The Influence of the Return Current and the Electron Beam on the X-Ray Flare Spectra Elena Dzifčáková, Marian Karlický Astronomical Institute of the Academy of Sciences of the Czech Republic Ondrejov, Czech Republic Motivation The electron beams accelerated during a flare in the corona create return currents in lower layers of the solar atmosphere. The electron beam and the return current affect the electron distribution function in the corona and thus the intensities of the spectral lines. How does the return current influence the intensities of the spectral lines in EUV and X-ray region? Is it possible to separate the effect of the return current on a spectrum from the effect of electron beams and to diagnose it? In the previous study we have considered a very simple model to know what kind of the results we can await. Now we have used better model with the more realistic electron distribution.Assumptions Initial state: particles have Maxwellian distributions with temperatures T and interact with the mono-energetic electron beam with velocity of 1.0  cm.s -1 (electron energy 28.4 keV). The electron beam produces the return current and interacts with the plasma through plasma waves. This modifies the electron distribution in the coordinate system of protons and ions (Fig. 1). The influence of the Coulomb thermalization on plasma distribution is neglected. The electron beam is present for a sufficiently long time to achieve the ionization and excitation equilibrium. The effect of possible pressure imbalance and subsequent plasma motions is ignored. Fig. 1: The interaction of the electron beam with plasma and formation of the return current in the 3D electromagnetic PIC model. The initial temperature of the plasma is T 0 =2x10 6 K and the ratio of the electron beam density to plasma density is n B :n e =1:10. The resulting electron distribution (d) consists relaxed beam, plasma bulk which is shifted to negative velocity (one part of the return current) and the tail with high negative velocities (second part of the return current). The Electron Energy Distribution Function The main effect on the shape of the model energy distribution has the ratio of the density of the electron beam to plasma density. The initial temperature has only a little effect on the distribution shape (Fig. 2). The high energy tail of the distribution is formed by the electron beam and high energy electrons of the return current. Fig. 2. The shape of the electron energy distribution function for three different initial conditions: black line: T 0 =2x10 6 K, n B :n e =1:10, full red line: T 0 =1x10 6 K, n B :n e =1:10, full green line: T 0 =2x10 6 K, n B :n e =1:20, dashed green line: the Maxwellian disitribution with T=2x10 6 K, dashed red line: the Maxwellian electron distribution with T=1x10 6 K. Abstract: The electron beams and the return current affect the electron distibution function in plasma during solar flares. A new model of the distribution function including the return current and electron beam is supposed and its influence on X-ray spectra has been computed. The comparison with the simple model of the return current is presented. Ionization equilibrium The approximations of the ionization and autoionization cross sections (C, N, O, Ne, Mg, Al, Si, S, Ar, Ca, Fe and Ni) have been taken from Arnaud and Rothenflug, 1985, A&ASS 60, 425. The cross sections have been integrated over the non-thermal distribution function to get the ionization rates. The recombination rates for the non-thermal distribution have been computed by using the approximation technique described in Dzifcakova, 1992, SP 140, 247. Contribution of the high energy tail of the distribution function to the ionization rate can be very important. The ionization state can correspond to the much higher temperature than the initial temperature of the plasma is. The changes in the ionization equilibrium of silicon are in Fig. 3. The magnitude of the changes depends on the ratio of the density of the electron beam to plasma electron density. The initial temperature influences the ionization equilibrium only a little. Fig. 3. The changes in the ionization equilibrium due to the return current and the electron beam for three different initial conditions: Full red line: T 0 =1x10 6 K, n B :n e =1:10, full green line: T 0 =2x10 6 K, n B :n e =1:10, full blue line: T 0 =2x10 6 K, n B :n e =1:20, dashed red line: Maxwellian distribution with T=1x10 6 K, dashed green line: Maxwellian distribution with T=2x10 6 K, full black lines: Maxwellian distribution with T=7.94x10 6 K and with T=1.26x10 7 K. Excitation equilibrium The original modification of CHIANTI* software and database has been used for computation of the synthetic spectra. The software and extended database now allows the computation of the excitation equilibrium and synthetic spectra under the assumption of non-thermal distributions and involves computation of satellite line intensities. X-Ray Spectrum We have computed Si X-ray spectrum in region Å. This part of the spectrum has been observed by RESIK during solar flares and we are able to compare our results with observations. not influenced the ratio of the density of the electron beam to the initial plasma density The effect of the initial conditions (T 0, n B :n e ) on the computed spectra is different. The character of the spectrum is not influenced by the initial temperature of plasma in the corona. It is determined by the ratio of the density of the electron beam to the initial plasma density (Fig. 4). * 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.

Fig. 4. The X-ray spectra for the T 0 =1x10 6 K with n B :n e =1:10 (left above), T 0 =2x10 6 K with n B :n e =1:10 (right above), T 0 =2x10 6 K, n B :n e =1:20 (left below) and for the Maxwellian distribution with T=1.29x10 7 K (right below). The comparison of the modelled spectra with the spectrum for the Maxwellian distribution shows that: the intensities of the Si XIII lines (5.28 Å, 5.40 Å) are higher for modelled distribution than for the Maxwellian distribution; the intensities of the Si XIId satellite lines (5.82 Å, 5.56 Å) are lower. Comparison with the simple model and observations The simple model simulated the electron beam as a mono- energetic beam and the return current was formed by all plasma electrons with the same drift velocity. The electron plasma distribution together with the mono-energetic beam is in Fig. 6, (thick black lines). The comparison of the computed spectra for the both models with observations is in Fig. 5. The synthetic spectra for both new and older model show the enhanced intensities of Si XIII lines (5.28 Å, 5.40 Å) in comparison with Maxwellian spectra. This is in agreement with observation (Kepa et al., 2006). The observations also show the enhanced intensity of the sallite lines (5.56 Å, 5.82 Å). This enhancement has been shown also for modelled spectra of in simple model. Presented new spectra show opposite effect. Fig. 6. The comparison of electron distribution functions for the presented and previous model. Green line: T 0 =2x10 6 K, n B :n e =1:10, red line T 0 =1x10 6 K, n B :n e =1:10, blue line T 0 =2x10 6 K, n B :n e =1:20, dashed green line: Maxwell, T 0 =2x10 6 K, dashed red line: Maxwell, T 0 =1x10 6 K, black line: simple model, distribution plus mono-energetic beam, T 0 =2x10 6 K, thin black lines: excitation energy of Si XIId 5.82 Å and Si XIII 5.68 Å. The gradient of the electron distribution is steeper if the drift velocity in plasma bulk is higher: T 0 n B :n e RC T RC B 1x10 6 K 1:1031%69% 2x10 6 K 1:1025%75% 2x10 6 K 1:2023%77% The most suitable conditions to get the similar distribution shape as in the simple model are for higher T 0 and lower n B :n e.Conclusions The electron beam together with the non-thermal electron distribution changes relative abundances of ions and intensities of the spectral lines. The changes in the shape of the electron distribution function in solar corona depends on the initial temperature and the ratio of the density of the electron beam to the background plasma density. The presence of the electron beam (or a distribution with enhanced number of particles in high energy tail) is able to change the ratio of the intensities of allowed spectral lines. The high energy tail of distribution does not influence the intensities of satellite lines. The presence of the return current in the solar corona affects the intensities of the satellite lines by different way what gives possibility to diagnose it. Fig. 5. The comparison of the X-ray spectra for the presented model (left, above), the previous simple model (right,above) with spectrum observed by RESIK during solar flare January 7, Why we got different results? The Fig. 6 shows electron distributions for both models. The excitation energy of the satellite line Si XIId 5.82 Å and excitation energy of the allowed line Si XIII 5.68 Å are marked there. We know that: the intensities of the satellite lines depend on the number of particles with the energy of the transition; the intensities of the allowed lines are integrals of the product of the cross section with the velocity over a distribution from the excitation energy. We need larger gradient of the distribution function, similar to gradient of the electron distribution in simple model, to have higher intensities of the satellite lines in our new model. The explanation of different results: there is different gradient of distributions in the presented and simple model for the energy range x10 3 eV. Therefore, we need to set the parameters (T 0, n B :n e ) of our model to get the agreement with the observations. simple model: all electrons have a same drift velocity; presented model: only a part of electrons have drift velocity to carry the return current in plasma bulk (RC B ) and the second part of electrons carries the return current in the high energy tail of the distribution (RC T ). The wave interaction between the electron beam and ambient plasma heats plasma and decreases the gradient of the distribution.