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Soft X-ray heating of the chromosphere
during solar flares A. Berlicki1,2
1Astronomický ústav AV CR, v.v.i., Ondrejov
2Astronomical Institute, University of
Wroclaw, Poland
Ondrejov, June 11, 2009
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The aim of the work We try to explain the
reasons of long-duration chromospheric H?
emission often observed during the gradual
phase of solar flares.
LC, Wroclaw, H?
Stellar chromospheres can also be strongly
illuminated by the soft X-rays
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• What kinds of chromospheric heating
  mechanisms
• are effective during solar flares
• Non-thermal electrons - impulsive phase of
  flares,
• Thermal conduction - upper chromosphere and
  transition region,
• Radiative heating by soft X-ray (?)

usually included in codes
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X-ray sources
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X-ray heating of the chromosphere a) B.
Somov (1975) - Solar Phys. 42, 235
proposition of such heating mechanism, b) J. C.
Henoux and Y. Nakagawa (1977) - Astron.
Astrophys. 57, 105 theoretical calculations
of the energy deposited in the chromosphere, c)
several papers which took into account this
mechanism of heating in the theoretical
modeling of the solar atmosphere (S. Hawley, W.
Abbett, C. Fang, J-C. Henoux, etc.) d) no
publications where the comparison between the
theoretical modeling and the observations
was performed.
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How much energy of X-ray radiation goes into the
chromsphere ?
The rate of energy conversion
,where
- rate of photoionization of i-th element
- energy of photoelectron, with ?i being the
ionization potential of the i-th element
The rate of creation of photoelectrons per unit
volume by the downward soft X-ray flux F?
z vertical geometrical scale
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The intensity I? of the soft X-ray radiation is
calculated from the transfer equation. PP
atmosphere
(no source function Tlt104 K)
NH total hydrogen density, ? - cosine of the
angle between the direction of photon propagation
and the vertical z
- total photoionization cross-section, depends
on z
?i - ionization cross-section (Brown Gould
1970) ?H hydrogen ionization cross-section x
nH/NH NH nH nHO
?ph photoionization cross-section ?T Thomson
scattering cross-section ?t total cross section
(Brown Gould 1970)
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The formal solution of the transfer equation
ZO
I?O(?)
Z
I?O(?) the intensity of SXR at the top of the
atmosphere (ZO). After introducing the column
mass
- mean molecular weight ( const in the
whole atmosph.)
and effective ionization cross-section in the
form
we can write
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Coming back to the rate of creation of
photoelectrons...
From the transfer equation we obtain
Taking into account that and previously
calculated I?(z,?) ,we have
How to obtain ?
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The geometry of irradiation
Dloop
Dchro ltlt Dloop
X-ray loop
Heated area
Dchro
Chromosphere
If Dchro ltlt Dloop , then we can assume
to be isotropic.
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If does not depent on ?, we get
exponential integral
where
Other forms of intensities of incident SXR are
also possible, e.g.
For any element i, the equation has a similar
form Therefore, the rate of energy
conversion from the SXR flux at wavelenght ? to
photoelectrons from i-th element is
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For all considered elements, but still at given
?
where
? 1/?
Finally, the total energy of soft X-rays within
the spectral range (?1,?2) deposited in the
atmosphere is

- isotropic
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at the top of the atmosphere
The simple case An isothermal X-ray source of
given temperature T and emission measure EM.
Power at ? where ?(?,T) is the emissivity of
optically thin plasma. For the plane-parallel
atmosphere the emergent SXR intensity
const for given X-ray source and with
The emissivity ?(?,T) of the hot plasma may be
taken from different previous calculations, e.g.
Raymond Smith (1977), or may be calculated
using SolarSoft procedures based on Mewe et al.
1985, 1986 papers.
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If the T and EM of the X-ray source is not known,
it is possible to assume some model of X-ray
structures, their heating function, e.g. in
coronal loop. It is used for the analysis of
X-ray heating of stellar atmospheres or accretion
disks (Hawley Fisher 1992). E.g. the coronal
heating rate in terms of TA and L of the X-ray
loop and the temperature in the loop as a
function of the distance z above the loop base
may be found by using the scaling low Hawley
and Fisher used such model to determine I?0. They
used an older values of emissivity from Raymond
and Smith (1977)
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Emissivity of optically thin plasma erg cm-3 s-1
Å-1 calculated for temperatures T2 and 10 MK
(mewe_spec.pro)
?? erg cm3 s-1 Å-1
T 2 MK T 10 MK
Mewe, Gronenschild, van den Oord, 1985, (Paper V)
A. A. Suppl., 62, 197 Mewe, Lemen, and van den
Oord, 1986, (Paper VI) A. A. Suppl., 65, 511
? Å
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An example of the distribution of intensity of
soft X-ray radiationat the upper boundary of the
chromosphere. (plane-parallel, isothermal source).
I?0 erg s-1 cm-2 Å-1
X-RAY SOURCE PARAMETER T8 MK, EM1?1048 cm-3,
A2?1018 cm2
? Å
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Comparison of the deposited energy of the soft
X-ray radiation in the model atmosphere VAL3C
(Vernazza et al. 1981).
dE(mcol)/dt erg s-1cm-3
VAL3C
X-RAY SOURCE T8 MK, EM1?1048 cm-3, A2?1018
cm2
Blue line emissivity from Raymond
Smith.(1977) Red line emissivity from Mewe et
al. (1985, 1986) mewe_spec.pro
mcol g cm-2
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Example of analysis
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Method
OPTICAL OBSERVATIONS (MSDP)
SOFT X-RAY OBSERVATIONS (SXT, XRT)
INPUT PARAMETERS OF THE MODEL
non-LTE CODE
MODEL
SYNTHETIC H? LINE PROFILE
OBSERVATIONAL H? LINE PROFILE
PARAMETERS OF SOFT X-RAY SOURCES
GRID OF MODELS
FITING THE PROFILES TO OBTAIN THE MODEL
CALCULATIONS OF THE AMOUNT OF THE SOFT
X-RAY RADIATION DEPOSITED IN MODEL (Mi) OF
THE CHROMOSPHERE
MODEL Mi
HEIGHT DISTRIBUTION OF THE ENERGY DEPOSITED
BY SOFT X-RAY RADIATION IN Mi MODEL OF
THE CHROMOSPHERE
HEIGHT DISTRIBUTION OF THE NET RADIATIVE
COOLING RATES IN Mi CHROMOSPHERIC MODEL
NRCR line transitions
COMPARISON OF BOTH DISTRIBUTIONS
CONCLUSIONS
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To analyse this heating mechanism we used the
observations of the flares
a) Optical observations (Multichannel
Subtractive Double Pass spectrograph- MSDP -
Wroclaw) to determine the H? line profiles used
in the modelling of solar chromosphere, b)
Soft X-ray observations (Yohkoh, SXT telescope)
to estimate the parameters of Soft X-ray
sources, c) Magnetic field and continuum
observations (SOHO/MDI) to perform the
spatial coalignment between optical (MSDP) and
soft X-ray (SXT) images.
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Theoretical
calculations a) Spectral distribution of the
soft X-ray intensity in 1300 Å spectral range
with the step of 1 Å at upper boundary of the
chromosphere within the analyzed parts of the
flares (plane-parellel approximation, sources
are isothermal) - Mewe et al., 1985 Mewe et
al., 1986 (Solar-Soft) ?? - emissivity (in
erg cm3 s-1 Å-1) dependent on plasma temperature
and on the wavelength (calculated with
mewe_spec.pro)
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b) construction of the grid of chromospheric
models made by modyfication of semiempirical
models VAL-C and F1-MAVN (parameters ?T and mO) -
to obtain the theoretical profiles of
hydrogen H? line - NLTE codes (P. Heinzel) - in
total 206 different models and profiles
Convolution of all synthetic profiles with the
Gauss function to make them comparable to the
observed profiles.
Parameters mO and ?T used for modyfication of
semiempirical chromospheric models VAL - C and
F1- MAVN.
Fitting procedure
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• c) calculation of the amount of energy deposited
  by soft X-rays in the models of
• the atmosphere obtained in the analyzed areas
  of the flares (plane-parallel
• approximation
• d) calculation of the net radiative cooling rates
  (radiative losses) for the
• chromospheric models determined by fittig the
  synthetic and observed H?
• line profiles - NLTE codes.
• ASSUMPTION
• The energy provided to given volume in the
  solar chromosphere in time unit is equal to the
  energy radiated from the same volume in the
  same time
• the time-scale of radiative processes in solar
  chromosphere is much shorter than the
  time-scale of thermodynamical processes
• during the gradual phase of solar flares the
  changes of different plasma parameters are
  slow and therefore the evolution of the flare can
  be described as a sequence of quasi?static
  models in energetic equilibrium.

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The flares used in the analysis
Date Active region(NOAA) Approximate coordinates GOES class Time of the flare UT
25 09 1997 8088 S27 E02 (-50, -560) C 7.2 1140 1400
21 06 2000 9046 N20 W05 (100, 280) C 4.5 1010 1100
One of the most important thing for this
analysis was to have simultaneous optical and
X-ray observations of the flares.
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25 SEPTEMBER 1997
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21 JUNE 2000
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Determination of the temperature (T) and emission
measure (EM) for all areas (A) at few moments of
time derived from SXT (Yohkoh) data. The areas
were located just above the chromosphere where
the H? line profiles were recorded.
These values were used for calculation the
distribution of mean intensity of the soft X-ray
radiation at upper boundary of the chromosphere
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25/09/1997
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Example of fitting
21-06-2000, 104608 UT, A 02-05-1998,
051246 UT, area A
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The energy deposit dE(h)/dt and the NRCR ?(h)
Assuming a steady-state, the net radiative
cooling rates must balance different energy
inputs/outputs at each depth of the atmosphere.
Contribution function of the H? line in F1 atm.
Contribution function
Deposit in area A at 120925 UT (25-09-1997)
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Conclusions
a) During the gradual phase for all analyzed
flares and for all areas the values of
radiative losses are much larger than the values
of the energy deposited by soft X-ray
radiation. b) The energy provided to the
chromosphere by soft X-ray radiation is NOT
sufficient to explain the prolonged H?
chromospheric emission often observed during
the late phase of many flares. c) There are
significant differences in height in the
chromosphere between the layers where the
core of H? line profile is formed and the
layers where deposited energy reach the maximum.
In such a case the intensities of central
parts of H? line profiles should not be
close related with the rates of deposited
energy. d) Effect of enhanced coronal pressure,
related to the chromospheric evaporation,
or thermal conduction may be responsible for the
enhanced chromospheric emission in the late
phases of flares. Future 2D modeling and both
SXR and n-th e- during the impulsive phase
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THE END