Photo-astrometric distances, extinctions, and astrophysical parameters for Gaia DR2 stars brighter than G = 18

Combining the precise parallaxes and optical photometry delivered by ${\it Gaia}$'s second data release (${\it Gaia}$ DR2) with the photometric catalogues of PanSTARRS-1, 2MASS, and AllWISE, we derive Bayesian stellar parameters, distances, and extinctions for 265 million stars brighter than $G=18$. Because of the wide wavelength range used, our results substantially improve the accuracy and precision of previous extinction and effective temperature estimates. After cleaning our results for both unreliable input and output data, we retain 137 million stars, for which we achieve a median precision of $5\%$ in distance, 0.20 mag in $V$-band extinction, and 245 K in effective temperature for $G\leq14$, degrading towards fainter magnitudes ($12\%$, 0.20 mag, and 245 K at $G=16$; $16\%$, 0.23 mag, and 260 K at $G=17$, respectively). We find a very good agreement with the asteroseismic surface gravities and distances of 7000 stars in the ${\it Kepler}$ and the ${\it K2}$-C3 and ${\it K2}$-C6 fields, with stellar parameters from the APOGEE survey, as well as with distances to star clusters. Our results are available through the ADQL query interface of the ${\it Gaia}$ mirror at the Leibniz-Institut f\"{u}r Astrophysik Potsdam (${\tt gaia.aip.de}$), and as binary tables at ${\tt data.aip.de}$. As a first application, in this paper we provide distance- and extinction-corrected colour-magnitude diagrams, extinction maps as a function of distance, and extensive density maps, demonstrating the potential of our value-added dataset for mapping the three-dimensional structure of our Galaxy. In particular, we see a clear manifestation of the Galactic bar in the stellar density distributions, an observation that can almost be considered a direct imaging of the Galactic bar. Finally, our results also serve to assess targeting strategies of the future 4MOST spectroscopic survey.