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Classical Cepheids (CCs) and RR Lyrae stars (RRLs) are important classes ofvariable stars used as standard candles to estimate galactic and extragalacticdistances. Their multiplicity is imperfectly known, particularly for RRLs.Astoundingly, to date only one RRL has convincingly been demonstrated to be abinary, TU UMa, out of tens of thousands of known RRLs. Our aim is to detectthe binary and multiple stars present in a sample of Milky Way CCs and RRLs. Inthe present article, we combine the Hipparcos and Gaia DR2 positions todetermine the mean proper motion of the targets, and we search for propermotion anomalies (PMa) caused by close-in orbiting companions. We identify 57CC binaries from PMa out of 254 tested stars and 75 additional candidates,confirming the high binary fraction of these massive stars. For 28 binary CCs,we determine the companion mass by combining their spectroscopic orbitalparameters and astrometric PMa. We detect 13 RRLs showing a significant PMa outof 198 tested stars, and 61 additional candidates. We determine that the binaryfraction of CCs is likely above 80%, while that of RRLs is at least 7%. Thenewly detected systems will be useful to improve our understanding of theirevolutionary states. The discovery of a significant number of RRLs in binarysystems also resolves the long-standing mystery of their extremely low apparentbinary fraction.

Multiplicity of Galactic Cepheids and RR Lyrae stars from Gaia DR2 - I. Binarity from proper motion anomaly