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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).
UW-Madison, Astronomy and Center for Magnetic
Self-Organization in Laboratory and Astrophysical Plasmas
Pogosyan D. (Univ. of Alberta)
Chepurnov A. (UW-Madison)
Beresnyak A. (UW-Madison)
* inertialvs. viscosityterm
Re ~ 15,000
Da Vinci’s view
Re ~VL/n ~1010 >> 1
n ~ rLvth, vth < V, rL<< L
Numerics will not
get to such Re in
Flows in ISM and
computers are and
will be different!
efforts scale as
Re of order <104
Is there any hope for progress?
C~<(v1-v2)2> ~ rm
m=2/3 for Kolmogorov model
<…> is averagingRevealing Order: Turbulence Spectra and Correlations
v( r ), r( r ), …
Fourier analysis of correlations
Spectrum : E(k) ~ k-n
We shall deal with relatively large scales using a velocity info
Slope ~ -5/3
of turbulence only
at small scales.
No reliable info for
Electron density spectrum
“Big power law in the sky”
is cited a lot because there
are no other good examples
Fluctuation of density at scale k
Density contours for > 25
Spectrum gets flat at M=10, thus
the fluctuations grow as scale
Beresnyak, Lazarian & Cho 05
A possible way to
filamentsMHD Turbulence in Partially Ionized Gas: New Regime
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
scale is not
Beresnyak & Lazarian 06
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
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)
Predicted spectra of
slab-type Alfven modes:
k-1.18 and k-1.45
PPV cubeVelocity Statistics VCA and VCS: Keeping Theorists Honest
2 new techniques
to recover turbulent
VCA and VCS
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
(Lazarian & Pogosyan 00, 06)
Modified from A Goodman
Density in PPV (xyv)
Correlation function in PPV
Real (xyz) density correlation
Relation of VCS to the velocity spectral index
S(v) observed line
change of VCS slope
Not affected by phase fraction
(noisy part of P1 filtered out)
- number of points over z, assuring absence of shot-noise
VCS was tested with Arecibo GALFA data
for both low and high resolution limits
Resolution was decreased to test the theory
by Chepunov &
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.
Studies of turbulence is
possible with X-rays using
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-
Thick channelsVelocity Channel Analysis(Lazarian & Pogosyan 00)
Application of VCA to SMC
were obtained for
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
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
LP 04, 06
HI, CO2 etc.)
predicted, e.g. K-3
Use of entire 3D PPV cubes is promising!
= antennae temperature at frequency n
(depends on both velocity and density)
nVCS and VCA versus Centroids
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
Turbulence is a basic property of ISM.
Magnetic field and velocity
in Cho & Lazarian 02
1.GS95 scaling for Alfven and slow modes:
New computations: Beresnyak & Lazarian 06
2.Isotropic acoustic-type fast modes:
Fast modes are
Incompressible turbulence shows spectrum flatter than
the GS95 model predicts. Why?
Maron & Goldreich 01
Boldyrev 05, 06, poster
Galtier et al. 05
in Beresnyak & Lazarian 06
causes some flattening
V and B show