5.3.8 Saturation correction

Author(s): Josep M. Carrasco

The current calibration is not perfectly accounting for saturation effects (see Figure 5.22 comparing residuals in the Hipparcos and Tycho-2 photometric transformations derived in Section 5.3.7 as a function of the magnitude).

In order to provide a tool to empirically correct this trend at bright magnitudes we fit here a relationship of this trend in Figure 5.22, combining both Hipparcos and Tycho-2 residuals. The resulting fitted relationships are the following:

Gcorr-G = -0.047344+0.16405G-0.046799G2+0.0035015G3
GBPcorr-GBP = -2.0384+0.95282G-0.11018G2
GRPcorr-GRP = -13.946+13.239GRP-4.23GRP2+0.4532GRP3

The ranges of applicability for these relationships are the following:

  • 2.0<Gobs<6.5 mag for the G relationship,

  • 2.0<Gobs<4.0 mag for the GBP relationship, and

  • 2.0<Gobs<3.5 mag for the GRP relationship.

Figure 5.22: Residuals of the fitted laws for Hipparcos and Tycho-2 in Table 5.7 as a function of the magnitude for G (top), GBP (center) and GRP (bottom) (Evans et al. 2018)