KAPPA: A Package for Synthesis of Optically Thin Spectra for the Non-Maxwellian Kappa-Distributions. III. Improvements to Ionization Equilibrium and Extension to Kappa < 2
Elena Dzifcakova, Jaroslav Dudik, Martina Pavelkova, Bozena Solarova, Alena Zemanova
The KAPPA package is designed for calculations of optically thin spectra for the non-Maxwellian \k{appa}-distributions. This paper presents extension of the database to allow calculations of the spectra for extreme values of \k{appa} < 2, which are important for accurate diagnostics of the \k{appa}-distributions in the outer solar atmosphere. In addition, two improvements were made to the ionization equilibrium calculations within the database. First, the ionization equilibrium calculations now include the effect of electron impact multi-ionization (EIMI). Although relatively unimportant for Maxwellian distribution, the EIMI becomes important for some elements such as Fe and low values of \k{appa}, where it modifies the ionization equilibrium significantly. Second, the KAPPA database now includes the suppression of dielectronic recombination at high electron densities, evaluated via the suppression factors. We find that at the same temperature, the suppression of dielectronic recombination is almost independent of \k{appa}. The ionization equilibrium calculations for the \k{appa}-distributions are now provided for a range of electron densities.
The non-Maxwellian $κ$-distributions have been detected in the solar transition region and flares. These distributions are characterized by a high-energy tail and a near-Maxwellian core and are known to have significant impact on the resulting optically thin spectra arising from collisionally dominated astrophysical plasmas. We developed the KAPPA package (http://kappa.asu.cas.cz) for synthesis of such line and continuum spectra. The package is based on the freely available CHIANTI database and software, and can be used in a similar manner. Ionization and recombination rates together with the …
New data for calculation of the ionization and recombination rates have have been published in the past few years. Most of these are included in CHIANTI database. We used these data to calculate collisional ionization and recombination rates for the non-Maxwellian kappa-distributions with an enhanced number of particles in the high-energy tail, which have been detected in the solar transition region and the solar wind. Ionization equilibria for elements H to Zn are derived. The kappa-distributions significantly influence both the ionization and recombination rates and widen the ion abundance p…
Spectroscopic observations made by the Extreme Ultraviolet Variability Experiment (EVE) on board the Solar Dynamics Observatory (SDO) during the 2012 March 7 X5.4-class flare (SOL2012-03-07T00:07) are analyzed for signatures of the non-Maxwellian kappa-distributions. Observed spectra were averaged over 1 minute to increase photon statistics in weaker lines and the pre-flare spectrum was subtracted. Synthetic line intensities for the kappa-distributions are calculated using the KAPPA database. We find strong departures (kappa < 2) during the early and impulsive phases of the flare, with subsequ…
We investigate the possibility of diagnosing the degree of departure from the Maxwellian distribution using single-ion spectra originating in astrophysical plasmas in collisional ionization equilibrium. New atomic data for excitation of Fe IX-XIII are integrated under the assumption of a kappa-distribution of electron energies. Diagnostic methods using lines of a single ion formed at any wavelength are explored. Such methods minimize uncertainties from the ionization and recombination rates, as well as the possible presence of non-equilibrium ionization. Approximations to the collision strengt…
Context. Recent studies on Kappa distribution functions invoked in space plasma applications have emphasized two alternative approaches which may assume the temperature parameter either dependent or independent of the power-index $κ$. Each of them can obtain justification in different scenarios involving Kappa-distributed plasmas, but direct evidences supporting any of these two alternatives with measurements from laboratory or natural plasmas are not available yet. Aims. This paper aims to provide more facts on this intriguing issue from direct fitting measurements of suprathermal electron po…
Modeling fast solar wind based on the kinetic theory is an important task for scientists. In this paper, we present a two-fluid model for fast solar wind with anisotropic Kappa-Maxwellian electrons and Bi-Maxwellian protons. In the simulation, the energy exchange between the plasma particles and low-frequency Alfvén waves is considered. A set of eleven coupled equations is derived by applying the zeroth- to fourth-order moments of the Vlasov equation and the modified electromagnetic Maxwell equations. A characteristic of the Kappa distribution (indicated by $κ$ index) is explicit in the equati…
Currently there is a concern about ability of the classical thermal (Maxwellian) distribution to describe quasi-steady-state plasma in solar atmosphere including active regions. In particular, other distributions have been proposed to better fit observations, for example, kappa- and $n$-distributions. If present, these distributions will generate radio emissions with different observable properties compared with the classical gyroresonance (GR) or free-free emission, which implies a way of remote detecting these non-Maxwellian distributions in the radio observations. Here we present analytical…
We investigate the nature of the spectral line profiles for transition region ions observed with the Interface Region Imaging Spectrograph (IRIS). In this context, we have analyzed an active-region observation performed by IRIS in its 1400 A spectral window. The transition-region lines are found to exhibit significant wings in their spectral profiles, which can be well-fitted with non-Maxwellian kappa-distribution. The fit with a kappa-distribution can perform better than a double Gaussian fit, especially for the strongest line, Si IV 1402.8 A. Typical values of $κ$ found are about 2, occurrin…
We demonstrate that a nonthermal distribution of particles described by a kappa distribution can be accurately approximated by a weighted sum of Maxwell-Boltzmann distributions. We apply this method to modeling collision processes in kappa-distribution plasmas, with a particular focus on atomic processes important for solar physics. The relevant collision process rate coefficients are generated by summing appropriately weighted Maxwellian rate coefficients. This method reproduces the rate coefficients for a kappa distribution to an estimated accuracy of better than 5%. This is equal to or bett…
The formation of the transition-region O IV and Si IV lines observable by the Interface Region Imaging Spectrograph (IRIS) is investigated for both Maxwellian and non-Maxellian conditions characterized by a kappa-distribution exhibiting a high-energy tail. The \ion{Si}{4} lines are formed at lower temperatures than the O IV lines for all kappa. In non-Maxwellian situations with lower kappa, the contribution functions are shifted to lower temperatures. Combined with the slope of the differential emission measure, it is possible for the Si IV lines to be formed at very different regions of solar…
Using spectroscopic data, we support the possibility of suprathermal distributions of coronal ions by fitting the equivalent kappa functions to their emission line profiles. We fit different kappa and Gaussian model functions to line profiles of the strong Fe xv line at 284.16 Angstroms, across two large-field spectroscopic rasters taken in a solar active region. Both single- and double-component Gaussian models are applied, as well as two kappa models, one with a free width parameter allowing for and the other with a constrained width that precludes "microturbulence". We then compare the good…
We use observations from the Interstellar Boundary Explorer (IBEX) and Ulysses to explore the possibility that the interstellar neutral helium flowing through the inner solar system possesses an intrinsic non-Maxwellian velocity distribution. In fitting the IBEX and Ulysses data, we experiment with both a kappa distribution and a bi-Maxwellian, instead of the usual Maxwellian assumption. The kappa distribution does not improve the quality of fit to either the IBEX or Ulysses data, and we find lower limits to the kappa parameter of kappa>12.1 and kappa>6.0 from the IBEX and Ulysses analyses, re…
We investigated the possibility of diagnosing the degree of departure from the Maxwellian distribution using the Fe XVII - Fe XVIII spectra originating in plasmas in collisional ionization equilibrium, such as in the cores of solar active regions or microflares. The original collision strengths for excitation are integrated over the non-Maxwellian electron $κ$-distributions characterized by a high-energy tail. Synthetic X-ray emission line spectra were calculated for a range of temperatures and $κ$. We focus on the 6-24 A spectral range to be observed by the upcoming Marshall Grazing-Incidence…
The X-ray emission of coronal flare sources can be explained considering the kappa electron distribution. Motivated by this fact, we study the problem of how hot plasma with the kappa distribution of electrons is confined in these sources. For comparison, we analyze the same problem but with the Maxwellian distribution. We use a 3-D particle-in-cell code, which is large in one direction and thus effectively only one-dimensional, but describing all electromagnetic effects. In the case with the Maxwellian distribution, and in agreement with the previous studies, we show a formation of the double…
We study the dispersion relation for parallel propagating ion-cyclotron (IC) waves in a dusty plasma, considering situations where the velocity dispersion along perpendicular direction is greater than along the parallel direction, and considering the use of product-bi-kappa (PBK) velocity distributions for the plasma particles. The results obtained by numerical solution of the dispersion relation, in a case with isotropic Maxwellian distributions for electrons and PBK distribution for ions, show the occurrence of the electromagnetic ion-cyclotron instability (EMIC), and show that the decrease …
Non-Maxwellian $κ$ electron energy distributions (EEDs) have been proposed in recent years to resolve the so-called ``electron temperature and abundance discrepancy problem'' in the study of planetary nebulae (PNe). Thus the need to develop diagnostic tools to determine from observations the EED of PNe is raised. Arising from high energy levels, the ultraviolet (UV) emission lines from PNe present intensities that depend sensitively on the high-energy tail of the EED. In this work, we investigate the feasibility of using the \ion{C}{2}]$λ$2326/\ion{C}{2}$λ$1335 intensity ratios as a diagnostic…
Shocks, turbulence and winds all influence the electron velocity distribution in hot plasmas, exciting lower-energy electrons and generating a high-energy (typically power-law) tail. This effect, typically described as a kappa distribution can affect both the line and continuum X-ray spectrum emitted by the plasma. Hahn & Savin (2015) proposed a "Maxwellian decomposition" to generate the rate coefficients of kappa distributions. Using their method and the AtomDB atomic database, we have developed a general model to calculate the emission from a plasma with a kappa distribution. We compare our …
Context. Coronal heating is currently thought to proceed via the mechanism of nanoflares, small-scale and possibly recurring heating events that release magnetic energy. Aims. We investigate the effects of a periodic high-energy electron beam on the synthetic spectra of coronal Fe ions. Methods. Initially, the coronal plasma is assumed to be Maxwellian with a temperature of 1 MK. The high-energy beam, described by a kappa-distribution, is then switched on every period $P$ for the duration of P/2. The periods are on the order of several tens of seconds, similar to exposure times or cadences of …
Heating of a plasma sheet in nonequilibrium ionization with nonthermal electrons
Kyung Hee University（庆熙大学）；Yunnan Observatories, Chinese Academy of Sciences（中国科学院云南天文台）；Air Force Research Laboratory（美国空军研究实验室）；G-LAMP NEXUS Institute/School of Space Research, Kyung Hee University（庆熙大学G-LAMP NEXUS研究所/空间研究学院）；Korea Astronomy & Space Science Institute（韩国天文学与空间科学研究院）
Most of our knowledge of the physical processes in distant plasmas is obtained through measurement of the radiation they produce. Here we provide an overview of the main collisional and radiative processes and examples of diagnostics relevant to the microphysical processes in the plasma. Many analyses assume a time-steady plasma with ion populations in equilibrium with the local temperature and Maxwellian distributions of particle velocities, but these assumptions are easily violated in many cases. We consider these departures from equilibrium and possible diagnostics in detail.
We review the presence and signatures of the non-equilibrium processes, both non-Maxwellian distributions and non-equilibrium ionization, in the solar transition region, corona, solar wind, and flares. Basic properties of the non-Maxwellian distributions are described together with their influence on the heat flux as well as on the rates of individual collisional processes and the resulting optically thin synthetic spectra. Constraints on the presence of high-energy electrons from observations are reviewed, including positive detection of non-Maxwellian distributions in the solar corona, trans…
Recent studies have outlined the interest for the evaluation of transport coefficients in space plasmas, where the observed velocity distributions of plasma particles are conditioned not only by the binary collisions, e.g., at low energies, but also by the energisation of particles from their interaction with wave turbulence and fluctuations, generating the suprathermal Kappa-distributed populations. This paper provides a first estimate of the main transport coefficients based on regularised Kappa distributions (RKDs), which, unlike standard Kappa distributions (SKDs), enable macroscopic param…
Transition region (TR) spectra typically show the Si IV 1402.8 A line to be enhanced by a factor of 5 or more compared to the neighboring O IV 1401.2 A, contrary to predictions of ionization equilibrium models and the Maxwellian distribution of particle energies. Non-equilibrium effects in TR spectra are therefore expected. To investigate the combination of non-equilibrium ionization and high-energy particles, we apply the model of the periodic electron beam, represented by a kappa-distribution that recurs at periods of several seconds, to plasma at chromospheric temperatures of 10^4 K. This s…
Solar flares produce hard X-ray emission of which the photon spectrum is often represented by a combination of thermal and power-law distributions. However, the estimates of the number and total energy of non-thermal electrons are sensitive to the determination of the power-law cutoff energy. Here we revisit an `above-the-loop' coronal source observed by RHESSI on 2007 December 31 and show that a kappa distribution model can also be used to fit its spectrum. Because the kappa distribution has a Maxwellian-like core in addition to the high-energy power-law tail, the emission measure and tempera…
A vexing puzzle in the study of planetary nebulae and \ion{H}{2} regions is that the plasma diagnostic results based on collisionally excited lines systematically differ from those based on recombination lines. A fairly speculative interpretation is the presence of nonthermal electrons with the so-called $κ$ energy distributions, yet there is little observational evidence to verify or disprove this hypothesis. In this paper, we examine the influence of $κ$-distributed electrons on the emissivities of \ion{O}{2} recombination lines using an approximate method, where the rate coefficients for a …
Quasi-linear approach of bi-Kappa distributed electrons with dynamic $κ$ parameter. EMEC instability
Universidad de Chile（智利大学）；KU Leuven（荷语鲁汶大学）；Ruhr-Universität Bochum（波鸿鲁尔大学）；University of Maryland, College Park（马里兰大学帕克分校）；Comisión Chilena de Energía Nuclear（智利国家核能委员会）；Universidad Andres Bello（安德烈斯贝略大学）；University of Maria Curie-Skłodowska（玛丽亚·居里-斯克沃多夫斯卡大学）
Analysis of 15314 electron velocity distribution functions (VDFs) within $\pm$2 hours of 52 interplanetary (IP) shocks observed by the \emph{Wind} spacecraft near 1 AU are introduced. The electron VDFs are fit to the sum of three model functions for the cold dense core, hot tenuous halo, and field-aligned beam/strahl component. The best results were found by modeling the core as either a bi-kappa or a symmetric (or asymmetric) bi-self-similar velocity distribution function, while both the halo and beam/strahl components were best fit to bi-kappa velocity distribution function. This is the firs…
The nonlinear dynamics of electron-acoustic localized structures in a collisionless and unmagnetized plasma consisting of "cool" inertial electrons, "hot" electrons having a kappa distribution, and stationary ions is studied. The inertialess hot electron distribution thus has a long-tailed suprathermal (non-Maxwellian) form. A dispersion relation is derived for linear electron-acoustic waves. They show a strong dependence of the charge screening mechanism on excess suprathermality (through κ). A nonlinear pseudopotential technique is employed to investigate the occurrence of stationary-profile…
Photoionization produces supra-thermal electrons, electrons with much more energy than is found in a thermalized gas at electron temperatures characteristic of nebulae. The presence of these high energy electrons may solve the long-standing t^2/ADF puzzle, the observations that abundances obtained from recombination and collisionally excited lines do not agree, and that different temperature indicators give different results, if they survive long enough to affect diagnostic emission lines. The presence of these non-Maxwellian distribution electrons is usually designated by the term kappa. Here…
Estimating the temperature of the solar wind particles and their anisotropies is particularly important for understanding the origin of these deviations from thermal equilibrium as well as their effects. In the absence of energetic events the velocity distribution of electrons reveal a dual structure with a thermal (Maxwellian) core and a suprathermal (Kappa) halo. This paper presents a detailed observational analysis of these two components, providing estimations of their temperatures and temperature anisotropies and decoding any potential interdependence that their properties may indicate. T…
The properties of solar flare plasma can be determined from the observation of optically thin lines. The emitting ion distribution determines the shape of the line, with an isothermal Maxwellian ion distribution producing a Gaussian profile. Non-Gaussian lines may indicate more complex ion distributions. We investigate the possibility of determining flare-accelerated non-thermal ion or plasma velocity distributions. We study EUV spectral lines during a flare SOL2013-05-15T01:45 using the Hinode EUV Imaging Spectrometer (EIS). The flare is located close to the eastern solar limb with an extende…
Given their uniqueness, the Ulysses data can still provide us with valuable new clues about the properties of plasma populations in the solar wind, and, especially, about their variations with heliographic coordinates. We revisit the electron data reported by by the SWOOPS instrument on-board of the Ulysses spacecraft between 1990 to early 2008. These observations reveal velocity distributions out of thermal equilibrium, with anisotropies (e.g., parallel drifts or/and different temperatures, parallel and perpendicular to the background magnetic field), and quasi-thermal and suprathermal popula…
