Solar flares: The gradual phase

One has to distinguish between two kinds of the gradual phase of flares: (1) a gradual phase during which no energy is released so that we see only cooling after the impulsive phase (a confined flare), and (2) a gradual phase during which energy release continues (a dynamic flare).The simplest case of (1) is a single-loop flare which might provide an excellent opportunity for the study of cooling processes in coronal loops. But most confined flares are far more complicated: they may consist of sets of unresolved elementary loops, of conglomerates of loops, or they form arcades the components of which may be excited sequentially. Accelerated particles as well as hot and cold plasma can be ejected from the flare site (coronal tongues, flaring arches, sprays, bright and dark surges) and these ejecta may cool more slowly than the source flare itself.However, the most important flares on the Sun are flares of type (2) in which a magnetic field opening is followed by subsequent reconnection of fieldlines that may continue for many hours after the impulsive phase. Therefore, the main attention in this review is paid to the gradual phase of this category of long-decay flares. The following items are discussed in particular: The wide energy range of dynamic flares: from eruptions of quiescent filaments to most powerful cosmic-ray flares. Energy release at the reconnection site and modelling of the reconnection process. The post-flare loops: evidence for reconnection; observations at different wavelengths; energy deposit in the chromosphere, chromospheric ablation, and velocity fields; loops in emission; shrinking loops; magnetic modelling. The gradual phase in X-rays and on radio waves. Post-flare X-ray arches: observations, interpretation, and modelling; relation to metric radio events and mass ejections, multiple-ribbon flares and anomalous events, hybrid events, possible relations between confined and dynamic flares.     

Fourier analysis of the light curves of eclipsing variables,II

The aim of the present paper will be to extend the Fourier methods of analysis of the light curves of eclipsing binaries, outlined in our previous communication (Kopal, 1975) in connection with systems whose components would appear as uniformly bright discs, to systems whose components exhibit discs characterized by an arbitrary radially-symmetrical distribution of brightness —i.e., an arbitrary law of darkening towards the limb — be it linear or nonlinear.In Section 2 which follows a few brief introductory remarks, fundamental equations will be set up which govern the light changes arising from the mutual eclipses of limb-darkened stars — be such eclipses total, partial or annular; and Section 3 will contain a closed algebraic solution for the elements of the occulation eclipses terminating in total phase. Such a solution proves to be no more complicated than it turned out to be for uniformly bright discs in our previous paper; and calls for no special functions for the purpose — as will be put in proper perspective in the concluding Section 4.The cases of transit eclipses terminating in an annular phase, of partial eclipses of occulation or transit type, will be similarly dealt with by Fourier methods in the next paper of the present series.     

Further notes on the associated alpha-functions and related integrals in the theory of the light changes of eclipsing variables

With a view to furthering the theory of the light changes of eclipsing variables, developed before systematically by Z. Kopal, this paper presents a number of new (and computable) expressions for the associated alpha-function _n ⁰ ,(r₁,r₂,) (and also for its partial derivatives), where _n ⁰ ,(r₁,r₂,) represents the fractional loss of light suffered by an eclipse of a circular disc of fractional radiusr ₁ (and darkened at the limb to thenth degree) by an opaque disc of radiusr ₂, with their centres separated by a fractional (projected) distance , provided that the transparency of the occulting disc increases with the angle of foreshortening in the same manner as the limb-darkening of the eclipsed star (that is, when the transparency functiong(, ) of the second aperture is given by Equation (4) below). Many of the explicit expressions derived here are valid for any type of eclipse, occultation or transit, regardless of whetherr ₁>r ₂ orr ₁<r ₂. and for any degreen of the adopted law of limb-darkening. It is also pointed out how some of the results obtained in this paper are related to the various representations given earlier in the literature for the case =0.     

Arsenic in contaminated soils and anthropogenic deposits at the Mokrsko,Roudný, and Kašperské Hory gold deposits,Bohemian Massif (CZ)

Soil, mine tailing, and waste dump profiles above three mesothermal gold deposits in the Bohemian Massif with different anthropogenic histories have been studied. Their mineralogical, major element, and arsenic (As) contents and the contents of secondary arsenic minerals were analyzed. The As-bearing minerals were concentrated and determined using X-ray diffraction (XRD) analysis, the Debye-Scherrer powder method, scanning electron microscopy (SEM), and energy-dispersive microanalysis (EDAX). The amorphous hydrous ferric oxides (HFO), As-bearing goethite, K-Ba- or Ca-Fe- and Fe- arsenates pharmacosiderite, arseniosiderite, and scorodite, and sulfate-arsenate pitticite were determined as products of arsenopyrite or arsenian pyrite oxidation. The As behaviour in the profiles studied differs in dependence on the surface morphology, chemical and mineralogical composition of the soil, mine wastes or tailings, oxidation conditions, pH, presence of (or distance from) primary As mineralization in the bedrock, and duration of the weathering effect. Although the primary As mineralization and the bedrock chemical composition are roughly similar, there are distinct differences in the As behaviour amongst the Mokrsko, Roudný and Kaperské Hory deposits.     

Coronal mass ejection associated with the stationary post-flare arch of 21–22 May 1980

By using a combination of X-ray (HXIS), H (Haleakala), white-light corona (Solwind), and zodiacal light (Helios) images on 21–22 May, 1980 we demonstrate, and try to explain, the co-existence of a coronal mass ejection with a stationary post-flare coronal arch. The mass ejection was seen, both by Solwind and Helios, in prolongation of the path of a powerful spray, whereas the active region filament did not erupt. A tentative comparison is made with other occurrences of stationary, or quasi-stationary post-flare coronal arches.     

Transient brightenings of interconnecting loops

We study sudden brightenings of coronal loops that interconnect active regions. Such brightenings often occur within one or two days after the birth of a new interconnecting loop, as well as in some old interconnections. The brightenings of young loops are obviously associated with the emergence of new magnetic flux near their footpoints, whereas some enhancements of old loops may be triggered by slowly moving disturbances propagating from other centers of activity. A few loop brightenings are associated with flares, but the loop does not brighten in consequence of energy supply from the flare. Both the flare and the loop brightening are independent consequences of one common agent, presumably newly emerging flux.Temperatures in brightened loops are between 3 and 4 × 10⁶ K and densities are < 2 × 10⁹ cm^–3, probably < 5 × 10⁸ cm^–3 in some old loops. The top part of a loop is the site of the most intense brightening in the initial phase of a loop enhancement. The most frequent lifetime of these brightenings is 6 to 7 hr.Hale Observatories are operated jointly by the Carnegie Institution of Washington and the California Institute of Technology.     

Tidal evolution in close binary systems

The aim of the present paper will be to give a mathematical outline of the theory of tidal evolution in close binary systems of secularly constant total momentum — an evolution activated by viscous friction of dynamical tides raised by the two components on each other. The first section contains a general outline of the problem; and in Section 2 we shall establish the basic expressions for the energy and momenta of close binaries consisting of components of arbitrary internal structure. In Section 3 we shall investigate the maximum and minimum values of the energy (kinetic and potential) which such systems can attain for given amount of total momentum; while in Section 4 we shall compare these results with the actual facts encountered in binaries with components whose internal structure (and, therefore, rotational momenta) are known to us from evidence furnished by the observed rates of apsidal advance.The results show that all such systems — be these of detached or semi-detached type — disclose that more than 99% of their total momenta are stored in the orbital momentum. The sum of the rotational momenta of the constituent components amounts to less than a percent of the total — a situation characteristic of a state close to the minimum energy for given total momentum. This appears, moreover, to be true not only of the systems with both components on the Main Sequence, but also of those possessing evolved components in contact with their Roche limits.Under such conditions, a synchronism between rotation and revolution (characteristic of both extreme states of maximum and minimum energy) is not only possible, but appears to have been actually approached — if not attained — in the majority of cases. In other words, it would appear that — in at least a large majority of known cases — the existing close binaries have already attained orbits of maximum distension consistent with their momenta; and tidal evolution alone can no longer increase the present separations of the components to any appreciable extent.The virtual absence, in the sky, of binary systems intermediate between the stages of maximum and minimum energy for given momentum leads us to conjecture that the process of dynamical evolution activated by viscous tides may enroll on a time-scale which is relatively short in comparison with their total age — even for systems like Y Cygni or AG Persei, whose total age can scarcely exceed 10⁷ yr. A secular increase of the semi-major axes of relative orbits is dynamically coupled with a corresponding variation in the velocity of axial rotation of both components through the tidal lag arising from the viscosity of stellar material. The differential equations of so coupled a system are given in Section 5; but their solution still constitutes a task for the future.The Lunar Science Institute Contribution No. 90. The Lunar Science Institute is operated by the Universities Space Research Association under Contract No. NSR 09-051-001 with the National Aeronautics and Space Administration.