Talk presented by Jaroslav Dudík et al. at the symposium From Atoms to Stars:the impact of Spectroscopy on Astrophysics, 26th-28th July 2011, Oxford, UK

1. Impact of nonthermal tails
and nonthermal distributions
on flare plasma diagnostics
Jaroslav Dudík 1,2, Elena Dzifčáková 2, Michal Homola 1,
Marian Karlický 2, Alena Kulinová 1,2, Jana Kašparová 2
1 – DAPEM, Faculty of Mathematics, Physics and Informatics,
Comenius University, Bratislava, Slovakia
2 - Astronomical Institute of the Academy of Sciences
Ondřejov, Czech Republic
„From Atoms to Stars: The Impact of Spectroscopy on Astrophysics“,
Celebrating the Career of Prof. Carole Jordan, Oxford, UK, July 27, 2011

2. Outline
I. The power-law distributions (nonthermal tails)
Motivation: RHESSI flare observations
II. The n-distributions
Definition and properties Seely et al. (1987)
Diagnostics from observations Dzifčáková et al. (2008)
Kulinová et al. (2011)
Physical background Karlický et al. (2011), in prep.
The nonthermal continuum Dudík et al. (2011), in prep.
III. The composed np-distributions Dzifčáková et al. (2011)
Construction: „know how“
Effect on ionization equilibrium and line intensities
Flare plasma diagnostics

3. I. The nonthermal tails
Veronig et al. (2010), ApJ 719, 655

4. The nonthermal tails
Gabriel & Phillips (1979),
MNRAS 189, 319:
Effect on the Fe XXIVd / Fe XXV
satellite/allowed line ratios
- excess excitation of the Fe XXV line
- decrease of the ratio by up to 40%
However, an increase is observed
(even with respect to Maxwellian):
Seely, Feldman & Doschek (1987),
ApJ, 319, 541

5. II. The n-distributions
n1
2ε1/2  ε  2
fn (ε)dε  Bn 3/2   eε/kBT dε
  kBT   kBT 
Peak narrower than Maxwellian
Very few low-energy electrons
Pseudo-temperature t :
3 n 
E  kt    1  kT
2 2 
Seely, Feldman & Doschek (1987),
ApJ 319, 541
Dzifčáková (1998), SoPh 187, 317

6. The n-distributions
Changes in ionization and excitation equilibrium – line intensities
Contribution functions - narrower and shifted to different t
Dzifčáková & Tóthová (2007), SoPh 240, 211; Dudík et al. (2011), AA 529, A103

7. Diagnostics from observations
Dzifčáková et al. (2008), AA 488, 311
Kulinová et al. (2011), AA, accepted

8. Observed spectra - RESIK

9. Diagnostics - results

10. Theoretical f-b continuum
Dudík et al. (2011), in prep.

11. Physical background - drifts
Karlický, Dzifčáková & Dudík (2011), in prep.:
„Moving Maxwell“ (Maxwellian with a drift velocity v0)
can be written as
With the f(E,v0) having the same gradient as the n-distribution.

12. Physical background - drifts

13. Diagnostics - RHESSI
Kulinová et al. (2011), AA, accepted

14. Diagnostics - RHESSI

15. III. The composed np-distributions
Dzifčáková, Homola & Dudík (2011), AA 531, A111:
Composed np-distribution: Bulk (n) + Tail (p)
n – index n describing the bulk
p – power-law index of the high-energy tail
EC – low-energy cutoff for the power-law tail
a/b – bulk/tail ratio, a + b = 1

16. Construction of the distribution
Conditions for EC :
- the power-law tail does not affect the plasma bulk
- less than 10% discontinuity at EC

17. Construction of the distribution

19. Ionization equilibrium – tail only

20. Ionization equilibrium – bulk + tail

21. Si XIId, XIII, XIV flare spectra

22. Conclusions
 High-energy tail can change the ionization equilibrium
Changes the temperature diagnostics from ratios of allowed lines
 Nonthermal bulk necessary to explain the Si XIId / Si XIII ratios
- has a physical explanation – drift velocities (return current)
- can also be diagnosed from RHESSI at < 6 keV
Composed distributions offer simple parametrization
of the true electron energy distributions in flares
Easy calculation of spectra using modified CHIANTI

23. Thank you for your attention