RR Lyrae stars with variable mean magnitudes

Context. A number of RR Lyrae stars show variable mean magnitudes in the OGLE survey light curves of the Galactic bulge. Hitherto this phenomenon was not studied, as it was generally assumed to be related to problems with the photometry. Aims. We investigate whether the mean magnitude variability of RR Lyrae variables is due to genuine astrophysical phenomena. Methods. We make use of the extended, and in many cases overlapping, light curves from multiple microlensing surveys, to study RR Lyrae stars with apparent mean-magnitude variations. A modified Fourier-series based fitting method is introduced to analyze the light curves showing mean-magnitude variations. Data from infrared surveys are also used to construct spectral energy distributions (SEDs). Results. 72 stars are presented where the mean-magnitude variations are most probably of genuine astrophysical origin, and not the result of problems with the photometry. The ratio of variation between the V and I bands is compatible with variable extinction by dust in most cases, but no infrared excess is detected in the SEDs. The occurrence rate of the phenomenon, after correcting for selection effects, is $\sim0.9\%$ among RR Lyrae variables in the OGLE bulge fields.