Detecting Gravitational Scattering of Interstellar Objects Using Pulsar Timing

Gravitational scattering events, in which the path of an interstellar object is deflected by a pulsar or the solar system, give rise to reflex motion which can potentially be detected using pulsar timing. We determine the form of the timing signal expected from a gravitational scattering event, which is ramp-like and resembles the signal produced by a glitch or a gravitational wave burst with memory (BWM), and investigate the prospects for detecting such a signal using a pulsar timing array. The level of timing precision currently achieved for some millisecond pulsars makes it possible to detect objects as small as $10^{-10}$ solar masses, less than the mass of the dwarf planet Ceres, at impact parameters as large as 1 AU. The signals produced by gravitational scattering could provide independent constraints on models of dark matter involving asteroid-mass objects or subhalos, and should be considered as potential false positives in searches for BWMs.