an); and comparison of Earth rotation parameters obtained by VLBI and by ground-based optical observations of Hipparcos stars. Although very different in terms of instruments, observational methods and objects involved, the various techniques generally agreed to within 10 milliarc-sec in the orientation and 1 milliarc-sec/yr in the rotation of the system. From appropriate weighting, the coordinate axes defined by the published catalogue are believed to be aligned with the extragalactic radio frame to within ±0.6 milliarc-sec at the epoch J1991.25, and non-rotating with respect to distant extragalactic objects to within ±0.25 milliarc-sec/yr.
The Hipparcos and Tycho Catalogues were then constructed such that the Hipparcos reference frame coincides, to within observational uncertainties, with the International Celestial Reference System (the ICRS), and representing the best estimates at the time of the catalogue completion (in 1996). The resulting Hipparcos reference frame is thus the materialisation of the ICRS in the optical. It extends and improves the J2000 (FK5) system, retaining approximately the global orientation of that system but without its regional errors.
Double and multiple stars
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Whilst of enormous astronomical importance, double stars and multiple stars provided considerable complications to the observations (due to the finite size and profile of the detector's sensitive field of view) and to the data analysis. The data processing classified the astrometric solutions as follows:
- single-star solutions: 100,038 entries, of which 6,763 were flagged as suspected double
- component solutions (Annex C): 13,211 entries, comprising 24,588 components in 12,195 solutions
- acceleration solutions (Annex G): 2,622 solutions
- orbital solutions (Annex O): 235 entries
- variability-induced movers (Annex V): 288 entries
- stochastic solutions (Annex X): 1,561 entries
- no valid astrometric solution: 263 entries (of which 218 were flagged as suspected double)
If a binary star has a long orbital period such that non-linear motions of the photocentre were insignificant over the short (3-year) measurement duration, the binary nature of the star would pass unrecognised by Hipparcos, but could show as a Hipparcos proper motion discrepant compared to those established from long temporal baseline proper motion programmes on ground. Higher-order photocentric motions could be represented by a 7-parameter, or even 9-parameter model fit (compared to the standard 5-parameter model), and typically such models could be enhanced in complexity until suitable fits were obtained. A complete orbit, requiring 7 elements, was determined for 45 systems. Orbital periods close to one year can become degenerate with the parallax, resulting in unreliable solutions for both. Triple or higher-order systems provided further challenges to the data processing.
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The highest accuracy photometric data were provided as a by-product of the main mission astrometric observations. They were made in a broad-band visible light passband, specific to Hipparcos, and designated Hp. The median photometric precision, for Hp<9 mag, was 0.0015 mag, with typically 110 distinct observations per star throughout the 3.5-year observation period. As part of the data reductions and catalogue production, new variables were identified and designated with appropriate variable star identifiers. Variable stars were classified as periodic or unsolved variables; the former were published with estimates of their period, variability amplitude, and variability type. In total some 11,597 variable objects were detected, of which 8237 were newly classified as variable. There are, for example, 273 Cepheid variables, 186 RR Lyr variables, 108 Delta Scuti variables, and 917 eclipsing binary stars. The star mapper observations, constituting the Tycho (and Tycho-2) Catalogue, provided two colours, roughly B and V in the Johnson UBV photometric system, 