An improved algorithm for separating clock delays from ionospheric effects in radio astronomy

TL;DR

This paper tackles the challenging problem of separating station clock delays from ionospheric dispersive delays in ultra-low-frequency radio data. It introduces a robust likelihood-based method that uses a von Mises (circular Gaussian) model to handle phase wrapping, enabling reliable disentanglement of $\Delta t$ and TEC terms even under solar maximum conditions and large relative bandwidths. The approach yields stable estimates for clock delays, and first- and second-order TEC terms with improved reliability over existing LOFAR processing (losoto), at the cost of higher computational load. The work has practical implications for large-scale LOFAR LBA surveys and paves the way for integrating robust clock–TEC separation into unified calibration pipelines, potentially reducing the need for simultaneous calibrator observations.

Abstract

Context: Low-frequency radio observations are heavily impacted by the ionosphere, where dispersive delays can outpace even instrumental clock offsets, posing a serious calibration challenge. Especially below 100 MHz, phase unwrapping difficulties and higher-order dispersion effects can complicate the separation of ionospheric and clock delays. Aims: We address this challenge by introducing a method for reliably separating clock delays from ionospheric effects, even under mediocre to poor ionospheric conditions encountered near solar maximum. Methods: The approach employs a key technique: we modelled our likelihood space using the circular Gaussian distribution (von Mises random variable) rather than non-circular distributions that suffer from $2π$ phase ambiguities. This ensures that noisier data are weighted less heavily than cleaner data during the fitting process. Results: The method reliably separates clock delays and ionospheric terms that vary smoothly in time whilst providing a good fit to the data. A comparison with the clock-ionosphere separation approach used in standard LOFAR data processing shows that our technique achieves significant improvements. In contrast to the old algorithm, which often fails to return reliable results below 100 MHz even under good ionospheric conditions, the new algorithm consistently provides reliable solutions across a wider range of conditions. Conclusions: This new algorithm represents a significant advance for large-scale surveys, offering a more dependable way to study ionospheric effects and furthering research in ionospheric science and low-frequency radio astronomy.

Figures (7)

• Figure 1: Phase solutions of the calibrator with station CS002 as reference. The frequencies below 20 MHz are RFI-corrupted and, therefore, flagged.
• Figure 2: Delays between stations for the calibrator with station CS002 as reference.
• Figure 3: First-order ionospheric term for the calibrator with station CS002 as reference. CS002 (blue) dots are hidden behind the CS004 (orange) dots because both TEC values are approximately 0.
• Figure 4: Second-order ionospheric term for the calibrator with station CS002 as reference. All the core stations have a second-order ionospheric term of approximately 0.
• Figure 5: Comparison of the ionospheric first-order terms derived in this paper and those computed using losoto for the example stations.