The ionization balance of the Fe in the solar corona for a non-Maxwellian electron distribution function

The ionization equilibrium of the Fe in the solar corona for a non-Maxwellian electron distribution with an enhanced number of particles in the high-energy tail is presented. A parametric form of the distribution function is used to demonstrate the changes in the ionization equilibrium with changes in the shape of the distribution. The results over the range of temperature 10⁵ K T 10⁸ K for different deviations of the distribution from a Maxwellian are given in tabular form. The results can be used for specific applications in the solar corona, especially in the active corona, where deviations from the Maxwellian distribution can be significant.     

THE Fe XXV EXCITATION EQUILIBRIUM IN THE SOLAR CORONA FOR THE ELECTRON POWER DISTRIBUTIONS USING A PSEUDO-TEMPERATURE

The excitation equilibrium of Fexxv in the solar corona for electron power distributions is presented. A parametric form of the distribution function is used to demonstrate the changes in the excitation equilibrium due to the shape of the distribution. A pseudo-temperature is used for better understanding of the changes in the excitation equilibrium. The Fexxv line intensities depend on the shape of the electron distribution and unusual Fe line ratios can be observed for non-thermal distribution. The results can be used in specific applications in the solar corona, especially in diagnostics of the impulsive phase of solar flares, where the deviations from the Maxwellian distribution can be large.     

Non-Maxwellian velocity distribution functions associated with steep temperature gradients in the solar transition region

Non-Maxwellian electron velocity distribution functions, computed for Dupree's (1972) model of the solar transition region in a previous paper, are used to calculate ionization rates for ions of carbon, nitrogen, and oxygen. Ionization equilibrium populations for these ions are then computed and compared with similar calculations assuming Maxwellian distribution functions for the electrons. The results show that the ion populations change (compared to the values computed with a Maxwellian) in some cases by several orders of magnitude depending on the ion and its temperature of formation.     

On the collisional energy transfer between the constituents of the coronal plasma

It has been suggested that the distribution functions characterizing the constituents of the solar coronal plasma are non-Maxwellian. If so, an accurate treatment of the collisional momentum and energy exchange between the plasma constituents within the framework of hydrodynamic models requires a re-evaluation of the general transfer integrals in multi-component plasmas. We have evaluated these integrals numerically for both Maxwellian and non-Maxwellian distribution functions of the plasma species avoiding the standard approximation for the collision cross sections frequently employed in the literature. Significant differences are shown to exist in the energy exchange rates for different distributions. We also demonstrate the inadequacy of the assumption of thermodynamic equilibrium in the innermost solar wind and reveal the importance of an accurate evaluation of the transfer integrals for the solar coronal plasma based on more realistic velocity distributions.Presented at the CESRA-Workshop on Coronal Magnetic Energy Release at Caputh near Potsdam in May 1994.     

Synthetic Spectra of the Fe VIII – Fe XVI Emission Lines for Electron Non-Thermal Distributions

A certain class of non-thermal electron distributions can exhibit more mono-energetic shape and a higher peak than the Maxwellian distribution. This type of electron distribution can be observed mainly in flaring plasmas. We have studied the influence of this kind of electron energy distribution on the excitation equilibrium of Fe VIII – Fe XVI in the solar corona. The changes in synthetic spectra of the emission lines belonging to these ions due to this non-thermal distribution are shown. The possibilities of finding the shape of the energy distribution function of electrons from the Fe line ratios are also discussed. The results can be used for diagnostics of coronal plasmas where the deviations of particle energy distributions from the Maxwellian one can be significant.     

Coronagraph observations of the coronal condensation of 4 February 1962

Climax coronagraph observations of the accessible Fe lines, as well as the Caxv 5694 line at the time of the 1962 total eclipse, are analyzed. The spectra show that the ionization equilibrium of iron is not substantially changed in an intense coronal condensation, at least for the stages x through xv. The only exception is Fexv 7059, for which density effects are important. The stability of the ionization distribution is explained by the dynamic nature of the Fe ionization, with ions entering on the high side (Fexvi and up) due to rapid heating and then cooling through the visible stages.Comparison of the ionization distributions inferred from radiative and collisional excitation of the iron lines shows that the excitation must be by collisions everywhere at the heights examined (less than 50 000 km).The iron abundance in the corona is found to be 10^–4 that of hydrogen, but this figure would be reduced by the amount of cyclic excitation.The peak electron density in the condensation is 8 × 10⁹, and the peak value of the 5694 line/ continuum ratio is 2.5, in good agreement with calculations by Chevalier and Lambert.The ratio of the infrared Fexiii lines is measured along the limb and found to vary with electron density as expected, the 10 747/10 798 ratio is 7 or less at densities much below 10⁹ and saturates at a value of 2 for densities above that amount.     

On coronal Fe abundances and temperatures from XUV emission lines

Data obtained by the OSO-7 spectroheliograph on strong XUV lines of five, different Fe ions from the outer equatorial corona are presented. Interpretation of the data with a spherically symmetric model atmosphere gives average ion abundances for lines of sight at 0.3R from the limb. Fe xvi is usually more abundant than Fe xv, xiv, xii and ix, but there are times when Fe xii is more abundant than the other ions. The deviation of measured relative abundances of Fe xii, xiv, and xvi from predictions of ionization equilibrium at one temperature seems to indicate that there are appreciable temperature variations along lines of sight. Element abundances are very uncertain since they appear to depend so heavily on likely but unknown density irregularities along lines of sight.     

Unreddened stars and the two-phase model of the interstellar medium

We have computed two phase models of the interstellar medium, with cosmic rays and X-rays assumed to be the main ionizing agents, heating due to photoelectron ejection from the interstellar grains. We show that it is possible to have a hot and tenuous intercloud medium in pressure equilibrium with the interstellar clouds for a wide range of physical conditions, possibly existing in the interstellar space. The atomic and ionic line observations towards Sco are shown to be consistent with the origin of these lines in the intercloud medium for a range of values of the ionizing flux. It is suggested that the intercloud medium may be predominantly neutral, with ionization rates consistent with the limits imposed by molecular observations. The mean fractional ionization of the intercloud medium is 1%.On leave from Tata Institute of Fundamental Research, Bombay, India.     

Oblique shock dynamics in nonextensive magnetized plasma

The detailed properties of the classical electromagnetic Weibel instability in a semi-relativistic anisotropic plasma are investigated for Maxwellian distribution. In this article, the effects of one particular factor affecting the growth rate of Weibel instability, Coulomb collision effect of electrons and ions, is studied and discussed based on the equilibrium semi-relativistic Maxwellian distribution function, in a dense and unmagnetized anisotropic plasma. An analytical expression is derived for the growth rate of the Weibel instability. The two limiting cases ( $\left| \xi\right| \ll1$ and $\left| \xi\right| \gg1$ ) are considered. It is shown that in the limit $\left| \xi\right| \ll 1$ , the quantity η, which is due to the collision term, will appear in the growth and in the conditions of the rate of the Weibel instability. The quantity χ symbolizes the contribution from relativistic terms which becomes unity as we approach the non-relativistic Maxwellian case, leading to the standard Weibel instability scenario. The increasing of η leads to decreasing of the growth rate, and with the decreasing of η the growth rate will increase.     

EFFECT OF PERPENDICULAR A.C. ELECTRIC FIELD ON THE OBLIQUE WHISTLER MODE INSTABILITY IN THE EARTH’S MAGNETOSPHERE

The elements of dielectric tensor and dispersion relation for obliquely propagating whistler waves with finite in an infinite magnetoplasma are obtained for a kappa distribution in the presence of perpendicular a.c. electric field. Integrals and modified plasma dispersion functions are reduced in power series form. Numerical calculations have been performed to obtain temporal growth rate and real frequencies of the plasma waves for magnetospheric plasma, using linear theory of dispersion relation. The effect and modification introduced by the perpendicular a.c. electric field on the temporal growth rates, real frequencies and resonance condition are discussed for kappa and Maxwellian distributions. Our results and their interpretation are compared with known whistler observations obtained by ground-based techniques and satellite observations.     

Ionization equilibrium in soft X-ray-emitting solar flares

Studies of the flare-produced line feature at 1.9 Å due to highly ionized iron show that it is emitted in conditions closely approximating steady-state ionization equilibrium. Calculations of the line flux per unit emission measure from time-dependent and steady-state ionization equilibria are compared with observed values during four flares in particular. Only for electron densities N _e 10¹⁰ cm^-3 do the time-dependent equilibrium values give as good an approximation to the observed values as the steady-state equilibrium. This lower limit is compared with values of N _e derived from analyses of the temperature decline in each of these events, and with estimates of N _e given by other workers.NAS/NRC Research Associate.     

Electron Excitation Rates in the Solar Corona for non-Maxwellian Electron Distributions

The influence of electron non-Maxwellian distributions (power and -distribution) on the electron excitation rate in the solar corona is demonstrated. It is shown that the deviations in electron excitation rate are sufficient to affect intensities of spectral lines. As an example the diagnostics of a power-law distribution are demonstrated for a simplified calculation of the resonance lines of Fexxiv, Fexxv and Fexxvi. The results can be used in diagnosing solar flare plasmas, where the deviations of the electron distribution from a Maxwellian distribution can be large.     

Positrons and low energy cosmic rays from supernovae

Burgeret al. (1970) calculated the positron flux from the decay of⁵⁶Co⁵⁶Fe from cosmic rays injected from supernovae. The plasma properties of the ejected matter are determined in the present calculation in order to include the ionization loss of the positrons as the matter expands. It is found that using the matter velocity distribution of previous supernova model calculations that roughly 10% of the positrons escape. The average lifetime in the galaxy due to ionization loss is found to be relatively small, 1.5×10⁵ yr, and with the above injection results in ×3, the observed flux. The same matter velocity distribution is subjected to ionization loss in the galaxy and a steady state low energy, 10E200 MeV, differential flux spectrum is found,J(E)E ^–1.2. This removes the difficulty of the high galactic energy density resulting from a steeper spectrum.     

Comment on the X-ray event of July 7, 1966

According to Snijders (1968) the decay profile of an X-ray burst determines the effective temperature describing the distribution of fast electrons in the emitting source. In this paper it is concluded that the observations of the hard X-ray burst of 7 July, 1966; 0038 UT are not in disagreement with the concept of thermal bremsstrahlung from electrons with a Maxwellian distribution of about 10⁸ K. Some physical parameters of the source are determined. The magnetic field strength is found to be about 1200 gauss. The initial temperature kT ₀ is approximately 40 keV.     

Self-consistent photoionization models of planetary nebulae luminescence: stellar ionizing continuum,nebular abundances,and evolution of the envelopes

The modern self-consistent photoionization model of planetary nebula luminescence is described. All of the processes which play an important role in the ionization and thermal equilibrium of the nebular gas are taken into consideration. The diffuse ionizing radiation is taken into account completely. The construction of the model is carried out for the radial distribution of gas density in the nebular envelope which is consistent with isophotal map of the nebula. The application of the model is illustrated on the example of the planetary nebulae BD+30°3639 and NGC 7293. It is shown that the continuum of the central star at 912 Å does not correspond to the blackbody spectrum but agrees with the spectrum of corresponding non-LTE model atmosphere. The radial distributions of electron density, electron temperature, and other parameters in the nebular envelopes are found.The evolution of the radial distribution of gas density in the planetary nebulae envelopes is investigated. Approximative analytical expression which describe both such distribution and its change with time is adjusted. It is shown that the nebular envelope is formed as a result of quiet evolution of the slow stellar wind of star-precursor, and the formation of the envelope begins from the decrease of star-precursor's mass loss rate. Obtained radial distributions of gas density in the envelopes of young nebulae rule out the idea that the planetary nebula is formed as a result of a rapid ejection of clear-cut envelope. So, there is no necessity for the superwind which is used for this purpose in theoretical calculations.A new method of the determination of planetary nebulae abundances is proposed. Unobserved ionization stages are taken into account with aid of the correlations between relative abundances of various ions which had been obtained from the grid of the photoionization models of planetary nebulae luminescence. Simple approximative expressions for the determination of He/H, C/H, N/H, O/H, Ne/H, Mg/H, Si/H, S/H, and Ar/H are found. The chemical composition of 130 Galactic planetary nebulae is revised. A comparative analysis of the abundances in the Galactic disk, bulge, and halo nebulae is carried out.     

Analysis of ion charge states in solar wind and CMEs

We discuss needs in dielectronic recombination data motivated by recent work directed at a quantitative understanding of ion charge states of various elements observed in situ in the solar wind and CMEs. The competing processes of ionization and recombination lead to departures from collision ionization equilibrium. The use of this as a diagnostic of acceleration and heating processes of the solar wind and CMEs is sensitive to the accuracy of the atomic rates in a way that steady state ionization equilibrium plasmas are not. The most pressing need is dielectronic recombination rates for ions Fe8+-12+. These are among the dominant species observed in various regions of the solar wind and CMEs, and in remotely sensed EUV spectra.     

Non-equilibrium ionization in the transition region network

We explore the consequences of the recently reported, persistent downflow of material within the supergranule network. The velocities observed by OSO-8, about 5 km s^-1 for C IV 1548 and 20 km s^-1 for O VI 1032, are sufficient to cause the ion distributions to differ significantly from those of ionization equilibrium. Using an accepted temperature model and two models of the velocity fields, we determine the ion distributions of carbon, nitrogen, and oxygen throughout the transition region and compare them with the equilibrium distributions. We then investigate how the temperature model must be modified in order to reconcile the computed line intensities with observed and show that a smaller temperature gradient, and possibly a different pressure distribution, are required. Finally, we demonstrate that the observed downflow is probably adequate to overcome the tendency for thermal diffusion to establish concentration gradients and thus the downflow keeps the atmosphere well mixed.     

Hydrogen ionization and n=2 population for model spicules and prominences

Using slab model atmospheres that are irradiated from both sides by photospheric, chromospheric, and coronal radiation fields we have determined the ionization and excitation equilibrium for hydrogen.The model atom consists of two bound levels (n = 1 and n = 2) and a continuum. Ly- was assumed to be optically thick with the transition in detailed radiative balance. The Balmer continuum was assumed to be optically thin with the associated radiative ionization dominated by the photospheric radiation field (T _rad = 5940 K). The ionization equilibrium was determined from an exact treatment of the radiative transfer problem for the internally generated Ly-c field and the impressed chromospheric and coronal field (characterized by T _rad = 6500K).Our calculations corroborate the hypothesis that N₂, the n = 2 population density, is uniquely determined by the electron density N _e. We also present ionization curves for 6000K, 7500K, and 10000K models ranging in total hydrogen density from 1 × 10¹⁰/cm³ to 3 × 10¹²/cm³. Using these curves it is possible to obtain the total hydrogen density from the n = 2 population density in prominences and spicules.The National Center for Atmospheric Research is sponsored by the National Science Foundation.