Poynting%20Flux%20Dominated%20Jets%20in%20Decreasing%20Density%20Atmospheres.%20I.%20The%20Non-relativistic%20Current-driven%20Kink%20Instability%20and%20the%20Formation%20of%20

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Poynting Flux Dominated Jets in Decreasing
Density Atmospheres. I. The Non-relativistic
Current-driven Kink Instability and the Formation
of Wiggled Structures
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• Masanori Nakamura and David L. Meier
• Astro-ph/0406405

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Introduction (1)
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MHD acceleration mechanism a model for
astrophysical jets
There has been a growing recognition in recent
years that the influence of strong magnetic
fields within the jet may extend beyond the
central engine into the region where the jet
freely propagates. This is particularly evident
in observations of jets in AGNs, QSOs, winds from
pulsars, and ?-ray burst sources (e.g., Perley,
Bridle, Willis 1984 Conway Murphy 1993
Hester et al. 2002 Coburn Boggs 2003).
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Introduction (2)
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Jets with a strong toroidal field encircling the
collimated flow current-carrying or Poynting
flux dominated (PFD) jets. Rotation of the
helical field drives a torsional Alfven wave
(TAW) forward in the direction of the jet
flow. TAW carries electromagnetic energy and
accelerate the plasma.
A cylindrical plasma column with helical magnetic
configuration is subject to MHD instabilities.
Classification of instabilities
pressure-driven(PD), Kelvin-Helmholtz(K-H),
current-driven(CD) instabilities (Kadomtsev 1966
Bateman 1980 Freidberg 1982).
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Introduction (3)
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PD instabilities considered not to be very
important for supersonic jet. K-H instabilities
important at the shearing boundary between the
jet and the external medium, particularly in
kinetic flux dominated (KFD) jets. On the other
hand, PFD jets should be especially susceptible
to CD instabilities because of the presence of
the strong axial electric current.
? The study of CD instabilities on jet flow is
important.
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Introduction (4)
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Purpose of this paper numerical investigation of
the nonlinear development of CD instabilities in
PFD jets, especially the CD kink (m1)
mode. Previous study (Nakamura, Uchida, Hirose
2001) simplified atmospheric conditions. This
study more realistic atmospheric situations,
including density, pressure, magnetic field, and
temperature gradients in the ambient medium.
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Basic Astrophysical Model (1)
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Basic Astrophysical Model (2)
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Near the central engine a rotating, magnetic
structure can be created (Blandford Znajek
1977 Blandford Payne 1982 Koide et al.
2002). How about the physical connection between
this central region and the sub-parsec region?
?not yet well understood. However, it is
reasonable to suppose some connection.
Assume a rotational structure.
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Basic Astrophysical Model (3)
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Assumption of a large scale poloidal magnetic
field in the ambient medium. The origin is not
yet fully understood. ?But, there are
observational suggestions of both synchrotron
emission and Faraday rotation. The magnetic field
assumed here might be the primordial
inter-stellar field (Kulsrud Andersen 1992 the
galactic field must have a primordial origin.) or
the central part of the amplified field by a
galactic turbulent dynamo process (Kronberg 1994
Han Wielebinski 2002, and reference therein) or
a field carried out from the central engin by a
low-velocity magnetized disk wind.
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MHD equations and Code
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Two-step Lax-Wendroff Scheme artificial viscosity
The numbers of the grid points 261x261x729
Add the term, -?(p0) for initial hydrostatic
equilibrium.
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Initial Conditions
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A current- (and therefore force-) free magnetic
field.
Plasma-beta is 0.01 at the origin.
Time is normalized by tA0 (Alfven crossing time)
Ring current
Simulation domain
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Boundary Conditions
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Free boundary
Free boundary
Free boundary
Physical variables except the magnetic field are
damped.
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The Four Models (1)
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Two models for ambient medium
A shallow-atmosphere model (a1) B
steep-atmosphere model (a2)
1 Highly PFD jets (FExB/Ftot0.9) 2. Mildly PFD
jets (FExB/Ftot0.6)
Four models of A-1, A-2, B-1, and B-2
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The Four Models (2)
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Alfven velocity is constant, but sound speed is
decreasing.
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The Four Models (3)
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Early jet evolution (1)
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Model A-1
The F-F compressive wave decelerates and steepens
into a fast-mode MHD bow shock due to a gradual
decreasing ambient VA (check the jump of Vz,
becoming super-fast magneto sonic).
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Early jet evolution (2)
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Model A-2
There is the contact discontinuity (CD) between
R-S and F-S. CDR-S decreasing and heating
magnetized jet itself. CDF-S compressing and
heating the ambient medium.
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Early jet evolution (3)
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Model B-1
Only a very low amplitude F-F compressive wave
front can be seen due to a constant ambient VA
(if CsltltVA, VF VA).
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Early jet evolution (4)
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Model B-2
The authors identify CD as defining the rest
frame of the jet flow.
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Intermediate jet evolution
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Nature of PFD jets as current-carrying jets (1)
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The return current density Jrc
The forward jet current density Jjc
The force-free parameter ?ff (J?B/JB) ?ff1
or 1 force-free
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Nature of PFD jets as current-carrying jets (2)
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The distribution of the force-free parameter and
the current density. Jet is force-free in almost
all region.
Large difference between highly and mildly PFD
jet (related to accumulation of Bf)
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Final evolutionary stages (1)
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Vz is still sub-Alfvenic, that is the highly PFD
jet remains Poynting flux dominated.
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Final evolutionary stages (2)
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Final evolutionary stages (3)
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The mildly PFD jet ? (mildly) kinetic energy flux
dominated (KFD) jet. The highly PFD jet with the
steep atmosphere ? an equipartition state between
the kinetic and Poynting fluxes. Jets propagating
in the trans-Alfvenic region before they become
kinetic energy dominated, can be deformed into
wiggled structures.
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Nonlinear growth of CD instabilities (1)
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Calculate the power spectrum.
Define the jet current.
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Nonlinear growth of CD instabilities (2)
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Calculate power spectrum of k?0.
Pure CD modes can develop typical on the Alfven
crossing time scale (Begelman 1998, etc.)
This is consistent with the result in this paper.
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Nonlinear growth of CD instabilities (3)
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Classical Kruskal-Shafranov (K-S) criterion.
Originally Fcrit is set equal to 2p.
Fgt Fcrit and Alfven mach number for azimuthal
velocity is not so much large (nearly equal to 0).
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Nonlinear growth of CD instabilities (4)
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Despite Fgt Fcrit, the jet is stable because of
relatively large MAF. This is consistent with the
linear theory (Appl 1996, Appl, Lery, Baty 2000)
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Nonlinear growth of CD instabilities (5)
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Thinking the balance of VF2/r - BF2/r/? - ?pm
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Nonlinear growth of CD instabilities (6)
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Models, B-1 and B-2 the sum of the first and
second term is nearly equal to 0. ?pm is also
nearly equal to 0.
Model A-1 The magnetic pinch term is a bit
grater than the centrifugal term (azimuthal
velocity is sub-Alfvenic), but the difference is
vanished by the gradient of the magnetic pressure.
Model A-2 The centrifugal term is nearly equal
to zero. ?The promotion of the pinch. ?The
magnetic pinch term and the magnetic pressure are
asymmetric with respect to the jet axis due to
the kink instabilities.
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Nonlinear growth of CD instabilities (7)
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How and where the classical K-S criterion is
violated?
Decrease of Bz in the region 0.3ltrlt1.0 makes the
situation of Fgt Fcrit.
Concentration of magnetic flux to near the
central axis due to the pinch
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Nonlinear growth of CD instabilities (8)
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How and where the classical K-S criterion is
violated?
Behind the R-S shock wave, the azimuthal velocity
becomes nearly equal to zero. ?The pinch effect
becomes strong. ?The classical K-S criterion is
violated.
F-F
F-S
R-S
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Suppression of MHD KH Instabilities due to the
External Magnetized Winds (1)
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The definition of winds in this paper is
current-free flow (the flow between the jet
current and the return current).
The condition for the stability is
surface Alfven speed
Hardee Rosen (2002)
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Suppression of MHD KH Instabilities due to the
External Magnetized Winds (2)
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Summary (1)
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Due to the centrifugal effect, rotating jets can
be stabilized against the CD kink mode beyond the
point predicted by the classical K-S
criterion. Non-rotating jets will be subject to
the CD kink mode when the classical K-S criterion
is violated. The driving force of the CD kink
mode is an asymmetrically distribution of
hoop-stress (the magnetic tension force). This is
caused by a sudden decrease of jet rotation and a
concentration of the poloidal magnetic flux
toward the central axis (which is related to a
reverse slow-mode MHD shock wave).
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Summary (2)
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The CD kink mode grows on time scales of order
of the local Alfven crossing time. The MHD KH
instability is suppressed even when flows become
super-Alfvenic.