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ISSN 0016 7932, Geomagnetism and Aeronomy, 2014, Vol. 54, No. 4, pp. 430­436. © Pleiades Publishing, Ltd., 2014. Original Russian Text © R.T. Gushchina, A.V. Belov, E.A. Eroshenko, V.N. Obridko, E. Paouris, B.D. Shelting, 2014, published in Geomagnetizm i Aeronomiya, 2014, Vol. 54, No. 4, pp. 470­476.

Cosmic Ray Modulation during the Solar Activity Growth Phase of Cycle 24
R. T. Gushchinaa, A. V. Belova, E. A. Eroshenkoa, V. N. Obridkoa, E. Paourisb, and B. D. Sheltinga
a Pushkov Institute of Terrestrial Magnetism, Ionosphere, and Radiowave Propagation, Russian Academy of Sciences, Kaluzhskoe shosse 4, Troitsk, Moscow oblast, 142190 Russia b Physical Faculty, University of Athens, 15771 Athens, Greece e mail: rgus@izmiran.ru

Received September 2, 2013; in final form, December 16, 2013

Abstract--Recent years allowed us to study long term variations in the cosmic ray (CR) intensity at an unusually deep solar activity (SA) minimum between cycles 23 and 24 and during the SA growth phase in cycle 24, which was the cycle when SA was the lowest for the epoch of regular ground based CR observations since 1951. The intensity maximum, the value of which depends on the particle energy, was observed in CR variations during the period of an unusually prolonged SA minimum: the CR density during the aformen tioned period (2009) is higher than this density at previous CR maxima in cycles 19­23 for low energy par ticles (observed on spacecraft and in the stratosphere) and medium energy particles (observed with neutron monitors). After 2009 CR modulation at the SA growth phase was much weaker over three years (2010­2012) than during the corresponding SA growth periods in the previous cycles. The possible causes of this anomaly in CR variations, which are related to the CR residual modulation value at a minimum between cycles 23 and 24 and to variations in SA characteristics during this period, were examined. The contribution of different solar magnetic field characteristics and indices, taking into account sporadic solar activity, has been esti mated. DOI: 10.1134/S0016793214040057

1. INTRODUCTION The 11 and 22 year cycles, which substantially differ from one another in phase, intensity, etc., are the main specific features of variations in solar magnetic fields. These variations create different CR variation types through the solar wind. As with the Sun, all cycles for CRs are different, and each cycle has its own specific features. This information is rather reliable, since long term CR variations have been studied for a long time--since 1936, based on the data of ionization chambers, and since 1951, based on those of neutron monitors (NMs). The average CR modulation, i.e., the parameter that can characterize a cycle as a whole, pronouncedly varies from cycle to cycle (Gushchina et al., 2012). Cosmic ray variations within a cycle are even more individual. Cosmic ray variations and vari ations in the CR modulation parameters, determined based on SA observations, make it possible to compare cycles, to consider CR variation features during differ ent CA cycle epochs, to reveal similarity and differ ence between cycles, and to try to determine the cause of differences between even and odd cycles. In recent years, CR variations have differed from previous variations especially strongly. First, an unusually low SA minimum in 2007­2010 caused a record growth in the CR density. To all appearances,

this density was never (during the period of regular observations) so close to the extraheliospheric level. Second, it is strange that CR modulation is unusually weak during the phases of growth and maximum of the current SA cycle (cycle 24). The aim of the proposed work is to determine the specific features and compare the CR variations in recent years with the variations in cycles 19­23. 2. DATA This study continues the series of previously pre sented works, e.g., (Belov et al., 2001, 2002, 2005; Gushchina et al., 2008), where long term CR modu lation was described using the multi parametric model, including the SA characteristics linearly related to the CR variation amplitude. The CR inten sity observations, global solar magnetic field charac teristics, and data on solar activity are the initial data for modeling CR variations. The spectrum of the long term CR variations for 1953­2012 was calculated using the previously proposed method (Belov et al., 1993). This method was used to determine the CR iso tropic component based on all available data on the CR intensity, obtained by the ground NM network (~40 monitors) and when the stratosphere was sounded at three points (Stozhkov et al., 2007). Fur

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ther analysis was performed using the monthly average variations in the intensity of CRs with 10 GV rigidity (A10 in percent relative to 2009), obtained from these data according to the above method: A10 is the ampli tude of long term galactic CR variations for particles with 10 GV rigidity, i.e., with an energy to which NMs are most sensitive. Since CR variations observed near the Earth are the integral result of numerous solar phenomena, a reli able empirical model for describing CR variations should combine at least several solar indices. The selection of solar magnetic field parameters for empir ical description of cycles in CRs is justified in (Belov et al., 2002, 2005; Gushchina et al., 2008). The characteristic of polar solar magnetic fields Hpol (the field value and direction) and two character istics of large scale fields: the integral energy index (Bss) (the radial magnetic field component squared, averaged over a fixed radius sphere, i.e., the solar wind source surface) and the heliospheric current sheet inclination () are used as indicators of global pro cesses on the Sun. The monthly average values of these quantities were calculated on the solar wind source surface. The field characteristics are calculated based on direct observations at solar observatories, which were performed from May 1976 up to the present and were completed with indirect magnetic field observa tions before 1976 and processed using the methods presented in (Obridko and Shelting, 1999; Vanyarkha, 1995). Different indices were used to take into account the effect of transient solar phenomena on CRs in the per formed analysis. For this purpose, Belov et al. (2007) determined the index of solar flares (xf), which takes into account the X ray flare power (1 flares were selected). It was shown that the CR modulation model is specified (the short period part of CR variations is presented in this model) if solar flare activity is addi tionally taken into account when the long term varia tions in 1976­2012 are described. The introduction of the Pi index, which was determined with account the number of coronal mass ejections (CMEs) during a month and the average plasma velocity (Paouris et al., 2012), was the next step in adequately reflecting SA in the CR long term variation model. The Pi index was calcu lated as follows: Pi = a [Nc/Nc(max) + b [Vp/Vp(max)], where a + b = 1, a and b > 0 ; Nc is the number of CMEs during a month; Vp is the average CME veloc ity; and Nc(max) and Vp(max) are the maximal values of these parameters during the 1996­2012 period, for which the data on CME obtained on the SOHO spacecraft are available (http://cdaw.gsfc.nasa.gov/ CME_list). The CR variations during the growth phase of cycles 23 and 24 are described much better if the Pi index is used to calculate the anticipated CR variations in 1996­2012. For the early period (before 1976, when it was impossible to calculate the CME and X ray flare indices), the Nssc index (the number of
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geomagnetic storms with sudden commencement), which reflects solar wind disturbances propagating in the heliosphere, was used to reflect the effect of local solar fields in the CR modulation model (http://www. wdcb.ru/stp/data/sudden.com/). Note that the above indices behave differently in solar cycles; this allows us to hope that a complete CR modulation pattern in SA cycles can be obtained if we construct the model using complementary indices (Fig. 1). We present here the anticipated and observed variations for a particle rigidity of 10 GV for cycles 19­ 24 and the contributions of variations in different indi ces to CR modulation. We constructed the CR modu lation model using a multi parametric regression analysis. This model rather adequately describes the general pattern of CR variations in 1957­2012 and has the following regression characteristics: the correla tion coefficient is = 0.86, and the rms deviation is = 2.79%. 3. SOLAR ACTIVITY GROWTH PHASE IN CYCLE 24 AND CR MODULATION DURING THIS PERIOD According to the data on the smoothed sunspot number and radioemission flux at a wavelength of 10.7 cm, the current solar cycle (cycle 24) had its first and, most probably, main maximum in February 2012. In April­May 2013, the Wolf number increased again, which possibly indicated that the second (low) peak in the development of the current solar cycle was formed. To all appearances, CR modulation in the considered cycle reached its maximum, but this maximum is near the minimal modulation level for other cycles (cycles 20 and 22) at the same solar magnetic field polarity and is very far from the maximal modulation level in any cycle. We compare the CR variations during the periods of growth and maximum of cycle 24 with the long term variations in different epochs of cycles 19­ 23. Changes in the CR variation average value for each cycle, i.e., the value that can be considered as a char acteristic of the CR cycle power, indicate that each cycle is individual. The deepest modulation ((Gush china et al., 2012), Fig. 1) is observed (the average val ues of variation from one SA cycle minimum to the minimum of another cycle were obtained relative to 1976) in cycle 22 (­7.3%), CRs were least affected by modulation in cycle 20 (­3.1%), and modulation suc cessively decreased in the remaining three odd cycles (­7.0, ­6.3, and ­4.6% in cycles 19, 21, and 23, respectively). Modulation was very insignificant, i.e., smaller than in the previous cycles, up to December 2012 in cycle 24. Analysis of the observed cycle 24, which is the cycle with the lowest solar activity during the CR observa tion period, makes it possible to assume that a small modulation depth is explained by not only low SA and, correspondingly, the small values of modulating char
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GUSHCHINA et al. Hpol 0 ­5 Bss CR (10 GV) variations, % 0 ­10 ­20 ­30 59 63 67 71 75 79 83 87 91 95 99 03 07 11 Years Model ­10 ­15 Contributions, %
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Fig. 1. Modulation of CRs in SA cycles 19­24. Bottom: the model and observations of CR variations (rigidity 10 GV); top: the contributions to modulation of Hpol, , Bss, and Nsss, used to construct the model.

acteristics, but also by the lower effect of these charac teristics on CRs. The inclination of the heliospheric current sheet has been used as a main parameter in the CR modula tion model for a rather long time (see e.g., (Belov, 2000)). Precisely inclination best correlates with long period CR variations. Inclination is beyond competition and is irreplaceable when one SA index is considered. Specifically, inclination cannot be replaced by sunspot numbers but can be combined with the latter index. However, sunspot numbers are successfully replaced by other similar indices, e.g., by the mean solar magnetic field. What do theorists think about it? First of all, we should not pursue an answer in the particle drift. A modulation drift theory is absent. Some available drift models cannot explain the main part of CR modula tion. Drift certainly enters into any sufficiently devel oped modulation model as one of the charged particle transfer mechanisms. Many up to date modulation models (e.g., (Ferreira et al., 2003; Potgieter, 2013)) take into account the heliospheric current sheet incli nation, which very substantially affects the modula tion depth. The current sheet is not only the zone where drift is most effective but is also the largest mag netic inhomogeneity in the heliosphere, with which CRs interact. An increase in inclination not only increases a drift path but also creates magnetic inho mogeneities of a different type. This was adequately considered in the recent works (Krymsky et al., 2001, 2007). A comparison of the observed and model CR den sity values (Fig. 1) indicates that the modulation depth in the last two years (beginning from 2010) would be larger if the index effectiveness remained unchanged. Figure 1 should be considered as follows. In 2010­

1012 (cycle 24), the inclination of the current sheet was actually considerable, and its contribution would be larger than 10% if its relation to CR modulation remained as before (see Fig. 1). However, the model of a particular cycle 24 and Fig. 2 indicate that the con tribution of the current sheet inclination was actually under 5% during this period. This indicates that the effect of the heliospheric current sheet inclination ()--the main modulating index--on CR modula tion changed (decreased). In this work we found that the regression coeffi cient for the current sheet inclination is 0.05%/° in the model of cycle 24 (Figs. 2a and 2b). This is smaller than the coefficient during previous periods for other cycles by a factor of 2­3 (e.g., ­0.16, ­0.14, and 0.12%/° for cycles 20 and 22 and for the entire period from 1957 to 2012, respectively). Therefore, when describing modulation in our model, we can state that the changes in the structural characteristic of the solar magnetic field (namely, current sheet inclination ) from 11.5° at the beginning of the cycle (the CR min imum in October 2009) to >70° (from April 2012 to 2013) affected the CR intensity less effectively than in other cycles. The contribution of variations to total modulation at the cycle 24 maximum is ~4.5%, which is twice as small as the contribution of the same varia tions in the previous even (20, 22; Figs. 3a and 3b) and odd (21, 23; Figs. 3c and 3d) cycles. When we modeled CR modulation during the SA growth phases in cycles 23 (1996­2001) and 24 (2009­2012), we used the Pi index as a parameter that reflects flare solar activity. In this case the modulation process is described with a higher statistical accuracy (e.g., the correlation coeffi cient is = 0.95, and the rms deviation is = 0.79% for the SA growth phase in cycle 24).
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COSMIC RAY MODULATION DURING THE SOLAR ACTIVITY (a) 10 A10, %, Bss, Pi, Hpol 0 ­10 ­20 ­30 ­40 08 09 10 (b) 2008­2012 Hpol Pi Bss Variations Model b 0 ­2 ­4 0 A10, % ­2 ­6 ­4 ­8 08 09 10 11 12 Years Contributions, % 11 12 Years Hpol
xf

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Pi Bss A10%

70 60 50 40 30 20 10 0 xf, , deg

Fig. 2. (a) The A10 CR variation amplitude and the Pi, Hpol, , Bss, and xf SA indices (in relative units) in 2008­2012; (b) the CR variations in 2008­2012. Bottom: the calculation and observations; top: the contributions of the above indices to modulation.

The effect of the large scale solar magnetic field energy (expressed in terms of the Bss index) on CR during the considered SA growth period in cycle 24 is evidently lower (Figs. 2a and 2b) than such an effect during similar SA growth periods in the previous cycles. However, this is mainly caused by a decrease in the Bss value. Note that the effect of short term local SA (characterized by the xf, Pi, and Nssc indi c e s) t o C R mo du lat io n is sli g htly lar ger th an 1 % i n the current cycle and is 5­10% in other cycles (e.g., in cycles 21­23). The obtained variations in the main modulating characteristics during the CR decline phase in cycle 24 and the role of these characteristics in CR variations result in the conclusion that the observed small modu lation depth can be explained by not only small solar indices but also by other specific features in SA during this period or by the heliospheric state at the beginning of a new cycle.
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4. RESIDUAL CR MODULATION AT SA MINIMUMS Residual modulation for different intervals about the minimums of cycles 19­22 was determined in sev eral works (Nagashima and Morishita, 1980; Garcia Munoz et al., 1977; Sirotina, 1989). The last SA min imum and a record increase in the CR density near the Earth make it possible to determine residual modula tion (0). We determined the 0 value for individual periods with a duration of 8­10 years near the mini mums of cycles 19­24. It was assumed that residual modulation is characterized by the free term in the regression equation. This parameter, which was obtained in our model for the period near the 1964 minimum, is 0 =3.7 ± 0.6%, which is close to the value determined in (Sirotina, 1989), where 0 = 3.6 ± 0.5%. In the years near the 1976 minimum, residual modulation is 0 = 7.6 ± 0.3% in our calculations (in (Sirotina, 1989), 0 = 4.1 ± 0.8%). We are more
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434 (a) Hpol Nscc ­5 A10, % ­10 ­15 65 66 67 (b) 68 Hpol xf Bss Variations ­5 ­10 ­15 ­20 ­25 ­30 87 88 89 A10, % 69 Variations Model

GUSHCHINA et al. (c) Contributions, % Bss Pi ­5 A10, % ­10 ­15 ­20 97 Contributions, % 98 99 00 (d) xf Hpol Variations ­4 ­6 ­8 ­10 ­12 ­14 ­16 ­18 77 Model A10, % 01 02 03 0 ­5 ­10 ­15 Contributions, % Model Variations 0 ­10 ­20 0 ­2 ­4 ­6 ­8 ­10 Contributions, % 10 Hpol

Bss

0 ­5 ­10 Model

Bss

90

91

92 Years

78

79

80

81

82 Years

Fig. 3. The CR variations (the model and observations) during the SA growth phase in (a), (b) cycles 20 and 22 and (c), (d) cycles 21 and 23. The top plots of panels (a)­(d) show the contribution of different indices to modulation.

inclined to believe in a new result, noting that Garcia Munoz et al. (1977) also wrote that modulation is sig nificant at the 1976 minimum (unfortunately, they did not indicate the modulation value). According to our model, 0 = 9.8 ± 0.3 and 5.2 ± 0.3% for the 1986 and 1996 minimums, respectively. For the last minimum (of cycle 24), we found that 0 = 9.2 ± 0.2%, which almost coincides with our result and the value obtained in (Nagashima and Morishita, 1980) for cycle 22 (0 = 9.8 ± 3.3%). Such considerable residual modulation during the period when CR density was anomalously high means that the heliosphere intensely affects comparatively high energy CRs even when SA is very low. There is a strong possibility that residual modulation from not only the last but also previous cycles can be observed in the heliosphere at the current cycle minimum. We should state that our modulation description, performed based on the assumption that the CR intensity is linearly related to the SA characteristics, can differ from a true character of this relation. Finally, we should note that the resid ual modulation value should be affected by the polarity of the general solar magnetic field, but we have not yet obtained an evident dependence. These circum stances allow us to be skeptical about available defini

tions of the residual modulation value and make the obtained values rather conventional. 5. DISCUSSION OF RESULTS Analyzing modulation during the SA growth phase and the maximum achieved in cycle 24, we arrive at the conclusion that insignificant modulation is most probably caused by anomalies that originated in the Sun and heliosphere. We can cite several SA observa tions that confirm such a conclusion. The magnetic flux values at the solar poles are lower than in the pre vious cycle by 40%, and the area of the polar coronal holes substantially decreased (Gibson et al., 2009). The heliophysicists determined (see, e.g., (Ishkov, 2013) and references therein) that the magnetic fields in the solar wind over the poles have generally decreased by a factor of approximately 3 during the last 30 years. A long interval with the smallest values from the beginning of observations (since 1947) was observed in the radioemission at a wavelength of 10.7 cm in 2008­2009. Sunspots were mostly absent in 2008­2009. Livingston and Penn (2009) indicated that the sunspot magnetic field strength has gradually decreased in recent times. If this result is confirmed, this can result in an absolutely new understanding of cyclic variations in SA (Obridko et al., 2012). In 2009
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the average solar wind velocity was 365 km/s (as com pared to 443 km/s during the entire long term previ ous period of solar wind measurements); the IMF strength also extremely decreased: 3.94 nT in 2009 as compared to 6.47 nT in 1964­2008. Some of the cited facts are evidently related to a decrease in one of the main modulating characteris tics, which is used to construct the CR modulation model with the ss index that gives information about the entire magnetic flux passing through the solar wind source surface. Changes in the structural characteristic of the solar magnetic field (the current sheet inclination, ) dur ing the indicated cycle phase do not differ in magni tude from variations during the corresponding peri ods of other cycles. A small regression coefficient in the equation that is used in the multi parametric model of the long period CR variation means that the effect of this parameter and, correspondingly, the con tribution of the variations in this main modulation index to CR modulation are decreased. It is still unclear what physical phenomena in the Sun and heliosphere are responsible for a similar anomaly. At a SA minimum, magnetic fields usually disap pear on small surface areas, and only the global mag netic field remains on the Sun (Obridko et al., 2012). Precisely this field becomes responsible for the origi nation of sunspots in a new cycle. This process was anomalous at a minimum between cycles 23 and 24. On the one hand, the magnetic field at the solar poles was much smaller than anticipated. According to the data of AMC ULISS, which passed over the solar poles, in 2008 the solar wind magnetic field and den sity became smaller by 35 and 20%, respectively. On the other hand, medium scale equatorial structures disappeared less pronouncedly than was usually observed, as a result of which the minimum phase started later. A considerable value of CR residual mod ulation at the cycle 24 minimum and a decreased con tribution of variations in the modulating parameter (the polar solar field, Hpol) may be related to the latter circumstances. 6. CONCLUSIONS The current SA cycle (cycle 24) differs in the extremely weak CR modulation caused by anomalies that have recently originated in the Sun and helio sphere, namely, the weakening of solar magnetic fields. A similar conclusion is confirmed by several dif ferent SA observations during the period of activity growth in cycle 24. In addition, it was revealed that the current sheet inclination affected CR modulation less intensely in 2009­2012. The inclination varies in the same range as during other cycles, but the effect of this influence is much lower.
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ACKNOWLEDGMENTS We are grateful to the Presidium of the Russian Academy of Sciences, Program 6 of Fundamental Studies, "Fundamental Properties of Matter and Astrophysics." This work was supported by the Russian Founda tion for Basic Research, project nos. 11 02 01478 and 11 02 13106. REFERENCES
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Translated by Yu. Safronov

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