What Astronomers Want to Know about ISM Turbulence

A. Lazarian (University of Wisconsin-Madison)

Problem• Turbulence is essential to understandstar formation, cosmic ray propagationetc.

• High ISM Reynolds numbers (Re≡Lv/νRm≡Lv/νm ) make brute force numericaltesting impossible.

Pragmatic ApproachEssential astrophysical questions may beanswered if one knows:

•Turbulent spectrum: distribution ofenergy at different scales

•Turbulent intermittency: properties ofsmall volume with extreme conditions

• Interaction of turbulence with cosmicrays

Abstract

While magnetized turbulence is an extremely complexphenomenon, a lot of advances in understandingastrophysical phenomena can be obtained if rathersimple statistical measures are known. We showexamples of the practical use of the measures ofturbulence spectra and intermittency and discuss howthe interactions with cosmic rays modify the spectrum.We describe techniques for obtaining the spectra ofISM velocity fluctuations and how they can be used totest both theory and numerics against observations.

Summary

• If turbulent spectra and turbulent anisotropies

are known it is possible to quantify most of the

essential ISM transport processes, e.g. heattransfer, CRs propagation.

• Turbulence in ISM exhibits intermittency, I.e.

small regions with extreme values of energydissipation. This dissipation is important, but not

sufficiently strong to radically change ISM

chemistry.

• Various ISM physical processes, e.g. CR

instabilities, modify the spectrum of ISM

turbulence. Thus the studies of turbulence

spectra are very informative.

• Turbulence spectra can be obtained from

observations with new techniques, I.e. VCA and

VCS. Both techniques have been successfullytested with synthetic and observational data.

Acknowledgement: NSF grant AST 0307869 and NSF

Center for Magnetic Self-Organization in Astrophysical

and Laboratory Plasmas (CMSO).

Questions

ISM turbulence is

complex. Is there

any hope for theoryadvances? Is there

any use of the

theory?

Turbulent Spectra

Examples of Applying the Theory

Spectrum Thermal conductivity

Beresnyak & Lazarian 06

Turbulence spectrum (and anisotropy)allows to predict thermal conductivity of

magnetized plasmas (e.g. in ISM). Above

the curve turbulent advection of heatdominates electron conductivity.

Lazarian 06

Turbulent Intermittency Effect of Cosmic Rays

Re=104Re=40

observed structures depend on Re

Testing Theory with Observations

Intermittency

measure

MA and Ms are Alfven and sonic Mach numbers

Intermittent

energy deposition

In some fraction of volume the energy densityis 104 higher than the mean value. However,

the fraction is small (cf. Falgarone et al. 2006)

Beresnyak & Lazarian 06

Kowal & Lazarian 06

Lazarian & Beresnyak 06

Gyroresonace instability transfers energyfrom CR mean free path (mfp) to CR

gyroradius. The instability is fed by the

energy of compressible motions and bothmodifies turbulence and decreases mpf.

New component

Velocity Channel

Analysis (VCA)Velocity Coordinate Spectrum (VCS)

Lazarian & Pogosyan 00

Application of VCS to Arecibo HI data

Successfully applied to SMC, Galactic HI, CO

emission data

High latitude HI

Lazarian & Pogosyan 04

Lazarian & Pogosyan 06

Chepurnov & Lazarian 06

Emission lines Absorption lines

Chepurnov et al. 06

S(v) is an observed spectral line,γ depends on the v spectral index α and observation geometry

�

P1(kv ) ≡ S(v)e−ikvvdv∫ 2∝ kv

−γ

Model with

T=102K fitsthe data for

different

resolutions.

Spectral index is steep (-3.9)

VCS uses info along

v-axis. It does not needgood spatial resolution

for emission line studies

and gets spectra whenabsorption is measured

along a few lines of sight