Temporal and energy behavior of cosmic ray fluxes in the periods of low solar activity
G. A. Bazilevskaya, M. S. Kalinin, M. B. Krainev, V. S. Makhmutov, A. K. Svirzhevskaya, N. S. Svirzhevsky
aa r X i v : . [ a s t r o - ph . S R ] N ov ND I NTERNATIONAL C OSMIC R AY C ONFERENCE , R
IO DE J ANEIRO T HE A STROPARTICLE P HYSICS C ONFERENCE
Temporal and energy behavior of cosmic ray fluxes in the periods of low solaractivity B AZILEVSKAYA
G. A., K
ALININ
M. S., K
RAINEV
M. B., M
AKHMUTOV
V. S., S
VIRZHEVSKAYA
A. K.,S
VIRHEVSKY
N. S.
Lebedev Physical Institute of the Russian Academy of Sciences, Moscow, Russia [email protected]
Abstract:
Modulation of galactic cosmic ray intensity is governed by several mechanisms including diffusion,convection, adiabatic energy losses and drift. Relative roles of these factors change in the course of an 11-yearsolar cycle. That can result in the changes in the energy dependence of the 11-year cosmic ray modulation. Theminimum between the solar cycles 23 and 24 was extremely deep and long-lasting which led to the record highcosmic ray fluxes low-energy particles dominating. This was a signature of unusually soft energy spectrum ofthe cosmic rays. In this work we examine the energy dependence of the 11-year modulation during the last threesolar cycles and argue that a soft energy spectrum was observed in the minimum of each cycle however only forparticles below of energy around 10 GeV. From mid 1980s the energy dependence of cosmic rays became softerfrom minimum to minimum of solar activity. The work is based on the cosmic ray data of the spacecraft, balloon-borne and the ground-based observations.
Keywords: cosmic ray modulation energy dependence
Modulation of galactic cosmic rays (GCRs) by solar ac-tivity is a wonderful phenomenon which includes a lotof physical processes concerning solar physics, nuclearphysics, plasma physics, geophysics etc. It is believed thatdiffusion, convection, adiabatic energy losses and drift leadto variability of particle fluxes in the heliosphere [1]. An11-year and 22-year solar cycles are the main manifesta-tions of the GCR modulation, however, the cycles differfrom each other following changes in solar activity. There-fore study of GCR modulation is very complicated prob-lem. During periods of low solar activity the GCR fluxesare maximal. The last solar minimum between cycles 23and 24 (hereafter cycles 23/24) was extraordinary deep andlong e.g. [2]. This resulted in the record high GCR fluxes[3, 4, 5, 6]. In our works [3, 7] we paid attention to un-usual energy dependence of the GCR modulation in the so-lar activity minimum of cycles 23/24. Here we comparethis finding with GCR behavior in the previous solar min-ima and try to match it with conditions in the near-Earth’sheliosphere.In conventional diffusion-convection theory rigidity de-pendence of GCR modulation is connected to rigidity de-pendence of interplanetary diffusion coefficient and causedinterest of many researchers, to mention a few [8, 9, 10,11, 12] and others. Bachelet et al. [8] concluded that forrigidity > >
0) and higher in the negative magneticcycles (A <
0) while behavior of GCRs below ≈
500 MeVis opposite. It is reflected in a crossover in the GCR en-ergy spectra related to magnetic cycles of different polarityand indicates on the rigidity dependence of the GCR driftand, probably, diffusion processes. Crossovers were alsofound from study of GCR modulation based on the balloonmeasurements [24]. Ahluwalia et al. [11] fulfilled a com-prehensive investigation of rigidity dependence of 11-yearmodulation for GCRs of 1-200 GV in the solar cycles 20-23. The power-law dependence was found with small dif-ference from cycle cycle. However, authors considered thecomplete amplitudes of GCR intensity, i.e. decrease fromminimum to maximum of solar activity. The changes in therigidity spectrum of GCR modulation within the 11-yearcycle were studied by Alania et al. [12]. They showed thatthe power-law index of the GCR modulation changed inphase with solar activity, i.e. the spectrum of the 11-yearmodulation was harder in minimum solar activity. This re-search was limited by 1967-2002 and rigidities above sev-eral GV.In this work we do not try to find the energy spectrumof the 11-year GCR modulation, but only trace qualitativechanges in the rigidity spectrum of the GCR on the timescale of several months, particularly around solar minimawhen the GCR intensity is of the highest value.
In the last minimum of solar activity a prevailing growthof rather low energy cosmic rays was observed [3, 7]. Ourprevious analysis included observations on balloons andon the ground-based neutron monitors. This work incor- osmic ray fluxes in the periods of low solar activity33 ND I NTERNATIONAL C OSMIC R AY C ONFERENCE , R
IO DE J ANEIRO porates, in addition to balloon and ground-based observa-tions, the results of cosmic ray measurements in space.Monitoring of GCR is being performed during morethan 6 decades - from 1950s up to present [15]. The bulkof observational data comprise the results of the neutronmonitor (NM) world-wide network [16] with geomagneticcutoffs R c from 0 GV to >
10 GV. Trying to select most sta-ble and long operating NM stations we finally have chosenApatity ( R c =0.57 GV), Oulu ( R c =0.57 GV), Kiel ( R c =2.36GV), Moscow ( R c =2.45 GV), Potcheftsroom ( R c =7.2 GV),Tsumeb ( R c =9.2 GV), Mexico ( R c =9.53 GV) and Huan-cayo/Haleakala ( R c =12.9 GV).The long-term cosmic ray balloon experiment being per-formed at Lebedev Physical Institute (LPI) [17] supple-ments the NM data series in the lower energy range. Usu-ally, the results of charged particle measurements in themaximum of the transition (Pfotzer) curve in the atmo-sphere at the polar regions are used that refer to effectiveenergy about several GeV [18]. Here, we use the fluxesof GCRs on the top of the atmosphere derived from theballoon measurements at the Murmansk region ( R c =0.57GV). The extrapolation of the transition curve to the top ofthe atmosphere gives a sum of primary GCR and albedofluxes. A special procedure of albedo allowance was de-veloped by A.N. Charakhchyan and T.N. Charakhchyan[19] based on the charged particle observations at latitudesof Murmansk, Moscow and Alma-Ata. The annual valuesof GCR intensities with R above geomagnetic cutoff overMurmansk ( E > ≈ . Figure 1 demonstrates theGCR intensities with E > E > The monthly averaged data of GCR observation weretreated. All the data were normalized to 100% in March J ( > . ) , m - s - s r - , d J / d E , m - s - s r - G e V - Year
Figure 1 : Galactic cosmic ray intensity vs. time. Uppercurve shows monthly averaged data J( E > Figure 2 : Scatter plots between the balloon J( E > J > .
18) and the NM Apatity in June 2000-November 2003 (left panel) and November 2007-January2009 (right panel). Data are normalized to 100% in March1987. The regression equations are shown.1987. To estimate the energy dependence of the GCR vari-ations connected to the 11-year solar activity we calculatedlinear regression between data series in the form Y = A + BX , where Y and X stand for the data of any two cosmic rayseries. This procedure was applied to finite time intervals.It is clear that for the given time period D T a regression co-efficient B is the ratio between the changes of intensity at Y and X stations in this time period: B = D Y / D X . Giventhe stations are sensitive to different cosmic ray energy thechanges in B reflect the changes in the energy dependenceof GCR modulation. For example, Fig. 2 shows scatterplots between the balloon J( E > J > .
18) and the NM Apatity. Left panel is for June 2000-November 2003. Change of 20% in the J > .
18 matcheswith 10% at the NM, a regression coefficient B =2.0 whichargues for a rather soft modulation spectrum. Right panelrefers to November 2007-January 2009. This time changeof 15% in the J > .
18 matches with 2% at the NM, aregression coefficient B =7.8 which corresponds to a hardmodulation spectrum. osmic ray fluxes in the periods of low solar activity33 ND I NTERNATIONAL C OSMIC R AY C ONFERENCE , R
IO DE J ANEIRO
Actually, the temporal variations in different data setsresult in high scatter of the regression coefficients when the D T periods are several months up to one year. To diminishthe scatter we averaged the data of the NMs with close ge-omagnetic cutoffs and got the combined sets, namely Ap-atity and Oulu, Kiel and Moscow. There are few NMs withhigh values of cutoff no one operating during the wholetime since 1958 till present. Each of them was treated sep-arately.Several D T intervals were tested from 6 to 18 months.Eventually a variable D T was applied which was chosenas periods of more or less smooth GCR intensity tem-poral changes. This is illustrated on the lower panel ofFig. 3 where the monthly results of charged particles mea-sured on balloons are plotted. Vertical bars are bound-aries of the chosen D T intervals. The regression coeffi-cients B were calculated always taking as Y a stationwith response to lower energy, i.e. IMP-PAMELA versus J > . J > .
18 versus Apatity-Oulu, Apatity-Oulu ver-sus Kiel-Moscow etc. Two upper panels of Fig. 3 presentthe selected results of this treatment. Middle panel givesthe time dependence of regression coefficients between Y =IMP-PAMELA and X = J > .
18 and between Y = J > .
18 and X =Apatiy-Oulu. Upper panel gives the regressionbetween Y =Apatity-Oulu and other NM stations taken as X . No clear time variations of B values related to 11-yearcycle can be found on this panel. From the middle panel ofFig. 3 one can see that before mid-1980s an 11-year modu-lation of regression coefficients can hardly be traced. How-ever beginning from solar cycle 21 a clear ≈ B values depend on difference in the effectiveenergy between the data sets taken as Y and X . An effec-tive energy of J > .
18 is estimated as ≈ < ≈ ≈
10 GeV: in the pe-riods of low solar activity the spectrum is steeper. More-over, the spectrum became even steeper in each subsequentminimum for solar cycles 21/22, 22/23, and 23/24. This re-flected in the record high GCR intensity as observed on bal-loons comparing to the observed by NMs in 2009 [3]. Thusthe steep GCR spectrum in 2009 was just development ofa process started in 1990s or even earlier. Surprisingly, thisfeature is more strongly marked in the energy range of ≈ J > .
18 versus Apatity-Oulu) than for energies0.1- ≈ J > . J > .
18 (July 2009) and toPAMELA (December 2009). Actually, between July andDecember 2009 GCR intensity was growing according toPAMELA and decreasing according to J > .
18. This ledto decrease of the regression coefficient.Our approach did not find any significant 11-year en-ergy dependence of modulation for the NM energy range.Slight tendency to such dependence could be traced in the
Figure 3 : Bottom panel: the D T intervals chosen for theregression calculation on the background of cosmic rayintensity as measured on balloons in the Pfotzer maxi-mum of Murmansk region. Vertical bars are the boundarieswhich isolate time intervals with more or less smoothedchanges in cosmic ray fluxes. Middle panel: regression co-efficients B versus time. Brown line is for regression of J > .
18 versus Apatity-Oulu, blue one, for regression of IMP-PAMELA versus J > .
18. Upper panel: coefficients B for regression of Apatity-Oulu versus NMs Kiel-Moscow(blue), Potcheftsroom (magenta), Tsumeb (green), Mexico(cyan), Huancayo/Haleakala (red).Apatity-Oulu versus Huancayo/Haleakala result (upper redline on the upper panel in Fig. 3) which reflects the mod-ulation spectrum between 10 and >
40 GeV [26] but it ishardly convictive. Unfortunately, Huancayo/Haleakala sta-tion was not operative during the solar minimum 23/24.Regression between Apatity-Oulu and other NMs virtuallydoes not depend on the solar cycle phase.According to the middle panel of Fig. 3 energy spec-trum of GCR in the maximum phase of solar activity wasrather hard and did not change from cycle to cycle while inthe minimum phase it became softer beginning from 1980s.Our analysis is qualitative and does not allow to trace de-tailed transformation of the spectrum from the hard form tothe soft and vice versa. However, a permanent softening inthe course of three solar minima could be connected to theoverall change of conditions in the heliosphere. It is indica-tive that no clear 11-year dependence of GCR modulationcan be seen before 1980 and no such dependence was ob-served in the heliospheric magnetic field [27]. On the otherhand, such a dependence has appeared after 1980 both inthe heliospheric magnetic field and GCR spectrum. Dur- osmic ray fluxes in the periods of low solar activity33 ND I NTERNATIONAL C OSMIC R AY C ONFERENCE , R
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Figure 4 : Time history of heliospheric magnetic field in-duction (blue) and rgression coefficients between J > . ≈ J > .
18 andNM Apatity-Oulu alongside with values of heliosphericmagnetic field induction. A certain negative correlationcan be noticed.Evolution of heliospheric conditions and GCR behaviorduring the last three solar cycles are discussed in more de-tail in accompanying papers [30, 31]. Using a rather sim-ple model of GCR modulation and taking into account evo-lution of physical conditions in the heliosphere it is pos-sible to understand and reconstruct GCR behavior duringlast three cycles of solar activity both for NM energy rangeand lower energies.
Qualitative analysis of the energy dependence of the GCRmodulation in the course of an 11-year solar cycle was ful-filled for low energy GCRs (below ≈
10 GeV) and GCRsrecorded by neutron monitors (above 10 GeV). No 11-yearsignatures were found in the modulation energy depen-dence since 1960s till mid 1980s in both energy intervals.Afterwards an 11-year variation appeared in the modula-tion of lower energy GCRs with softer energy spectrumat minima of solar activity. Moreover, the spectrum be-came steeper in each subsequent minimum for solar cycles21/22, 22/23, and 23/24. No such behavior was observedfor the GCRs of higher energy. Attempts to understand theobservational data in the context of recent modulation the-ory are undertaken in accompanying papers [30, 31].
Acknowledgment:
Authors thank colleagues maintaining op-erations and data processing of neutron monitors and space-crafts, as well as OMNI data base. This work was partly sup-ported by Russian Foundation for Basic Research (grants 11-02-00095a, 12-02-00215a, 13-02-00585a, 13-02-10006k) and by the Program ”Fundamental Properties of Matter and Astrophysics”of the Presidium of the Russian Academy of Sciences.