Electron Acceleration and Transport in Microwave Flaring Loops

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Electron Acceleration and Transport in Microwave
Flaring Loops
Nobeyama Symposium, 25-29 October 2004 Kyosato,
Japan

• V. Melnikov
• (Radiophysical Research Institute, Russia)

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Nobeyama Radioheliograph
Nobeyama Radioheliograph
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Microwave flaring loops studies and their
implication for the problem of Electron
Acceleration and Transport

• The first works on microwave flaring loops using
  observations with high spatial resolution
  discovered two kinds of microwave sources
• - single compact loop-top sources and
• double sources with their peaks located close to
  the conjugate magnetic footpoints.
• (Marsh and Hurford(1980), Kundu et al.(1982),
• Kawabata et al. (1982), Nakajima (1983))

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Several new studies were published during last
years developing further understanding of the
problem Hanaoka 1997 Nishio et al 1997 -
footpoint and asymmetric sources Bastian et al.
1998, - a review Lee et al 2000, - dynamics of
spectral properties, electron anisotropy Kundu et
al 2001, - microwave brightness distribution in
limb loops Altyntsev et al. 2002, - subsecond
sources Melnikov et al. 2002, - looptop source
and inhomogeneity of electron distribution White
et al. 2002 - modeling and derivation of
microwave source parameters Lee et al. 2002
electron transport in two interacting
loops Yokoyama et al. 2002, - spectral index
distribution along a loop Fleishman Melnikov
2003, - influence of electron pitch angle
anisotropy Melnikov et al 2004, - dynamics of
brightness distribution along a loop Karlicky
2004 looptop source on the postflare phase Su
Huang 2004 polarization of looptop and
footpoint sources
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This talk will be restricted mainly to properties
of single well resolved loop-like microwave
sources.

• Microwave brightness distribution along a flaring
  loop
• Spectral distribution along a flaring loop
• Model simulations of high energy electron
  distributions along a loop and their GS-emission
  
• Dynamics of the brightness and spectrum slope
  distribution along a flaring loop
• Gyrosynchrotron emission from anisotropic
  electron distributions and its applications
  (intensity and spectral index distributions).

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Loop top source in the event 12 Jan 2000 (a limb
flare)

• Red area brightness distribution
• at 34 GHz.
• Contours
• - dark hard X-ray emission
• (HXT/M2)
• light 17 GHz radio emission
• (NoRH)

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Radio brightness and magnetic field distributions
(a disk flare)
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Microwave brightness distribution along flaring
loops (f 34 GHz).
Melnikov, Reznikova, Shibasaki 2004
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Disagreement with the existing microwave loop
models
The brightness peaks of optically thin GS
emission have to be near the footpoints of
extended loops with a nonuniform magnetic field
as shown by Alissandrakis and Preka-Papadema
(1984), Klein et al (1984) due to strong
dependence of GS intensity on the magnetic field
strength. For example, if the electron power
law spectral index ?4, then
The possibility to have a hump in brightness near
the loop top due to the effect of optical thick
emission (Preka-Papadema Alissandrakis 1992,
Bastian et al 1998) is ruled out in our case
since for all the events under study the
frequency spectral index between 17 and 34 GHz is
negative and, therefore, the microwave emission
from the loops is optically thin at least at 34
GHz.
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Bastian, Benz Gary (1998)
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Attempts to reconcile existing models with NoRH
observations
12 Jan 2000 (a limb flare)
Middle panel Spatial profiles of the constant
field best-fit models as a function of distance
along the loop. Bottom panel for inhomogeneous
magnetic field and different transverse
dimensions of the model loop at 17 and 34 GHz (to
get them both optically thick).
Kundu, Nindos, White Grechnev, 2001
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Time Delays of Emission From the Loop Top
13 March 2000

• The burst of emission from the loop top is
  delayed against the burst from the footpoint
  source by several seconds. This delay is more
  pronounced at 34 GHz than at 17 GHz.
• Time profiles of emission from the loop top are
  wider and their decay is slower than those from
  the region near the footpoint.

17 GHz, I 17 GHz, V 34
GHz, I
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Time delays of emission from the loop top
28 August 1999

• There is almost no delay between the time
  profiles from the regions near two conjugate
  footpoints.
• For all the events the flux peaks from footpoint
  sources are coincident in time with the flux
  peaks of hard X-ray emission (in Fig. the
  vertical line indicates the moment of the hard
  X-ray emission peak)
• Time delays indicate the trapping and
  accumulation of high energy electrons in the
  upper part of an extended loop and lack of these
  processes near footpoints.
• (Melnikov, Reznikova, Yokoyama, Shibasaki,
  2002).

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Time delays at higher frequencies
13 March 2000

• The peak of the emission at higher frequency, 34
  GHz, is delayed against that at 17 GHz.
• This is well pronounced for the loop-top part of
  the sources. However, there are no such well seen
  delays for the footpoint parts.
• The footpoint emission at both frequencies peaks
  almost simultaneously with the peak of the
  corresponding hard X-ray burst.

Interpretation Delays at higher frequencies from
the looptop can be explained by longer lifetime
of the trapped higher energy electrons
responsible for the higher frequency emission
(Melnikov Magun, 1998). The absence of the
similar delay in the footpoint source excludes
the origin of the delay in the looptop due to
electron spectral hardening during the
acceleration process itself.
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We suggest that the probable explanation of the
loop-top source is trapping, accumulation and,
as a result,an enhanced density of mildly
relativistic electrons in the upper part of a
flaring loop..
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Kinetics of Nonthermal Electrons in Magnetic
Loops
In a magnetic loop part of injected electrons are
trapped due to magnetic mirroring and the other
part precipitates into the loss-cone. A real
distribution strongly depends on the pitch-angle
dependence of the injection function
S(E,?,s,t). Fokker-Plank equation
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Kinetics of Nonthermal Electrons in Magnetic
Loops
If the energy of electrons E gt 200 keV, their
lifetime, ?, in a magnetic trap with n01010cm-3
is more than 50s. So, if their injection is
impulsive, ?t lt ?, the collisional terms in the
Fokker-Plank equation can be omitted and the
exact solution can be represented as follows.
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Model of a microwave source
Magnetic field distribution B(s)
B0(1s2/s02) Nonthermal electrons - power law
energy dependence g(E) g0 E-? - pitch-angle
distributions 1. Beam-like distribution
?(?0) exp-(1-?02)/ ?12 2. Isotropic
pitch-angle distribution ?0 C const 3.
Pancake distribution ?(?0) exp?02/ ?12

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Calculations of gyrosynchrotron emission from the
model source
For calculations of gyrosynchrotron emission we
use exact expressions for absorption and emission
coefficients in the magnetized plasma (Eidman
1958, 1959 Ramaty 1969 Fleishman Melnikov,
2003).

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Results of simulations
Beam-like injection
Isotropic injection
Pancake injection
Melnikov V.F., Shibasaki K., Reznikova V.E. ApJ,
2002, 580, L185
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These results were obtained only for the loops
close to the limb, where the effect of magnetic
field inhomogeneity is most strong. For
calculations we choosed the angle between the
magnetic field vector and line of sight ?80o.
For this case two strong peaks of radio
emission are observed even for the isotropic
injection while the well defined peak of the
number density exists in the loop cente. Only
in the case of the pancake injection we can get a
pronounced radio brightness peak at the center of
a limb loop. A degree of brightness concentration
to the loop center (the ratio ILT/IFP can vary in
a wide range depending on the parameter ?0 of the
gaussian distribution function.
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What is the physical reason for the existence of
microwave loop-top sources?
We consider that the most probable explanation of
the loop-top source is a strong concentration
of mildly relativistic electrons in the upper
part of a flaring loop.. It follows from our
simulations that this strong concentration can
occur due to the perpendicular to magnetic field
pitch-angle anisotropy of high energy
electrons. These findings put important new
constraints on - the particle acceleration/
injection mechanisms and - the kinetics of high
energy electrons in flaring magnetic loops.
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What accelerationinjection mechanisms can
produce anisotropic distributions perpendicular
to magnetic field?
Indeed This conclusion is in disagreement with
the current theoretical ideas on particle
acceleration process in solar flares -
DC-electric field (along the loop axes)
acceleration, - stochastic MHD-turbulent
cascade acceleration in which the acceleration
occurs along the magnetic field lines. On the
other hand, the mechanisms like the acceleration
in current sheets (e.g. Syrovatskii, Litvinenko
and Somov, Somov and Kosugi, 1997) look quite
favorable to produce highly anisotropic electron
distributions near the looptop. I would also
mention the model proposed by Vlahos et al.,
2004. As well, all types of the betatron
mechanism, for instance, considered by Karlicky
and Kosugi, 2004, also agree with our finding.
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A New approach to an old problem(L. Vlahos, 2004)

• From one current sheet to millions

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Betatron Acceleration in Collapsing Magnetic
Trap(Karlicky, Kosugi, 2004)
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Whats about transport effects?

• The second possibility to get anisotropic
  distribution of electrons is some transport
  effects
• Enhanced pitch-angle scattering and energy losses
  near footpoints due to
• higher plasma density in the lower parts of a
  loop
• enhanced level of whistler (or some other)
  turbulence.
• This is under consideration now (based on the
  F-PEq)
• In this case we expect some dynamics or
  redistribution of the microwave brightness along
  the flaring loop In the beginning of a burst the
  regions which are closer to footpoints should be
  relatively brighter than the looptop.

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Some new constraints on the acceleration/transport
models following from spatial distribution
dynamics
Lets consider temporal variations of 1) the
radio brightness and 2) frequency spectral slope
distributions along a microwave flaring loop
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High frequency spectral index variations along a
loop.
Yokoyama et al. 2002, ApJ, 576, L87.
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High frequency spectral index variation along a
loop
(Melnikov, Reznikova, Yokoyama, Shibasaki,
2002).
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High frequency spectral index variation along a
loop
We have confirmed the result by Yokoyama et al
(2002) that Microwave spectrum near footpoints
is considerably softer (by 0.5-1) than near the
loop top during the main peak of the bursts under
our study
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High frequency spectral index variation along a
loop

• ? decreases in the rise and decay phases of the
  bursts both near footpoints and near the looptop
  (in agreement with the result by Melnikov Magun
  1998 obtained without spatial resolution)
• A new finding the decrease of ? (flattening
  of the microwave spectrum) during the decay phase
  goes remarkably faster in the regions close to
  the footpoints than near the loop top.

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Brightness distribution dynamics, 13
March 2000
Melnikov, Shibasaki, Reznikova, ApJ, 2002
Melnikov, Reznikova, Shibasaki, ApJ, 2004
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Brightness distribution dynamics, 23
October 2000
34
Brightness distribution dynamics, 24 August 2002
(main peak, 34 GHz)
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• The microwave brightness along the flaring loop
  is not constant
• - In the beginning of a burst the regions
  which are closer to footpoints are relatively
  brighter than the looptop.
• - In the burst maximum and on the decay phase
  the situation changes to the opposite.
• The ratio of the intensities Ilt/Ifp is always
  higher for 34 GHz than for 17 GHz. Possibly it
  means that higher energy electrons are more
  concentrated to the looptop than less energetic
  ones. In the other words, they are more
  anisotropic perpendicular to magnetic field.

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Some transport effects?

• We expect some dynamics or redistribution of the
  microwave brightness and spectrum along the
  flaring loop because of enhanced pitch-angle
  scattering and energy losses near footpoints due
  to
• higher plasma density in the lower parts of a
  loop
• enhanced level of whistler (or some other)
  turbulence.
• This is under consideration now (based on solving
  the Fokker-Plank Equation for the non-stationary
  case).

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Model simulations of the GS-spectrum from
electrons with pitch-angle anisotropy(Fleishman
Melnikov, ApJ 2003)
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Spectral slope at high frequencies

• NkE-? - power law electron distribution
• J f-? - frequency spectrum
• Synchrotron emission (sgt100, E/mc2gtgt1)
• ? (?-1)/2 (Korchak and Terletskii 1952
• Getmantsev 1952)
• Gyrosynchrotron emission (slt100, E/mc2lt1)
• ? 0.90? -1.22 (Dulk and Marsh 1982)

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Influence of the electron distribution anisotropy
on the frequency spectrum

• The angular width of the emission beam
• ? ? -1 mc2/E
• ? In ultra-relativistic limit (? -1 ltlt 1), the
  anisotropy does not change the emission
  spectrum.
• For solar flare conditions, the broad band
  microwave emission are mainly generated by
  mildly relativistic electrons
• ? the anisotropy does influence the emission
  spectrum.

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Model

• Since our goal is to reveal the proper effect of
  the pitch-angle anisotropy on the gyrosynchrotron
  emission,
• we consider
• - a uniform source with
• a constant magnetic field and
• time-independent distribution of fast electrons.
• For calculations we used exact expressions for
  absorption and emission coefficients in the
  magnetized plasma (Eidman 1958, 1959 Ramaty
  1969).

(Fleishman Melnikov, ApJ 2003)
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1. Power-law distribution of electrons over
momentum
2. Pitch-angle distribution of the sin-N type
3. Pitch-angle distribution of the gaussian type
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Results of simulations (for the case of rarefied
plasma, ? p/?B 0.3)

• Electron pitch-angle
• distribution of the sin-N type.

• We see considerable change of microwave
  parameters with for the quasi-parallel
  propagation
• (? 0.8)
• a) decrease of intensity
• increase of the degree of polarization and
• Increase of the spectral index
• Spectral index approaches the relativistic limit
  from above.

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Results of simulations2. Electron pitch-angle
distribution of the loss-cone type

• f2(?) exp-?2/ ?02
• cos(?), ? BV.
• In this case we see much stronger dependence of
  all emission parameters on the anisotropy
  compared with the sin-N pitch-angle distribution
  is clearly seen.
• Spectral index approaches the relativistic limit
  from above.

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Implications for the observed spectral index and
intensity variations
The results presented show clearly that a
pitch-angle anisotropy can make an important
contribution to the observed spectral index and
intensity variations in the optically thin part
of the spectrum. For the disc flares the
foot-point source is observed at a quasiparallel
direction, while the loop-top source is observed
at a quasitransverse direction. Since
anisotropic distributions provide systematically
softer spectra and lower intensity of
gyrosynchrotron radiation (at quasiparallel
directions, the case of the foot-point source)
than the isotropic or weakly anisotropic
distribution (at quasitransverse directions, the
case of the loop-top source), this agrees well
with the Nobeyama Radioheliograph data.
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Conclusions

• We have shown that the microwave looptop sources
  indicate on strong concentration of mildly
  relativistic electrons in the upper part of a
  flaring loop.
• The strong concentration is connected with the
  perpendicular to magnetic field pitch-angle
  anisotropy of high energy electrons.
• The microwave brightness along the flaring loop
  is not constant In the beginning of a burst the
  regions which are closer to footpoints are
  relatively brighter than the looptop. In the
  burst maximum and on the decay phase the
  situation changes to the opposite.
• Pitch-angle anisotropy of high energy electrons
  can influence significantly the intensity,
  spectrum and polarization along a microwave
  flaring loops.
• All these findings put important new
  constraints on the particle acceleration/injection
  mechanisms and on the kinetics of high energy
  electrons in flaring magnetic loops.