Systematic and Stochastic Variations in Pulsar Dispersion Measures

We analyze deterministic and random variations in dispersion measure (DM) due to the full three-dimensional velocities of pulsars and the solar system combined with electron-density variations on a wide range of length scales. Previous treatments have largely ignored the role of the changing pulsar distance while favoring interpretations that involve only the change in sky position due to transverse motion. Linear trends seen in DM time series of many pulsars over 5-10~year timescales may signify sizable DM gradients in the interstellar medium that are sampled by the changing direction of the line of sight to the pulsar. However, we show that parallel motions can also account for linear trends, for the apparent excess of DM variance over that extrapolated from scintillation measurements, and for the apparent non-Kolmogorov scalings of DM structure functions inferred in some cases. Motions of pulsars through atomic gas may produce bow-shock ionized gas that also contributes to DM variations. We discuss possible causes of periodic or quasi-periodic changes in DM, including seasonal changes in the ionosphere, the annual variation of the solar elongation angle, structure in the heliosphere-interstellar medium boundary, and substructure in the interstellar medium. We assess the role of the solar cycle on the amplitude of ionospheric and solar-wind variations. Interstellar refraction can produce cyclic timing variations due to the error in transforming arrival times to the solar system barycenter. We apply our methods to both DM time series and DM gradient measurements in the literature and assess which are consistent with a Kolmogorov medium and which are not. Finally, we discuss the implications of DM modeling in precision pulsar timing experiments.