Gaussian process model for the local stellar velocity field from Gaia data release 2

We model the local stellar velocity field using position and velocity measurements for 4M stars from the second data release of Gaia. We determine the components of the mean or bulk velocity in similar to 27 000 spatially defined bins. Our assumption is that these quantities constitute a Gaussian process where the correlation between the bulk velocity at different locations is described by a simple covariance function or kernel. We use a sparse Gaussian process algorithm based on inducing points to construct a non-parametric, smooth, and differentiable model for the underlying mean stellar velocity field. We estimate the Oort constants A, B, C, and K and find values in excellent agreement with previous results. Maps of the velocity field within 2 kpc of the Sun reveal complicated substructures, which provide clear evidence that the local disc is in a state of disequilibrium. We present the first three-dimensional map of the divergence of the stellar velocity field and identify regions of the disc that may be undergoing compression and rarefaction.