Tomographic approach to resolving the distribution of LISA Galactic binaries

The space based gravitational wave detector LISA (Laser Interferometer Space Antenna) is expected to observe a large population of Galactic white dwarf binaries whose collective signal is likely to dominate instrumental noise at observational frequencies in the range ${10}^{\ensuremath{-}4}$ to ${10}^{\ensuremath{-}3}\text{ }\text{ }\mathrm{Hz}$. The motion of LISA modulates the signal of each binary in both frequency and amplitude---the exact modulation depending on the source direction and frequency. Starting with the observed response of one LISA interferometer and assuming only Doppler modulation due to the orbital motion of LISA, we show how the distribution of the entire binary population in frequency and sky position can be reconstructed using a tomographic approach. The method is linear and the reconstruction of a delta-function distribution, corresponding to an isolated binary, yields a point spread function (psf). An arbitrary distribution and its reconstruction are related via smoothing with this psf. Exploratory results are reported demonstrating the recovery of binary sources, in the presence of white Gaussian noise.