Soft X-ray heating of the chromosphere during solar flares

A. Berlicki1,2

1Astronomick stav AV R, v.v.i., Ondejov 2Astronomical Institute, University of Wrocaw, PolandOndejov, 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. 2LC, Wrocaw, HStellar chromospheres can also be strongly illuminated by the soft X-rays

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 includedin 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.

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How much energy of X-ray radiation goes into the chromsphere ?The rate of energy conversion:- rate of photoionization of i-th element- energy of photoelectron, with i being the ionization potential of the i-th element,where: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:- total photoionization cross-section, depends on zNH total hydrogen density, - cosine of the angle between the direction of photon propagation and the vertical zi - ionization cross-section (Brown & Gould 1970)H hydrogen ionization cross-sectionx = nH+/NHNH = nH+ + nHO ph photoionization cross-sectionT Thomson scattering cross-sectiont total cross section (Brown & Gould 1970)(no source function T

The formal solution of the transfer equation:IO() 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:ZZOwe can write:IO()

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:DloopDchroDchro

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 photoelectronsfrom 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[ ]

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 at the top of the atmosphereThe 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 I0. They used an older values of emissivity from Raymond and Smith (1977)

Emissivity of optically thin plasma [erg cm-3 s-1 -1] calculated for temperatures T=2 and 10 MK (mewe_spec.pro) T = 2 MKT = 10 MK [] [erg cm3 s-1 -1]Mewe, Gronenschild, van den Oord, 1985, (Paper V) A. & A. Suppl., 62, 197Mewe, Lemen, and van den Oord, 1986, (Paper VI) A. & A. Suppl., 65, 511

An example of the distribution of intensity of soft X-ray radiation at the upper boundary of the chromosphere. (plane-parallel, isothermal source). []I0 [erg s-1 cm-2 -1]X-RAY SOURCE PARAMETER: T=8 MK, EM=11048 cm-3, A=21018 cm27

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]Blue line emissivity from Raymond & Smith.(1977)Red line emissivity from Mewe et al. (1985, 1986) mewe_spec.promcol [g cm-2]X-RAY SOURCE:T=8 MK, EM=11048 cm-3, A=21018 cm2VAL3C

Example of analysis

OPTICALOBSERVATIONS(MSDP)SOFT X-RAYOBSERVATIONS (SXT, XRT)non-LTE CODEINPUT PARAMETERSOF THE MODELMODELSYNTHETIC HLINE PROFILEOBSERVATIONALH LINE PROFILEFITING THE PROFILESTO OBTAIN THE MODELMODEL MiPARAMETERS OF SOFT X-RAY SOURCES CALCULATIONS OF THE AMOUNTOF THE SOFT X-RAY RADIATIONDEPOSITED IN MODEL (Mi)OF THE CHROMOSPHEREHEIGHT DISTRIBUTION OFTHE ENERGY DEPOSITED BY SOFT X-RAY RADIATIONIN Mi MODEL OF THECHROMOSPHEREHEIGHT DISTRIBUTION OF THENET RADIATIVE COOLING RATESIN Mi CHROMOSPHERIC MODELCOMPARISON OF BOTHDISTRIBUTIONSCONCLUSIONSGRID OF MODELSMethodNRCR linetransitions

To analyse this heating mechanism weused 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 spectral range with the step of 1 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 -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 profilesParameters mO and T used for modyfication of semiempirical chromospheric models VAL - C and F1- MAVN.Convolution of all synthetic profiles with the Gaussfunction to make them comparable to the observed profiles.8Fitting procedure

Values of mO [g/cm2]

Values of (T [K]

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

0.0

200

400

600

800

1000

1200

1400

1600

1800

Values of mO [g/cm2]

Values of (T [K]

(1.0(10(4

(5.0(10(5

0.0

1.9(10(4

4.9(10(4

9.9(10(4

1.3(10(3

(300

(150

0.0

200

400

600

800

1000

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 quasistatic models in energetic equilibrium. 9

The flares used in the analysisOne of the most important thing for this analysis was to have simultaneousoptical and X-ray observations of the flares. 10

DateActive region (NOAA) Approximate coordinates GOES classTime of the flare [UT]25 09 19978088S27 E02 (-50, -560)C 7.211:40 14:0021 06 20009046N20 W05 (+100, +280)C 4.510:10 11:00

25 SEPTEMBER 199711

21 JUNE 200016

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 ofthe soft X-ray radiation at upper boundary of the chromosphere17

25/09/1997

Example of fitting 21-06-2000, 10:46:08 UT, A 02-05-1998, 05:12:46 UT, area A

Deposit in area A at 12:09:25 UT (25-09-1997)Contribution functionThe 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 theatmosphere.Contribution functionof the H line in F1 atm.

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

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