Correction to the photometric colors of the Gaia Data Release 2 with the stellar color regression method

The second Gaia data release (DR2) delivers accurate and homogeneous photometry data of the whole sky to an exquisite quality, reaching down to the unprecedented milli-magnitude (mmag) level for the G, GRP, and GBP passbands. However, the presence of magnitude-dependent systematic effects at the 10 mmag level limits its power in scientific exploitation. In this work, using about half-million stars in common with the LAMOST DR5, we apply the spectroscopy-based stellar color regression method to calibrate the Gaia G-GRP and GBP-GRP colors. With an unprecedented precision of about 1 mmag, systematic trends with G magnitude are revealed for both colors in great detail, reflecting changes in instrument configurations. Color dependent trends are found for the GBP-GRP color and for stars brighter than G~11.5 mag. The calibration is up to 20 mmag in general and varies a few mmag/mag. A revised color-color diagram of Gaia DR2 is given, and some applications are briefly discussed.