A. Gallenne, P. Kervella, N. R. Evans, J. Milli, E. Sivkova, W. Gieren, G. Pietrzyński, G. Bras, V. Hocdé, W. Kiviaho, N. Nardetto, B. Pilecki, B. Zgírski

Cepheids are key distance indicators and benchmarks for stellar evolution, yet most of them are members of binary or multiple systems. While spectroscopic surveys and Gaia proper-motion anomalies reveal a high binary fraction, the population of resolved companions remains poorly characterised. We aim to search for and characterise visual companions to bright Galactic Cepheids using high-contrast imaging and to derive quantitative limits on undetected companions to constrain the architecture of Cepheid multiple systems. We observed 47 Cepheids with SPHERE using the ZIMPOL instrument in classical imaging mode and the V, R, and I filters. The data were obtained in pupil-stabilised mode and analysed using PCA-based imaging technique. For detected companions, we injected negative fake companions in a Monte Carlo approach to measure the relative astrometry. For non-detections, synthetic companions were injected to compute 5sigma contrast curves as a function of separation. We detected companions with a signal-to-noise ratio of > 5 for 8 Cepheids, corresponding to about 17% of the sample. Our SPHERE imaging confirms previously known visual companions with improved astrometry and reveals new wide components for AP Pup, T Vel, and TX Del) at projected separations of 0.16-0.9". For the remaining Cepheids, we derived typical maximum contrasts of 10, 11, and 12mag at 0.25", 0.5", and > 1, respectively. For a sub-set of targets, these limits ruled out main sequence companions more massive than late-K dwarfs beyond 0.5". Our SPHERE survey provides the first homogeneous set of high-contrast optical constraints on wide companions of Galactic Cepheids. The low detection rate of visual companions compared to the high overall binary fraction implies that most companions inferred from radial velocities and Gaia astrometry are either closer than 20mas or significantly fainter than the limits reached here.