An In-Depth Spectroscopic Analysis of the Blazhko Star RR Lyr? I. Characterisation of the star: abundance analysis and fundamental parameters

Aims. The knowledge of accurate stellar parameters is a keystone in several fields of stellar astrophysics, such as asteroseismology and stellar evolution. Although the fundamental parameters can be derived both from spectroscopy and multicolour photometry, the results obtained are sometimes affected by systematic uncertainties. In this paper, we present a self-consistent spectral analysis of the pulsating star RR Lyr, which is the primary target for our study of the Blazhko effect. Methods. We used high-resolution and high signal-to-noise ratio spectra to carry out a consistent parameter determination and abun-dance analysis for RR Lyr. The LLmodels code was employed for model atmosphere calculations, while SYNTH3 and WIDTH9 codes were used for line profile calculation and LTE abundance analysis. We provide a detailed description of the methodology adopted to derive the fundamental parameters and the abundances. Stellar pulsation reaches high amplitudes in RR Lyrae stars, and as a consequence the stellar parameters vary significantly over the pulsation cycle. The abundances of the star, however, are not expected to change. From a set of available high-resolution spectra of RR Lyr we selected the phase of maximum radius, at which the spectr