Stability of the solar system

If the solar system is considered as a mechanical clockwork consisting of its present members which attract each other as mass-points, the extent of its present approach to secular stability (i.e., the state of minimum potential energy) — manifested by the existence of a number of nearcommensurabilities of the present orbital periods, not only of the planets, but also of their satellites —could not have been attained in a time-span of 4.6×10⁹ yr of its age by gravitational perturbations alone.The existence of such commensurabilities — striking in many instances— could then be understood only on the assumption that either (a) the solar system was actually born with the present 2-, 3- and 4-term couplings between the orbital period of the planets already built-in from the outset (which is improbable on any known grounds); or (b) that these couplings — in particular, the 25 Jupiter-Saturn commensurability — have arisen as a result of tidal interaction between proto-planetary globes of much larger dimensions than these planets possess today. For the present dimensions and mutual distances of these planets, their tidal interaction in 10⁹ yr would exert but negligible effects; and during that time neither their masses, nor the scale of the solar system underwent any essential change.Therefore, a hypothesis is proposed that the situation now obtaining had its origin in the early days of the formation of the solar system, when the planetary globes — in particular, those of Jupiter and Saturn (now in the terminal stage of Kelvin contraction) — were very much larger than they are today; and when, as a result, the tidal coupling between them operated at a much higher rate than at the present time.Paper presented at the European Workshop on Planetary Sciences, organised by the Laboratorio di Astrofisica Spaziale di Frascati, and held between April 23–27, 1979, at the Accademia Nazionale del Lincei in Rome, Italy.     

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.     

Unusual coronal activity following the flare of 6 November 1980

For almost 30 hr after the major (gamma-ray) two-ribbon flare on 6 November 1980, 03:30 UT, the Hard X-Ray Imaging Spectrometer (HXIS) aboard the SMM satellite imaged in > 3.5 keV X-rays a gigantic arch extending above the active region over the limb. Like a similar configuration on 22 May 1980, this arch formed the lowest part of a stationary post-flare radio noise storm recorded at metric wavelengths at Nançay and Culgoora. 6.5 hr after the flare a coronal region below the arch started quasi-periodic pulsations in X-ray brightness, observed by several SMM instruments. These brightness variations had no response in the chromosphere (H), very little in the transition layer (O v), but they clearly correlated with similar variations in brightness at 169 MHz. There were 13 pulses of this kind, with apparent periodicity of about 20 min, until another flare occurred in the active region at 15:00 UT. All the brightenings appeared within a localized area of about 30000 km² in the northern part of the active region, but they definitely did not occur all at the same place.The top of the X-ray arch, at an altitude of 155 000 km, was continuously and smoothly decaying, taking no part in the striking variations below it. Therefore, the area variable in brightness does not seem to be the footpoint of the arch, as we supposed for similar variations on 22 May. More likely, it is a separate region connected directly with the source of the radio storm; particles accelerated in the storm may be dumped into the low corona and cause the X-ray enhancements. The X-ray arch was enhanced by two orders of magnitude in 3.5–5.5 keV X-ray counts and the temperature increased from 7.3 × 10⁶ to 9 × 10⁶ K when the new two-ribbon flare occurred at 15:00 UT. Thus, it is possible that energy is brought into the arch via the upper parts of the reconnecting flare loops - a process that can continue for hours.     

Problems connected with the tangential metric coefficient in the Schwarzschild metric: A possible solution

Four situations are shown where the Schwarzschild metric cannot be used or is subject to unsurmountable problems. The first is the question of a metric useful for PPN-formalism checking different gravitational theories. The second problem occurs in connection with Mach's principle, when the flatness of the spacetime inside a massive hollow sphere is a generally accepted solution. The metrical discontinuity on the same spherical shell is a third problem. The fourth one is the anisotropy of the mass-energy of a test particle in the gravitational field. Three principles for solution are proposed:

1. The space is not dilated, but rather contracted, in the gravitational field; then the measurement-rods are shorter and measured distances have greater magnitudes.
2. The potential energy is to be related to a potential level where a stationary observer is placed and the general relativistic potential must be used.
3. A new metric must be introduced which is distinct from the Schwarzschild metric, so that the space in the gravitational field is warped isotropically.

Then the problems stated are shown to be easily solvable.     

Linear hydromagnetic stability of a differentially rotating non-uniformly stratified fluid layer

Summary Our discussion is concerned with the common effect of the non-uniformity of layer rotation and stratification. We have assumed a model of differential rotation with the upper part of the layer rotating more slowly, the bottom part more quickly. The upper part of the layer is stratified stably, the bottom part unstably.The thermal instabilities are preferred in the strong differential rotation case and they are the most easily excited by a strong magnetic field (10²–10³). The direction of its propagation is westward in the uniformly stratified layer and eastward in the non-uniformly stratified layer.     

Window technique for climate trend analysis

Climatic characteristics are affected by various systematic and occasional impacts: besides the changes in the observing system (locations of the stations of the meteorological network, instruments, observing procedures), the possible local-scale and global natural and antropogenic impacts on climatic conditions should be taken into account. Apart from the predictability problems, the phenomenological analysis of the climatic variability and the determination of past persistent climatic anomalies are significant problems, among other aspects, as evidence of the possible anomalous behavior of climate or for climate impact studies. In this paper, a special technique for the identification of such shifts in the observational series is presented. The existence of these significant shorter or longer term changes in the mean characteristics for the properly selected adjoining periods of time is the necessary condition for the formation of any more or less unidirectional climatic trends. Actually, the window technique is based on a complete set of orthogonal functions. The sensitivity of the proposed model on its main parameters is also investigated. This method is applied for hemispheric and Hungarian data series of the mean annual surface temperature.Contribution to Clima Locarno — Past and Present Climate Dynamics; Conference September 1990, Swiss Academy of Sciences — National Climate Program     

On the determination of the European gravimetric geoid

Summary The method of the automated computation of the gravimetric deflections of the vertical and of the geoidal heights for the European region is described. The work was carried out during the period 1986–1988 by the Topographic Service of the Czechoslovak Army. The computation applies to 20 sheets of the international map 1:1 000 000 (total area of =16^c, =30^c - see Fig. 1). The mean values of the free-air anomalies for each surface element =5, =7.5, approximately 9 × 9 km, were used with radius of integration of 300 km.     

A chromospheric response to pulse beam heating

Starting from the new flare models of Karlický (1990) and Karlický and Hénoux (1991), we present here the first time-dependent numerical simulations of hydrogen plasma excitation and ionization on time scales of less than one second. These time scales are consistent with the spiky behaviour of the kinetic temperature produced by non-thermal collisional processes. Such temperature spikes represent a chromospheric response to a series of short-duration electron beam pulses which are supposed to heat the flare atmosphere. Self-consistent numerical solution of a simplified, time-dependent, non-LTE problem for a three-level hydrogen atom model with continuum allows us to predict theoretically a qualitative behaviour of the H line intensity variations on very short time intervals. Our H temporal profiles, evaluated at the line center and for = 1 Å, can be qualitatively compared with some recent flare observations obtained with high temporal resolution.     

Earthquake hazard of the northern parts of the Bohemian Massif and Western Carpathians

The new procedure of earthquake hazard evaluation developed by Kijko and Sellevoll is tested and applied for the border region of Czechoslovakia and Poland. The new method differs from the conventional approach. It incorporates the uncertainty of earthquake magnitudes, and accepts mixed data containing only large historical events and recent, complete catalogues. Seismic hazard has been calculated for nine regions determined in the border area. In the investigated area, data of historical catalogues are uncertain or, in many cases, the epicentral intensities are unknown. Thus, a number of assumptions have to be adopted in data preparation of catalogues since the year 1200. The calculated values of parameters b in the Gutenberg-Richter frequency-intensity relation as well as the return periods, seem to be reasonable and are generally confirmed by the results obtained from catalogues for the last 80–130 years.