Constraining Dark Matter Density Profiles in UFDs with Wide Binaries: Forecast for the Chinese Space Station Survey Telescope

The internal structure of dark matter halos on sub-galactic scales remains a key open question, particularly in the context of the core-cusp problem. Ultra-faint dwarf galaxies (UFDs), owing to their extreme dark matter dominance, provide a promising laboratory to probe these density profiles through stellar tracers. In this work, we assess the capability of the Chinese Space Station Telescope (CSST) to detect and characterize wide binary stars in the nearby UFD Segue 1, using mock observations. We generate mock binary populations based on our existing $N$-body simulations and incorporate realistic CSST observational conditions, including the expected deep-field limiting magnitude ($g\sim 27.5$ mag) and a photometric completeness of approximately $90\mathrm{\%}$. The two-point correlation function (2PCF) of stellar pairs is used as a statistical tool to recover the binary fraction under these assumptions. We find that CSST can robustly detect wide binaries at the $3\sigma$ level for binary fractions as low as $f_b\gtrsim 0.01$, provided a stellar sample size of $N_{\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{r}}\gtrsim 2300$. However, distinguishing between cusped and cored dark matter profiles is significantly more demanding, requiring $N_{\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{r}}\gtrsim 6000$ and $f_b\gtrsim 0.1$ within $\sim 40\mathrm{k}\mathrm{p}\mathrm{c}$.