Spectro-temporal analysis of ultra-fast radio bursts using per-channel arrival times

TL;DR

The paper develops a per-channel arrival-time analysis to measure FRB spectro-temporal properties, enabling precise d t/dν measurements across a wide range of morphologies including ultra-FRBs. By fitting channel-wise Gaussian profiles and linking arrival times with frequency through a linear model, it yields key metrics such as the sub-burst slope, duration, and center frequency, and reveals a robust sub-burst slope–duration scaling that extends to ultra-FRBs and aligns with TRDM predictions. The study analyzes 433 bursts from 12 repeating FRB sources, uncovering strong correlations among $ u_0$, $\sigma_t$, $\sigma_ u$, and $ ext{d}t/ ext{d} u$, and provides drift-rate measurements that extend the mapping between drift and duration. Compared with Gaussian and ACF methods, the arrival-times approach offers robust performance across complex morphologies and blended components, while highlighting the persistent influence of dispersion and scattering on spectro-temporal inferences; the authors also release the analysis code in FRBGUI for community use.

Abstract

Fast radio bursts (FRBs), especially those from repeating sources, exhibit a rich variety of morphologies in their dynamic spectra (or waterfalls). Characterizing these morphologies and spectro-temporal properties is a key strategy in investigating the underlying unknown emission mechanism of FRBs. This type of analysis has been typically accomplished using two-dimensional Gaussian techniques and the autocorrelation function (ACF) of the waterfall. These techniques are effective and precise at all duration scales, but can be limited in the presence of scattered tails, complex morphologies, or recently observed microshot forests. Here, we present a technique that involves the tagging of per-channel arrival times of an FRB to perform spectro-temporal measurements using a Gaussian profile model for each channel. While scattering and dispersion remain important and often dominating sources of uncertainty in measurements, this technique provides an adaptable and firm foundation for obtaining spectro-temporal properties from all types of FRB morphologies. We present measurements using this technique of several hundred bursts across 12 repeating sources, including over 400 bursts from the repeating sources FRB 20121102A, FRB 20220912A, and FRB 20200120E, all of which exhibit recently observed microsecond-long ultra-FRBs, as well as 143 multi-component drift rates. In addition to retrieving the known relationship between sub-burst slope and duration, we explore other correlations between burst properties. We find that the sub-burst slope law extends smoothly to ultra-FRBs, and that ultra-FRBs appear to form a distinct population in the duration-frequency relation.

Figures (13)

• Figure 1: (a) Arrival times method for burst B43 of Snelders2023. The top and rightmost panels show the integrated time series and spectrum, respectively, of the waterfall, shown in the center. In the time series, the 1D Gaussian fits are shown with a black line. The vertical dashed line denotes the peak time of the burst. The reddish bar indicates the 2$\sigma_{t,\text{1D}}$ window used in the arrival times temporal filter. The faint blue shaded regions in the time series and spectrum are the 1$\sigma$ regions of their corresponding fits. The spectrum for this burst is found by integrating over the 2$\sigma_{t,\text{1D}}$ region of the pulse. The dash-dot line denotes the center frequency. The waterfall is displayed with white points indicating the arrival times found in each frequency channel, which are then used in the linear fit to obtain $\text{d}t/\text{d}\nu$, shown in the bottom sub-panel. For each fit, the corresponding reduced-$\chi^2$ is shown in its corresponding panel. (b) Same as above but for burst B25 of Sheikh2024Sheikh2024a, which has two sub-bursts. The plot shows how different components are separated for measurement. Components are labeled alphabetically from left to right and each set of arrival time points are colored according to the sub-burst they are associated with. The red line indicates the drift rate measurement $\Delta t / \Delta \nu$ obtained for this burst and the red xs denote the center frequency of each component. The bottom sub-panel shows the linear fit and arrival times of the last component.
• Figure 2: Burst 5-04 from Zhang2023 from FRB 20220912A. Same as Figure \ref{['fig:arrmethod']}, but showcasing measurements from two sub-components blended together. The black dash-dot line in the time series indicates the position of the manual cut. The drift rate shown includes a component truncated by the observing band, and will be marked specially in figures to come. The bottom sub-panel shows the linear fit and arrival times of the last component.
• Figure 3: Distribution of burst properties analysed, as measured by the arrival times pipeline. From left to right, the center frequency, sub-burst duration, and sub-burst bandwidth distributions are shown. Bins from each source are stacked. Sources with the most overall bursts (starting with FRB 20220912A) are at the bottom of each bin. Note that the last two colors listed in the legend are repetitions, but these sources only include 4 bursts and their bars are too narrow to see. Inset in the middle panel is an additional plot showing the duration distribution of FRBs shorter than 1 ms with a bin width of 40 $\upmu$s. Sub-bursts here refers to the components of each FRB, each of which have been separated and measured independently.
• Figure 4: Plot of the inverse normalized sub-burst slope, $\nu (\text{d}t/\text{d}\nu)$, versus the sub-burst duration, $\sigma_t$, for a cohort of FRBs from multiple repeating sources. All measurements were obtained using the arrival times pipeline. The duration axis is displayed on a logarithmic scale. The inset panel provides a zoomed view of ultra-FRBs with durations below our selected upper limit of 300 $\upmu$s. The marker shape denotes the source of the burst, while bursts are colored by frequency, ranging from around 100 MHz to nearly 7.5 GHz. The dashed-dotted line represents a general linear fit to the data from FRB 20121102A, the source with the most extensive set of observations. Bursts shown here are generally measured at the DM of the shortest duration burst in their cohort; see the text and Table \ref{['tab:sources']} for additional details on the DMs used for measurements. The residuals between all bursts and the plotted fit are shown in the bottom panel. Overall, we observe good agreement with the linear fit across all sources within the uncertainties, consistent with previous analyses. Drift rate measurements obtained from waterfalls with multiple resolved components are overlaid with larger markers and a white border. These measurements generally align with the fit for sub-burst slopes, but they exhibit more outliers. Some drift rates fall outside the chosen axis limits. See Figure \ref{['fig:extradata']} for a version of this plot with measurements from other studies.
• Figure 5: Corner plot of burst properties measured from 12 repeating FRB sources. Marker shape denotes the FRB source. Points are colored by their reported flux density, as indicated by the color bar. Note that some points are colored by the average flux density, as described in the text. Uncolored points have missing flux densities. The strongest correlations are seen in the three $\text{d}t/\text{d}\nu$ plots along the bottom row. The blue fit line shown in the $\text{d}t/\text{d}\nu$--$\nu_0$ plot is the fit found from FRB 20121102A data reported in Chamma2023. The blue and orange fit lines in the $\sigma_t$--$\nu_0$ plot are fit to bursts with duration greater and less than 300 $\upmu$s. See the text for details.