Temporal Changes in the Rigidity Spectrum of Forbush Decreases Based on Neutron Monitor Data
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- Alania, M.V., Wawrzynczak, A., Sdobnov, V.E. et al. Sol Phys (2013) 286: 561. doi:10.1007/s11207-013-0273-0
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The Forbush decrease (Fd) of the Galactic cosmic ray (GCR) intensity and disturbances in the Earth’s magnetic field generally take place simultaneously and are caused by the same phenomenon, namely a coronal mass ejection (CME) or a shock wave created after violent processes in the solar atmosphere. The magnetic cut-off rigidity of the Earth’s magnetic field changes because of the disturbances, leading to additional changes in the GCR intensity observed by neutron monitors and muon telescopes. Therefore, one may expect distortion in the temporal changes in the power-law exponent of the rigidity spectrum calculated from neutron monitor data without correcting for the changes in the cut-off rigidity of the Earth’s magnetic field. We compare temporal changes in the rigidity spectrum of Fds calculated from neutron monitor data corrected and uncorrected for the geomagnetic disturbances. We show some differences in the power-law exponent of the rigidity spectrum of Fds, particularly during large disturbances of the cut-off rigidity of the Earth’s magnetic field. However, the general features of the temporal changes in the rigidity spectrum of Fds remain valid as they were found in our previous study. Namely, at the initial phase of the Fd, the rigidity spectrum is relatively soft and it gradually becomes hard up to the time of the minimum level of the GCR intensity. Then during the recovery phase of the Fd, the rigidity spectrum gradually becomes soft. This confirms that the structural changes of the interplanetary magnetic field turbulence in the range of frequencies of 10−6 – 10−5 Hz are generally responsible for the time variations in the rigidity spectrum we found during the Fds.
KeywordsForbush decrease Geomangetic disturbances Rigidity spectrum
The short-term depressions in the cosmic ray flux reaching the Earth are called the Forbush decreases (Fds). They are caused by the interplanetary counterpart of coronal mass ejections (CMEs) (and the shocks they drive) and also by the corotating interaction regions (CIRs) originating from the Sun.
The geomagnetic disturbances and Fds have a common origin in the interplanetary space, namely the Earth’s encounter with a strong interplanetary structure. However, the magnitudes of geomagnetic disturbances and Fds are not proportional to each other (e.g., Kane, 1977, 2010). According to Dungey’s (1961) mechanism, relatively high-energy particles of the solar wind rush towards the Earth but are diverted around the Earth in circular orbits in the equatorial plane. These particles form a ring current at several Earth radii and cause large geomagnetic field reduction. The reduction in the terrestrial magnetic field strength is measured by the Dst index (disturbance storm time index; Sugiura 1964). Measurements of the Dst index and the magnitude of Fds indicate some similarity in their interplanetary sources. However, there are significant differences in the exact evolution of these indices (Cane 2000). In general, both rise with increasing interplanetary magnetic field (IMF) and solar wind velocity V. The most important difference is that Fds are governed by the conditions in a large volume of the heliospheric region, while Dst variation depends on the local situation in the magnetotail near the Earth. In general not all CMEs are geoeffective, and many smaller geomagnetic disturbances are not related to CMEs.
Kudela and Brenkus (2004) analyzed the decreases in the Galactic cosmic ray (GCR) intensity along with simultaneous changes in the Dst index in the period of 1982 – 2002. Their analysis shows that the relation between GCR flux and geomagnetic activity is complex. The relationship between Fd magnitudes and geomagnetic activity during 1978 – 1996 was studied by Belov et al. (2001). By analyzing more than one thousand events they found a correlation coefficient r≈0.42 between the Fd magnitude and the maximum geomagnetic disturbance index Kp; the correlation with Dst was smaller. They also recognized that large Fds were associated with disturbances Kp≥8 in the interplanetary space causing significant changes in the Earth’s magnetosphere.
Kane (2010) analyzed the relationship between the magnitude of Fds measured at the Climax station and the Dst index for 17 Fds in the 23rd solar cycle, and showed that the maximum negative Dst generally did not occur at the time of the maximum of Fd magnitude. However, for extreme events (six events with largest Dst and corresponding Fds) in earlier cycles 19 – 22 he found the existence of negative correlation (correlation coefficient r≈−0.70) between Dst and Fd magnitude. These investigations show that the relation between Fds and geomagnetic disturbances is quite complex.
One of the fundamental characteristics of Fds is the dependence of the amplitude of Fd (difference between the GCR intensity at the onset and the minimum times of an Fd) on the rigidity R of GCR particles. The rigidity spectrum of an Fd can be found based on the magnitude of the Fd calculated from the minimum point of the GCR intensity. However, to study the rigidity dependence of Fd based only on the rigidity spectrum taken at one time point is not sufficient to understand its dynamics. The time evolution of the rigidity spectrum of the Fd was studied by Alania and Wawrzynczak (2008, 2012) and by Wawrzynczak and Alania (2005a, 2005b, 2010). They showed that the rigidity spectrum δD(R)/D(R)∝R−γ of the great majority of Fds gradually becomes hard during the decreasing and minimum phases and then gradually becomes soft in the recovery phase. Consequently, the exponent γ of the rigidity spectrum is large (γ≈1−1.6) at the initial phase, gradually decreases up to the minimum (or near minimum) of GCR intensity (γ≈0.4 – 0.6), and then increases during the recovery phase (γ≈1 – 1.6).
Wawrzynczak and Alania (2005a, 2005b, 2010) and Alania and Wawrzynczak (2008, 2012) have shown that the temporal changes in the exponent γ of the rigidity spectrum of the Fds found by neutron monitors and muon telescopes are related to the changes in the power spectral density (PSD) of the IMF turbulence (PSD∝f−ν, here f is the frequency). This relationship is expected owing to the dependence of the diffusion coefficient K∥ of GCR particles on the rigidity R, K∥∝Rα; here the coefficient α depends on the exponent ν of the PSD of the IMF turbulence according to the quasi-linear theory (QLT) as α=2 – ν (Jokipii, 1966, 1971; Hasselman and Wibberentz 1968; Toptygin 1985). As was shown by Wawrzynczak and Alania (2005a, 2005b, 2010), Alania and Wawrzynczak (2008, 2012), and Alania, Iskra, and Siluszyk (2008, 2010), the exponent γ is related to α. Namely, γ≈2 – ν in the range of frequency of the IMF turbulence f≈ ∼10−6 – 10−5 Hz, to which the neutron monitors and muon telescopes respond. The validity of the QLT (Jokipii, 1966, 1971) for the GCR particles with energy ≥ 1 GeV is confirmed by the weakly nonlinear theory (WNLT; Shalchi et al.2004), nonlinear parallel diffusion theory (NLPA; Qin 2007) and by Droge (2003), Shalchi and Schlickeiser (2004), and Shalchi (2009).
to calculate changes in the geomagnetic cut-off rigidity for various neutron monitor stations during three large Fds of the 23rd solar cycle (6 – 30 July 2000, 19 October − 11 November 2003, and 6 – 23 September 2005) by the spectrographic global survey method and corresponding corrections for the amplitudes of Fds,
to settle the relationship between the changes in the geomagnetic cut-off rigidity and the variations in the Dst index, and then to find a reliable average relation between Dst and the correction for the GCR intensity ΔJ, and
to estimate how the changes in the cut-off rigidity of various neutron monitor stations influence the temporal changes in the power-law exponent of the rigidity spectrum of the Fd events.
2 Experimental Data and Analysis Methods
We analyze the largest three Fds of the 23rd solar cycle, i.e., 6 – 30 July 2000 (Fd I), 19 October − 11 November 2003 (Fd II), and 6 – 23 September 2005 (Fd III). During these Fds were observed significant geomagnetic disturbances that could affect the vertical geomagnetic cut-off rigidity and correspondingly the level of GCR intensity registered by neutron monitors. Consequently, one could expect distortion of the rigidity spectrum of the Fds calculated from the neutron monitor data. As a result it turned out necessary to correct for the GCR intensities observed by neutron monitors by incorporating the changes in the cut-off rigidity ΔRc and then to calculate the rigidity spectrum of the Fd events.
2.1 Results from the SGS Method
To find the changes in the cut-off rigidity ΔRc during the analyzed Fds from different neutron monitors we have used the spectrographic global survey (SGS) method developed by Dvornikov, Sdobnov, and Sergeev (1983) and Dvornikov and Sdobnov (2002). This method allows investigating variations in the cosmic ray rigidity spectrum and anisotropy by using the data from ground measurements, along with the changes in the geomagnetic cut-off rigidity based on the data from the world-wide network of neutron monitor stations. The list of used neutron monitor stations is given in the Appendix.
Correlation coefficients between the changes in the Dst index and variations in the geomagnetic cut-off rigidity ΔRc for Climax, Hermanus, and Haleakala neutron monitor stations during three considered Fds (data presented in Figure 2).
Correlation coefficients Dst [nT] vs. ΔRc [GV]
10 – 20 July 2000
28 Oct – 8 Nov 2003
9 – 25 Sep 2005
Correlation coefficients between the changes in the Dst index and changes in the GCR intensity correction ΔJ for Climax, Hermanus, and Haleakala neutron monitor stations during three considered Fds (data presented in Figure 4).
Correlation coefficients Dst [nT] vs. ΔJ [%]
10 – 20 July 2000
28 Oct – 8 Nov 2003
9 – 25 Sep 2005
2.2 Rigidity Spectrum of the Forbush Decreases
Figures 7 – 9 also present the rigidity spectrum exponent γ of Fds calculated from the amplitudes of the Fds corrected for the geomagnetic disturbances by the obtained relation between the Dst index and the correction for the GCR intensity ΔJ (see the Appendix). The data from the neutron monitor stations used in the calculation were corrected on the days when Dst index was <−30 nT. One can see (Figures 7 – 9) that the rigidity spectrum exponent γ obtained this way (the blue line) fits within the error bars the exponent γ calculated from the GCR intensity corrected by the result of the SGS method. We infer that the relation between Dst and ΔJ can be used for the estimation of the rigidity spectrum exponent γ taking into account the geomagnetic disturbances.
3 Summary and Conclusions
The spectrographic global survey (SGS) method was applied to calculate the changes in the vertical cut-off rigidity caused by geomagnetic disturbances during three large Fds of the 23rd solar cycle (6 – 30 July 2000, 19 October − 11 November 2003, and 6 – 23 September 2005). The data from the neutron monitor stations were corrected for geomagnetic disturbances during the considered three Fds. The power law exponent γ of the rigidity spectrum (δD(R)/D(R)∝R−γ) of Fds found by neutron monitor station data uncorrected for geomagnetic disturbances is different from that corrected for them. Namely, the rigidity spectrum obtained from the corrected data is harder than that calculated from the uncorrected data. However, the time profiles of the changes in the exponent γ in both cases are similar. At the initial phase of the Fd, the rigidity spectrum is relatively soft (γ is large) and it gradually becomes hard (γ decreases) up to the time of the (near) minimum level of the GCR intensity. Then during the recovery phase the rigidity spectrum gradually becomes soft (γ increases). This supports the previously presented results (i.e. Alania and Wawrzynczak, 2008, 2012), vindicating that the structural changes in the IMF turbulence in the range of frequencies of 10−6 – 10−5 Hz, to which the neutron monitors and muon telescopes respond, are mainly responsible for the time variations in the exponent γ of the rigidity spectrum of Fds. The presented calculations show that, to an acceptable extent, the data from neutron monitor stations can be corrected for geomagnetic disturbances during Fds using the Dst index.
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