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We present 87 candidates for RR Lyrae variable stars in binary systems, basedon our new search using the light-travel time effect (LTTE) and observed -calculated ($O-C$) diagrams in the Galactic bulge time-series photometry of theOptical Gravitational Lensing Experiment. Out of these, 61 are new candidates,while 26 have been announced previously. Furthermore, 12 stars considered asbinary candidates in earlier works are discarded from the list, either as theywere found to have $O-C$ diagrams incompatible with the LTTE or because theirlong-term periodicity is definitely caused by the Blazhko effect. This sampleof RR Lyrae binary candidates allows us to draw the first firm conclusionsabout the population of such objects: no candidate has an orbital period below1000 days, while their occurrence rate steadily increases with increasingperiod, and peaks between 3000 and 4000 days; however, the decrease in thenumber of stars toward even longer periods is probably the result ofobservational biases. The eccentricities show a very significant concentrationbetween 0.25 and 0.3, with a quarter of candidates found in this single bin,overlaid on an otherwise flat distribution between 0.05 and 0.6. Only six starshave higher inferred eccentricities above 0.6. Lastly, the distribution of themass functions is highly peculiar, exhibiting strong trimodality. We interpretthese modes as the presence of three distinct groups of companions, withtypical inferred masses of $\sim0.6$, $\sim0.2$, and$\sim0.067\,\mathrm{M}_\odot$, which can be associated with populations ofwhite dwarf and main sequence, red dwarf, and brown dwarf companions,respectively.

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