10.5.3 Calibration models

The SOS Cep&RRL pipeline for Cepheid uses tools such as the period-luminosity (PL) relations in the $G$ band and the period-Wesenheit (PW) relations, where the Wesenheit magnitude is defined as $W=G-1.90(G_{\mathrm{BP}}-G_{\mathrm{RP}})$ (see also Clementini et al. 2019). These relations are used differently depending on regions of the sky. We divided the sky in five different regions: the first four encompass the large local galaxies LMC, SMC, M31, and M33, while the fifth region is defined as everything beyond the previous four regions and we call it the Milky Way (MW) sample. For the first four galaxies, we adopt both PL and PW relations, when colours are available, otherwise we use only the PL relation. On the contrary, in the MW we only use the PW relation, as we do not have reliable estimates of the reddening values for all stars. Every PL/PW relation has been calibrated in order to be applied to the pipeline. In Gaia DR3, we adopted the PL/PW calibrations of Ripepi et al. (2019) based on the Gaia DR2 data for the LMC, SMC and MW. As for M31 and M33, we adopted the relations devised for the LMC after proper re-scaling to take into account the different distance moduli (see Ripepi et al. 2023, for further details). The pipeline uses additional diagnostics, such as the diagrams period vs Fourier parameters and period ratio vs period in the fundamental mode for multi-mode Cepheids. These diagnostic diagrams are divided in sub-regions with the main goal of identifying the mode of pulsation of Classical Cepheids. The precise sub-divisions are calibrated on the basis of literature data (see Clementini et al. 2016, 2019, for full details).