The Background Model of the Medium Energy X-ray telescope of Insight-HXMT

The Medium Energy X-ray Telescope (ME) is one of the main payloads of the Hard X-ray Modulation Telescope (dubbed as Insight-HXMT). The background of Insight-HXMT/ME is mainly caused by the environmental charged particles and the background intensity is modulated remarkably by the geomagnetic field, as well as the geographical location. At the same geographical location, the background spectral shape is stable but the intensity varies with the level of the environmental charged particles. In this paper, we develop a model to estimate the ME background based on the ME database that is established with the two-year blank sky observations of the high Galactic latitude. In this model, the entire geographical area covered by Insight-HXMT is divided into grids of $5^{\circ}\times5^{\circ}$ in geographical coordinate system. For each grid, the background spectral shape can be obtained from the background database and the intensity can be corrected by the contemporary count rate of the blind FOV detectors. Thus the background spectrum can be obtained by accumulating the background of all the grids passed by Insight-HXMT during the effective observational time. The model test with the blank sky observations shows that the systematic error of the background estimation in $8.9-44.0$ keV is $\sim1.3\%$ for a pointing observation with an average exposure $\sim5.5$ ks. We also find that the systematic error is anti-correlated with the exposure, which indicates the systematic error is partly contributed by the statistical error of count rate measured by the blind FOV detectors.