Similarities and Distinctions in Cosmic-Ray Modulation during Different Phases of Solar and Magnetic Activity Cycles
11 Similarities and Distinctions in Cosmic-Ray Modulation during Different Phases ofSolar and Magnetic Activity Cycles
O.P.M. Aslam · Badruddin
Department of Physics, Aligarh Muslim University, Aligarh-202002, India.e-mail: [email protected]
Abstract
We study the solar-activity and solar-polarity dependence of galactic cosmic-ra y intensity(CRI) on the solar and heliospheric parameters playing a significant role in solar modulation. We utilizethe data for cosmic-ray intensity as measured by neutron monitors, solar activity as measured by sunspotnumber (SSN), interplanetary plasma/field parameters, solar-wind velocity [ V ] and magnetic field [ B ], aswell as the tilt of the heliospheric current sheet [ Λ ] and analyse these data for Solar Cycles 20 - 24 (1965 _ i.e. low, high, increasing, and decreasing solaractivity. We perform regression analysis to calculate and compare the CRI-response to changes indifferent solar/interplanetary parameters during (i) different phases of solar activity and (ii) similaractivity phases but different polarity states. We find that the CRI-response is different during negative( A <0) as compared to positive ( A >0) polarity states not only with SSN and Λ but also with B and V . Therelative CRI-response to changes in various parameters, in negative ( A <0) as compared to positive ( A >0)state, is solar-activity dependent; it is ≈ ≈ Keywords
Cosmic ray modulation · solar activity · solar magnetic polarity · solar wind · interplanetarymagnetic field · heliospheric current sheet
1. Introduction
Cosmic rays are modulated as they traverse into the heliosphere. Measurements have shown thatcosmic - ray intensity varies on different time scales. On a longer time scale, the cosmic-ray intensityvariations in anti-phase with solar activity having ≈ e.g., see (Venkatesan and Badruddin, 1990; Storini et al., et al., , ≈ e.g., Jokipii and Thomas, 1981; Potgieter and Moraal, 1985; Webber and Lockwood, 1988; Potgieter, 1995;Cliver and Ling, 2001; Laurenza et al., f(r , P, t) is the cosmic-ray distribution with respect to particle rigidity [ P ], then the cosmic ray variationwith time [ t ] and position [ r ] is given by = − ∙ − < > ∙ + ∙ ( ∙ ) + ∙ ) (1) The first term on the right-hand side represents an outward convection caused by the solar-wind velocity [ V ] . The second term represents the gradient and curvature drifts in the global heliospheric magnetic field.The drift velocity for weak scattering is given by < >= ∇ × (2)The third term represents the diffusion caused by turbulent irregularities in the background heliosphericmagnetic field [ B ]. The last term describes the adiabatic energy change depending on the sign of thedivergence of solar-wind velocity [ V ]. Thus we see that in each of the four terms, directly or indirectly,either solar-wind velocity [ V ] or heliospheric magnetic field [ B ] is involved (see, e.g., reviews by, Heber,2013; Kota, 2013; Strauss, Potgieter, and Ferreira, 2012 and references therein).Although sunspots have been used as a convenient index of solar activity, anti-correlated with cosmic-ray intensity, it has been recognized that they are not intrinsically related to the problem of solarmodulation of cosmic rays. However, the diffusion coefficient changes during ≈ Λ ] of the heliosphere current sheet (HCS) is an important index used for the studyof drift effects. However, it is not just the heliospheric current-sheet tilt angle that matters but globalgradient and curvature drift effects dependent on the polarity of the global solar magnetic field. Theeffects of drifts on cosmic rays are such that positively charged cosmic ray particles drift primarily fromthe polar regions towards lower latitudes and outward along the HCS in the A >0 polarity state. In the A <0 states, the positive particle-drift directions essentially reverse, and they drift inward along the HCSand then up to higher latitudes. For negatively charged particles, the drift directions are opposite tothose of positively charged particles in any given polarity state of the heliosphere. There are indicationsthat cosmic-ray intensity decreases more rapidly as sunspot number (SSN) increases during the increasingphase of solar cycles when solar polarity is negative ( A <0) than when A is positive ( A >0) (Van Allen2002; Singh, Singh, and Badruddin , A <0 and A >0solar-polarity states have been observed with tilt angle [ Λ ] changes also (Smith and Thomas, 1986;Webber and Lockwood, 1988; Smith, 1990; Badruddin , Singh, and Singh, 2007). Although the bothparameters SSN and
Λ indicate their different effectiveness in modulating cosmic-ray intensity indifferent polarity conditions of the heliosphere, it will be interesting to explore whether the cosmic-rayresponse is different with the parameters V and B also, in different polarity states of the heliosphere ( A <0and A >0). Although there is some indication of such effects (with V , B ) during solar minimum(Richardson, Cane, and Wibberenz , A <0 and A >0), inview of the current paradigm of cosmic-ray transport (Jokipii and Wibberenz, 1998; Kota, 2013), i.e. particle drifts play an important role during low to moderate solar activity, while solar maxima aredominated by large-scale diffusion barriers, called global merged interaction regions (GMIRs), sweepingout the cosmic rays (Burlaga et al., ≈ Λ as well as with V and B and two derivatives of V and B, i.e. interplanetary electric field ( E = BV /1000 mV m -1 ) and BV [mV s -1 ], considered important for solar modulation ofcosmic rays (Sabbah 2000; Ahluwalia 2005; Sabbah and Kudela, 2011). This study has been done notonly during increasing including maximum phases of different Solar Cycles but also during four activityphases (low, increasing, decreasing, and high) of Solar Cycles 20 –
23, and the increasing phase of Cycle24 (up to 2011).
2. Results and Discussion
In Figure 1, we have plotted solar [SSN] and interplanetary parameters [ V , B ], standard deviation of fieldvector [ B ( σ B )], their derivatives [ BV /1000, BV
2] (omniweb.gsfc.nasa.gov), tilt angle [ Λ ; wso.stanford.edu]and cosmic ray intensity [CRI: cosmicrays.oulu.fi ] for Solar Cycles 20, 21, 22, 23, and 24 (up to 2011).This figure is shown to highlight the nature of changing activity in different solar cycles and the natureof simultaneous variations in various parameters considered for the analysis presented in this article. Figure 1
Solar-rotation-averaged solar [SSN] and interplanetary [ V , B ] parameters, standard deviation of the vectorfield [ σ B ], their derivatives [ BV /1000, BV [Λ] and cosmic-ray intensity for Solar Cycles 20, 21, 22, 23, and 24(up to 2011), increasing and including maximum phase of solar cycles are hatched in red. For the analysis we considered, at first, the increasing including maximum phase of Solar Cycles 20, 21,22, and 23 (see Figure 1; shaded portions); this is mainly the period when the CRI depression(modulation) takes place before it starts recovering to its pre-decrease level to complete the cycle.
Differences in CRI profiles during alternate polarity cycles are well known; these differences areconsidered to be the consequence of drift effects (Jokipii and Thomas, 1981; Venkatesan and Badruddin,1990; Potgieter, 1995; Jokipii and Wibberenz, 1998; Kota, 2013 and references therein). As shown inFigure 1, there are large temporal variations in 27-day averages of different parameters. Thus, informationthat is more useful may be obtained if we compare the variations in CRI during similar phases of differentSolar Cycles with variations in relevant solar and interplanetary parameters.
Figure 2a
Comparison of 27-day averages of various solar and interplanetary parameters during increasing, includingmaximum, phase of Solar Cycles 20 (right panel) and 21 (left panel). Note CRI (gray shaded) scale is inverted in thesefigures.
Figure 2b
Temporal variations of CRI and various solar/interplanetary parameters during increasing including maximumphase of Solar Cycles 22 (right panel) and 23 (left panel). Note CRI (gray hatching) scale is inverted in these figures.
In Figure 2a and 2b) we compare, during the increasing and including maximum phase of Solar Cycles20, 21, 22, and 23, 27-day averages of various solar and interplanetary parameters [SSN, B , σ B , Λ, E, and BV
2) with variations in CRI. Note that the cosmic-ray intensity scale is inverted for better comparison.Although the trends in changes in CRI appear to match with many of the parameters considered, stepchanges in CRI do not appear to track well with many of these parameters, and also, not consistentlysimilar in all the four Solar Cycles. Although these figures provide a general trend for comparison ofchanges in CRI and various solar/interplanetary parameters during the increasing and includingmaximum phase of different Solar Cycles 20 - 23, they do not provide us with a quantitative informationabout relatively poorly or better related parameters.A careful examination of Figure 2a and 2b shows that there appears to be a slight shift in theoccurrence of steps in CRI changes and some of the solar/interplanetary parameters. This may be due tosome time lag between the changes in CRI and these solar/interplanetary parameters. Thus, we havedetermined the time lag between the solar rotation averaged CRI and various solar/interplanetaryparameters during increasing including maximum phase of Solar Cycles 20, 21, 22, and 23 (see Table 1).We found that, at the time scale of solar rotations, there is no (zero) time lag between CRI andinterplanetary plasma/field parameters [ e.g., V, B ]. However, the lag between CRI and
SSN/Λ varies from three to 15 solar rotations during increasing including maximum phase of differentSolar Cycles. After introducing the time lag, wherever applicable as given in Table 1, we calculate therate of change of CRI with changes in different parameters ( ∆ I / ∆ P ). The calculated values of ∆ I / ∆ P , andthe correlation coefficients ( R ) between CRI and various parameters are given in Table 1.We observe from this table that, although there is some indication that the CRI decreases at a fasterrate with increase in certain parameters, ( e.g. HCS tilt) during A <0 as compared to A >0, however, such adifference is not consistently seen with all the parameters when ∆ I / ∆ P is calculated during the increasingand including maximum phase of different Solar Cycles (20, 21, 22, and 23). Such a difference may beexpected if drifts were a dominant effect in solar modulation during increasing including maximumphase of different solar cycles. However, it is also likely that drifts are fully turned off during solarmaximum or they are there but masked by other more aggressive processes (Kota, 2013). If such is thecase, then excluding the solar maximum and performing analysis by considering only the increasing phase of different solar cycles is likely to be more informative for gaining insight about the modulationprocess.Cliver, Richardson, and Ling (2013) remarked that the effects of gradient and curvature drifts aremost notable at the onset of modulation cycles in A >0 epochs when CRI responds weakly to increase in B and Λ. The weak response of the CRI to changes in B during the rise of odd numbered cycles ( A >0epochs) is attributed to drift-induced preference for positively charged particles to approach the innerheliosphere from the poles at these times (Jokipii and Thomas, 1981) and the relative confinement ofcoronal mass ejections to low latitudes at the onset of the Solar (modulation) Cycle (Gopalswamy et al., i.e. diffusion is the dominant process during the solarmaximum while drift dominates at minima.Thus, we consider first only the increasing phase of Solar Cycle 24 (30 rotations after the minimumof Solar Cycle 23) and calculate the rate of change in Oulu CRI (cutoff rigidity Rc = 0.80 GV, Latitude = 65.05° N and Longitude = 25.47° E) (Table 2) with different parameters [ ∆ I / ∆ P ] andcompared these results with a similar period of the three previous Solar Cycles 21, 22, and 23. To checkthe consistency of these results, a similar analysis for the same periods is done for another neutronmonitor (Newark; neutronm.bartol.udel.edu) with cutoff rigidity Rc = 2.09 GV, Latitude = 39.7° N andLongitude = 75.7° W; these results are also tabulated (see Table 3). A careful examination of thevalues of ∆ I / ∆ P at both of the neutron monitors (Tables 2 and 3) shows that the CRI decreases at afaster rate with an increase in almost all of the parameters considered in this analysis [ SSN, Λ, V , B , σ B , E, and BV
2] in the A <0 polarity epoch. In fact the decrease in CRI with increase in various parameters is ≈ A <0 polarity state (Cycle 22 and 24) as compared to A >0 polarity state (Cycle 21 and 23) (see Table 4). Figure 3a
Change in CRI withSSN during different (low,increasing, decreasing, and high)solar-activity periods in twopolarity states ( A <0 and A >0).Best-fit linear curves along withcorrelation coefficients are alsogiven in each case. There is some indication thatthe response of the cosmic raysto solar-wind speed changesduring solar minima ofdifferent polarity ( A <0 and A >0) are different (Badruddin , Yadav, and Yadav, 1985 ; Richardson, Cane, andWibberenz, 1999; Singh andBadruddin, 2007; Gupta andBadruddin, 2009;Modzelowska and Alania,2011). For low B values (< 6 nT), in A >0 epochs, CRI is reported to decrease more slowly as B increases than in the case for A <0 epochs ( e.g. Wibberenz, Richardson, and Cane, 2002; Cliver,Richardson, and Ling, 2013). There were also suggestions for the polarity dependence of thetransport parameters such as parallel mean free path [ λ ‖ ], with its value being substantially largerduring solar minimum periods with negative polarity ( A <0) than in those with positive polarity (Chenand Bieber, 1993). However, the implications of these results are not in agreement with those of driftmodel calculations ( e.g. see Kota and Jokipii,1991; Richardson, Cane,and Wibberenz, 1999). Figure 3b
Change in CRI withrespect to heliospheric currentsheet tilt [ Λ] during different(low, increasing, decreasing,and high) solar activity periodsand polarity states of theheliosphere. The reducedresponsiveness of cosmicrays to sunspots or tiltangle increases during A >0 epochs in theincreasing phase of SolarCycles as compared to the A <0 epoch are consideredto be supportive of driftmodels of CRImodulation (Smith and Thomas, 1986; Webber and Lockwood, 1988; Smith, 1990; Van Allen, 2000;Cliver and Ling, 2001; Badruddin, Singh, and Singh, 2007; Singh, Singh, and Badruddin, 2008). It needsto be clarified whether similar differences in CRI response to V and B changes in A <0 and A >0 suggestfor any epoch-dependent convection/diffusion effects (transport parameters) in CRI modulation or whether the observed differences in the effectiveness of V and B too are actually a consequence of different accessroutes for charged particles in A <0 and A >0 polarity conditions. Figure 3c
Change in CRI withsolar wind velocity [ V ] duringdifferent (low, increasing,decreasing, and high) solaractivity periods in two polaritystates ( A <0 and A >0). It will be interesting to seewhether such differences in ∆ I / ∆ P in A <0 and A >0 polarityepochs are similar in nature andmagnitude or different duringdifferent levels/phases of solarcycles. From visual inspectionof sunspot cycles, we havedivided the solar cycles intofour parts; increasing,maximum (high), decreasing,and minimum (low) solar-activity periods. The periodsconsidered for this particularanalysis are 1989 - 1991(maximum), 1992 - 1994(decreasing), 1995 - 1997(minimum), 1997 - 1999 (increasing), 2000 - 2002 (maximum), 2003 - 2005 (decreasing), 2007 - 2009(minimum), and 2009 - 2011 (increasing). In order to keep the number of data points equal for regressionanalysis, 40 solar rotations ( ≈ three years) data of each of these parts were used. In this way we haveconsidered two similar phases ( e.g. low activity) in two different polarity epochs ( A <0 and A >0) of equalduration (40 solar rotations ≈ three years). Similarly, we have also considered two similar phases ( e.g. increasing and decreasing) of solar activity in two different epochs, one in A <0 and other in A >0, of the same duration (40 solar rotations) from the latest three Cycles 22, 23, and 24. We have also consideredtwo periods of similar (high) solar activity but mixed polarity. During these periods, the data (especially V and B ) are of better quality with fewer data gaps. The scatter plots along with best-fit linear curves areplotted for Oulu NM count rate (see Figure 3a-3d). Figure 3d
Change in CRI withinterplanetary magnetic field [ B ]during different (low,increasing, decreasing, andhigh) solar activity periods intwo polarity states. To ensure the reliabilityof the observed results, wehave calculated the valuesof ∆ I / ∆ P during exactlythe same periods foranother neutron monitor(Newark) located atdifferent latitude andlongitude on the earth.These values withcorrelation coefficients ( R )are given in Table 5a(during low activity),Table 5b (duringincreasing activity), Table5c (during decreasingactivity) and Table 5d (during high solar activity). In this computation, we have taken care that allindividual periods are of equal length (40 solar rotations). To quantify how much reduced or enhanced isthe CRI-response to changes in various solar/interplanetary parameters, we have calculated the ratio in thevalues of ∆ I / ∆ P during two polarity states in three solar activity conditions. These values are tabulated in Table 6. Critical examinations of Figures 3a-3d, Tables 5a-5d and Table 6 lead us to conclude thefollowing.i. CRI decreases at a faster rate with solar/interplanetary parameters in A <0 than A >0 during low,increasing and decreasing solar activity.ii. During high solar activity (a period of mixed polarity), the rate of change in CRI with change inmost of the solar/interplanetary parameters in almost same during two consecutive Solar Cycles 22and 23.iii. The CRI with solar-wind velocity, in particular, is correlated strongly in A <0 ( R = -0.80) ascompared to A >0 ( R = -0.61) during low solar-activity epochs. During the decreasing activityphase, the correlation is comparatively much better in A <0 ( R = -0.87) as compared in A >0 ( R =0.12) epochs.iv. During low solar-activity conditions, the CRI response to changes in various parameters is ≈ twoto three times or even more in A <0 as compared to A >0 polarity.v. During decreasing and increasing solar-activity conditions the CRI response to changes insolar/interplanetary parameters is about ≈ A <0 as compared to A >0 polarityconditions.vi. During high solar-activity conditions in Cycle 22 and 23, no significant difference in CRI-response to changes in various solar/interplanetary parameters is observed. Moreover, thecorrelations are also not good, in general and with tilt angle in particular, in this period.The variable Sun controls the structure of the heliosphere and the modulation of cosmic rays throughthe level of solar activity, the tilt of the heliospheric current sheet, the velocity of the solar wind and thestrength and turbulence of the interplanetary magnetic field (McDonald, Webber, and Reames, 2010).Determination of diffusion effects is a challenging astrophysical problem, because it requires anunderstanding of the properties of magnetic fields and turbulence, it also demands accurate theories fordetermining diffusion tensor ( e.g. Pei et al., B ] has been known for a long time ( e.g. Burlaga and Ness, 1998; Cane etal., K ‖ ] as well as the perpendicular diffusion coefficient [ K ⊥ ] isassumed to be g e n e r a l l y i n v e r s e l y proportional to B in theoretical modeling of solar modulation(Jokipii and Davila, 1981; Reinecke, Moraal, and McDonald, 2000). Drift velocities of CRI increasewith decreasing B . Thus, it would be interesting to look whether t h e K ‖ and/or K ⊥ relation with B shows any polarity-dependent effect, a t least during low solar-activity periods, in view of our resultsshowing the polarity-dependent CRI-response to changes in B .In the drift formulation of cosmic-ray modulation (Kota and Jokipii, 1983; Potgieter, 2013 andreferences therein) positively charged cosmic rays preferentially enter the heliosphere from the directiontied to the solar poles during A >0 periods ( e.g. ≈ ≈ A <0 periods( e.g. ≈ ≈ e.g., Laurenza et al.,
3. Conclusions
We find that the CRI decreases at a faster rate with an increase in both SSN and Λ as well as with V and B and their derivatives [ BV , BV
2] when the solar magnetic parameter A is negative than when A is positive.Thus not only SSN and Λ but also the parameters V and B exhibit different effectiveness in modulating theCRI during A <0 as compared to A >0 solar-polarity epochs. This rate is found to be faster by a factor of1.5 to 2 in A <0 than in A >0, during the increasing and decreasing phases of solar activity cycles andeven two to three times faster in low activity periods. More specifically, we find that during A <0increasing phase of solar cycles, CRI decreases at about twice the faster rates with an increase in SSN, Λ, B, and E while this rate is about 1.5 times higher with V , σ B, and BV
2, as compared to rates during a similarphase of other solar cycles in A >0 epochs. There is essentially no consistent difference in CRIeffectiveness to changes in various parameters during high solar activity in different solar cycles.All four terms (convection, diffusion, drift, and adiabatic energy change) in Parker ’ s transportequation involve V and/or B in one form or the other. Out of these four terms, only the curvature andgradient drifts are considered to be solar-polarity dependent. However, from our results it appears that theresponse of both V and B (which are included in convection/diffusion terms) to changes in CRI are solar-polarity dependent during all phases of solar cycle except solar maximum.This observed difference in the CR-effectiveness of different parameters in A <0 and A >0 polarity epochs(in similar solar activity conditions) may be ascribed to different access routes of cosmic-ray particles in A <0 and A >0 polarity states as predicted by drift dominated models of cosmic ray modulation.However, the possibility of polarity-dependent effects on transport parameters needs to be explored. Acknowledgements
We thank Station Manager Ilya Usoskin and Sodankyla Geophysical Observatory forthe online availability of Oulu-neutron monitor data. We also thank the National Science Foundation(supporting Bartol Research Institute neutron monitors) and Principle Investigator John W. Bieber for theonline availability of Newark neutron monitor data. Availability of solar and plasma/field data throughthe NASA/GSFC OMNI Web interface and the HCS inclination data (courtesy of J.T. Hoeksema) arealso acknowledged. We also thank the reviewer for useful and constructive comments.
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