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Diagnostics of Non-thermal Electron Distribution using synthetic and flare spectra

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### Diagnostics of Non-thermal Electron Distributionusing synthetic and flare spectra

Elena Dzifčáková, Alena Kulinová

Department of Astronomy, Physics of the Earth and Meteorology

FMPhI Comenius University, Bratislava

Motivation

The observed X-ray spectra of the impulsive phase of the solar flare often can not be explained by using the assumption of the electron Maxwell\'s distribution. The unusual spectral line ratios indicate the presence of a non-thermal electron distribution.

We want to diagnose the shape of the electron distribution function from the observed spectra. The satellite lines and allowed lines belonging to ions in different degree of ionization seem to be suitable for such a kind of diagnostics.

The non-thermal diagnostics has been applied on the RESIK X-ray spectra of the impulsive phase of the solar flares.

The non-thermal electron distributions with higher and narrower peak than Maxwell’s distribution can be observed when energy is deposited into tail of distribution with rate that is sufficiently high to overcome the equilibrium process.

We assumed that non-thermal distribution is of a kind of Power distribution.

Thefree electrons have a power distribution with parameters n and T:

The mean energy of the power distribution is .

The pseudo-temperature t is the temperature of a Maxwell’s distribution with the mean energy that is equal to the mean energy of the power distribution, i.e. .

1/2

Introduction - Power distribution

Figure 1.The power distributions for different values of n as a function of E/kT (a) and E/k = 3E/(n+2)kT (b). The Maxwell distribution has n = 1. The mean energy of the particles is the same for all distributions in Figure 1b.

Introduction - II

The non-thermal electron distributions change the ionization and excitation equilibrium. This leads to the changes in the ratios of the spectral line intensities and allows us to diagnose the shape of electron distribution.

The ionization equilibrium for power distributions was calculated by Dzifčáková (2005).

Synthetic spectra have been calculated using special modification of CHIANTI packagewhich allows us to compute spectra for electron non-thermal distributions(Dzifčáková, 2006). New software and extended database allows computation of the excitation equilibrium for non-thermal distributions and involves computation of satellite line intensities. This modification will be included in new version of CHIANTI.

CHIANTI is a collaborative project involving the NRL (USA), RAL (UK), MSSL (UK), the Universities of Florence (Italy) and Cambridge (UK), and George Mason University (USA). The software is distributed as a part of SolarSoft.

Diagnostics

In general, the spectral lines used for diagnostics should have:

- sufficient line intensities to be measured
- the changes in their intensities due to the changes in the distribution shape should be larger than the errors in the determination of their intensities.

Three lines of Si ions from the forth RESIK spectral channel (5 - 6 Å) seemed to be suitable for diagnostics:

5.2168 Å Si XIV 1s 2S1/2 - 3p 2P3/2

5.6807 Å Si XIII 1s2 1S0 - 1s 3p 1P1

5.8162 Å Si XII d 1s2 2p 2P3/2 - 1s 2p (3P) 3p 2D5/2

All lines are blended. The intensities of blends has been added to the intensities of the strongest lines.

Diagnostics - calculations

Synthetic spectra in the region of 5 - 6 Å have been calculated using ‘the non-thermal’ modification of CHIANTI package (Dzifčáková, 2006).

The spectra has been calculated using:

- isothermal approximation for constant t (logt = 6.7 - 7.3, with the step 0.02),
- constant ne = 1010 cm-3,
- RESIK abundnces (courtesy of C. Chifor, DAMTP, Cambridge, UK),
- column EM = 1022 cm-5,
- FWHM=15.7, 20.0, 24.0 mÅ.

The line ratio does not depend on electron density for the lines we have used for diagnostics.

Diagnostics of n and the mean energy of the power distribution

The parameter ncan be determined from the line ratios,

Si XIV (5.217)/Si XIII (5.681) vs Si XIII (5.681) /Si XIId (5.816)

For known parameter nit is possibleto determine from the dependence of one line ratio on log

Data

- RESIK datawere provided by Dr. Barbara Sylwester and Dr. Janusz Sylwester from Space Research Center of Polish Academy of Sciences, Wroclaw
- The data included absolute X-ray spectra from all four RESIK channels: 3.40-3.80 Å, 3.83-4.27 Å, 4.35-4.86 Å, 5.00-6.05 Å and covered the M4.9 solar flare on Jan 7, 2003, AR 10 251, S14E81, 23:25 – 23:33 – 23:40 UT.
- For non-thermal analysis we have used 88 spectra from the fourth channel where Si XII d - Si XIV lines dominate.
- Spectra have been time averaged by minutes using their exposure start times.

RHESSI light curves

- Green arrows indicate flare (GOES):

beginning 23:25UT

maximum 23:33UT

end 23:40UT

- The Blue line indicates the time of type III radio pulses: 23:31-23:33 UT
- The peak of the high-energynon-thermal emission 23:32 UT

25 – 50 keV

Courtesy of C. Chifor, DAMTP, Cambridge, UK

EIT image with RHESSI contours in two energy bands :

6 – 12 keV

and

25 – 50 keV

Courtesy of C. Chifor

DAMTP, Cambridge, UK

Before theanalysis of the spectra the linear approximation of continuum has been subtracted.

There appeared strange “mounds” in the spectra.

We have supposed they are due to any artificial effect.

We have approximated them by Gaussians.

Finally, their fits have been removed from the spectra.

Results – FWHM = 20 mÅ

flare: 23:25 – 23:33 – 23:40 UTradio pulses:23:31-23:33 UT

0 – pre-flare n ~ 1

1 – 23:26 UT n ~1

2 – 23:28 UT n ~ 5

3 – 23:29 UT n ~ 5

4 – 23:30 UT n ~ 7

5 – 23:31 UT n ~ 11

6 – 23:36 UT n ~??

7 – 23:40 UT n ~ 7

8 – 23:41 UT n ~ 5

9 – 23:42 UT n ~ 3

10 – 00:21 UT n ~ 1

11 – 15 n ~ 1

Maxwellian

5

4

6

Time evolution of parameter n and pseudo-temperature t:

parameter n

kt=(n+2)kT/3

The parameter n of the power distribution reaches value of 11 during the rising phase of the flare and is about 2 x 107 K.

Observed spectra vs synthetic spectra 23:28 UT

n =5 , log t = 7.122, EM = 6.6 x 1020 cm-5FWHM = 20 mÅ

Observed spectra vs synthetic spectra 23:28 UT

Si XIII

Si XII d

Si XIII

Si XIV

Si XII d

Courtesy of C. Chifor, DAMTP, Cambridge, UK

Observed spectra vs synthetic spectra 23:28 UT

n = 1 , log t = 7.007, EM = 9.8 x 1020 cm-5FWHM = 20 mÅ

Observed spectra vs synthetic spectra 23:30 UT

n =7 , log t = 7.212, EM = 3.8 x 1021 cm-5 FWHM = 20 mÅ

Observed spectra vs synthetic spectra 23:30 UT

n = 1 , log t = 7.092, EM = 4.7 x 1021 cm-5FWHM = 20 mÅ

Observed spectra vs synthetic spectra 23:36 UT

Si XII d

n =11 , log t = 7.270, EM = 2.8 x 1021 cm-5 FWHM = 20 mÅ

Observed spectra vs synthetic spectra 23:36 UT

Si XIII

Si XIV

Si XII d

Si XIII

Si XII d

Courtesy of C. Chifor, DAMTP, Cambridge, UK

Observed spectra vs synthetic spectra 23:36 UT

Si XII d

n = 1 , log t = 7.087, EM = 3.8 x 1021 cm-5FWHM = 20 mÅ

Results - logT and logt

- Squares – T derived from the line EM loci analysis
- Circles – Tmax corresponding to the maximum for the DEM curves
- Solid curve – T calculated from the ratio of 2 GOES channels assuming isothermal plasma
- Triangles – T derived from the slope of RHESSI continua
- Diamonds – t derived from non-thermal analysis

Courtesy of C. Chifor, DAMTP, Cambridge, UK

Results

- The non-thermal analysis of X-ray spectra observed by RESIK during the analysed flare indicated the presence of non-thermal distribution of free electrons.
- The plasma seems to be non-thermal during the impulsive phase of the flare but the highest deviation form Maxwell distribution is found about the maximum of the flare – type III radio bursts, RHESSI 25 – 50 keV non-thermal emission.
- It was possible to reproduce flare spectra with sufficient accuracy by non-thermal (power) distribution with particular parameters n and t. We could model at the same time rather high intensity of Si XIV and Si XIII lines together with strong intensities of satellite lines. This is not possible in the case of Maxwell distribution.
- The comparison of thermal and non-thermal analysis has shown a good agreement between the thermal temperatures derived by different methods (DAMTP, UK) and its equivalent, the pseudo-temperature t, derived from non-thermal analysis.

Conclusions

- It is possible to probe the non-thermality of the free electron distribution in flaring plasma. The estimated errors of measurements are about 30%.
- There are several other sources of inaccuracyaffecting the results:
- separation of continuum – at present we are not able to calculate the continuum under the assumption of the power distribution of free electrons
- mounds ???
- including blends into the intensities of spectral lines – e.g. in the vicinity of Si XIII 5.681 Ålinethere are more than 20 Si XII d satellite lines and importance of these satellites increases with an increase of n
- natural inhomogenity of plasma parameters in flaring plasma

Acknowledgement

This work has been supported by the Scientific Grant Agency VEGA, Slovakia, grant No.1/2026/05. We are very thankful for the open data policy of RESIK, RHESSI and GOES. CHIANTI is a collaborative project involving project involving the Naval Research Observatory and George Mason University (U.S.A.), the Rutherford Appleton Laboratory, the Mullard Space Science Laboratory and University of Cambridge (U.K.) and the University of Florence (Italy). CC is grateful for scholarship support received from the University of Cambridge Overseas Trust, an Isaac Newton Studentship from the Cambridge Institute of Astronomy and an Overseas Research Student Award. GDZ thanks PPARC for its support DAMTP for its hospitality. HEM acknowledges the support of PPARC. BS and JS acknowledge support from the Polish Ministry of Science grant 1.P03D.017.29.

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