Frequency-Dependent Dispersion Measures and Implications for Pulsar Timing

Understand

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.