Download X-ray heating of the chromosphere

Soft X-ray heating of the chromosphere
during solar flares
A. Berlicki1,2
1Astronomický
ústav AV ČR, v.v.i., Ondřejov
2Astronomical
Institute, University of Wrocław, Poland
Ondřejov, June 11, 2009
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, Wrocław, H
Stellar chromospheres can also be strongly illuminated by the soft X-rays
2
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
X-ray sources
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.
3
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
The intensity I of the soft X-ray radiation is calculated from the transfer equation.
PP atmosphere:
(no source function – T<104 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)
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:
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
?
The geometry of irradiation:
Dloop
Dchro << Dloop
X-ray loop
Chromosphere
If Dchro << Dloop , then we can assume
Heated area
to be isotropic.
Dchro
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:
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
]
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.
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)
Emissivity of optically thin plasma [erg cm-3 s-1 Å-1] calculated
for temperatures T=2 and 10 MK (mewe_spec.pro)
 [erg cm3 s-1 Å-1]
1E-23
T = 2 MK
T = 10 MK
1E-24
1E-25
1E-26
1E-27
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
1E-28
0
100
 [Å]
200
300
An example of the distribution of intensity of soft X-ray radiation
at the upper boundary of the chromosphere. (plane-parallel, isothermal source).
I0 [erg s-1 cm-2 Å-1]
X-RAY SOURCE PARAMETER:
T=8 MK, EM=11048 cm-3, A=21018 cm2
1E+5
1E+4
1E+3
1E+2
10
0
100
 [Å]
200
300
7
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
1
X-RAY SOURCE:
T=8 MK, EM=11048 cm-3, A=21018 cm2
0.1
0.01
1E-3
1E-4
1E-5
1E-6
1E-7
Blue line – emissivity from Raymond & Smith.(1977)
Red line – emissivity from Mewe et al. (1985, 1986) mewe_spec.pro
1E-8
1E-6
1E-5
1E-4
1E-3
mcol [g
0.01
cm-2]
0.1
1
10
Example of analysis
Method
SOFT X-RAY
OBSERVATIONS
(SXT, XRT)
OPTICAL
OBSERVATIONS
(MSDP)
non-LTE CODE
INPUT PARAMETERS
OF THE MODEL
MODEL
PARAMETERS OF
SOFT X-RAY SOURCES
SYNTHETIC H
LINE PROFILE
OBSERVATIONAL
H LINE PROFILE
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
HEIGHT DISTRIBUTION OF
THE ENERGY DEPOSITED
BY SOFT X-RAY RADIATION
IN Mi MODEL OF THE
CHROMOSPHERE
MODEL Mi
HEIGHT DISTRIBUTION OF THE
NET RADIATIVE COOLING RATES
IN Mi CHROMOSPHERIC MODEL
COMPARISON OF BOTH
DISTRIBUTIONS
NRCR line
transitions
CONCLUSIONS
To analyse this heating mechanism we
used the observations of the flares:
a) Optical observations (Multichannel Subtractive Double Pass spectrographMSDP - 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.
4
Theoretical calculations
a) Spectral distribution of the soft X-ray intensity in 1–300 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)
PC
EM    T 
I     I  

4A
4A
0
6
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
Values of mO [g/cm2]
0.0
1.0106
1.6106
2.5106
4.0106
6.3106
1.0105
1.6106
2.5106
4.0106
6.3106
1.0104
1.6106
2.5106
3.2106
Values of T [K]
0.0
200
400
600
800
1000
Values of mO [g/cm2]
4
1.010
5.0105
0.0
1.9104
4.9104
9.9104
1.3103
Values of T [K]
300
150
0.0
200
400
600
800
1000
1200
1400
1600
1800
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
8
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.
9
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
11:40 – 14:00
21 – 06 – 2000
9046
N20 W05 (+100, +280)
C 4.5
10:10 – 11:00
One of the most important thing for this analysis was to have simultaneous
optical and X-ray observations of the flares.
10
25 SEPTEMBER 1997
11
21 JUNE 2000
16
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
17
25/09/1997
Example of fitting
3E+6
3E+6
2E+6
2E+6
1E+6
1E+6
0
-2
-1
0
1
2
21-06-2000, 10:46:08 UT, A
0
-2
-1
0
1
2
02-05-1998, 05:12:46 UT, area A
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 12:09:25 UT (25-09-1997)
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
24
THE END