The Roche Limit

The role of tides in deforming and possibly disrupting a secondary body orbiting about a primary body has been known for a considerable time. This was first inspired by the observations of ocean tides on Earth and then seen as playing an important role in the formation and evolution of the Earth–Moon system. Finally, in the beginning of the 20th century it was generally thought to have a significant role in the formation of the solar system through the tidal disruption of the Sun. Here, an overview of the historical developments of the ideas concerned with tidal disruption of a secondary body that can lead to mass loss is given. Some discussion of possible extensions to consider more realistic situations where the secondary body may not be moving on a circular orbit and may not rotate so as to maintain the phase-on configuration to the primary body is also given.     

An empirical model of the daily evolution of the coronal index

Global changes of the solar activity can be expressed by the coronal index that is based upon the total irradiance of the coronal 530.3 nm green line from observations at five stations. Daily mean values of the coronal index of solar activity and other well-correlated solar indices are analyzed for the period 1966–1998 covering over three solar cycles. The significant correlation of this index with the sunspot number and the solar flare index have led to an analytical expression which can reproduce the coronal index of solar activity as a function of these parameters. This expression explains well the existence of the two maxima during the solar cycles taking into account the evolution of the magnetic field that can be expressed by some sinusoidal terms during solar maxima and minima. The accuracy between observed and calculated values of the coronal index on a daily basis reaches the value of 71%. It is concluded that the representative character of the coronal index is preserved even when using daily data and can therefore allow us to study long-term, intermediate and short-term variations for the Sun as a star, in association with different periodical solar–terrestrial phenomena useful for space weather studies.     

Microtextures and crystal chemistry in P21/c pigeonites

Summary ?A single-crystal X-ray investigation was performed on crystals of P2₁/c natural pigeonite with varying Ca and Fe^* ( = Fe²⁺ + Mn²⁺) contents, in order to verify the effect of microtextural disorder on structure refinements and to constrain the crystal chemistry of pigeonite. Antiphase domains and exsolution lamellae affect differently the refinement results. In a crystal free of exsolution the structure obtained after refinement with all reflections is an average of that of the antiphase domains and of their boundaries, whereas in an exsolved crystal it represents only the structure of the prevailing pigeonite lamellae. The refinement using only h + k odd reflections seems to give the structure of the Ca-free pigeonite characteristic of the antiphase domains rather than that of Ca-rich domain walls. The ratio of the scale factors in refinements with all reflections and with only h + k odd reflections allows the ratios of the exsolved augite and pigeonite phases to be estimated. The crystal chemistry of the investigated samples follows the trends outlined by data on Ca-free and Fe-free synthetic samples. In particular, it is shown that Ca and Fe^* substitution for Mg induce similar changes in the average structure, i.e. both induce an expansion in the M1 polyhedron and decrease the difference between the M2–O3 distances. Received October 18, 2001; revised version accepted February 15, 2002     

Probing the nuclear activity with supermassive black holes

We report three new or updated techniques for probing the parameters of active galaxies based on the masses of their central black holes M_BH). First, we derived a near-IR analog of the bulge luminosity versus M_BH relationship. The low scatter makes it a promising new tool to study the black hole demographics. Next, we present relations between M_BH and the10 μm and 2-10 keV nuclear luminosity. They may help to study the M_BH evolution over wide redshift ranges. Finally, we measured M_BH in quasars from z ∼ 3.4 to z ∼ 0.3 to search directly for M_BH growth. Surprisingly, we found no evidence for growth implying that the majority of quasar host galaxies have undergone their last major merger at z ≥ 3. This revised version was published online in August 2006 with corrections to the Cover Date.     

Speckle interferometry observations of asteroids at tng

The Speckle camera of the 3.5 m Telescopio Nazionale Galileo (TNG) has been used to measure apparent sizes and shapes of a number of main belt asteroids. The average size measurements are in a generally good agreement with the results of indirect IRAS-based radiometric techniques. The measured shapes are compared with predictions based on previously derived spin axis directions and lightcurve photometry of some of the observed objects. Also in this case the agreement is reasonable and the speckle observations allow us to discriminate in some cases between the two pole solutions usually found for each object. No clear evidence of binaries was found. The results show that the TNG speckle camera can be a powerful tool to resolve relatively large main belt asteroids and to calibrate the results of the IRAS survey.     

Size and shape evolution of pores in a viscoplastic matrix under compression

The frequent use of soils and earth materials for hydraulic capping and for geo‐environmental waste containment motivated our interest in detailed modelling of changes in size and shape of macro‐pores to establish links between soil mechanical behaviour and concurrent changes in hydraulic and transport properties. The objective of this study was to use finite element analysis (FEA) to test and extend previous analytical solutions proposed by the authors describing deformation of a single macro‐pore embedded in linear viscoplastic soil material subjected to anisotropic remote stress. The FEA enables to consider more complex pore geometries and provides a detailed picture of matrix yield behaviour to explain shortcomings of approximate analytical solutions. Finite element and analytical calculations agreed very well for linear viscous as well as for viscoplastic materials, only limited for the case of isotropic remote stress due to the simplifications of the analytical model related to patterns and onset of matrix‐yielding behaviour. FEA calculations were compared with experimental data obtained from a compaction experiment in which pore deformation within a uniform modelling clay sample was monitored using CAT scanning. FEA predictions based on independently measured material properties and initial pore geometry provided an excellent match with experimentally determined evolution of pore size and shape hence lending credence to the potential use of FEA for more complex pore geometries and eventually connect macro‐pore deformation with hydraulic properties. Copyright © 2006 John Wiley & Sons, Ltd.     

The petrogenesis of type B1 Ca‐Al‐rich inclusions: The spinel perspective

Abstract— Minor element variations in MgAl₂O₄ spinel from the type B1 calcium‐aluminum‐rich inclusion (CAI) Allende TS‐34 confirm earlier studies in showing correlations between the minor element chemistry of spinels with their location within the inclusion and with the chemistry of host silicate phases. These correlations result from a combination of crystallization of a liquid produced by re‐melting event(s) and local re‐equilibration during subsolidus reheating. The correlation of the Ti and V in spinel inclusions with the Ti and V in the adjacent host clinopyroxene can be qualitatively explained by spinel and clinopyroxene crystallization prior to melilite, following a partial melting event. There are, however, difficulties in quantitative modeling of the observed trends, and it is easier to explain the Ti correlation in terms of complete re‐equilibration. The correlation of V in spinel inclusions with that in the adjacent host clinopyroxene also cannot be quantitatively modeled by fractional crystallization of the liquid produced by re‐melting, but it can be explained by partial re‐equilibration. The distinct V and Ti concentrations in spinel inclusions in melilite from the edge regions of the CAI are best explained as being affected by only a minor degree of re‐equilibration. The center melilites and included spinels formed during crystallization of the liquid produced by re‐melting, while the edge melilites and included spinels are primary. The oxygen isotope compositions of TS‐34 spinels are uniformly ¹⁶O‐rich, regardless of the host silicate phase or its location within the inclusion. Similar to other type B1 CAIs, clinopyroxene is ¹⁶O‐rich, but melilite is relatively ¹⁶O‐poor. These data require that the oxygen isotope exchange in TS‐34 melilite occurred subsequent to the last re‐melting event.