Coronal Loop Models Research Articles

Modeling of Coronal EUV Loops Observed withTRACE. I. Hydrostatic Solutions with Nonuniform Heating

Recent observations of coronal loops in EUV wavelengths with the Transition Region and Coronal Explorer (TRACE) and the Extreme-Ultraviolet Imaging Telescope (EIT) on the Solar and Heliospheric Observatory (SOHO) demonstrated three new results that cannot be explained by most of the existing loop models: (1) EUV loops are near-isothermal along their coronal segments, (2) they show an overpressure or overdensity compared with the requirements of steady state loops with uniform heating, and (3) the brightest EUV loops exhibit extended scale heights up to 4 times the hydrostatic scale height. These observations cannot be reconciled with the classical RTV (Rosner, Tucker, & Vaiana) model, they do not support models with uniform heating, and they even partially violate the requirements of hydrostatic equilibrium. In this study we are fitting for the first time steady state solutions of the hydrodynamic equations to observed intensity profiles, permitting a detailed consistency test of the observed temperature T(s) and density profiles ne(s) with steady state models, which was not possible in previous studies based on scaling laws. We calculate some 500 hydrostatic solutions, which cover a large parameter space of loop lengths (L ? 4-300 Mm), of nonuniform heating functions (with heating scale heights in the range of ?H ? 1-300 Mm), approaching also the limit of uniform heating (?H L). The parameter space can be subdivided into three regimes, which contain (1) solutions of stably stratified loops, (2) solutions of unstably stratified loops (in the case of short heating scale heights, ?H,Mm ? ), and (3) a regime in which we find no numerical solutions (when ?H,Mm ). Fitting the hydrostatic solutions to 41 EUV loops observed with TRACE (selected by the criterion of detectability over their entire length), we find that only 30% of the loops are consistent with hydrostatic steady state solutions. None of the observed EUV loops is consistent with a uniform heating function while in quasi-steady state. Those loops compatible with a steady state are found to be heated near the footpoints, with a heating scale height of ?H = 12 ? 5 Mm, covering a fraction ?H/L = 0.2 ? 0.1 of the loop length. These results support coronal heating mechanisms operating in or near the chromosphere and transition region.

CHANDRA-LETGS X-ray observations of Capella

We report an analysis of the X-ray spectrum of Capella from 6 to 175 Aobtained with the Low Energy Transmission Grating Spectrometer (LETGS) on board of the X-ray space observatory CHANDRA. Many emission line features appear that can be resolved much better as compared to former instruments (EUVE and ASCA). Coronal electron densities (n e ) and temperatures (T ) of brightly emitting regions are constrained by an analysis of ratios of density- and temperature-sensitive lines of helium-like ions and highly ionized iron atoms. Lines emitted by e.g., O VII & VIII, Mg X-XII, Si XII-XIV, Fe IX, X & XV-XXIII are used to derive T . Line ratios in the helium-like triplets of C V, N VI, O VII, Mg XI, and Si XIII yield T in the range 0.5-10 MK, and n e in the range 109 -1013 cm-3 . The Fe IX/X ratio yields 0.9 MK, while lines from Fe XVIII to XXII give 6-10 MK. Flux ratios of Fe XX-XXII lines indicate for the electron densities an upper limit in the range (2-5) 1012 cm-3 . From line ratios of Fe XVII and Fe XVIII we derive constraints on the optical depth τ of ~1-1.5. An emission measure distribution is derived from Fe line intensities. Results for element abundances (relative to Fe) from a 4-T model are: O and Ne/Fe about solar, N, Mg and Si/Fe ~2 solar. The results for T and n e are described in terms of quasi-static coronal loop models and it is shown that the X-ray emission originates from compact structures much smaller than the stellar radii.

Intermittent heating in a model of solar coronal loops

X-ray and EUV observations of the solar corona reveal a very complex and dynamic environment where there are many examples of structures that are believed to outline the Sun's magnetic field. In this present study, the authors investigate the temporal response of the temperature, density and pressure of a solar coronal plasma contained within a magnetic loop to an intermittent heating source generated by Ohmic dissipation. The energy input is produced by a one-dimensional MHD flare model. This model is able to reproduce some of the statistical properties derived from X-ray flare observations. In particular the heat deposition consists of both a sub-flaring background and much larger, singular dissipative events. Two different heating profiles are investigated: (a) the spatial average of the square of the current along the loop and (b) the maximum of the square of the current along the loop. For case (a), the plasma parameters appear to respond more to the global variations in the heat deposition about its average value rather than to each specific event. For case (b), the plasma quantities are more intermittent in their evolution. In both cases the density response is the least bursty signal. It is found that the time-dependent energy input can maintain the plasma at typical coronal temperatures. Implications of these results upon the latest coronal observations are discussed.

Observation and Modeling of the Solar Transition Region. II. Identification of New Classes of Solutions of Coronal Loop Models

In the present work we undertake a study of the quasi-static loop model and the observational consequences of the various solutions found. We obtain the most general solutions consistent with certain initial conditions. Great care is exercised in choosing these conditions to be physically plausible (motivated by observations). We show that the assumptions of previous quasi-static loop models, such as the models of Rosner, Tucker, & Vaiana (RTV) and Veseckey, Antiochos, & Underwood, (VAU) are not necessarily valid for small loops at transition region temperatures. We find three general classes of solutions for the quasi-static loop model, which we denote radiation-dominated loops, conduction-dominated loops, and classical loops. These solutions are then compared with observations. Departures from the classical scaling law of RTV are found for the solutions obtained. It is shown that loops of the type that we model here can make a significant contribution to lower transition regions emission via thermal conduction from the upper transition region.

Coronal Heating by Resonant Absorption: The Effects of Chromospheric Coupling

We present the first 2.5 dimensional numerical model calculations of the nonlinear wave dynamics and heating by resonant absorption in coronal loops with thermal structuring of the transition region and higher chromosphere. The numerical calculations were done with the Versatile Advection Code. The transition region can move freely and is transparent for mass motions from chromosphere to corona. The loops are excited at the chromospheric level by linearly polarized monochromatic Alfven waves. We find that the efficiency of resonant absorption can be much lower than in equivalent line-tied coronal loop models. The inefficiency is due to the fast rate at which slow magnetosonic waves are nonlinearly generated in the chromosphere and transition region. This leads to considerable transfer of energy from the Alfven wave to the magnetosonic waves. Consequently, only a relatively small fraction of the Poynting flux that is injected into the loop system at the chromospheric level is available at the coronal level. Cavity leakage and detuning also have a negative impact on the efficiency, but less so than the nonlinear energy transfer. Inclusion of radiative and conductive losses improves the efficiency of resonant absorption. While the efficiency of resonant absorption heating is low, our results indicate that heating by compression and dissipation of the slow magnetosonic waves and shocks can easily lead to a temperature rise of a few percent, and for larger driver amplitudes even to a rise over 10%. Hence, our results support the idea of indirect coronal heating through the nonlinear generation of magnetosonic waves that was put forward more than 20 yr ago. Furthermore, the large transition region and coronal density oscillations that are associated with the slow magnetosonic waves provide an explanation for some observed coronal and transition region loop extreme-ultraviolet intensity variations.

Effects on UV lines observations of stationary plasma flows confined in coronal loops

We describe a method which uses a rather detailed model of coronal loop hosting a siphon flow as a diagnostic tool to interpret solar UV and X-ray observations in selected bands and lines. We apply the method to investigate the deviations from ionization equilibrium induced by stationary plasma flows confined in coronal loops and their effects on the UV and EUV emission lines observed by the instruments on board SOHO. We present results on the detailed synthesis of loop emission in a set of selected emission lines observed by CDS and SUMER, taking into account the non-equilibrium of ionization effects.

Current sheet formation due to nonlinear kink modes in periodic and line-tied configurations

The full magnetohydrodynamic evolution of kink instabilities in cylindrical geometry is computed. The equilibria investigated serve as generic models of coronal loops. The effects of both periodic and line-tying boundary conditions at the axial ends of the cylinder are compared and contrasted. The net axial current, which is distributed internally to the loop, can be varied from case to case. It is found that one effect of the line-tying boundary condition is that the minimum length for the onset of a kink instability is increased. For line-tied loops, resonant surfaces do not exist, though linear analysis shows that there may or may not occur quasi-resonant regions, i.e., regions of strong gradients, which, however, are confined to the loop apex, far from the line-tied boundaries. When such a region is present for the linear mode, the formation and nonlinear development of current layers is confined to the central region of the loop. In a case where no such regions exist for the linear mode (corresponding to k⋅B≠0 in the periodic cylinder), current concentrations appear two thirds of the way from the center of the loop. This effect disappears in the axially periodic case. The consequences of these results for solar physics are discussed.

Density Structure in a Multicomponent Coronal Loop

We investigate the variation of species densities and electric field along a static model coronal loop consisting of electrons, protons, and heavier ions in a gravitationally stratified stellar atmosphere in an attempt to relate photospheric and coronal loop abundances. The loop plasma is assumed to be confined along a strong magnetic field line, so all forces transverse to the magnetic field are taken to be in balance and the loop can be modeled as a one-dimensional structure. Differential gravitational stratification of the ion species induces a polarization electric field along the loop. By invoking charge quasi-neutrality, we devise an iteration scheme to compute numerical solutions for the species densities and to prescribed accuracy; we also derive approximate analytic solutions. For confined coronal plasma loops that are sufficiently long lived for gravitational settling to occur (e.g., 1 day), severe reduction in coronal ion densities would be expected. Our self-consistent, multicomponent treatment predicts higher loop densities than those predicted by a model that neglects the effect of the heavy ions on the electric field; the density enhancement is an increasing function of the distance along the loop and of the ion charge and ranges from 4% for twice-ionized species to 33% for 14 times-ionized species at the top of an isothermal loop with T = 3 × 106 K and a radius of 109 cm.

Resonant Absorption of Alfven Waves in Steady Coronal Loops

The effect of equilibrium flow on linear Alfven resonances in coronal loops is studied in the compressible viscous MHD model. By means of a finite element code, the full set of linearised driven MHD equations are solved for a one-dimensional equilibrium model in which the equilibrium quantities depend only on the radial coordinate. Computations of resonant absorption of Alfven waves for two classes of coronal loop models show that the efficiency of the process of resonant absorption strongly depends on both the equilibrium parameters and the characteristics of the resonant wave. We find that a steady equilibrium shear flow can also significantly influence the resonant absorption of Alfven waves in coronal magnetic flux tubes. The presence of an equilibrium flow may therefore be important for resonant Alfven waves and coronal heating. A parametric analysis also shows that the resonant absorption can be strongly enhanced by the equilibrium flow, even up to total dissipation of the incoming wave.

Quasi‐Modes as Dissipative Magnetohydrodynamic Eigenmodes: Results for One‐dimensional Equilibrium States

Quasi-modes, which are important for understanding the MHD wave behavior of solar and astro-physical magnetic plasmas, are computed as eigenmodes of the linear dissipative MHD equations. This eigenmode computation is carried out with a simple numerical scheme, which is based on analytical solutions to the dissipative MHD equations in the quasi-singular resonance layer. Nonuniformity in magnetic field and plasma density gives rise to a continuous spectrum of resonant frequencies. Global discrete eigenmodes with characteristic frequencies lying within the range of the continuous spectrum may couple to localized resonant Alfven waves. In ideal MHD, these modes are not eigenmodes of the Hermitian ideal MHD operator, but are found as a temporal dominant, global, exponentially decaying response to an initial perturbation. In dissipative MHD, they are really eigenmodes with damping becoming independent of the dissipation mechanism in the limit of vanishing dissipation. An analytical solution of these global modes is found in the dissipative layer around the resonant Alfvenic position. Using the analytical solution to cross the quasi-singular resonance layer, the required numerical effort of the eigenvalue scheme is limited to the integration of the ideal MHD equations in regions away from any singularity. The presented scheme allows for a straightforward parametric study. The method is checked with known ideal quasi-mode frequencies found for a one-dimensional box model for the Earthïs magnetosphere (Zhu & Kivelson). The agreement is excellent. The dependence of the oscillation frequency on the wavenumbers for a one-dimensional slab model for coronal loops found by Ofman, Davila, & Steinolfson is also easily recovered.

The analysis system for astrophysical plasmas (ASAP) of the Osservatorio Astronomico di Palermo

We present the software package ASAP, mainly devoted to the presentation and analysis of fluid models of astrophysical plasmas. ASAP allows to generate optically thin X-ray and UV spectra emitted by plasma of given density, temperature and velocity, by means of well established spectral synthesis codes; the emission can then be easily folded with the instrumental response of interest and compared directly with measurements, or can be used to predict the performance of planned instruments. As examples of typical applications of the ASAP package, we show high resolution emission spectra derived from 1D static models of coronal loops, detailed fitting with coronal loop models of observations made with the ROSAT/PSPC instrument, hydrodynamic simulations of a solar flaring loop as seen by the Yohkoh satellite, and the evolution of line emission from a dense blob of interstellar plasma subject to the passage of a shock. The package, designed to be highly flexible, modular, and easily expandable, is expected to evolve and grow rapidly in response to new needs and required tasks. It operates within the IDL environment, and it is under consideration for being included in the SOHO Archive System.

Observational tests for nonequilibrium ionization in the solar corona

Nonequilibrium ionization may be produced by a variety of processes in the solar corona, for example, by mass flows through the large temperature gradients of the transition region or by impulsive heating and cooling. Any deviation from equilibrium ionization would have a strong effect on the radiation from the corona and on the interpretation of solar observations; hence, it is important to determine observational signatures of nonequilibrium. The temperature-sensitive line ratios can be used as such signatures. We examine the line ratios: C IV I(1548.2 A)/I(312.4 A), O IV I(789.4 A)/I(554.4 A), O V I(629.7 A)/I(172.2 A), O VI I(1031.9 A)/I(173.0 A) and O VI I(1031.9 A)/I(150.1 A). These line ratios are calculated for four coronal loop models that have a steady flow and that are known to have significant departures from equilibrium ionization. Our results indicate that, in general, nonequilibrium causes a considerable reduction in the line ratios, more than an order of magnitude in the downflowing leg of the loop model with the largest mass flows. We find that the C IV line ratio is the most sensitive to nonequilibrium. We discuss the implications of our results for observations, specifically, the observations expected from the upcoming SOHO mission.

Observing stellar coronae with the Goddard High Resolution Spectrograph. 1: The dMe star AU microscopoii

We report on an observation of AU Mic taken with the Goddard High Resolution Spectrograph (GHRS) aboard the Hubble Space Telescope. The data consist of a rapid sequence of spectra covering the wavelength range 1345-1375 A with a spectral resolution of 10,000. The observations were originally intended to search for spectral variations during flares. No flares were detected during the 3.5 hr of monitoring. A method of reducing the noise while combining the individual spectra in the time series is described which resulted in the elimination of half of the noise while rejecting only a small fraction of the stellar signal. The resultant spectrum was of sufficient quality to allow the detection of emission lines with an integrated flux of 10(exp -15) ergs/sq cm(sec) or greater. Lines of C I, O I, O V, Cl I, and Fe XXI were detected. This is the first indisputable detection of the 1354 A Fe XXI line, formed at T approximately = 10(exp 7) K, on a star other than the Sun. The line was well resolved and displayed no significant bulk motions or profile asymmetry. From the upper limit on the observed line width, we derive an upper limit of 38 km/s for the turbulent velocity in the 10(exp 7) K plasma. An upper limit is derived for the flux of the 1349 A Fe XII line, formed at T approximately = 1.3 x 10(exp 6) K. These data are combined with contemporaneous GHRS and International Ultraviolet Explorer (IUE) data to derive the volume emission measure distribution of AU Mic over the temperature range 10(exp 4)-10(exp 7) K. Models of coronal loops in hydrostatic equilibrium are consistent with the observed volume emission measures of the coronal lines. The fraction of the stellar surface covered by the footprints of the loops depends upon the loop length and is less than 14% for lengths smaller than the stellar radius. From the upper limit to the estimated width of the Fe XXI line prfile we find that the we cannot rule out Alfven wave dissipation as a possible contributor to the required quiescent loop heating rate.

Siphon Flows in Stratified Coronal Loops

AbstractWe have developed a detailed siphon flow model for coronal loops. We find scaling laws relating the characteristic parameters of the loop, explore systematically the space of solutions and show that supersonic flows are impossible for realistic values of heat flux at the base of the upflowing leg.

A coronal loop model for the production of X-ray and radio flares in the RS CVn binary HR 1099

The RS CVn binary stellar system HR 1099 is a source of both X-ray and radio flares. We present here a model of the system in which the two types of flare are produced by the same population of mildly-relativistic (γ ≲ 10) electrons, injected into a coronal loop. After reviewing possible radiation mechanisms we conclude that, given the probable conditions in the flaring region, the radio emission is gyrosynchrotron radiation and the X-ray emission is thermal bremsstrahlung. The thermal X-ray source must lie in the stellar chromosphere, but the apparent absence of plasma absorption at radio frequencies indicates that the radio source is located high in the coronal loop. Using the relationships given by Dulk and Marsh (1982) for the radio emission from a power-law electron energy spectrum,N(γ)α (γ - 1)−δ, we conclude that 3 ≲δ ≲ 7, with ≳ 30% of the electron population trapped in the radio source. Some implications of these results for one particular version of the model are discussed.

Radio emission of loop structures on the sun at near-critical frequencies

An exact formula is derived for the optical thickness of an inhomogeneous plasma layer (Epstein layer) that simulates a loop structure on the sun for a wave of TE polarization and oblique incidence. Constraints on the angle of incidence on the current layer are found for which the formula for optical thickness also describes well the case of TM polarization. Elementary coronal-loop models are examined and it is shown that the radioemission intensity spectrum without allowance for the magnetic field can have a broad peak at frequencies close to the plasma frequency at the center of the layer. A comparison with observation data is performed.

Thermal conduction and modeling of static stellar coronal loops

We have modeled stellar coronal loops in static conditions for a wide range of loop length, plasma pressure at the base of the loop and stellar surface gravity, so as to describe physical conditions that can occur in coronae of stars ranging from low mass dwarfs to giants as well as on a significant fraction of the Main-Sequence stars.

A Model for Intermediate Temperature Solar Coronal Loops

AbstractSimple hydrostatic equilibrium models have been very successful at describing the physical conditions in hot coronal loops (T > 106 K). However, equilibrium models of cooler loops predict densities that are much lower than observed. We follow the evolution of a hot loop which undergoes a sudden reduction in heat input. The physical conditions in the cooling loop show significant departures from equilibrium. Such models appear to be able to reproduce the physical conditions observed in intermediate temperature loops (105 < T < 106 K).

Rocket observations and modelling of flux-tubes

The solar observations at high angular resolution have led to the discovery that the solar magnetic field is structured in filamentary fields at the photospheric level. Manifestations of these fluxtubes can be diagnosed with EUV images (with the Transition Region Camera Rocket Experiment, TRC) at 220nm in the middle photosphere, at 160nm in the temperature minimum region or in the Ly alpha and C IV lines formed at temperatures 20 000K and 100 000K in the transition region. In the frame of a thin flux tube modelling of the TRC data, the vertical variation of tube parameters and the conditions for thermalisation in the upper photosphere are discussed. We consider constraints from EUV observations on current models of flux-tubes and coronal loops including non LTE calculations, dynamic and magnetic effects.

The effects of nonequilibrium ionization on the radiative losses of the solar corona

The emissivity of the ions of carbon and oxygen has been recalculated for a set of solar coronal loop models with a steady state siphon flow. The ion densities were calculated from the plasma velocities, temperatures, and densities of the models, and large departures from equilibrium were found. For purposes of comparison, the emissivity was calculated with and without the approximation of ionization equilibrium. Considerable differences in the radiative loss function Lambda(T) curve between equilibrium and nonequilibrium conditions were found. The nonequilibrium Lambda(T) function was then used to solve again the steady state flow equations of the loop models. The differences in the structure of these models with respect to the models calculated adopting the Lambda(T) curve in equilibrium are discussed.