Pulsar Timing Errors from Asynchronous Multi-Frequency Sampling of Dispersion Measure Variations

TL;DR

This paper investigates how non-simultaneous multi-frequency observations affect pulsar timing accuracy due to dispersion measure variations, providing guidelines for data collection to achieve nanosecond precision.

Contribution

It quantifies the impact of asynchronous sampling on timing errors and offers prescriptions for observation timing to improve pulsar timing precision.

Findings

Simultaneous measurements within one day reduce errors below 10 ns.

Increasing from two to three observations improves timing precision by about a factor of two.

Diminishing returns occur when adding more than three observations for dispersion correction.

Abstract

Free electrons in the interstellar medium cause frequency-dependent delays in pulse arrival times due to both scattering and dispersion. Multi-frequency measurements are used to estimate and remove dispersion delays. In this paper, we focus on the effect of any non-simultaneity of multi-frequency observations on dispersive delay estimation and removal. Interstellar density variations combined with changes in the line-of-sight from pulsar and observer motions cause dispersion measure variations with an approximately power-law power spectrum, augmented in some cases by linear trends. We simulate time series, estimate the magnitude and statistical properties of timing errors that result from non-simultaneous observations, and derive prescriptions for data acquisition that are needed in order to achieve a specified timing precision. For nearby, highly stable pulsars, measurements need to be simultaneous to within about one day in order that the timing error from asynchronous DM correction is less than about 10 ns. We discuss how timing precision improves when increasing the number of dual-frequency observations used in dispersion measure estimation for a given epoch. For a Kolmogorov wavenumber spectrum, we find about a factor of two improvement in precision timing when increasing from two to three observations but diminishing returns thereafter.