Frequency-Dependent Dispersion Measures and Implications for Pulsar Timing

TL;DR

This paper investigates how frequency-dependent dispersion measures caused by small-scale electron-density fluctuations affect pulsar timing, revealing that these effects introduce correlated noise and pose challenges for high-precision measurements.

Contribution

It provides analytical and simulation-based quantification of frequency-dependent DM and TOA perturbations, highlighting their impact on pulsar timing accuracy and noise modeling.

Findings

Frequency-dependent DMs cause nanosecond to microsecond timing errors.

Chromatic DMs introduce low-pass correlated noise in timing residuals.

Increasing bandwidth alone may not improve timing precision due to chromatic effects.

Abstract

We analyze the frequency dependence of the dispersion measure (DM), the column density of free electrons to a pulsar, caused by multipath scattering from small scale electron-density fluctuations. The DM is slightly different along each propagation path and the transverse spread of paths varies greatly with frequency, yielding time-of-arrival (TOA) perturbations that scale differently than the inverse square of the frequency, the expected dependence for a cold, unmagnetized plasma. We quantify DM and TOA perturbations analytically for thin phase screens and extended media and verify the results with simulations of thin screens. The rms difference between DMs across an octave band near 1.5~GHz $\sim 4\times10^{-5}\,{\rm pc\ cm^{-3}}$ for pulsars at $\sim 1$~kpc distance. TOA errors from chromatic DMs are of order a few to hundreds of nanoseconds for pulsars with DM $\lesssim 30$~pc~cm$^{-3}$ observed across an octave band but increase rapidly to microseconds or larger for larger DMs and wider frequency ranges. Frequency-dependent DMs introduce correlated noise into timing residuals whose power spectrum is `low pass' in form. The correlation time is of order the geometric mean of the refraction times for the highest and lowest radio frequencies used and thus ranges from days to years, depending on the pulsar. We discuss the implications for methodologies that use large frequency separations or wide bandwidth receivers for timing measurements. Chromatic DMs are partially mitigable by using an additional chromatic term in arrival time models. Without mitigation, our results provide an additional term in the noise model for pulsar timing; they also indicate that in combination with measurement errors from radiometer noise, an arbitrary increase in total frequency range (or bandwidth) will yield diminishing benefits and may be detrimental to overall timing precision.