magnetospheric sawtooth events during the solar cycle 23

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JOURNAL OF GEOPHYSICAL RESEARCH: SPACE PHYSICS, VOL. 118, 6378–6388, doi:10.1002/2013JA018819, 2013 Magnetospheric sawtooth events during the solar cycle 23 X. Cai 1 and C. R. Clauer 1 Received 1 March 2013; revised 2 October 2013; accepted 4 October 2013; published 22 October 2013. [1] The Earth’s magnetosphere and ionosphere have a variety of responses to different solar activities. As a result, there are several types of magnetosphere response modes; one of which is termed sawtooth injection events. Currently, it is still unclear whether sawtooth events occurrence has a solar cycle dependence. Partially, this is due to a lack of an event list which covers a full solar cycle. In this research, we have extended our original event list to cover the solar cycle 23, which now includes 126 events from 1996 to 2007. Sawtooth events have been grouped into three categories based on their solar wind drivers: interplanetary coronal mass ejections, stream interaction regions, and others. Then we examine in detail whether sawtooth events occurrence has dependencies on solar cycle and season. We also test a hypothesis that sawtooth events occurrence is related to a threshold of total eroded magnetic flux at the magnetopause regardless of solar wind structures. This paper suggests understanding sawtooth events and other convection modes from solar wind magnetic flux or energy aspect rather than from structure aspect, which is an important idea to understand the complicated magnetosphere dynamics. Citation: Cai, X., and C. R. Clauer (2013), Magnetospheric sawtooth events during the solar cycle 23, J. Geophys. Res. Space Physics, 118, 6378–6388, doi:10.1002/2013JA018819. 1. Introduction [2] The solar wind energy is transferred to the Earth’s magnetosphere and lower atmosphere through two main processes: viscous interaction [e.g., Axford, 1964] and mag- netic reconnection [e.g., Dungey, 1961, 1963]. The first process could occur during any interplanetary magnetic field (IMF) orientation, while the second has an IMF orienta- tion preference. The dayside reconnection site could be in low-/high-latitude region if IMF is southward/northward. During strong southward IMF, the dayside reconnection rate at the magnetopause increases as more IMF reconnects or IMF reconnects faster with the closed geomagnetic field lines than that during quiet intervals. Due to this imbal- ance reconnection rate between the dayside magnetopause and the nightside distant tail, the magnetic flux in the tail lobes grows. In the near tail, the plasma sheet begins to thin accordingly. When the near-Earth plasma sheet reaches about zero thickness or due to other unknown trigger mech- anisms, the near-Earth nightside reconnection occurs thus bringing the newly reconnected geomagnetic field lines back to the dayside, accompanied by various magnetosphere and ionosphere disturbances, for example, magnetic field dipo- larization observed at geostationary orbit, polarization of the auroral oval, and an enhanced westward electrojet connected 1 Bradley Department of Electrical and Computer Engineering, Virginia Polytechnic Institute and State University, Blacksburg, Virginia, USA. Corresponding author: X. Cai, Bradley Department of Electrical and Computer Engineering, Virginia Polytechnic Institute and State University, Blacksburg, VA 24061, USA. ([email protected]) ©2013. American Geophysical Union. All Rights Reserved. 2169-9380/13/10.1002/2013JA018819 via field-aligned currents to the tail current. Through this process, the magnetosphere loads energy from solar wind and unloads the stored solar wind energy to the ionosphere and lower atmosphere. [3] This energy loading-unloading process produces a fundamental magnetosphere response mode namely magne- tospheric substorms (hereafter substorms) [e.g., McPherron et al., 1973]. Other than substorms, the magnetosphere response modes include steady magnetospheric convection events (SMCs) and sawtooth injection events (sawtooth events) [McPherron et al., 2007]. [4] Sawtooth events are found to share common features with isolated substorms. For example, aurora intensification and expansion [Henderson et al., 2006a, 2006b], develop- ment of field-aligned current wedge system [Kitamura et al., 2005; Clauer et al., 2006], evolution of DP1 (disturbance polar of the first type) ionospheric potential pattern [Cai et al., 2006a], and magnetic dipolarization process at geosta- tionary orbit [Henderson, 2004; Huang et al., 2005; Cai et al., 2006b]. [5] However, there are also differences between sawtooth events and isolated substorms. A sawtooth event consists of a series of gradual decrease and rapid increase observed in energetic particle flux at geosynchronous orbit (i.e., particle injection [Sauvaud and Winckler, 1980]), while an isolated event only has one variation cycle. Moreover, the intensity of aurora brightening, the magnitude of the DP1 potential, the strength of the field-aligned currents, and the change of the magnetic tilt angle (angle between the magnetic field line and the equatorial plane) at geostationary orbit are clearly larger during sawtooth events than those during isolated sub- storms. Sawtooth events also involve a wider longitudinal range of configuration change in the magnetosphere. 6378

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JOURNAL OF GEOPHYSICAL RESEARCH: SPACE PHYSICS, VOL. 118, 6378–6388, doi:10.1002/2013JA018819, 2013

Magnetospheric sawtooth events during the solar cycle 23X. Cai1 and C. R. Clauer1

Received 1 March 2013; revised 2 October 2013; accepted 4 October 2013; published 22 October 2013.

[1] The Earth’s magnetosphere and ionosphere have a variety of responses to differentsolar activities. As a result, there are several types of magnetosphere response modes; oneof which is termed sawtooth injection events. Currently, it is still unclear whethersawtooth events occurrence has a solar cycle dependence. Partially, this is due to a lack ofan event list which covers a full solar cycle. In this research, we have extended ouroriginal event list to cover the solar cycle 23, which now includes 126 events from 1996to 2007. Sawtooth events have been grouped into three categories based on their solarwind drivers: interplanetary coronal mass ejections, stream interaction regions, andothers. Then we examine in detail whether sawtooth events occurrence has dependencieson solar cycle and season. We also test a hypothesis that sawtooth events occurrence isrelated to a threshold of total eroded magnetic flux at the magnetopause regardless of solarwind structures. This paper suggests understanding sawtooth events and other convectionmodes from solar wind magnetic flux or energy aspect rather than from structure aspect,which is an important idea to understand the complicated magnetosphere dynamics.

Citation: Cai, X., and C. R. Clauer (2013), Magnetospheric sawtooth events during the solar cycle 23, J. Geophys. Res. SpacePhysics, 118, 6378–6388, doi:10.1002/2013JA018819.

1. Introduction[2] The solar wind energy is transferred to the Earth’s

magnetosphere and lower atmosphere through two mainprocesses: viscous interaction [e.g., Axford, 1964] and mag-netic reconnection [e.g., Dungey, 1961, 1963]. The firstprocess could occur during any interplanetary magnetic field(IMF) orientation, while the second has an IMF orienta-tion preference. The dayside reconnection site could be inlow-/high-latitude region if IMF is southward/northward.During strong southward IMF, the dayside reconnection rateat the magnetopause increases as more IMF reconnects orIMF reconnects faster with the closed geomagnetic fieldlines than that during quiet intervals. Due to this imbal-ance reconnection rate between the dayside magnetopauseand the nightside distant tail, the magnetic flux in the taillobes grows. In the near tail, the plasma sheet begins tothin accordingly. When the near-Earth plasma sheet reachesabout zero thickness or due to other unknown trigger mech-anisms, the near-Earth nightside reconnection occurs thusbringing the newly reconnected geomagnetic field lines backto the dayside, accompanied by various magnetosphere andionosphere disturbances, for example, magnetic field dipo-larization observed at geostationary orbit, polarization of theauroral oval, and an enhanced westward electrojet connected

1Bradley Department of Electrical and Computer Engineering, VirginiaPolytechnic Institute and State University, Blacksburg, Virginia, USA.

Corresponding author: X. Cai, Bradley Department of Electrical andComputer Engineering, Virginia Polytechnic Institute and State University,Blacksburg, VA 24061, USA. ([email protected])

©2013. American Geophysical Union. All Rights Reserved.2169-9380/13/10.1002/2013JA018819

via field-aligned currents to the tail current. Through thisprocess, the magnetosphere loads energy from solar windand unloads the stored solar wind energy to the ionosphereand lower atmosphere.

[3] This energy loading-unloading process produces afundamental magnetosphere response mode namely magne-tospheric substorms (hereafter substorms) [e.g., McPherronet al., 1973]. Other than substorms, the magnetosphereresponse modes include steady magnetospheric convectionevents (SMCs) and sawtooth injection events (sawtoothevents) [McPherron et al., 2007].

[4] Sawtooth events are found to share common featureswith isolated substorms. For example, aurora intensificationand expansion [Henderson et al., 2006a, 2006b], develop-ment of field-aligned current wedge system [Kitamura et al.,2005; Clauer et al., 2006], evolution of DP1 (disturbancepolar of the first type) ionospheric potential pattern [Cai etal., 2006a], and magnetic dipolarization process at geosta-tionary orbit [Henderson, 2004; Huang et al., 2005; Cai etal., 2006b].

[5] However, there are also differences between sawtoothevents and isolated substorms. A sawtooth event consists ofa series of gradual decrease and rapid increase observed inenergetic particle flux at geosynchronous orbit (i.e., particleinjection [Sauvaud and Winckler, 1980]), while an isolatedevent only has one variation cycle. Moreover, the intensityof aurora brightening, the magnitude of the DP1 potential,the strength of the field-aligned currents, and the change ofthe magnetic tilt angle (angle between the magnetic field lineand the equatorial plane) at geostationary orbit are clearlylarger during sawtooth events than those during isolated sub-storms. Sawtooth events also involve a wider longitudinalrange of configuration change in the magnetosphere.

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CAI AND CLAUER: SAWTOOTH DURING SOLAR CYCLE 23

[6] These observed facts have led to a belief that saw-tooth events are large substorms [e.g., Henderson et al.,2006a; Huang et al., 2003; Pulkkinen et al., 2007]. By care-fully examining the global auroral observations during twosawtooth events, Henderson et al. [2006a, 2006b] foundthat each tooth onset consists of a localized premidnightsector onset on the equatorward branch of preexisting dou-ble oval configuration, which is similar to a storm time“embedded” substorm. This suggests that the overall mag-netosphere during sawtooth events is more active than thatduring isolated substorms. In Cai et al. [2011], they extendedthis idea and proposed that both sawtooth events and iso-lated substorms, among storm time substorms and periodicsubstorms, are members of the substorm family. The sub-storm family involves a variety of magnetosphere modeswith impulsive energy loading-unloading processes inthe magnetotail.

[7] Nevertheless, sawtooth events are much less under-stood compared to substorms, especially long-term variationtrend. For example, it is unclear whether sawtooth occur-rence has solar cycle and seasonal dependence. To answerthis, a sawtooth event list covering several cycles is desir-able. However, as the original definition of sawtooth eventsrelies on the Los Alamos National Laboratory (LANL) satel-lite observations only, the data availability and quality putconstraints for identifying purpose. Practically, it is only pos-sible to identify sawtooth events in the solar cycle 23 withhigh confidence using the traditional identification method[e.g, Cai and Clauer, 2009].

[8] To investigate this solar cycle dependence, we haveextended the sawtooth event list [Cai and Clauer, 2009]back to 1996 to cover almost the full solar cycle 23. Thenwe examine the relationship between yearly sawtooth eventsoccurrence and yearly sunspot number (SSN) in detail.The seasonal dependence is estimated from the numbers ofsawtooth events around equinoxes and solstices.

[9] In this paper, we also examine why sawtooth eventsoccur during a wide range of solar wind drivers during thesolar cycle 23. A hypothesis is that sawtooth events occur-rence is related to a threshold of total eroded magnetic fluxon the dayside which is independent from solar wind struc-tures. We test this hypothesis by examining total erodedmagnetic flux during the loading phase of each tooth. Therelationship between the total eroded magnetic flux and thecritical magnetosphere state is also investigated. The criti-cal magnetosphere state is represented by the polar auroralelectrojet AE index and equatorial ring current SYMH index.

2. Methodology[10] Our sawtooth event list is extended from the Cai

and Clauer [2009] event list using the same criteria: (1)the particle injections are seen around both local noon andlocal midnight (˙3 h magnetic local time) and (2) injectionsoccurred quasiperiodically. We have identified six eventsand nine events in 1996 and 1997, respectively. That makesa total of 126 sawtooth events and 487 individual teeth fromJanuary 1996 to December 2007.

[11] As sawtooth events could occur during a widerange of solar wind conditions [Cai, 2007], we also dividesawtooth events into three groups based on their solarwind driver structures: sawtooth events during interplane-

tary coronal mass ejections (ICME-sawtooth events), saw-tooth events during stream interaction region events (SIR-sawtooth events), and sawtooth events that occurred duringother solar wind drivers (other-sawtooth events).

[12] The ICME and SIR event lists were provided byDr. Lan Jian (Research Scientist at Goddard Space FlightCenter). The events were identified manually by a combi-nation of total perpendicular pressure (Pt) and the expectedsignatures of solar wind plasma and magnetic field [Jian etal., 2006a; , 2006b]. Pt is the sum of the magnetic pressureand plasma thermal pressure perpendicular to the magneticfield [Russell et al., 2005]. The thermal pressure includes thecontribution from proton, electron, and ˛ particles. Pt wasfound to be the key component in determining the evolutionof the magnetic structures. There were 268 ICMEs and 498SIRs in the solar cycle 23 from 1996 to 2008, respectively.

[13] To help answer why sawtooth events occur during awide range of solar wind conditions during the solar cycle23, we propose a hypothesis: during a time scale of load-ing phase of substorms (which is usually 1 or 2 h), thetotal eroded magnetic flux (ˆMP) has to reach a thresholdfor sawtooth events to occur, and this threshold is indepen-dent of solar wind structures. The underlying assumption isthat sawtooth events could be explained to a certain extentusing the substorm phenomenological model [McPherron etal., 1973]. We feel that this assumption is reasonably validas sawtooth events share common features with substorms[e.g., Henderson et al., 2006a, 2006b; Clauer et al., 2006].

[14] To test this hypothesis, we examine the histogramsof ˆMP of three groups of sawtooth events and one con-trol group from 1998 to 2007. The control group of artificialsawtooth events is created by randomly choosing onsets dur-ing that interval. The durations of loading and unloadingphases are the same as each tooth. The ˆMP is defined asˆMP =

Rload dˆMP/dt dt =

Rload v4/3B2/3

T sin8/3(�c/2) dt, where�c is IMF clock angle is which defined as tan–1(By/Bz), andBT is the transverse IMF strength

qB2

x + B2y in geocentric

solar magnetospheric (GSM) coordinate system. The for-mula of the rate of open magnetic flux at the magnetopausedˆMP/dt is from Newell et al. [2007]. It has considered therate of IMF field lines approaching the magnetopause whichis v, the percentage of IMF lines which merge sin8/3(�c/2),IMF magnitude BT, and the merging line length (BMP/BT)1/3

(BMP is the Earth’s magnetic field at the magnetopause).Among 20 candidate functions, they found this formula cor-relates best with 9 out of 10 variables which characterize themagnetosphere state. The variables include Dst, Kp, AE, AU,AL, and five other indices. The magnetic flux is integratedduring loading phase or stretching phase only. The loadingphase is defined as the interval when the energetic particleflux at geosynchronous orbit slowly decreases from its localmaximum to its local minimum.

[15] We notice that the units of dˆMP/dt and ˆMP werenot specified in Newell et al. [2007]. Milan et al. [2012]pointed out that dˆMP/dt is synonymous with the rate atwhich flux is open at the dayside ˆD. Therefore, the unit ofˆMP should be the same as magnetic flux, i.e., weber or Wb.This unit could not be derived from the dimensional analy-sis of the formula (i.e., (m/s)4/3 T2/3), which is probably dueto neglect of a normalizing factor [Milan et al., 2012], con-stant or slow-varying variable (with respect to sawtooth time

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CAI AND CLAUER: SAWTOOTH DURING SOLAR CYCLE 23

1996 1998 2000 2002 2004 2006 20080

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Figure 1. The yearly sawtooth events occurrence and SSNsfrom 1996 to 2008. The sawtooth events occurrence is rep-resented in squares and connected by solid line, while SSNsare illustrated in circles and connected by dashed line. Referto the left Y axis for SSN and right Y axis for the number ofsawtooth events.

scale � 1 h) with dimensions. The constant can be consid-ered as ˛�1 m2/3 s1/3 T1/3, where ˛ has no dimension and willbe estimated by comparing the ˆMP and the open magneticflux estimated in the polar region. The unit of the constant

is carefully chosen to obtain the correct unit Weber of ˆMP(Patrick Newell, personal communication, 2013). Therefore,in this paper, we add the unit Wb to ˆMP, emphasizing itsphysical meaning.

[16] Here we use 1 min resolution-propagated solar winddata downloaded from OMNIWeb at Goddard Space FlightCenter (omniweb.gsfc.nasa.gov/ow_min.html). The solarwind data have been shifted from L1 point to the Earth’s bowshock nose using minimum variance analysis [Weimer et al.,2003; Weimer and King, 2008] and/or cross product [Knetteret al., 2004]. To avoid calibration issue from different satel-lites, we use solar wind data from the ACE satellite only.So we constrain our events from 1998 to 2007 when testingthe hypothesis.

[17] We also explore whether the magnetosphere has toreach a critical state for sawtooth events occurrence andwhether there is a relationship between eroded flux ˆMP andthe critical state. The magnetosphere state is represented by1 min AE and SYMH indices, which describe the intensityof auroral electrojet and equatorial ring current. Both indiceswere obtained from Kyoto World Data Center for Geo-magnetism. The critical magnetosphere state before onset isdefined as the mean of AE and SYMH from 10 min beforeeach onset to onset, i.e., AE and SYMH.

Figure 2. Three typical sawtooth events that occurred during (a) ICME, (b) SIR, and (c) complex driver.For each example, (top) the 24 h plot of the energetic proton flux (50 keV to 450 keV) measurements fromLANL satellites is shown. The local midnight and local noon of each satellite are illustrated by moonand asterisk, respectively. The vertical line represents the onset of each individual tooth, whose universaltime is given on the top. (bottom) Three days of solar wind pressure Pd and southward IMF Bz in GSMcoordinate system. The dashed horizontal line marks zero Bz. The solar wind data have been propagatedto 17 RE in front of the Earth. The entire sawtooth interval has been shaded in gray.

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CAI AND CLAUER: SAWTOOTH DURING SOLAR CYCLE 23

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Figure 3. (top) Yearly SSN, number of yearly ICME-sawtooth/SIR-sawtooth events, and yearly (left)ICME and (right) SIR events. In each panel, the yearly SSN has been multiplied by one third to share thesame Y axis with other parameters. (bottom left) The ratio of sawtooth events driven by three differentsolar wind drivers in each year. (bottom right) ICME and SIR geoefficiencies (or probability) to producesawtooth events. ICME-sawtooth, SIR-sawtooth, and other-sawtooth are plotted in red, blue, and green,respectively. The SSN is represented in dashed line, and the yearly ICME/SIR are in solid line.

3. Solar Cycle Dependence[18] To examine the solar cycle dependence of sawtooth

events occurrence, the number of sawtooth events every yearis plotted on the top of yearly SSN. Then sawtooth events arefurther divided into three groups based on their solar winddrivers: ICME-sawtooth events, SIR-sawtooth events, andother-sawtooth events.

[19] Figure 1 showed the yearly sawtooth events occur-rence and yearly SSN in the solar cycle 23 from 1996 to2008. The figure is similar to Figure 1 in Cai et al. [2011]except it now includes sawtooth events in 1996 and 1997.The sawtooth events occurrence shows a complex pattern.As pointed by Cai et al. [2011], sawtooth events occur-rence shows double peaks in 1998 and 2002 during thesolar cycle 23. It reaches its minimum around solar mini-mum 1996 and 2007. It has another minimum around solarmaximum 2000. The highest occurrence rate is in the initialdescending phase.

[20] To understand why the sawtooth occurrence has acomplex pattern, we further group sawtooth events based ontheir solar wind structures. Cai [2007] has identified threetypes of solar wind drivers: ICME, SIR, and complex. Forsimplicity, these three groups are named ICME-sawtoothevents, SIR-sawtooth events, and other-sawtooth events inthis paper. Figure 2 gives three typical examples fromeach group. The first sawtooth event on 11 August 2000(Figure 2a) was discussed in detail by Henderson et al.[2006b]. During this event, solar wind Pd was low and IMFBz was strong and southward. And the IMF orientation alsochanged smoothly (not shown here). Clearly, this sawtoothevent occurred during a magnetic cloud, which constitutesabout 30% of ICME events [e.g., Klein and Burlaga, 1982].

The second sawtooth event (Figure 2b) was during a SIR,which was a characteristic of fluctuating IMF Bz. The thirdexample (Figure 2c) was accompanied with southward IMFbut with short durations of northward IMF. This group ofsawtooth events include all sawtooth events whose solarwind drivers are found neither in Jian’s ICME event list norin SIR event list. So solar wind drivers for those events arenot well-defined structures, instead, they could be a mixtureof different structures such as a shock and an ICME.

[21] As shown in Figure 3 (top), the solar cycle depen-dence of sawtooth events is estimated from yearly SSN andyearly sawtooth events driven by ICME and SIR. The cor-relation coefficients r between ICME-/SIR-sawtooth eventsand SSN are 0.779 and –0.180, respectively. Evidently, theICME-sawtooth events have a strong correlation with thesolar cycle, while SIR-sawtooth events have very low orno correlation. This is mainly because ICME events havea strong solar cycle correlation (r = 0.844) but SIR eventshave a moderate correlation (r = –0.519). In Figure 3 (bot-tom left), the ratio of sawtooth events driven by differentsolar wind drivers are assessed. Clearly, the ICME-drivenevents are dominant (� 80%) around solar maximum in2000, and the SIR-driven events are dominant (� 90%)around solar minimum such as in 2006. For complex solarwind-driven sawtooth events, its contribution could be ashigh as 50% during solar minimum 1996 and in the initialdescending phase 2003.

[22] The geoefficiency (or probability) of ICME and SIRto drive sawtooth events is plotted in Figure 3 (bottom right).The geoefficiency is defined as the ratio of the number ofICME/SIR events with sawtooth events to the number oftotal ICME/SIR events in each year. In general, ICMEs are

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CAI AND CLAUER: SAWTOOTH DURING SOLAR CYCLE 23

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Figure 4. Observed and predicted yearly sawtooth eventsfrom 1996 to 2008. The observed occurrence is representedas squares and connected in solid line. The estimated occur-rence is illustrated as crosses and connected in dashedline. The upper and lower dashed lines are the estimatedoccurrence using the maximum and mean calculated geo-efficiencies from Figure 3. The estimated occurrence usingconstant and variable geoefficiencies are colored in blackand orange.

more effective to produce sawtooth events than SIRs exceptaround solar minimum. The geoefficiency of ICME has amaximum value of 32.1% and mean value 18.6%. While forSIR, the maximum value is 22.0% and mean is 10.6%.

[23] Using these geoefficiencies, we now attempt to pre-dict yearly sawtooth events if we assume that sawtoothevents are driven by ICME and SIR only. The formula isnsaw = CICME � nICME + CSIR � nSIR, where CICME and CCIRare the geoefficiencies, nsaw, nICME, and nSIR are the yearlynumbers of sawtooth events, ICME, and SIR.

[24] We have conducted two tests based on the follow-ing two different assumptions: (1) ICME and SIR geoef-ficiencies are constants, and they could be approximatedas the maximum and mean values mentioned above; and(2) similar to the previous assumption, except that both theCME and SIR geoefficiencies decrease by 10% at solarmaximum 2000.

[25] The results are shown in Figure 4. The two profilesusing the maximum and mean geoefficiencies seem to putupper and lower limits for sawtooth occurrence. For the firsttest, the predicted number of sawtooth events agrees rea-sonably well with observed number of events. However, thesawtooth occurrence is overestimated around the solar max-imum 2000 and underestimated around the initial decliningphase 2002. For the second test, the geoefficiencies of ICMEand SIR both decrease by 10 at solar maximum 2000; thepredicted number of sawtooth events agrees better with theobserved pattern than that from the first test.

[26] From the above tests, it is apparent that there areonly a small portion of ICMEs and SIRs that are accompa-nied with sawtooth events. In other words, sawtooth eventsoccur during a certain type of ICME and SIR. A possibleexplanation is that the solar wind driving should not be toostrong nor too weak for sawtooth events occurrence. We pro-pose this threshold is the dayside-coupled solar wind energywhich could be represented as the total eroded magnetic fluxˆMP. Therefore, it is natural to examine whether there is athreshold ofˆMP for sawtooth events occurrence, which willbe discussed in detail later.

4. Seasonal Dependence[27] The seasonal dependence of sawtooth events is

examined from monthly sawtooth events occurrence. Thenumbers of sawtooth events are binned by calendar month.The histogram is shown as grey bars in Figure 5. Eachseason is defined as an interval ˙15 days centered onequinoxes/solstices. For simplicity, the equinoxes and sol-stices from 1996 to 2007 are chosen as 20 March, 21 June, 22September, and 21 December, although the actual times havea small shift from year to year. As shown in Figure 5, saw-tooth events occurrence has a clear preference of equinoxes,or Fall especially. There are 11, 8, 21 and 8 events inSpring, Summer, Fall and Winter, respectively. And the Falloccurrence is twice as Spring occurrence. Therefore similarto other geomagnetic activity [e.g., Chapman and Bartels,1940], sawtooth events occurrence is also found to have asemiannual variation and with peaks around equinoxes. Wenotice that the actual peak in Spring is in April, which maysuggest the Russell-McPherron (R-M) effect [Russell andMcPherron, 1973] and Rosenberg-Coleman (R-C) effect[Rosenberg and Coleman, 1969].

[28] Those two effects have been proposed to explainthe geomagnetic semiannual variation [Svalgaard, 2011].They are considered as geometrical effects which describehow the spiral IMF converts to a geomagnetically south-ward component at the Earth around equinoxes. Consideringthe obliquity of the Earth and the Sun which are 23.44ıand 7.25ı, respectively, the Spring peak and Fall peak areactually around 7 April and 11 October [McPherron et al.,2009].

[29] To further understand why Fall occurrence is largerthan Spring occurrence, the sawtooth events occurrence atSpring and Fall peak in each year is plotted in Figure 6a.The Spring and Fall are defined as˙15 days around 7 Apriland 11 October following McPherron et al. [2009]. The per-centage or ratio is defined as the ratio of the number ofsawtooth events in that season to the total sawtooth events inthat year. The actual number of events in that season is alsoshown on the top. There are more sawtooth events in Fallthan in Spring during the solar ascending phase from 1997

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Figure 5. Normalized ratio of sawtooth events whichoccurred during each month in grey bar. The actual num-bers of sawtooth events are given on top of the bars. Theblack bars illustrate the number of sawtooth events˙15 daysaround equinoxes and solstices.

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CAI AND CLAUER: SAWTOOTH DURING SOLAR CYCLE 23

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Figure 6. (a) The percentages of sawtooth events in Springand Fall from 1996 to 2007. The actual number of events ineach season is shown on top of the grey bar. The ratios ofthe IMF polarities which share the right Y axis are illustratedin solid and dashed lines, which represent IMF “Away” and“Toward.” (b) Distributions of IMF spiral angle at 17 RE infront of the Earth for the whole year, Spring and Fall. Hereonly 4 years 1998–1999 and 2004–2005 are shown, whichare illustrated by blue solid line, green solid, orange dashedline, and red dashed line. The outer circle is 5%.

to 2001. However, this asymmetry changes to the oppositein the descending phase.

[30] Evidently, this Spring and Fall asymmetry seemsto be associated with solar cycle. However, it is unclearwhether this Spring-Fall asymmetry is related to IMF polar-ity. Based on a typical picture of pure R-M effect “Springtoward Fall away,” the geomagnetic activity tends to occurduring Toward IMF at Spring and Away IMF at Fall. There-fore, the ratio of the Away or Toward IMF are plotted inFigure 6b. The spiral angle is defined in the geocentric solarequatorial (GSE) plane. In the GSE coordinate system, Xaxis is pointing toward the Sun and Y component is in theecliptic plane and is positive toward dusk. The ratio of Awayor Toward IMF is the sum of spiral angle distribution [90ı,180ı] and [–90ı, 0ı]. We found that IMF polarity showeda solar cycle dependence. As shown in the yearly spiralangle distributions (Figure 6b), the spiral angles are orient-ing along –45ı and 135ı. There were slightly more AwayIMF and less Toward IMF in the ascending phase than in thedescending phase. While a similar trend is seen in Spring, adominance of Away IMF is found in Fall. In 1999 Fall, morethan 65% of time the IMF was Away which may result ina Fall preference of sawtooth events. Since there was onlyone sawtooth event, the definite interpretation still needs fur-ther examination. In 2004 Fall, the IMF was Toward morefrequently which decreased sawtooth events occurrence.

[31] In summary, like other geomagnetic activity, saw-tooth events occurrence is found to have a preference of

equinoxes especially Fall. The seasonal dependence alsovaries with solar cycle. The Fall preference is prominentduring the ascending phase.

5. Eroded Magnetic Flux on the Dayside DuringSawtooth Events

[32] As shown previously, sawtooth events could occurduring a wide range of solar wind conditions. Therefore,it is a challenge to understand the triggering mechanism.One hypothesis is that the magnetosphere obtains a certainamount of solar wind energy or the total eroded magneticflux ˆMP on the dayside during sawtooth events regardlessof solar wind structure. To test this hypothesis, it is nec-essary to examine ˆMP during the loading phase of eachtooth. The critical magnetosphere state before each onsetis inferred from AE and SYMH indices. The relationshipbetween the eroded magnetic flux and the critical magneto-sphere state is also examined in detail. Specific questions areas follows: (1) Does the critical magnetosphere state dependon the magnetic flux threshold? and (2) Does the daysidemagnetosphere have a magnetic flux threshold?

[33] As shown in Figure 7, there is no relationshipbetween AE and ˆMP during sawtooth events. The sameconclusions are seen during all three groups of sawtoothevents. Similarly, SYMH has no clear relationship withˆMP,although it shows a trend of increase with a large ˆMP forSYMH between –20 nT and –50 nT during SIR-sawtoothevents and other-sawtooth events. The SYMH during ICME-sawtooth events could be stronger than 80 nT, which is theupper limit of the other two groups.

[34] To examine the difference between the histograms inFigure 7, the cumulative distribution functions (CDFs) ofˆMP, AE, and SYMH corresponding to different solar winddrivers are plotted in Figure 8. The CDFs for three groups ofsawtooth events are on the right of that for the control groupsuggesting that the magnetosphere during sawtooth eventscouples more magnetic field flux than that during the con-trol group. The threshold seems to be about 106, which is

Complex SW ICME driven SIR driven

0 -50 -100 -150

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3

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5

6

7

Load

ed S

W e

nerg

y, lo

g 10

0

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20

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io (%

)

Figure 7. Scatter plots between ˆMP during sawtoothevents and AE and SYMH. In each plot, ICME-sawtoothevents, SIR-sawtooth events, and other-sawtooth events arerepresented by red, blue, and green circles, respectively. Thecontrol group with random onsets is plotted as gray circles.The histograms of ˆMP are plotted on the right. And thehistograms of AE and SYMH are plotted on top.

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C omplex S W IC ME driven S IR driven

SYMH, nT

0.00

0.25

0.50

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10

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0.00

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tio

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Figure 8. (top) Histograms of loaded energy, AE, and SYMH. (bottom) The cumulative distributionfunctions (CDFs) of the total eroded magnetic flux, AE, and SYMH. The sawtooth events driven byICME, SIR, and complex solar wind are plotted in red, blue, and green, respectively. The control group isplotted in gray. The three dashed lines in CDFs represent the first, second, and third quartiles, which are25%, 50%, and 75%.

slightly higher during ICME-sawtooth events than the othertwo groups. The auroral electrojet during sawtooth events isalso stronger than that during the control group. There seemsno difference between sawtooth events corresponding to dif-ferent drivers. The equatorial ring current during sawtoothevents are generally larger than during the control group.The ring current during ICME-sawtooth events is evidentlylarger than that during the other two groups.

[35] Next Kolmogorov-Smirnov test (K-S test) [Massey,1951] and Anderson-Darling test (A-D test) [Anderson andDarling, 1952] are used to test whether the two histogramsin Figure 8 are the same or not. These two tests are nonpara-metric tests, which means that there are no assumptions ofunderlying distributions of data. A-D test is similar to K-Stest except it gives more weight in the tails. Under the nullhypothesis, the two distributions are the same. The hypoth-esis is tested at 5% significance level or 95% confidencelevel. The results are listed in Table 1. The histograms of thecontrol group have been tested with those driven by differ-ent solar wind (not shown). The hypotheses have all beenrejected. That means that considering the threshold of ˆMPand the critical magnetosphere state, sawtooth events aresignificantly different from the control group.

[36] The ˆMP during ICME-sawtooth events is signifi-cantly different from that during the other two groups, whilethere is no significant difference between SIR-sawtoothevents and other-sawtooth events. The polar magnetosphereshows no significant difference between ICME-, SIR-,and other-sawtooth events. The ring current during ICME-sawtooth events is significantly different from that duringother two groups, while there is no significant differencebetween these two groups.

[37] Therefore, the magnetosphere does need to couplea certain amount of ˆMP for sawtooth events to occur. Itis slightly higher during ICME-sawtooth events than thatduring the other two groups of events. The polar magneto-

sphere experiences a similar process regardless of solar winddrivers. The excessive energy loaded on the dayside duringICME-sawtooth events is dissipated through an enhancedring current.

6. Discussion[38] To evaluate sawtooth events occurrence during the

solar cycle, we extended the sawtooth event list [Cai andClauer, 2009] to include 1996 and 1997. Now the newevent list includes sawtooth events from January 1996 toDecember 2007, which expands almost the full solar cycle23. We note that the actual solar cycle 23 ended in December2008 based on observed sunspot number. As the LANL dataafter January 2008 have been classified, the number of saw-tooth event in that year remains unknown. However, sincesawtooth event occurrence is estimated yearly and there isonly one data point missing at solar minimum, we feel con-fident that the current results could represent the sawtoothevent variation trend during the solar cycle 23.

[39] Using the sawtooth event list from 1996 to 2007,we have examined whether sawtooth event occurrence hasa solar cycle dependence. The occurrence has a complexpattern, with low occurrence at both solar minimum andmaximum. The high occurrence is found in the initial declin-ing phase. A similar two-peak feature has also been foundfor intense storm occurrence by Gonzalez et al. [1990] dur-ing solar cycles 20 and 21. They suggest that the peakscorrespond to the similar dual-peak distribution of south-ward IMF Bz with intensities larger than 10 nT and durationslonger than 3 h. Since most of sawtooth events occur dur-ing intense storms [Cai et al., 2011], our results agree withtheir results.

[40] We then further separate sawtooth events basedon solar wind drivers and again examine the solar cycledependence. ICME-sawtooth events show a solar cycle

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Table 1. Statistical Analysis to Test Whether the Two Distributions as Shown in Figure 8 are the Same or Not a

K-S test A-D test

Parameter Groups D p Results A2 p Results

ˆMP

CME and SIR 0.31 < 0.01 Rejected 16.0 < 0.01 RejectedCME and COM 0.26 0.014 Rejected 3.29 0.019 RejectedSIR and COM 0.16 0.37 Accepted 1.03 0.34 Accepted

AECME and SIR 0.050 0.97 Accepted 0.40 0.84 Accepted

CME and COM 0.17 0.21 Accepted 1.54 0.17 AcceptedSIR and COM 0.19 0.14 Accepted 2.00 0.09 Accepted

SYMHCME and SIR 0.48 < 0.01 Rejected 38.61 < 0.01 Rejected

CME and COM 0.57 < 0.01 Rejected 21.02 < 0.01 RejectedSIR and COM 0.19 0.14 Accepted 1.16 0.28 Accepted

aUnder the null hypothesis, the two distributions are the same. The statistical test results are given as “Accepted” or “Rejected,”which means that the two distributions are the same or different at 5% significance level. Rejected is highlighted in italic and bold.

dependence, while SIR-sawtooth events do not. This depen-dence is similar to the ICME and SIR occurrence patterns inthe solar cycle 23. Although the number of ICMEs stronglyfollows the solar cycle, the number of SIRs does not. Saw-tooth events are dominated by ICME-sawtooth events atsolar maximum and SIR-sawtooth events at solar minimum.At solar maximum 2000, 80% of the sawtooth events weredriven by ICMEs. And at solar minimum 2006, 90% of thesawtooth events are driven by SIRs. The geoefficicency ofICME to drive sawtooth events has a maximum value of32.1% and mean 18.6%, while the geoefficiency of SIR is22.0% and 10.6%. The geoefficiency of those ICMEs seemsto agree with magnetic cloud occurrence, which is roughlyone third of the total ICMEs [Klein and Burlaga, 1982].

[41] Based on the calculated geoefficiency of ICME andSIR, we made an attempt to predict sawtooth occurrencebased on the numbers of ICME and SIR nsaw = CICME �nICME +CSIR�nSIR, where CICME and CCIR are the geoefficien-cies and nsaw, nICME, and nSIR are yearly numbers of sawtoothevents, ICMEs and SIRs. The calculated occurrence usingconstant maximum and mean geoefficiency provide a goodestimate of the upper and lower boundaries. However, theoccurrence around solar maximum is overestimated. Afterdecreasing the geoefficiency by 10% around the maximum,the calculated occurrence agrees better with the observedsawtooth events occurrence. Considering that we neglect thethird group of events which are driven by complex solarwind driving, the prediction is pretty good. The formulacould be used to predict sawtooth events based on ICMEand SIR observations when LANL satellites had limitedspatial coverage before 1996 or have been classified thusunavailable to the public after 2008. The estimated numberof sawtooth events in 2008 is between 5 and 9.

[42] Similar to other geomagnetic activities, sawtoothevents occurrence is found to have a semiannual variationwith peaks around equinoxes. Moreover, it has a Spring-Fallasymmetry. The occurrence is higher in Fall/Spring duringthe ascending/descending phase in the solar cycle 23.

[43] Svalgaard [2011] listed four broad categories ofhypotheses to explain the semiannual variation: “Axial”hypothesis, “Equinoctial” hypothesis, “R-M” hypothesis,and lack of “Solar Illumination.” Axial and R-M hypothe-ses are related to the obliquities of the Sun and the Earth,which are 7.25ı and 23.44ı, respectively. They are consid-ered as “Excitation” mechanism. Axial effect comes fromthe variation of the Earth’s heliographic latitude which is

between –7.25ı and 7.25ı. And the spiral IMF actually linesin the solar equatorial plane. R-C effect is an Axial effect.R-M hypothesis is a geometrical effect when convertingthe spiral IMF from Geocentric Solar Equatorial coordi-nate system to GSM coordinate system. At equinoxes, theSun-Earth geometry maximizes the projection of the spiralIMF along the Earth dipole direction thus enhances mag-netic reconnection. Equinoctial hypothesis believes that theangle between the solar wind flow and the Earth’s dipole axisplays an important role. The full range of this angle is [55ı,125ı] [Svalgaard et al., 2002]. Lack of Solar Illuminationincludes the effect of ionospheric conductivity. These lattertwo hypotheses are “Modulation” mechanisms.

[44] As the typical duration of sawtooth events is 10 h,Equinoctial hypothesis may not be a good candidate toexplain its semiannual variation pattern. The tilt angle couldchange by more than 10ı, which brings large uncertainty.Although the ionospheric conductivity controls the iono-sphere electrodynamics, its contribution to sawtooth eventsoccurrence is beyond the scope of this paper.

[45] Therefore, we concentrate on R-C and R-M effects.As shown in Figures 5 and 6, the semiannual occurrencepattern of sawtooth events is indeed affected by the com-bination of R-C and R-M effects. If the solar magneticfield was an ideal dipole and only R-C and R-M effectswere included, we would expect a Spring-Fall symmetryin sawtooth events occurrence. That means there shouldbe equal numbers of sawtooth events in Spring and Fall.However, we found that there is a Spring-Fall asymmetry,and this asymmetry changed from Fall preference in theascending phase to the Spring preference in the descend-ing phase. So obviously, there are other mechanisms suchas internal solar variation [Echer and Svalgaard, 2004]which have to be included to fully understand the sawtoothsemiannual occurrence pattern. As pointed by Häkkinen etal. [2003], the combined contributions of R-C/R-M effectsand equinoctial hypothesis could only explain 50% of theobserved variability.

[46] A similar asymmetry was also found by Oh and Yi[2011] when they examined storm (|Dst| > 90 nT) occur-rence with IMF polarity at solar minimum. They foundthat storms tend to be stronger in August only if the IMFis antiparallel (away) with the Earth’s. As most of saw-tooth events were accompanied with intense storms [Cai etal., 2011], our results agree with their conclusions. How-ever, Oh and Yi [2011] only examined two solar minimums

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during which the background solar magnetic field could beconsidered as a dipole. Here we have investigated the asym-metry in the solar cycle 23 and found that the asymmetrychanged after the solar magnetic field reversed in 2000[Russell et al., 2012]. Before the reversal, the northernmagnetosphere had positive magnetic field polarity whichmeans that IMF was away from the Sun. As pointed out byRosenberg and Coleman [1969], the northern solar hemi-sphere could be hotter than the southern solar hemisphere inthe ascending phase. Such a greater northern activity tendsto push the solar wind to the southern hemisphere thus themagnetic field originating in the northern solar hemispherecan be also observed in the southern blue heliosphere. Thisnorth-south asymmetry in heliosphere during the solar cycle23 was confirmed by Ulysses observations [Smith, 2011].It was suggested that the asymmetry is due to a displace-ment or offset of the current sheet from the solar equator.It is also likely that this asymmetry changes every solarmagnetic cycle. To test this idea, we could examine the com-puted coronal magnetic field synoptic charts at 2.5 or 3.25 RSsince 1975, based on daily observations of the Sun’s globalmagnetic field provided by Wilcox Solar Observatory.

[47] From the above analysis on sawtooth occurrence inthe solar cycle 23, we suggest that there might be a physicalmeaning of decreased occurrence around the solar maxi-mum. The magnetosphere needs to couple a certain amountof ˆMP, and this threshold could be reached during a widerange of solar wind drivers, i.e., ICMEs and SIRs.

[48] With this idea, we examine the ˆMP during the load-ing phase (or stretching phase) of each individual tooth. Acontrol group is created by randomly chosen onsets but keptthe same durations. The control group has the same numberof events as the actual sawtooth events. Indeed, the mag-netosphere has coupled about two times larger flux duringsawtooth events than that during control group. The his-togram of ˆMP has a narrow distribution. There are about80% of events with ˆMP between 106 and 106.5 Wb. Thisconfirms that there is a ˆMP threshold for sawtooth eventoccurrence. The threshold is slightly larger during ICMEsthan that during SIRs and other solar wind drivers.

[49] Now we examine the possible relationship betweenthe threshold of ˆMP and the critical magnetosphere state.The magnetosphere state is represented by AE and SYMHindices from 10 min before the onset to the onset. Themagnetosphere state during sawtooth events is consider-ably higher than that during the control group. Surprisingly,the histograms of AE during different solar wind driversshow similar distributions. There is no significant differencebetween them using both K-S and A-D statistical tests. Thering current during ICME-sawtooth events is significantlystronger than that during other events.

[50] Based on these results, we would suggest severalimportant factors about sawtooth events: (1) there is a nar-row ˆMP window for sawtooth events to occur. Using thecoupling function from Newell et al. [2007], it is estimatedto be between 106 and 106.5 Wb. If the loaded energy duringsawtooth time scale (� 1 h) is larger than that, the magneto-sphere is driven into a nonlinear or chaotic system [Baker etal., 1990]. The magnetosphere changes from a periodic andpredictable system to a aperiodic and quasi-random system[Shaw, 1984]. If the energy is smaller than that, the magneto-sphere could dissipate energy in other modes such as steady

magnetospheric convection events. (2) This threshold couldbe reached during a wide range of solar wind conditionsalthough it is slightly higher during ICME-sawtooth eventsthan the other two groups. (3) The critical polar magneto-sphere state is independent of solar wind drivers. This meansa similar energy-loading mechanism worked regardless ofsolar wind structure. (4) The ring current in the equatorialregion during ICMEs is stronger than that during other solarwind structure.

[51] A similar threshold in the total magnetic flux in thetail lobe during sawtooth events was identified by Huangand Cai [2009], Huang et al. [2009], and Huang [2011].They found that the magnetic flux during sawtooth events ishigher than that during isolated substorms and SMC events.Sawtooth events occur when the magnetotail reaches a criti-cal state (� 1 GWb), which suggests that there is a thresholdin tail current sheet. Huang et al. [2009] further comparedthe magnetic flux in the tail lobe with GEOTAIL observa-tions and that in the polar cap with aurora observations. Theyconfirmed a magnetic flux threshold in the polar cap. How-ever, the maximum flux could vary with the dayside-mergingelectric field and ring current strength. Note that Huang[2011] did not distinguish different solar wind drivers.

[52] However, there is a discrepancy between the mag-nitude of the these thresholds. The threshold of the totaleroded magnetic flux on the dayside is � 106 Wb found inthis paper, which is three orders smaller than the magneticflux in the polar cap and the tail lobe identified by Huanget al. [2009]. With independent data source from DefenseMeteorological Satellite Program, Lockwood et al. [2009]estimated that the polar cap flux during substorms and steadymagnetospheric convection events are on the order of 108,which should be around the low limit of that during sawtoothevents. The average peak magnetic flux during sawtoothevents is 109 Wb or 1 GWb based on DeJong et al. [2007,Figure 10].

[53] Although the dayside-eroded magnetic flux only con-tributes partly to the total open magnetic flux in the polarcap, the ratio of these two could be 0.1–0.2 during sawtoothevents based on aurora observations as shown in DeJonget al. [2007, Figure 10]. This ratio is much larger than� 0.001 found here. Therefore, using the formula of Newellet al. [2007] directly without modifications will underesti-mate the coupled magnetic flux. As pointed out by Milanet al. [2012], the formula does not include a normalizingfactor ˛�1/m2/3 s–4/3 T1/3 thus can not give a predicted recon-nection rate. From our work, ˛ is estimated to be on orderof 103.

[54] Here we propose a model to explain sawtooth events.Sawtooth events are basically a series of energy loading-unloading processes. This process is similar to isolatedsubstorm but with wider local time extent. The magneticflux loaded on the dayside can either come from continuousmagnetic reconnection such as during ICME or intermit-tent magnetic reconnection such as during SIR or complexsolar wind driver. The reconnected flux propagates to thenightside and accumulates in the tail lobe. The onset of theexpansion phase is determined by the magnitude of accu-mulated flux and the storage capacity of the tail lobe. Thestorage capacity of the tail lobe is also controlled by solarwind parameters. Naturally, the onset will occur when theaccumulated flux exceeds the storage capacity of the tail

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lobe. However, it will also occur when the capacity changesdue to a sudden solar wind change. This could explainwhy some teeth seem directly driven. After the loadedenergy is released, the tail could not be fully recovered toa quiet background as more flux keeps coming. The subse-quent teeth thus are embedded in blue active magnetosphere[Henderson et al., 2006a; Hubert et al., 2008], which leadsto a wider local time response. If the coming flux is small, itis possible that the magnetotail fully recovers and this energyunloading looks more like an isolated substorm.

[55] This model is simply a small extension of sub-storm phenomenological model [McPherron et al., 1973].We would emphasize that sawtooth events along with iso-lated substorms are members of substorm family. Substormfamily includes magnetosphere activity involving energyloading-unloading process. To understand sawtooth events,we suggest following this tradition and focusing on funda-mental physical process instead of concentrating on solarwind structures.

7. Summary[56] Using the sawtooth event list from January 1996 to

December 2007 which covers solar cycle 23, we have exam-ined whether there are solar cycle and seasonal dependenciesof sawtooth events occurrence.

[57] First, we found that sawtooth events occurrenceshows a complex pattern of solar activity which is repre-sented by SSN. The small rate occurs not only around solarminimum but also around solar maximum. The high rate isseen in the initial solar descending phase. After further sep-arating sawtooth events based on their solar wind driver, wefound that ICME-sawtooth events do have a clear solar cycledependence, while SIR-sawtooth events do not. This is dueto the fact that ICME has a strong solar cycle dependence,while SIR do not. The average geoefficiency of ICME isabout 20% and SIR is 10%. The geoefficiency drops dur-ing both solar maximum and solar minimum. Therefore,we conclude that the complex relationship between saw-tooth events and solar activity results from (1) the differentsolar cycle dependence of each solar wind driver and (2) thegeoefficiency that varies with solar cycle.

[58] Second, we found that sawtooth events occurrencehas an equinox preference and specially Fall preference. TheFall preference is prominent during the ascending phase dur-ing which the IMF polarity was Away around the season.Therefore, other than R-M effect and R-C effect, we sug-gest that other mechanisms such as internal solar variationscontribute to the seasonal asymmetry.

[59] Third, the total eroded magnetic flux ˆMP on thedayside of the magnetosphere is examined. The ˆMP is theintegral of coupling function during the growth phase orstretching phase of sawtooth events. The critical magneto-sphere state is roughly represented by AE and SYMH indices.It is found that during sawtooth events, the ˆMP has a nar-row distribution. There are approximately 80% of eventswith ˆMP between 106 and 106.5 Wb. The strength of theauroral electrojet in the polar region is independent of solarwind driver type. During ICME, magnetosphere has coupledslightly more flux than that during other solar wind drivers.The excessive energy has been dissipated in the equatorialregion as enhanced ring current. We conclude that there is an

energy threshold for sawtooth event to occur, and the thresh-old is slightly higher during ICMEs than during the othergroups. It is 106 Wb if using the coupling function fromNewell et al. [2007]. Therefore, we suggest to understandsawtooth events and other convection modes from energyaspect, instead of from solar wind structure type.

[60] Acknowledgments. We thank Weimer for his insightful discus-sions on sawtooth semiannual variations. This material is based on the worksupported by the National Science Foundation under grant AGS. 1049403.Partial support has also come from NSF grant ANT-0839858. We would liketo thank LANL and GSFC OMNI websites for providing the online data.

[61] Masaki Fujimoto thanks the reviewers for their assistance inevaluating this paper.

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