Gravity-darkening in eclipsing binaries

A quantitative analysis of the ellipticity effect in close binary systems of the W Ursae Maioris type with spectroscopically known mass-ratios discloses that the photometric ellipticities of these variables are, in general, more than twice as large as the dynamical ellipticities (due to the geometrical distortion alone) computed for contact models of centrally condensed stars. If, moreover, this excess of the photometric over dynamical ellipticity is attributed to the phenomenon of gravity-darkening over distorted surfaces of the constituent components, this darkening must be present to a considerablylarger degree than that predicted by the theory of radiative transfer — a result difficult to reconcile with the existence of extensive sub-surface convection zones in late-type Main-Sequence stars. If, on the other hand, gravity-darkening is present in W UMa-type systems in the amount predicted by the theory (let alone in the presence of sub-surface convection), the only effective way of reconciling the theory with the observations would be to assume that the mean fractional radii of their constituent components are appreciablylarger than those appropriate for contact models in which the two components just fill the largestclosed Roche equipotentials capable of containing their mass. In other words, it would appear that the W UMa-type stars considered in this paper may constitute a single dumb-bell figure rather than two distinct components; and that the observed variations of light, colour or radial velocity are invoked by the axial rotation (and consequent variable cross-section) or this dumb-bell figure rather than to the contribution of individual stars.     

Dynamical tides in close binary systems

The aim of the present paper will be to investigate the circumstances under which an irreversible dissipation of the kinetic energy into heat is generated by the dynamical tides in close binary systems if (a) their orbit is eccentric; (b) the axial rotation of the components is not synchronized with the revolution; or (c) the equatorial planes are inclined to that of the orbit.In Section 2 the explicit form of the viscous dissipation function will be set up in terms of the velocity-components of spheroidal deformation arising from the tides; in Section 3, the principal partial tides contributing to the dissipation will be detailed; Section 4 will be devoted to a determination of the extent of stellar viscosity — both gas and radiative; while in the concluding Section 5 quantitative estimates will be given of the actual rate at which the kinetic energy of dynamical tides gets dissipated into heat by viscous friction in stellar plasma.The results disclose that the amount of heat produced per unit time by tidal interaction between components of actual close binaries equals only about 10^–10th part of their nuclear energy production; and cannot, therefore, affect the internal structure of evolution of the constituent stars to any appreciable extent. Moreover, it is shown that the kinetic energy of their axial rotation can be influenced by tidal friction only on a nuclear, rather than gravitational (Kelvin) time-scale — as long as plasma or radiative viscosity constitute the sole sources of dissipation. However, the emergence of turbulent viscosity in secondary components of late spectral types, which have evolved away from the Main Sequence, can accelerate the dissipation 10⁵–10⁶ times, and thus give rise to appreciable changes in the elements of the system (particularly, in the orbital periods) over time intervals of the order of 10⁵–10⁶ years. Lastly, it is pointed out that, in close binary systems consisting of a pair of white dwarfs, a dissipation of the kinetic energy through viscous tides in degenerate fermion-gas could produce enough heat to account, by itself, for the observed luminosity of such objects.     

Dynamical tides in close binary systems

The aim of the present paper will be to deduce the explicit form of differential equations which govern dynamical tides in close binary systems, with simplifications which are permissible for the mass-point model (Section 2), as well as for one exhibiting finite but high internal density concentration (Section 3). It is pointed out that, whereas the exact formulation of the problem leads to a simultaneous system of equations of sixth order (fourth in the inviscid case), this order reduces to four (or two for inviscid fluids) for the mass-point model; and to five (three for inviscid case) if the density concentration is high but finite.In the last section of this paper the coefficientsC _i,j which specify the amplitudes of the individual partial tides are explicitly formulated as functions of the time.     

Triaxiality of Halley's Comet

There are many aspects of observational evidence that cometary nuclei have irregular or nonspherical shape. The triaxial figure of the Halley's Comet nucleus is a well known fact. Therefore, the nucleus shape plays a significant role in consideration of the formation and evolution of comets and several attempts have been made to explain their nonsphericity. These studies were mainly based on the random-walk schemes for the aggregation processes. Although some results indeed lead to irregularities and deviation from sphericity, the spherical or irregular shape seem to be prevailing results. On the other hand the triaxial figure can be formed by the tidal and rotational forces. Thus, the assumption that the shape of the cometary nucleus due to some of these effects is in principle acceptable. In here assumed scenario already evolved cometary nucleus is situated as a satellite in the gravitation field of a planetary-like body. Since the rigidity of the nucleus is low, it may be easily transferred in the state of a synchronous satellite and in its shape could be imprinted the dynamical effects from this epoch. Here presented results indicate, that such a possibility should be seriously considered. The theory of this process is applied to the nucleus of comet Halley. It is shown, that the nucleus might be synchronously orbiting around a planetary-like hypothetical body with a period of 0.7 days. The minimal bulk tensile strength of the cometary material of about 10² N m^–2 is estimated.     

The granite hosted gold deposit of Moulin de Chéni (Saint-Yrieix district,Massif Central,France): petrographic,structural, fluid inclusion and oxygen isotope constraints

The Moulin de Chéni orogenic gold deposit is the only granite-hosted deposit of the Saint-Yrieix district, French Massif Central. It occurs in 338±1.5 Ma-old peraluminous leucogranites and is characterized by intense microfracturing and bleaching of the granite in relation to pervasive sulfide crystallization. Formation of quartz veins and gold deposition occurred in two successive stages: an early mesozonal stage of quartz-sulfide (Fe-As-S) deposition, usually devoid of gold and a late epizonal stage of base metal and gold deposition. Both stages postdate peak metamorphism and granite intrusion. The genesis of the deposit is the result of four successive fluid events: (1) Percolation of aqueous-carbonic metamorphic fluids under an assumed lithostatic regime of 400–450 °C, at a maximum depth of 13 km; (2) Formation of the main quartz lodes with coeval K-alteration and introduction of As and S from aqueous-carbonic fluids percolating along regional faults. Arsenopyrite and pyrite deposition was linked to the alteration of Fe-silicates into K-feldspar and phengite at near-constant iron content in the bulk granite. Temperature was similar to that of the preceding stage, but pressure decreased to 100–50 MPa, suggesting rapid uplift of the basement up to 7.5 km depth; (3) The resulting extensional tectonic leads to the deposition of gold, boulangerite, galena and sphalerite in brecciated arsenopyrite and pyrite from aqueous fluids during a mixing process. Temperature and salinity decrease from 280 to 140 °C and 8.1 wt% eq. NaCl to 1.6 wt% eq. NaCl, respectively; (4) Sealing of the late fault system by barren comb quartz which precipitated from dilute meteoric aqueous fluids (1.6 wt% eq. NaCl to 0.9 wt% eq. NaCl) under hydrostatic conditions at 200–150 °C.Editorial handling: B. Lehmann     

Ab-initio calculations of the proton location in topaz-OH,Al<Subscript>2</Subscript>SiO<Subscript>4</Subscript>(OH)<Subscript>2</Subscript>

The position of hydrogen in the structure of topaz-OH was determined by means of ab-initio quantum-mechanic calculations. Static lattice energy calculations predict the existence of four non-equivalent positions of protons, which are characterized by O4–H1... O1, O4–H2... O2, O4–H3... O3 and O4–H4... O4 hydrogen bonds. The distribution of the protons between positions of local equilibrium is controlled by the proton–proton avoidance rule and the strength of the hydrogen bonds. The most favourable configuration of hydrogen atoms is achieved for adjacent protons, which form O4–H3... O3 and O4–H4... O4 hydrogen bonds, respectively. The thermal excitation of atoms at a temperature of 55 K is large enough for the hydrogen atoms occasionally to change their positions to form O4–H1... O1 and O4–H2... O2 bonds. At ambient pressures and higher temperatures the protons are in a dynamic exchange between the allowed positions of local minima. As a consequence, for nearly room-temperature conditions, the dynamic change between different structural configurations leads to the violation of all possible symmetry elements and with that to space group #E5/E5#1. The flipping of the protons between different sites is achieved by simple rotation of the OH-dipole and does not produce any significant distortion of the framework of topaz, whose symmetry remains that of the space group Pbnm. Therefore, no reduction of symmetry has been observed in former X-ray studies on topaz-OH. Calculated IR absorption spectra of topaz-OH were found to be in good agreement with measured spectra. According to the calculations, the two favourable configurations of protons might correspond to the measured peak splitting within the OH-stretching range. An experimentally observed low-frequency band at 3520 cm^–1 was assigned to the OH-stretching of the O4–H3... O3 bond, while the band at 3600 cm^–1 was attributed to OH-stretching of the O4–H4... O4 hydrogen bond. The broad peak in FAR-IR frequency range at 100–150 cm^–1 is attributed to the stretching of H3... O3 and H4... O4 contacts. The rate of proton exchange at 670 K among different sites was estimated by ab-inito molecular dynamic simulations. The calculations predict that flipping of adjacent protons between O4–H3... O3 and O4–H4... O4 bonds at 670 K occur at a rate of about 1.96 THz.     

Solar radiative output and its variability: evidence and mechanisms

Electromagnetic radiation from the Sun is Earths primary energy source. Space-based radiometric measurements in the past two decades have begun to establish the nature, magnitude and origins of its variability. An 11-year cycle with peak-to-peak amplitude of order 0.1 % is now well established in recent total solar irradiance observations, as are larger variations of order 0.2 % associated with the Suns 27-day rotation period. The ultraviolet, visible and infrared spectral regions all participate in these variations, with larger changes at shorter wavelengths. Linkages of solar radiative output variations with solar magnetism are clearly identified. Active regions alter the local radiance, and their wavelength-dependent contrasts relative to the quiet Sun control the relative spectrum of irradiance variability. Solar radiative output also responds to sub-surface convection and to eruptive events on the Sun. On the shortest time scales, total irradiance exhibits five minute fluctuations of amplitude %, and can increase to as much as 0.015 % during the very largest solar flares. Unknown is whether multi-decadal changes in solar activity produce longer-term irradiance variations larger than observed thus far in the contemporary epoch. Empirical associations with solar activity proxies suggest reduced total solar irradiance during the anomalously low activity in the seventeenth century Maunder Minimum relative to the present. Uncertainties in understanding the physical relationships between direct magnetic modulation of solar radiative output and heliospheric modulation of cosmogenic proxies preclude definitive historical irradiance estimates, as yet.Received: 26 August 2004, Published online: 16 November 2004 Correspondence to: Claus Fröhlich