The Stellar Abundances and Galactic Evolution Survey (SAGES). IV. Surface Gravity Estimation and Giant-Dwarf Separation with the DDO51 Filter

Reliable estimation of stellar surface gravity (log $g$) for a large sample is crucial for evaluating stellar evolution models and understanding galactic structure; However, it is not easy to accomplish due to the difficulty in gathering a large spectroscopic data set. Photometric sky survey using a specific filter, on the other hand, can play a substantial role in the assessment of log $g$. The Stellar Abundances and Galactic Evolution Survey (SAGES) utilizes eight filters to provide accurate stellar parameters for $\sim10^{7}$ stars, with its DDO51 intermediate-band filter specifically designed for robust log $g$ determination. In this work, the observed SAGES $u_{\rm SC}$ and $v_{\rm SAGES}$ photometry, the synthetic photometry in $g$, $r$, $i$, and DDO51 bands derived from \textit{Gaia} XP spectra are employed to investigate the importance of the DDO51 filter in the determination of log $g$. We applied machine-learning-based extinction correction and employed XGBoost models, trained on stellar parameters from LAMOST, to predict log $g$ using photometric data. By comparing model predicted log $g$ with LAMOST values, we find that including DDO51 filter improve the accuracies of log $g$ estimates by 21.0\% (from 0.224\,dex to 0.177\,dex) overall, and by 26.5\% (from 0.302\,dex to 0.222\,dex ) for GK-type stars, as compared to those obtained without DDO51. The DDO51 filter is also validated to be particularly effective for metal-poor stars ([Fe/H]$<$-1.0), where it significantly mitigates systematic biases. Our findings highlight the diagnostic power of the SAGES DDO51 filter, providing enhanced stellar characterization vital for future in-depth studies of the Milky Way.