Obtaining turbulence properties from surveys

Jungyeon ChoChungnam National University, Korea

Cho & Ryu (2009, ApJL)Cho et al. (2013, in prep.)

ISM is in turbulent state

Observed line width > thermal line width

Molecular Clouds: V ~ a few km/sec

Turbulence

Big power law (WIM): Armstrong & Spangler (1995)

Slope ~ -5/3

Elec

t ron

d ens

it y sp

ectru

m

AUpc

HI cloud (SMC) : Stanimirovic+(1999)

HI column density power-law spectrum

Important turbulence properties

-Driving scale-Density fluctuation ()-…

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.

ln

2)ln(lnexp

2

1ln)(ln 2

20

2ddP

for a mass-conserving system2

ln2

0

Slide from J. Kim (modified)

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

3D isothermal HD (Nordlund & Padoan 1999)

3D isothermal MHD (Ostriker+ 2001)

We observe projected quantities (e.g. ,…)Question: Can we obtain ?

Density (MHD)

To observer

=projected

PPV cube

v

Intensity

V

Itot

Centroid

2 useful observables

Column density of turbulence

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

~

~l (L/l)1/2 l (L/l)1/2

>0 <0

l=???

Cho & Ryu (2009) showed that l ~ Lint, where Lint is the integral scale

~ Lint (L/Lint)1/2

FTk1

k2

k~1/l

E(k)

~ Lint (L/Lint)1/2

Lint=

Conclusions

-If we observe optically thin line emissions, we can get

1. Driving scale 2.

3….