1. Soft X-ray heating of the chromosphere during solar flares A. Berlicki 1,2 1 Astronomický ústav AV ČR, v.v.i., Ondřejov 2 Astronomical Institute, University of Wrocław, Poland Ondřejov, June 11, 2009

2. 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. 2 LC, Wrocław, H  Stellar chromospheres can also be strongly illuminated by the soft X-rays

3. 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

4. X-ray sources

5. 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

6. 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

7. The intensity I of the soft X-ray radiation is calculated from the transfer equation. PP atmosphere: - total photoionization cross-section, depends on z N H – total hydrogen density,  - cosine of the angle between the direction of photon propagation and the vertical z  i - ionization cross-section (Brown & Gould 1970)  H – hydrogen ionization cross-section x = n H+ /N H N H = n H+ + n H O  ph – photoionization cross-section  T – Thomson scattering cross-section  t – total cross section (Brown & Gould 1970) (no source function – T<10 4 K)

8. The formal solution of the transfer equation: I O (  ) – the intensity of SXR at the top of the atmosphere (Z O ). After introducing the column mass - mean molecular weight (= const in the whole atmosph.) and effective ionization cross-section in the form: Z ZOZO we can write: I O (  )

9. 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 ?

10. The geometry of irradiation: D loop D chro D chro << D loop X-ray loop Chromosphere Heated area If D chro << D loop, then we can assume to be isotropic.

11. 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:

12. 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 [ ]

13. 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 atmosphere 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.

14. 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 T A 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)

15. Emissivity of optically thin plasma [erg cm -3 s -1 Å -1 ] calculated for temperatures T=2 and 10 MK (mewe_spec.pro) T = 2 MK T = 10 MK [Å]  [erg cm 3 s -1 Å -1 ] 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

16. An example of the distribution of intensity of soft X-ray radiation at the upper boundary of the chromosphere. (plane-parallel, isothermal source). [ Å ] I 0 [erg s -1 cm -2 Å -1 ] X-RAY SOURCE PARAMETER: T=8 MK, EM=1  10 48 cm -3, A=2  10 18 cm 2 7

17. Comparison of the deposited energy of the soft X-ray radiation in the model atmosphere VAL3C (Vernazza et al. 1981). dE(m col )/dt [erg s -1 cm -3 ] Blue line – emissivity from Raymond & Smith.(1977) Red line – emissivity from Mewe et al. (1985, 1986) mewe_spec.pro m col [g cm -2 ] X-RAY SOURCE: T=8 MK, EM=1  10 48 cm -3, A=2  10 18 cm 2 VAL3C

18. Example of analysis

19. OPTICAL OBSERVATIONS (MSDP) SOFT X-RAY OBSERVATIONS (SXT, XRT) non-LTE CODE INPUT PARAMETERS OF THE MODEL MODEL SYNTHETIC H  LINE PROFILE OBSERVATIONAL H  LINE PROFILE FITING THE PROFILES TO OBTAIN THE MODEL MODEL M i PARAMETERS OF SOFT X-RAY SOURCES CALCULATIONS OF THE AMOUNT OF THE SOFT X-RAY RADIATION DEPOSITED IN MODEL (M i ) OF THE CHROMOSPHERE HEIGHT DISTRIBUTION OF THE ENERGY DEPOSITED BY SOFT X-RAY RADIATION IN M i MODEL OF THE CHROMOSPHERE HEIGHT DISTRIBUTION OF THE NET RADIATIVE COOLING RATES IN M i CHROMOSPHERIC MODEL COMPARISON OF BOTH DISTRIBUTIONS CONCLUSIONS GRID OF MODELS Method NRCR line transitions

20. 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. 4

21. 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 cm 3 s -1 Å -1 ) dependent on plasma temperature and on the wavelength (calculated with mewe_spec.pro) 6

22. b) construction of the grid of chromospheric models made by modyfication of semiempirical models VAL-C and F1-MAVN (parameters  T and m O ) - to obtain the theoretical profiles of hydrogen H  line - NLTE codes (P. Heinzel) - in total 206 different models and profiles Parameters m O and  T used for modyfication of semiempirical chromospheric models VAL - C and F1- MAVN. Convolution of all synthetic profiles with the Gauss function to make them comparable to the observed profiles. 8 Fitting procedure

23. 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

24. The flares used in the analysis One of the most important thing for this analysis was to have simultaneous optical and X-ray observations of the flares. 10 DateActive region (NOAA) Approximate coordinates GOES class Time of the flare [UT] 25 – 09 – 19978088S27 E02 (-50, -560)C 7.211:40 – 14:00 21 – 06 – 20009046N20 W05 (+100, +280)C 4.510:10 – 11:00

25. 25 SEPTEMBER 1997 11

26. 21 JUNE 2000 16

27. 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

28. 25/09/1997

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

30. Deposit in area A at 12:09:25 UT (25-09-1997) Contribution function 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.

31. 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

32. THE END