Issue |
A&A
Volume 500, Number 2, June III 2009
|
|
---|---|---|
Page(s) | 901 - 908 | |
Section | The Sun | |
DOI | https://doi.org/10.1051/0004-6361/200811364 | |
Published online | 29 April 2009 |
Relationship between non-thermal electron energy spectra and GOES classes
R. Falewicz1 - P. Rudawy1 - M. Siarkowski2
1 - Astronomical Institute, University of Wrocaw, 51-622 Wroc
aw, ul. Kopernika 11, Poland
2 -
Space Research Centre, Polish Academy of Sciences, 51-622 Wrocaw, ul. Kopernika 11, Poland
Received 17 November 2008 / Accepted 31 March 2009
Abstract
Aims. We investigate influence of variations in the energy spectrum of non-thermal electrons on the resulting GOES classes of solar flares.
Methods. Twelve observed flares with various soft-to-hard X-ray emission ratios were modeled using different non-thermal electron energy distributions. Initial values of the flare physical parameters including geometrical properties were estimated using observations.
Results. We found that, for a fixed total energy of non-thermal electrons in a flare, the resulting GOES class of the flare can change significantly by varying the spectral index and low energy cut-off of the non-thermal electron distribution. Thus, the GOES class of a flare depends not only on the total non-thermal electrons energy but also on the electron beam parameters. For example, we were able to convert a M2.7 class solar flare into a merely C1.4 class one and a B8.1 class event into a C2.6 class flare. The results of our work also suggest that the level of correlation between the cumulative time integral of HXR and SXR fluxes can depend on the considered HXR energy range.
Key words: Sun: chromosphere - Sun: corona - Sun: flares - Sun: magnetic fields - Sun: X-rays, gamma rays
1 Introduction
The source and acceleration mechanisms of particles in solar flares remain far from being understood. During the flare impulsive phase, it is commonly accepted that, non-thermal electron beams are accelerated in the solar corona and move along magnetic field lines to the chromosphere, where they deposit their energy. Here, most non-thermal electrons lose their energy in Coulomb collisions, while a tiny part of the electron energy is converted into hard X-rays (HXR) by bremsstrahlung. The heated chromospheric plasma evaporates and radiates over a wide spectral range from hard X-rays or gamma rays to radio emission. Hard and soft X-ray fluxes emitted by solar flares are generally related, in a way first described by Neupert (1968), who found that the time derivative of the soft X-ray flux approximately matches the microwave flux during the flare impulsive burst. A similar effect was also observed for hard X-ray emission (Dennis & Zarro 1993). Since hard X-ray and microwave emissions is produced by non-thermal electrons and soft X-rays are generated by thermal emission from hot plasma, the Neupert effect suggests that non-thermal electrons are directly produce by plasma heating. Lin et al. (1984) were the first to observe hard X-ray emission above 25 keV from microflares using balloon-borne observations. Later studies using RHESSI observations (Hannah et al. 2008; Qiu et al. 2004; Battaglia et al. 2005) show that time, spatial, and spectral characteristics of microflares are similar to those of large flares. However, there is no universal, unambiguous correlation between the released total energy of the flare and the observed HXR radiation.
![]() |
Figure 1: Images of twelve analysed flares taken with the Yohkoh SXT or HXT/LO (gray scale images) and HXT/M2 or HXT/HI (contours) instruments. |
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Many flares exhibit low SXR emission (as indicated by their GOES emission), but strong, HXR emission above 30 keV (Gburek & Siarkowski 2002; McDonald et al. 1999; Siarkowski et al. 2006; Qiu et al. 2004). These events are commonly called ``non-correlated'' flares. Analytical estimations by McDonald et al. (1999) demonstrated that, in these flares, only a small part of the total energy carried by the non-thermal electrons is transferred to the ambient material during the chromospheric evaporation process. Even so, analysis of the HXR emission of these flares allows one to estimate the energy flux of non-thermal electrons and numerically simulate the energy losses and hydrodynamic effects of the chromospheric evaporation, thus allowing investigations of the energy budgets of the solar flares.
In this paper, we investigate the influence of non-thermal electron
energy distribution on the resulting GOES classes of flares
and energy used by chromospheric evaporation. Our goal is to
separate the influence the spectral index ()
and low energy
cut-off (
)
of the non-thermal electron distribution, taken to
be a power law in energy, from the total energy of the electrons. To
do this, we calculated a grid of 1D models to describe the time
evolution of twelve observed solar flares. The models of each
observed flare were calculated using identical total energies
delivered by non-thermal electrons but with various appropriate
combinations of
and
.
For each model, we calculated
the resulting GOES 1-8 Å flux (i.e. GOES class
of the event) as well as the evaporation energy.
In the following, we describe the observed flares (Sect. 2), the model calculation (Sect. 3), the results obtained (Sect. 4), and we present our discussion and conclusions in Sect. 5.
Table 1: Physical parameters of observed flares.
2 Observations
We selected 12 disk flares observed by the Yohkoh satellite, of simple single-loop X-ray structure and maximum hard X-ray flux not less than 10 cnts/s per subcollimator of the M2 channel (33-53 keV) of the HXT instrument (Kosugi et al. 1991). Details are given in Table 1. Five flares were analysed by McDonald et al. (1999) (four being correlated and one non-correlated), a further seven flares were taken from the HXT Flare Catalogue (Sato et al. 2006), four being correlated and three non-correlated. The correlated and non-correlated events are denoted in Table 1 with letters C and N, respectively.
The flares were also observed with the Yohkoh SXT grazing-incidence telescope (Tsuneta et al. 1991) and Bragg Crystal Spectrometer (BCS, Culhane et al. 1991), as well as the GOES X-ray photometers (1-8 Å and 0.5-4 Å bands). HXT images of the flares were reconstructed using a standard Pixon method (Metcalf et al. 1996) with variable accumulation times and an assumed threshold count rate of 200 counts in the M2 band (33-53 keV); these are shown in Fig. 1. SXR images (also shown) of ten flares were taken with Be119/SXT, but for two flares, due to a lack of the SXT images, we present images taken with HXT in its L0 (14-23 keV) channel.
HXT spectra were analysed to obtain the photon spectral index
()
at the flare peak time in the M2 channel, flux scaling
factor (flux at 1 keV = a0), and cut-off energy in the electron
distribution (
). The SXT images allowed us to estimate the
single loop semi-length (L0) and cross-section (S). These are
given in Table 1.
![]() |
Figure 2: Synthesised BCS CaXIX and BCS SXV fluxes (blue lines), and the observed fluxes (asterisks) of the C2.7 class solar flare observed on 1992 February 2. |
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3 Methods of analysis
Solar flare hard X-ray emission 10-20 keV is generally
believed to be produced by bremsstrahlung emitted by non-thermal
electrons. A power-law dependence of the emitted spectrum implies
that the non-thermal electrons have a power law energy distribution
(Brown 1971; Tandberg-Hanssen & Emslie 1988) and this in turn requires a low energy
cut-off
to the electron spectrum to prevent an infinite total
electron energy. A arbitrary value of
has been defined by
numerous authors between 15 and 25 keV (see e.g., McDonald et al. 1999 and
references therein). Thus,
occupies the energy range where
thermal emission can dominate and so it is very difficult to
determine its correct value from observations.
With the improved spectral resolution of the RHESSI
instrument, the thermal and non-thermal spectral components can be
more clearly separated. Direct inversion of photon spectra is now
also possible to deduce the ``mean electron flux distribution''
(Brown et al. 2006). However, the problem of estimating remains (e.g., Kontar et al. 2008). In the absence of RHESSI
data for these flares, our approach has been to compare the
Yohkoh/HXT observations of the 12 flares with the results of
model calculations. We investigated the relation between the
non-thermal electron spectra and the GOES class of the
thermal flare, which is produced by evaporation processes, using the
observed parameters of the 12 flares. Our calculations accounted for
the observed energy distributions of the non-thermal electrons and
time variations in the observed X-ray fluxes, dimensions of the
flaring loops from SXR images, estimated main initial physical
parameters of the thermal plasma (density, temperature), and energy
gains and losses.
We analysed each flare in two steps: (a) we modeled the observed flare that most closely resembled the synthesised and observed GOES and BCS light curves (when available); (b) we investigated how the variations in the non-thermal electron energy spectra influence the synthesised GOES fluxes of a solar flare model.
The geometry of each flaring loop (volume (V), loop cross-section
(S), and half-length (L0)) were determined using images taken
with SXT and HXT (see Table 1). The loop cross sections were
estimated to be the areas within a level equal to 30% of the
maximum flux in the HXT/M2 channel. Loop half-lengths L0 were
estimated from the distances between the centres of gravity of the
HXT/M2 footpoints, assuming that the loop has a semi-circular shape.
The volume of the loop V then equals
.
Temperatures (
)
and emission measures (EM) were estimated
using GOES 1-8 Å and 0.5-4 Å fluxes using the filter-ratio method proposed by Thomas et al. (1985). We used an updated version of this paper by White et al. (2005). A detailed description of this method is also given by Siarkowski et al. (2008). Mean electron densities (
)
were estimated from emission measures (EM) and volumes (
V=2 L0 S).
Assuming a power-law hard X-ray photon spectra
,
we calculated time variations in the
spectral indices (
)
and scaling factors a0 (flux at 1
keV) for the impulsive phases of all 12 flares. Electron spectra of
the form of
can be calculated from power-law
photon spectra using the thick target approximation
(Tandberg-Hanssen & Emslie 1988):
![]() |
(1) |
where S is the loop cross-sectional area, R is the Earth-Sun distance (1 AU








The estimated total energy carried by the non-thermal electrons is
very sensitive to the assumed low energy cut-off of the electron
spectrum, ,
because of the power-law nature of the energy
distribution. A variation in the
value of just a few keV can
add or remove a substantial amount of energy from/to the modeled
system, so
must be selected with great care. We estimated
as follows. First, we derived low energy cut-offs of the
energy spectra using the slightly modified semi-analytical model of
McDonald et al. (1999). While these authors used a fixed value of
(equal to 20 keV) for all flares, we calculated
for each flare
using an iterative method. The flare energy budget was calculated
using GOES and HXT data. When the total energies calculated
from HXR data and those emitted in the SXR range disagreed, we
iteratively changed the value of
(in steps of 0.1 keV) until
agreement was reached. This method is the most direct way of
estimating
from the energy balance. We then slightly modified
the value of
yet further to obtain the closest agreement
between the synthesised and observed GOES classes and BCS
fluxes of each flare. Examples of the agreement between observed and
synthesised BCS light curves are shown in Fig. 2, while the observed
and synthesised GOES curves are shown in Fig. 3. The
estimated
was used as a fixed value, while the electron
spectral index
and corresponding scaling factor A varied
in time for each particular model of event. The values of the main
physical parameters, including
and estimated
,
observed at the maximum of the HXR emission, are given in Table 1
for all twelve flares.
![]() |
Figure 3: Synthetic X-ray fluxes in 0.5-4 Å and 1-8 Å bands calculated using a numerical model of the M2.7 class solar flare observed on 1991 December 16 (blue thick line) and the corresponding fluxes recorded with the GOES 7 satellite (thin grey lines). |
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By vary the electron energy spectral index
and appropriate
adjustment of A and
,
one can easily change the amount of the
energy used for the evaporation process while still fixing the total
energy flux delivered by non-thermal electrons:
![]() |
(2) |
For each time step during each flare and with values of



Table 2: Results of the numerical models of analysed flares.
We used a modified Naval Research Laboratory solar flux tube model code kindly made available to the solar community by Mariska and his co-workers (Mariska et al. 1989,1982). Although a typical flaring loop is a 3-D structure surrounded by a possibly complex active region, it can be modeled for many purposes with both a simple 1-D hydrodynamic model and the NRL Code. We included a few modifications to the code: new radiative loss and heating functions; inclusion of the VAL-C model (Vernazza et al. 1981) of the initial structure of the lower part of the loop (extended using Solar Standard Model data; Bahcall & Pinsonneault 2004), and use of double precision in the calculations. The heating of the plasma by a non-thermal electron beam was modeled using the approximation given by Fisher (1989). A mesh of new values of the radiative loss function was calculated using the CHIANTI (version 5.2) software (Dere et al. 1997; Landi et al. 2006) for the temperature 104-108 K and densities range 108-1014 cm-3. For each flare, a grid of models was calculated using various non-thermal electron beam models, all having the same total energy. All models were calculated for periods lasting from the beginning of the impulsive phase to beyond maximum of the soft X-ray emissions. These periods were about 150-200 s. The time steps in the models were about 0.0005-0.001 s.
We estimated the evaporation energy
to be the difference
between the total energy delivered by the non-thermal electrons
and the total energy lost by radiation over the entire
loop,
(i.e.
)
during the
impulsive phase. As mentioned before, the main parameters of each
calculated model (time-dependent fluxes of the non-thermal
electrons, and the lengths and cross-sections of the flaring loops)
were evaluated using observational data (see Sect. 2).
4 Results
We analysed each flare in two steps. First, we compiled a model
using observed geometrical and physical parameters, including
and
.
The correctness of these models was validated by
comparing the synthesised GOES 1-8 Å and 0.5-4 Å, BCS
SXV and BCS CaXIX fluxes with the observed fluxes. We found good
agreement between observations and the modeled data. For example,
the observed and synthesised BCS SXV and BCS CaXIX fluxes of the
C2.7 class solar flare observed on 1992 February 2 are shown in Fig. 2 while the calculated and observed GOES X-ray light-curves
of the M2.7 event on 1991 December 16 are shown in Fig. 3. The
values of the flux maxima are reproduced very well but the
noticeably large discrepancies during the early rise and late decay
phases are caused by a lack of additional pre- and post-impulsive
flare heating in our model. In the second step, we calculated
several numerical models of each event for various appropriate
combinations of the electron spectral index
and low-energy
cut-off
,
where the total energy delivered by the non-thermal
electrons was fixed to be equal to the observed energy.
The model calculations also provide e.g., pressure, temperature, density, velocity and column mass as functions of time and position along the loop. For all reasonable sets of physical parameters of the flaring loops, we found a rapid inflow of chromospheric material into the loop (i.e., chromospheric evaporation). Large-scale macroscopic motions of the dense plasma toward the loop-tops and rapid increases in the plasma temperature, pressure, and electron density all agree well with commonly accepted schemes of chromospheric evaporation. After the energy deposition period, the plasma contained in the flaring loop gradually cools, but the model calculations generally ended before returning to a hydrostatic equilibrium.
For all twelve flares, we found that by fixing the total energy
delivered by non-thermal electrons, the resulting observed
GOES class of the induced solar flare varied significantly
when the spectral index and low energy cut-off of the non-thermal
electrons spectra were changed. The variations in the GOES
classes and the proportion of the total energy contributed by
evaporation are given in Fig. 4. The upper-left
panel shows models of M2.7 GOES class correlated flare
observed on 1991 December 16. The observed low energy cut-off is equal to 25.8 keV and is assumed to remain constant during the
calculations. The spectral index
is equal to 4.6 (here and
for the other three events shown in Fig. 4, we indicate the value of
at the time of maximum of the impulsive phase). The
upper-right panel shows models of the C2.7 GOES class
non-correlated flare observed on 1992 February 2. The observed
and
are equal to 18.9 keV and 4.0. The lower-left panel
shows models of the B8.1 GOES class non-correlated flare
observed on 1993 October 3. The observed
and
are
equal to 23 keV and 3.7, respectively. The bottom right panel shows
models of the M2.4 GOES class correlated flare observed on
2000 July 27. The observed
and
are equal to 19.8 keV
and 4.2, respectively. The spectral indexes
of each model
varied in time while its observational values increased or decreased
by a constant factor, i.e., in our models, we took various values of
that differed from
by between 0 and
2,
where
is the observed
at any given time
during the flare. The black, filled squares represent models
calculated using non-thermal electron beams with main parameters
that were deduced from observations. The total ranges of the modeled
GOES classes and
for all flares are shown in Table 2.
We now describe results obtained for the most representative events, two correlated flares (1991 December 16, 2000 July 27) and two non-correlated flares (1992 February 2 and 1993 October 3). All flares had a simple, single-loop structure. In the following, GOES classes are given with the pre-flare level subtracted.
4.1 M2.7 flare on 1991 December 16
The M2.7 flare at 04:54 UT on 1991 December 16 occurred in an active
region NOAA 6961 (N04W45). The flare appeared in SXR as a single
loop with semi-length 15 400 km (see Fig. 1). The impulsive HXR
(>23 keV) occurred between 04:55:50 UT and 04:56:28 UT. The
cross-section of the loop was estimated from HXR images to be
cm2.
![]() |
Figure 4:
Variations in the observed GOES classes and shares
of the evaporation energy
|
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A flare model was calculated using parameters of the photon spectra
and scaling factors a0 calculated as a function of time from hard X-ray fluxes observed in the HXT M1 and M2channels, while
was estimated and fixed to be equal to 25.8 keV. The total non-thermal electron energy was estimated to be
erg, while the evaporation energy was
erg (=
). Alternative
models were calculated for the same total energy
but with
changed from the initial value of 4.6 by
and with
changed from the initial value of
by
4 keV (see
Fig. 4, top-left panel). For
lowered by 2 and
raised
by 4 keV, the evaporation energy decreased to 7% of
only
when the GOES class decreased to only C1.4. In contrast,
when
was increased by 2 and
lowered by 4 keV, the
observed GOES class of the event increased to M9.4 while
the evaporation energy increased to 79% of
.
Calculations
made for all combinations of
and
give flares of
GOES class between C1.4 and M9.4.
4.2 C2.7 flare on 1992 February 2
The C2.7 flare on 1992 February 2 at 11:33 UT-11:38 UT occurred in
the active region NOAA 7042 (S14W41). It was observed with
HXT/Yohkoh and GOES only (see Fig. 1). The
impulsive HXR (>23 keV) peak occurred between 11:33:18 UT and
11:33:28 UT, only 10 s long. HXT/LO images of the flare show the
X-ray emission as a single loop of semi-length (9800 km).
The loop foot points were observed only in HXT channels M2 and H.
The loop cross-section was estimated to be
cm2.
The flare model was calculated as for the previous flare. The total energy was
erg and the evaporation energy was
erg, (=
). Alternative models were calculated for the same total non-thermal electron energy
but with
in the range -1 to +2 from the initial value of
,
and with
in the range
4 keV from the initial value of
(see Fig. 4, top-right panel). Calculations made for all combinations of spectral index and low energy cut-off give flares of GOES classes in the range B6.3 and C5.6.
4.3 B8.0 flare on 1993 October 3
The B8.1 flare on 1993 October 3 occurred between 09:06 UT and 09:07 UT in the active region NOAA 7590 (N11W04). The flare was visible in SXT as a single loop of semi-length 28 800 km (see Fig. 1). The impulsive HXR (>23 keV) emission occurred between 09:06:40 UT
and 09:07:15 UT. The cross-section of the loop was estimated to be
cm2.
A flare model was calculated using the total energy, which equaled
erg. The evaporation energy was equal
to
erg, (=
). Alternative
models were calculated for the same total energy
but with
changed by between 0 and +2 from the initial value of
and with
changed from the initial value of
by
4 keV (see Fig. 4, bottom-left panel). The spectral index was
increased by 2 and the energy cut-off was lowered by 2 keV, and the
corresponding evaporation energy of the flare increased to
and the GOES class of the flare increased
to C2.6. Calculations for all combinations of spectral index and
energy cut-off provided flares of GOES classes varying from
B4.4 to C2.6.
4.4 M2.4 flare on 2000 July 27
The M2.4 flare on 2000 July 27 occurred between 04:08 UT-04:13 UT
in the active region NOAA 9090 (N10W72). The flare was visible in
SXT as a single loop with semi-length 8700 km (see Fig. 1).
The HXR (>23 keV) emission occurred between 04:07:54 UT and
04:08:30 UT. Using the reconstructed HXR images, we estimated the
cross-section of the loop to be
cm2.
The flare model was calculated in the same way as for the previous
events. The total energy was
ergs and
the evaporation energy
ergs (=
). The alternative models of the flare were calculated for
the same total energy
but by
changing from its
initial value by -1 to -2 and with
changed from the
initial value of
by
keV (see Fig. 4, bottom-right
panel). When the spectral index was increased by 2 and the energy
cut-off lowered by 4 keV, the evaporation energy of the flare
increased to 80% of
and the GOES class of the
flare increased to M4.5. In contrast, when
decreased by 1
and
increased by 4 keV the observed GOES class of the
event decreased to only C3.2, while the evaporation energy decreased
to
.
Calculations for all combinations of
and
produced flares with GOES classes varying from
C3.2 to M4.6.
5 Discussion and conclusions
![]() |
Figure 5:
Variations in the synthesised GOES classes and
X-ray fluxes of the numerical models of the four solar flares
obtained for various |
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We have presented results of an energy model calculation for twelve
flares with various soft to hard X-ray emission ratios. We focused
on the influence of varying the energy spectrum of the non-thermal
electrons on both the observed GOES classes of the flares
and their evaporation energies
.
Many numerical models of
the events were calculated using observed and modified energy
distributions of the non-thermal electrons (various appropriate
combinations of the electron spectral index
and low energy
cut-off
,
but fixed values of the total energy delivered by
non-thermal electrons
), observed geometry of the loops,
and initial values of the main physical parameters of the plasma
estimated using observational data. We first showed that for fixed
initial parameters of the flare loop (geometry and physical
parameters of the plasma) and fixed total non-thermal electron
energy, one can significantly change the resulting GOES
class of the flare by appropriately changing of the electron index
and low energy cut-off of the electron spectra while maintaining the
total energy at a constant value. For example, we were able to
convert the M2.7 GOES class correlated flare into a C1.4
class non-correlated-like flare, and a B8.1 GOES class
non-correlated flare into a C2.6 class correlated-like flare.
The ratio of the radiated energy to the energy in evaporation processes, as well as the observed GOES classes of the events vary for various combinations of the spectral index and low energy cut-off. It is obvious that both the total delivered energy and the energy spectrum of the non-thermal electron beam (described by spectral index and low energy cut-off) are important to determining the course and magnitude of the evaporation processes and the observed soft X-ray emission of the flares (i.e., their GOES class).
An estimation of the energy carried by non-thermal electrons is very
sensitive to an assumed value of the low energy cut-off of the
energy spectrum due to the power-law nature of the energy
distribution. A change in the
value of only a few keV can add
or remove a substantial amount of energy from/to the modeled system.
The spectral index of the non-thermal electron spectrum is also
crucial, while the low-energy fraction of the electrons heats the
chromospheres most effectively (see also McDonald et al. 1999). For the
same total energy, the beam of non-thermal electrons with a softer
spectrum could produce a solar flare of greater GOES
importance. This is demonstrated in Fig. 4, where variations in the
observed GOES classes and evaporation energies
are
shown for four flares. As an example, one can track the behaviour of
the M2.7 flare on 1991 December 16. The model calculated using a
non-thermal electron beam with principal parameters deduced from
observations, the GOES class is equal to M2.7 and the
evaporation energy equals 30% of the total energy delivered by the
non-thermal electrons. The same observed solar flare, modeled using
a non-thermal electron beam of spectral index
that has
decreased by 1, has a slightly lower GOES class equal to M1.3
and significantly lower evaporation energy equal to 18%
.
By increasing additionally the low energy cut-off
by 2 keV, we
obtained an even lower GOES class and
model equal
to C4.0 and 9%
,
respectively. In contrast, for a steeper
electron spectrum and increased population of low energy electrons
(decreased
), both the GOES classes and
increase. Thus, for the M2.7 flare described above, the non-thermal
electron beam that has an energy spectral index
that has
increased by 1, has a slightly higher GOES class of M3.9 and
higher evaporation energy of 40%
.
By decreasing
additionally the low energy cut-off
by 2 keV (and hence
expanding the low-energy electron population), we obtained an even
higher GOES class and
of the model of M6.3 and
58%, respectively. The ranges of the modeled GOES classes
and
for all analysed events are given in Table 2.
The overall changes in GOES classes and
are
similar for all our analysed events. In general, the SXR emission
increases for softer HXR spectra and decreases for harder spectra.
That is, the steeper electron spectra produce a higher amount of
evaporated material. This behaviour is induced by spatial variations
in the efficiency of the non-thermal electron energy deposition
mechanism. The energy deposition mechanism is most efficient in the
transition region and upper part of the chromosphere, but its
particular spatial distribution depends on the true distribution of
the column mass of plasma encountered by non-thermal electrons.
However, the magnitude of changes observed for a particular flare
depends on the flare's physical properties.
A non-thermal electron beam containing a large population of high-energy electrons (i.e., with a hard spectrum) penetrates deep into the chromospheric plasma, where it deposits most of its energy, and from where energy is efficiently radiated. The remaining part of the transmitted energy is deposited in the upper part of the chromosphere and/or transition region, causing moderate ``gentle evaporation''. On the other hand, a non-thermal electron beam with a soft spectrum deposits most of its energy in the upper part of the chromosphere and/or transition region, where the density is relatively low, giving rise to ``explosive evaporation''.
Our results show that the parameters and properties of the solar flares depend not only on the initial hydrodynamic properties of the flaring loop and the total amount of the delivered energy but also on properties of the primary source of energy, and time and spatial variations in the processes leading to the electron acceleration. Thus, the level of correlation between the cumulative time integral of HXR and SXR fluxes depends on the HXR energy range. This conclusion is in accordance with results of the statistical analysis of flares by Veronig et al. (2002) and microflares by Qiu et al. (2004) observed with RHESSI indicating that only half of the events show a time behaviour consistent with the expectations based on the Neupert effect. Qiu et al. (2004) also showed that the correlation predicted by the Neupert effect is greatest for the photon energy range of 14-20 keV.
In Fig. 5, we show the variations in the synthesised GOES
classes and X-ray fluxes of the numerical models of the four solar
flares obtained for various
and
and constant total
energy delivered by non-thermal electrons. The arrows indicate the
variations in the GOES classes and X-ray fluxes of the
models, while the open circles represent 369 flares taken from the
HXT Flare Catalogue (Sato et al. 2006). As can be seen the,
relationships between the soft and hard X-ray fluxes obtained from
the models go far beyond the range of the ``correlation belt'' of soft
and hard X-ray fluxes recorded for the observed solar flares, up to
high HXR fluxes. For example, by changing the hardness of the
non-thermal electron spectrum and low energy cut-off, the M2.7 flare
observed on 1991 December 16 was converted into the C2.4
GOES class event with an HXT/M2 peak emission above 1000 cnts/s/sc (see Fig. 5, thick arrow). Many flares of low GOES class
but high hard X-ray flux have been observed with Yohkoh and
RHESSI. However, one does not appear observe flares of
similar GOES class with high X-ray flux; these extremely
``small-hard'' flares do not appear to exist (i.e., flare that would
be located in the upper-left corner at the Fig. 5). This than
imposes restrictions on the flare electron spectra and therefore on
acceleration mechanisms.
Acknowledgements
The authors would like to thank the Yohkoh team for excellent solar data and software. They are also grateful to the anonymous referee for useful comments and suggestions. This work was supported by the Polish Ministry of Science and Higher Education, grant No. N203 022 31/2991 and by the European Community's Seventh Framework Programme (FP7/2007-2013) under grant agreement No. 218816 (SOTERIA).
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All Tables
Table 1: Physical parameters of observed flares.
Table 2: Results of the numerical models of analysed flares.
All Figures
![]() |
Figure 1: Images of twelve analysed flares taken with the Yohkoh SXT or HXT/LO (gray scale images) and HXT/M2 or HXT/HI (contours) instruments. |
Open with DEXTER | |
In the text |
![]() |
Figure 2: Synthesised BCS CaXIX and BCS SXV fluxes (blue lines), and the observed fluxes (asterisks) of the C2.7 class solar flare observed on 1992 February 2. |
Open with DEXTER | |
In the text |
![]() |
Figure 3: Synthetic X-ray fluxes in 0.5-4 Å and 1-8 Å bands calculated using a numerical model of the M2.7 class solar flare observed on 1991 December 16 (blue thick line) and the corresponding fluxes recorded with the GOES 7 satellite (thin grey lines). |
Open with DEXTER | |
In the text |
![]() |
Figure 4:
Variations in the observed GOES classes and shares
of the evaporation energy
|
Open with DEXTER | |
In the text |
![]() |
Figure 5:
Variations in the synthesised GOES classes and
X-ray fluxes of the numerical models of the four solar flares
obtained for various |
Open with DEXTER | |
In the text |
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