Predicted properties of galactic and magellanic classical Cepheids in the SDSS filters

We present the first extensive and detailed theoretical scenario for the interpretation of Cepheid properties observed in the SDSS filters. Three sets of nonlinear convective pulsation models, corresponding to the chemical compositions of Cepheids in the Milky Way, the Large Magellanic Cloud and the Small Magellanic Cloud, respectively, are transformed into the SDSS bands by relying on updated model atmospheres. The resulting observables, namely the instability strip boundaries and the light curves, as well as the period-luminosity (PL), the Wesenheit and the period-luminosity-colour relations, are discussed as a function of the metal content, for both the fundamental and the first overtone mode. The fundamental PL relations are found to deviate from linear relations when computed over the whole observed Cepheid period range, especially at the shorter wavelengths, confirming previous findings in the Johnson-Cousins bands. The obtained slopes are found to be mildly steeper than the ones of the semi-empirical and the empirical relations available in the literature and covering roughly the same period range, with the discrepancy ranging from similar to 13 per cent in u to similar to 3 per cent in z.