Monitoring solar activity during 23/24 solar cycle minimum through VLF radio signals

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Introduction
During quiet solar conditions, ionization i.e. production of electron content within lower ionospheric D-region, within altitude range 50-90 km, is in general related to photoionization processes caused by UV Lyman-α spectral line 121.6 nm, EUV spectral lines ranging from 102.7 nm to 118.8 nm and galactic cosmic rays. One of frequent extraterrestrial causing agents, that become major source of electron density perturbations within D-region, are X-ray solar flare events (0.1-0.8 nm) (Whitten & Poppoff, 1965;Wang et al., 2020;Hayes et al., 2021). Due to additional ionization, electron density height profile of the lower ionosphere changes (Mitra, 1974). Such perturbations affect propagation of Very Low Frequency (VLF) radio signals within Earth-ionosphere waveguide, causing deviations from their regular propagation patterns stable at unperturbed solar conditions (Thomson, 1993;McRae & Thomson, 2000). Since electron production rate coefficients can be considered directly proportional to intensity of incident X-radiation (Ratcliffe et al., 1972), perturbations of VLF radio signals induced by solar flares can be used as diagnostic tool for exploration of lower ionospheric electron content behavior during such events (see Barta et al., 2022, and references therein).
Utilization of VLF radio signals, as the remotesensing technique for exploration of the lower ionosphere (Thomson et al., 2011;McRae & Thomson, 2000;McRae & Thomson, 2004;Thomson et al., 2005), is widely adopted and extensively used by many research groups over several decades, e.g. (Silber & Price, 2017) and references therein. Response of the lower ionosphere to analyzed solar flare events, numerically was modeled by the use of Long Wave Propagation Capability (LWPC) (Ferguson, 1998) software relying on application of Wait's theory (Wait & Spies, 1964).
Effects of low intensity solar flare events of C and B classes, during 23/24 solar minimum, between descending branch of 23 rd and ascending branch of 24 th solar cycle, were inspected by monitoring recordings of VLF radio signals recorded in Belgrade (44.85 N,20.38 W) Serbia, within time period from 2008 to 2010. Data related to solar X-rays is obtained from Geostationary Operational Environmental Satellite (GOES) archive database (https://satdat. ngdc.noaa.gov/sem/goes/data/avg/).

Observations
Periods of quiet solar activity, like during solar minimums, are of great interest for studying quiet ionospheric conditions and accompanying quiet i.e. unperturbed states within Earth-ionosphere waveguide related to VLF radio signals' transmission. In addition, since solar background X radiation during such periods is of small amount, low class solar flare events, like those of lower C class and moderate B class, when occur, are easily noticeable and recognizable, clearly distinguishing themselves from surrounding sections of unperturbed VLF radio signals. This gives a unique opportunity to examine characteristics of low class solar flare events, which are otherwise masked by high solar background X radiation during periods of usual more intense solar activity. An example of active Sun during solar maximum in April 2014 and quiet Sun during solar minimum in December 2019 are given in Figure 1, left and right, respectively. In 23/24 solar minimum, during 2008 there were 8 C class and 1 M class solar flare events reported, with X-ray background flux up to A8.1, while during 2009 there were 28 C class solar flare events reported, with X-ray background flux up to B1.4 ( Figure 2). VLF radio signal recordings obtained from the Absolute Phase and Amplitude Logger receiving station (AbsPAL), located and operating at the Institute of Physics in Belgrade, Serbia, was used as instrumental setup. Within inspected time period from 2008 to 2010, several VLF radio signals were simultaneously recorded by AbsPAL station in Belgrade. Geographical position and transmitter's characteristics of VLF radio signals propagating towards Belgrade are given in Table 1.

Results and discussion
Inspection of low intensity solar flare events of C and B class, on recorded VLF radio signals, was done according to provided solar X radiation listings from GOES database. During inspected period 2008-2010, low class solar flare events exhibited expected behavior, with amplitude perturbations of absolute amount in general of several tenth parts of dB up to few dB and with phase delay perturbations of absolute amount of few degrees to up to 16 o . Some typical   Electron density height profile within Earth's lower ionosphere changes due to the incident solar X-ray radiation during solar flare events, causing in general descending and "sharpening" of the ionospheric lower boundary. Model of VLF radio signals propagation within Earth-ionosphere waveguide (Wait & Spies, 1964), that describes the electron density by reflecting edge sharpness, denoted by β (km −1 ) and reflecting edge height, denoted by H (km), was used for purposes of numerical simulations of VLF radio signal propagation through Earth-ionosphere waveguide. Obtained results through simulations are in good agreement with VLF signal amplitude and phase delay data measured in Belgrade. Electron density height profiles N e (z), within altitude range 50-90 km, were obtained through the equation (Wait & Spies, 1964): Numerical simulations were conducted for the entire time evolution of chosen solar flare events, with parameter pairs (β/H ) held constant along VLF radio signal's GCPs, depicting "average" ionospheric conditions within waveguide. VLF radio signal's amplitude and phase delay perturbations ∆A (dB) and ∆P ( o ), were determined by comparing measured perturbed to the measured unperturbed amplitude and phase delay values and are calculated as: ∆A = A f lare -A unpert and ∆P = P f lare -P unpert . During simulations through iterative process, the goal was to achieve as close as possible to measured data, both absolute values of simulated amplitude and phase delay and relative amount of perturbations. Results obtained through numerical simulations are in good agreements with measured data. Calculated electron density height profiles during maximum of X-ray solar irradiance, in case of NAA/24.0 kHz signal trace, are given in (Figure 13 et al., 2007;Grubor et al., 2008;McRae & Thomson, 2004;Kolarski et al., 2011;Nina et al., 2011Nina et al., , 2012Kolarski & Grubor, 2014;Kolarski et al., 2022;Srećković et al., 2021a,b). It is possible to draw conclusions about the intensity of the causing X-ray solar flare events, based upon perturbation amounts obtained from VLF radio signal recordings, when taking into consideration single VLF radio signal trace.
However, same solar flare event can produce perturbations different both in pattern and in intensity, when observed on different VLF radio signal traces. Typical examples are in general perturbations induced by solar flare events of moderate and lower intensity classes as recorded in Belgrade during active solar periods on NAA and GQD radio signals. In such cases, NAA signal's both amplitude and phase delay follow in pattern incident X-ray solar irradiance, while in case of GQD signal, amplitude and phase delay follow incident X-ray solar irradiance in pattern, but like mirrored images and only in some cases of higher class solar flare events this feature is more or less mitigated (Žigman et al., 2007;Grubor et al., 2008;Kolarski & Grubor, 2014). Aside to main factor of solar flare intensity (Grubor et al., 2008;Kolarski & Grubor, 2014), this behavior is also strongly under the influence of VLF GCP trace characteristics (Kolarski & Grubor, 2015;Šulić & Srećković, 2014;Šulić et al., 2016). For example, measured absolute perturbation as observed on GQD radio signal trace, in case of C3.7 solar flare event was ∆A f lare =1 dB and ∆P f lare =11.

Summary
Two year time period of VLF radio signal recordings from Belgrade AbsPAL database, corresponding to 23/24 solar minimum, was examined in order of getting better insight of effects that low intensity solar flare events of C and B classes have on the lower ionospheric region and transmission of VLF radio signals within Earth-ionosphere waveguide. According to GOES database, during inspected period 2008-2010, 38 solar flare events of C and M class were reported, with X-ray background flux in range up to A8.1 for 2008 and B1.4 for 2009. Low intensity solar flare events of C and B class were monitored on all recorded VLF radio signals. Depending on solar flare occurrence time and VLF radio signal's GCP towards Belgrade receiver station, some flares were simultaneously observed on several VLF radio signals, however, detailed analysis in this paper was conducted for cases of NAA/24.0 kHz and GQD/22.1 kHz signal traces.
As expected, majority of low class solar flare events in general revealed perturbations of absolute amount of several tenth parts of dB up to few dB and of few degrees to up to 16 o , following the manner of incident solar X-ray flux. However, there were also cases that fall out of the pattern, when relatively weak solar flare events such as C3.7, produced perturbations of 5 dB and 13 o , while relatively stronger ones, such C6.5 gave perturbations of similar amount, as 5 dB and 15 o . Due to low X-ray background flux, in some cases even B class solar flare events induced noticeable perturbations, as in case of B8.35 with perturbation of 1.5 dB and 10 o .
Numerical simulations were conducted using LWPC software package, with goal of achieving simulated VLF data as close as possible to measured VLF data in Belgrade, both in case of absolute values and in case of relative amount of perturbations. Results obtained through iterative numerical simulations are in good agreements with real VLF data measured in Belgrade (Žigman et al., 2007;Grubor et al., 2008;Kolarski et al., 2011;Nina et al., 2011). In case of NAA/24.0 kHz signal, perturbations induced by low class solar flare events produced "sharpening" and descending of the lower ionospheric boundary, as in cases of presented solar flare events reflection height went from unperturbed value of 74 km to 72.3, 70.1 and 69.7 km, while become "sharper" compared to unperturbed value of 0.3 km −1 reaching 0.33 and 0.44 km −1 . Estimated N e (74 km) are realistic and in line with other studies (McRae & Thomson, 2004;Nina et al., 2012;Kolarski & Grubor, 2014;Kolarski et al., 2022;Srećković et al., 2021a,b).