Solar flare effects (SFE) on geomagnetic fields across latitudes

A comprehensive study of Solar Flare Effects (SFE) across latitudes has been carried out using an extensive data set of two geomagnetic elements H and Z selected from 1997 to 2005. The X (intense) and M (medium) solar flares were examined under quiet conditions. Nine stations extending from equatorial to high latitudes were used in the study. Data employed in this work include minute data of geomagnetic field, solar flare and hourly data of geomagnetic field. On the whole, about one hundred and fifty four (154) solar flares were selected. Each of these flares was critically studied and analyzed to see its response on the geomagnetic H and Z components. Only fifteen to thirty four flares showed the signature in the different stations. The study revealed that pre-solar flare and solar flare amplitude variations are least in the mid latitude stations, followed by the equatorial and low latitude stations and the highest in the high latitude stations. The pre-solar flare amplitude variations and solar flare amplitude variations of Z failed to show any clear pattern. Correlation existed between the solar flare amplitude variations of H and the pre-solar flare amplitude variations. The ratios of ∆H SFE /∆Ho and ∆Z SFE /∆Zo were greater than zero for all the stations used in the study. This implies that the solar flare effects enhance geomagnetic field across latitudes.


INTRODUCTION
The effects of solar flare and other solar activity phenomena on geomagnetic components and lives, communication, navigation systems as well as power distribution system have been studied. Solar flare affects the geomagnetic field by increasing ionization mainly in the E region, partially in the D region and occasionally in the F regions. Rastogi et al. (1997) argued that the dense plasma clouds from the sun are stopped at the magnetopause when the magnetic pressure of the earth's magnetic field balances dynamic pressure of the plasma and there is a sharp rise in H component of the earth's magnetic pressure as the magnetosphere is compressed. Lorentz force deflects the charged particles making them to travel around the planet instead of entering it.
A flare is a sudden, rapid, intense and violent explosion in a sun's atmosphere leading to intense variation in brightness. Solar flares are produced when the magnetic energy that has built up in the solar atmosphere is suddenly released. Around sunspots are active regions *Corresponding author. E-mail: obiageli.ugonabo@unn.edu.ng.
Author(s) agree that this article remain permanently open access under the terms of the Creative Commons Attribution License 4.0 International License where intense magnetic fields build up and penetrate the photosphere linking the corona to the solar interior. Solar flares are produced mainly in two preferred longitude ranges; the active regions (Zhang et al., 2011). The energy released is as high as 6  10 25 J, millions of 100megaton H-bomb exploding at the same time; it takes about eight minutes to reach the earth. Radiations are emitted across the entire electromagnetic spectrum and affect all the layers of the solar atmosphere, heating up plasma to tens of millions of kelvin; accelerating electrons, protons and heavier ions to near the speed of light. There are three stages in the production of a solar flare. At the first stage magnetic energy is released. Soft x-rays are detected here. The second stage involves accelerating electrons, protons and heavier ions to energies above 1 MeV. At this stage, radio waves, hard x-rays and gamma rays are released and could be detected. The third stage involves the gradual build up and decay of soft x-rays. Large flares are less frequent than small flares. Usually, there is an increase in the number of solar flares as the sun approaches the maximum part of its eleven year cycle. Baker and Martyne (1953) reported that the prevailing current system in the dip latitudes is the equatorial electrojet current and that the basic reason for the existence of the electrojet is the high cowling conductivity at the dip equator. But many authors argue that the dayto-day variability in the solar quiet (Sq) variation in low latitudes is mostly due to the variation in the dynamo electric fields rather than the conductivity (Dunford, 1970;Onwumechili and Ezema, 1976;Okeke and Hamano, 2000). Onwumechili and Ogbuehi (1962) studied the diurnal characteristics of fluctuations in the horizontal intensity H at Ibadan and compared them with the characteristics of solar flares. They thus suggested that the fluctuations under quiet conditions are caused by fluctuations in the quality and quantity of ionized wave radiation from the sun. Rishbeth (1969) explained that additional current exists under quiet conditions. This is confirmed by Campbell (1982) and Campbell (1987) who showed great enhancement of the 24 h component of the daily geomagnetic field occurred with strong summer time maxima in the annual variation of the variation of the H, D and Z components above 70° latitude. Campbell (1982) showed that in the mid latitudes occur the lowest values of Sq geomagnetic variations. In high latitudes, the Sq variation does not correspond to simple current systems like the electrojet. Rastogi (1996) discovered that during the normal electrojet period, a solar flare produced a positive change in H, a negative change in Y and Z, the effect on ΔY (negative) increased linearly with increasing value of ΔH. This suggested that the solar flare effects on all the three geomagnetic components were plainly the augmentation of the ionospheric current over station in agreement with Ugonabo et al. 113 the conclusion of Saben (1968). Rastogi et al. (1997) explained that the solar flare effects are associated with the arrival of enhanced electromagnetic radiations from the sun, which while traversing the ionosphere, generate additional ionizations mainly in the E, partially in the D-and sometimes in the F-region. They discovered that the solar flare effects registered on the magnetograms are augmentation of the ionospheric current and equally discovered an equatorial enhancement in ΔH due to solar flare effects which is observed to be similar in nature to the latitudinal variation of Sq (H) at low latitudes. Okeke et al. (1998) suggested from their study that ionospheric conductivity mainly controls the magnitude of the day to day variability of geomagnetic hourly amplitude at low latitudes, while electric field and wind systems controls the phase and randomness. Okeke and Okpala (2005) in their study of the solar flare effect of 6th May 1998 in a section of the Euro-African zone observed that every geomagnetic SFE is unique and characterized by abnormal signature of the event, and the current system of the geomagnetic SFE is not a simple augmentation of the Sq currents as there exist phase difference between the two current systems. The phase difference between the SFE and the Sq field suggests that the current system maybe flowing at different layers of the ionosphere whose cause and the contribution of the ionosphere layers need to be studied. Okeke and Ichoja (2011) studied the impact of severe solar flare effects (SFE) and sudden storms commencement (SSC) on geomagnetic fields, in dip equator, low and mid latitude stations. The results of the analyses revealed a positive enhancement of the horizontal intensity (H) in the dip equator and negative excursions of the vertical intensities (Z) in low and mid latitude stations. Strong correlation was found to exist between the vertical intensities of the solar flare and sudden storm commencement (Z SFE and Z SSC ), while the horizontal intensities of SFE and SSC (H SFE and H SSC ) were poorly correlated. Qian et al. (2012), used model simulations to investigate possible additional contributions from electrodynamics, and found that the vertical E×B drift in the magnetic equatorial region plays a significant role in the ionospheric response to solar flares. Ugonabo et al. (2013) analyzed solar flare effects on geomagnetic H component at equatorial and low latitudes and the results revealed that pre-solar flare and solar flare amplitude variations of H are high in equatorial and low latitude stations. Correlation existed between the solar flare amplitude variations of H and the pre-solar amplitude variations. The ratios of ΔH SFE /ΔHo were greater than zero for the three stations used in the study. Hence, solar flare effects enhance the geomagnetic field in the equatorial and low latitudes.
This study seeks to investigate the effects of solar flares on geomagnetic fields across latitudes using X and M solar flares occurring on quiet conditions from 1997 to 2005.

Sources of data
The minute data of the geomagnetic field were collected from the INTERMAGNET website, the solar flare data were accessed from the National Geophysical Data Centre of the National Oceanic and Atmospheric Administration, Boulder, USA, the hourly data of the geomagnetic field and the international quiet days were accessed from World Data Centre for Geomagnetism, Kyoto, Japan. M and X solar flares that occurred mostly on the international 10 quietest days for each month from 1997 to 2005 were selected.

Pre-solar flare and solar flare effect amplitudes
The amplitude variations in H and Z components just before the start time of the flare with respect to 0000 h value on the same day were computed. These will enable us understand the effect of the solar flare on these components. The amplitude variations were defined as ΔH o and ΔZ o after Okeke and Okpala (2005) and Ugonabo et al. (2013) as: where H bf and Z bf are the values of field components recorded just before the start time of the flare and H oo and Z oo are the values at 0000 h UT. Okeke and Okpala (2005) also defined the enhancements due to solar flare on the components H and Z are defined as ΔH sfe and ΔZ sfe and were obtained as: where H pf and Z pf are the values of the geomagnetic H and Z fields at the peak (time) of the flare.

THEORETICAL ESTIMATION OF SFE CURRENT
According to Okeke and Okpala (2005) and Ugonabo et al. (2013) as in Volland and Taubenheim (1958), relative portions of the solar flare effect current flowing in the Elayer can be drawn as the following.
The S q current 0 i is made up of E i 0 which flows in the maximum level of the E region and the remaining portion oR i flowing in other regions. This means that total S q current is giving by: Equally, additional current i of geomagnetic SFE is made up of E i in the E-region maximum and a portion D i in other regions. Therefore, we have: Hence, total current flowing during the SFE is given by: But magnetic horizontal intensity is proportional to the current, we can therefore write: Equation 10 can be written in a more general form as: is the slope and φ is the intercept, which is theoretically zero as could be inferred from Equation 10. Equation 11 therefore suggests a correlation between ∆H SFE and ∆H o for any location where SFE signature has been observed. Thus, in a linear regressed ∆H SFE -∆H o plot, the slope (≈K) is a statistical measure of enhancement or reduction in the geomagnetic Hcomponent. It is an enhancement if K>0, in which case, a positive correlation is envisaged, otherwise K<0 and a negative correlation is envisaged.

METHOD OF DATA ANALYSIS
The solar quiet (Sq) field base line is the field average of the value H23, H24, H1, Z23, Z24 and Z1 are the values of the H and Z components at the twenty-third and the twenty-fourth hours preceeding the day and the first hour of the day, respectively. H00 and Z00 are the average values of the H and Z components respectively.
The deviation from the midnight at a particular hour (t) was calculated using Equations 5.3 and 5.4. and tabulated for all the nine stations. Ratios greater than zero imply that SFE is enhancing the geomagnetic field and vice versa. Table 1 shows the nine stations used in the study with their geographic positions. Figure 1a to d shows some sample plots of H against the Universal Time for flares that occur on 30th May, 2002 at AAE, 27th November, 1999 at BNG and TAM and 16th May,1999 at THY. The same Figure 1e and f also shows two sample plots of Z against the universal time for flares that occurred on the 27th November, 1999 at BNG and NGK. Each of the plots shows the flare signature (the starting period, the peak and the end period). Tables 2 and 3 show the computed values of ∆H SFE /∆H o and ∆Z SFE /∆Z o , respectively for the different stations. Figure 2a to i shows the plots of the ratios of ∆H SFE to ∆H o for all the stations, while Table 4 gives the summary of the regression analyses result as drawn from Figure 2.

RESULTS AND DISCUSSION
As could be seen from the longitudes in Table 1, most of the stations used in the study are 1 h ahead of GMT (example BNG, THY, NCK, BEL, NGK and ABK), NUR is 2 h ahead and AAE is 3 h ahead. Therefore, conversion to local times did not yield any appreciable differences. Furthermore, most of the flares used were noon flares.
In the equatorial and low latitude stations, AddisAbaba station having nineteen solar flare events depicted four flares whose ratios of twenty-four flares depicted ratios between 1.06 and 6.50. At Belsk station, twenty-eight solar flare events depicted four flares with ratios ranging between 0.43 and 0.93, three flares with ratios equal to one and twenty-four flares with ratios between 1.1 and 5.70. Finally, at Niemegk station, twenty-seven solar flare events recorded only three flares with ratios ranging between 0.5 and 0.96, two flares with ratios equal to one and twenty-two flares with ratios between 1.03 and 5.20. In the high latitudes, only two stations were used, Nurmijarvi and Abisko. At Nurmijarvi station, nineteen solar flare events recorded eight flares whose ratios of Abisko, seventeen solar flare events depicted five flares with ratios between 0.17 and 0.74 and twelve flares with ratios between 1.08 and 6.00. Table 4 gives a clear correlation between ∆H SFE and ∆H o with a positive slope in all the stations. The results are statistically significant at 95% confidence. It could be observed from the distribution of slope that the degree of enhancement of the H-component by SFE is highest at high latitudes (ABK and NUR) stations and lowest at mid latitudes (THY, NCK, BEL and NGK) stations. The same Table 4 also depicts that the intercepts deviate significantly from the theoretical prediction of zero. This could arise as a result of the coarse approximations of the local times and minor effects of longitudinal variations (Okeke and Okpala, 2005). The results therefore suggest

Conclusions
The results of the study revealed that SFE consists ) greater than zero. The results of the study imply that SFEs enhance geomagnetic field across all the latitudes (equatorial, low, mid and high). SFE on geomagnetic field is not a simple augmentation at the pre-flare ionospheric currents over these stations. The results are in agreement with Rastogi (1996).
The results revealed that pre-solar flare and solar flare amplitude variations of H are least in mid latitude stations and highest in the high latitude stations. The pre-solar flare and solar flare amplitude variations of Z did not show any clear pattern.
Positive correlation existed between the solar flare amplitude variations of H and the pre-solar amplitude variations and all the results are statistically significant at 95% confidence.
It is clearly obvious that SFEs enhances geomagnetic field across the latitudes studied. This is drawn from the result of the ratios of ∆H SFE /∆H o and ∆Z SFE /∆Z o , being greater than zero in all the nine stations.