The calibrations of DAMPE $\gamma$-ray effective area

The DArk Matter Particle Explorer (DAMPE) is a cosmic-ray detector as well as a pair-converting $\gamma$-ray telescope. The effective area, reflecting the geometrical cross-section area, the $\gamma$-ray conversion probability and the photon selection efficiency, is important in the $\gamma$-ray analyses. In the work, we find a significant time variation in the effective area, as large as $\sim -4\%/{\rm yr}$ at 2 GeV for the high-energy trigger. We derive the data-based correction factors to the effective areas and apply corrections to both the effective areas and the exposure maps. The calibrated exposure can be $\sim 12\%$ smaller than the Monte Carlo one on average at 2 GeV. The calibration is further verified using the observation of the Vela pulsar, showing the spectral parameters with the correction are more consistent with those in the Fermi-LAT catalog than the ones without correction. All the corrections are now implemented in the latest version of the DAMPE $\gamma$-ray analysis toolkit DmpST.