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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).
| New periodic variables from the Hipparcos epoch photometry
Two selection statistics are used to extract new candidate periodicvariables from the epoch photometry of the Hipparcos catalogue. Theprimary selection criterion is a signal-to-noise ratio. The dependenceof this statistic on the number of observations is calibrated usingabout 30000 randomly permuted Hipparcos data sets. A significance levelof 0.1 per cent is used to extract a first batch of candidate variables.The second criterion requires that the optimal frequency be unaffectedif the data are de-trended by low-order polynomials. We find 2675 newcandidate periodic variables, of which the majority (2082) are from theHipparcos`unsolved' variables. Potential problems with theinterpretation of the data (e.g. aliasing) are discussed.
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