Parameters of 220 million stars from Gaia BP/RP spectra

We develop, validate and apply a forward model to estimate stellar atmospheric parameters ($T_{\rm eff}$, $\log{g}$ and $\mathrm{[Fe/H]}$), revised distances and extinctions for 220 million stars with XP spectra from $\textit{Gaia}$ DR3. Instead of using $\textit{ab initio}$ stellar models, we develop a data-driven model of $\textit{Gaia}$ XP spectra as a function of the stellar parameters, with a few straightforward built-in physical assumptions. We train our model on stellar atmospheric parameters from the LAMOST survey, which provides broad coverage of different spectral types. We model the $\textit{Gaia}$ XP spectra with all of their covariances, augmented by 2MASS and WISE photometry that greatly reduces degeneracies between stellar parameters, yielding more precise determinations of temperature and dust reddening. Taken together, our approach overcomes a number of important limitations that the astrophysical parameters released in $\textit{Gaia}$ DR3 faced, and exploits the full information content of the data. We provide the resulting catalog of stellar atmospheric parameters, revised parallaxes and extinction estimates, with all their uncertainties. The modeling procedure also produces an estimate of the optical extinction curve at the spectral resolution of the XP spectra ($R \sim 20-100$), which agrees reasonably well with the ${R(V) = 3.1}$ CCM model. Remaining limitations that will be addressed in future work are that the model assumes a universal extinction law, ignores binary stars and does not cover all parts of the Hertzsprung-Russell Diagram ($\textit{e.g.}$, white dwarfs).