Mean Motion Resonances, Gas Drag, and Supersonic Planetesimals in the Solar Nebula

We examine the orbital evolution of planetesimals under the influence of Jupiter's perturbations and nebular gas drag, under the assumption that gas persisted in the asteroid region for some time after Jupiter attained its final mass. Two distinct mechanisms, associated with the 2 : 1 and 3 : 2 mean motion resonances, can excite eccentricities to high values, despite the damping effect of drag. If Jupiter's eccentricity was comparable to its present value, planetesimals can be temporarily trapped in the 2 : 1 resonance. Bodies crossing the 3 : 2 resonance can enter a region of phase space with overlapping high-order resonances. Both mechanisms can produce eccentricities greater than 0.5 for asteroid-sized planetesimals. The combination of resonant perturbations and drag causes secular decay of semimajor axes, resulting in migration of bodies from the outer to inner belt. Inclinations remain low, implying significant collisional evolution during this migration. Velocities of resonant bodies relative to the gas are highly supersonic; these would have been a source of shock waves in the solar nebula.This revised version was published online in October 2005 with corrections to the Cover Date.     

The 2dF Galaxy Redshift Survey: galaxy luminosity functions per spectral type

We calculate the optical b _J luminosity function (LF) of the 2dF Galaxy Redshift Survey (2dFGRS) for different subsets defined by their spectral properties. These spectrally selected subsets are defined using a new parameter, η , which is a linear combination of the first two projections derived from a Principal Component Analysis. This parameter η identifies the average emission- and absorption-line strength in the galaxy rest frame spectrum, and hence is a useful indicator of the present star formation. We use a total of 75 000 galaxies in our calculations, chosen from a sample of high signal-to-noise ratio, low-redshift galaxies observed before 2001 January. We find that there is a systematic steepening of the faint-end slope ( α ) as one moves from passive  ( α =-0.54)  to active  ( α =-1.50)  star-forming galaxies, and that there is also a corresponding faintening of the rest frame characteristic magnitude   M *-5 log₁₀( h )  (from −19.6 to −19.2). We also show that the Schechter function provides a poor fit to the quiescent (Type 1) LF for very faint galaxies  [ M _{b J}-5 log₁₀( h )  fainter than −16.0], perhaps suggesting the presence of a significant dwarf population. The LFs presented here give a precise confirmation of the trends seen previously in a much smaller preliminary 2dFGRS sample, and in other surveys. We also present a new procedure for determining self-consistent k -corrections, and investigate possible fibre-aperture biases.     

The 2dF Galaxy Redshift Survey: the dependence of galaxy clustering on luminosity and spectral type

We investigate the dependence of galaxy clustering on luminosity and spectral type using the 2dF Galaxy Redshift Survey (2dFGRS). Spectral types are assigned using the principal-component analysis of Madgwick et al. We divide the sample into two broad spectral classes: galaxies with strong emission lines ('late types') and more quiescent galaxies ('early types'). We measure the clustering in real space, free from any distortion of the clustering pattern owing to peculiar velocities, for a series of volume-limited samples. The projected correlation functions of both spectral types are well described by a power law for transverse separations in the range  2<( σ / h ^-1 Mpc)<15  , with a marginally steeper slope for early types than late types. Both early and late types have approximately the same dependence of clustering strength on luminosity, with the clustering amplitude increasing by a factor of ∼2.5 between L * and 4 L *. At all luminosities, however, the correlation function amplitude for the early types is ∼50 per cent higher than that of the late types. These results support the view that luminosity, and not type, is the dominant factor in determining how the clustering strength of the whole galaxy population varies with luminosity.     

An introduction to wave propagation in anisotropic media

Summary. Wave motion in an anisotropic solid is fundamentally different from motion in an isotropic solid, although the effects are often subtle and difficult to recognize. There are such a wide range of three-dimensional variations possible in anisotropic media that it is difficult to understand the behaviour of wave motion without experimentation. Laboratory experiments are very difficult to construct and extensive numerical experiments have now given many theoretical insights so that the behaviour of waves in anisotropic media is now comparatively well understood. This introduction summarizes some of the relationships and insights required for this understanding.     

Surface wave dispersion and Earth structure in south-eastern China

Summary. A reconnaissance study of crust and mantle structure in southeastern China was made using surface waves confined to that region from recent earthquakes. Data from the WWSSN stations ANP arid SEO, and from the digital stations TATO and MAT, were used to measure fundamental-mode group velocities of Love and Rayleigh waves over nine paths in south-eastern China, an area which has been technically quiet since the early Cenozoic. Crustal structure in this region is typical of stable continents, but shear-wave velocities in the uppermost mantle are low for a continent, 4.45 km s⁻¹ or less. Other seismological data support this observation.