Searching for new globular clusters in M 31 with Gaia EDR3

We found 50 new globular cluster (GC) candidates around M\,31 with Gaia Early Data Release 3 (EDR3), with the help from Pan-STARRS1 DR1 magnitudes and Pan-Andromeda Archaeological Survey (PAndAS) images. Based on the latest Revised Bologna Catalog and \textit{simbad}, we trained 2 Random Forest (RF) classifiers, the first one to distinguish extended sources from point sources and the second one to further select GCs from extended sources. From 1.85 million sources of $16^m{<}g{<}19.5^m$ and within a large area of $\sim$392\,deg$^2$ around M\,31, we selected 20,658 extended sources and 1,934 initial GC candidates. After visual inspection of the PAndAS images to eliminate the contamination of non-cluster sources, particularly galaxies, we finally got 50 candidates. These candidates are divided into 3 types (\textbf{a}, \textbf{b}, \textbf{c}) according to their projected distance $D$ to the center of M\,31 and their probability to be a true GC, $P_{GC}$, which is calculated by our second RF classifier. Among these candidates, 14 are found to be associated (in projection) with the large-scale structures within the halo of M\,31. We also provided several simple parameter criteria for selecting extended sources effectively from the Gaia EDR3, which can reach a completeness of 92.1\% with a contamination fraction lower than 10\%.