1. Obtaining turbulence properties from surveys Jungyeon Cho Chungnam National University, Korea Cho & Ryu (2009, ApJL) Cho et al. (2013, in prep.)

2. ISM is in turbulent state

3. Observed line width > thermal line width Molecular Clouds:  V ~ a few km/sec  Turbulence

4. Big power law (WIM): Armstrong & Spangler (1995) Slope ~ -5/3 Electron density spectrum AU pc

5. HI cloud (SMC) : Stanimirovic+(1999) HI column density  power-law spectrum

6. Important turbulence properties -Driving scale -Density fluctuation (   ) -…

7. Density PDF Numerical studies (for example, VS94, PN97, PN99, Passot and VS 98, E. Ostriker et al. 01) showed that density PDFs of isothermal (gamma=1), turbulent flows follow a log-normal distribution. for a mass-conserving system Slide from J. Kim (modified)

8. 1D isothermal HD ( Passot & Vazquez-Semadeni 94 )

9. 3D isothermal HD ( Nordlund & Padoan 1999 )

10. 3D isothermal MHD ( Ostriker+ 2001 )

11. We observe projected quantities (e.g. ,…)  Question: Can we obtain   ? Density (MHD) To observer  =projected 

12. PPV cube v Intensity V  I tot   Centroid 2 useful observables

13. Column density of turbulence

14. Velocity centroids (Mach=2.3, Alfven Mach=0.7) This last expression valid for optically thin media, w/emissivity proportional to density (e.g. cold HI) From A. Esquivel

15.    ~ ~ l   (L/l) 1/2  l    (L/l) 1/2  >0  <0   l=???

16. Cho & Ryu (2009) showed that l ~ L int, where L int is the integral scale    ~ L int    (L/L int ) 1/2 FT k1k1 k2k2 k~1/l E  (k)

17.    ~ L int    (L/L int ) 1/2  L int =

18. Conclusions -If we observe optically thin line emissions, we can get 1. Driving scale 2.   3….