Extrasolar planets and the rotation and axisymmetric mass-loss of evolved stars

I examine the implications of the recently found extrasolar planets on the planet-induced axisymmetric mass-loss model for the formation of elliptical planetary nebulae (PNe). This model attributes the low departure from spherical mass-loss of upper asymptotic giant branch (AGB) stars to envelope rotation which results from deposition of orbital angular momentum of the planets. Since about half of all PNe are elliptical, i.e., have low equatorial to polar density contrast, it was predicted that about 50 per cent of all Sun-like stars have Jupiter-like planets around them, i.e., a mass about equal to that of Jupiter, M _J, or more massive. In the light of the new findings that only 5 per cent of Sun-like stars have such planets, and a newly proposed mechanism for axisymmetric mass-loss, the cool magnetic spots model, I revise this prediction. I predict that indeed ∼50 per cent of PN progenitors do have close planets around them, but the planets can have much lower masses, as low as ∼0.01 M _J, in order to spin-up the envelopes of AGB stars efficiently. To support this claim, I follow the angular momentum evolution of single stars with main-sequence mass in the range of 1.3–2.4 M_⊙ , as they evolve to the post-AGB phase. I find that single stars rotate much too slowly to possess any significant non-spherical mass-loss as they reach the upper AGB. It seems, therefore, that planets, in some cases even Earth-like planets, are sufficient to spin-up the envelope of these AGB stars for them to form elliptical PNe. The prediction that on average several such planets orbit each star, as in the Solar system, still holds.     

On the Sitnikov problem

A mapping which reflects the properties of the Sitnikov problem is derived. We study the mapping instead of the original differential equations and discover that there exists a hyperbolic invariant set. The theoretical prediction of the disorder region agrees remarkably with numerical results. We also discuss the LCEs and KS-entropy of the dynamical system.This project is supported by the National Science Foundation of China.     

P–T modelling of the andalusite–kyanite–andalusite sequence and related assemblages in high-Al graphitic pelites. Prograde and retrograde paths in a late kyanite belt in the Variscan Iberia

The exceptional andalusite–kyanite–andalusite sequence occurs in Al‐rich graphitic slates in a narrow pelite belt on the hangingwall of a ductile normal fault in NW Variscan Iberia. Early chiastolite is replaced by Ky–Ms–Pg aggregates, which are overgrown by pleochroic andalusite near granites intruded along the fault. Slates plot in AKFM above the chloritoid‐chlorite tie‐line. Their P–T grids are modelled with Thermocalc v2.7 and the 1998 databases in the NaKFMASH and KFMASH systems. The univariant reaction Ctd + And/Ky = St + Chl + Qtz + H₂O ends at progressively lower pressure as F/FM increases and A/AFM decreases, shrinking the assemblage Cld–Ky–Chl, and opening a chlorite‐free Cld–Ky trivariant field on the low temperature reaction side. This modelling matches the observed absence of chlorite in high F/FM rocks, which is restricted to low pressure in the andalusite stability field. The P–T path deduced from modelling shows a first prograde event in the andalusite field followed by retrogression into the kyanite field, most likely coupled with a slight pressure increase. The final prograde evolution into the andalusite field can be explained by two different prograde paths. Granite intrusion caused the first prograde part of the path with andalusite growth. The subsequent thermal relaxation, together with a_H2O decrease, generated the retrograde andalusite–kyanite transformation, plus chlorite consumption and chloritoid growth. This transformation could have been related to folding in the beginning, and aided later by downthrowing due to normal faulting. Heat supplied by syntectonic granite intrusion explains the isobaric part of the path in the late stages of evolution, causing the prograde andalusite growth after the assemblage St–Ky–Chl. Near postectonic granites, a prograde path with pressure decrease originated the assemblage St–And–Chl.     

西秦岭文县地区关家沟组海底扇沉积体系

对西秦岭南部文县地区关家沟组的成因,学者之间的认识存在较大分歧,长期以来被看作是可与南沱组对比的冰碛层.关家沟组形成于新元古代末期(晚震旦世),沿扬子板块西北边缘分布.根据地层剖面和扇地质体的平面填图研究表明,关家沟组存在两种沉积体系--海底扇沉积体系和盆地沉积体系;海底扇沉积体系中发育大量的各种类型的粒序层理及鲍玛层序;扇体的剖面结构相似于Walker(1979)提出的海底扇反旋回沉积序列,层理类型与Winn和Dott(1979)提出的海底扇的层理类型类似;扇体的平面结构(填图追索圈定)清楚地显示了海底扇砂砾岩与盆地相页岩、硅质岩之间的穿插相变关系.其剖面结构可划分出4个级别的不对称它旋回性韵律,显示出扇体向盆地推进和相对海平面的降低.研究表明关家沟组砂砾岩为海底扇沉积体系,而非冰碛层.     

Model of VLBI observation within the relativistic framework

In this paper we derive the post-newtonian expressions for the VLBI time delay and gravitational delay in the barycentric coordinate system of the solar system. We discuss the effect of the various bodies and their range of action. From the transformation between the barycentric and the geocentric systems we then give the VLBI observational model in the geocentric system. Our final results are given by formula (16) for the gravitational delay and by formula (25) for the VLBI time delay.     

BOOK REVIEWS

Book Reviewed in this article: Women, Work, and Ideology in the Third World . Haleh Afshar, ed. The Birth of the National Park Service. The Founding Years 1913–33 . Horace M. Albright Theatres of Accumulation: Studies in Asian and Latin American Urbanization . Warwick Armstrong and T.G. McGee. New Tools for Social Scientists, Advances and Applications in Research Methods . William D. Berry and Michael S. Lewis -Beck , eds . Uncertain Dimensions: Western Overseas Empires in the Twentieth Century . Raymond F. Betts. Geography of Sugar Cane . Helmut Blume. The Mines of Neptune: Minerals and Metals from the Sea . Elisabeth Mann Borgese. Geographical Dimensions of Energy . F.J. Calzonetti and B.D. Solomon, eds. Statistical Methods for Geographers . W. A. V. Clark and P. L. Hosking. In The Wake of Columbus, Islands and Controversy . John DeVorsey, Jr., and John Parker, eds. Housing, States and Localities . Peter Dickens, Simon Duncan, Mark Goodwin and Fred Gray. Physician Location and Specialty Choice . Richard L. Ernst and Donald E. Yett. Practical Ecology for Geography and Biology: Survey, Mapping, and Data Analysis . D.D. Gilbertson , M. Kent and F.B. Pyatt Large Scale Water Transfers: Emerging Environmental and Social Experiences . Genady N. Golubev and Asit K. Biswas, eds. The Nature of the Environment . Andrew Goudie. Planning for Population Change . W.T.S. Gould and R. Lawton. The Niger and its Neighbors: Environmental History and Hydrobiology. Human Use and Health Hazards of the Major West African Rivers . A.T. Grove, ed. Remote Sensing of Ice and Snow . Dorothy K. Hall and Jaroslav Martinec. Atlas of Antebellum Southern Agriculture . Sam Bowers Hilliard. Galilee Divided; The Israel-Lebanon Frontier, 1916-1984 . Frederic C. Hor . Plains Country Towns . John C. Hudson. Agricultural Geography: A Social and Economic Analysis . Brian W. Ilbery. Industry in the 1980s: Structural Change and Interdependence . U.N. Industrial Development Organization. Crabgrass Frontier: The Suburbanization of the United States . Kenneth T. Jackson. The Industrial Geography of Italy . Russell King. Studies in Linguistic Geography: The Dialects of English in Britain and Ireland . John M. Kirk, Stewart Sanderson, J.D.A. Widdowson, eds. Tourism: A Community Approach . Peter E. Murphy. Cities and Services: The Geography of Collective Consumption . Steven Pinch. An Historical Geography of Europe 1800–1914 . Norman J. G. Pounds. An Introduction to Human Ecology Research on Agricultural Systems in Southeast Asia . A. Terry Rambo and Percy E. Sajise, eds. Discovering Past Landscapes . Michael Reed, ed. Managing the Ocean: Resources, Research, Law . Jacques G. Richardson, ed. Carta fitosociologica de la transecta botanica de la Patagonia Austral . F.A. Roig , Juan Anchorema , Orlando Dollenz , A.M. Faggi and Eduardo Mandez Intermetropolitan Migration in Canada: Changing Determinants over Three Decades . R. Paul Shaw. Chinese Cities—The Growth of the Metropolis since 1949 . Victor F. Sit, ed. Urbanization in the World-Economy . Michael Timberlake, ed. The Al Business: Commercial Uses of Artificial Intelligence . Patrick H. Winston and Karen A. Prendergast, eds.     

Statistical estimation of the apex of a sediment distribution system from paleocurrent data

Precise statistical models are proposed for the distribution of paleocurrent directions in distributary systems. These models are based on a von Mises distribution for directions of paleocurrents in a system. The method of maximum likelihood is used to obtain an estimated position and confidence regions for the apex of the system. Both axial data (where only the trend of the paleocurrent is known) and directional data (where the direction of paleoflow is known) can be used. These models have been applied to two fluvial distributary systems in flat-lying Miocene deposits in the Ebro Basin, northern Spain. The estimate of the position of the apex of one of these systems is in good agreement with the position at the basin margin predicted from sedimentary facies information. The estimate of the position of the apex of the second system lies outside of the sedimentary basin; this result is considered to indicate that the distributary system had several feeder points along the basin margin, a situation which is predicted also from facies distributions. This statistical procedure can be used successfully on small data sets of around a hundred paleocurrent readings provided that they are scattered evenly across the area or lie in a wide arc.     

The effect of long-lived vortical circulation on the dynamics of dust particles in the mid-plane of a protoplanetary disc

We investigate the response of dust particles in the mid-plane of a protoplanetary disc to the turbulent velocity field of long-lived, large-scale vortical circulation. The dynamical problem is studied through numerical integrations of the equations of motion for individual particles (the sizes of which range from centimetres to metres) subject to the solar gravity and the friction drag of the nebular gas. It is found, neglecting the thickness of the disc, that the particles do not drift inwards to the central star as occurs in a standard symmetrical nebula. Vortices tend to capture a large number of the particles. The effectiveness of this size-selective concentration mechanism depends not only on the value of the drag and the distance from the Sun, but also on the elongation of the vortex and its characteristic lifetime. Typical anticyclonic vortices with exponential decay times of 30 orbital periods and semi-axis ratios of 4 can increase the local surface density by a factor of 4 in a lifetime and accumulate 0.03–0.3 Earth masses. If the elongation is significant (>7), the vortex cannot concentrate any significant amount of solid material. Vortices with an elongation of about 2 are the most effective as regards trapping of dust. We have also found analytical expressions for the capture time as well as capture constraints as a function of the friction parameter, the elongation of the vortex and the impact parameter. By increasing the lifetime and the surface density of the solid particles, this confining mechanism can make the agglomeration of the solid material of the nebula (through collisional aggregation or gravitational instabilities) much more efficient than previously believed. This offers new possibilities for the formation of the planetesimals and the giant planet cores, and may explain the rapid formation of extrasolar giant planets.