm GAUSSCLUMPS: Model the cloud as a sum of triaxial Gaussian components. ‣ Can distinguish tight blends of clumps ‣ Clump properties follow immediately ‣ Tendency to create many small clumps CPROPS: Use contouring like CLUMPFIND, but do not try to divide contested emission. ‣ Identify local maxima larger than all neighbors ‣ Require >2  contrast above merge level with other maxima Segmentation into Clumps

13. Clump Numbers - 13 CO CLFINDGAUSSCPROPS

14. Clump Numbers - 13 CO CLFINDGAUSSCPROPS Number of clumps 26452000594 fraction of total flux decomposed 100%64%9.3%

15. Distribution of Masses CLFINDGAUSS CPROPS

16. Distribution of Radii CLFINDGAUSS CPROPS

17. Luminosity vs. Radius CLFINDGAUSSCPROPS While molecular clouds as a whole have approximately constant surface density, clumps within them seem to have approximately constant volume density.

18. Line width vs. Radius CLFINDGAUSSCPROPS No strong correlation, especially for latter 2 methods.

19. Luminosity vs. Line width CLFINDGAUSSCPROPS Not independent of previous two relations!

20. Virial vs. Luminous Mass CLFINDGAUSSCPROPS x-axis: T b R 2  y-axis: R  2

21. α >>1: clump must be confined by external pressure α ~1: clump is close to self-gravitating α <<1?? Virial Parameter

22. Conclusions Clump properties related to size depend a lot on how they are defined! CLUMPFIND, designed to mimic decomposition “by eye,” favours structures a few times larger than the beam size. It segments all emission, even an extended underlying component. GAUSSCLUMPS is unique in allowing clumps to overlap in position-velocity space. It also segments extended emission, but tends to put it in small (unresolved) clumps. CPROPS doesn’t segment extended emission; may underestimate clump masses & radii. GAUSSCLUMPS and CPROPS both tend to find a few massive clumps & many low-mass ones.

23. Conclusions Linewidth doesn’t correlate well with other properties. Clump flux and radius (R 3 ) do correlate well, suggesting clumps all have similar densities. This correlation probably governs the virial parameter,   R  2 /M  (M/M J ) -2/3. M J   3  -1/2, so if velocity dispersion and density changes little with size, Jeans mass won’t either, and only largest clumps will be bound.