The AstraLux-TESS high-spatial resolution imaging survey. Search for stellar companions of 215 planet candidates from TESS

Chance-aligned sources or blended companions can cause false positives in planetary transit detections or simply bias the determination of the candidate properties. In the era of high-precision space-based photometers, the need for high-spatial resolution images has demonstrated to be critical for validating and confirming transit signals. This already applied to the Kepler mission, it is now applicable to the TESS survey and will be critical for PLATO. We present the results of the AstraLux-TESS survey, a catalog of high-spatial resolution images obtained with the AstraLux instrument (Calar Alto) in the context of the TESS Follow-up Observing Program. We use the lucky-imaging technique to obtain high-spatial resolution images from planet candidate hosts included mostly in two relevant regimes: exoplanet candidates belonging to the level-one requirement of the TESS mission (planets with radii $R<4~R_{\oplus}$), and candidates around intermediate-mass stars. Among the 185 planet host candidate stars observed, we found 13 (7%) to be accompanied by additional sources within 2.2 arcsec separation. Among them, six are not associated to sources in the Gaia DR3 catalog, thus contaminating the TESS light curve. We provide upper limits and probabilities to the possible existence of field contaminants through the sensitivity limits of our images. Among the isolated hosts, we can discard hazardous companions (bright enough to mimic a planetary transit signals) for all their planets. The results from this catalog are key for the statistical validation of small planets (prime targets of the TESS mission) and planets around intermediate-mass stars in the main-sequence. These two populations of planets are hard to confirm with the radial velocity technique. Our results also demonstrate the importance of this type of follow-up observations for future transit missions like PLATO, even in the Gaia era.