CSST Preparations: Galaxy Completeness and S\'ersic Profile Fitting across the Wide, Deep, and Extreme Fields

The upcoming imaging survey of the Chinese Space-station Survey Telescope (CSST) will deliver high-resolution imaging of an unprecedented number of galaxies for galaxy studies. To understand CSST's capability, and to support the preparation of early-science programs, we generate 470,526 mock CSST images for 22,406 simulated galaxies with $M_*>10^9 M_\odot$, whose parameters are calibrated to match real HST observations spanning photometric redshift $0<z\lesssim7$, across seven CSST filters and three planned survey depths: wide, deep, and extreme. We then perform source detection and S\'ersic fitting. For point sources, we found that the 95% completeness magnitude in the g band reaches 26.3, 27.4, and 28.5 mag for the wide, deep, and extreme fields, respectively. For extended galaxies, their spatial extent dilutes the surface brightness, leading to brighter 95% completeness magnitudes of 24.4, 25.9, and 27.1 mag. The detection completeness remains above 95% at $z\lesssim3-4$ in the extreme field, while the corresponding redshift limits are $z\approx1$ in the deep field and $z\approx0.5$ in the wide field. Using three fitting codes, GALFIT, AstroPhot, and SourceXtractor++, we quantify measurement biases and uncertainties in galaxy magnitude ($m$), effective radius ($R_e$), effective surface brightness ($\mu_e$), S\'ersic index ($n$), and axis ratio ($q$). On average, for fainter galaxies, the reduced signal-to-noise ratio leads to systematic overestimates in $m$, $R_e$, and $\mu_e$, and underestimates in $n$ and $q$. These biases, as well as the associated scatter, become progressively smaller in deeper fields. Overall, our results provide quantitative constraints on sample selection and the robustness of morphological measurements in CSST early-science and legacy surveys.