Astrometric view of companions in the inner dust cavities of protoplanetary disks

Protoplanetary disks with inner dust cavities (often referred to as "transition disks") are potential signposts of planet formation. We use Gaia astrometry to search for planetary and stellar companions in a sample of 98 transition disks, assessing the occurrence rate of such companions and their potential influence on cavity formation. For the 98 Young Stellar Objects (YSOs), we compute Gaia proper motion anomalies which, together with the RUWE, identify companions with mass ratios $q \gtrsim 0.01$ at $\sim$0.1-30 au. We assess the impact of disk gravity, accretion, disk-scattered light, dippers, starspots, jets, and outflows on the measured proper motion anomalies, concluding that astrometric techniques such as the one of this work can be robustly applied to YSOs. Significant proper motion anomalies are found in 31 transition disks (32% of the sample), indicative of companions. We recover 85% of known companions within our sensitivity range. We model the semi-major axis and mass required for a companion to reproduce the observed astrometric signals. Most inferred companions have $M > 30$ M$\rm{_{J}}$, placing many within or near the stellar mass regime. Seven sources host companions compatible with a planetary mass ($M < 13$ M$\rm{_{J}}$, HD 100453, J04343128+1722201, J16102955-3922144, MHO6, MP Mus, PDS 70, and Sz 76). For the non-detections, we provide the companion masses and semi-major axes that can be excluded in future searches. About half (53%) of detected companions cannot be reconciled with having carved the observed dust cavities. We find that transition disks host as many companions within our sensitivity range as do randomly sampled groups of YSOs and main-sequence stars. If dust cavities are shaped by companions, such companions must reside at larger orbital separations than those of the companions detected here, and we predict them to be of planetary mass. [abridged]