On a new and homogeneous metallicity scale for Galactic classical Cepheids - I. Physical parameters.

We gathered more than 1130 high-resolution optical spectra for more than 250 Galactic classical Cepheids. The spectra were collected with different optical spectrographs: UVES at VLT, HARPS at 3.6m, FEROS at 2.2m MPG/ESO, and STELLA. To improve the effective temperature estimates, we present more than 150 new line depth ratio (LDR) calibrations that together with similar calibrations already available in the literature allowed us to cover a broad range in wavelength (between 5348 and 8427 angstrom) and in effective temperatures (between 3500 and 7700 K). This means the unique opportunity to cover both the hottest and coolest phases along the Cepheid pulsation cycle and to limit the intrinsic error on individual measurements at the level of ~100 K. Thanks to the high signal-to-noise ratio of individual spectra we identified and measured hundreds of neutral and ionized lines of heavy elements, and in turn, have the opportunity to trace the variation of both surface gravity and microturbulent velocity along the pulsation cycle. The accuracy of the physical parameters and the number of Fe I (more than one hundred) and Fe II (more than ten) lines measured allowed us to estimate mean iron abundances with a precision better than 0.1 dex. Here we focus on 14 calibrating Cepheids for which the current spectra cover either the entire or a significant portion of the pulsation cycle. The current estimates of the variation of the physical parameters along the pulsation cycle and of the iron abundances agree quite well with similar estimates available in the literature. Independent homogeneous estimates of both physical parameters and metal abundances based on different approaches that can constrain possible systematics are highly encouraged.