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CK Bootis: a W UMa system with a small mass ratio
We present an analysis of BVR light curves of an eclipsing binary {CKBootis}, a system with a very small mass ratio. The light curves appearto exhibit a typical O'Connell effect. The light curves are analyzed bymeans of the latest version of the WD program. The asymmetry of thelight curves is explained by a cool star spot model. The simultaneousBVR synthetic light curve analysis gives a tiny mass ratio of 0.12, anextremely large fill-out factor of 0.65, and a very small differencebetween the component temperatures of 90 K. The absolute parameters ofthe system were also derived by combining the photometric solutions withthe radial velocity data. The mass of the secondary is very low (0.15M_ȯ) and it continues losing mass. Thirty seven new times ofminimum are reported. It is found that the orbital period of the systemhas a quasi periodic variation, superimposed on a period increase. Thelong-term period increase rate is deduced to be dP/dt = 3.54 x10-7 d yr-1, which can be interpreted as being dueto mass transfer from the less massive star to the more massivecomponent.
| Statistical Constraints for Astrometric Binaries with Nonlinear Motion
Useful constraints on the orbits and mass ratios of astrometric binariesin the Hipparcos catalog are derived from the measured proper motiondifferences of Hipparcos and Tycho-2 (Δμ), accelerations ofproper motions (μ˙), and second derivatives of proper motions(μ̈). It is shown how, in some cases, statistical bounds can beestimated for the masses of the secondary components. Two catalogs ofastrometric binaries are generated, one of binaries with significantproper motion differences and the other of binaries with significantaccelerations of their proper motions. Mathematical relations betweenthe astrometric observables Δμ, μ˙, and μ̈ andthe orbital elements are derived in the appendices. We find a remarkabledifference between the distribution of spectral types of stars withlarge accelerations but small proper motion differences and that ofstars with large proper motion differences but insignificantaccelerations. The spectral type distribution for the former sample ofbinaries is the same as the general distribution of all stars in theHipparcos catalog, whereas the latter sample is clearly dominated bysolar-type stars, with an obvious dearth of blue stars. We point outthat the latter set includes mostly binaries with long periods (longerthan about 6 yr).
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