Frequency-dependent dispersion measures and implications for pulsar timing

Abstract

The dispersion measure (DM), the column density of free electrons to a pulsar, is shown to be frequency dependent because of multipath scattering from small-scale electron-density fluctuations. DMs vary between propagation paths whose transverse extent varies strongly with frequency, yielding arrival times that deviate from the high-frequency scaling expected for a cold, uniform, unmagnetized plasma (1/frequency2). Scaling laws for thin phase screens are verified with simulations; extended media are also analyzed. The rms DM difference across an octave band near 1.5 GHz is ~ 4 × 10-5 pc cm-3 for pulsars at ~1 kpc distance. The corresponding arrival-time variations are a few to hundreds of nanoseconds for DM <~30 pc cm-3 but increase rapidly to microseconds or more for larger DMs and wider frequency ranges. Chromatic DMs introduce correlated noise into timing residuals with a power spectrum of "low pass" form. The correlation time is roughly the geometric mean of the refraction times for the highest and lowest radio frequencies used, ranging from days to years, depending on the pulsar. We discuss implications for methodologies that use large frequency separations or wide bandwidth receivers for timing measurements. Chromatic DMs are partially mitigable by including an additional chromatic term in arrival time models. Without mitigation, an additional term in the noise model for pulsar timing is implied. In combination with measurement errors from radiometer noise, an arbitrarily large increase in total frequency range (or bandwidth) will yield diminishing benefits and may be detrimental to overall timing precision.