Inferring the three-dimensional distribution of dust in the Galaxy with a non-parametric method Preparing for Gaia

We present a non-parametric model for inferring the three-dimensional (3D) distribution of dust density in the Milky Way. Our approach uses the extinction measured towards stars at different locations in the Galaxy at approximately known distances. Each extinction measurement is proportional to the integrated dust density along its line of sight (LoS). Making simple assumptions about the spatial correlation of the dust density, we can infer the most probable 3D distribution of dust across the entire observed region, including along sight lines which were not observed. This is possible because our model employs a Gaussian process to connect all LoS. We demonstrate the capability of our model to capture detailed dust density variations using mock data and simulated data from the Gaia Universe Model Snapshot. We then apply our method to a sample of giant stars observed by APOGEE and Kepler to construct a 3D dust map over a small region of the Galaxy. Owing to our smoothness constraint and its isotropy, we provide one of the first maps which does not show the fingers of God effect.