Time-dependent simulations of steady C-type shocks

Using a time-dependent multifluid, magnetohydrodynamic code, we calculated the structure of steady perpendicular and oblique C-type shocks in dusty plasmas. We included relevant processes to describe mass transfer between the different fluids, radiative cooling by emission lines and grain charging, and studied the effect of single- and multiple-sized grains on the shock structure. Our models are the first of oblique fast-mode molecular shocks in which such a rigorous treatment of the dust grain dynamics has been combined with a self-consistent calculation of the thermal and ionization structures including appropriate microphysics. At low densities, the grains do not play any significant rôle in the shock dynamics. At high densities, the ionization fraction is sufficiently low that dust grains are important charge and current carriers and, thus, determine the shock structure. We find that the magnetic field in the shock front has a significant rotation out of the initial upstream plane. This is most pronounced for single-sized grains and small angles of the shock normal with the magnetic field. Our results are similar to previous studies of steady C-type shocks showing that our method is efficient, rigorous and robust. Unlike the method employed in the previous most detailed treatment of dust in steady oblique fast-mode shocks, ours allow a reliable calculation even when chemical or other conditions deviate from local statistical equilibrium. We are also able to model transient phenomena.     

Spatially distributed modelling of soil erosion and sediment yield at regional scales in Spain

Initiated by the need to quantify erosion rates and the impacts of global changes on erosion, several attempts have been made to apply erosion models at regional scales. However, these models have often been directed towards on-site soil erosion estimates, emphasising sheet and rill erosion processes, and disregarding gully erosion, channel erosion and sediment transport. These models are therefore of limited use for the assessment of sediment yield, off-site impacts of erosion, and for the development of environmental management to control these impacts at regional scale. This study analyses and compares three spatially distributed models for the prediction of soil erosion and/or sediment yield at regional scales: the WATEM-SEDEM model that is based on the empirical Revised Universal Soil Loss Equation (RUSLE) in combination with a sediment transport equation, the physics-based Pan European Soil Erosion Risk Assessment model (PESERA), and a newly developed Spatially Distributed Scoring model (SPADS). The three models were applied to 61 Spanish drainage basins and model predictions were evaluated against data on measured reservoir sedimentation rates. Global data sets on land use, climate, elevation and soil characteristics were used as model input for WATEM-SEDEM and SPADS, whereas published soil erosion estimates of PESERA at 1 km² resolution were used directly. SPADS and WATEM-SEDEM provided best results after separate calibration for basins with a Sediment Delivery Ratio (SDR) higher than 5% and those with an SDR lower than 5%. In this way, SPADS explained 67% of variation in sediment yield, while WATEM-SEDEM explained 48% of the variation. PESERA represents a promising alternative to the use of empirical models at the regional scale as it can be applied to very diverse environments with little calibration. However, PESERA provides soil erosion rates and not sediment yield estimates. For most basins PESERA soil erosion rates vary between fifty and close to zero percent of total sediment yield. Two major factors may explain this discrepancy between modelled soil erosion rates and measured sediment yield. First, it may be that PESERA underestimates soil erosion under Mediterranean conditions, although PESERA soil erosion rates are of the same order of magnitude as erosion rates measured in erosion plot studies. Second, gully-, river channel erosion and sediment transport processes may be much more important than sheet- and rill erosion for regional scale sediment yield in these environments. These issues therefore require further attention in future model development. Although spatially lumped models provide better predictions of sediment yield at the basin scale, and while validation of the predicted spatial patterns of sources and sinks of sediment requires further research, spatially distributed models are expected to be of value to support management decisions regarding the assessment of on-site and off-site impacts of erosion at the regional scale.     

Sunspot nests

For the period August 1959–December 1964 the Greenwich Photoheliographic Results were searched for sunspot nests. Such a nest is a sequence of sunspot groups that appear within a small area on the solar surface and that last for several months. The search procedure is described and data for 41 probable sunspot nests are given. At least three quarters of these nests appear to be real, and not chance clusters.The nests are the same type of activity sequences as the Fleckenherde discovered by Becker (1955) and the complexes of activity pointed out by Gaizauskas et al. (1983). The complexes of activity as defined by Bumba and Howard (1965) are different patterns, however; the relation between complexes and the nests is shown.Some properties of the nests are: (i) many nests appear as double structures; (ii) single nests and components of double nests are quite compact: the effective areas are comparable to those of medium-large sunspot groups; (iii) each nest rotates at its own steady rate about the Sun; (iv) the intrinsic scatter in the rotation rates is much larger than the trend in the differential rotation; (v) displacements in latitude are less than a few meters per second; (vi) many nests live for 6 to 15 Carrington rotation periods, the minimum lifetime is not yet determined; (vii) the fraction of the sunspot groups that are members of nests is large (at least 30%).     

Generalized polytropes: Stellar structure with a boltzmann factor

In order to study the structure of a chemically homogeneous star in equilibrium, a density profile of the form T ^N exp(–µm(–)/kT) is suggested. As for polytropes, qualitative aspects of the resulting stellar model can be discussed analytically. In particular it is shown that one reobtains forN=3 Eddington's standard model, whereas forN<3 nearly polytropic models result. WhenN>3, the effective polytropic index does vary appreciably over the star. Numerical results indicate that the proposed density profile is quite reasonable in view of the simplicity of the model. From a comparison of the degree of precision of a polytropic approximation with that of the newly proposed model it follows that the new approximation is definitely better than the polytropic one. It is suggested that the model may be useful to study the structure of stellar clouds, clusters and (spherical) galaxies.Now at Department of Applied Mathematics, Queen Mary College, University of London, England.     

The oblateness effect on the solar radiation incident at the top of the atmospheres of the outer planets

Calculations of the daily solar radiation incident at the top of the atmospheres of Jupiter, Saturn, Uranus, and Neptune, with and without the effect of the oblateness, are presented in a series of figures illustrating the seasonal and latitudinal variation of the ratio of both insolations. It is shown that for parts of the summer, the daily insolation of an oblate planet is increased, the zone of enhanced solar radiation being strongly dependent upon the obliquity, whereas the rate of increase is fixed by both the flattening and the obliquity. In winter, the oblateness effect results in a more extensive polar region, the daily solar radiation of an oblate planet always being reduced when compared to a spherical planet. In addition, we also numerically studied the mean daily solar radiation. As previously stated by A.W. Brinkman and J. McGregor (1979, Icarus, 38, 479–482), it is found that in summer the horizon plane is tilted toward the Sun for latitudes less than the subsolar point, but is titled away from the Sun beyond this latitude. It follows that the mean summer daily insolation is increased between the equator and the subsolar point, but decreased poleward of the above-mentioned limit. In winter, however, the horizon plane is always tilted away from the Sun, causing the mean winter daily insolation to be reduced. The partial gain of the mean summertime insolation being much smaller than the loss during winter season evidently yields a mean annual daily insolation which is decreased at all latitudes.     

Corrections to the improved lunar ephemeris

Based primarily upon the formation of new conditional equations using analytical partial derivatives of the moon's mean elements, meridian circle observations of the moon from 1952–67 have been examined to determine corrections to the constants of lunar theory and to the fundamental coordinate system (FK4). With certain exceptions, the new corrections are in agreement with those published earlier by the author. Systematic corrections to FK4 are surprisingly large, although in agreement with some other recent determinations. New corrections to the lunar ephemeris, resulting from the discussion, are also presented.     

Approximate spectral analysis by least-squares fit

An approximate method of spectral analysis called successive spectral analysis based upon the mean-quadratic approximation of an empirical function by generalised trigonometric polynomial with both unknown frequencies and coefficients is developed. A few quotations describing some properties of the method as well as one of the possible methods for numerical solution are given.     

Accuracy of close binary mass determinations from parallaxes

Absolute masses for W Ursae Majoris and Algol-type close binaries can be determined from their parallax, if observed, and the relative sizes of the stars and their mass ratio, obtained from a light curve solution. An error propagation study compares the typical order of magnitude of the various terms involved, and shows how accurate parallaxes have to be in order to make the procedure work, i.e., making the parallax term not larger than the combined non-parallax terms, and producing reasonably low mass errors. Some comments are made on the possibilities with respect to the HIPPARCOS program.Communication presented at the International Conference on Astrometric Binaries, held on 13–15 June, 1984, at the Remeis-Sternwarte Bamberg, Germany, to commemorate the 200th anniversary of the birth of Friedrich Wilhelm Bessel (1784–1846).     

Models for the formation of binary and millisecond radio pulsars

The peculiar combination of a relatively short pulse period and a relatively weak surface dipole magnetic field strength of binary radio pulsars finds a consistent explanation in terms of (i) decay of the surface dipole component of neutron-star magnetic fields on a timescale of (2–5) × 10⁶ yr, in combination with (ii) spin-up of the rotation of the neutron star during a subsequent mass-transfer phase. The four known binary radio pulsars appear to fall into two different categories. Two of them, PSR 0655 + 64 and PSR 1913 + 16, have short orbital periods (<25 h) and high mass functions, indicating companion masses 0.7M⊙ (∼1 (± 0.3) M⊙ and 1.4 M⊙, respectively). The other two, PSR 0820 + 02 and PSR 1953 + 29, have long orbital periods (117d), nearly circular orbits, and low, almost identical mass functions of about 3×10^-3 M⊙, suggesting companion masses of about 0.3M⊙. It is pointed out that these two classes of systems are expected to be formed by the later evolution of binaries consisting of a neutron star and a normal companion star, in which the companion was (considerably) more massive than the neutron star, or less massive than the neutron star, respectively. In the first case the companion of the neutron star in the final system will be a massive white dwarf, in a circular orbit, or a neutron star in an eccentric orbit. In the second case the final companion to the neutron star will be a low-mass (∼ 0.3 M⊙) helium white dwarf in a wide and nearly circular orbit. In systems of the second type the neutron star was most probably formed by the accretion-induced collapse of a white dwarf. This explains in a natural way why PSR 1953 + 29 has a millisecond rotation period and PSR 0820 + 02 has not. Among the binary models proposed for the formation of the 1.5-millisecond pulsar, the only ones that appear to be viable are those in which the companion disappeared by coalescence with the neutron star. In such models the companion may have been a red dwarf of mass 0.03M⊙, a neutron star, or a massive (>0.7M⊙) white dwarf. Only in the last-mentioned case is a position of the pulsar close to the galactic plane a natural consequence. In the first-mentioned case the progenitor system most probably was a cataclysmic-variable binary in which the white dwarf collapsed by accretion.     

The eruption of active region filaments and its relation to the triggering of a solar flare

The formation and eruption of active region filaments is supposed to be caused by the increase of a concentrated current embedded in the active region background magnetic field of an active region according to the theory of Van Tend and Kuperus (1978).The onset of a filament eruption is due to either changes in the background magnetic field or the increase of the filament current intensity. Both processes can be caused by the emergence of new magnetic flux as well as by the motion of the photospheric footpoints of the magnetic field lines. It is shown that if the background field evolves from a potential field to a nearly force-free field the vertical equilibrium of the current filament is not affected, but large forces are generated along the filament axis. This is identified as the cause of filament activation and the increase in filament turbulence during the flare build-up phase. Depending on the evolution of the background field and the current filament, two different scenarios for flare build-up and filament eruption are distinguished.This work was done while one of the authors (M.K.) was participating in the CECAM workshop on Physics of Solar Flares held at Orsay, France, in June 1979.