Gravitational lensing of millisecond pulsars

Gravitational lensing can significantly magnify the images of astrophysical sources, but only if the source lies within the Einstein ring of the lens. In consequence the chance of any Galactic star magnifying a more distant source is extremely small - much less than one in a million. However, the extra light travel-time ('Shapiro delay') introduced by the presence of a lens can be large even when there is negligible effect on the image magnification, and as the relative positions of source and lens change so does the delay. In this paper we quantify these changes and the corresponding influence on apparent timing properties of pulsars. While the total Shapiro delay can be large, it is the temporal variations in this quantity which are measurable with pulsar timing. We find that the magnitude of the expected delay variations is too small to be detectable except during strong lensing events, which are extremely rare. Even in the case of a high velocity pulsar in the Galactic Plane, the stochastic Shapiro delay is typically expected not to have a substantial influence on the timing properties. In consequence the viability of a pulsar-based time standard is not adversely affected by gravitational lensing.