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Numerical study of multiple solar flare induced modulation of Very Low Frequency (VLF) diurnal profile

Sourav Palit, Subhajit Bhattacharyya, Taraknath Bera, Sandip K. Chakrabarti

TL;DR

The paper tackles reconstructing the diurnal VLF signal modulation caused by multiple solar flares by building a forward, physics‑based model of the lower ionosphere. It integrates EUV and X‑ray ionization (Chapman‑like EUV formulation and GEANT4‑based X‑ray ionization), a four‑species ion‑chemistry evolution, and LWPC‑based VLF propagation to reproduce the observed VTX→ICSP Kolkata VLF amplitude day when several flares occur. Key findings show peak electron density enhancements near 90 km altitude and peak time delays between X‑ray maxima and ionization responses, with the modeled VLF amplitude alignment closely matching observations. The work demonstrates the ionosphere as a high‑energy transient detector and advances space weather monitoring by linking flare spectra to VLF sky‑wave signatures, while outlining areas for refinement and broader application.

Abstract

Earth's ionosphere is a perpetual detector of ionizing radiation received from celestial objects, particularly the Sun. Solar ionizing radiation in the form of extreme ultraviolet (EUV) and X-rays during both quiet and active phase of the Sun, and charged particles associated with a solar wind imprint their ionization signatures on the ionosphere. Although due to the bipolar nature of the geomagnetic field, the events, such as the solar coronal mass ejections (CMEs) and associated solar wind enhancement, usually disturb the polar ionosphere only, the UV and X-rays from the solar flares produce sudden ionospheric disturbances (SIDs) in low-mid-latitude part of the earth's ionosphere. Such ionospheric disturbances are studied with the help of the influence they exert on radio waves propagating through earth-ionosphere waveguide. For the lower part of the ionosphere, called the D region, prominent modification in electron-ion density during solar flares can be observed via deviation in earth bound Very Low Frequency (VLF) wave signal from its ambient diurnal profile. In earlier work, successful model of the deviation in VLF amplitude due to different classes of solar flares was formulated. There, calculation of rate of ionization with Monte Carlo simulation and ion-chemistry evaluation of plasma density enhancement followed by a radio propagation simulation was used. Presently, we attempt to numerically reconstruct the modulation in VLF signal from its diurnal pattern produced by multiple solar flares occurring over a single day. Successful reconstruction of the VLF signal modulation for such a complex flaring scenario points to the accuracy of our understanding of the ionization effect due to solar activity on the lower ionosphere, and strengthen our claim to use earth's ionosphere as a high energy space transient event detector.

Numerical study of multiple solar flare induced modulation of Very Low Frequency (VLF) diurnal profile

TL;DR

The paper tackles reconstructing the diurnal VLF signal modulation caused by multiple solar flares by building a forward, physics‑based model of the lower ionosphere. It integrates EUV and X‑ray ionization (Chapman‑like EUV formulation and GEANT4‑based X‑ray ionization), a four‑species ion‑chemistry evolution, and LWPC‑based VLF propagation to reproduce the observed VTX→ICSP Kolkata VLF amplitude day when several flares occur. Key findings show peak electron density enhancements near 90 km altitude and peak time delays between X‑ray maxima and ionization responses, with the modeled VLF amplitude alignment closely matching observations. The work demonstrates the ionosphere as a high‑energy transient detector and advances space weather monitoring by linking flare spectra to VLF sky‑wave signatures, while outlining areas for refinement and broader application.

Abstract

Earth's ionosphere is a perpetual detector of ionizing radiation received from celestial objects, particularly the Sun. Solar ionizing radiation in the form of extreme ultraviolet (EUV) and X-rays during both quiet and active phase of the Sun, and charged particles associated with a solar wind imprint their ionization signatures on the ionosphere. Although due to the bipolar nature of the geomagnetic field, the events, such as the solar coronal mass ejections (CMEs) and associated solar wind enhancement, usually disturb the polar ionosphere only, the UV and X-rays from the solar flares produce sudden ionospheric disturbances (SIDs) in low-mid-latitude part of the earth's ionosphere. Such ionospheric disturbances are studied with the help of the influence they exert on radio waves propagating through earth-ionosphere waveguide. For the lower part of the ionosphere, called the D region, prominent modification in electron-ion density during solar flares can be observed via deviation in earth bound Very Low Frequency (VLF) wave signal from its ambient diurnal profile. In earlier work, successful model of the deviation in VLF amplitude due to different classes of solar flares was formulated. There, calculation of rate of ionization with Monte Carlo simulation and ion-chemistry evaluation of plasma density enhancement followed by a radio propagation simulation was used. Presently, we attempt to numerically reconstruct the modulation in VLF signal from its diurnal pattern produced by multiple solar flares occurring over a single day. Successful reconstruction of the VLF signal modulation for such a complex flaring scenario points to the accuracy of our understanding of the ionization effect due to solar activity on the lower ionosphere, and strengthen our claim to use earth's ionosphere as a high energy space transient event detector.
Paper Structure (10 sections, 3 equations, 15 figures)

This paper contains 10 sections, 3 equations, 15 figures.

Table of Contents

  1. Introduction
  2. Observation and data accumulation for simulation
  3. Methodology
  4. Calculation of Ionization
  5. Ionization due to EUV photons
  6. Flare X-ray Ionization
  7. Ion-Chemistry Model
  8. VLF reconstruction with LWPC code
  9. Results
  10. Discussions and Conclusions

Figures (15)

  • Figure 1: X ray fluxes in two different wavelength ranges, binned for one minute duration, for the day of $5^{th}$ of January 2025 showing multiple solar flares, mostly M-class ones, obtained from the GOES-18 data and plotted against proper setting of date and time at http://sprg.ssl.berkeley.edu/ tohban/browser/
  • Figure 2: VLF amplitude for the whole day-time of $5^{th}$ of January 2025 transmitted from VTX transmitter (19.8 kHz) and received at ICSP receiver Kolkata is shown in the Figure. The dotted vertical lines correspond to peaks in VLF amplitude in response to the peaks of the transients or flares of diferrent brightness in solar soft X-ray light curve.
  • Figure 3: The Top panel shows the VLF great circular path (GCP) between the transmitter VTX and the receiving station at ICSP, Kolkata. The Figures in the Bottom panel show the subsolar points during the peaks of the first three M-class solar flares (a,c,d) and the C-class flare (b) at 5.5 hr (UT) the effects of which on the VLF amplitude are shown by verticle dashed lines in Figure \ref{['amp']}. The Bottom Figures are obtained using Day and Night World Map of https://www.timeanddate.com. At the terminators the lightest to darkest twilight shadows represent Civil, Nautical and Astronomical Twilight respectively.
  • Figure 4: Soft X-ray flux from 1–8 $\AA$ (1.55 – 12.40 keV) obtained from GOES satellite data of the first 12 hours (UT) of $5^{th}$ of January 2025
  • Figure 5: UV photon flux in unit of $photon.cm^{-2}s^{-1}$ in the range of 0.1 - 50 nm obtained from SOHO/SEM for the the first 12 hours (UT) of $5^{th}$ of January 2025
  • ...and 10 more figures