Studies of RR Lyrae Variables in Binary Systems I.: Evidence of a Trimodal Companion Mass Distribution.

We present 87 candidates for RR Lyrae variable stars in binary systems, based on our new search using the light-travel time effect (LTTE) and Observed - Calculated ($O-C$) diagrams in the Galactic bulge time-series photometry of the Optical Gravitational Lensing Experiment. Out of these, 61 are new candidates, while 26 have been announced previously. Furthermore, 12 stars considered as binary candidates in earlier works are discarded from the list, as they were found to either have $O-C$ diagrams incompatible with the LTTE, or because their long-term periodicity is definitely caused by the Blazhko effect. This sample of RR Lyrae binary candidates allows us to draw the first firm conclusions about the population of such objects: no candidate has an orbital period below 1000 days, while their occurrence rate steadily increases with increasing period, and peaks between 3000 and 4000 days; however, the decrease in the number of stars towards even longer periods is probably the result of observational biases. The eccentricities show a very significant concentration between 0.25 and 0.3, with 1/4 of candidates found in this single bin, overlaid on an otherwise flat distribution between 0.05 and 0.6. Only 6 stars have higher inferred eccentricities than the latter value. Lastly, the distribution of the mass functions is highly peculiar, exhibiting strong trimodality. We interpret these modes as the presence of three distinct groups of companions, with typical inferred masses of $\sim0.6$, $\sim0.2$ and $\sim0.067\,\mathrm{M}_\odot$, which can be associated with populations of white dwarf and main sequence, red dwarf, and brown dwarf companions, respectively.