Mapping the nano-Hertz gravitational wave sky
We describe a new method for extracting gravitational wave signals from pulsar timing data. We show that any gravitational wave signal can be decomposed into an orthogonal set of sky maps, with the number of maps equal to the number of pulsars in the timing array. These maps may be used as a basis to construct gravitational wave templates for any type of source, including collections of point sources. A variant of the standard Hellings-Downs correlation analysis is recovered for statistically isotropic signals. The template based approach allows us to probe potential anisotropies in the signal and produce maps of the gravitational wave sky.