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The knowledge of accurate stellar parameters is a keystone in several fieldsof stellar astrophysics, such as asteroseismology and stellar evolution.Although the fundamental parameters can be derived both from spectroscopy andmulticolour photometry, the results obtained are sometimes affected bysystematic uncertainties. In this paper, we present a self-consistent spectralanalysis of the pulsating star RR Lyr, which is the primary target for ourstudy of the Blazhko effect. We used high-resolution and high signal-to-noiseratio spectra to carry out a consistent parameter determination and abundanceanalysis for RR Lyr. We provide a detailed description of the methodologyadopted to derive the fundamental parameters and the abundances. Stellarpulsation attains high amplitudes in RR Lyrae stars, and as a consequence thestellar parameters vary significantly over the pulsation cycle. The abundancesof the star, however, are not expected to change. From a set of availablehigh-resolution spectra of RR Lyr we selected the phase of maximum radius, atwhich the spectra are least disturbed by the pulsation. Using the abundancesdetermined at this phase as a starting point, we expect to obtain a higheraccuracy in the fundamental parameters determined at other phases. The set offundamental parameters obtained in this work fits the observed spectrumaccurately. Through the abundance analysis, we find clear indications for adepth-dependent microturbulent velocity, that we quantified. We confirm theimportance of a consistent analysis of relevant spectroscopic features,application of advanced model atmospheres, and the use of up-to-date atomicline data for the determination of stellar parameters. These results arecrucial for further studies, e.g., detailed theoretical modelling of theobserved pulsations.

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