Diagnostics of non-thermal n-distribution Kulinová, A. AÚ AVČR, Ondřejov, ČR FMFI UK, Bratislava, SR

Diagnostics of non-thermal n-distribution Observed flux Ionization Level population Non-thermal n-distribution Distribution diagnostics using RESIK spectra Results

Observed flux (optically thin line) Line flux observed at a distance d from the Sun [ergs.cm -2.s -1 ]: G(T,N e ) is a line contribution function [ergs.cm 3.s -1 ]: N(X i m )/N(X m ) – relative population of an excited state i of an ion X m – it is a function of T and N e N(X m )/N(X) – relative population of an ion X m – it is a function of T N(X)/N(H) is an abundance of element X

Ionization and recombination - I 1. Photoionization vs. Radiative recombination (RR) Total number of radiative recombinations (RR) per unit volume and time: Summing over all levels i an j we can obtain total rate coefficient [cm 3 s -1 ]:

Ionization and recombination - II 2. Collisional ionization (CI) vs. 3-body recombination: Total number of collisional ionizations per unit volume and time: Summing over all levels i an j we can obtain total rate coefficient [cm 3 s -1 ]:

3. Excitation-autoionization (EA) vs. Dielectronic recombination (DR) Mechanism populating the energetic levels above the ionization threshold (so called doubly excited states): a) excitation by inelastic collision with a free electron – excitation of an electron from closed inner shell of an excited ion b) dielectronic capture – – the free electrons must have energy E = E j – E i – rate coeff. C DIELC is obtained from The doubly excited state can either autoionize or stabilize through radiative decay, producing a satellite line Ionization and recombination - III

Ionization and recombination - IV The total number of ionizations per unit volume and time resulting from EA process from X m to X m+1 The total number of dielectronic recombinations per unit volume and time is given by: Time evolution of the populations of each of n ionization stages of elemenent X:

Excitation of ions - I Statistical equilibrium (SE) for levels below the ionization threshold: These equation involve the most important excitation and de-excitation processes in the solar corona: C ij D – collisional de-excitation C ij E – collisional excitation A ij – excitation and de-excitation due to radiative decay Generally, calculations of the relative level population is coupled with relative ion population when we need to account for dielectronic recombination and autoionization.

Excitation of ions - II Population of levels above the ionization threshold The SE for levels of ion X m above the ionization threshold must take into account autoionization and excitation through DR. Since higher excited levels are usually less populated than the ground state, and the autoionization rates are large, these levels can be considered to be in coronal model approximation: C gi DIELC – diel. capture Simple way how to treat this calculation is to consider that the two processes on the LHS of the previous equation are completely independent from each other and they deal with ground levels of different target ions X g m and X g m+1 therefore we can separate the population of the level i of the X m in the sum of populations given by the each of the processes and calculate them separately: usually

Non-thermal n-distribution - I This kind of distribution occurs when a beam of accelerated electrons appears in plasma and is neutralized by the so called return current (Dzifcakova and Karlicky, 2008, SP, 250, 329). Both the electron beam and the return current modify the initial electron distribution function. The non-thermal n-distribution considered in our study describes the bulk of non-thermal plasma electrons but it does not include the effects of the high- energy tail.

Non-thermal n-distribution - II Changes the ionization and excitation equilibrium - all rates are sensitive to the electron distribution function - changes in the ratios of spectral line intensities The line fluxes are also sensitive on functional relation of particular cross sections on energy To diagnose the shape of the non-thermal distribution it is useful to pick up three (or more) spectral lines in different ionization stages and at least one of them ought to be the satellite line The ionization equilibrium for Fe using n-distribution has been computed by Dzifcakova (1998, SP 178, 317) and for C, N, O, Ne, Mg, Al, Si, S, Ar, Ca and Ni Dzifcakova ( ). The set of theoretical spectra has been calculated using a modified version of CHIANTI package and atomic database version 5.2

Bragg Crystal Spectrometer (BCS) and REntgenovsky Spektrometr s Izognutymi Kristalami (RESIK) These two instruments were bragg crystal spectrometers (bent crystals) which operated on satellite missions dedicated to observe the Sun. BCS operated on YOHKOH ( ) – viewed the whole Sun in X-rays – 4 bent crystals covered the selected wavelength ranges ( Å, Å, Å, Å) to observe resonance line complexes of H-like Fe XXVI and He-like Fe XXV, Ca XIX and S XV; resolving power  ~ RESIK operated on CORONAS-F ( ) - viewed the whole Sun in X- rays – 4 bent crystals covered the selected wavelength ranges ( Å, Å, Å, Å) to observe the emission lines of H-like, He- and Li-like ions of Ar, K, S, Si; resolving power  ~ 1000 We have applied the diagnostics of the n-distribution to RESIK data. We decided to use the lines of Si XIId, Si XIII and Si XIV which dominate the Å channel.

Diagnostics The best diagnostic are the ratios of satellite and allowed lines of ions of one element in different ionization stages. The satellite lines sample the electron distribution function at discrete energies while the intensities of the allowed lines depend on the integral of the product of the collisional cross sections with electron velocity over the distribution function from the excitation energy. The following lines from RESIK spectra from Channel 4 have been used: ion wavelength transition Si XIV 5.217, s 2 S 1/2 – 2p 2 P 1/2,3/2 Si XIII 5.681, s 2 1 S 0 – 1s 3p 1,3 P 1 Si XIId s 2 2p 2 P 1/2,3/2 – 1s 2p 3p 2 D 3/2,5/ s 2 2p 2 P 3/2 – 1s 2p 3p 2 D 3/2

Synthetic spectra A grid of synthetic spectra (5 - 6 Å) has been calculated using ‘the non- thermal’ modification of CHIANTI package (Dzifčáková, 2006): isothermal approximation - log  = 6.7 – 7.3 with step 0.02 constant n e = cm -3 column EM = cm -5, FWHM=20.0 mÅ the ionization equilibrium for n-distributions was calculated by Dzifčáková (2005). 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.

RESIK spectra – all chanels Before the analysis of the spectra the linear approximation of continuum has been subtracted. 7 - Jan , class M4.9 – 'mounds' 21- Jan , class C8.1 – Level2 data

7 – Jan – 2003: 23:25 – 23:33 – 23:40 UT, M4.9, S14E81 – diagnostics of n

GOES-08 light curve and radio data Jan 7th, 2003: 23:25 – 23:33 – 23:40 UT, M4.9, S14E81 Observed type III: 23:31 – 23:32 UT n = 11 and log(  )=7.296 K 23:31 UT time int. of observed spectra: 23:20 – 00:35 UT

21 – Jan – 2003: 02:23 – 02:28 – 02:33 UT, C8.1, N14E09 - diagnostics of n

GOES-08 light curve and radio flux Jan, 21th, 2003: 02:23 – 02:28 – 02:33 UT, C8.1, N14E09 Observed type III: 02:24 – 02:29 UT n = 11 and log(  )=7.267 K 02:26 UT time int. of observed spectra: 02:24 – 02:34 UT

4 – Oct – 2002: 05:34 – 05:38 – 05:41 UT, M4.0, S19W09 - diagnostics of n

4 – Oct – 2002: 05:34 – 05:38 – 05:41 UT, M4.0, S19W09 GOES 08 RHESSI Radio Flux time int. of observed spectra: 05:30 – 05:54 UT

6 – Feb – 2003: 02:07 – 02:12 – 02:14 UT, C3.4, S16E55 - diagnostics of n

6 – Feb – 2003: 02:07 – 02:12 – 02:14 UT, C3.4, S16E55 time int. of observed spectra: 02:06 – 02:34 UT

Results We have tried to diagnose the shape of non-thermal n-distribution The diagnostics using allowed and satellite transitions is effective tool but it needs reliable observations It is possible to probe the non-thermality of the free electron distribution in flaring plasma but the estimated errors of measurements are about 30%-50%! the non-thermality correlates well with radio emission

Thank you for attention :o)

Ionization and recombination - I For ionization and recombination processes we consider: 1. Photoionization vs. Radiative recombination 2. Collisional ionization vs. 3-body recombination 3. Excitation-autoionization vs. Dielectronic recombination

Time evolution of parameter ‘n’ and log(  ): 7 – Jan – 2003: 23:25 – 23:33 – 23:40 UT, M4.9, S14E81 – diagnostics of  The parameter 'n' of the n-distribution reaches value of 11 about 23:31 UT and 23:36 UT and reaches log(  )=7.296 K and log(  )=7.264 K, respectively.

21 – Jan – 2003: 02:23 – 02:28 – 02:33 UT, C8.1, N14E09 – diagnostics of  Time evolution of parameter ‘n’ and log(  ): The parameter 'n' of the n-distribution reaches value of 11 and log(  )=7.267 K about 02:26 UT.