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Advances in Space Research 52 (2013) 951–956

a–x Effect and peculiarities of the 27-day variationsof the galactic cosmic rays intensity, solar wind and

solar activity parameters

A. Gil a,⇑, M.V. Alania a,b

a Institute of Mathematics and Physics, Siedlce University, Polandb Institute of Geophysics, Tbilisi State University, Tbilisi, Georgia

Received 29 December 2012; received in revised form 30 March 2013; accepted 17 May 2013Available online 23 May 2013

Abstract

We show that the amplitudes of the 27-day variations of galactic cosmic ray (GCR) intensity, solar wind and solar activity parametershave a periodicity with duration of three to four Carrington rotation periods (3–4 CRP). We assume that the general reason for thisphenomenon may be related to similar cyclicity of topological structure of the solar magnetic field lines created owing to the asymmetryof turbulent solar dynamo and solar differential rotation transforming the Sun’s poloidal magnetic field to the toroidal (a–x effect), andvice versa.� 2013 COSPAR. Published by Elsevier Ltd. All rights reserved.

Keywords: Solar dynamo; Sun’s differential rotation; 27-Day variation of GCR

1. Introduction

Although, relations between the 27-day variation andsolar dynamo still are not studied dynamically, there canbe mentioned a paper of Le Mouel et al. (2007), who con-sidered the 27-day indicator in sunspot numbers and thesolar dynamo. Recently we found (Gil and Alania, 2011,2012) a new type of quasi-periodic changes, i.e. a distinctcyclicity with duration of three to four Carrington rota-tions periods (3–4 CRP) in the temporal changes of theamplitudes of the 27-day variations of the GCR intensity,parameters of solar activity (SA) and solar wind. Weassume that the observed quasi-periodic changes, i.e. the3–4 CRP cyclicity is related with the recurring structureof the solar magnetic field. It comes into sight due to theconversion of the poloidal magnetic field into the toroidalowing to the turbulent solar magnetic dynamo and

0273-1177/$36.00 � 2013 COSPAR. Published by Elsevier Ltd. All rights rese

http://dx.doi.org/10.1016/j.asr.2013.05.022

⇑ Corresponding author.E-mail addresses: gila@uph.edu.pl (A. Gil), alania@uph.edu.pl (M.V.

Alania).

differential rotation of the Sun (a�x effect). Our purposein this paper is to study features of the 3–4 CRP recurrenceof the 27-day variations of the GCR intensity, parametersof SA and solar wind.

2. Experimental data, results and discussion

To investigate the properties of the 3–4 CRP periodicity,we analyse long-term changes of various parameters mea-sured on the Earth and in the space near the Earth’s orbit.We use daily data of Rome and Kiel neutron monitors inthe period of 1958–2012 and Nagoya muon telescope inthe period of 1970–2005. We also use daily data of param-eters recognised as good proxies of solar activity, e.g. coro-nal green line intensity (CGLI) with wavelength of530.3 nm, emitted by ionised iron Fe XIV (e.g. Rybak,1994). In our studies we are using data in the period of1970–2008. The next considered parameter is the solarwind plasma temperature (SWt) in the period 1973–2012,measured in Kelvin. We take into account the strengthand components (B, Bx, By, Bz) of the interplanetary

rved.

0.1

0.5

0.9

1.3

77-01 77-04 77-07 77-09 77-12 78-03 78-05 78-08 78-11

A27 I [%]

CR

a

0

0.4

0.8

1.2

77-01 77-04 77-07 77-09 77-12 78-03 78-05 78-08 78-11

A13.5 I [%]

CR

b

0

0.4

0.8

1.2

77-01 77-04 77-07 77-09 77-12 78-03 78-05 78-08 78-11

A9 I [%]

CR

c

0

20

40

60

77-01 77-04 77-07 77-09 77-12 78-03 78-05 78-08 78-11

A27 CGLI [acu]

CR

d

Fig. 1. (a–d) Sequences of the 3–4 CRP cycling in the 1977–1978 in amplitudes of the first three harmonics of the 27-day variation of the GCR intensity byRome neutron monitor, A27 I (amplitudes of the 27-day variation of the GCR intensity, (a), A13.5 (b), A9 (c) and amplitudes of the 27-day variation ofthe coronal green line intensity for 355�, CGLI in absolute coronal units (acu) (d) with marked standard error. On the abscissa the unit equals 27 days.(For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

0

0.1

0.2

0.3

0.4

0.5

2010-01 2010-03 2010-06 2010-09 2010-11

A 27I [%]

CR

a

5

10

15

20

25

2010-01 2010-03 2010-06 2010-09 2010-11

A 27 B [nT]

CR

b

0

20

40

60

80

100

2010-01 2010-03 2010-06 2010-09 2010-11

A 27 SWt [K]

CR

c

0

20

40

60

80

100

2010-01 2010-03 2010-06 2010-09 2010-11

A 27 AE [nT]

CR

d

Fig. 2. (a–d) Sequences of the 3–4 CRP cycling in the 2010 in amplitudes of the 27-day variations of the: GCR intensity by Rome neutron monitor, A27 I(a), the strength of the IMF, B in nT (b), solar wind plasma temperature SWt in K (c) and AE index in nT (d) with marked standard error. On the abscissathe unit equals 27 days.

952 A. Gil, M.V. Alania / Advances in Space Research 52 (2013) 951–956

0

0.5

1

1.5

2

2.5

3

1980-08 1980-11 1981-01 1981-04 1981-07 1981-09

A 27I [%]

CR

a

0

0.5

1

1.5

2

2.5

1980-08 1980-11 1981-01 1981-04 1981-07 1981-09

CR

b]%[I5.31A

0

0.3

0.6

0.9

1.2

1980-08 1980-11 1981-01 1981-04 1981-07 1981-09

CR

dA27 I [%] of N0VV

0

0.3

0.6

0.9

1.2

1.5

1980-08 1980-11 1981-01 1981-04 1981-07 1981-09

CR

c]%[I9A

0

0.4

0.8

1.2

1980-08 1981-02 1981-07 1981-12 1982-06 1982-11

A13.5 I [%] of N0VV e

CR

0

0.2

0.4

0.6

0.8

1980-08 1981-02 1981-07 1981-12 1982-06 1982-11

A9 I [%] of N0VV f

CR

0

1

2

3

4

5

6

1980-08 1980-11 1981-01 1981-04 1981-07 1981-09

CR

jA27 of Bx[nT]

0

0.2

0.4

0.6

1980-08 1981-02 1981-07 1981-12 1982-06 1982-11

A9 I [%] of N2WW i

CR

0

0.3

0.6

0.9

1.2

1980-08 1980-11 1981-01 1981-04 1981-07 1981-09

CR

gA27I [%] of N2WW

0

0.2

0.4

0.6

0.8

1

1.2

1980-08 1981-02 1981-07 1981-12 1982-06 1982-11

A13.5 I [%] of N2WW h

CR

Fig. 3. (a–j) Sequences of the 3–4 CRP cycling in the 1980–1982 in amplitudes of the first three harmonics of the 27-day variation of the GCR intensity byKiel neutron monitor, A27 I (a), A13.5 (b), A9 (c), amplitudes of the first three harmonics of the 27-day variations of the GCR intensity by Nagoya muontelescope in two directions (N0VV: (d–f); N2WW: (g–I): A27 I (d, g), A13.5 (e, h), A9 (f, i) and amplitudes of the 27-day variations of the x-component ofthe IMF, Bx (j) with marked standard error. On the abscissa the unit equals 27 days.

A. Gil, M.V. Alania / Advances in Space Research 52 (2013) 951–956 953

954 A. Gil, M.V. Alania / Advances in Space Research 52 (2013) 951–956

magnetic field (IMF) in the period of 1973–2012. Finally,we are using the auroral electrojet index (AE) measuredin nT in the period of 1963–2012. AE index is a measureof global electrojet operation in the auroral region and iscommonly used in studies of solar-terrestrial connections(e.g. Pallocchia et al., 2008).

To reveal periodicities from series of data we use powerspectral analyses method. To find amplitudes of the 27-dayvariations of different parameters in this paper we use har-monic analysis method (e.g. Kincaid and Cheney, 2002).

We calculate the amplitudes of the 27-day variations ofthe above-described parameters by means of daily datausing the harmonic analyses method during each solarrotation interval for whole period:

yðkDtÞ ¼ a0

2þXN=2

n¼1

an cos2pT

nkDt� �

þ bn sin2pT

nkDt� �� �

;

where an ¼2

N

XN

k¼0

yðkDtÞ cos2pkn

N;

bn ¼2

N

XN

k¼0

yðkDtÞ sin2pkn

N:

N ¼ 27 days and A27 of Y ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffia2

1 þ b21

q;

A13:5 of Y ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffia2

2 þ b22

q; A9 ofY ¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffia2

3 þ b23

q;

are the amplitudes of the first three harmonics of the 27-day variation of parameters that are in our interest (we de-noted it Y for general).

If we track the temporal changes of the amplitudes ofthe 27-day variation of the GCR intensity (A27 I) for morethan 730 Carrington rotations (1958–2012), besides the 11-year variation of the amplitudes of the 27-day recurrence ofthe GCR intensity it is tough to reveal any short-periodregularities in this long data series. Gil and Alania (2011)firstly recognised an existence of patterns with differentcycling (in units of Carrington rotations, CR) of the ampli-tudes of the 27-day variation of the GCR intensity. Amongthem more clearly established one is three to four Carring-ton rotations period (3–4 CRP). We proceed to study the

0.35

0.45

0.55

0.65

0.75

0.85A3 CRP of A27I [%]

1964-66 1975-77 1985-87 1995-97 2007-2009

a

A>0 A>0

A<0

A<0

A<0

Fig. 4. Average amplitudes of the 3 CRP periodicity (a) and 4 CRP periodicrhombuses) and Rome (pink squares) neutron monitors in 1958–2012. (For inreferred to the web version of this article.)

3–4 CRP cycling using data of neutron monitors, muontelescopes and parameters of solar wind, solar and geomag-netic activity. Figs. 1–3 present the 3–4 CRP quasi-period-icity occurring in the amplitudes of the first threeharmonics of the 27-day variation of the GCR intensityby neutron monitors (Figs. 1a–c, 2a and 3a–c) and muontelescope (Fig. 3d–i), coronal green line intensity for 355�(Fig. 1b), the solar wind plasma temperature (Fig. 2c),the AE index (Fig. 2d), the x-component (Fig. 3j) andstrength of the IMF (Fig. 2b). There are presented threeperiods: 1977–1978 (Figs. 1a–d), 2010 (Figs. 2a–d) and1980–1982 (Figs 3a–j). The tendency of the 3–4 CRP recur-rence occurs in the changes of the amplitudes of the 2ndand 3rd harmonics of the 27-day variation of the GCRintensity (Figs. 1b and c, 3b and c). Similar changes areobserved in muon telescopes data (Fig. 3d-i). Unfortu-nately, due to high level of dispersion the 3–4 CRP quasi-periodicity is not so obvious as in neutron monitors data.Sabbah and Kudela (Kudela, 2013) using Lomb algorithmhave shown that the frequency 0.34 corresponding to �3CRP is clearly visible in muon data. It should be noted thatBai and Sturrock (1991), Bai (2003) revealed the periodicityof 84 days (close to 3–4 CRP) in the solar flare data duringsolar cycle 20. The same periodicity was reported by Joshiet al. (2006) in the daily sunspot number and sunspot areain the southern hemisphere during cycle 23.

The 3–4 CRP recurrence has rather sporadic character.It can exist for short periods (e.g. even for 2 years), butafter that it disappears, so as to emerge again after fewrotations. We suppose that the found 3–4 CRP quasi-peri-odicity is a universal property of solar activity connectedwith the solar dynamo and differential rotation of theSun. However, other processes, not very clearly visible,but still existing can sometimes disturb it. Using Kiel neu-tron monitor experimental data in 1958–2012 the length ofthe time intervals with the 3–4 CRP cyclic changes can beestimated on �45%.

Due to differential rotation of the Sun, the helioequato-rial regions perform 3–4 rotations (with the sidereal rota-tion period of �25 days, or with the sinodic period of�27 days), but polar regions perform only 2–3 rotations

0.25

0.35

0.45

0.55

0.65

0.75

A4 CRP of A27I [%]

1964-66 1975-77 1985-87 1995-97 2007-2009

b

A<0

A<0A<0

A>0

A>0

ity (b) in different polarity epochs of solar magnetic cycle for Kiel (blueterpretation of the references to colour in this figure legend, the reader is

A. Gil, M.V. Alania / Advances in Space Research 52 (2013) 951–956 955

(with the sidereal rotation period of �34–35 days, or withthe sinodic period of 36–37 days). Owing to x effect theequatorial toroidal magnetic field lines are fully wrappedaround the Sun and reach to the heliolongitudes with theorigin of the poloidal magnetic field lines (in the polarregions) from which the toroidal field was generated. Wedo not exclude a possibility that time scales of the 3–4CRP can be considered as a mode of the processesdescribed in (Hotta and Yokoyama, 2010); namely due topowerful diffusivity sketch nearby to the surface, the poloi-dal field is transported down to the tachocline by the diffu-sion, and the toroidal field is transported in the tachoclineby the meridional flow. It seems that fully wrapped toroidalmagnetic field lines create a peculiar topological structureof magnetic field on the Sun, which has quasi-periodiccharacter with duration of 3–4 CRP. Besides the 3–4CRP, there are observed recurring structures with largerduration, as well. Also, one can suppose that the rates ofthe Sun’s differential rotation changes versus heliolatitudes(Badalyan, 2010; Suzuki, 2012), i.e. the difference of therotation periods is changeable between the equatorial andpolar regions, or/solar dynamo has turbulent character(e.g. Pipin and Seehafer, 2008; Graham et al., 2010) andthe observed quasi-periodicities with 3–4 CRP are resultsof variable the a–x effects (e.g. Parker, 1993; Roald andThomas, 1997). It is worth to underline that Tomczyket al. (1995) mentioned about a changeable character ofthe differential rotation’s distribution inside the convectionzone of the Sun.

2.1. Polarity dependence of the 3–4 CRP of the amplitudes of

the 27-day variation of the GCR intensity

It is of interest whether or not the 3–4 CRP quasi-peri-odicity manifests the polarity dependence. For this pur-pose, the harmonic analysis on the amplitudes of the 27-day variation of the GCR intensity of Kiel and Rome neu-tron monitors has been performed with periods of threeCarrington rotation (CR) and of 4 CR, respectively.

Results of calculations present Fig. 4a and b. Each pointrepresents the average value of the amplitudes of the 3CRP or 4 CRP in the minimum epoch of SA. One canobserve very clear polarity dependence. Namely, the ampli-tudes of the 3 CRP (Fig. 4a) and 4 CRP (Fig. 4b) period-icities are larger in the negative polarity (A < 0) periodsthan in the positive polarity periods (A > 0). It should beunderlined, that for the 3 CRP and 4 CRP polarity depen-dence there is some exception; in the last minimum epoch(negative polarity period, 2007–2009) amplitudes of the 3CRP and 4 CRP periodicities have similar values as inthe 1995–1997 (positive polarity period). We could ascribethis phenomenon to the anomaly increasing diffusion coef-ficient of cosmic rays (Moraal and Stoker, 2010) during thelast unusual prolonged minimum epoch of SA when anom-alous decrease of turbulence and strength of the IMF, andsolar wind velocity had taken place, as well.

3. Conclusions

(1) We identify relatively clearly established quasi-recur-rence with duration of three to four Carrington rota-tion periods (3–4 CRP) in the temporal changes ofthe amplitudes of the first three harmonics of the ofthe 27-day variations of the GCR intensity (by neu-tron monitors and Multi-Directional Cosmic-RayMuon Telescope at Nagoya), parameters of solarwind and solar activity.

(2) We assume that the 3–4 CRP recurring structure iscreated by joint processes of the turbulent solar mag-netic dynamo and differential rotation of the Sunleading to the conversion of the poloidal magneticfield into the toroidal (a�x effect).

(3) We show the polarity dependence of the 3 CRP and 4CRP periodicities of the amplitudes of the 27-dayvariation of the GCR intensity. Amplitudes of the3–4 CRP quasi-periodicity are larger in the negativepolarity (A < 0) periods than in the positive polarity(A > 0).

Acknowledgments

Authors acknowledge: the Investigators of the Romeand Kiel neutron monitor, and Researcher of the websites:http://www.nmdb.eu/, http://omniweb.gsfc.nasa.gov/,ftp://ftp.ngdc.noaa.gov/STP/SOLAR_DATA.

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