Calculation and Uncertainty of Fast Radio Burst Structure Based on Smoothed Data

TL;DR

This paper introduces a new smoothing method using discrete cosine transform to accurately estimate the dispersion measure of fast radio bursts and quantify the uncertainty in the measurement.

Contribution

A novel smoothing filter based on discrete cosine transform is proposed, enabling precise estimation of FRB structure and its uncertainty from high-resolution data.

Findings

Effective in analyzing FRB data from ASKAP

Provides quantitative uncertainty estimates

Improves accuracy of dispersion measure calculation

Abstract

Studies of the time-domain structure of fast radio bursts (FRBs) require an accurate estimate of the FRB dispersion measure in order to recover the intrinsic burst shape. Furthermore, the exact DM is itself of interest when studying the time-evolution of the medium through which multiple bursts from repeating FRBs propagate. A commonly used approach to obtain the dispersion measure is to take the value that maximizes the FRB structure in the time domain. However, various authors use differing methods to obtain this structure parameter, and do not document the smoothing method used. Furthermore, there are no quantitative estimates of the error in this procedure in the FRB literature. In this letter, we present a smoothing filter based on the discrete cosine transform, and show that computing the structure parameter by summing the squares of the derivatives and taking the square root immediately lends itself to calculation of uncertainty of the structure parameter. We illustrate this with FRB181112 and FRB210117 data, which were detected by the Australian Square Kilometre Array Pathfinder, and for which high-time-resolution data is available.