Spectrophotometric Variability of Mira

Data from the Pulkovo spectrophotometric data base on the absolute quasimonochromatic fluxes from oCet in the 320–1080 nm range are used to determine the physical parameters of this star in different phases of its light curve. The continuum emission layer is found to expand between the phases of the cycle corresponding to the rising and falling branches of the light curve. The average expansion velocity is 32 km/s. By the time the star’s brightness has fallen by roughly three magnitudes, its radius has increased by almost a factor of three. Over this same time the temperature of the layer has fallen from 3000 K to 2200 K. For this expansion velocity, the calculated mass rate loss is ⊙ M /year.__________Translated from Astrofizika, Vol. 48, No. 2, pp. 175–189 (May 2005).     

VLA and MERLIN observations of RZ Cassiopeiae

We present radio interferometric observations of the Algol-type binary system RZ Cassiopeiae made with the VLA and MERLIN arrays at 6 cm over an incomplete orbital cycle of the system (1.195 d). We detected RZ Cas with both instruments. The images were unresolved in both cases, with angular extents comparable to the synthesized beams. The peak flux density in the VLA image was 1.14 mJy beam⁻¹ and in the MERLIN image it was 0.93 mJy beam⁻¹. The derived brightness temperatures are  4.02 × 10⁸  and  4.35 × 10⁸ K  and the effective electron energies are 0.347 and 0.346 MeV for the MERLIN and VLA data respectively. The radio light curve shows an interesting modulation centred close to the primary eclipse which seems to correlate with ASCA SIS observations of the system. The results can be interpreted as an emitting region on the outer hemisphere of the cool component aligned along the centroid axis of the binary system.     

Geometric Derivation of the Delaunay Variables and Geometric Phases

We derive the classical Delaunay variables by finding a suitable symmetry action of the three torus T³ on the phase space of the Kepler problem, computing its associated momentum map and using the geometry associated with this structure. A central feature in this derivation is the identification of the mean anomaly as the angle variable for a symplectic S ¹ action on the union of the non-degenerate elliptic Kepler orbits. This approach is geometrically more natural than traditional ones such as directly solving Hamilton–Jacobi equations, or employing the Lagrange bracket. As an application of the new derivation, we give a singularity free treatment of the averaged J ₂-dynamics (the effect of the bulge of the Earth) in the Cartesian coordinates by making use of the fact that the averaged J ₂-Hamiltonian is a collective Hamiltonian of the T³ momentum map. We also use this geometric structure to identify the drifts in satellite orbits due to the J ₂ effect as geometric phases.