| Abstract
| - Aims. We aim at detecting and characterizing the main-sequence companions of a sample of known and suspected Galactic binary Cepheids. The long-term objective is to accurately and independently measure the Cepheid masses and distances. Methods. We used the multi-telescope interferometric combiners CHARA/MIRC and VLTI/PIONIER to detect and measure the astrometric positions of the high-contrast companions orbiting 16 bright Galactic Cepheids. We made use of the CANDID algorithm to search for the companions and set detection limits from interferometric observations. We also present new high-precision radial velocity measurements which were used to fit radial pulsation and orbital velocities. Results. We report the detection of the companions orbiting the Cepheids U Aql, BP Cir, and S Mus, possible detections for FF Aql, Y Car, BG Cru, X Sgr, V350 Sgr, and V636 Sco, while no component is detected around U Car, YZ Car, T Mon, R Mus, S Nor, W Sgr, and AH Vel. For U Aql and S Mus, we performed a preliminary orbital fit combining their astrometric measurements with newly obtained high-precision single-line radial velocities, providing the full set of orbital elements and pulsation parameters. Assuming the distance from a period-luminosity (P-L) relation for both Cepheids, we estimated preliminary masses of MU Aql = 4.97 ± 0.62 M⊙ and MS Mus = 4.63 ± 0.99 M⊙. For YZ Car, W Sgr, V350 Sgr, and V636 Sco, we revised the spectroscopic orbits using new high-precision radial velocities, while we updated the pulsation parameters for BP Cir, BG Cru, S Nor, and AH Vel. Our interferometric observations also provide measurements of the angular diameters, which can be used in a Baade-Wesselink type analysis. Conclusions. We now have several astrometric detections of Cepheid companions. When radial velocities of the companions are available, such systems will provide accurate and independent masses and distances. Orbital parallaxes with an accuracy better than 5% will be particularly useful for a better calibration of the P-L relation. The final Gaia parallaxes will also be particularly helpful for single-line spectroscopic systems, where mass and distance are degenerate. Mass measurements are necessary for a better understanding of the age and evolution of Cepheids.
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