Studies of Velocity Fluctuations: Keep Theorists Honest!

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 sayWhat 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/ > 10~100

Re ~ 15,000

* inertial vs. viscosity term

Da Vinci’s view

Re=40 Re=10000

Challenge: Turbulent ISMChallenge: Turbulent ISM

Re ~VL/ ~1010 >> 1

~ rLvth, vth < V, rL<< L

Is there any hope for progress?

Pc scalesNumerics will not get to such Re in foreseeable future. Flows in ISM and computers are and will be different!

Computational efforts scale as Re4!!! Currently maxRe of order <104

Is Visual Correspondence Enough?

Is Visual Correspondence Enough?

0 max

Synthetic observations M=10

MHD 5123

Emission Nebulae

Beresnyak, Lazarian & Cho 05

NSF reviewer:”The proposed work is in danger of being criticized for studying artificial situations that isolate particular physical concepts”

Revealing Order: Turbulence Spectra and Correlations

Spectrum : E(k) ~ k-n

k

E(k)E(k)

=

+

+….

v( r ), r, … Fourier analysis of correlations

k-n

n=5/3 forKolmogorov model

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

m=2/3 for Kolmogorov model

<…> is averaging

We shall deal with relatively large scales using a velocity infoSlope ~ -5/3

Ele

ctro

n d

en

s ity

sp

ect

r um

AUpc

Electron density fluctuations trace of turbulence only at small scales.No reliable info for large scales

A Rare Quantitative Example

Armstrong, Rickett & Spangler(1995)Armstrong, Rickett & Spangler(1995)

“Big power law in the sky” is cited a lot because there are no other good examples

v

log

Shallow Density in Supersonic MHD Turbulence

Shallow Density in Supersonic MHD Turbulence

Spectrum gets flat at M=10, thus the fluctuations grow as scale gets smaller

Fluctuation of density at scale kDensity contours for > 25 mean density

Beresnyak, Lazarian & Cho 05

A possible way to create TSAS

MHD 5123

M=10E(k)

k

For partially ionized gas viscosity is important

while resistivity is not.

B

~0.3pc in WNM

MHD Turbulence in Partially Ionized Gas: New Regime

MHD Turbulence in Partially Ionized Gas: New Regime

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

Resistive scale is not L/Rm, but L/Rm1/2

Beresnyak & Lazarian 06

Density filaments

Length of filaments is large scale, may be related to TSASCho, Lazarian Vishniac 02

Long filaments of density Cho & Lazarian 03

E(k)

k

QuickTime™ and aYUV420 codec decompressor

are needed to see this picture.

Formation of Density Structures in Viscous Turbulent Flow

Formation of Density Structures in Viscous Turbulent Flow

Projected density: MHD simulations 5123

Magnetic field in viscous fluid compresses density

Beresnyak & Lazarian 06

Small scale slowly evolving structures overheating of ISM is not a problem

Generation of Slab Alfvenic Turbulence by Cosmic RaysGeneration 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

Velocity Statistics VCA and VCS: Keeping Theorists Honest

Velocity Statistics VCA and VCS: Keeping Theorists Honest

Modified from A Goodman

x

y

z

PPV cube

Vx

y

Velocity slice Column density

3d dimension is velocity

Velocity Channel Analysis (VCA) relates spectra of velocity slices to spectra of turbulent velocity(Lazarian & Pogosyan 00, 04)

Velocity Coordinate Spectrum (VCS) relates spectra of velocity along velocity coordinate to spectra of turbulent velocity (Lazarian & Pogosyan 00, 06)

2 new techniques to recover turbulent velocity spectra VCA and VCS

Mathematical Setting in Lazarian & Pogosyan 00

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

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

high resolutionLOSgeometry pencil beam flat beam

lowresolution

parallel 2/(α-3) 4/(α-3) 6/(α-3)crossing 2/(α-3) 3/(α-3) 4/(α-3)

Relation of VCS to the velocity spectral index

Not affected by phase fraction

Velocityindex

Synthetic observations change of VCS slope

High resolution

Low resolution

€

P1

( kv

) ≡ S ( v ) e− ik

vv

dv∫

2

∝ kv

− γ

VCS expression:

S(v) observed line

VCA (spatial spectrum, Ny=Nz=32768) VCS (spectrum over v, Nz=32768)

αu= 4.0

needed Nz: 20000

αu=3.67

needed Nz:420000

€

Nz ≈15LsLinjNch

2

α u −3 - number of points over z, assuring absence of shot-noise

(noisy part of P1 filtered out)

VCA/VCS SimulationsVCA/VCS Simulations

VCS: Application to Real DataVCS: Application to Real Data

.

Data handling by Chepunov & Lazarian 06

Data provided by Stanimirovic

VCS was tested with Arecibo GALFA data for both low and high resolution limits

Temperature 100 K

Resolution was decreased to test the theory

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

Future Missions: Spectrum of Turbulence with Constellation X

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

Studies of turbulence is possible with X-rays using new missions Hydra A

Galaxy Cluster

Velocity Channel Analysis(Lazarian & Pogosyan 00)

Velocity Channel Analysis(Lazarian & Pogosyan 00)

“Shallow” density n>-3

“Steep” density n<-3

“Thin” channels

“Thick” channels

Thin channels

Thick channels

Synthetic maps tests

(d~rm

=nγ =nγ

Ps~ K-γ

“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-

Velocity structure function

Spectrum intensity channels

Application of VCA to SMC Spectra shallow than Kolmogorov were obtained for velocity in Stanimirovic & Lazarian 01

VCS and VCS: ProspectsVCS and VCS: Prospects

spectrum compression factor = 8Absorption 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

To increase velocity coverage use heavy species.

Possible to separate thermal and non-thermal contributions to line width.

Measure cold gas temperature.

In addition:

Emission lines with self-absorption LP 04, 06(applications: HI, CO2 etc.)New asymptotics predicted, e.g. K-3Use of entire 3D PPV cubes is promising!

VCS from a single absorption line

VCS and VCA versus CentroidsVCS and VCA versus Centroids

zzsz dvvyxvyxS ),,(),( ∫= Definition:s= antennae temperature at frequency depends on both velocity and density)

s

Centroids are OK to reveal anisotropy due to magnetic field (Lazarian et al.01), distinguish between subAlfvenic and superAlfvenic turbulence.

From Esquivel & Lazarian 05Centroids may not be good to study M>1 turbulence (Esquivel & Lazarian 05).

Necessary criterion for centroids to reflect velocities is found in Lazarian & Esquivel 03

SummarySummary

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 ModelCompressible Extension of

GS95 MHD Turbulence ModelMagnetic field and velocityin Cho & Lazarian 02

New computations: Beresnyak & Lazarian 06

Fast modes are isotropic

Elongated Alfven eddies

1.GS95 scaling for Alfven and slow modes:

2.Isotropic acoustic-type fast modes:

Does GS95 Model Require Improvements?

Does GS95 Model Require Improvements?

Incompressible turbulence shows spectrum flatter than the GS95 model predicts. Why?

Maron & Goldreich 01Boldyrev 05, 06, posterGaltier et al. 05

Different explanations

Polarization intermittency in Beresnyak & Lazarian 06 causes some flattening V and B

show different anisotropies and scalings