Studying Ionospheric Phase Structure Functions Using Wide-Band uGMRT (Band-4) Interferometric Data

TL;DR

The paper tackles ionospheric phase disturbances that limit low-frequency interferometry by quantifying spatial phase fluctuations through the phase structure function $ \Xi(r) $. Using a ten-hour nighttime Band-4 uGMRT dataset on 3C48, it computes TEC-derived phase delays and analyzes $ \Xi(r) $ with 1D and 2D anisotropic models. The fitted 1D law yields $ \beta \approx 1.71 \pm 0.07 $ and $ r_{ m diff} \approx 6.68 \, \mathrm{km} $, while the 2D fit gives an anisotropy ratio of $ r_{ m diff,maj}/r_{ m diff,min} \approx 2.17 $. An angle-resolved analysis indicates that, although many structures are aligned with the geomagnetic field, medium-scale Travelling Ionospheric Disturbances (MSTIDs) produce non-field-aligned anisotropy. These findings have practical implications for direction-dependent calibration in tied-array VLBI and SKA pathfinders, and underscore the value of Band-4 observations for mid-frequency ionospheric studies.

Abstract

Interferometric observations of the low-frequency radio sky ($<$ 1~GHz) are largely limited by systematic effects introduced by the ionosphere. In this study, we use a ten-hour nighttime observation of the bright radio source 3C48, carried out with the upgraded Giant Metrewave Radio Telescope (uGMRT), to examine how ionospheric conditions affect radio signals. We focus on measuring phase fluctuations caused by the ionosphere and analyse how these variations change with antenna separation using the spatial phase structure function. Our results, based on data from three sub-bands between 575 and 725~MHz, show a clear power-law trend consistent with turbulent behaviour. We introduce the diffractive scale as a scalar measure of ionospheric conditions, which could guide future calibration strategies. Furthermore, we find that the turbulence is anisotropic, with properties that vary by direction. The smallest diffractive scales do not always align with Earth's magnetic field, suggesting the influence of medium-scale Travelling Ionospheric Disturbances (MSTIDs). The contribution of these wave-like MSTIDs to the structure function follows a power-law with a slope close to 2.0, indicating their dominant role in shaping the observed anisotropic phase fluctuations.

Figures (10)

• Figure 1: Differential TEC ($\delta {\rm TEC}$) for the RR polarization of uGMRT baselines relative to the reference antenna 'C06' as a function of time. The colour bar indicates baseline length. (Top row) Baselines within the central square. (Bottom row) Extended antenna arm baselines.
• Figure 2: Phase structure function at approximately 587.5 MHz. The blue points represent the measured phase variance as a function of baseline length, while the red solid line shows the fitted one-dimensional power-law model.
• Figure 3: Two-dimensional phase structure function at 587.5 MHz. The green dotted and red solid lines represent the major and minor axis projections, respectively, based on the 2D structure function model described in Equation \ref{['eq:2DKolmogorov']}.
• Figure 4: The figure shows the phase structure function where the data is binned by the angle relative to the projected Earth's magnetic field. The colour bar indicates the angle in degrees.
• Figure 5: Phase structure function comparing two groups of baselines based on their angle to the Earth's magnetic field: those nearly aligned (between $0^\circ$ and $20^\circ$, shown with blue solid lines) and those nearly perpendicular (between $70^\circ$ and $90^\circ$, shown with red dotted lines). Each line shows a 1D power-law fit of phase variance with baseline length.