Stellar and substellar companions from Gaia EDR3 -- Proper motion anomaly and resolved common proper motion pairs

The multiplicity of stars, down to the substellar regime, is a parameter of fundamental importance for stellar formation, evolution, and planetology. The census of multiple stars in the solar neighborhood is however incomplete. The presence of a companion in orbit around a star affects its proper motion. We aim at detecting companions of Hipparcos stars from the proper motion anomaly (PMa) they induce on their host star, that is, the difference between their long-term Hipparcos-Gaia and short-term Gaia proper motion vectors. We also aim at detecting resolved, gravitationally bound companions of the Hipparcos stars (117,955 stars), and of the Gaia EDR3 stars closer than 100 pc (542,232 stars). Using the Hipparcos and EDR3 data, we revise the PMa catalog for the Hipparcos stars. To identify gravitationally bound visual companions, we search the EDR3 catalog for common proper motion (CPM) candidates. The detection of tangential velocity anomalies with a median accuracy of 26 cm/s per parsec of distance is demonstrated with the EDR3. This improvement by a factor 2.5 compared to the DR2 results in detection limits well into the planetary mass regime for many targets. We identify 37,515 Hipparcos stars with a PMa S/N>3, that is, a fraction of 32% (30% in the DR2) and 12,914 (11%) hosting CPM bound candidate companions. Including the RUWE>1.4 as an additional indicator, 50,720 stars of the Hipparcos catalog (43%) exhibit at least one signal of binarity. Among the EDR3 stars located within 100 pc, we find CPM bound candidate companions for 39,490 stars (7.3% of the sample). The combination of the PMa, CPM and RUWE indicators significantly improves the exhaustivity of the multiplicity survey. The detection of CPM companions of very bright stars provides a useful proxy to estimate their distance with a higher accuracy than Hipparcos.