2.7 Expected Measurement Capabilities

Roughly speaking, GAIA will observe all objects brighter than $V=20$ in the Astrometric Instruments (astrometry and broad-band photometry) and all objects brighter than $V=16-17$ in the Spectrometric Instrument (radial velocity measurements and medium-band photometry). The sample that will thus be observed, almost unimaginable in size and accuracy by any previous standards, will contain a significant portion of the Galaxy's stars, including huge numbers of exotic objects sparsely represented in the solar neighbourhood, thus helping to put many fields of astronomical research on a more sound statistical basis. The final catalogue will approximately contain $340\,000$ objects down to $V=10$, $26 \times 10^6$ to $V=15$, $250 \times 10^6$ to $V=18$ and over $10^9$ to $V=20$. The average sky density of the final catalogue at $V=20$ will thus be about 25000  stars/ deg$^2$. Large numbers of peculiar objects such as solar system minor planets (1 million), extra-solar planets ($30\,000$), supernovae ($100\,000$) and quasars ($500\,000$) will be detected and observed as a natural part of the main observing programme, while, a special observing strategy had to be designed for the detection and observation of about 3 million galaxies, as is described in Section 5.1.

As for the accuracy of the measured quantities, a clear distinction must be made between the epoch accuracy and the all-mission accuracy. The former is the accuracy of a measured quantity obtained from only one observation of the object, while the latter is the accuracy obtained at the end of the mission, when all the observations of the same object have been put together and all attitude, calibration and sky data are available. Actually, due to the short exposure times, single observations are obtained with a relatively low signal-to-noise ratio, and the all-mission accuracy is then about $\sqrt{N}$ times better, where $N$ is the total number of observations. The single observation accuracy is however sufficient to determine proper motions and parallaxes from multi-epoch positions and light curves for variable stars from multi-epoch brightnesses.

From a statistical standpoint, the accuracy of both astrometric and photometric measurements is basically determined by the number of detected photons emitted by the object. As for GAIA, since the one-scan exposure time is fixed and the number of observations is approximately the same all over the sky, the main paramenter determining the all-mission astrometric and photometric accuracy is therefore the brightness of the observed object. A weaker dependence on the object's position on the sky and spectrum can then be seen, arising from the scanning law followed by the satellite and the spectral response curve of the detectors, respectively.

The all-mission astrometric accuracy averaged over the sky is given in Table 2.2 for a G2V star of different $G$ magnitudes. On the basis of Galaxy models the accuracy of parallaxes and proper motions can be translated into relative errors on distances and tangential velocities. It is estimated that 21 million distances will be determined to better than 1 per cent, 46 million better than 2 per cent, 116 million better than 5 per cent and 220 million better than 10 per cent. As for proper motions, 44 million will be determined to better than 0.5 km/s, 85 million better than 1 km/s, 210 million better than 3 km/s, 300 million better than 5 km/s and 440 million better than 10 km/s.

Table 2.2: GAIA all-mission astrometric accuracy. Median all-mission accuracy of positions, proper motions and parallaxes at different $G$ magnitudes for a G2V star from a 5 year mission. The median value is calculated over uniformly distributed sky regions.

$G$	mag	10	11	12	13	14	15	16	17	18	19	20	21
Position	$\mu\textrm{as}$	3	3	3	4	6	9	15	23	39	70	140	440
Proper Motion	$\mu\textrm{as}$/yr	3	3	3	4	5	8	13	20	34	60	120	380
Parallax	$\mu\textrm{as}$	4	4	4	5	7	11	17	27	45	80	160	500

Expected accuracies of epoch photometry in the $G$ band and all-mission photometry in the $fgriz$ bands are given in Figure 2.9. Accuracies of a few hundredths of magnitude are expected for stars of most spectral types of $G \simeq 18$. When combined with the medium-band photometric measurements performed by the spectrometric instrument, paramenters such as the spectral class, effective temperature, surface gravity, metallicity, interstellar extinction and color excess will be determined for most observed objects. Distances and absolute magnitudes of objects whose parallax is too small to be measured astrometrically will also be obtained from photometric measurements.

Figure 2.9: GAIA broad-band photometric precision. Median expected broad-band photometric precision for stars of different spectral types as function of $I_C$ magnitude. Single-scan precision in the very broad $G$ band and 100-scan precision in the five broad $fgriz$ bands. An extinction of $A_V=0$ was assumed. Vertical lines indicate saturation of the CCD at bright stars. The quoted figures are for the Astro-1. For the Astro-2 the photometric performance is expected to be the same for bright stars and slightly better for faint stars, due to a different CCD binning (see Section 5.1). From [Høg, Fabricius, Knude and Makarov 1999].

The accuracy of radial velocity measurements is expected to be in the 1-10 km/s range, the former value being achieved for stars brighter than $V \simeq 15$ and the latter for stars of $V \simeq 17$.