Electron acceleration by electric fields near the footpoints of current-carrying coronal magnetic loops

We analyze the electric fields that arise at the footpoints of a coronal magnetic loop from the interaction between a convective flow of partially ionized plasma and the magnetic field of the loop. Such a situation can take place when the loop footpoints are at the nodes of several supergranulation cells. In this case, the neutral component of the converging convective flows entrain electrons and ions in different ways, because these are magnetized differently. As a result, a charge-separating electric field emerges at the loop footpoints, which can efficiently accelerate particles inside the magnetic loop under appropriate conditions. We consider two acceleration regimes: impulsive (as applied to simple loop flares) and pulsating (as applied to solar and stellar radio pulsations). We have calculated the fluxes of accelerated electrons and their characteristic energies. We discuss the role of the return current when dense beams of accelerated particles are injected into the corona. The results obtained are considered in light of the currently available data on the corpuscular radiation from solar flares.     

MICROWAVE EMISSION FROM CORONAL HEIGHTS: STUDY OF A NON-THERMAL RADIO FLARE

Two small radio flares following the great gamma-ray burst on 11 June 1991 are studied. We analyse the different association of emission features at microwaves, decimeter waves, and soft and hard X-rays for the events. The first flare has well-defined emission features in microwaves and soft and hard X-rays, and a faint decimetric signature well after the hard X-ray burst. It is not certain if the decimetric event is connected to the burst features. The second event is characterized by an almost simultaneous appearance of hard X-ray burst maxima and decimetric narrowband drift bursts, but soft X-ray emission is missing from the event. With the exception of the possibility that the soft X-ray emission is absorbed along the way, the following models can explain the reported differences in the second event: (1) Microwave emission in the second event is produced by 150 keV electrons spiraling in the magnetic field relatively low in the corona, while the hard X-ray emission is produced at the beginning of the burst near the loop top as thick-target emission. If the bulk of electrons entered the loop, the low-energy electrons would not be effectively mirrored and would eventually hit the footpoints and cause soft X-ray emission by evaporation, which was not observed. The collisions at the loop top would not produce observable plasma heating. The observed decimetric type III bursts could be created by plasma oscillations caused by electron beams traveling along the magnetic field lines at low coronal heights. (2) Microwave emission is caused by electrons with MeV energies trapped in the large magnetic loops, and the electrons are effectively mirrored from the loop footpoints. The hard X-ray emission can come both from the loop top and the loop footpoints as the accelerated lower energy electrons are not mirrored. The low-energy electrons are not, however, sufficient to create observable soft X-ray emission. The type III emission in this case could be formed either at low coronal heights or in local thick regions in the large loops, high in the corona.     

Connection Between Chromospheric Events and Photospheric Dynamics

We analyzed chromospheric events and their connection to oscillation phenomena and photospheric dynamics. The observations were done with the New Solar Telescope of Big Bear Solar Observatory using a broad-band imager at the wavelength of a TiO band and FISS spectrograph scanning Ca?ii and Hα spectral lines. The event in Ca?ii showed strong plasma flows and propagating waves in the chromosphere. The movement of the footpoints of flux tubes in the photosphere indicated flux tube entanglement and magnetic reconnection as a possible cause of the observed brightening and waves propagating in the chromosphere. An upward propagating train of waves was observed at the site of the downflow event in Hα. There was no clear relationship between photospheric waves and the Ca?ii and Hα events. Our observations indicate that chromospheric waves that were previously thought to originate from the photosphere may be generated by some events in the chromosphere as well.     

Initial phase of chromospheric evaporation in a solar flare

In this paper we discuss the initial phase of chromospheric evaporation during a solar flare observed with instruments on the Solar Maximum Mission on May 21, 1980 at 20:53 UT. Images of the flaring region taken with the Hard X-Ray Imaging Spectrometer in the energy bands from 3.5 to 8 keV and from 16 to 30 keV show that early in the event both the soft and hard X-ray emissions are localized near the footpoints, while they are weaker from the rest of the flaring loop system. This implies that there is no evidence for heating taking place at the top of the loops, but energy is deposited mainly at their base. The spectral analysis of the soft X-ray emission detected with the Bent Crystal Spectrometer evidences an initial phase of the flare, before the impulsive increase in hard X-ray emission, during which most of the thermal plasma at 10⁷ K was moving toward the observer with a mean velocity of about 80 km s^-1. At this time the plasma was highly turbulent. In a second phase, in coincidence with the impulsive rise in hard X-ray emission during the major burst, high-velocity (370 km s^-1) upward motions were observed. At this time, soft X-rays were still predominantly emitted near the loop footpoints. The energy deposition in the chromosphere by electrons accelerated in the flare region to energies above 25 keV, at the onset of the high-velocity upflows, was of the order of 4 × 10¹⁰ erg s^-1 cm^-2. These observations provide further support for interpreting the plasma upflows as the mechanism responsible for the formation of the soft X-ray flare, identified with chromospheric evaporation. Early in the flare soft X-rays are mainly from evaporating material close to the footpoints, while the magnetically confined coronal region is at lower density. The site where upflows originate is identified with the base of the loop system. Moreover, we can conclude that evaporation occurred in two regimes: an initial slow evaporation, observed as a motion of most of the thermal plasma, followed by a high-speed evaporation lasting as long as the soft X-ray emission of the flare was increasing, that is as long as plasma accumulation was observed in corona.     

The footpoints of giant arches

We have detected chromospheric footpoints of the giant post-flare coronal arches discovered by HXIS a few years ago. H photographs obtained at Big Bear and Udaipur Solar Observatories show chromospheric signatures associated with 5 sequential giant arch events observed in the interval from 6 to 10 November, 1980. The set of footpoints at one end of the arches consists of enhancements within a plage at the northeast periphery of the active region and the set of footpoints at the other end of the arch consists of brightenings of the chromosphere south of the active region. Both sets of footpoints show very slow brightness variations correlated in time with the brightness variations of the X-ray arches. Current-free modelling of the coronal magnetic field by Kopp and Poletto (1989), based on a Kitt Peak magnetogram, confirms the identification of the two sets of footpoints by showing magnetic field lines connecting them.The brightenings appear as a succession of point-like enhancements whose individual lifetimes are of the time-scale of minutes but which continue to occur for periods of several hours. This behaviour allows us to infer a fine structure in the coronal arches, undetectable in the X-ray images. The discovery of these brightenings and their location at the periphery of the active region also alters our conception of the relationship of the giant arches to the flares that begin concurrently with them. The giant arch phenomenon appears now to be either: (1) a long-lived, semi-permanent, coronal structure which is revived and fed with plasma and energy by underlying dynamic flares, or alternatively (2) a system of high-altitude loops which open at the onset of every such flare and subsequently reconnect over intervals of many hours.     

Sub-terahertz emission from solar flares: The plasma mechanism of chromospheric emission

We consider the plasma mechanism of sub-terahertz emission from solar flares and determine the conditions for its realization in the solar atmosphere. The source is assumed to be localized at the chromospheric footpoints of coronal magnetic loops, where the electron density should reach n ≈ 10¹⁵ cm^?3. This requires chromospheric heating at heights h ? 500 km to coronal temperatures, which provides a high degree of ionization needed for Langmuir frequencies ν _p ≈ 200–400 GHz and reduces the bremsstrahlung absorption of the sub-THz emission as it escapes from the source. The plasma wave excitation threshold for electron-ion collisions imposes a constraint on the lower density limit for energetic electrons in the source, n ₁ > 4 × 10⁹ cm^?3. The generation of emission at the plasma frequency harmonic ν ≈ 2ν _p rather than the fundamental tone turns out to be preferred. We show that the electron acceleration and plasma heating in the sub-THz emission source can be realized when the ballooning mode of the flute instability develops at the chromospheric footpoints of a flare loop. The flute instability leads to the penetration of external chromospheric plasma into the loop and causes the generation of an inductive electric field that efficiently accelerates the electrons and heats the chromosphere in situ. We show that the ultraviolet radiation from the heated chromosphere emerging in this case does not exceed the level observed during flares.     

Locations of Footpoints of Transequatorial Interconnecting Loops

We discuss footpoints of loops seen by Yohkoh in soft X-rays that connect active regions across the equator (transequatorial interconnecting loops – TILs). While most TILs are rooted in moderately strong fields at peripheries of active regions, there are also cases when these loops are anchored in very weak or very strong fields, ranging from < 30 G to several hundred gauss. Some have their footpoints near sunspot penumbrae, creating `X-ray fountains' in a combination with active region loops. But TILs are never rooted in sunspots. The most likely explanation is that magnetic field lines leave spots almost vertically so that TILs rooted in them extend high into the corona and density in them is below the limit of visibility in X-rays. The fact that in force-free modeling some TILs are rooted in sunspots is most probably due to the difference between field-line connections in `vacuum' and in the highly conductive plasma on the Sun. Some TILs end before they reach active regions which sometimes may indicate the real situation, but mostly this `gap' is probably due to a temperature decrease near the loop footpoints which makes them invisible in X-rays. In that case the fact that these cool lowest parts of TILs are never found in TRACE or SOHO EIT images indicates that plasma density in TILs must be very low. Still, the total absence of any counterparts of X-ray TILs in TRACE and EIT images is puzzling and, therefore, other possible interpretations of the `gap' origin are also briefly mentioned.     

3-D MHD simulation of the generation of a shell current loop with closure current

We present results for the generation process of a shell current loop by using a three-dimensional ideal MHD code. It is shown that a shell current loop with a diffuse closure current can be generated due to the twisting motions of the loop footpoints. It is also shown that during the generation of a shell current loop, plasma density enhancement propagates along a shell current loop. It is suggested that the generation process of a shell current loop may be related to the movement of soft X-ray enhancement from the footpoints along a loop before onset of a solar flare.     

FISS Observations of Vertical Motion of Plasma in Tiny Pores

Pores can be exploited for the understanding of the interaction between small-scale vertical magnetic field and the surrounding convective motions as well as the transport of mechanical energy into the chromosphere along the magnetic field. For better understanding of the physics of pores, we investigate tiny pores in a new emerging active region (AR11117) that were observed on 26 October 2010 by the Solar Optical Telescope (SOT) on board Hinode and the Fast Imaging Solar Spectrograph (FISS) of the 1.6 meter New Solar Telescope (NST). The pores are compared with nearby small magnetic concentrations (SMCs), which have similar magnetic flux as the pores but do not appear dark. Magnetic flux density and Doppler velocities in the photosphere are estimated by applying the center-of-gravity method to the Hinode/Spectro-Polarimeter data. The line-of-sight motions in the lower chromosphere are determined by applying the bisector method to the wings of the Hα and the Ca?ii 8542 Å line simultaneously taken by the FISS. The coordinated observation reveals that the pores are filled with plasma which moves down slowly and are surrounded by stronger downflow in the photosphere. In the lower chromosphere, we found that the plasma flows upwards inside the pores while the plasma in the SMCs is always moving down. Our inspection of the Ca?ii 8542 Å line from the wing to the core shows that the upflow in the pores slows down with height and turns into downflow in the upper chromosphere while the downflow in the SMCs gains its speed. Our results are in agreement with the numerical studies which suggest that rapid cooling of the interior of the pores drives a strong downflow, which collides with the dense lower layer below and rebounds into an upflow.     

Subsonic flows in the coronal-interplanetary regions of closed field lines

In the coronal-interplanetary space the plasma motion, in a reference frame corotating with the Sun, is aligned with the magnetic field. Just like the solar wind, which is the supersonically expanding flow along open field lines, the flow along closed field lines is mainly driven by the pressure gradient. The flow in the regions of closed field lines is subsonic, being determined by the conditions at the two footpoints of the magnetic flux tube.The National Center for Atmospheric Research is sponsored by the National Science Foundation.     

Determination of the True Shape of Coronal Loops

Using line of sight velocity measurements from the SUMER and CDS instruments aboard SOHO, in conjunction with a simple geometrical model, we reconstructed the true, 3D shape and the velocity of plasma flow along coronal loops. The projection of the loop on the sky and the position of the footpoints define a family of curves. Assuming that the loop is located on a plane, the line of sight velocity can be used to select the most plausible solution. For two loops, observed in the Ne viii? 770 Å and O v? 630 Å spectral lines, we find asymmetric, subsonic uni-directional flows, with velocity maxima of ≈?80 km?s^?1 near the footpoints. The loops are highly inclined with respect to the vertical, by 55^○ and 70^○, respectively; thus the true height of the loop tops from the photospheric level is ≈?20^′′, comparable to the isothermal scale height.     

Motions in solar magnetic tubes

Three independent observations by rocket, Skylab, and OSO-8 have all indicated the presence of steady downflows of the order of a few kilometers per second in the solar transition region overlying the chromospheric network. Using density estimates at these heights from traditional transition region models, we find that the downward mass fluxes associated with these velocities are comparable with the estimated upward mass flux in spicules, originating in the same regions. Since both observations and theoretical calculations show that the solar wind can accept only a small fraction of the upward spicule flux, we suggest that the downflow represents spicular material returning to the chromosphere after being heated to coronal temperatures. In this context, the differential velocity measurement of Cushman and Rense is interpreted as indicating a difference in downflow speeds rather than a difference in expansion speeds.Moreover, the enthalpy flux associated with the downflow of coronal material into these regions is shown by various estimates to exceed the inward heat flow expected by thermal conduction and it may constitute the dominant energy source for the transition region. Simplified analytical models are used to explore the nature of the transition region overlying the supergranulation boundaries, under the assumption that the thermal structure results from a balance of the downward convection of enthalpy and radiative losses. Models based upon these considerations are shown to be consistent with the observed emission measures.The National Center for Atmospheric Research is sponsored by the National Science Foundation.     

A Statistical Study of Transequatorial Loops

We identify 356 transequatorial loops (TLs) from the data set of Yohkoh Soft X-Ray Telescope (SXT) in the period of solar cycles 22 and 23. The classification of the TLs can be made on two bases. One is according to the magnetic polarities of the footpoints of TLs, and the other is according to the number of TLs in the same region. Based on the first criterion, TLs fall into two categories: PTLs in which the magnetic polarities of the footpoints are the same as the preceding polarities and FTLs in which the footpoint polarities are the same as the following polarities of active regions, respectively. It is found that PTLs have a preference; about 66% of the TLs are PTLs, and this preference of PTLs is independent of the solar cycle. The percentage of FTLs is about 34%. Based on the second criterion, TLs are also divided into two categories: the number of TLs in a region is either single (STLs) or multiple (MTLs). In addition, we find that the number of TLs, PTLs, and FTLs have good correlations with solar cycle indices. By comparing the number of TLs and the number of active regions in each year, we obtain the ratio between them. The separation of footpoints and their yearly variations are calculated, and we find that our result is consistent with spörer's law.     

The discrete and localized nature of the variable emission from active regions

Using data from the Extreme Ultraviolet (EUV) Spectroheliometer onSkylab, we study the empirical characteristics of the variable emission in active regions. These simultaneous multi-wavelength observations clearly confirm that active regions consist of a complex of loops at different temperatures. The variable emission from this complex has very well-defined properties that can be quantitatively summarized as follows: (1) It is localized predominantly around the footpoints where it occurs at discrete locations. (2) The strongest variability does not necessarily coincide with the most intense emission. (3) The fraction of the area of the footpoints,δn/N, that exhibits variable emission, varies by ±15% as a function of time, at any of the wavelengths measured. It also varies very little from footpoint to footpoint. (4) This fractional variation is temperature dependent with a maximum around 10⁵ K. (5) The ratio of the intensity of the variable to the average background emission, δI/Ī, also changes with temperature. In addition, we find that these distinctive characteristics persist even when flares occur within the active region.     

Multiple downflow velocities above sunspotss

Supersonic transition zone downflow appears to be commonly occurring above sunspots. The downflow has been observed in 29 emission lines in the ultra-violet spectrum with the High Resolution Telescope and Spectrograph (HRTS) on two rocket flights and on 5 consecutive days during the Spacelab-2 mission. Spectra from the second rocket flight, contain the most extreme example of downflow, showing speeds up to 180 km s^–1 and extending over 60 are sec along the slit. The observations demonstrate the existence of several different distinctive flow speeds within the 1 arc sec resolution element throughout the temperature range 7000–240 000 K.Paper presented at the 11 th European Regional Astronomical Meetings of the IAU on New Windows to the Universe, held 3–8 July, 1989, Tenerife, Canary Islands, Spain     

The effect of non-uniform magnetic field on the slow mode oscillations

In this paper, the slow MHD mode oscillations of the coronal plasma are studied. The aim is to identify the effect of structuring (such as magnetic field, temperature, density, and pressure) on the frequencies of oscillations. We modelled the coronal medium as a low-β plasma with longitudinally density and pressure stratifications and a weakly inhomogeneous magnetic field varied slowly with height and radial directions. The linearized ideal MHD equations reduced to a single Klein–Gordon differential equation for square of oscillatory frequencies. The eigenfunctions and analytical dispersion relations are derived. The dispersion relations were solved numerically. In the case of uniform magnetic field, the previous studies verified. Our numerical results show that, the frequencies and their ratios are very sensitive functions of pressure scale height, and slightly varying functions of inhomogeneity parameter of magnetic field. By changing the magnetic field strength between the apex and footpoints of the loop about 50%, the frequencies ratio are changed about 5%. We concluded that, the pressure scale height and temperature gradient are first order effects and inhomogeneity of magnetic field is a second order effect on the slow mode oscillations.     

Impulsive phase of flares in soft X-ray emission

Observations using the Bent Crystal Spectrometer instrument on the Solar Maximum Mission show that turbulence and blue-shifted motions are characteristic of the soft X-ray plasma during the impulsive phase of flares, and are coincident with the hard X-ray bursts observed by the Hard X-ray Burst Spectrometer. A method for analysing the Ca xix and Fe xxv spectra characteristic of the impulsive phase is presented. Non-thermal widths and blue-shifted components in the spectral lines of Ca xix and Fe xxv indicate the presence of turbulent velocities exceeding 100 km s^-1 and upward motions of 300–400 km s^-1.The April 10, May 9, and June 29, 1980 flares are studied. Detailed study of the geometry of the region, inferred from the Flat Crystal Spectrometer measurements and the image of the flare detected by the Hard X-ray Imaging Spectrometer, shows that the April 10 flare has two separated footpoints bright in hard X-rays. Plasma heated to temperatures greater than 10⁷ K rises from the footpoints. During the three minutes in which the evaporation process occurs an energy of 3.7 × 10³⁰ ergs is deposited in the loop. At the end of the evaporation process, the total energy observed in the loop reaches its maximum value of 3 × 10³⁰ ergs. This is consistent with the above figures, allowing for loss by radiation and conduction. Thus the energy input due to the blue-shifted plasma flowing into the flaring loop through the footpoints can account for the thermal and turbulent energy accumulated in this region during the impulsive phase.On leave from Torino University, Italy.     

Spatially Resolved Microwave Observations of Multiple Periodicities in a Flaring Loop

Quasi-periodic pulsations (QPPs) with at least three simultaneously existing spectral components with periods P≥30 s, P≈20 s, and about P≈10 s were detected during the decay phase of a solar flare on 3 July 2002, observed with the Nobeyama Radioheliograph (NoRH). A detailed study of the spatial structure of the Fourier amplitudes of QPPs along a flaring loop has revealed different spatial distributions of the three components. It is shown that the source of the QPPs with period P≥30 s has its maximum amplitude in the inner region of the loop, between the footpoints. QPPs with period P≈20 s are localized at the periphery of the loop, mainly in the outer parts of the footpoints. The spatial distribution of oscillations with period about P≈10 s contains three regions of high QPP amplitudes: two near the footpoints and one in the middle of the flaring region. It is shown that the observed properties of the spectral components are most accurately described by the fundamental, second, and third harmonics of the kink mode standing waves. This is the first identification of the kink mode in flare loops which is based on strict limitations derived from data on the spatial structure of a pulsating flare region.     

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.     

Twisted magnetic flux tubes: Effect of small twist

The shape of a magnetic flux tube is investigated when photospheric motion causes small twist at the magnetic footpoints. Using a Fourier-Bessel series expansion, the previous results of Zweibel and Boozer (1985) and Steinolfson and Tajima (1987), when the twist is small, are substantiated. A twisting motion that is restricted to a finite region is investigated. Inside the twisted region, the tube contracts, but in the outer region the field remains straight, except for a slight expansion at the outside of the loop near the footpoints. The amount of twist depends on the radial position and can in fact be larger in the contracted region with the twist decreasing as the tube expands. An axial boundary-layer region is present, as noted by the above authors, through which the field adjusts to the line-tied magnetic footpoint positions. An analysis of the boundary layer shows that the thickness remains constant as the loop-length is increased with the result that the main part of the loop has constant cross-sectional area and can be described by cylindrically-symmetric fields. This new 1-D model predicts the main behaviour of the loop without the need to solve the more complicated 2-D problem directly. It is speculated that the boundary layers will remain even when the twist becomes large and a simple example is presented. A detailed parametric study of different twist profiles shows how the central part of the loop responds.Using the result that the majority of the loop can be described by a constant cross-sectional area, a model for a toroidal loop is presented that models coronal loops in a more realistic manner. The main result from this section is that the coronal loops can only remain in equilibrium if they are confined by an external magnetic field (possibly potential in nature) and not by a gas pressure unless additional physical effects are included.