solar proton event in december 2006

ISSN 0016�7932, Geomagnetism and Aeronomy, 2009, Vol. 49, No. 2, pp. 146–152. © Pleiades Publishing, Ltd., 2009.Original Russian Text © V.M. Dvornikov, V.E. Sdobnov, 2009, published in Geomagnetizm i Aeronomiya, 2009, Vol. 49, No. 2, pp. 156–162.

146

1. INTRODUCTION

December 2006 is characterized by the series ofsolar events related to active region 0930. In particular,at 1140 UT on December 5, the GOES�11 spacecraftregistered an increase in the proton flux in the energyrange 0.8–4.0 MeV, caused by the X9 solar flare withcoordinates S07, E68 that occurred on December 5,2006 (the flare onset, maximum, and end wereobserved at 1021, 1035, and 1045 UT, respectively).The fluxes of higher�energy particles started increas�ing much later (at approximately 1600–1700 UT)[http://sgd.ngdc.noaa.gov/sgd/].

The X3 solar flare began at 0217 UT on December13 in the region with coordinates S05, W23 and wasaccompanied by the coronal mass ejection (CME) andsolar proton event (SPE). The GOES�11 satellite reg�istered that the intensity of low�energy particlesstarted increasing at 0325–0330 UT. The beginning ofan increase in the intensity of high�energy cosmic rays(CRs) was registered at the ground�based network ofneutron monitors (GLE) at 0250 UT on December13, 2006. These events caused disturbances (the great�est of which occurred on December 6 and 15) in theinterplanetary medium and in the Earth’s ionosphereand magnetosphere. Specifically, a large geomagneticstorm (Dst ~ –150 nT) was observed on December 15.

The aim of the present work is to study the manifesta�tions of this complex of phenomena in the interplanetaryspace based on the variations in the CR rigidity spectrum,the parameters of which reflect the electromagnetic char�acteristics of the interplanetary medium according to themodel of modulation by regular electromagnetic fields ofthe heliosphere [Dvornikov et al., 2006].

2. DATA AND METHOD

In an analysis we used the data of proton intensityobservations in the 4–9, 9–15, 15–40, 40–80, 80–165, and 165–500 MeV energy ranges, obtained onthe GOES�11 satellite, averaged over the hourly timeintervals and corrected for the geometric factor[http://spidr.ngdc.gov/spidr/index.html]. The data onthe variations in the intensity of higher�energy CRswere obtained based on the surface measurements atthe global network of neutron monitors (32 stations),using the method of global spectrographic survey(GSS) [Dvornikov and Sdobnov, 1997]. The GSSmethod makes it possible to obtain information aboutvariations in the angular and energy distributions ofprimary CRs outside the Earth’s magnetosphere andin the planetary system of geomagnetic cutoff rigidities(GCRs) during each hour of observations. We ana�lyzed the variations in the rigidity spectrum, anisot�ropy, and threshold GCRs during December 1–31,2006, relative to the base level on June 10, 2004.

To describe the CR rigidity spectrum in a widerange of energies, we used the expression obtained byDvornikov et al. [2006]

(1)

J R( ) Aε

2ε0

2–( )

ε ∆ε+( )2

ε02–

��

3/2

=

×ε ∆ε+

ε��

2 ε ∆ε+( )2

ε02– ε

2ε0

2–( )–

ε2

ε02–( )

��

γ–

,

Solar Proton Event in December 2006V. M. Dvornikov and V. E. Sdobnov

Institute of Solar–Terrestrial Physics, Siberian Branch, Russian Academy of Sciences, P.O. Box 4026, Irkutsk, 664033 Russia

e�mail: [email protected]; [email protected]

Received July 31, 2008; in final form, November 10, 2008

Abstract—The variations in the rigidity spectrum and anisotropy of cosmic rays in December 2006 have beenstudied based on the surface measurements of the cosmic ray intensity at the global network of stations, usingthe method of global spectrographic survey. It has been indicated that the highest degree of anisotropy (to~50%) with the maximal intensity of particles with a rigidity of 4 GV in the direction from the Sun (an asymp�totic direction of about –25° and 160°) was observed at 0400 UT on December 13. The parameters of the cos�mic ray rigidity spectrum, which reflect the electromagnetic characteristics of the heliospheric fields duringthe studied period, have been determined when the surface and satellite measurements of protons in theenergy range from several megaelectronvolts to several tens of gigaelectronvolts were jointly analyzed. Theobserved anisotropy and variations in cosmic rays in a wide energy range have been explained based on ananalysis of the results.

DOI: 10.1134/S0016793209020029

GEOMAGNETISM AND AERONOMY Vol. 49 No. 2 2009

SOLAR PROTON EVENT IN DECEMBER 2006 147

where ε is the total particle energy, ε0 is the rest energy,A and γ are the indices of the galactic spectrum, and ∆εare particle energy changes in heliospheric electro�magnetic fields defined by the expression:

(2)

Equation (1) was obtained based on the Liouvilletheorem on the assumption that sources of solar parti�cles (SCRs) are absent in the considered range of ener�gies. If this assumption is violated, expression (1) doesnot describe the observed particle spectrum, and thesediscrepancies can be used to identify SCR arrival.

Expression (2) was obtained by solving the equa�tion of particle motion in the general form in a driftapproximation [Morozov and Solov’ev, 1963], assum�ing that polarization and vortex electric fields can begenerated in the heliosphere along with the inducedelectric field. Indications that such fields are generatedwere obtained during the laboratory experiments per�formed by L. Lindberg (see [Alfvén, 1983] and refer�ences therein).

The ∆ε1, ∆ε2, α, β, and R0 spectral parametersreflect the following characteristics of the heliosphere:R0 is the parameter characterizing the scale of struc�tural formations in the heliosphere with nonstationaryelectromagnetic fields; parameter ∆ε1 characterizesCR energy variations due to the gradient and centrifu�gal particle drifts in helical IMF against the inducedelectric field and is proportional to the IMF strength;and ∆ε2 characterizes such variations in CME fieldsand is proportional to the CME field strength and thesolar wind (SW) velocity [Dvornikov and Sdobnov,2002]. Parameter β = B/B0 (B0 and B are the strengthsof background IMF and IMF variable in time, respec�tively) reflects the effect of nonstationary (in time)magnetic fields on the CR spectrum (at a particle mag�

netic rigidity of R ≤ R0), and parameter α = /B2

reflects the effect of polarization electric fields (Epl).Quasi�step functions f(R, R0) and f(R, b + R0) areintroduced in order to give a weight to any mechanismby which the particle energy changes in the energyintervals [0.108, R0], [R0, R0 + b], and [R0 + b, ∞] GV,where b = 5 GV. These functions tend to unity at R <R0 or R < b + R0 and to zero at R > R0 or R > b + R0.The expression for the quasi�step function, the func�tion parameters, and constant ∆ε0 (taking into accountresidual modulation for low�energy particles) wereempirically determined by Dvornikov [2007].

The parameters of the CR rigidity spectrum andanisotropy were determined for each hour of observa�tions during the entire studied period.

∆ε R( ) ∆ε0 ∆ε1 1 f R b R0+,( )–[ ]+=

+ ∆ε2 1 f R b R0+,( )–[ ] f R R0,( )

+ ε 1 eα/2–( ) ε β ε2

ε02–( ) ε0

2+( )–+[ ] f R R0,( ),

Epl2

3. RESULTS OF ANALYSIS

Triangles in three upper panels of Fig. 1 present thedata of proton intensity observations in the energyranges 4–9 MeV (0.108 GV), 9–15 MeV (0.149 GV),and 5 GV (the average particle rigidity for the giveninterval is shown in brackets), and solid curves demon�strate the results of the calculations performed usingthe model spectrum and the obtained spectrumparameters. The fourth and fifth panels present theaverage hourly values of the first and second sphericalharmonic amplitudes, respectively, in the angular dis�tribution of particles with a rigidity of 4 GV. The fol�lowing four panels demonstrate the ∆ε1, ∆ε2, α, β, andR0 parameters of the rigidity spectrum determinedduring the studied period. The next four panels showthe IMF magnitude, angles Ψ and λ (characterizingthe IMF vector orientation in the interplanetaryspace), and the SW velocity. The lower panel presentsthe GCR variations at Rc = 4 GV together with the Dstindex.

Figure 2 demonstrates the intensity profiles of CRs,with the rigidities shown on the plots, during Decem�ber 10–20.

Figure 3 shows the differential rigidity spectra ofCRs at isolated instants of the studied period togetherwith the CR background spectrum. The results ofmodel spectrum calculations at the instants shown onthe plots are demonstrated by curve 2, and trianglescorrespond to the observational data. The calculatedbackground spectrum and the observational data areshown by curve 1 and dots, respectively.

Figure 4 presents the relative variations in theintensity of CRs with R = 4 GV depending on theasymptotic direction in the solar–ecliptic geocentricsystem of coordinates for different instants on Decem�ber 13, 2006, during the period of GLE observation.

4. DISCUSSION AND CONCLUSIONS

A comparison of the time variations in the param�eters of the CR rigidity spectrum (Fig. 1, panels 7, 8)with the intensity profiles of low�energy protons (twoupper panels in Fig. 1) makes it possible to concludethat an intensification of low�energy CRs is caused byan acceleration of interplanetary medium particles bypolarization and vortex electric fields (an increase inparameters α and β), which began on December 5when the Earth crossed the current sheet.

An analysis of Figs. 2 and 3 indicates that the usedtype of spectrum adequately describes the observeddependence of the CR intensity on the CR rigidity onthe entire analyzed time interval except 0400 and 0500UT on December 13 (during the initial GLE stage).This circumstance makes it possible to conclude thatthe variations in the intensity of energetic particles inthe considered range of energies are caused by achange in the energy of galactic CRs under the actionof electromagnetic fields, originating in the helio�

148


DVORNIKOV, SDOBNOV

103

100

10−3

0.108 GV

0.149 GV

5 GV

102

100

10−3

10−5

8 × 10−6 Pro

ton

(cm

2 s s

r M

eV)–

1

40

20

0

A1,

%

18

0

A2,

%

0.8

0.4

0

de1

de,

GV de2

0.240.200.160.12

α

321

β

01.6

0.8

0R0,

GV

16

8

0

|B|,

nT

360

180

0

Ψ,

deg

9030

−30−90

λ,

deg

1000

600

200

V,

km

/s

0.30

−0.3−0.6

∆R

, G

V

0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30December 2006

Dst

0−80−160 D

st,

nT

Fig. 1. Triangles in three upper panels present the data of proton intensity observations in the energy ranges 4–9 MeV (0.108 GV),9–15 MeV (0.149 GV), and 5 GV; solid curves demonstrate the results of the calculations performed using the model spectrumand the obtained spectrum parameters. The fourth and fifth panels present the average hourly values of the first and second spher�ical harmonic amplitudes, respectively, in the angular distribution of particles with a rigidity of 4 GV. Panels 6–9 demonstrate the∆ε1, ∆ε2, α, β, and R0 parameters of the rigidity spectrum. Panels 10–13 show the IMF magnitude, angles Ψ and λ (characteriz�ing the IMF vector orientation in the interplanetary space), and the SW velocity. The lower panel presents the GCR variations atRc = 4 GV together with the Dst index.



101

10−1

10−30.108 GV

0.149 GV

0.223 GV

100

10−2

10−4

100

10−2

10−4

0.336 GV

0.488 GV

100

10−2

10−4

100

10−2

10−4

0.835 GV100

10−2

10−4

2.00 GV10−3

10−4

10−5

5.00 GV1.1 × 10−5

9 × 10−6

7 × 10−6

10.00 GV

2.0 × 10−6

1.8 × 10−6

10 12 14 16 18 20December 2006

prot

on (

cm2

s sr

MeV

)–1

Fig. 2. Time variations in the intensity of CRs with different rigidities during December 10–20.

150


DVORNIKOV, SDOBNOV

10−1

10−1

10−3

10−5

10−7

1

2

2400 UT Dec. 5, 2006

1010.1

Pro

ton

(cm

2 s s

r M

eV)–

1

10−1

10−3

10−5

10−72400 UT Dec. 12, 2006

1010.1

1

2

Pro

ton

(cm

2 s s

r M

eV)–

1

10−1

10−3

10−5

10−7

0400 UT Dec. 13, 2006

1

2

1010.1

Pro

ton

(cm

2 s s

r M

eV)–

1

101

10−1

10−3

10−5

10−7

1010.1R, GV

1100 UT Dec. 14, 2006Pro

ton

(cm

2 s s

r M

eV)–

1

1

2

101

10−3

10−5

10−72400 UT Dec. 7, 2006

1010.1

1

2

10−1

10−3

10−5

10−7

0300 UT Dec. 12, 2006

1

2

1010.1

1010.1

0500 UT Dec. 13, 2006

1

210−1

10−3

10−5

10−7

0900 UT Dec. 15, 2006

1

2

10−1

10−3

10−5

10−7

1010.1R, GV

Fig. 3. Differential rigidity spectra of CRs at isolated instants of the studied period together with the CR background spectrum.Curves 1 and 2 correspond to the calculated background and model spectra, respectively. Triangles and dots are the observationaldata.

sphere as a result of propagation of SCRs, which inturn move in the region of lower energies (owing to anenergy exchange with galactic CRs and SW plasma

particles) and are only registered at momentaryinstants (e.g., at 0400 and 0500 UT on December 13,2006, see Fig. 3), judging by the differences between



the model and observed spectra in the regions of lowenergies.

The behavior of parameter R0 indicates that theacceleration processes are accompanied by anincrease in the regions with nonstationary electromag�netic fields. GLEs are observed when R0 becomeshigher than 1–2 GV (at corresponding values ofparameters α and β).

The behavior of parameters A1 and A2 (see thefourth and fifth panels in Fig. 1) indicates that consid�erable anisotropy is observed when GLEs are regis�tered. An analysis of the distribution of particles with

R = 4 GV over the direction of arrival indicates that theCR fluxes were maximal at 0400 UT from the direc�tion 170°, –20° (~150%), i.e., almost from the anti�sunward direction.

Based on the obtained results and taking intoaccount the results obtained when the variations in theparameters of the CR rigidity spectrum before SPEwere studied [Dvornikov, 2007], we proposed the fol�lowing scenario of CR acceleration in the solar coronaand heliosphere. It is assumed that magnetic fieldsabove solar active regions have a filamentary structure.If magnetic fields of filamentary structures increase in

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3034

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30343842

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3842 46

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56

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3636

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3636

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4040

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4444

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44 48

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48

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52

56

90

60

30

0

−30

−60

−90

0300 UT Dec. 13, 2006 R = 4 GV

60 120 180 240 300 360

0400 UT Dec. 13, 2006 R = 4 GV90

60

30

0

−30

−60

−90

0

60 120 180 240 300 3600500 UT Dec. 13, 2006 R = 4 GV

90

60

30

0

−30

−60

−900 60 120

0

180 240 300 360

Fig. 4. Relative variations in the intensity of CRs with R= 4 GV depending on the asymptotic directions in the solar–ecliptic geo�centric system of coordinates for different instants on December 13, 2006, during the period of GLE observation.

152


DVORNIKOV, SDOBNOV

the course of time, particles (with the Larmor radiussmaller than the lateral dimensions of these structures)start drifting into filaments and are accelerated due tothe betatron procedure. An increase in the currentsforming these structures causes an increase in the elec�trodynamic force of the magnetic field of these cur�rents, which tends to extend the current circuit. Thisforce is usually neutralized by the electrodynamicforces of the adjacent current circuits, gas pressure,and forces of gravity. However, if the current exceeds acertain critical value, the balance of forces can beupset, and two adjacent current circuits will merge orthe current circuit will break, which is accompanied byan explosive process and precipitation of acceleratedparticles. This will result in an increase in lateraldimensions of filamentary structures and in disappear�ance of small�scale fields. When precipitating beamsof accelerated particles propagate in inhomogeneousfields of the solar corona and heliosphere, they arepolarized because protons and electrons drift in oppo�site directions, as a result of which charges are sepa�rated and the potential difference originates betweenthe beam boundaries along the magnetic drift trajec�tory, if the density of accelerated particles is nonuni�form in space. This circumstance results in the gener�ation of a polarization electric field, which increases inthe course of time, and (as a consequence) polariza�tion drift of background particles of the SW plasma,solar corona, and galactic CRs along this field, i.e., inthe acceleration of particles of the solar corona andinterplanetary medium, the Larmor radius of which issmaller than the lateral dimensions of a given beam.The origination of the depolarization field�alignedcurrents results in the generation of the current systemand the magnetic field and, consequently, the vortexelectric field accelerating particles due to the betatronprocedure, etc. Thus, the energy exchange takes placebetween accelerated particles and background parti�cles of the plasma of the solar corona, SW, and galacticCRs, which results in the generation of the helio�

spheric current and IMF structures; i.e., the process ofparticle acceleration and propagation in the helio�sphere is self�coordinated with electromagnetic fields.

ACKNOWLEDGMENTS

This work was partially supported by the integra�tion project No. 3.10 of the Siberian Branch of theRussian Academy of Sciences and by the Presidium ofthe Russian Academy of Sciences, program NeutrinoPhysics, in the scope of the project Studying Modula�tion Effects of Cosmic Rays Using the Method ofGround�Based and Stratospheric Monitoring.

REFERENCES

H. Alfvén, Cosmic Plasma (Reidel, Dordrecht, 1981;Mir, Moscow, 1983).

V. M. Dvornikov and V. E. Sdobnov, “Time Variationsof the Cosmic Ray Distribution Function during aSolar Event of September 29, 1989,” J. Geophys. Res.A 102, 24 209–24 219 (1997).

V. M. Dvornikov and V. E. Sdobnov, “Variations in theRigidity Spectrum and Anisotropy of Cosmic Rays atthe Period of Forbush Effect on July 12–15,” Intern. J.Geomagn. Aeron. 3 (3), 217 (2002).

V. M. Dvornikov, M. V. Kravtsova, A. A. Lukovnikova,and V. E. Sdobnov, “Variations in the Hard CR Spec�trum during the Event of January 2005,” Izv. Akad.Nauk, Ser. Fiz. 71 (7), 985–977 (2007).

V. M. Dvornikov, M. V. Kravtsova, and V. E. Sdobnov,“Correlations between Variations of Cosmic RaysSpectrum and Interplanetary Medium Parameters,” inProceedings of the 2nd International Symposium SEE�2005, Nor�Amberd, Armenia, 2006, pp. 172–175.

A. I. Morozov and L. S. Solov’ev, “Charged ParticleMotion in Electromagnetic Fields,” Vopr. Teor. Plazmy2 (1963).

http://spidr.ngdc.gov/spidr/index.html

http:sgd.ngdc.noaa.gov/sgd/

solar proton event in december 2006

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