Quantifying the α Index of Gamma-Ray Burst Spectra Using Ground-based Very Low-frequency Measurements

Abstract The spectral index α is critical to the studies of the emission theory of gamma-ray bursts (GRBs). However, due to the low-energy threshold and systematic uncertainties, space-borne detectors struggle to accurately measure α for energies below ∼10 keV. Photons in this energy range deposit most of their energy within the D -region ionosphere, which directly controls the propagation of very low-frequency (VLF) signals. To address the satellite limitation, we have proposed a novel method to estimate α by leveraging the high sensitivity of VLF signals to the disturbance of the D -region ionosphere. Using the VLF data collected in Antarctica, we have identified and investigated four GRB events with clear VLF responses that occurred between 2022 and 2023. The α values derived from the GRB signature in VLF measurements show excellent agreement with Fermi Gamma-ray Burst Monitor measurements; the absolute difference between the Fermi-measured and VLF-derived α is as small as 0.02. Moreover, this method has the advantage of largely extending the low-energy limitation of satellite measurements (down to ∼2 keV), which is particularly helpful for bright GRB events. Therefore, with a network of VLF receivers, this approach can provide an accurate and reliable determination of the low-energy spectral index and serve as an important backup for satellite measurements.