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Ionisation Equilibrium for the Non-Maxwellian Electron \(n\)-Distributions in Solar Flares: Updated Calculations

  • Solar and Stellar Flares
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An Erratum to this article was published on 25 January 2016

Abstract

We use the latest available atomic data to calculate the ionisation and recombination rates for the non-Maxwellian \(n\)-distributions, which were shown previously to provide a good fit to the enhanced intensities of dielectronic satellite lines during solar flares. The ionisation and recombination coefficients are subsequently used to derive the ionisation equilibrium. To do so, we consider odd values of \(n\) ranging from 1 to 19, i.e., from Maxwellian to strongly non-Maxwellian cases. These calculations involve all elements with proton number up to 30, i.e., H to Zn. The \(n\)-distributions modify both the ionisation and the recombination rates. The ionisation rates decrease more steeply at lower pseudo-temperatures, while the radiative recombination rate is reduced due to a lower number of low-energy electrons. The peaks of the dielectronic recombination rates become narrower. These changes are reflected in the ionisation equilibrium. Ion abundance peaks become narrower and can also be shifted, mostly towards higher temperatures. The He-like ions are an important exception, as they are formed in a larger temperature range than that for the Maxwellian distribution. The ions Si xiii – xiv used previously for the diagnostics of the \(n\)-distributions are affected only weakly, confirming the determination of \(n\). The ionisation equilibria are available as the electronic supplementary material in a format compatible with the CHIANTI database.

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References

  • Abdel-Naby, S.A., Nikolić, D., Gorczyca, T.W., Korista, K.T., Badnell, N.R.: 2012, Dielectronic recombination data for dynamic finite-density plasmas. XIV. The aluminum isoelectronic sequence. Astron. Astrophys. 537, A40. DOI . ADS .

    Article  ADS  Google Scholar 

  • Altun, Z., Yumak, A., Badnell, N.R., Colgan, J., Pindzola, M.S.: 2005, Erratum: Dielectronic recombination data for dynamic finite-density plasmas. VI. The boron isoelectronic sequence. Astron. Astrophys. 433, 395. DOI . ADS .

    Article  ADS  Google Scholar 

  • Altun, Z., Yumak, A., Badnell, N.R., Loch, S.D., Pindzola, M.S.: 2006, Dielectronic recombination data for dynamic finite-density plasmas. XI. The sodium isoelectronic sequence. Astron. Astrophys. 447, 1165. DOI . ADS .

    Article  ADS  Google Scholar 

  • Altun, Z., Yumak, A., Yavuz, I., Badnell, N.R., Loch, S.D., Pindzola, M.S.: 2007, Dielectronic recombination data for dynamic finite-density plasmas. XIII. The magnesium isoelectronic sequence. Astron. Astrophys. 474, 1051. DOI . ADS .

    Article  ADS  Google Scholar 

  • Asai, A., Nakajima, H., Shimojo, M., Yokoyama, T., Masuda, S., Krucker, S.: 2009, Imaging spectroscopy on preflare coronal nonthermal sources associated with the 2002 July 23 flare. Astrophys. J. 695, 1623. DOI . ADS .

    Article  ADS  Google Scholar 

  • Badnell, N.R.: 2006, Dielectronic recombination data for dynamic finite-density plasmas. X. The hydrogen isoelectronic sequence. Astron. Astrophys. 447, 389. DOI . ADS .

    Article  ADS  Google Scholar 

  • Badnell, N.R., O’Mullane, M.G., Summers, H.P., Altun, Z., Bautista, M.A., Colgan, J., Gorczyca, T.W., Mitnik, D.M., Pindzola, M.S., Zatsarinny, O.: 2003, Dielectronic recombination data for dynamic finite-density plasmas. I. Goals and methodology. Astron. Astrophys. 406, 1151. DOI . ADS .

    Article  ADS  Google Scholar 

  • Battaglia, M., Kontar, E.P.: 2013, Electron distribution functions in solar flares from combined X-ray and extreme-ultraviolet observations. Astrophys. J. 779, 107. DOI . ADS .

    Article  ADS  Google Scholar 

  • Bautista, M.A., Badnell, N.R.: 2007, Dielectronic recombination data for dynamic finite-density plasmas. XII. The helium isoelectronic sequence. Astron. Astrophys. 466, 755. DOI . ADS .

    Article  ADS  Google Scholar 

  • Bian, N.H., Emslie, A.G., Stackhouse, D.J., Kontar, E.P.: 2014, The formation of kappa-distribution accelerated electron populations in solar flares. Astrophys. J. 796, 142. DOI . ADS .

    Article  ADS  Google Scholar 

  • Brown, J.C.: 1971, The deduction of energy spectra of non-thermal electrons in flares from the observed dynamic spectra of hard X-ray bursts. Solar Phys. 18, 489. DOI . ADS .

    Article  ADS  Google Scholar 

  • Bryans, P., Landi, E., Savin, D.W.: 2009, A new approach to analyzing solar coronal spectra and updated collisional ionization equilibrium calculations. II. Updated ionization rate coefficients. Astrophys. J. 691, 1540. DOI . ADS .

    Article  ADS  Google Scholar 

  • Burge, C.A., MacKinnon, A.L., Petkaki, P.: 2014, Effect of binary collisions on electron acceleration in magnetic reconnection. Astron. Astrophys. 561, A107. DOI . ADS .

    Article  ADS  Google Scholar 

  • Colgan, J., Pindzola, M.S., Badnell, N.R.: 2004, Dielectronic recombination data for dynamic finite-density plasmas. V: The lithium isoelectronic sequence. Astron. Astrophys. 417, 1183. DOI . ADS .

    Article  ADS  Google Scholar 

  • Colgan, J., Pindzola, M.S., Whiteford, A.D., Badnell, N.R.: 2003, Dielectronic recombination data for dynamic finite-density plasmas. III. The beryllium isoelectronic sequence. Astron. Astrophys. 412, 597. DOI . ADS .

    Article  ADS  Google Scholar 

  • Dere, K.P.: 2007, Ionization rate coefficients for the elements hydrogen through zinc. Astron. Astrophys. 466, 771. DOI . ADS .

    Article  ADS  Google Scholar 

  • Dere, K.P., Landi, E., Mason, H.E., Monsignori Fossi, B.C., Young, P.R.: 1997, CHIANTI – An atomic database for emission lines. Astron. Astrophys. Suppl. 125, 149. DOI . ADS .

    Article  ADS  Google Scholar 

  • Dere, K.P., Landi, E., Young, P.R., Del Zanna, G., Landini, M., Mason, H.E.: 2009, CHIANTI – An atomic database for emission lines. IX. Ionization rates, recombination rates, ionization equilibria for the elements hydrogen through zinc and updated atomic data. Astron. Astrophys. 498, 915. DOI . ADS .

    Article  ADS  Google Scholar 

  • Dudík, J., Dzifčáková, E., Karlický, M., Kulinová, A.: 2011, The bound-bound and free–free radiative losses for the nonthermal distributions in solar and stellar coronae. Astron. Astrophys. 529, A103. DOI . ADS .

    Article  ADS  Google Scholar 

  • Dudík, J., Kašparová, J., Dzifčáková, E., Karlický, M., Mackovjak, Š.: 2012, The non-Maxwellian continuum in the X-ray, UV, and radio range. Astron. Astrophys. 539, A107. DOI . ADS .

    Article  ADS  Google Scholar 

  • Dzifčáková, E.: 1998, The ionization equilibrium in the solar corona for the electron power distribution. Solar Phys. 178, 317. ADS .

    Article  ADS  Google Scholar 

  • Dzifčáková, E.: 2005, The excitation equilibrium of Si XII and Ca XIX in the solar corona for electron power distribution. In: Danesy, D., Poedts, S., De Groof, A., Andries, J. (eds.) Proceedings of the 11th European Solar Physics Meeting – The Dynamic Sun: Challenges for Theory and Observations. ESA SP-600, 120. ADS .

    Google Scholar 

  • Dzifčáková, E., Dudík, J.: 2013, H to Zn ionization equilibrium for the non-Maxwellian electron \(\kappa\)-distributions: Updated calculations. Astrophys. J. Suppl. 206, 6. DOI . ADS .

    Article  ADS  Google Scholar 

  • Dzifčáková, E., Kulinová, A.: 2001, The Fe XXV excitation equilibrium in the solar corona for the electron power distributions using a pseudo-temperature. Solar Phys. 203, 53. DOI . ADS .

    Article  ADS  Google Scholar 

  • Dzifčáková, E., Homola, M., Dudík, J.: 2011, The ionization equilibrium and flare line spectra for the electron distribution with a power-law tail. Astron. Astrophys. 531, A111. DOI . ADS .

    Article  Google Scholar 

  • Dzifčáková, E., Karlický, M., Dudík, J.: 2013, Dielectronic satellite lines and double layers in solar flares. Astron. Astrophys. 550, A60. DOI . ADS .

    Article  Google Scholar 

  • Dzifčáková, E., Kulinová, A., Chifor, C., Mason, H.E., Del Zanna, G., Sylwester, J., Sylwester, B.: 2008, Nonthermal and thermal diagnostics of a solar flare observed with RESIK and RHESSI. Astron. Astrophys. 488, 311. DOI . ADS .

    Article  ADS  Google Scholar 

  • Ferouani, A.K., Inal, M.K., Csanak, G.: 2013, Ne IX line G-ratio in a non-Maxwellian and anisotropic plasma. J. Phys. B 46, 085701. DOI . ADS .

    Article  ADS  Google Scholar 

  • Fleishman, G.D., Kuznetsov, A.A.: 2014, Theory of gyroresonance and free-free emissions from non-Maxwellian quasi-steady-state electron distributions. Astrophys. J. 781, 77. DOI . ADS .

    Article  ADS  Google Scholar 

  • Fletcher, L., Dennis, B.R., Hudson, H.S., Krucker, S., Phillips, K., Veronig, A., Battaglia, M., Bone, L., Caspi, A., Chen, Q., Gallagher, P., Grigis, P.T., Ji, H., Liu, W., Milligan, R.O., Temmer, M.: 2011, An observational overview of solar flares. Space Sci. Rev. 159, 19. DOI . ADS .

    Article  ADS  Google Scholar 

  • Gabriel, A.H., Phillips, K.J.H.: 1979, Dielectronic satellite spectra for highly charged helium-like ions. IV. Iron satellite lines as a measure of non-thermal electron energy distributions. Mon. Not. R. Astron. Soc. 189, 319. ADS .

    Article  ADS  Google Scholar 

  • Karlický, M.: 2012, The \(n\)-distribution of electrons and double layers in the electron-beam-return-current system of solar flares. Astrophys. J. 750, 49. DOI . ADS .

    Article  ADS  Google Scholar 

  • Karlický, M., Dzifčáková, E., Dudík, J.: 2012, On the physical meaning of \(n\)-distributions in solar flares. Astron. Astrophys. 537, A36. DOI . ADS .

    Article  Google Scholar 

  • Kulinová, A., Kašparová, J., Dzifčáková, E., Sylwester, J., Sylwester, B., Karlický, M.: 2011, Diagnostics of non-thermal distributions in solar flare spectra observed by RESIK and RHESSI. Astron. Astrophys. 533, A81. DOI . ADS .

    Article  ADS  Google Scholar 

  • Landi, E., Young, P.R., Dere, K.P., Del Zanna, G., Mason, H.E.: 2013, CHIANTI – An atomic database for emission lines. XIII. Soft X-ray improvements and other changes. Astrophys. J. 763, 86. DOI . ADS .

    Article  ADS  Google Scholar 

  • Lin, R.P., Hudson, H.S.: 1971, 10 – 100 keV electron acceleration and emission from solar flares. Solar Phys. 17, 412. DOI . ADS .

    Article  ADS  Google Scholar 

  • Lin, R.P., Dennis, B.R., Hurford, G.J., Smith, D.M., Zehnder, A., Harvey, P.R., Curtis, D.W., Pankow, D., Turin, P., Bester, M., Csillaghy, A., Lewis, M., Madden, N., van Beek, H.F., Appleby, M., Raudorf, T., McTiernan, J., Ramaty, R., Schmahl, E., Schwartz, R., Krucker, S., Abiad, R., Quinn, T., Berg, P., Hashii, M., Sterling, R., Jackson, R., Pratt, R., Campbell, R.D., Malone, D., Landis, D., Barrington-Leigh, C.P., Slassi-Sennou, S., Cork, C., Clark, D., Amato, D., Orwig, L., Boyle, R., Banks, I.S., Shirey, K., Tolbert, A.K., Zarro, D., Snow, F., Thomsen, K., Henneck, R., McHedlishvili, A., Ming, P., Fivian, M., Jordan, J., Wanner, R., Crubb, J., Preble, J., Matranga, M., Benz, A., Hudson, H., Canfield, R.C., Holman, G.D., Crannell, C., Kosugi, T., Emslie, A.G., Vilmer, N., Brown, J.C., Johns-Krull, C., Aschwanden, M., Metcalf, T., Conway, A.: 2002, The Reuven Ramaty High-Energy Solar Spectroscopic Imager (RHESSI). Solar Phys. 210, 3. DOI . ADS .

    Article  ADS  Google Scholar 

  • Mazzitelli, G., Mattioli, M.: 2002, Ionization balance for optically thin plasmas: Rate coefficients for Cu, Zn, Ga, and Ge ions. At. Data Nucl. Data Tables 82, 313. DOI . ADS .

    Article  ADS  Google Scholar 

  • Mazzotta, P., Mazzitelli, G., Colafrancesco, S., Vittorio, N.: 1998, Ionization balance for optically thin plasmas: Rate coefficients for all atoms and ions of the elements H to NI. Astron. Astrophys. Suppl. 133, 403. DOI . ADS .

    Article  ADS  Google Scholar 

  • Milligan, R.O., Kerr, G.S., Dennis, B.R., Hudson, H.S., Fletcher, L., Allred, J.C., Chamberlin, P.C., Ireland, J., Mathioudakis, M., Keenan, F.P.: 2014, The radiated energy budget of chromospheric plasma in a major solar flare deduced from multi-wavelength observations. Astrophys. J. 793, 70. DOI . ADS .

    Article  ADS  Google Scholar 

  • Mitnik, D.M., Badnell, N.R.: 2004, Dielectronic recombination data for dynamic finite-density plasmas. VIII. The nitrogen isoelectronic sequence. Astron. Astrophys. 425, 1153. DOI . ADS .

    Article  ADS  Google Scholar 

  • Nahar, S.N.: 1996, Total electron–ion recombination of Fe III. Phys. Rev. A 53, 2417. DOI . ADS .

    Article  ADS  Google Scholar 

  • Nahar, S.N.: 1997, Electron–ion recombination of Fe II. Phys. Rev. A 55, 1980. DOI . ADS .

    Article  ADS  Google Scholar 

  • Nahar, S.N., Bautista, M.A.: 2001, Electron–ion recombination rate coefficients and photoionization cross sections for astrophysically abundant elements. VI. Ni II. Astrophys. J. Suppl. 137, 201. DOI . ADS .

    Article  ADS  Google Scholar 

  • Nikolić, D., Gorczyca, T.W., Korista, K.T., Badnell, N.R.: 2010, Dielectronic recombination of argon-like ions. Astron. Astrophys. 516, A97. DOI . ADS .

    Article  ADS  Google Scholar 

  • Oka, M., Ishikawa, S., Saint-Hilaire, P., Krucker, S., Lin, R.P.: 2013, Kappa distribution model for hard X-ray coronal sources of solar flares. Astrophys. J. 764, 6. DOI . ADS .

    Article  ADS  Google Scholar 

  • Oka, M., Krucker, S., Hudson, H.S., Saint-Hilaire, P.: 2015, Electron energy partition in the above-the-looptop solar hard X-ray sources. Astrophys. J. 799, 129. DOI . ADS .

    Article  ADS  Google Scholar 

  • Osterbrock, D.E.: 1974, Astrophysics of Gaseous Nebulae. ADS .

    Google Scholar 

  • Petkaki, P., MacKinnon, A.L.: 2007, Particle acceleration by fluctuating electric fields at a magnetic field null point. Astron. Astrophys. 472, 623. DOI . ADS .

    Article  ADS  Google Scholar 

  • Petkaki, P., MacKinnon, A.L.: 2011, Acceleration of charged particles by fluctuating and steady electric fields in a X-type magnetic field. Adv. Space Res. 48, 884. DOI . ADS .

    Article  ADS  Google Scholar 

  • Phillips, K.J.H., Feldman, U., Landi, E.: 2008, Ultraviolet and X-ray Spectroscopy of the Solar Atmosphere, Cambridge University Press, Cambridge. ADS .

    Book  Google Scholar 

  • Seely, J.F., Feldman, U., Doschek, G.A.: 1987, Observation of nonthermal energy distributions during the impulsive phase of solar flares. Astrophys. J. 319, 541. DOI . ADS .

    Article  ADS  Google Scholar 

  • Shull, J.M., van Steenberg, M.: 1982, The ionization equilibrium of astrophysically abundant elements. Astrophys. J. Suppl. 48, 95. DOI . ADS .

    Article  ADS  Google Scholar 

  • Simões, P.J.A., Kontar, E.P.: 2013, Implications for electron acceleration and transport from non-thermal electron rates at looptop and footpoint sources in solar flares. Astron. Astrophys. 551, A135. DOI . ADS .

    Article  ADS  Google Scholar 

  • Sylwester, J., Sylwester, B., Phillips, K.J.H.: 2008, RESIK observations of helium-like argon X-ray line emission in solar flares. Astrophys. J. Lett. 681, L117. DOI . ADS .

    Article  ADS  Google Scholar 

  • Sylwester, J., Gaicki, I., Kordylewski, Z., Kowaliński, M., Nowak, S., Płocieniak, S., Siarkowski, M., Sylwester, B., Trzebiński, W., Bakała, J., Culhane, J.L., Whyndham, M., Bentley, R.D., Guttridge, P.R., Phillips, K.J.H., Lang, J., Brown, C.M., Doschek, G.A., Kuznetsov, V.D., Oraevsky, V.N., Stepanov, A.I., Lisin, D.V.: 2005, Resik: A bent crystal X-ray spectrometer for studies of solar coronal plasma composition. Solar Phys. 226, 45. DOI . ADS .

    Article  ADS  Google Scholar 

  • Veronig, A.M., Rybák, J., Gömöry, P., Berkebile-Stoiser, S., Temmer, M., Otruba, W., Vršnak, B., Pötzi, W., Baumgartner, D.: 2010, Multiwavelength imaging and spectroscopy of chromospheric evaporation in an M-class solar flare. Astrophys. J. 719, 655. DOI . ADS .

    Article  ADS  Google Scholar 

  • Zatsarinny, O., Gorczyca, T.W., Korista, K.T., Fu, J., Badnell, N.R., Mitthumsiri, W., Savin, D.W.: 2005a, Dielectronic recombination data for dynamic finite-density plasmas. II. The oxygen isoelectronic sequence. Astron. Astrophys. 438, 743. DOI . ADS .

    Article  ADS  Google Scholar 

  • Zatsarinny, O., Gorczyca, T.W., Korista, K.T., Fu, J., Badnell, N.R., Mitthumsiri, W., Savin, D.W.: 2005b, Dielectronic recombination data for dynamic finite-density plasmas. IV. The carbon isoelectronic sequence. Astron. Astrophys. 440, 1203. DOI . ADS .

    Article  ADS  Google Scholar 

  • Zatsarinny, O., Gorczyca, T.W., Fu, J., Korista, K.T., Badnell, N.R., Savin, D.W.: 2006, Dielectronic recombination data for dynamic finite-density plasmas. IX. The fluorine isoelectronic sequence. Astron. Astrophys. 447, 379. DOI . ADS .

    Article  ADS  Google Scholar 

  • Zharkova, V.V., Arzner, K., Benz, A.O., Browning, P., Dauphin, C., Emslie, A.G., Fletcher, L., Kontar, E.P., Mann, G., Onofri, M., Petrosian, V., Turkmani, R., Vilmer, N., Vlahos, L.: 2011, Recent advances in understanding particle acceleration processes in solar flares. Space Sci. Rev. 159, 357. ADS . DOI .

    Article  ADS  Google Scholar 

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  1. Astronomical Institute, Academy of Sciences of the Czech Republic, Fričova 298, 25165, Ondřejov, Czech Republic

    Elena Dzifčáková & Jaroslav Dudík

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  1. Elena Dzifčáková
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  2. Jaroslav Dudík
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Correspondence to Elena Dzifčáková.

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Solar and Stellar Flares: Observations, Simulations, and Synergies

Guest Editors: Lyndsay Fletcher and Petr Heinzel

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Dzifčáková, E., Dudík, J. Ionisation Equilibrium for the Non-Maxwellian Electron \(n\)-Distributions in Solar Flares: Updated Calculations. Sol Phys 290, 3545–3558 (2015). https://doi.org/10.1007/s11207-015-0734-8

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