Transcript Turbulent Reconnection in Partially Ionized Interstellar Gas

3D Reconnection of Weakly Stochastic
Magnetic Field and its Implications
Alex Lazarian
Astronomy Department and Center for Magnetic SelfOrganization in Astrophysical and Laboratory Plasmas
Collaboration: Ethan Vishniac, Grzegorz Kowal and Otminowska-Mazur
Solar Flares and Coronal Mass Ejections arise from
magnetic reconnection
Gamma Ray Bursts, Dynamo and Magnetotail
activity are other examples of reconnection
But the problem is more fundamental.
Without the proof of fast reconnection all MHD numerical
research is a “naked emperor” from the famous tale
H.C. Andersen:”Not only was the material so
beautiful, but the clothes made from it had the
special power of being invisible to everyone
who was stupid or not fit for his post.”
Turkish version: "A turban such than one
born in wedlock will see it, while the bastard
will see it not"
But reconnection should be slow to explain accumulation of flux required for
solar flares.
Astrophysical reconnection was always associated with a
particular kind of waves
Handwaving reconnection
by D. Uzdensky
It is good to see whether other types of waves or non-linear interactions can do the job
Sweet-Parker model exhibits long and thin current
sheets; very slow speed ~ 10-6 VA for ISM
B
Vin
Vout
Vout
Vin
Ohmic diffusion
Mass conservation
Free outflow
RECONNECTION
RATE
For ISM Rm>1012.
Petschek model does not work for uniform
resistivities
X point
Both dimensions
are comparable.
Fast reconnection
VR~ VA
Anomalous effects stabilize Petschek model, but are
very restrictive
Hall MHD
ion current
Petcheck + anomalous effects
e current
(Drake et al. ‘98)
Very stringent requirement: mean free path of
an electron is comparable with astrophysical L
Is reconnection slow otherwise? Bad news for most of astrophysical simulations.
While electrons make many gyrations over a
collision time, reconnection is collisional for
interstellar medium
>> 1.
For ISM the collisionality parameter is
But the condition for the reconnection to be “collisionless” is different, i. e.
,
is resistive width.
is ion inertial length and
<1
Thus the interstellar gas is in collisionless if
and the current sheet length of sheets
Too small!!!
The idea of different mechanism responsible for
fast reconnection in different media does not
correspond to the principle of parsimony
Ockham’s razor: “entities should not be multiplied needlessly”
William Ockham 1288-1348
Astrophysical fluids are turbulent and magnetic
field lines are not laminar
Density fluctuations
ISM Turbulence Spectrum
Slope ~ -5/3
WHAM emission: density fluctuations
Chepurnov & Lazarian 2010
Scincillations
and scattering
Modified from Armstrong,
Rickett & Spangler(1995)
pc
AU
Doppler shifted velocity exhibits turbulent spectrum as revealed by
the VCS technique
emission
Sensitive to supersonic turbulence is cold gas.
Reveals E(k)~k-1.85 for Arecibo high latitude data
(Chepurnov et al. 10)
VCS technique by Lazarian & Pogosyan
(00, 06, 08)
Turbulence was discussed in terms of reconnection, but
results were inconclusive
Microturbulence affects the effective resistivity by inducing anomalous effect
Some papers which attempted to go beyond this:
Speizer (1970) --- effect of line stochasticity in collisionless plasmas
Jacobs & Moses (1984) --- inclusion of electron diffusion perpendicular mean B
Strauss (1985), Bhattacharjee & Hameiri (1986) --- hyperresistivity
Matthaeus & Lamkin (1985) --- numerical studies of 2D turbulent reconnection
On the contrary, Kim & Diamond (2001) conclude that turbulence makes any
reconnection slow, irrespectively of the local reconnection rate
Reconnection of 3D weakly turbulent magnetic fields involves
many simultaneous reconnection events
Turbulent reconnection:
1. Outflow is determined by
field wandering.
2. Reconnection is fast with
Ohmic resistivity only.
Key element:
L/l|| reconnection
simultaneous events
B dissipates on a small
scale l|| determined by
turbulence statistics.
Lazarian & Vishniac (1999)
Local reconnection rate is slow for Alfvenic turbulence due to
eddy anisotropy
Conservative scenario:
Local reconnection is Sweet-Parker
lperp
l||
Vrec, local l||= Valfen lperp
Vrec, local=h/ lperp
Vrec, local=Vl Rm -1/4
if l|| scales as l2/3perp
(as in Goldreich-Sridhar 95)
Constraint due to Ohmic diffusion provides reconnection
velocity faster than VA
l||
L
The general requirement:
V rec, global =L/l|| Vrec, local
For Goldreich-Shridhar 95 model of MHD turbulence the reconnection
rate is
V rec, global = Valfven Rm1/4> Valfven !!!!!!
Bottle neck is the outflow width: field wandering determines the
reconnection rate (tested by Kowal et al. 09, next talk)
Predictions in Lazarian &
Vishniac (1999):
No dependence on anomalous or
Ohmic resistivities!
As
it translates into
In 10 years a substantial convergence between the models
occured
Hall MHD 1999
Our model
Lazarian & Vishniac 1999
Hall MHD 2009
Drake et al. 2006
Our model is the one of volume filled
reconnection. John Raymond attempted to
test our model searching for volume
reconnection, but by that time the Hall
MHD model also evolved…
Stochastic reconnection accelerates energetic particles without
appealing to plasma effects
GL03 versus Drake et al. 06:
Cosmic rays get
spectrum steeper
than from shocks
Drake et al. 2006 is 2D model
with collapsing islands. The
backreaction of accelerated
electrons is accounted for.
De Gouveia Dal Pino & Lazarian 2003
Applications to pulsars, microquasars, solar flare acceleration (De Gouveia Dal Pino
& Lazarian 00, 03, 05, Lazarian 05).
In the presence of reconnection regular increase of energy is
clearly seen
3D turbulent reconnection
Pure Turbulence
Reconnection can provide a solution to anomalous cosmic ray
measurements by Voyagers and to observed anisotropies of CR
Effect of solar cycle
Effect of rotation
Lazarian & Opher 2009: Sun rotation
creates B-reversals in the heliosheath
inducing acceleration via reconnection.
Lazarian & Desiati 2010: Sun 11 year
cycles creates B-reversals in the heliotail
inducing CR acceleration.
Turbulent reconnection produces flares
when the initial state of field is laminar
Hoang et al.
If field is laminar, the reconnection is
slow and field accumulates. As
turbulence level increases, the
reconnection increases enhancing
turbulence further (LV99). The finite
time instability develops.
Reconnection
rate for flux in
the box without
external driving
Vishniac & Lazarian 1999
Ciaravella & Raymond 08 observed thick extended outflow regions associated with flares.
Corresponds to what we expect and contradicts to Petscheck.
Time
Allegoric summary: Emperor is not naked, reconnection
is fast in most cases of realistically turbulent astro fluids.
Many implications are to be explored.
We used both an intuitive measure, Vinflow, and a
new measure of reconnection
New measure:
Calculations using the new measure are
consistent with those using the intuitive one
reconnection
LaminarStochastic
Sweet-Parker
reconnection
Initial reconnection without inflow:
formation of Sweet-Parker layer
Old measure is slightly larger
due toCoincide
diffusionassymptotically
Intuitive, “old” measure is
the measure of the influx of
magnetic field
New measure probes the
annihilation of the flux
Reconnection layer structure depends on the
scale of energy injection
k=8
Turbulence with different scales
-
Laminar Sweet-Parker
reconnection
k=16
Turbulence can enhance reconnection even in 2D
via ejecting of islands
-- forcing
--outlfow
Slower than in 3D as no multiple reconnection events are possible. The
rate depends on both forcing and resistivity.
The range of direct applicability of collisionless
reconnection is rather limited
Reconnection is collisionless if
Sweet-Parker sheet thickness
Which translates into a restrictive: for
Yamada et al. (2006)
Which makes a lot of astrophysical environments, e.g. ISM, disks, stars
collisional! Does it mean that all numerics in those fields is useless?
Turbulent reconnection efficiently accelerates
cosmic rays by first order Fermi process
Model of acceleration in De
Gouveia Dal Pino & Lazarian 00
VR
Voutflow
outflow
Cosmic ray bouncing
back and forth
mirrow
B
Applications to pulsars, microquasars, solar flare acceleration (De Gouveia Dal Pino &
Lazarian 00, 04, Lazarian 04).
Original Petschek reconnection fails for
generic astrophysical situations
Large scale fields:
X point over
many parsecs?
Inflow of matter
Outflow
of matter
If the outflow slot
is very small reconnection is slow
because of the mass conservation constraint.
Observations suggest that Solar reconnection layers are thick and not X-points (Raymond
et al. 07). Also in most of ISM, stars, protostellar disks the reconnection is in collisional
regime.
Reconnection of weakly stochastic field
Tests of new measure: no effect of flux diffusion
Coincide within fluctuations
Reconnection of weakly stochastic field
New measure gives zero for no field reversal