1. Nonthermal distributions in the solar and stellar coronae
J. Dudík 1,2, E. Dzifčáková 2,
M. Karlický 2, A. Kulinová 1,2
1 – DAPEM, Faculty of Mathematics, Physics and Informatics,
Comenius University, Slovakia
2 – Astronomical Institute, Academy of Sciences of the Czech Republic
Radiative (M)-HD Seminary, April 14th, 2011, Ondřejov

2. Outline I. The nonthermal distributions k–distributions
n–distributions
Why nonthermal distributions?
Definition and basic properties, the pseudotemperature
II. Radiative-loss function in solar and stelar coronae
Contributions from lines and continuum
Bremsstrahlung
Contribution from individual elements or ions
Consequences
III. The nonthermal continuum
Bremsstrahlung continuum in X-rays and radio
Free-bound continuum and flare diagnostics

3. k-distributions: definition
Owocki & Scudder (1983), Dzifčáková (2006a):
k   Maxwellian distribution

4. Fe Ionization equilibrium
Dzifčáková (2002): Changes in the Fe IX – XVI ionization equilibrium for the k-distributions with respect to Maxwellian one are significant:

5. k-distributions: why
Study the emission – need to know about the microphysics
Suprathermal component (“high-energy tail”) present during flares and also in solar wind
Maksimovic et al. (1997): solar wind velocity distribution is better approximated by one k-distribution than with one or sum of two Maxwellians
Collier (2004): if the mean particle energy is not held constant, the entropy is not maximalized by a Maxwellian, but by the k-distribution
Tsallis (1988), Leubner et al. (2002, 2005, 2008) – non-extensive theory
Dudík et al. (2009): considerable influence on the EUV filter responses
Dzifčáková & Kulinová (2010, 2011) - k-distribution diagnosed in transition region spectra (Si III line ratios) and in flares (Fe XII line ratios)
Their presence in AR corona is still an open question. Nevertheless...

6. Dzifčáková & Kulinová (2010)
Solar Phys., 263, 25

7. n-distributions: definition
Seely, Feldman & Doschek (1987), Dzifčáková & Tóthová (2007):
n = 1 Maxwellian distribution
Pseudo-temperature t :

8. n-distributions: why/when
Consistent with X-Ray spectra observed with flares
(Dzifčáková et al. 2008, A&A 488, 311; Kulinová et al., 2011, A&A, subm.)

9. The radiative losses II.
Emissivity eij of a spectral line line – transition from the level i to level j in a k-times ionized element x is given by:
FIP effect
Radiative losses ER:

12. Synthetic line spectra
Modification of CHIANTI, spectra for C,N,O,Ne,Mg,Al,Si,S,Ar,Ca,Fe,Ni

13. Nonthermal bremsstrahlung
For Maxwellian distribution:
For the k-distributions (Dudík et al., 2011, A&A, in press):

25. Atomic data errors

27. Bremsstrahlung spectrum
III.
Bremsstrahlung spectrum

28. Bremsstrahlung - spectrum

29. Freebound continuum

30. Freebound continuum

31. Conclusions
Conditions in solar corona allow for non-thermal distributions.
Their influence on the radiative losses is much higher than other effects
Total radiative losses are lower for k-distributions,
 lesser requirement for heating input
higher for n-distributions
 cooling processes for flares
Crucial for theoretical modeling of the solar corona and flares
Spectral synthesis for nonthermal distributions now complete
 new diagnostic possibility for flare spectra

32. Ďakujem za pozornosť