Soft X-ray Heating of the Chromosphere during Solar Flares

1. Soft X-ray heating of the chromosphere during solar flares A. Berlicki1,2 1Astronomický ústav AV ČR, v.v.i., Ondřejov2Astronomical 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. LC, Wrocław, H Stellar chromospheres can also be strongly illuminated by the soft X-rays 2

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 (?) usuallyincluded incodes

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: ,where: - rate of photoionization of i-th element - energy of photoelectron, with ibeing 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

7. The intensity I of the soft X-ray radiation is calculated from the transfer equation. PP atmosphere: (no source function – T<104 K) NH – totalhydrogendensity,  - cosineof theangle 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 – photoionizationcross-section T – Thomson scatteringcross-section t – total cross section (Brown & Gould 1970)

8. 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:

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: Dloop Dchro << Dloop X-ray loop Heatedarea Dchro Chromosphere IfDchro << Dloop , then we canassume 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. at the top of the atmosphere Thesimplecase: An isothermalX-raysource of giventemperature T and emissionmeasure EM. Power at: where(,T)istheemissivity of opticallythinplasma. For theplane-parallelatmospheretheemergent SXR intensity: = const for given X-ray source and with Theemissivity(,T) of the hot plasmamay be takenfromdifferentpreviouscalculations, e.g. Raymond & Smith (1977), ormay be calculatedusingSolarSoftproceduresbased 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 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)

15. Emissivity of opticallythinplasma[erg cm-3 s-1Å-1] calculated for temperatures T=2 and 10 MK (mewe_spec.pro)  [erg cm3 s-1Å-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]

16. An example of thedistribution of intensity of soft X-rayradiationattheupperboundary of thechromosphere. (plane-parallel, isothermalsource). I0 [erg s-1 cm-2Å-1] X-RAY SOURCE PARAMETER: T=8 MK, EM=11048 cm-3, A=21018 cm2  [Å] 7

17. Comparison of thedeposited energy of the soft X-rayradiation inthe model atmosphere VAL3C (Vernazza et al. 1981). dE(mcol)/dt [erg s-1cm-3] VAL3C X-RAY SOURCE: T=8 MK, EM=11048 cm-3, A=21018 cm2 Blueline– emissivityfrom Raymond & Smith.(1977) Red line– emissivityfromMewe et al. (1985, 1986) mewe_spec.pro mcol [g cm-2]

18. Example of analysis

19. Method SOFT X-RAY OBSERVATIONS (SXT, XRT) OPTICAL OBSERVATIONS (MSDP) INPUT PARAMETERS OF THE MODEL non-LTE CODE MODEL SYNTHETIC H LINE PROFILE PARAMETERS OF SOFT X-RAY SOURCES 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 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

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 cm3 s-1Å-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 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 8

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. Theflaresusedintheanalysis One of the most importantthing for thisanalysis was to havesimultaneous optical and X-rayobservations of theflares. 10

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. The energy deposit dE(h)/dt and the NRCR (h) Assuming a steady-state, the net radiative coolingratesmust 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)

31. Conclusions a) Duringthegradualphase for allanalyzedflares and for allareas thevalues of radiativelossesare much largerthanthevalues of the energy deposited by soft X-rayradiation. b) The energy provided to thechromosphere by soft X-rayradiation is NOT sufficient to explaintheprolongedHchromospheric emissionoftenobservedduringthelatephase of many flares. c) Therearesignificantdifferencesinheightinthechromosphere betweenthelayerswherethecore of Hline profile isformed and thelayerswheredeposited energy reachthemaximum. In such a casetheintensities of central parts of Hlineprofilesshould not be closerelatedwiththerates of deposited energy. d) Effect of enhancedcoronalpressure, related to thechromospheric evaporation, or thermal conductionmay be responsible for the enhancedchromosphericemissioninthelatephases of flares. Future: 2D modeling and both SXR and n-th e-duringtheimpulsivephase 24

32. THE END