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For the vast majority of stars in the second Gaia data release, reliabledistances cannot be obtained by inverting the parallax. A correct inferenceprocedure must instead be used to account for the nonlinearity of thetransformation and the asymmetry of the resulting probability distribution.Here we infer distances to essentially all 1.33 billion stars with parallaxespublished in the second \gaia\ data release. This is done using a weak distanceprior that varies smoothly as a function of Galactic longitude and latitudeaccording to a Galaxy model. The irreducible uncertainty in the distanceestimate is characterized by the lower and upper bounds of an asymmetricconfidence interval. Although more precise distances can be estimated for asubset of the stars using additional data (such as photometry), our goal is toprovide purely geometric distance estimates, independent of assumptions aboutthe physical properties of, or interstellar extinction towards, individualstars. We analyse the characteristics of the catalogue and validate it usingclusters. The catalogue can be queried on the Gaia archive using ADQL athttp://gea.esac.esa.int/archive/ and downloaded fromhttp://www.mpia.de/~calj/gdr2_distances.html .

Estimating distances from parallaxes IV: Distances to 1.33 billion stars in Gaia Data Release 2