Transcript MHD Turbulence in Interstellar Medium

Stochastic Reconnection
in Partially Ionized
Gas:Progress Report
A. Lazarian (UW-Madison)
Collaboration with
J. Cho (UW-Madison and CITA)
A.Esquivel (UW-Madison)
H. Yan (UW-Madison)
E. Vishniac (Johns Hopkins)
Questions to address?
• How does turbulence affect
reconnection?
• What are the properties of
turbulence in partially ionized gas?
• How does partial ionization change
the expected reconnection rate?
Motivation: Interstellar Fields
• Turbulent: Re ~VL/n ~1010 >> 1
n ~ rLvth, vth < V, rL<< L
Armstrong & Spangler (1995)
Slope ~ -5/3
pc
AU
Lazarian& Pogosyan (00) &
Starnimirovic & Lazarian (01)
showed Kolmogorov velocity
spectrum of HI here.
What is the effect of Interstellar
Tubrulence?
• Makes boundary conditions difficult to
control.
• X point reconnection is not feasible unless
large scale field reconfigure themselves
over hundreds of parsec scales.
• Fast local (e.g. X point) reconnection does
not guarantee fast reconnection if the global
outflow regions are narrow.
Relation to Center Activities
• Properties of turbulence: related to
“Magnetic Chaos and Transport”
• Reconnection and properties of turbulence
are related to “Ion Heating”.
• Reconnection is an essential part of the
picture of “Dynamo” and “Angular
Momentum Transport”
What is Stochastic Reconnection?
• Stochastic reconnection:
• The natural state of fluids
is turbulence.
• Presence of an stochastic
component of the B field.
• Magnetic field lines dissipate
not on their entire scale length
(L), but on a smaller scale (||)
determined by turbulence
statistics.
• Many simultaneous S-P
reconnections.
Lazarian & Vishniac (1999)
Properties of Stochastic
Reconnection
• Can be both fast and slow
(depending on the level of
turbulence) (dB!)
• Allows flares of reconnection.
• Depends of the properties of
turbulence
Partially ionzed gas:possible
effects
• Free diffusion of neutrals out of the
current sheet. Probably not so
important (Vishniac & Lazarian 1998,
Heitsch & Zweibel 2003).
• Turbulence is affected by damping
caused by neutrals. Is it fatal?
Turbulence in partially ionized
gas:Theoretical expectations
(from Lazarian, Vishniac & Cho 2004)
• In partially ionized gas MHD turbulence
does not vanish at the viscous damping
scale.
• Magnetic intermittency increases with
decrease of the scale.
• Turbulence gets resurrected at ion
decoupling scale.
B
Viscosity is important
while resistivity is not.
Viscous magnetized
fluid
Does viscous damping scale
is the scale at which MHD
turbulence ends?
~0.3pc in WNM
Viscosity Damped Turbulence:
New Regime of MHD Turbulence
E(k)~k-1
Expected:
k-1 for magnetic field
k-4 for kinetic energy
Cho, Lazarian & Vishniac 2002b
intermittent
Scale dependent
intermittency
Numerical testing confirms that
magnetic turbulence does not die!!!
Viscosity damped turbulence
protrudes up to the scales
at which neutrals decouple from
ions. After that the normal
MHD turbulence in ionic fluid
is restored. Lazarian, Vishniac & Cho (2003)
Yet to be tested with two fluid code
Results: Expected Reconnection
Rates for Phases of ISM
(from Lazarian, Vishniac & Cho 2004)
• Molecular cloud: 0.1 VA (L30/l303/2)
• Dark cloud: 0.1 VT MA1/2b5/4(L30/l301/4)
• Cold Neutral Medium:
0.08 VTM2b-1/2(L30/l303/2)
Some Astrophysical
Implications
• Removal of magnetic field during star
formation
• Solar flares and particle acceleration
Numerical Testings
• Numerical testing of the stochastic
reconnection idea
• Further testing of the divergence of the field
lines in the new regime of turbulence.
• Numerical testing of the resurrection of
turbulence prediction (using two fluid
code).
Summary
• Interstellar reconnection happens in
turbulent medium and on very large scales.
• Turbulence and external forcing makes
large scale X point not probable.
• Stochastic reconnection is fast, but it may
also be slow.
• The research requires interaction with other
directions of the Center.
Compressible MHD Turbulence:
Stimulating Prior Work
Higdon 1984 (anisotropy in compressible
MHD turbulence)
Goldreich & Shridhar 1995 (incompressible
MHD theory, hints about compressibility)
Lithwick & Goldreich 2001 (effects of
compressibility)
Choice is biased by author’s preferences.
Longer list is in Cho, Lazarian & Vishniac 2003.
Implication 1: CR transport
Big difference!!!
(Kolmogorov)
Fast modes
From Yan & Lazarian 2002
Alfven modes are inefficient.
Fast modes are efficient in spite of damping
What are the scattering rates for
different ISM phases?
Gyroresonance
TTD
From Yan & Lazarian 2004
Solid line is analytical results
Symbols are numerical results
(a) gyroresonance is dominant;
(b) the scattering in partially ionized media is not important.
Implication 2: Dust Dynamics
• Gyroresonace with
fast modes is most
efficient
• Grains get supersonic
• Grains may get
aligned
Grain size
From Yan & Lazarian 2003
Implication 3: Decay of MHD
turbulence
Incompressible MHD turbulence
• Fast decay of MHD
turbulence reported
earlier is not due to
coupling of
compressible and
incopressible motions!
decays fast.
tcas~k-2/3
Cascade time follows
Kolmogorov scaling
Inportant for star formation.
Cho, Lazarian, & Vishniac 2002a
Normal MHD
Turbulence
Viscosity
damped regime
Large
LargeScales
scales
(Small k only)
Magnetic
structures
perpendicular
to mean B.
Intermittency is prominent
for new regime at small
scales.
Small Scales
(Large k only)
Intermittent structures
Smaller and smaller
structures forming
at scales smaller
than the damping
scale.
From Cho, Lazarian & Vishniac 2003
Ordinary MHD
New regime
Cho, Lazarian & Vishniac 2003
Viscosity damped turbulence exhibits
scale-dependent intermittency!
Corresponds to prediction in Lazarian, Vishniac & Cho 2003
From Cho & Lazarian 2003
Viscosity damped MHD turbulence results in a shallow
spectrum of density fluctuations. Could there be a relation
to tiny scale structures observed in the ISM?
Why E(k)~k-1?
• Magnetic fluctuations evolve due to shear at the damping
scale. => Cascade of magnetic energy with the fixed rate:
Bl2 = const => B 2 ~ const, or E(k)~k-1
l
tdiss
kE(k)~Bl
Expect to see a lot of magnetic structure below
the viscous damping scale (e.g. below 0.3pc for WNM)
Genus analysis (cont.)
• A shift from the mean can
reveal “meatball” or “Swiss
cheese” topology.
• Genus curve of the HI in the
SMC and from compressible
MHD simulations.
• The SMC show a evident
“Swiss cheese” topology, the
simulations are more or less
symmetric.
• Genus are a quantitative
measure of the topology,
allows to test simulations &
observations.
SMC
MHD