DM-power: an algorithm for high precision dispersion measure with application to fast radio bursts

We present DM-power, a new method for precisely determining the dispersion measure (DM) of radio bursts, and apply it to the Fast Radio Burst (FRB) source FRB~20180916B. Motivated by the complex structure on multiple time scales seen in FRBs, DM-power optimizes the DM by combining measurements at multiple Fourier frequencies in the power spectrum of the burst. By optimally weighting the measurements at each Fourier frequency, DM-power finds a burst DM that effectively incorporates information on many different burst timescales. We validate this technique on simulated Gaussian pulse profiles with a precision down to $\sigma_{\rm DM} \sim 0.001~{\rm pc~cm}^{-3}$, and then apply it to bursts from pulsar B0329+54 and FRB~20180916B. The precision of these DM measurements are sufficient to measure a statistically significant variation in DM over a $\approx 2$ hr span. While this variation could be the result of electron density variations along the line of sight, it is more like that the observed variation is the result of intrinsic frequency-dependent burst structure that can mimic a dispersive delay.