We analyze the structure and stability of singular singly quantized vortices in a rotating spin-1 Bose-Einstein condensate. We show that the singular vortex can be energetically stable in both the ferromagnetic and polar phases despite the existence of a lower-energy nonsingular coreless vortex in the ferromagnetic phase. The spin-1 system exhibits an energetic hierarchy of length scales resulting from different interaction strengths, and we find that the vortex cores deform to a larger size determined by the characteristic length scale of the spin-dependent interaction. We show that in the ferromagnetic phase the resulting stable core structure, despite apparent complexity, can be identified as a single polar core with an axially symmetric density profile which is nonvanishing everywhere. In the polar phase, the energetically favored core deformation leads to a splitting of a singly quantized vortex into a pair of half-quantum vortices that preserves the topology of the vortex outside the extended core region, but breaks the axial symmetry of the core. The resulting half-quantum vortices exhibit nonvanishing ferromagnetic cores.

We demonstrate how conservation of longitudinal magnetization can have pronounced effects on both stability and structure of vortices in the atomic spin-1 Bose-Einstein condensate by providing a systematic characterization of nonsingular and singular vortex states. Constructing spinor wave functions for vortex states that continuously connect ferromagnetic and polar phases, we systematically derive analytic models for nonrotating cores of different singular vortices and for composite defect states with distinct small-and large-distance topology. We explain how the conservation law provides a stabilizing mechanism when the coreless vortex imprinted on the condensate relaxes in the polar regime of interatomic interactions. The resulting structure forms a composite defect: The inner ferromagnetic coreless vortex deforms toward an outer singly quantized polar vortex. We also numerically show how other even more complex hierarchies of vortex-core topologies may be stabilized. Moreover, we analyze the structure of the coreless vortex also in a ferromagnetic condensate and show how reducing magnetization leads to a displacement of the vortex from the trap center and eventually to the deformation and splitting of its core where a singular vortex becomes a lower-energy state. For the case of singular vortices, we find that the stability and the core structure are notably less influenced by the conservation of magnetization.

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A rare eclipse of the mysterious object Aurigae will occur in 2009-2011. We report an updated single-lined spectroscopic solution for the orbit of the primary star based on 20 years of monitoring at the CfA, combined with historical velocity observations dating back to 1897. There are 518 new CfA observations obtained between 1989 and 2009. Two solutions are presented. One uses the velocities outside the eclipse phases together with mid-times of previous eclipses, from photometry dating back to 1842, which provide the strongest constraint on the ephemeris. This yields a period of 9896.0 ± 1.6 days (27.0938 ± 0.0044 years) with a velocity semiamplitude of 13.84 ± 0.23 km s −1 and an eccentricity of 0.227 ± 0.011. The middle of the current ongoing eclipse predicted by this combined fit is JD 2,455,413.8 ± 4.8, corresponding to 2010 August 5. If we use only the radial velocities, we find that the predicted middle of the current eclipse is nine months earlier. This would imply that the gravitating companion is not the same as the eclipsing object. Alternatively, the purely spectroscopic solution may be biased by perturbations in the velocities due to the short-period oscillations of the supergiant.