A model of hot loops associated with solar flares

A dynamical model is proposed for the formation of soft X-ray emitting hot loops in solar flares. It is examined by numerical simulations how a solar model atmosphere in a magnetic loop changes its state and forms a hot loop when the flare energy is released in the form of heat liberation either at the top part or around the transition region in the loop.When the heat liberation takes place at the top part of the loop which arches in the corona, the plasma temperature around the loop apex rises rapidly and, as the result, the downward thermal conductive flux is increased along the magnetic tube of force. Soon after the thermal conduction front rushes into the upper chromosphere, a local peak of pressure is produced near the conduction front and the chromospheric material begins to expand into the corona to form a high-temperature (10⁷ K-3 × 10⁷ K at the loop apex) and high-density (10¹⁰ cm^–3-10¹¹ cm^–3 at the loop apex) loop. The velocity of the expanding material can reach a few hundred kilometres per second in the coronal part. The thermal conduction front also plays a role of piston pushing the chromospheric material downward and gives birth to a shock wave which propagates through the minimum temperature region into the photosphere. If, on the other hand, the heat source is placed around the transition region in the loop, the expansion of the material into the corona occurs from the beginning of the flare and the formation process of the hot loop differs somewhat from the case with the heat source at the top part of the loop.Thermal components of radiations emitted from flare regions, ranging from soft X-rays to radio wavelengths, are interpreted in a unified way by using physical quantities obtained as functions of time and position in our flare loop model as will be discussed in detail in a following paper.     

Evolution of the high-temperature plasma in the 15 June 1973 flare

The analysis of the high temperature plasma in Fe xxiii–xxiv in the 15 June 1973 flare is presented. The observations were obtained with the NRLXUV spectroheliograph on Skylab. The results are: (1) There was preheating of the active region in which the flare occurred. In particular, a large loop in the vicinity of the flaring region showed enhanced brightness for many hours before the flare. The loop disappeared when the flare occurred, and returned in the postflare phase, as if the energy flux which had been heating the large loop was blocked during the flare and restored after the flare was gone. The large magnetic fields did not change significantly. (2) The flare occurred in low-lying loop or loops. The spatial distribution of flare emission shows that there was a temperature gradient along the loop. (3) The high temperature plasma emitting Fe xxiii and xxiv had an initial upward motion with a velocity of about 80 km s^–1. (4) There was large turbulent mass motion in the high temperature plasma with a random velocity of 100 to 160 km s^–1. (5) The peak temperature of the hot plasma, determined from the Fe xxiii and xxiv intensity ratio, was 14 × 10⁶ K. It decreased slightly and then, for a period of 4 min, remained at 12.6 × 10⁶ K before dropping sharply to below 10 × 10⁶ K. The density of the central core of the hot plasma, determined from absolute intensity of Fe xxiv 255 Å line, was of the order of 10¹¹ cm^–3.The persistence of the high level of turbulence and of the high temperature plateau in the decaying phase of the flare indicates the presence of secondary energy release. From the energy balance equation the required energy source is calculated to be about 3 to 7 ergs cm^–3 s^–1.Ball Brothers Research Corporation.     

Discrete subresolution structures in the solar transition zone

During operations on the Spacelab-2 Shuttle mission, the NRL High Resolution Telescope and Spectrograph (HRTS) recorded spectra of a variety of solar features in the 1200–1700 Å wavelength region which contains spectral lines and continua well suited for investigating the temperature minimum, the chromosphere and transition zone. These data show that, at the highest spatial resolution, the transition zone spectra are broken up from a continuous intensity distribution along the slit into discrete emission elements. The average dimensions of these discrete transition zone structures is 2400 km along the slit, but an analysis of their emission measures and densities shows that the dimensions of the actual emitting volume is conciderably less. If these structures are modelled as an ensemble of subresolution filaments, we find that these filaments have typical radii of from 3 to 30 km and that the cross-sectional fill factor is in the range from 10^–5 to 10^–2. The transport of mass and energy through these transition zone structures is reduced by this same factor of 10^–5 to 10^–2 which has significant consequences for our understanding of the dynamics of the solar atmosphere. Because the HRTS transition zone line profiles are not broadened by resolved large-spatial-scale solar velocity fields, the line widths of the Civ lines have been analyzed. The average line width is 0.195 Å (FWHM) and requires an average nonthermal velocity of 16 km s^–1 (most-probable) or 19 km s^–1 (root-mean-square) which is lower than previously observed values.     

Plasma waves caused by transient heat conduction in a coronal loop and anomalous resistivity

Numerical simulation is made of the transient heat conduction during local heating in a model coronal magnetic loop with an axial electric current. It is assumed that a segment near the top of the normal coronal loop is heated to above 10⁷ K by a sufficiently small heat input as compared with the total flare energy. A hump appears in the velocity distribution of electrons moving down the temperature gradient with speeds slightly below the thermal one. Consequently, electron plasma waves are excited. The high intensity of the waves persists in the upper region of the loop for more than a second until the termination of the simulation. The energy density of the plasma waves normalized with respect to thermal density is 10^–3.5 at maximum. A theoretical estimate gives an anomalous resistivity 5 orders of magnitude greater than an initial value. Based on the above result, we propose a model for impulsive loop flares.     

Spatial and temporal variations of solar coronal loops

Skylab EUV observations of an active region near the solar limb were analyzed. Both cool (T < 10⁶ K) and hot (T > 10⁶ K) loops were observed in this region. For the hot loops the observed intensity variations were small, typically a few percent over a period of 30 min. The cool loops exhibited stronger variations, sometimes appearing and disappearing in 5 to 10 min. Most of the cool material observed in the loops appeared to be caused by the downward flow of coronal rain and by the upward ejection of chromospheric material in surges. The frequent EUV brightenings observed near the loop footpoints appear to have been produced by both in situ transient energy releases (e.g. subflares) and the infall/impact of coronal rain. The physical conditions in the loops (temperatures, densities, radiative and conducting cooling rates, cooling times) were determined. The mean energy required to balance the radiative and conductive cooling of the hot loops is approximately 3 × 10^–3 erg cm^–3 s^–1. One coronal heating mechanism that can account for the observed behavior of the EUV emission from McMath region 12634 is heating by the dissipation of fast mode MHD waves.     

Steady models for the hard X-ray loops in the solar corona

In some gradual hard X-ray bursts with high intensity, hard X-ray source (15–40 keV) is steadily located in the corona along with softer X-ray source (5–10 keV).Two stationary models, high density and high temperature models, are proposed to solve the difficult problem of confinement of hot (or nonthermal) plasma in the direction of the magnetic field along the loops in the corona. In both models, an essential point is that the effective X-ray source is composed of fine dense filamentary loops imbeded in a larger rarefied coronal loop, and the electron number density in the filaments is so high as 10¹¹–10¹² cm^-3. If the density is so high heat conduction can be as reasonably small as of the order of 10²⁷ erg s ^-1 for the given emission measures of observed X-rays, since the required cross-sectional area is small and also classical conduction is valid. Collisional confinement of thermal tail, and nonthermal electrons if any, up to 50–60 keV in the filaments is also possible, so that the hard X-ray images can be loop like structure instead of double source (foot points).High density model is applicable to the coronal filamentary loops with temperature T _m < 5 × 10⁷ K at the loop summit. The heat flow from the summit downwards is lost almost completely by the radiation from the loop during the conduction to the foot points. A continuous energy release is assumed near the summit to maintain the stationary temperature T _m, and pressure balance is maintained along the loop. In this model, the number density at the summit is given by n _m - 10⁶ T _m ² /s_m, where s _m is the length of the loop from the summit to the foot point, and the distribution of temperature and density along the loop are given by T = T _m(s/s_m)^1/3 and n = n _m(s/s_m)^-1/3, respectively.High temperature model is applicable to the filamentary loops with higher temperature up to about 10^8.5 K and comparatively lower number density as 10¹¹ cm^-3 for the requirement of magnetic confinement of the hot plasma in radial direction. The radiation from the loop is negligibly small in this model so that the heat flux is nearly conserved down to the foot points. In this case, temperature gradient is smaller than that of the high density model, depending on the tapering of the magnetic bottle.In both models, the differential emission measure is maximum at the highest temperature T _m and the brightness distribution along the loop shows a maximum around the summit of the loop if some magnetic tapering is taken into account.     

Energy balance in the chromosphere-corona transition region

The classical picture of the transition region is that of a thin spherically symmetric shell maintained in a steady average thermodynamical state by a balance between conductive heating from the hot overlying corona and radiative losses. The further analysis of existing extreme ultraviolet flux data casts doubt on the correctness of this simple model. It is shown that the downward heat flux between the chromosphere and corona cannot be nearly as large as the value 6 × 10⁵ erg cm^–)= 13.46 - 2.99 sin² s^–1 derived in previous studies by assuming a planar atmosphere, and in fact is insufficient to balance transition-region radiative losses. An alternative picture is developed, consisting of a transition region network covering only a small fraction of the solar disk. The dissipation of mechanical energy, previously neglected in many calculations of theoretical transition region models, appears to play a dominant role in the local energy balance of the network.The National Center for Atmospheric Research is sponsored by the National Science Foundation.     

The masers of E-type methanol in orion KL and SGR B2

Using a simplified model the statistical equilibrium and radiative transfer equations of E-type-CH₃OH are solved for Orion KL and SgrB2. According to our calculation results and the observation data taken by Matsakiset al. (1980) and Morimotoet al. (1985a, b), the physical conditions of both sources are estimated. In theJ ₂-J ₁ E methanol maser region of Orion KL, the density, kinetic temperature, dust temperature, and the fractional abundance are 0.8–2×10⁶ cm^–3, 150, 30–90 K, 0.8–8×10^–6. In the 4_–1-3₀ E and 5_–1-4₀ E methanol maser region of Sgr B2 the correspondance physical conditions above are 10⁴ cm³, 45, 23 K, and 7×10^–7, respectively.     

The coronal and transition region temperature structure of a solar active region

Using measurements of EUV and X-ray spectral lines we derive the differential emission measure vs electron temperature T from the transition region to the corona of an active region (10⁵ T <5 × 10⁶ K). The total emission measure and radiative losses are of order 3 × 10⁴⁸ cm^–3 and 4 × 10²⁶ ergss^–1 respectively. The emission measure at T > 10⁶ K (i.e. that mainly responsible for the X-ray emission) is about 75% of the total. We also examine the use of Mg x 625 Å as an indicator of coronal electron density. A set of theoretical energy balance models of coronal loops in which the loop divergence is a variable parameter is presented and compared with the observations. Particular attention is given to the limitations inherent in any such comparison.     

A model of impulsive loop flares caused by anomalous heat conduction

Numerical simulation is made of the impulsive loop flare caused by transient heat conduction along the loop with an applied axial electric current.It is assumed that a segment near the top of the coronal loop is heated to above 10⁷ K by a heat input that is small compared with the total flare energy, which is given by the magnetic energy of the initial current. Due to the heat conduction, a hump appears in the velocity distribution of electrons, which may excite electron plasma waves with a sufficiently high intensity to cause an anomalous resistivity, as shown theoretically in a previous paper. In that paper, an effect of the plasma waves on the dynamics of electrons was taken into account consistently, but an anomalous heating due to an ohmic dissipation of the initial current under the anomalous resistivity was not taken into account.The aim of the present study is to study the subsequent dynamics of the heated gas caused by the anomalous heating, but in order to avoid an unpractically long computation time, the energy density of the plasma waves is estimated by the energy density of electrons in the velocity hump, without taking into account the effect of the plasma waves consistently in the dynamics of the electrons.The initial current starts to decay gradually by an ohmic dissipation under the anomalous resistivity occurring near the top of the loop to heat this region more. The enhanced heat conduction causes the velocity humps in a wider location. Consequently, the anomalous heating continues and spreads in a self-generating way even after the end of the initial minor heating. Thus the temperature near the loop top becomes above 10⁸ K and the high-temperature region spreads in both directions along the loop with such a high speed as (2–3) × 10⁴ km s^–1, which is nearly equal to the speed of flux-limited heat conduction. On the other hand, induced electric field estimated from the anomalous resistivity is 3.3 × 10⁷ V at the termination of the present simulation, under the modest initial current of 1.5 A m^–2.X-ray emissions expected from the present model loop, show three sources, two footpoints with unequal brightness and a coronal source expanding along the loop in both directions.     

Analysis of the emission line spectra of a solar flare observed from Skylab

The EUV emission spectra in the wavelength range 110–1900 Å of the 5 September 1973 flare observed with the NRL slit spectrograph on Skylab are studied. The results are: (1) The chromospheric and transition-zone lines are greatly enhanced during the flare. In particular, the allowed lines are enhanced more than the intersystem lines. The Ni ii and P ii lines show the greatest enhancement with a factor of 800 increase in intensity. Other lines such as O i, C i, Si iii, S iii, S iv, O iv, O v, and N v show increases in intensity 10–100 times during the flare. (2) The chromospheric lines, although greatly enhanced during the flare, maintain their sharp and gaussian profiles and are not appreciably broadened. The transition zone lines, on the other hand, show a red-shifted component during the initial phase of the flare. The deduced downward velocity in the transition zone is 50 km s^–1. In addition, there are large turbulent mass motions. The downward mass motion is probably caused by the pressure imbalance between the flare hot plasma at 13 × 10⁶ K and the cooler plasma at 10⁵ K. (3) The density of the 10⁵ K flare plasma, as deduced from density-sensitive lines, is greater than 10¹² cm^-3. The depth of the 10⁵ K plasma in the flare transition zone is only of the order of 0.1 km, giving a steep temperature gradient. Consideration of the energy balance between the conductive flux and the radiative energy losses shows that, indeed, the high density in the transition zone requires that its thickness be very small. This is a consequence of the maximum radiative efficiency at the temperature around 10⁵ K in the solar plasma.Ball Brothers Research Corporation.     

Prominence–corona transition region plasma diagnostics from SOHO observations

New results concerning prominence observations and in particular the prominence–corona transition region (PCTR) are presented. In order to cover a temperature range from 2 × 10⁴ to 7 × 10⁵ K, several emission lines in many different ionization states were observed with SUMER and CDS on board SOHO. EM and DEM were measured through the whole PCTR. We compared the prominence DEM with the DEM from other solar structures (active region, coronal hole and the chromosphere–corona transition region (CCTR)). We notice a displacement of the prominence DEM minimum towards lower temperatures with respect to the minimum of the other structures. Electron density and pressure diagnostics have been made from the observed C III lines. Local electron density and pressure for T ∼ 7 × 10⁴ K are respectively log N _e = 9.30_−0.34 ^+0.30 and 0.0405_−0.014 ^+0.012. Extrapolations over the entire PCTR temperature range are in good agreement with previous SOHO results (Madjarska et al., 1999). We also provide values of electron density and pressure in two different regions of the prominence (center and edge). The Doppler velocity in the PCTR shows a trend to increase with temperature (at least up to 30 km s -1 at T ∼ 7 × 10⁴ K), an indication of important mass flows. A simple morphological model is proposed from density and motion diagnostics. If the prominence is taken as a magnetic flux tube, one can derive an opening of the field lines with increasing temperature. If the prominence is represented as a collection of threads, their number increases with temperature from 20 to 800. Derived filling factors can reach values as low as 10⁻³ for a layer thickness of the order of 5000 km. The variation of non-thermal velocities is determined for the first time, in the temperature range from 2 × 10⁴ to 7 × 10⁵ K. The quite clear similarity with the CCTR non-thermal velocities would indicate that heating mechanisms in the PCTR could be the same as in the CCTR (wave propagation, turbulence MHD).     

Transequatorial loops interconnecting McMath regions 12472 and 12474

We discuss the life-story of a transequatorial loop system which interconnected the newly born active region McMath 12474 with the old region 12472. The loop system was probably born through reconnection accomplished 1.5 to 5 days after the birth of 12474 and the loops were observed in soft X-rays for at least 1.5 days. Transient sharpenings of the interconnection and a striking brightening of the whole loop system for about 6 hr appear to be caused by magnetic field variations in the region 12474. A flare might have been related to the brightening, but only in an indirect way: the same emerging flux could have triggered the flare and at the same time strengthened the magnetic field at the foot-points of the loops. Electron temperature in the loop system, equal to 2.1 × 10⁶ K in its quiet phase, increased to 3.1 × 10⁶ K during the brightening. Electron density in the loop system was 1.3 × 10⁹ cm^–3 and it could be estimated to 7 × 10⁸ cm^–3 prior to the brightening. During the brightening the loops became twisted. There was no obvious effect whatsoever of the activity in 12474 upon the in erconnected old region. The final decay of the loop system reflected the decay of magnetic field in the region 12474.     

Density and temperature diagnostics of solar emission lines from NeVI and MgVI

Line intensity ratios of NeVI lines with respect to a resonance line of MgVI have been considered for electron density and temperature determinations within the chromosphere-corona transition region. The electron pressure within the transition region has been assumed to be constant. In addition, these ratios would enable us to estimate the relative element abundances of neon to magnesium. An attempt has been made to explain the extreme ultraviolet intensities of NeVI and MgVI lines as observed by ATM ultraviolet spectrometer. The observed intensities correspond to the average quiet-Sun conditions near solar minimum. Theoretical intensities for NeVI and MgVI lines have been computed using a model solar atmosphere. Theoretical intensities obtained by using the values 3.98 × 10^–5 and 3.16 × 10^–5 for element abundance of Ne and Mg, respectively, seem to agree well with the expected intensities. The agreement between some of the expected and computed intensities suggests the need for future observations at higher spectral resolutions to resolve difficulties arising out of blending due to two or more lines.     

Electron density and temperature structure of two limb active regions observed by SOHO-CDS

The analysis of two active regions on the limb using observations from SOHO-CDS allows us to determine the electron density and temperature distribution of the coronal emission. We find that the active regions have hot cores (3×10⁶ K) with larger cooler (10⁶ K) loop structures extending above the limb. The electron number density, determined using the Si X diagnostic line ratio, is found to be highest in the active region core (greater than 2.3×10⁹ cm^–3). Electron number density values are determined for a range of spectral lines from different ions and are found to increase with temperature between 0.8 and 2.5×10⁶ K. These results are consistent with recent models of enhanced heating along the compact core of active regions, where the magnetic field shear is strongest.     

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.Three alternative formulations of heat conduction have been used in the energy balance equation, depending on the ratio ₀/L _Tbetween electron mean free path and temperature scale height: Spitzer's formulation for ₀/L _Tless than 2 × 10^–3, the Luciani, Mora, and Virmont non-local formulation for ₀/L _Tbetween 2 × 10^–3 and 6.67 × 10^–3 and the limited free-streaming formulation for ₀/L _Tlarger than 6.67 × 10^–3.We report the characteristics of all loop models studied, and present examples to illustrate how the temperature and density stratification can be drastically altered by the different conductivity regimes. Significant differences are evident in the differential emission measure distribution vs temperature, an important observable quantity. We also show how physical conditions of coronal plasma, and in particular thermal conduction, change with stellar surface gravity.We have found that, for fixed loop length and stellar gravity, a minimum of loop-top plasma temperature occurs, corresponding to the highest value of base plasma pressure for which the limited free-streaming conduction occurs. This value of temperature satisfies the appropriate scalingT 10^–9 L g, in cgs units.     

Large-Scale Structure of the Atmosphere of the Quiet Sun,Coronal Holes,and Plages as Deduced by Tomography Study

We present here the results of emission tomography studies, based on a new differential deconvolution method (DDM) of Laplace transform inversion, which we use for reconstruction of the coronal emission measure distributions in the quiet Sun, coronal holes and plage areas. Two methods are explored. The first method is based on the deconvolution of radioemission brightness spectra in a wide wavelength range (1 mm–100 cm) for temperature profile reconstructions from the corona to the deeper chromosphere. The second method uses radio brightness measurements in the cm–dm range to give a coronal column emission measure (EM).Our results are based on RATAN-600 observations in the range 2.0–32 cm supplemented by the data of other observatories during the period near minimum solar activity. This study gives results that agree with known estimates of the coronal EM values, but reveals the absence of any measurable quantities of EM in the transition temperature region 3 × 10⁴ –10⁵ K for all studied large-scale structures. The chromospheric temperature structure (T _e = 20,000–5800 K) is quite similar for all objects with extremely low-temperature gradients at deep layers.Some refraction effects were detected in the decimeter range for all Types of large-scale structures, which suggests the presence of dense and compact loops (up to N _e =(1–3)× 10⁹ cm^-3 number density) for the quiet-Sun coronal regions with temperature T _e > 5× 10^-5 K.     

Search for Microflaring Activity in the Magnetic Network

We analyze the temporal behavior of network bright points (NBPs) searching for low-atmosphere signatures of flares occurring on the magnetic network. We make use of a set of data acquired during coordinated observations between ground-based observatories (NSO/Sacramento Peak) and the MDI instrument on board SOHO. Light curves in chromospheric spectral lines show only small-amplitude temporal variations, without any sudden intensity enhancement that could suggest the presence of a transient phenomenon such as a (micro)flare. Only one NBP shows spikes of downward velocity, of the order of 2–4 km s^–1, considered as signals of compression associated with a (micro)flare occurrence. For this same NBP, we also find a peculiar relationship between the magnetic and velocity fields fluctuations, as measured by MDI. Only for this point the B–V fluctuations are well correlated, suggesting the presence of magneto-acoustic waves propagating along the magnetic structure. This correlation is lost during the compression episodes and resumes afterward. An A6 GOES soft X-ray burst is temporally associated with the downward velocity episodes, suggesting that this NBP is the footpoint of a flaring loop. This event has a total thermal energy content of about 10²⁸ erg, and, hence, belongs to the microflare class.     

The diffusion model of cosmic-ray propagation

We set up diffusion equations for the nuclear component of cosmic rays and solve these to find the ratio of light to medium nuclei in the cosmic rays as well as the gamma-ray distribution in our Galaxy. From a comparison of our calculated quantities with observational data we determine the values of various parameters appearing in the model. We find that best agreement between theory and observations is obtained if the cosmic-ray confinement region consists of a narrow disk of total height 160 pc and radius 16 kpc, where the cosmic-ray sources are located, and an extensive halo of height 20 kpc. The diffusion coefficient near the Sun must be between 10²⁶ and 10²⁷ cm² s^–1 while it equals 10²⁸ to 10²⁹ cm² s^–1 in the halo. Finally, we find that the diffusion coefficient in the Galaxy must depend on the gas density as a power law with an index of the order of –1.