Seismology of stellar envelopes: probing the outer layers of a star through the scattering of acoustic waves

The outer layers of Sun-like stars are regions of rapid spatial variation which modulate the p-mode frequencies by partially reflecting the constituent acoustic waves. With the accuracy that has been achieved by current solar observations, and that is expected from imminent stellar observations, this modulation can be observed from the spectra of the low-degree modes. We present a new and simple theoretical calculation to determine the leading terms in an asymptotic expansion of the outer phase of these modes, which is determined by the structure of the surface layers of the star. Our procedure is to compare the stellar envelope with a plane-parallel polytropic envelope, which we regard as a smooth reference background state. Then we can isolate a seismic signature of the acoustic phase and relate it to the stratification of the outer layers of the convection zone. One can thereby constrain theories of convection that are used to construct the convection zones of the Sun and Sun-like stars. The accuracy of the diagnostic is tested in the solar case by comparing the predicted outer phase with an exact numerical calculation.     

A high resolution,multiproxy Late‐glacial record of climate change and intrasystem responses in northwest England

A lacustrine carbonate sequence from Hawes Water, Lancashire, UK, has been studied using stable isotopic, lithological, pollen and mineral magnetic analysis. The data reveal four abrupt climatic oscillations in the Late‐glacial Interstadial leading up to the onset of the Loch Lomond Stadial. The data also point to climatic warming relatively early within the stadial, ca. 12 500 GRIP yr, prior to the onset of the Holocene. The oxygen isotope record is taken as a signature of climate forcing against which the response of the lake‐system can be monitored. By adopting this approach it is revealed that the response of the biological system to the rapid climatic oscillations is non‐linear and primarily a function of the antecedent conditions. A significant end‐Devensian isotopic excursion (A) is matched by only minor changes in the cold‐adapted floras and faunas. During the warmer interstadial, the response of the biological ecosystem (events B–D) is clearly influenced by thresholds: major changes in the catchment vegetation associated with relatively minor oscillations in the isotopic signature. The stratigraphical patterns reveal significant lag effects between the onset of climate deterioration and resulting changes in vegetation. Copyright © 2002 John Wiley & Sons, Ltd.     

On the r-mode spectrum of relativistic stars: the inclusion of the radiation reaction

We consider both mode calculations and time-evolutions of axial r modes for relativistic uniformly rotating non-barotropic neutron stars, using the slow-rotation formalism, in which rotational corrections are considered up to linear order in the angular velocity Ω. We study various stellar models, such as uniform density models, polytropic models with different polytropic indices n , and some models based on realistic equations of state. For weakly relativistic uniform density models and polytropes with small values of n , we can recover the growth times predicted from Newtonian theory when standard multipole formulae for the gravitational radiation are used. However, for more compact models, we find that relativistic linear perturbation theory predicts a weakening of the instability compared to the Newtonian results. When turning to polytropic equations of state, we find that for certain ranges of the polytropic index n , the r mode disappears, and instead of a growth, the time-evolutions show a rapid decay of the amplitude. This is clearly at variance with the Newtonian predictions. It is, however, fully consistent with our previous results obtained in the low-frequency approximation.     

Elastic solutions for stresses in a transversely isotropic half‐space subjected to three‐dimensional buried parabolic rectangular loads

In many areas of engineering practice, applied loads are not uniformly distributed but often concentrated towards the centre of a foundation. Thus, loads are more realistically depicted as distributed as linearly varying or as parabola of revolution. Solutions for stresses in a transversely isotropic half‐space caused by concave and convex parabolic loads that act on a rectangle have not been derived. This work proposes analytical solutions for stresses in a transversely isotropic half‐space, induced by three‐dimensional, buried, linearly varying/uniform/parabolic rectangular loads. Load types include an upwardly and a downwardly linearly varying load, a uniform load, a concave and a convex parabolic load, all distributed over a rectangular area. These solutions are obtained by integrating the point load solutions in a Cartesian co‐ordinate system for a transversely isotropic half‐space. The buried depth, the dimensions of the loaded area, the type and degree of material anisotropy and the loading type for transversely isotropic half‐spaces influence the proposed solutions. An illustrative example is presented to elucidate the effect of the dimensions of the loaded area, the type and degree of rock anisotropy, and the type of loading on the vertical stress in the isotropic/transversely isotropic rocks subjected to a linearly varying/uniform/parabolic rectangular load. Copyright © 2002 John Wiley & Sons, Ltd.     

The influence of a non‐associated flow rule on the calculation of the factor of safety of soil slopes

This paper presents a method that incorporates a non‐associated flow rule into the limit analysis to investigate the influence of the dilatancy angle on the factor of safety for the slope stability analysis. The proposed method retain's the advantage of the upper bound method, which is simple and has no stress involvement in the calculation of the energy dissipation and the factor of safety. Copyright © 2001 John Wiley & Sons, Ltd.     

The β Cephei instability strip

We carried out a series of linear stability analyses of the radial and low-degree non-radial p modes for stellar models with initial masses of     . The stellar models were computed by using convective overshoot distance     , 0.25 and 0.40  H _P. Our numerical results show that the β Cephei instability strip forms a horn-shaped region pointing upwards near the main sequence on the Hertzsprung–Russell diagram (HRD). The lower part of the instability strip for the radial modes join the zero-age main-sequence (ZAMS) at     , while the top of the instability strip extends up to     . The instability strip for the non-radial modes is even wider. The overall instability strip is dominated by the radial and non-radial fundamental modes. The first overtone (the radial-order index     is also pulsationally unstable. We have shown that the β Cephei stability is almost independent of the overshoot parameter d _over used for the stellar models, while it depends critically on the metal abundance. With decreasing metal abundance, the instability region shrinks and eventually disappears for     .     

Late Holocene great earthquakes and relative sea‐level change at Kenai,southern Alaska

Kenai, located on the west coast of the Kenai Peninsula, Alaska, subsided during the great earthquake of AD 1964. Regional land subsidence is recorded within the estuarine stratigraphy as peat overlain by tidal silt and clay. Reconstructions using quantitative diatom transfer functions estimate co‐seismic subsidence (relative sea‐level rise) between 0.28±0.28 m and 0.70±0.28 m followed by rapid post‐seismic recovery. Stratigraphy records an earlier co‐seismic event as a second peat‐silt couplet, dated to ～1500–1400 cal. yr BP with 1.14±0.28 m subsidence. Two decimetre‐scale relative sea‐level rises are more likely the result of glacio‐isostatic responses to late Holocene and Little Ice Age glacier expansions rather than to co‐seismic subsidence during great earthquakes. Comparison with other sites around Cook Inlet, at Girdwood and Ocean View, helps in constructing regional patterns of land‐level change associated with three great earthquakes, AD 1964, ～950–850 cal. yr BP and ～1500–1400 cal. yr BP. Each earthquake has a different spatial pattern of co‐seismic subsidence which indicates that assessment of seismic hazard in southern Alaska requires an understanding of multiple great earthquakes, not only the most recent. All three earthquakes show a pre‐seismic phase of gradual land subsidence that marked the end of relative land uplift caused by inter‐seismic strain accumulation. Copyright © 2005 John Wiley & Sons, Ltd.     

Effects of clumping on temperature – I. Externally heated clouds

We present a study of radiative transfer in dusty, clumpy star-forming regions. A series of self-consistent, 3D, continuum radiative transfer models are constructed for a grid of models parametrized by central luminosity, filling factor, clump radius and face-averaged optical depth. The temperature distribution within the clouds is studied as a function of this parametrization. Among our results, we find that: (i) the effective optical depth in clumpy regions is less than in equivalent homogeneous regions of the same average optical depth, leading to a deeper penetration of heating radiation in clumpy clouds, and temperatures higher by over 60 per cent; (ii) penetration of radiation is driven by the fraction of open sky (FOS) – which is a measure of the fraction of solid angle along which no clumps exist; (iii) FOS increases as clump radius increases and as filling factor decreases; (iv) for values of   FOS >0.6–0.8  the sky is sufficiently 'open' that the temperature distribution is relatively insensitive to FOS; (v) the physical process by which radiation penetrates is preferentially through streaming of radiation between clumps as opposed to diffusion through clumps; (vi) filling factor always dominates the determination of the temperature distribution for large optical depths, and for small clump radii at smaller optical depths; (vii) at lower face-averaged optical depths, the temperature distribution is most sensitive to filling factors of 1–10 per cent, in accordance with many observations; (viii) direct shadowing by clumps can be important for distances approximately one clump radius behind a clump.     

Late Quaternary submarine bedforms and ice‐sheet flow in Gerlache Strait and on the adjacent continental shelf,Antarctic Peninsula

Geophysical data from Gerlache Strait, Croker Passage, Bismarck Strait and the adjacent continental shelf reveal streamlined subglacial bedforms that were produced at the bed of the Antarctic Peninsula Ice Sheet (APIS) during the last glaciation. The spatial arrangement and orientation of these bedforms record the former drainage pattern and flow dynamics of an APIS outlet up‐flow, and feeding into, a palaeo‐ice stream in the Western Bransfield Basin. Evidence suggests that together, they represent a single ice‐flow system that drained the APIS during the last glaciation. The ice‐sheet outlet flowed north/northeastwards through Gerlache Strait and Croker Passage and converged with a second, more easterly ice‐flow tributary on the middle shelf to form the main palaeo‐ice stream. The dominance of drumlins with low elongation ratios suggests that ice‐sheet outlet draining through Gerlache Strait was comparatively slower than the main palaeo‐ice stream in the Western Bransfield Basin, although the low elongation ratios may also partly reflect the lack of sediment. Progressive elongation of drumlins further down‐flow indicates that the ice sheet accelerated through Croker Passage and the western tributary trough, and fed into the main zone of streaming flow in the Western Bransfield Basin. Topography would have exerted a strong control on the development of the palaeo‐ice stream system but subglacial geology may also have been significant given the transition from crystalline bedrock to sedimentary strata on the inner–mid‐shelf. In the broader context, the APIS was drained by a number of major fast‐flowing outlets through cross‐shelf troughs to the outer continental shelf during the last glaciation. Copyright © 2004 John Wiley & Sons, Ltd.     

Depositional and post‐depositional history of warm stage deposits at Knocknacran,Co. Monaghan,Ireland: implications for preservation of Irish last interglacial deposits

Organic‐rich deposits, uncovered during overburden removal from mantled gypsum karst at Knocknacran opencast gypsum mine, Co. Monaghan, are the best candidate to date for a last interglacial record in Ireland. The two till and organic‐rich deposits (preserved at different quarry elevations) were emplaced on to a Tertiary dolerite surface during high‐energy flood events and subsequently folded and faulted by movement towards sinkholes in underlying gypsum. Uranium–thorium disequilibrium dating suggests that the organic‐rich deposits in the upper section were hydrologically isolated at ca. 41 ka and those in the lower section at ca. 86 ka. Interpretation of the pollen content, although tentative because of the depositional and post‐depositional history of the material, suggests that the organic material originated in a warm stage possibly warmer than the post‐Eemian interstadials. The unusual setting of preservation may indicate that in situ, last interglacial deposits have generally been removed by erosion in Ireland. Copyright © 2004 John Wiley & Sons, Ltd.