Radiative acceleration in Schwarzschild space–times

We examine the radial motion of a material particle in the intense radiation field of a static spherically symmetric compact object with spherical emitting surface outside the Schwarzschild radius. This paper generalizes previous work which dealt with radial motion in the Thomson limit, where the radiation force is simply proportional to the radiative flux. In the general case the average time component of the 4-momentum transferred to the particle is not negligible compared with its rest mass. Consequently, we find that the frequency dependence of the radiation force owing to Compton scattering for highly energetic photons gives rise to an increase in the effective mass of the test particle. In this work we outline the effects of this frequency dependence and compare these with the results in the Thomson limit. We present the frequency dependent saturation velocity curves for a range of stellar luminosities and radiation frequencies and present the resulting phase-space diagrams corresponding to the radial test particle trajectories. In particular, the stable equilibrium points which exist in the Thomson limit are found to be absent in the general case.     

Partial redistribution effects on line polarization in the presence of velocity fields

Velocity fields in line formation regions strongly affect the line polarization. The conventionally used observer's frame method of solving the polarized transfer equation becomes expensive and inaccurate for partial redistribution problems, when large amplitude velocity fields have to be considered in the observer's frame. An alternative method of solution is the comoving frame method. Partial redistribution problems are solved using comoving frame formalism for line polarization caused by resonance scattering.     

An iterative technique for solving equations of statistical equilibrium

Superlevel partitioning is combined with a simple relaxation procedure to construct an iterative technique for solving equations of statistical equilibrium. In treating an N -level model atom, the technique avoids the N ³ scaling in computer time for direct solutions with standard linear equation routines and also does not fail at large N due to the accumulation of round-off errors. As a consequence, the technique allows detailed model atoms with N ≳10³ , such as those required for iron peak elements, to be incorporated into diagnostic codes for analysing astronomical spectra. Tests are reported for a 394-level Fe  ii ion and a 1266-level Ni  i – iv atom.     

Self‐similar solution of a plane‐strain fracture driven by a power‐law fluid

This paper analyses the problem of a hydraulically driven fracture, propagating in an impermeable, linear elastic medium. The fracture is driven by injection of an incompressible, viscous fluid with power‐law rheology and behaviour index n?0. The opening of the fracture and the internal fluid pressure are related through the elastic singular integral equation, and the flow of fluid inside the crack is modelled using the lubrication theory. Under the additional assumptions of negligible toughness and no lag between the fluid front and the crack tip, the problem is reduced to self‐similar form. A solution that describes the crack length evolution, the fracture opening, the net fluid pressure and the fluid flow rate inside the crack is presented. This self‐similar solution is obtained by expanding the fracture opening in a series of Gegenbauer polynomials, with the series coefficients calculated using a numerical minimization procedure. The influence of the fluid index n in the crack propagation is also analysed. Copyright © 2002 John Wiley & Sons, Ltd.     

Modelling line profiles in infalling cores

Results are presented from a model of molecular line formation in collapsing star-forming cores. The study includes, for the first time, a self-consistent chemical and dynamical model which is then directly coupled to an appropriate radiative transfer model. The assumptions of chemical uniformity or simple monotonic variations within such cores are shown to be unacceptable. The results show that the abundance variations and the line profiles are highly sensitive to the assumed values of the free parameters in the chemical model. Extreme caution is therefore advised in the quantitative analysis of emission-line profiles from infall sources. The implied degeneracy can be overcome by multiple line-of-sight observations of many species and transitions.     

Turbulence in Class 0 and I protostellar envelopes

We estimate the levels of turbulence in the envelopes of class 0 and I protostars using a model based on measurements of the peak separation of double-peaked asymmetric line profiles. We use observations of 20 protostars of both class 0 and I taken in the  HCO⁺(J = 3 → 2)  line that show the classic double-peaked profile. We find that some class 0 sources show high levels of turbulence, whilst others demonstrate much lower levels. In class I protostars, we find predominantly low levels of turbulence. The observations are consistent with a scenario in which class 0 protostars form in a variety of environments and subsequently evolve into class I protostars. The data do not appear to be consistent with a recently proposed scenario in which class 0 protostars can only form in extreme environments.     

A new European testate amoebae transfer function for palaeohydrological reconstruction on ombrotrophic peatlands

Proxy climate data can be obtained from reconstructions of hydrological changes on ombrotrophic (rain‐fed) peatlands using biological indicators, such as testate amoebae. Reconstructions are based on transfer functions, relating modern assemblage composition to water table and moisture content, applied to fossil sequences. Existing transfer functions in Europe and elsewhere are limited geographically and there are often problems with missing or poor analogues. This paper presents a new palaeohydrological transfer function based on sampling raised mires from across Europe. Relationships between assemblages and hydrological variables are described using ordination analyses. Transfer functions are developed for depth to water table (n = 119) and moisture content (n = 132) with root mean squared errors (RMSEP) of 5.6 cm and 2.7% respectively. Both transfer functions have an r² of 0.71, based on ‘leave one out’ cross‐validation. Comparisons with an existing transfer function for Britain show that the European transfer function performs well in inferring measured water tables in Britain but that the British data cannot be used to infer water tables for other European sites with confidence. Several of the key missing and poor analogue taxa problems encountered in previous transfer functions are solved. The new transfer function will be an important tool in developing peat‐based palaeoclimatic reconstructions for European sites. Copyright © 2006 John Wiley & Sons, Ltd.