Blanco DECam Bulge Survey (BDBS) V. Cleaning the foreground populations from Galactic bulge colour-magnitude diagrams using Gaia EDR3

Aims. The Blanco DECam Bulge Survey (BDBS) has imaged more than 200 square degrees of the southern Galactic bulge, providing photometry in the ugrizy filters for similar to 250 million unique stars. The presence of a strong foreground disk population, along with complex reddening and extreme image crowding, has made it difficult to constrain the presence of young and intermediate age stars in the bulge population. Methods. We employed an accurate cross-match of BDBS with the latest data release (EDR3) from the Gaia mission, matching more than 140 million sources with BDBS photometry and Gaia EDR3 photometry and astrometry. We relied on Gaia EDR3 astrometry, without any photometric selection, to produce clean BDBS bulge colour-magnitude diagrams (CMDs). Gaia parallaxes were used to filter out bright foreground sources, and a Gaussian mixture model fit to Galactic proper motions could identify stars kinematically consistent with bulge membership. We applied this method to 127 different bulge fields of 1 deg(2) each, with |l|<= 9.5 degrees and -9.5 degrees <= b <=-2.5 degrees. Results. The astrometric cleaning procedure removes the majority of blue stars in each field, especially near the Galactic plane, where the ratio of blue to red stars is less than or similar to 10%, increasing to values similar to 20% at higher Galactic latitudes. We rule out the presence of a widespread population of stars younger than 2 Gyr. The vast majority of blue stars brighter than the turnoff belong to the foreground population, according to their measured astrometry. We introduce the distance between the observed red giant branch bump and the red clump as a simple age proxy for the dominant population in the field, and we confirm the picture of a predominantly old bulge. Further work is needed to apply the method to estimate ages to fields at higher latitudes, and to model the complex morphology of the Galactic bulge. We also produce transverse kinematic maps, recovering expected patterns related to the presence of the bar and of the X-shaped nature of the bulge.