The Influence of the Return Current and the Electron Beam on the X-Ray Flare Spectra
Elena Dzifčáková, Marian Karlický
Astronomical Institute of the Academy of Sciences of the Czech Republic
251 65 Ondrejov, Czech Republic
Abstract: The electron beams and the return current affect the electron distibution function in plasma during solar flares. A new model of the distribution function including the return current and electron
beam is supposed and its influence on X-ray spectra has been computed. The comparison with the simple model of the return current is presented.
Motivation
• The electron beams accelerated during a flare in the corona
create return currents in lower layers of the solar atmosphere.
• The electron beam and the return current affect the electron
distribution function in the corona and thus the intensities of the
spectral lines.
• How does the return current influence the intensities of the
spectral lines in EUV and X-ray region?
• Is it possible to separate the effect of the return current on a
spectrum from the effect of electron beams and to diagnose it?
In the previous study we have considered a very simple model to
know what kind of the results we can await. Now we have used
better model with the more realistic electron distribution.
Assumptions
• Initial state: particles have Maxwellian distributions with
temperatures T and interact with the mono-energetic electron beam
with velocity of 1.01010 cm.s-1 (electron energy 28.4 keV).
• The electron beam produces the return current and interacts with
the plasma through plasma waves. This modifies the electron
distribution in the coordinate system of protons and ions (Fig. 1).
• The influence of the Coulomb thermalization on plasma
distribution is neglected.
• The electron beam is present for a sufficiently long time to
achieve the ionization and excitation equilibrium. The effect of
possible pressure imbalance and subsequent plasma motions is
ignored.
Fig. 1: The interaction of the
electron beam with plasma and
formation of the return current in
the 3D electromagnetic PIC
model. The initial temperature of
the plasma is T0=2x106 K and
the ratio of the electron beam
density to plasma density is
nB:ne=1:10.
The resulting
electron distribution (d) consists
relaxed beam, plasma bulk
which is shifted to negative
velocity (one part of the return
current) and the tail with high
negative velocities (second part
of the return current).
The Electron Energy Distribution Function
The main effect on the shape of the model energy distribution has
the ratio of the density of the electron beam to plasma density. The
initial temperature has only a little effect on the distribution shape
(Fig. 2). The high energy tail of the distribution is formed by the
electron beam and high energy electrons of the return current.
Fig. 2. The shape of the
electron energy distribution
function for three different
initial conditions: black line:
T0=2x106K, nB:ne=1:10, full
red
line:
T0=1x106K,
nB:ne=1:10, full green line:
T0=2x106K,
nB:ne=1:20,
dashed green line: the
Maxwellian
disitribution
with T=2x106K, dashed red
line:
the
Maxwellian
electron distribution with
T=1x106K.
Ionization equilibrium
• The approximations of the ionization and autoionization cross
sections (C, N, O, Ne, Mg, Al, Si, S, Ar, Ca, Fe and Ni) have been
taken from Arnaud and Rothenflug, 1985, A&ASS 60, 425. The
cross sections have been integrated over the non-thermal
distribution function to get the ionization rates.
• The recombination rates for the non-thermal distribution have
been computed by using the approximation technique described
in Dzifcakova, 1992, SP 140, 247.
• Contribution of the high energy tail of the distribution function to
the ionization rate can be very important. The ionization state can
correspond to the much higher temperature than the initial
temperature of the plasma is.
The changes in the ionization equilibrium of silicon are in Fig. 3.
The magnitude of the changes depends on the ratio of the density
of the electron beam to plasma electron density. The initial
temperature influences the ionization equilibrium only a little.
Fig. 3. The changes in the ionization equilibrium due to the return current and the
electron beam for three different initial conditions: Full red line: T0=1x106K,
nB:ne=1:10, full green line: T0=2x106K, nB:ne=1:10, full blue line: T0=2x106K,
nB:ne=1:20, dashed red line: Maxwellian distribution with T=1x106K, dashed green
line: Maxwellian distribution with T=2x106K, full black lines: Maxwellian
distribution with T=7.94x106K and with T=1.26x107K.
Excitation equilibrium
• The original modification of CHIANTI* software and database has
been used for computation of the synthetic spectra.
• The software and extended database now allows the computation
of the excitation equilibrium and synthetic spectra under the
assumption of non-thermal distributions and involves computation
of satellite line intensities.
X-Ray Spectrum
We have computed Si X-ray spectrum in region 5.15 - 6.0 Å. This
part of the spectrum has been observed by RESIK during solar
flares and we are able to compare our results with observations.
The effect of the initial conditions (T0, nB:ne) on the computed
spectra is different. The character of the spectrum is not influenced
by the initial temperature of plasma in the corona. It is determined
by the ratio of the density of the electron beam to the initial
plasma density (Fig. 4).
* CHIANTI is a collaborative project involving the NRL (USA), RAL (UK), MSSL (UK),
the Universities of Florence (Italy) and Cambridge (UK), and George Mason
University (USA). The software is distributed as a part of SolarSoft.
Fig. 4. The X-ray spectra for the T0=1x106K with nB:ne=1:10 (left above),
T0=2x106K with nB:ne=1:10 (right above), T0=2x106K, nB:ne=1:20 (left below) and
for the Maxwellian distribution with T=1.29x107K (right below).
Fig. 5. The comparison of the X-ray spectra for the presented model (left,
above), the previous simple model (right,above) with spectrum observed by
RESIK during solar flare January 7, 2003.
Why we got different results?
The comparison of the modelled spectra with the spectrum for the
Maxwellian distribution shows that:
• the intensities of the Si XIII lines (5.28 Å, 5.40 Å) are higher for
modelled distribution than for the Maxwellian distribution;
• the intensities of the Si XIId satellite lines (5.82 Å, 5.56 Å) are
lower.
Comparison with the simple model and
observations
The simple model simulated the electron beam as a monoenergetic beam and the return current was formed by all plasma
electrons with the same drift velocity. The electron plasma
distribution together with the mono-energetic beam is in Fig. 6,
(thick black lines). The comparison of the computed spectra for the
both models with observations is in Fig. 5.
The synthetic spectra for both new and older model show the
enhanced intensities of Si XIII lines (5.28 Å, 5.40 Å) in comparison
with Maxwellian spectra. This is in agreement with observation
(Kepa et al., 2006). The observations also show the enhanced
intensity of the sallite lines (5.56 Å, 5.82 Å). This enhancement has
been shown also for modelled spectra of in simple model.
Presented new spectra show opposite effect.
The Fig. 6 shows electron distributions for both models. The
excitation energy of the satellite line Si XIId 5.82 Å and excitation
energy of the allowed line Si XIII 5.68 Å are marked there. We
know that:
• the intensities of the satellite lines depend on the number of
particles with the energy of the transition;
• the intensities of the allowed lines are integrals of the product of
the cross section with the velocity over a distribution from the
excitation energy.
We need larger gradient of the distribution function, similar to
gradient of the electron distribution in simple model, to have higher
intensities of the satellite lines in our new model .
The explanation of different results:
there is different gradient of distributions in the presented and
simple model for the energy range 103 - 3x103 eV.
Therefore, we need to set the parameters (T0, nB:ne) of our model
to get the agreement with the observations.
• simple model: all electrons have a same drift velocity;
• presented model: only a part of electrons have drift velocity to
carry the return current in plasma bulk (RCB) and the second part
of electrons carries the return current in the high energy tail of the
distribution (RCT). The wave interaction between the electron beam
and ambient plasma heats plasma and decreases the gradient of
the distribution.
Fig. 6. The comparison of electron distribution functions for the presented and
previous model. Green line: T0=2x106K, nB:ne=1:10, red line T0=1x106K,
nB:ne=1:10, blue line T0=2x106K, nB:ne=1:20, dashed green line: Maxwell,
T0=2x106K, dashed red line: Maxwell, T0=1x106K, black line: simple model,
distribution plus mono-energetic beam, T0=2x106K, thin black lines: excitation
energy of Si XIId 5.82 Å and Si XIII 5.68 Å.
The gradient of the electron distribution is steeper if the drift
velocity in plasma bulk is higher:
T0
nB:ne
RCT
RCB
1x106K
1:10
31%
69%
2x106K
1:10
25%
75%
2x106K
1:20
23%
77%
The most suitable conditions to get the similar distribution shape
as in the simple model are for higher T0 and lower nB:ne.
Conclusions
• The electron beam together with the non-thermal electron
distribution changes relative abundances of ions and intensities of
the spectral lines.
• The changes in the shape of the electron distribution function in
solar corona depends on the initial temperature and the ratio of the
density of the electron beam to the background plasma density.
• The presence of the electron beam (or a distribution with
enhanced number of particles in high energy tail) is able to change
the ratio of the intensities of allowed spectral lines. The high energy
tail of distribution does not influence the intensities of satellite lines.
• The presence of the return current in the solar corona affects the
intensities of the satellite lines by different way what gives
possibility to diagnose it.