An in-depth spectroscopic analysis of the Blazhko Star RR Lyr. I. Characterisation of the star: abundance analysis and fundamental parameters

Context. 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 from both spectroscopy and multicolour photometry, the results obtained are sometimes affected by systematic uncertainties. 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. Aims. We present a self-consistent spectral analysis of the pulsating star RR Lyr, which is the primary target of 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 abundance analysis for RR Lyr. The LLMODELS code was employed for model atmosphere calculations, while the SYNTH3 and WIDTH9 codes were used for line profile calculations and LTE abundance analysis. We describe in detail the methodology adopted to derive the fundamental parameters and the abundances. From a set of available high-resolution spectra of RR Lyr, we selected the phase of maximum radius at which the spectra are least disturbed by the pulsation. Using the abundances determined at this phase as a starting point, we expect to be able to determine the fundamental parameters determined at other phases more accurately. Results. The set of fundamental parameters obtained in this work fits the observed spectrum accurately. From the abundance analysis, we find clear indications of a depth-dependent microturbulent velocity, that we quantify. Conclusions. We confirm the importance of a consistent analysis of relevant spectroscopic features, the application of advanced model atmospheres, and the use of up-to-date atomic line data for determining stellar parameters. These results are crucial for further studies, e.g., detailed theoretical modelling of the observed pulsations