On the expansions of intermediate orbit for general planetary theory

Intermediate orbit for general planetary theory is constructed in the form of multivariate Fourier series with numerical coefficients. The structure and efficiency of the derived series are illustrated by giving various statistical properties of the coefficients.The ability of the recently proposed elliptic function approach to compress the Fourier series representing the intermediate orbit is investigated. Our results confirm that when mutual perturbations of a pair of planets are considered the elliptic function approach is quite efficient and allows one to compress the series substantially. However, when perturbations of three or more planets are under study the elliptic function approach does not give any advantages.     

Axial convergence in a well-mixed estuary

Transverse secondary circulations involving surface convergence, observed in a well-mixed estuary in North Wales, are made visible by the collection of surface material along an axial line which extends continuously for many kilometres through the estuary. The circulation and axial convergence, however, are seen only during the flood phase of the tide and no similar behaviour has been observed during the ebb phase.Convergent circulations in the estuary are associated with small but steady transverse density gradients in the cross-section, produced by non-uniform advection of the longitudinal gradient through the channel. A diagnostic model, using measured mean distributions of cross-sectional density, indicates surface transverse velocities (～0.1 ms^?1) similar to those observed in the estuary. The model further predicts appreciable transverse divergent currents at a fractional depth of 0.75: a prediction which has been tested in the estuary using a vertical array of accurately resolving current direction indicators.     

The Relation between the Amplitude and the Period of Solar Cycles

The maximum amplitudes of solar activity cycles are found to be well anti-correlated (r = -0.72) with the newly defined solar cycle lengths three cycles before (at lag -3) in 13-month running mean sunspot numbers during the past 190 years. This result could be used for predicting the maximum sunspot numbers. The amplitudes of Cycles 24 and 25 are estimated to be 149.5±27.6 and 144.3±27.6, respectively.     

Morphological redshift estimates for galaxy clusters in a Sunyaev–Zel'dovich effect survey

We develop a new method to estimate the redshift of galaxy clusters through resolved images of the Sunyaev–Zel'dovich effect (SZE). Our method is based on morphological observables which can be measured by actual and future SZE experiments. We test the method with a set of high-resolution hydrodynamical simulations of galaxy clusters at different redshifts. Our method combines the observables in a principal component analysis. After calibrating the method with an independent redshift estimation for some of the clusters, we show – using a Bayesian approach – how the method can give an estimate of the redshift of the galaxy clusters. Although the error bars given by the morphological redshift estimation are large, it should be useful for future SZE surveys where thousands of clusters are expected to be detected; a first preselection of the high-redshift candidates could be done using our proposed morphological redshift estimator. Although not considered in this work, our method should also be useful to give an estimate of the redshift of clusters in X-ray and optical surveys.     

An atlas of the optical spectrum of supernova 1987A in the large magellanic cloud

Photographic spectra of SN1987A in the LMC have been obtained from 1987 February 25 to 1988 June 30. Microdensitometer tracings of these have been reduced to intensity and corrections for instrumental response have been applied to the spectra. This paper presents these data in an atlas format, discusses the reduction procedures in detail, and presents radial velocity measurements of selected lines in the spectra     

Modelling Gas And Dust Release From Comet Hale–Bopp

Numerical simulations of the evolving activity of comet Hale-Bopp are presented, assuming a porous, spherical nucleus, 20 km in radius, made of dust and gas-laden amorphous ice. The main effects included are: crystallization of amorphous ice and release of occluded gas, condensation, sublimation and flow of gases through the pores, changing pore sizes, and flow of dust grains. The model parameters, such as initial pore size and porosity, emissivity, dust grain size, are varied in order to match the observed activity. In all cases, a sharp rise in the activity of the nucleus occurs at a large heliocentric distance pre-perihelion, marked by a few orders of magnitude increase in the CO and the CO₂ fluxes and in the rate of dust emission. This is due to the onset of crystallization, advancing down to a few meters below the surface, accompanied by release of the trapped gases. A period of sustained, but variable, activity ensues. The emission of water molecules is found to surpass that of CO at a heliocentric distance of 3 AU. Thereafter the activity is largely determined by the behaviour of the dust. If a dust mantle is allowed to build up, the water production rate does not increase dramatically towards perihelion; if most of the dust is ejected, the surface activity increases rapidly, producing a very bright comet. This revised version was published online in July 2006 with corrections to the Cover Date.