1999A&A...351..393H

As a cause of possible uncertainty of the pulsar time scale, we investigated the gravitational time delay due to the motion of the intervening stars and MACHOs. We calculated the amplitudes of cubic, quartic and quintic trends in the residual of the times of arrival (TOA) of the pulse from pulsar due to gravitational time delay. It is shown that the cubic trend becomes dominant when the timing measurement accuracy is relatively high, say higher than 10 micro second at the case of the intervening star's mass is 1 M_☉. The optical depth of three trends are shown as a function of TOA residual. The optical depth for detecting the cubic trend is approximately proportional to the 2/3 th power of the mass over the timing measurement accuracy, and to the square of the observational period. Typical order of this optical depth is 0.1 for a pulsar of a few kpc distance and observed over 10 years with the timing measurement accuracy of 10 ns.