# 10.9.3 Calibration models

Microlensing events change the observed brightness sometimes by orders of magnitude. In the process of recognising Microlensing events using the goodness of model fit, it is important to use the measurement uncertainties, which may reflect a scatter across a wide range of magnitudes. We wanted to use the reduced $\chi^{2}$ in the evaluation of the best fitting model, but we noticed that the original $\sigma^{\mathrm{gdr3}}_{G}$ lead to reduced $\chi^{2}\ll 1$ for genuine microlensing events. So we rescaled the uncertainties on $G$ magnitudes to match the expected scatter in Gaia DR3 data. We used Gaia DR3 mean $G$ vs its standard deviation to derive the expected lowest possible uncertainty $\sigma^{\mathrm{exp}}_{G}$ for each $G$ measurement, assuming 30 observations on average per object, using the following formulae:

 $\sigma^{\mathrm{exp}}_{G}=\begin{cases}\sqrt{30}\times 10^{0.17\times 13.5-5.1% }&~{}~{}\mathrm{for}~{}G<13.5~{}\mathrm{mag}\\ \sqrt{30}\times 10^{0.17\times G-5.1}&~{}~{}\mathrm{for}~{}G>=13.5~{}\mathrm{% mag},\\ \end{cases}$ (10.11)

which is added in quadrature to the Gaia DR3 uncertainty $\sigma^{\mathrm{gdr3}}_{G}$ for estimating the employed value $\sigma^{\mathrm{new}}_{G}$:

 $\sigma^{\mathrm{new}}_{G}=\sqrt{\left(\sigma^{\mathrm{gdr3}}_{G}\right)^{2}+% \left(\sigma^{\mathrm{exp}}_{G}\right)^{2}}.$ (10.12)

The $G_{\rm BP}$ and $G_{\rm RP}$ data often contained outliers; therefore, in order to avoid incorrect Microlensing model to be driven by those outliers, we rescaled uncertainties in $G_{\rm BP}$ and $G_{\rm RP}$ time series by a constant factor of 10. This enforced $G_{\rm BP}$ and $G_{\rm RP}$ data points to have negligible contribution to the Microlensing model.