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Scientific Report 2007-2009<br />
Astronomy & Astrophysics<br />
A5. Search for periodicities in the solar energetic proton fluxes<br />
Past studies revealed that many solar activity phenomena<br />
undergo both periodic and quasi-periodic variations<br />
on different time scales. Nevertheless, only a few<br />
attempts were made so far to detect corresponding variations<br />
in the occurence frequency of solar energetic particle<br />
events. We tried to fill this gap searching for periodicities<br />
in the proton fluxes, measured in the interplanetary<br />
space, on time scales ranging from a few Bartels rotations<br />
(27 days) up the the Schwabe period (≈11 years).<br />
Figure 1: The wavelet power (normalized to the 95% significant<br />
level) corresponding to the most relevant periods (as<br />
<strong>report</strong>ed in the legend) are plotted as a function of time for<br />
channel P2 (top) and channel P11 (bottom). An upper cutoff<br />
was applied to the data in order to smooth the discontinuities.<br />
Our study was based on the data collected by the<br />
Charged Particle Measurement Experiment (CPME),<br />
aboard the satellite IMP 8, orbiting at ≈35 Earth radii in<br />
the period from 1974 to 2001. Measurements were performed<br />
in ten differential energy channels, but we used<br />
only those taken in channels P2 (0.50 - 0.96 MeV) and<br />
P11 (190 - 440 MeV), which were not affected by an<br />
experiment malfunction occurred in 1989. Data were<br />
analyzed using the wavelet transform (WT), a technique<br />
which offers an important advantage with respect to the<br />
Fourier transform, because it allows localization in time<br />
of possible periodicities which are not present continuously<br />
in the data set. It is known, however, that the<br />
WT may lead to erroneus results, when applied to discontinuous<br />
data, such as the proton fluxes considered in<br />
our study. We investigated this issue by applying the<br />
wavelet analysis to suitable test functions. It turned out<br />
that eventual spurious frequencies can be discarded by<br />
introducing an upper cutoff to reduce the amplitude of<br />
the stronger discontinuities present in the data set.<br />
Discarded the spurious periods, our analysis revealed<br />
variations of the proton fluxes on the following time<br />
scales (see Figure 1):<br />
T = 3.8 years. This period has been singled out in<br />
both the energy channels from 1977 to 1985 (the active<br />
phase of solar cycle 21). It closely resembles the 3.7 year<br />
period exhibited by the protospheric magnetic field in<br />
the same time interval.<br />
T = 1.7 - 2.2 years. This modulation, also present in<br />
both the energy channels, is better observed from 1988<br />
to 1993 (i.e., around the sunspot maximum of the cycle<br />
22). It corresponds to the ”quasi biennial oscillations”<br />
(QBO) which are known to characterize several features<br />
of the solar activity: e.g., the number of H flares, the<br />
total sunspot area, the 10.7 cm radio emission, and the<br />
flux of the energetic electrons. The common origin of<br />
all these phenomena is supported by the simultaneous<br />
disappearance of their modulation during quiet periods.<br />
T = 0.8 - 0.9 years. This modulation is observed in<br />
shorter time intervals: its linkage with the variations of<br />
other solar parameters deserves other studies.<br />
We also note the lack, in our data set, of significant<br />
modulations on time scales of 150 days and 5 - 6<br />
years. However, the 150 day period (the so called ”Rieger<br />
period”), revealed in several solar activity parameters,<br />
could have been hardly singled out in our analysis, as<br />
the proton fluxes were averaged over Bartels rotations<br />
(27 days). On the other hand, the absence of the 5.5<br />
year modulation appear to be more significant. In fact<br />
it supports the hypothesis, advanced by some author,<br />
that this periodicity, observed, e.g., in the sunspot number,<br />
is an artifact produced by the asymmetric shape of<br />
the solar cycle.<br />
We finally stress that the procedure we successfully<br />
introduced here to discard spurious periodicities may<br />
be useful when the WT is applied to other sets of data<br />
with strong discontinuities.<br />
References<br />
1. M. Lorenza, et al., Journ. Geophys. Res. 114, A01103,<br />
(2009)<br />
2. M. Storini, et al., Adv. Space Res. 41, 70 (2008).<br />
Authors<br />
G. Moreno<br />
<strong>Sapienza</strong> Università di Roma 152 Dipartimento di Fisica