3.3.4 Pseudo-colours in source update

Under certain conditions it is possible to derive an approximate estimate of the colour of a source from its astrometric solution (source update), utilizing the chromatic displacements of the image centroids, known as chromaticity. Effectively, the astrometric instrument acts as a spectrometer with extremely low resolution. Astrometric colour information obtained in this way are called pseudo-colours. The necessary conditions for the determination of pseudo-colours are

  • that the astrometric instrument has some significant chromaticity – this is in practice always the case for Gaia;

  • that the chromaticity was uncorrected in the pre-processing – this is the case for Gaia DR2, where the PSF/LSF calibration was still chromatic;

  • that the chromaticity is adequately calibrated in the AGIS primary solution by means of sources with known colours, i.e. GBP-GRP from the photometric processing.

As described in Section 3.3.6 the last condition was also satisfied for Gaia DR2: the along-scan geometric instrument model includes terms of the form

ηcal=+(νeff-νeffref)χ, (3.102)

where χ is the chromaticity parameter and νeff the effective wavenumber (in μm-1) of the source. The latter was computed from the colour index C=GBP-GRP using the analytical approximation

νeff=2.0-1.8πarctan(0.331+0.572C-0.014C2+0.045C3), (3.103)

derived from pre-launch calibrations of the photometric bands and standard stellar flux libraries. The arctan transformation constrains νeff roughly to the passband of G, or 340–910 nm, even for extreme (spurious) values of C. A reference value νeffref=1.6 close to the mean value for solar-type stars was adopted. Once χ has been calibrated as a function of time, CCD, etc. in a primary solution for sources with known colours, it can be used to estimate the pseudo-colour Ψ of an arbitrary sources by including the corresponding term in the source update model:

ηobs=+(Ψ-νeffref)χ. (3.104)

In this equation χ is regarded as known (from the geometric instrument calibration) and Ψ is an additional unknown per source, solved together with the usual five astrometric parameters. This solution also provides an estimate of standard uncertainty of Ψ. From Equation 3.102 and Equation 3.104 it is clear that Ψνeff is expected.

Figure 3.11: Pseudo-colour versus effective wavelength. νeff is the effective wavenumber computed from GBP-GRP, using Equation 3.103; Ψ is the astrometrically determined pseudo-colour. The straight line is the 1:1 relation; the coloured dots show different formal errors: σΨ<0.01 μm-1 (red), <0.03 (grey), <0.1 (green), no restriction (orange). Data are only shown for a random sample of about 3 million sources.

Figure 3.11 shows the relation between νeff and Ψ for a random sample of the sources with colours from the photometric processing. The agreement is reasonable at least when the formal uncertainty of Ψ is not too large. The plot includes a small number of points to the right, at unrealistically large νeff, indicating that for these sources the colour index is too blue and Ψ may provide a less biased colour estimate.