Detecting hyperbolic scattering of interstellar objects with NANOGrav pulsar timing data

The extraordinary stability of pulsars as clocks makes them highly sensitive probes of a number of astrophysical phenomena, up to and including gravitational waves. In particular, the first extrasolar planets ever discovered were around a pulsar (Wolszczan & Frail 1992). In its ongoing observing campaign, the North American Nanohertz Observatory for Gravitational Waves (NANOGrav) has collected over 500 pulsar-years of high precision pulsar timing data. In such a large dataset, even rare events may be observed to occur with some frequency. With this in mind, I consider whether scattering of rogue planets or planetesimals, or other similarly-sized interstellar objects such as dark matter clumps, by pulsars or by the solar system, may be detectable in current or future NANOGrav data. I find that objects as small as 10^-10 solar masses (around the size of the largest asteroids) may be detected at impact parameters of order 1 AU with current sensitivities. While the probability of a scattering event involving an interstellar planetesimal of this size occuring in the present NANOGrav dataset is small, NANOGrav may be sensitive enough in this respect to place significant constraints on the occurrence of dark matter clumps in this mass range.