Data Reductions - Hipparcos
When in contact with one of the three ground-stations, the Hipparcos astrometry satellite returned an uninterrupted flow of data to the ground at a rate of 24 kbit/s. For more than three years, after the successful implementation of the 'revised-orbit' mission, this situation prevailed for more than 60 per cent of the time on average. The resulting data stream contained positional and photometric information from the primary optical detection system on board, which measured the relative along-scan separation of programme stars present within the combined fields of view of the Hipparcos telescope, as well as information from the satellite's attitude measurement and control system. The data reductions then consisted of re-assembling these data into a system of star positions, distances and space motions of the 120,000 observed stars. An auxiliary catalogue (the Tycho Catalogue, which is of lower positional precision but which contains additional photometric information) of about one million stars was constructed from the data stream which was sent down by the satellite's star mappers. (In 2000, following a reanalysis of the star mapper data the Tycho-2 Catalogue was released. Tycho-2 contains positions, motions, brightness and colours for 2,539,913 stars, more than doubling the number of stars in the original Tycho Catalogue.)
Within the main data reduction consortia (NDAC and FAST) and the Tycho consortium (TDAC), effort initially focussed on a full validation of the complex data processing chains eventually turning to the 'mass' data processing which was started within the groups in mid-1991.
The data processing proceeded as follows. Measurements taken over an interval of about 10 hours, corresponding to the orbital period of the satellite in its revised elliptical orbit, were combined together. The first part of the adopted 'three-step' analysis method consisted of estimating the relative one-dimensional positions of all the stars contained in the strip of sky scanned over the 10-hour interval (roughly a circle of 1 degree width), each with respect to the others. Essential inputs to this task were the modulation signals for each star, analysed to yield an intensity and a phase of modulation (the relative phases themselves provide an estimate of the relative positions of the stars in the scanning direction), and estimates of the satellite attitude throughout its scanning motion.
Typically, about 2,000 stars are contained within such a strip of the sky. Strong closure conditions exist in the system of equations that describe these 'great circles' on the sky, and this fact enables a solution to be made of the transformation that describes how the sky actually 'maps' onto the focal surface of the instrument. Monitoring this transformation versus time gives an indication of how well the equations can be solved, how accurate the determined star positions are, and how the instrument itself changes with time.
Every ten-hour orbit yielded a set of 2,000 one-dimensional star positions covering one great circle on the sky. In the data analysis process, these results were calculated from the raw satellite data, then put aside, until enough circles were available to carry out step 2 of the three-step procedure. This involved the interconnection, and interlocking, of a large number of such circles, obtained over a period of a few months - this is referred to as the 'sphere solution' step in the Hipparcos terminology.
Since all the stars in the great-circle step are connected only relatively to each other, the one-dimensional positions derived have, in practice, an unknown origin, or zero-point. In connecting together large numbers of these circles, it is evident that these origins can no longer be viewed as arbitrary - only one value for the origin of each circle will give the most consistent results for all the circles taken together. The sphere solution is essentially the process of solving for the origins of the circles and, in the process, converting the relative positions on the circles into 'absolute' (but still one-dimensional) positions.
The final part of the three-step method consisted of collecting together the absolute one-dimensional positions for each star observed on each great circle, and examining how these various pieces of information could be assembled to yield not only the star's two-dimensional position on the sky (in right ascension and declination) but also its space motion and its distance. The very large number of observations (typically 100 over a 2-3 year mission) and the small number of 'astrometric parameters' (just 5 per star) that were being solved for, meant that there was generally sufficient information available to indicate whether these parameters had been well estimated, or whether the achieved fit indicated that the star is a component of a double or multiple system.
The whole of the three-step procedure therefore actually results in an improvement of the observed star positions. However, the results, especially in the early stages of the mission data processing, still include a dependence on the original poorly known star positions available from ground-based observations. The entire solution has to be iterated, perhaps several times, using the newly derived positions as inputs to the attitude estimation. This results in the derivation of new and improved positions from the sphere solution process.
Further details of the reductions can be found in Volume 3 of the 3-volume publication ESA SP-1111; and in papers contained in Volume 258 of Astronomy & Astrophysics (1992).