The stellar parameters of RR Lyrae stars vary considerably over a pulsation cycle, and their determination is crucial for stellar modelling. We present a detailed spectroscopic analysis of the pulsating star RR Lyr, the prototype of its class, over a complete pulsation cycle, based on high-resolution spectra collected at the 2.7-m telescope of McDonald Observatory. We used simultaneous photometry to determine the accurate pulsation phase of each spectrum and determined the effective temperature, the shape of the depth-dependent microturbulent velocity, and the abundance of several elements, for each phase. The surface gravity was fixed to 2.4. Element abundances resulting from our analysis are stable over the pulsation cycle. However, a variation in ionisation equilibrium is observed around minimum radius. We attribute this mostly to a dynamical acceleration contributing to the surface gravity. Variable turbulent convection on time scales longer than the pulsation cycle has been proposed as a cause for the Blazhko effect. We test this hypothesis to some extent by using the derived variable depth-dependent microturbulent velocity profiles to estimate their effect on the stellar magnitude. These effects turn out to be wavelength-dependent and much smaller than the observed light variations over the Blazhko cycle: if variations in the turbulent motions are entirely responsible for the Blazhko effect, they must surpass the scales covered by the microturbulent velocity. This work demonstrates the possibility of a self-consistent spectroscopic analysis over an entire pulsation cycle using static atmosphere models, provided one takes into account certain features of a rapidly pulsating atmosphere.
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