Pulsar timing arrays (PTAs) can be used to search for very low frequency (10 −9 -10 −7 Hz) gravitational waves (GWs). In this paper we present a general method for the detection and localization of single-source GWs using PTAs. We demonstrate the effectiveness of this new method for three types of signals: monochromatic waves as expected from individual supermassive binary black holes in circular orbits, GWs from eccentric binaries and GW bursts. We also test its implementation in realistic data sets that include effects such as uneven sampling and heterogeneous data spans and measurement precision. It is shown that our method, which works in the frequency domain, performs as well as published time-domain methods. In particular, we find it equivalent to the F e -statistic for monochromatic waves. We also discuss the construction of null streams -data streams that have null response to GWs, and the prospect of using null streams as a consistency check in the case of detected GW signals. Finally, we present sensitivities to individual supermassive binary black holes in eccentric orbits. We find that a monochromatic search that is designed for circular binaries can efficiently detect eccentric binaries with both high and low eccentricities, while a harmonic summing technique provides greater sensitivities only for binaries with moderate eccentricities.

We use the outer gap model to explain the spectrum and the energy-dependent light curves of the X-ray and soft γ -ray radiations of the spin-down powered pulsar PSR B1509-58. In the outer gap model, most pairs inside the gap are created around the null charge surface and the gap's electric field separates the two charges to move in opposite directions. Consequently, the region from the null charge surface to the light cylinder is dominated by the outflow current while that from the null charge surface to the star is dominated by the inflow current. We suggest that the viewing angle of PSR B1509−58 only receives the inflow radiation. The incoming curvature photons are converted to pairs by the strong magnetic field of the star. The X-rays and soft γ -rays of PSR B1509−58 result from the synchrotron radiation of these pairs. Magnetic pair creation requires a large pitch angle, which makes the pulse profile of the synchrotron radiation distinct from that of the curvature radiation. We carefully trace the pulse profiles of the synchrotron radiation with different pitch angles. We find that the differences between the light curves of different energy bands are due to the different pitch angles of the secondary pairs, and that the second peak appearing at E > 10 MeV comes from the region near the star, where the stronger magnetic field allows pair creation to happen with a smaller pitch angle.