  In this paper, the X-ray Earth occultation (XEO) of the Crab Nebula is
investigated by using the Hard X-ray Modulation Telescope (Insight-HXMT). The
pointing observation data on the 30th September, 2018 recorded by the Low
Energy X-ray telescope (LE) of Insight-HXMT are selected and analyzed. The
extinction lightcurves and spectra during the X-ray Earth occultation process
are extracted. A forward model for the XEO lightcurve is established and the
theoretical observational signal for lightcurve is predicted. The atmospheric
density model is built with a scale factor to the commonly used MSIS density
profile within a certain altitude range. A Bayesian data analysis method is
developed for the XEO lightcurve modeling and the atmospheric density
retrieval. The posterior probability distribution of the model parameters is
derived through the Markov Chain Monte Carlo (MCMC) algorithm with the
NRLMSISE-00 model and the NRLMSIS 2.0 model as basis functions and the best-fit
density profiles are retrieved respectively. It is found that in the altitude
range of 105--200 km, the retrieved density profile is 88.8% of the density of
NRLMSISE-00 and 109.7% of the density of NRLMSIS 2.0 by fitting the lightcurve
in the energy range of 1.0--2.5 keV based on XEOS method. In the altitude range
of 95--125 km, the retrieved density profile is 81.0% of the density of
NRLMSISE-00 and 92.3% of the density of NRLMSIS 2.0 by fitting the lightcurve
in the energy range of 2.5--6.0 keV based on XEOS method. In the altitude range
of 85--110 km, the retrieved density profile is 87.7% of the density of
NRLMSISE-00 and 101.4% of the density of NRLMSIS 2.0 by fitting the lightcurve
in the energy range of 6.0--10.0 keV based on XEOS method. This study
demonstrates that the XEOS from the X-ray astronomical satellite Insight-HXMT
can provide an approach for the study of the upper atmosphere.
