Data-driven stellar intrinsic colors and dust reddenings for spectro-photometric data: From the blue-edge method to a machine-learning approach

Abstract: Intrinsic colors (ICs) of stars are essential for the studies on both stellar physics and dust reddening. In this work, we developed an XGBoost model to predict the ICs with the atmospheric parameters $T_{\rm eff}$, ${\rm log}\,g$, and $\rm [M/H]$. The model was trained and tested for three colors at Gaia and 2MASS bands with 1,040,446 low-reddening sources. The atmospheric parameters were determined by the Gaia DR3 GSP-phot module and were validated by comparing with APOGEE and LAMOST. We further confirmed that the biases in GSP-phot parameters, especially for $\rm [M/H]$, do not present a significant impact on the IC prediction. The generalization error of the model estimated by the test set is 0.014 mag for $(G_{\rm BP}\,{-}\,G_{\rm RP})0$, 0.050 mag for $(G{\rm BP}\,{-}\,K_{\rm S})0$, and 0.040 mag for $(J\,{-}\,K{\rm S})0$. The model was applied to a sample containing 5,714,528 reddened stars with stellar parameters from Andrae et al. (2023) to calculate ICs and reddenings. The high consistency in the comparison of $E(J\,{-}\,K{\rm S})$ between our results and literature values further validates the accuracy of the XGBoost model. The variation of $E(G_{\rm BP}\,{-}\,K_{\rm S})/E(G_{\rm BP}\,{-}\,G_{\rm RP})$, a representation of the extinction law, with Galactic longitude is found on large scales. This work preliminarily presents the feasibility and the accuracy of the machine-learning approach for IC and dust reddening calculation, whose products could be widely applied to spectro-photometric data. The data sets and trained model can be accessed via \url{https://doi.org/10.5281/zenodo.12787594}. The models for more bands will be completed in the following works.