A Measurement Model for Precision Pulsar Timing

Abstract: This paper describes a comprehensive measurement model for the error budget of pulse arrival times with emphasis on intrinsic pulse jitterand plasma propagation effects (particularly interstellar scattering), which are stochastic in time and have diverse dependences on radio frequency. To reduce their contribution, timing measurements can be made over a range of frequencies that depends on a variety of pulsar and instrumentation-dependent factors that we identify. A salient trend for high signal-to-noise measurements of millisecond pulsars is that time-of-arrival precision is limited either by irreducible interstellar scattering or by pulse-phase jitter caused by variable emission within pulsar magnetospheres. A cap on timing errors implies that pulsars must be confined to low dispersion measures (DMs) and observed at high frequencies. Use of wider bandwidths that increase signal-to-noise ratios will degrade timing precision if nondispersive chromatic effects are not mitigated. The allowable region in the DM-frequency plane depends on how chromatic timing perturbations are addressed. Without mitigation, observations at 1.4~GHz or 5~GHz are restricted to $\DM\lesssim 30$ and $\lesssim 100~\DMu$, respectively. With aggressive mitigation of interstellar scattering and use of large telescopes to provide adequate sensitivity at high frequencies (e.g. Arecibo, FAST, phase 1 of the SKA, and the SKA), pulsars with DMs up to 500~$\DMu$ can be used in precision timing applications. We analyze methods that fit arrival times vs. frequency at a given epoch prior to multi-epoch fitting. While the terms of greatest astrophysical interest are achromatic (e.g. orbital and gravitational wave perturbations), measurements may ultimately be limited by similarly achromatic stochasticity in a pulsar's spin rate.