  We generalize the Green-Kubo approach, previously applied to bulk systems of
spherically symmetric active particles [J. Chem. Phys. 145, 161101 (2016)], to
include spatially inhomogeneous activity. The method is applied to predict the
spatial dependence of the average orientation per particle and the density. The
average orientation is given by an integral over the self-part of the van Hove
function and a simple Gaussian approximation to this quantity yields an
accurate analytical expression. Taking this analytical result as input to a
dynamic density functional theory approximates the spatial dependence of the
density in good agreement with simulation data. All theoretical predictions are
validated using Brownian dynamics simulations.
