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Studies of Velocity Fluctuations: Keep Theorists Honest!

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### Studies of Velocity Fluctuations: Keep Theorists Honest!

Lazarian A.

UW-Madison, Astronomy and Center for Magnetic

Self-Organization in Laboratory and Astrophysical Plasmas

Collaboration with

Pogosyan D. (Univ. of Alberta)

Chepurnov A. (UW-Madison)

Beresnyak A. (UW-Madison)

What I am going to say

- Critical remarks: “What is our future?”
- Possible models of TSAS
- New quantitative techniques to study velocity spectra.

Chaotic order and Re number

- For turbulence Reynolds number Re = VL/n > 10~100

* inertialvs. viscosityterm

Re ~ 15,000

Da Vinci’s view

Re=40

Re=10000

Challenge: Turbulent ISM

Re ~VL/n ~1010 >> 1

n ~ rLvth, vth < V, rL<< L

Numerics will not

get to such Re in

foreseeable future.

Flows in ISM and

computers are and

will be different!

Pc scales

Computational

efforts scale as

Re4!!!

Currently max

Re of order <104

Is there any hope for progress?

0

max

Is Visual Correspondence Enough?NSF reviewer:”The proposed work is in danger of being criticized for

studying artificial situations that isolate particular physical concepts”

Emission Nebulae

Synthetic observations M=10

MHD 5123

Beresnyak, Lazarian & Cho 05

C~<(v1-v2)2> ~ rm

m=2/3 for Kolmogorov model

<…> is averaging

Revealing Order: Turbulence Spectra and Correlationsv( r ), r( r ), …

Fourier analysis of correlations

Spectrum : E(k) ~ k-n

=

+

+

….

E(k)

k-n

n=5/3

for

Kolmogorov

model

Dk

Armstrong, Rickett & Spangler(1995)

We shall deal with relatively large scales using a velocity info

Slope ~ -5/3

Electron density

fluctuations trace

of turbulence only

at small scales.

No reliable info for

large scales

Electron density spectrum

“Big power law in the sky”

is cited a lot because there

are no other good examples

pc

AU

Shallow Density in Supersonic MHD Turbulence

Fluctuation of density at scale k

Density contours for > 25

mean density

Spectrum gets flat at M=10, thus

the fluctuations grow as scale

gets smaller

M=10

E(k)

v

Beresnyak, Lazarian & Cho 05

log

MHD 5123

A possible way to

create TSAS

k

filaments

MHD Turbulence in Partially Ionized Gas: New RegimeB

For partially ionized gas

viscosity is important

while resistivity is not.

Long filaments of density

Cho & Lazarian 03

MHD turbulence does not stop at the viscous

scale in partially ionized gas but creates a

magnetic cascade up to decoupling scale

Lazarian, Vishniac & Cho 04

~0.3pc in WNM

Length of

filaments

is large

scale, may

be related

to TSAS

Cho, Lazarian

Vishniac 02

E(k)

Resistive

scale is not

L/Rm, but

L/Rm1/2

k

Beresnyak & Lazarian 06

Formation of Density Structures in Viscous Turbulent Flow

Magnetic field in viscous fluid compresses density

Projected density: MHD simulations 5123

Small scale slowly evolving structures

overheating of ISM is not a problem

Beresnyak & Lazarian 06

Generation of Slab Alfvenic Turbulence by Cosmic Rays

How do cosmic rays modify compressible MHD turbulence?

Turbulent compressions of magnetic field creates

compressions of cosmic rays and those create waves at

Larmor radius rL ( model by Lazarian & Beresnyak 06)

Instability growth

Predicted spectra of

slab-type Alfven modes:

k-1.18 and k-1.45

x

V

PPV cube

Velocity Statistics VCA and VCS: Keeping Theorists Honest2 new techniques

to recover turbulent

velocity spectra

VCA and VCS

Velocity slice

Column density

y

Velocity Channel Analysis (VCA)

relates spectra of velocity slices

to spectra of turbulent velocity

(Lazarian & Pogosyan 00, 04)

z

x

Velocity Coordinate Spectrum (VCS)

relates spectra of velocity along

velocity coordinate to spectra of

turbulent velocity

(Lazarian & Pogosyan 00, 06)

3d dimension

is velocity

Modified from A Goodman

Mathematical Setting in Lazarian & Pogosyan 00

Density in PPV (xyv)

Velocity distribution

Correlation function in PPV

where

Real (xyz) density correlation

Velocity correlation

VCS: Predictions and TestingLazarian & Pogosyan 06, Chepurnov & Lazarian 06

Relation of VCS to the velocity spectral index

VCS expression:

S(v) observed line

Synthetic observations

change of VCS slope

Velocity

index

High resolution

Low resolution

Not affected by phase fraction

VCA/VCS Simulations

(noisy part of P1 filtered out)

- number of points over z, assuring absence of shot-noise

VCS: Application to Real Data

.

VCS was tested with Arecibo GALFA data

for both low and high resolution limits

Resolution was decreased to test the theory

Data handling

by Chepunov &

Lazarian 06

Temperature

100 K

Data provided by Stanimirovic

Theory predicts suppression by a factor exp (-aTkv^2). Correcting

for it recovers the slope and gets the temperature of cold gas.

Future Missions: Spectrum of Turbulence with Constellation X

Studies of turbulence is

possible with X-rays using

new missions

Hydra A

Galaxy Cluster

Constellation X will get turbulent spectra with VCS technique (Lazarian & Pogosyan 06) in 1 hour

Chepurnov & Lazarian 06

“n” is the density spectral index, E~k2P, P~k-n , “m” is related to the velocity energy spectral index as m=-3+ , Ev~ k2Pv, Pv~k-

Thin channels

Thick channels

Velocity Channel Analysis(Lazarian & Pogosyan 00)(d~rm)

Velocity

structure

function

Spectrum

intensity

channels

Ps~ K-g

Application of VCA to SMC

Spectra shallow

than Kolmogorov

were obtained for

velocity in

Stanimirovic &

Lazarian 01

VCS and VCS: Prospects

Absorption lines can be used to study

turbulence (extragalactic objects,

Lyman alpha, supernovae remnants).

Emission and absorption studies can

be combined to get both density and

velocity statistics for unresolved objects

spectrum compression factor = 8

VCS from a single

absorption line

In addition:

To increase velocity coverage use heavy species.

Possible to separate thermal and non-thermal

contributions to line width.

Measure cold gas temperature.

Emission lines with

self-absorption

LP 04, 06

(applications:

HI, CO2 etc.)

New asymptotics

predicted, e.g. K-3

Use of entire 3D PPV cubes is promising!

= antennae temperature at frequency n

(depends on both velocity and density)

rs

n

VCS and VCA versus CentroidsDefinition:

Centroids are OK to reveal anisotropy

due to magnetic field (Lazarian et al.01),

distinguish between subAlfvenic

and superAlfvenic turbulence.

Centroids may not be good to study M>1

turbulence (Esquivel & Lazarian 05).

From Esquivel & Lazarian 05

Necessary criterion for centroids to

reflect velocities is found in

Lazarian & Esquivel 03

Summary

Turbulence is a basic property of ISM.

- Computers may mislead us unless we understand the underlying physics.
- Observers should keep theorists in check.
- VCS is a new promising technique.
- The wealth of surveys can be used to study ISM (identify sources and sinks of energy) and test theories of turbulent ISM.

Compressible Extension of GS95 MHD Turbulence Model

Magnetic field and velocity

in Cho & Lazarian 02

1.GS95 scaling for Alfven and slow modes:

Elongated Alfven

eddies

New computations: Beresnyak & Lazarian 06

2.Isotropic acoustic-type fast modes:

Fast modes are

isotropic

Does GS95 Model Require Improvements?

Incompressible turbulence shows spectrum flatter than

the GS95 model predicts. Why?

Maron & Goldreich 01

Boldyrev 05, 06, poster

Galtier et al. 05

Different

explanations

Polarization intermittency

in Beresnyak & Lazarian 06

causes some flattening

V and B show

different

anisotropies

and scalings

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