Thermal equilibria of coronal magnetic loops

Equations of thermal equilibrium along coronal loops with footpoint temperatures of 2 × 10⁴ K are solved. Three fundamentally different categories of solution are found, namely hot loops with summit temperatures above about 4 × 10⁵ K, cool loops which are cooler than 8 × 10⁴ K along their whole length and hot-cool loops which have summit temperatures around 2 × 10⁴ K but much hotter parts at intermediate points between the summit and the footpoints. Hot loops correspond to the hot corona of the Sun. The cool loops are of relevance for fibrils, for the cool cores observed by Foukal and also for active-region prominences where the magnetic field is directed mainly along the prominence. Quiescent prominences consist of many cool threads inclined to the prominence axis, and each thread may be modelled as a hot-cool loop. In addition, it is possible for warm loops at intermediate summit temperatures (8 × 10⁴K to 4 × 10⁵ K) to exist, but the observed differential emission measure suggests that most of the plasma in the solar atmosphere is in either the hot phase or the cool phase. Thermal catastrophe may occur when the length or pressure of a loop is so small that the hot solution ceases to exist and there are only cool loop solutions. Many loops can be superimposed to form a coronal arcade which contains loops of several different types.     

Catastrophic cooling and high-speed downflow in quiescent solar coronal loops observed with TRACE

Observations with the Transition Region and Coronal Explorer, TRACE, show frequent catastrophic cooling and evacuation of quiescent solar coronal loops over active regions. We analyze this process using image sequences taken in passbands showing plasma from a few million degrees down to less than 100 000 K, taken at a cadence of 90 s. The loop evacuation often occurs after plasma high in the corona has cooled to transition-region or even chromospheric temperatures. The cooling loops frequently show Lyman-α and C iv emission developing initially near the loop tops; later, that cool plasma usually slides down on both sides of the loop. The relatively cool material often forms clumps that move at speeds of up to 100 km s⁻¹. The downward acceleration is no more than 80 m s⁻², less than of the surface gravity. Cooling appears to progress with delays of the order of up to 10³ s between thin, neighboring strands within flux bundles with cross-sections of at least 1–2 Mm, so that hot and cool loops are transiently outlined at essentially the same location. The falling material at temperatures of ≲ 0.1 MK shows no evidence of loop braiding on scales above the resolution of ∼1 Mm; loop cross-sections appear independent of height. Existing numerical models suggest that the observed catastrophic loop-top cooling in non-flaring conditions can occur if the loop heating precipitously drops by 1.5 orders of magnitude or more, first and most strongly high in the corona. Using order-of-magnitude geometrical arguments, we estimate that loop bundles in the interior of an active region undergo catastrophic cooling on average once every 2 days, while in a decayed bipolar region that time interval is approximately a week. Supplementary material to this paper is available in electronic form at http://dx.doi.org/10.1023/A:1005211925515     

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.     

The Nature of Blinkers and the Solar Transition Region

Solar plasma that exists at around 10⁵ K, which has traditionally been referred to as the solar transition region, is probably in a dynamic and fibril state with a small filling factor. Its origin is as yet unknown, but we suggest that it may be produced primarily by one of five different physical mechanisms, namely: the heating of cool spicular material; the containment of plasma in low-lying loops in the network; the thermal linking of cool and hot plasma at the feet of coronal loops; the heating and evaporating of chromospheric plasma in response to a coronal heating event; and the cooling and draining of hot coronal plasma when coronal heating is switched off. We suggest that, in each case, a blinker could be produced by the granular compression of a network junction, causing subtelescopic fibril flux tubes to spend more of their time at transition-region temperatures and so to increase the filling factor temporarily.     

Ultraviolet Observations of a Dynamic Event in the Solar Corona

The Solar Ultraviolet Measurements of Emitted Radiation instrument (SUMER) observations show high Doppler shifts and temporal variations in profiles of ultraviolet lines from low temperature gas in the corona above the active region NOAA 7974. The profiles indicate 100 km s^-1 flows coming from an almost stationary source that appears bright in the lines of N III and Si III. The variations in line-of-sight velocities and intensities suggest small knots of cooling plasma emanating from a small region high in the corona. A few arc sec sunward of the region where the cool flows are seen is an elongated region of enhanced higher temperature, low velocity Ne VI and Mg VI line emission.     

The XUV structure of solar active regions

XUV spectroheliograms of 2 active regions are studied. The images are due to lines emitted at temperatures between 8 x 10⁴ K and 2 x 10⁶ K and thus are indicative of transition region and coronal structures. The hot coronal lines are formed solely in loop structures which connect regions of opposite photospheric magnetic polarity but are not observed over sunspots. Transition region lines are emitted in plages overlying regions of intense photospheric magnetic field and in loops or loop-segments connecting such regions. The hot coronal loops are supported hydrostatically while only some of the transition zone loops are. The coronal and transition zone loops are distinctly separated and are not coaxial. A comparison of direct measurements of electron densities using density sensitive line ratios with indirect measurements using emission measures and path lengths shows the existence of fine structures of less than a second of arc in transition region loops. From a similar analysis, hot coronal loops do not have any fine structure below about 2 seconds of arc.     

Spatial distribution of XUV emission and density in a loop prominence

We have studied the spatial distribution of XUV emission in the 14 August, 1973 loop prominence observed with the NRL spectroheliograph on Skylab. The loop prominence consists of two large loops and is observed in lines from ions with temperatures ranging from 5 × 10⁴ K to 3 × 10⁶ K. The loops seen in low temperature (10⁶K) lines such as from He ii, Ne vii, Mg vii, Mg viii, and Si viii are systematically displaced from loops seen in higher temperature lines such as from Si xii, Fe xv, and Fe xvi. The cross section of the loop, particularly in cooler lines is nearly constant along the loop. For hotter loops in Si xii, Fe xv, and Fe xvi, however, emission at the top of the loop is more intense and extended than that near the footpoints, which makes the loops appear wider at the top.There is no evidence that the 14 August loop prominence consists of a cooler core surrounded by a hot sheath as in some active region and sunspot loops reported by Foukal (1975, 1976). Rather, the observed spatial displacement between cooler and hotter loops suggest that the 14 August loop prominence is composed of many magnetic flux tubes, each with its own temperature.Ball Corporation. Now with NASA/Marshall Space Flight Center.     

Active Regions Observed in Extreme Ultraviolet Light by the Coronal Diagnostic Spectrometer on Soho

We present observations of five active regions made by the Coronal Diagnostic Spectrometer (CDS) on the Solar and Heliospheric Observatory (SOHO). CDS observes the Sun in the extreme ultraviolet range 150–780 Å. Examples of active region loops seen in spectral lines emitted at various temperatures are shown. Several classes of loops are identified: those that are seen in all temperatures up to 2 x 10⁶ K; loops seen at 10⁶ K but not reaching 1.6 x 10⁶ K; those at temperatures 2– 4 x 10^-5 K and occasionally at 6 x 10^-5 K but not reaching 10⁶ K. An increasing loop size with temperature and the relationship between the cool and hot structures is discussed. CDS observations reveal the existence of loops and other unresolved structures in active regions, at temperatures between 1.5– 4 x 10^-5 K, which do not have counterparts in lines emitted above 8 x 10^-5 K. Bright compact sources only seen in the transition region lines are investigated. These sources can have lifetimes of up to several days and are located in the vicinity of sunspots. We study the variability of active region sources on time scales from 30 sec to several days. We find oscillatory behaviour of Hei and Ov line intensities in an active region on time scales of 5–10 min.     

Thermal equilibria of coronal magnetic loops with non-constant cross-sectional area

Equations of thermal equilibrium along coronal loops are solved in the absence of gravity but where the cross-sectional area changes along the loop. The footpoint temperature is assumed to be 2 × 10⁴ K. Several fundamental types of solution are found, namely hot loops, cool loops, hot-cool loops (where the footpoints and summits are cool but the intermediate parts are hotter) and warm loops (cool along most of their lengths except the summits). On increasing the cross-sectional area the summit temperature generally increases slightly except for warm loops where no increase in temperature is recorded and hot-cool loops where a dramatic increase in summit temperature may occur. The cool and hot-cool loops may model elementary fibril structures within prominences.     

Thermal equilibria of coronal magnetic arcades

A coronal magnetic arcade can be thought of as consisting of an assembly of coronal loops. By solving equations of thermal equilibrium along each loop and assuming a base temperature of 2 × 10⁴ K, the thermal structure of the arcade can be found. By assuming a form for the plasma pressure in the arcade, the possible thermal structures can be shown to depend on three parameters. Arcades can contain hot loops with summits hotter than 400 000 K, cool loops at temperatures less than 80 000 K along their lengths, hot-cool loops with cool summits and cool footpoints but hotter intermediate portions, and warm loops, cooler than 80 000 K along most of their lengths but with summits as hot as 400 000 K. For certain arcades, there exist regions where more than one kind of loop is possible. If the parameters describing the arcade are varied, it is possible for non-equilibrium to occur when a type of solution ceases to exist. For example, hot or warm loops can cease to exist so that only cool solutions are possible when the arcade size or pressure is decreased, while warm or cool loops may give way to hot-cool loops when the heating is reduced or the pressure is increased.     

Type I noise storms and the structure of the extreme ultraviolet corona

The spatial fine structure of the solar corona as observed in the EUV line Fexv is compared with the occurrence of major type I metric noise storms. In all cases, strong changes in the loop structure of the corona are observed. On the disk, these coronal changes are correlated to the emergence of new magnetic flux in the vicinity of existing large active regions. The reverse is demonstrated: during noise storm free periods no coronal changes can be observed. Noise storms at the limb seem to originate in open field configurations over active regions. In all cases, reconnection of coronal magnetic fields over large distances are the cause of noise storms rather than changes of magnetic fields within an active region. Noise storms disappear or are weak at the limb because of foreground absorption in chains of active regions. The observed intensities of active region loops at the limb show that a density of 1.3 × 10⁹ cm^?3 which corresponds to a plasma frequency of 100 MHz can occur over a wide variety of altitudes because active region loops are not in hydrostatic equilibrium.     

Morphology and spatial distribution of XUV and X-ray emissions in an active region observed from Skylab

We studied the morphology and spatial distribution of loops in an active region, using coordinated observations obtained with both the S082A XUV spectroheliograph and the S056 grazingincidence X-ray telescope on Skylab. The active region loops in the temperature range 5 × 10⁵ –3 × 10⁶ K fall basically into two distinctive groups: the hot loops with temperatures 2–3 × 10⁶ K as observed in coronal lines and X-rays, and the relatively cool loops with temperature 5 × 10⁵ –1 × 10⁶ K as observed in transition-zone lines (Ne vii, Mg ix). The brightest hot coronal loops in the active region are mostly low-lying, compact, closely-packed, and show greater stability than the transition-zone loops, which are fewer in number, large, and slender. The observed aspect ratio of the hot coronal loops is in the range of 0.1 and 0.2, which are almost two orders of magnitude larger than those for the Ne vii loops. Brief discussion of the MHD stability of the loops in terms of the aspect ratio is presented.     

The relationship between UV and X-ray active region structures

Yohkoh and the Coronal Diagnostic Spectrometer (CDS) on the Solar and Heliospheric Observatory (SOHO) jointly observed two brightenings in active region NOAA 7981 on 6 August 1996. Combining the UV data from CDS with information from the high time resolution coronal images obtained with the Soft X-ray Telescope (SXT) on Yohkoh, provides us with important information on the relationship between the transition region and corona. Our observations show that cool plasma (T_e = 2.2 x 10^-5 K) can lie at the same altitude as the hot coronal plasma (T_e = 1–4 x 10⁶ K). The lower temperature structure is not formed from the cooling of the hotter coronal loop. We are also able to observe a low temperature cut-off of T_e = 1–4 x 10⁶ K for a loop which repeatedly brightened over the period of approximately one day.     

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.     

Erratum to: The Maunder Minimum and the Sun as the Possible Source of Particles Creating Increased Abundance of the <Superscript>14</Superscript>C Carbon Isotope

Solar flares take place in regions of strong magnetic fields and are generally accepted to be the result of a resistive instability leading to magnetic reconnection. When new flux emerges into a pre-existing active region it can act as a flare and coronal mass ejection trigger. In this study we observed active region 10955 after the emergence of small-scale additional flux at the magnetic inversion line. We found that flaring began when additional positive flux levels exceeded 1.38×10²⁰ Mx (maxwell), approximately 7 h after the initial flux emergence. We focussed on the pre-flare activity of one B-class flare that occurred on the following day. The earliest indication of activity was a rise in the non-thermal velocity one hour before the flare. 40 min before flaring began, brightenings and pre-flare flows were observed along two loop systems in the corona, involving the new flux and the pre-existing active region loops. We discuss the possibility that reconnection between the new flux and pre-existing loops before the flare drives the flows by either generating slow mode magnetoacoustic waves or a pressure gradient between the newly reconnected loops. The subsequent B-class flare originated from fast reconnection of the same loop systems as the pre-flare flows.     

Enthalpy flux cooling of the solar corona

Models of the solar corona which include the effects of hot downflowing material are considered. Temperature-height profiles of the quiet and flaring corona are derived, under the assumptions of hydrostatic equilibrium and that the dominant cause of transition region heating is due to the enthalpy of the downflowing matter. In addition, scaling laws for the lengths of coronal loops are derived. It is found that inclusion of the downward enthalpy flux leads to a loop scaling law for quiet Sun loops which does not differ appreciably from that of Rosner et al. (1978). However, inclusion of the effects of enthalpy flux lead to a scaling law for compact flare loops of L = (3.6 × 10⁹)T _infc ^sup0.55 cm, which predicts much smaller loop sizes than expected from the quiet Sun loop law; these predicted lengths, however, are in agreement with the observed small sizes of compact flare loops.     

The formation of flare loops by magnetic reconnection and chromospheric ablation

Slow-mode shocks produced by reconnection in the corona can provide the thermal energy necessary to sustain flare loops for many hours. These slow shocks have a complex structure because strong thermal conduction along field lines dissociates the shocks into conduction fronts and isothermal subshocks. Heat conducted along field lines mapping from the subshocks to the chromosphere ablates chromospheric plasma and thereby creates the hot flare loops and associated flare ribbons. Here we combine a non-coplanar compressible reconnection theory with simple scaling arguments for ablation and radiative cooling, and predict average properties of hot and cool flare loops as a function of the coronal vector magnetic field. For a coronal field strength of 100 G the temperature of the hot flare loops decreases from 1.2 × 10⁷ K to 4.0 × 10⁶ K as the component of the coronal magnetic field perpendicular to the plane of the loops increases from 0% to 86% of the total field. When the perpendicular component exceeds 86% of the total field or when the altitude of the reconnection site exceeds 10⁶km, flare loops no longer occur. Shock enhanced radiative cooling triggers the formation of cool H flare loops with predicted densities of 10¹³ cm^–3, and a small gap of 10³ km is predicted to exist between the footpoints of the cool flare loops and the inner edges of the flare ribbons.     

POST-FLARE LOOPS OF 26 JUNE 1992 – IV. Formation and Expansion of Hot and Cool Loops

Observations of the post-flare loops after the X3.9 flare which occurred on 25 June, 1992 at 20:11 UT by the Yohkoh/SXT in X-rays, as well as in H obtained at 5 different observatories, have provided a unique, longest ever, set of data for a study of the relationship between the hot and cool post-flare loops as they evolve. At any given time, the altitude difference between the hot X-ray loops of 6–7× 10⁶ K and the cool H loops of 1.5× 10⁴ K is related to the expansion rate of the loop systems and their cooling time. Therefore, measurements of the expansion rate and relative height of hot and cool loops can provide direct observational values for their cooling times. We measured the altitude of hot and cool loops for 15 and 19 hours, respectively, and found that the cooling time increased as the density of the loops decreased. We found a reasonably good agreement between the observed cooling times and those obtained from model calculations, although the observed values were always somewhat longer than the theoretical ones. Taking into account evolutionary effects, we also found similar shapes and configurations of hot and cool loops during the entire observing period and confirmed that, at any time, hot loops are at higher altitude than cool loops, suggesting that cool loops indeed evolve from hot loops. These results were used to check the validity of the reconnection model.     

The temperature-density structure of coronal loops in hydrostatic equilibrium

The temperature and density structure are computed for a comprehensive set of coronal loops that are in hydrostatic and thermal equilibrium. The effect of gravity is to produce significant deviations from the usual uniform-pressure scaling law (T(pL) ^1/3) when the loops are taller than a scale height. For thermally isolated loops it lowers the pressure throughout the loop, which in turn lowers the density significantly and also the temperature slightly; this modifies the above scaling law considerably. For more general loops, where the base conductive flux does not vanish, gravity lowers the summit pressure and so makes the radiation decrease by more than the heating. This in turn raises the temperature above its uniform pressure value for loops of moderate length but lowers it for longer loops. A divergence in loop cross-section increases the summit temperature by typically a factor of 2, and decreases the density, while an increase in loop height (for constant loop length) changes the temperature very little but can halve the density.One feature of the results is a lack of equilibrium when the loop pressure becomes too large. This may explain the presence of cool cores in loops which originally had temperatures below 2 × 10⁶ K. Loops hotter than 2 × 10⁶ K are not expected to develop cool cores because the pressure necessary to produce non-equilibrium is larger than observed.