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2.1 The Measurement Principle and the Scanning Law

The main objective of the GAIA mission is to perform global or wide field astrometry as opposed to local or narrow field astrometry. In local astrometry a star's position can only be measured with respect to neighbouring stars in the same field. Even with an accurate instrument, the errors become prohibitive when making a survey, due to the need of combining measurements obtained in different fields, and thus affected by systematic and accidental errors. The principle of global astrometry, is instead to link stars with large angular distances in a network where each star is connected to a large number of other stars in every direction. In order to do so, the measurement of large angular distances through the simultaneous observation of two fields of view separated by a large angle is required.

This principle, first demonstrated by the success of the Hipparcos mission, can be exemplified by the problems encountered in the measurement of stellar parallaxes as it can be obtained with narrow-field instruments, illustrated in Figure 2.1. These are usually based on the measurement of the motion of a star S with respect to a number of background stars near to S on the sky, which are themselves in parallactic motion. The relation between the relative parallax $ \pi_{rel}=(\phi_2-\phi_1)/2$ of S with respect to a generic background star S$ _0$ and the absolute parallax of S $ \pi_{abs}$ is then $ \pi_{abs}=\pi_{rel}+\pi_0$, where $ \pi_0$ is the absolute parallax of S$ _0$. In practice, one has to estimate the average absolute parallax of the background stars, and this estimation introduces an error that usually dominates the global error budget. This limitation presently does not allow to measure parallaxes with an accuracy better than about a few mas. In wide-field astrometry, instead, the measurement of large angular distances allows one to measure the absolute parallax $ \pi_{abs}=(\phi_2-\phi_1)/2$ of a star without the need to apply poorly determined correction factors, and the accuracy can thus be improved by orders of magnitude.

Figure 2.1: Narrow-field and wide-field astrometry. In narrow-field astrometry the measurement of the parallax of a star S involves the application of a poorly determined correction to the observed value to take into account the parallactic motion of background stars such as S$ _0$, whereas in wide-field astrometry one can directly measure absolute parallaxes, thus obtaining a much better accuracy.

Accordingly, the GAIA payload must therefore provide two lines of sight, which can be obtained either with a single telescope and a beam combiner, as in Hipparcos, or with two separate telescopes. In either case, an high stability and an accurate knowledge of the variations of the basic angle between the two lines of sight is required in order to calibrate the astrometric measurements. The beam combiner option, however, leads to severe opto-mechanical problems for large-aperture (say above one meter or so) telescopes. Besides, the superposition of two fields of view onto a single focal plane causes crowding and object confusion on the focal plane, which become appreciable when observing faint objects. Therefore, the two-telescope concept was retained for the GAIA design and later refined with the inclusion of a third spectrometric telescope.

Figure 2.2: GAIA scanning law. The satellite spin and Sun axes at an angle of 55 deg are indicated, together with the lines of sight of the two astrometric instruments and two consecutive great circles. The satellite spin period is of about 3 hours, and the corresponding scanning speed is thus of 120 arcsec/s.

For a continuous accurate calibration of the basic angle, the two astrometric lines of sight must point to the same sky regions at small time intervals. This is achieved by means of an axisymmetric payload and a three-hour period (i.e. 120 arcsec/s) spin motion of the satellite about its symmetry axis, which is perpendicular to the instruments' lines of sight. From the instruments' standpoint, the stars thus cross each field of view with a uniform motion. As for Hipparcos, the scan direction is a privileged one, and the position measurements are essentially performed in this direction only. The complete and uniform sky coverage that is needed to build the star network is then obtained through a slow precession of the spin axis about the Sun axis. The angle between these two axes, or Sun angle, is thus kept constant, in order to minimize the thermal gradients in the payload. For GAIA, the optimization of the scanning law has led to a un angle of 55  deg (43  deg for Hipparcos) and a precession period of 72 days (57 days for Hipparcos). This scanning law ensures that each sky region is observed several times during the whole mission with nearly isotropic orientations of the scanning directions. The slow precession of the spin axis generates a line of sight motion across scan of 0.51 deg over a spin period, while the field of view height is 0.68 deg. The overlapping between consecutive scans allows the calibration of some instrumental parameters such as the basic angle using the same stars. The GAIA scanning law is illustrated in Figure 2.2, while its typical sky coverage pattern is exemplified by the actual scanning of the Hipparcos satellite over a short period shown in Figure 2.3.

Figure 2.3: GAIA/Hipparcos sky coverage. The top figure shows the path of Hipparcos spin axis over a four-month period. The scan direction is indicated by the arrows. The bottom figure shows the actual scanning by Hipparcos during one complete precession of the spin axis (57 days). For clarity, only one reference great circle out of five is indicated. The actual scanning is five times denser.

The apparent peculiarity of the adopted observation strategy draws a sharp distinction between scanning satellites like GAIA and conventional ``point-and-stare'' space observatories such as the HST. The distinction is fairly similar to the one existing between conventional ground-based telescopes and meridian circles, i.e. the telescopes that are typically used for ground-based astrometric measurements. Like meridian circles, GAIA will only detect relatively bright stars, due to the short exposure times that are allowed by a continuously scanning instrument. Unlike meridian circles, however, GAIA will be able to combine many observations of any sky region, obtained at different epochs and at different position angles, so as to significantly raise the all-mission signal-to-noise ratio. The number of observations of a given sky region mainly depends on its ecliptic latitude, owing to the fact that the chosen scanning pattern is symmetrical with respect to the Sun-satellite direction. The number of observations of 5000 random sky regions by both astrometric instruments is given as a function of the ecliptic latitude for a 5-year mission in Figure 2.4. The maximum, average and minimum number of observations are about 420, 170 and 100 (i.e. 210, 85 and 50 per astrometric instrument), respectively, where the latter value is obtained for sky regions near the ecliptic.

Figure 2.4: Number of observations of 5000 random sky regions by both astrometric instruments over a 5-year mission as function of ecliptic latitude. The average number of observations is 170. Courtesy of Lennart Lindegren, Lund Observatory.

next up previous contents
Next: 2.2 The Spacecraft Up: 2. The GAIA Mission Previous: 2. The GAIA Mission   Contents
Mattia Vaccari 2000-12-05