Relationship between solar energetic particle intensities and coronal mass ejection kinematics using STEREO/SECCHI field of view
aa r X i v : . [ a s t r o - ph . S R ] F e b Astronomy & Astrophysicsmanuscript no. 39537corr © ESO 2021February 26, 2021
Relationship between solar energetic particle intensities andcoronal mass ejection kinematics using STEREO/SECCHI field ofview
Anitha Ravishankar and Grzegorz Michałek
Astronomical Observatory of Jagiellonian University, Krakow, Polande-mail: [email protected] e-mail: [email protected]
February 26, 2021
ABSTRACT
Solar energetic particles (SEPs) accelerated from shocks driven by coronal mass ejections (CMEs) are one of the major causes ofgeomagnetic storms on Earth. Therefore, it is necessary to predict the occurrence and intensity of such disturbances. For this purposewe analyzed in detail 38 non-interacting halo and partial halo CMEs, as seen by the
Solar and Heliospheric Observatory / LargeAngle and Spectrometric Coronagraph (SOHO / LASCO), generating SEPs (in >
10 MeV, >
50 MeV, and >
100 MeV energy channels)during the quadrature configuration of the
Solar TErrestrial RElations Observatory (STEREO) twin spacecrafts with respect tothe Earth, which marks the ascending phase of solar cycle 24 (i.e., 2009–2013). The main criteria for this selection period is toobtain height–time measurements of the CMEs without significant projection e ff ects and in a very large field of view. Using the datafrom STEREO / Sun Earth Connection Coronal and Heliospheric Investigation (STEREO / SECCHI) images we determined severalkinematic parameters and instantaneous speeds of the CMEs. First, we compare instantaneous CME speed and Mach number versusSEP fluxes for events originating at the western and eastern limb; we observe high correlation for the western events and anticorrelationfor the eastern events. Of the two parameters, the Mach number o ff ers higher correlation. Next we investigated instantaneous CMEkinematic parameters such as maximum speed, maximum Mach number, and the CME speed and Mach number at SEP peak fluxversus SEP peak fluxes. Highly positive correlation is observed for Mach number at SEP peak flux for all events. The obtainedinstantaneous Mach number parameters from the emperical models was verified with the start and end time of type II radio bursts,which are signatures of CME-driven shock in the interplanetary medium. Furthermore, we conducted estimates of delay in time anddistance between CME, SEP, and shock parameters. We observe an increase in the delay in time and distance when SEPs reach peakflux with respect to CME onset as we move from the western to the eastern limb. Western limb events (longitude 60 ◦ ) have the bestconnectivity and this decreases as we move towards the eastern limb. This variation is due to the magnetic connectivity from the Sunto the Earth, called the Parker spiral interplanetary magnetic field (IMF). Comparative studies of the considered energy channels of theSEPs also throw light on the reacceleration of suprathermal seed ions by CME-driven shocks that are pre-accelerated in the magneticreconnection. Use \ titlerunning to supply a shorter title and / or \ authorrunning to supply a shorter list of authors.
1. Introduction
Solar energetic particles (SEPs) are one of the major causesof geomagnetic disturbances on Earth (Cane et al., (1987);Gosling 1993; Reames 1999; Kahler 2001; Aschwanden2012). The timescales, spectra, composition and charge states,and the associated radio bursts observed at 1 AU of these par-ticles categorize them into impulsive SEP events accelerated atcoronal flare reconnection sites (Cane et al., 1986), and gradualSEP events accelerated by coronal mass ejection (CME) shocksor interplanetary shocks (Gosling 1993; Reames 1995; Reames1999). In the aspect of potential space weather impacts, the grad-ual SEP events with high proton fluxes are the prime threats thatcause disturbances of Earth’s magnetosphere and upper atmo-sphere.The di ff usive shock acceleration theory has been well stud-ied, and it is a widely accepted mechanism for energizing theions in gradual SEP events (e.g., Jokipii 1982; Lee 1983, Lee2000; Lee et al. 2012; Desai & Giacalone 2016). Charged par-ticles can be accelerated by collisionless shocks, provided thespatial di ff usion allows some particles to traverse the shockmany times. They gain energy because the scattering centers are embedded in converging plasma flows across the shock.Apart from the CME driver speed, other characteristic speeds(such as the Alfvén speed) of the ambient medium determine thestrength of the shock (Krogulec et al. 1994; Mann et al. 1999;Gopalswamy et al., 2001; Mann et al. 2003; Gopalswamy et al.2008a; Gopalswamy et al. 2008b; Gopalswamy et al. 2010). Asexplained by Mäkelä et al. 2011, the formation of a fast-modeshock occurs in front of the CME when the CME speed rel-ative to the ambient medium exceeds the local Alfvén speed.Thus, the particle acceleration in the CME-driven shocks in thecorona and IP space can be a ff ected by the variations in theCME speed due to evolution of the propelling Lorentz and aero-dynamic drag forces (Gopalswamy et al. 2000; Yashiro et al.,2004; Gopalswamy 2006) and in the Alfvén speed (see, e.g.,Gopalswamy et al., 2001; Mann et al. 2003).The Mach number is an important parameter used to de-termine the strength of shock fronts. Of the several methodsused to calculate the Mach number (e.g., Vinas & Scudder 1986;Gopalswamy et al. 2010; J. C. Kasper’s database ), we use thestandard approach of considering the Alfvén speed, solar wind http: // / shocks / Article number, page 1 of 18 & Aproofs: manuscript no. 39537corr speed, and the CME speed. These three parameters change withheliocentric distance (mostly decreasing), which influences theMach number. Here, the shock forms when the CME speed ex-ceeds the sum of the Alfvén speed and the solar wind speed(Gopalswamy et al. 2010).A good indicator of SEPs accelerated due to coronal and in-terplanetary shocks are type II bursts (Cliver et al., 1999). Thesebursts are caused by electrons accelerated by shocks (see, e.g.,Kahler 1982; Kahler et al. 2000; Cane et al. 2002; Cliver et al.2004; Gopalswamy et al. 2005; Cho et al. 2008). Gradual SEPsare often associated with metric type II bursts (150 to 15 MHz)and are generated close to the Sun ≤ sun (Gopalswamy et al.2009). Other methods of direct detection of shocks are the insitu measurements of the discontinuous jump in density, tem-perature, flow speed, and magnetic field in the solar wind dataGopalswamy et al. 2010.The average speed of CMEs is the widely used parame-ter for correlation studies with the associated SEP peak flux(see Kahler 2001; Vourlidas et al. 2010; Richardson et al. 2014;Richardson et al. (2015); Pande et al., 2018;; Xie et al. 2019).However, Liou et al. 2011 presented the approach of correlat-ing fast-forward shock Mach numbers with the intensity of solarenergetic oxygen (O) and helium-4 ( He) particles at (E > ≈ − ), and obtained a good linear correlation for two SEPevents that occurred on 28–31 October 2003. The results suggestthat the Mach number of IP shocks is one of the primary param-eters controlling the intensity of SEPs measured in the vicinityof the Earth. Ravishankar & Michałek 2020a further investigatedthis approach on a sample of 25 non-interacting CMEs and theirassociated SEPs that occurred during the period 2009–2013, us-ing multiple spacecrafts: the Solar TErrestrial RElations Obser-vatory (STEREO)-A and -B and the
SOlar and HeliosphericObservatory (SOHO) for CMEs, and the
Geostationary Oper-ational Environmental Satellite (GOES-13) for SEPs. Instanta-neous speeds such as the CME maximum speed, Mach numberat CME maximum speed, and CME speed and Mach numberat SEP peak flux were investigated, and better correlations wereobtained compared to the average speed.The main limitation of our work in Ravishankar & Michałek2020a was the small population of the considered CMEs (25events). In the present work we significantly expanded our sta-tistical research with a sample of 38 non-interacting CMEs andtheir associated SEP events near the quadrature configuration ofSTEREO. The CME kinematics were determined using the datafrom STEREO / Sun Earth Connection Coronal and HeliosphericInvestigation (SECCHI) (Brueckner et al. 1995; Howard et al.2008). STEREO / SECCHI data for CMEs was used instead ofSOHO as STEREO o ff ered a larger field of view, and the possi-bility to determine velocities at instances of SEP onset and peakflux, which occur at varied distances from the Sun, with min-imal projection e ff ects. The GOES-13 / Energetic Particle Sen-sor (EPS), part of the
Space Environment Monitor (SEM), wasused to study the associated SEP intensities at three energybands ( >
10 MeV, >
50 MeV, and >
100 MeV). We also consid-ered di ff erent models of the solar magnetic field to obtain accu-rate Alfvén and solar wind speeds. We verified the obtained theMach number with the start and end time of type II radio bursts,which are signatures of CME-driven shocks in the interplanetarymedium. The start and end time of type II radio bursts should beconsistent with instances when the CMEs reach a speed of Mach1. We carefully consider correlations between di ff erent speedsof CMEs and SEP peak fluxes in the three energy channels. Wealso investigated these coe ffi cients for di ff erent subsamples ofevents based on their longitudes (disk, disk-west, disk-east). The important result of this paper is that the Mach number at SEPpeak flux can be very good indicator of peak intensities of SEPs.This good correlation is observed even for eastern limb eventswhere the magnetic connectivity of Sun and the Earth are poor.This article is organized as follows. The data and methodused for the study are described in Section 2. In Section 3 wepresent results of our study. The conclusions and discussions arepresented in Section 4. Fig. 1.
Heliographic locations of the solar flares associated with 38 non-interacting CMEs generating SEPs.
2. Data and method
In our study we used observations from the STEREO / SECCHItelescopes, and employed the technique to determine the instan-tanous speed of CMEs (Ravishankar & Michałek 2020a). In thefollowing subsection we describe the method we used for ourstudy.
In our study we concentrate only on CMEs generating SEPevents. On further investigation the events were classifiedinto halo (width = ◦ ) and partial-halo (width > ◦ ) CMEsby the SOHO / LASCO CME catalog (Yashiro et al., 2004,Gopalswamy et al., 2009). These events are better observedfrom STEREO instruments during their quadrature configuration(Bronarska & Michalek 2018). We constricted the event sam-ple to the period of ascending phase of solar cycle 24 (i.e.,2009–2013) as it marks the approximate quadrature configura-tion of STEREO. The twin spacecrafts STEREO-A and -B areat ≈ ◦ separation with respect to the Earth. This position waschosen as it o ff ered advantages in the accurate determination ofplane-of-sky speeds, which are close to the true radial speed ofhalo CMEs with insignificant projection e ff ects. The data fromthe STEREO / SECCHI coronagraphs COR1 and COR2, and theheliospheric imagers HI1 and HI2 can be obtained from the
UKSolar System Data Centre (UKSSDC) database; they were usedto perform manual measurements of height–time data points todetermine the speed of CMEs. We focused our study on non-interacting CMEs as the velocities of interacting CMEs could bechanged unpredictably along its propagation in the interplane-tary medium. Each event in our sample was checked in the im- cdaw.gsfc.nasa.gov / CME_list https: // / solar / stereo / data.htmlArticle number, page 2 of 18nitha Ravishankar and Grzegorz Michałek: Relationship between solar energetic particle intensities and coronal mass ejection kinematics usingSTEREO / SECCHI field of view V e l o c i t y [ k m s - ] | | | | | | | | 1 10 20 30 40 50 60 70Distance [R SUN ]N17W66 T MAX =2012/03/13T18:22:00V
MAX = 2397km s -1 R MAX = 12.3R
SUN ______
10 MeV Protons ______
Velocity ______
50 MeV Protons ______
100 MeV Protons ______
Mach Number _ _ _ _ V A +V SW ............ Mach Number=1 ........................
Start and end Type II I on s [ c m - s - s r - ] ............ Max Flux of 10MeV V e l o c i t y [ k m s - ] | | | | | | | 1 10 20 30 40 50 60Distance [R SUN ]N09E89 T MAX =2011/09/22T11:22:00V
MAX = 1587km s -1 R MAX = 5.22R
SUN ______
10 MeV Protons ______
Velocity ______
50 MeV Protons ______
100 MeV Protons ______
Mach Number _ _ _ _ V A +V SW ............ Mach Number=1 ........................
Start and end Type II I on s [ c m - s - s r - ] ............ Max Flux of 10MeV
Fig. 2.
13 March 2012 event located at the west limb (left panel) and 22 September 2011 event located at the east limb (right panel). The plotshows the CME speed from STEREO (black line) with error bars, SEP flux in the >
10 MeV energy band (red line), >
50 MeV energy band (blueline), and >
100 MeV energy band (green line). The sum of Alfvén and solar wind speed [V A + V SW ] (dashed orange line) and the scaled Machnumber (orange line) are shown. The start and end times of the associated type II burst are added (dotted cyan line). The CME maximum velocity[V MAX ] and time [T
MAX ] and the distance at CME peak velocity [R
MAX ] (dotted black line) at V
MAX , SEP peak flux in the >
10 MeV energy band(dotted red line), and the scaled Mach number = ages from both of the twin satellites so that the measurementswere done from the images that showed better quality.The SEPs associated with the CMEs were selected in the >
10 MeV, >
50 MeV, and >
100 MeV energy bands. The eventswith flux value ≥ >
10 MeV, ≥ >
50 MeV,and ≥ >
100 MeV energy bands were considered forthe study as their proton flux is higher than the average back-ground flux. The threshold value for >
100 MeV is changedto ≥ ≥ ff erences in generation of SEP fluxes with respect tothe location of event eruption. Hence, we investigate these dif-ferences further in this article. The data from the SEM instru-ment on board the GOES-13 geostationary satellite recorded inthe National Oceanic and Atmospheric Administration (NOAA)database was used to analyze the SEP fluxes. Source locationsof CMEs were obtained from associated X-ray flares using theHinode Flare Catalogue (Watanabe et al., 2012), and are shownin figure 1. The properties of the DH type II bursts that aresignatures of these CME-driven shocks can be obtained fromthe WIND / Waves and STEREO database of (Bougeret et al.,1995).During the quadrature configuration of STEREO (2009 -2013) we found 61 SEP events with the above-mentioned cri-teria for their fluxes, but we could only analyze 38 among themdue to limitations with their associated CMEs. We observed 15interacting CMEs, 5 CMEs erupting on the backside of the Sun,and 3 CMEs that are too weak from which we could not ob-tain su ffi cient height–time data points for the analysis. Of the 38events in the sample, 19 events (50%) originate at the disk center(-20 ◦ < longitude < ◦ ), 12 events (31%) at the west limb (lon-gitude > ◦ ), and 7 events (18%) at the east limb (longitude < -20 ◦ ). The majority of the observed events originate at the westlimb and disk center, and only a few on the east limb. This isdue to the magnetic connectivity of Sun with the Earth, whichis explained in detail in the following subsections. It is worthnoting that the presented sample of events are the complete list https: // satdat.ngdc.noaa.gov / sem / goes / data / avg / https: // hinode.isee.nagoya-u.ac.jp / flare_catalogue / https: // cdaw.gsfc.nasa.gov / CME_list / radio / waves_type2.html of non-interacting halo or partial halo CMEs that generate SEPswith the above-mentioned flux values in the three energy bandsduring the period 2009 - 2013, which also marks the ascendingphase of solar cycle 24. A summary of these 38 events is given inTable 6. The data presented in the table and explained in figure2 are the basis of our study. They are explained in detail in thefollowing sections.The SEPs generated by the backside CMEs are of particu-lar interest. Gopalswamy et al. 2020 demonstrated that backsideCMEs can produce significant fluxes of energetic protons. In ourresearch we found five such events. A thorough analysis of theirassociated active region on the Sun allowed us to determine thesource location of the backside CME responsible for the produc-tion of energetic particles. Two of them (28 January 2011 and 23July 2012) were located just over the edge of the solar disk, butthe other three (21 March 2011, 04 June 2011, and 08 Novem-ber 2012) were located as far as ≈ ◦ behind the west limb ofthe Sun. This means that SEPs can be produced from sources lo-cated not only in the visible part of the Sun’s disk, but even veryfar ( ≈ ◦ ) beyond the east (Gopalswamy et al. 2020) and west(our study) limb of the disk. These results demonstrate the abil-ity of backsided events to cause space weather e ff ects at Earth,and therefore accurate predictions of SEPs will need to includesuch events. The average speed determined using the linear fit method in theSTEREO field of view is not a good indicator of CME kine-matics as the speed varies significantly during its propagation inthe interplanetary medium (Ravishankar and Michałek 2019).Therefore, it is important to study other parameters that donot o ff er approximate relations. Ravishankar & Michałek 2020apresented the first set of results on comparative studies on av-erage speeds and instantaneous speed to determine which ofthese parameters o ff ers an accurate correlation with the peakfluxes of the associated SEPs. The results show that instanta-neous speeds such as the maximum speed and speed at SEPpeak flux o ff er better correlation. In addition, the Mach num-ber at CME maximum speed and the Mach number at SEP Article number, page 3 of 18 & Aproofs: manuscript no. 39537corr peak flux showed promising results. The comparative study ofSOHO / Large Angle and Spectrometric Coronagraphs (LASCO)and STEREO / SECCHI for CMEs shows that the correlationobtained for STEREO is much higher as its quadrature con-figuraturion point of view helped with accurate measurementsof true radial speed of halo events, whereas these halo eventsare subject to significant projection e ff ects by SOHO / LASCO(Bronarska & Michalek 2018). In this paper we follow the samemethod, but unlike Ravishankar & Michałek 2020a the studyuses the full STEREO / SECCHI suite of instruments with com-pletely new measurements of height–time data points. To ob-tain the instantaneous velocities we applied linear fits to fivesuccessive height–time points. By shifting the linear fits pointby point through all of the height–time points we acquired theinstantaneous CME speeds. Practically, two successive height–time points are su ffi cient to determine the speed, but as manualmeasurements are subject to unpredictable random errors, weused five successive points to obtain the most reasonable results.Details of this method are described by Bronarska & Michalek2018 in their article. If we have the instantaneous velocities ofCMEs, we could determine the instantaneous Mach numbers andother interesting kinematic parameters of CMEs.In figure 2 two CME events (13 March 2012 and 22 Septem-ber 2011) and their associated parameters varying with time anddistance are presented separately. These panels demonstrate theparameters considered in our study in relation to SEP fluxes. Forcomparison we present diagrams for a western disk event (leftpanel) and an eastern limb event (right panel). The figure showsthe instantaneous CME speeds (with error bars) obtained frommanual measurements of STEREO data (errors were obtainedusing the bootstrap method (Michalek et al. 2017)). The valuesof the maximum velocity (V MAX ) and the time (T
MAX ) and dis-tance at (R
MAX ) are shown on the right corner of the figures. Thepeak fluxes of the SEPs in the respective energy channels aredetermined. The start and end time of the type II burst repre-sents the CME-driven shock, obtained from WIND / Waves andSTEREO database, are shown as the two vertical dotted cyanlines, respectively.The propagation times for accelerated protons to reach theEarth vary in the considered energy range. SEPs take 69 ( > >
50 MeV), and 22 ( >
100 MeV) minutes to reachthe Earth. Their detection is formally delayed by about an hourcompared to the observations carried out by coronagraphs as thismeans that the slowest protons arrive one hour later than light.The delay is about 10 minutes less because the peaks of SEPsare reached when the CMEs are at some distance from the Sun.This delay has been taken into account in figure 2 and in ourconsiderations. However, for the consideration of the relation-ship between SEP flux peak and the maximum CME speed, thisproblem is completely negligible. This e ff ect can only be rel-evant to the correct determination of the speed of CME at SEPpeak. As can be seen in figure 2 (dotted red line), this speed is de-termined at some distance from the Sun, where its change is veryslow. The CME, after reaching maximum velocity, propagates atalmost constant speed. In one hour the CME velocity can changeby not more than 5%. On the other hand, the error in determiningthe speed using a linear fit is about 15% (Michalek et al. 2017).Therefore, we could neglect this e ff ect in our study.Mach number, which is the most important parameter con-sidered in our study, mostly depends on the magnetic field anddensity of the plasma. We investigated two methods of calculat-ing the magnetic field needed to determine the Alfvén speed. TheDulk and McLean (1978) method determines the coronal mag-netic field above active regions when the CMEs erupt, which is more common during the ascending phase of the solar cycle. TheLeBlanc et al., (1998), Mann et al. (1999), Gopalswamy et al.,(2001), and Eselevich and Eselevich (2008) method is applica-ble to determining the magnetic field for quiet regions, mainlyrelated to prominence eruptions, usually during the descend-ing phase of the solar cycle. Using these two methods andthe plasma density model by LeBlanc et al., (1998), we deter-mined the Alfvén speed for each considered event. Our analy-sis shows that a much better prediction was obtained with theDulk and McLean (1978) model as it matches the time framechosen for study (i.e., ascending phase of solar cycle 24), thusin our further considerations we employed the Alfvén speed ob-tained from this model. The solar wind speed was determinedusing the model presented by Sheeley et al., (1997). Having de-termined the Alfvén speed (V A ) and solar wind speed (V S W ),along with the measured instantaneous CME speed (V
CME ), wecan simply determine the instantaneous Mach number (M A ): M A = V CME / (V A + V S W ). The estimated sum of V A + V S W is shownin both panels of figure 2 as dashed orange line and the Machnumber (scaled by 600 for better visualization) is represented bythe continuous orange line. The horizontal dotted orange line (at600 km s − ) reflects the value of Mach number equal to 1. Thesignificance of Mach number is explained in detail in section 3.5.The important factors that determine the peak intensitiesof these accelerated particles are the CME ejection speed andtheir magnetic connectivity with the Earth. West limb events(longitude = ◦ ) have the best connectivity, and this decreases aswe move towards east and to the farther western limb (longitude > ◦ ). Due to this variation in connectivity along the solar disk,we observe delays in the time at which the SEPs reach maximumintensity with respect to the onset of the associated CMEs. Forwell-connected events, the SEPs reach peak fluxes quickly afterthe CME onset and maximum velocity from the Sun (see leftpanel of figure 2) and the delay increases in the case of easternevents as the ejections must expand enough so that their frontsare well connected magnetically to the Earth (right panel of fig-ure 2). Similar delays in both distance and time are observedbetween the maximum Mach number and SEP peak flux. Conse-quently, when the CME expands, its speed decreases. This meansthat when we observe the maximum intensities of energetic par-ticles, especially for eastern events, the ejection speed may bemuch lower than their maximum value. The V A and V S W aremuch lower at these points as they decrease slowly with distance(r), but as V
CME decreases signifcantly the observed Mach num-bers are consequently lower as well. To be precise, we observe aMach number < ff ects. According to Bronarska & Michalek2018, the real or space velocity should be V INS + INS , whereV
INS is the measured instantaneous velocity. As we observe theprojected speeds, the Mach number obtained due to these speedsfor limb events is less than 1. It could be also be a result of deter-mination of V A , and depends on the model of the magnetic field,which is not perfect.Interesting observations are made concerning the start andend times of the associated type II bursts shown by the verti-cal cyan lines in figure 2. In the left panel that shows the west-ern event, we observe the onset of type II burst, CME velocity,Mach number, and SEPs approximately at the same time. How-ever for the eastern event shown in right panel, the SEP peakin the >
10 MeV channel is delayed by about 22 hours with re-spect to the CME onset. Among the seven eastern events in oursample, three are not associated with type II bursts as seen inthe database. The remaining four eastern events also display thedelays with respect to the CME onset. The type II bursts, which
Article number, page 4 of 18nitha Ravishankar and Grzegorz Michałek: Relationship between solar energetic particle intensities and coronal mass ejection kinematics usingSTEREO / SECCHI field of view
500 1000 1500 2000Velocity [km s -1 ]0.010.101.0010.00100.00 I on s [ c m - s - s r - ] a)corr= 0.1 0.6 0.9 I on s [ c m - s - s r - ] b)corr= 0.27 0.75 0.91
400 600 800 1000 1200 1400 1600Velocity [km s -1 ]0.010.101.00 I on s [ c m - s - s r - ] c)corr= -0.3 -0.3 -0.4 I on s [ c m - s - s r - ] d)corr= -0.36 -0.40 -0.48 Fig. 3.
Plots showing correlation between instantaneous velocity and Mach number vs SEP flux for the 13 March 2012 event (panels a and b) andthe 22 September 2011 event (panels c and d). are signatures of CME-driven shocks, do not depend on the mag-netic connectivity of the Sun and Earth; instead, the SEP prop-agation is a ff ected by the connectivity. For the eastern eventsthe determined CME speed and Mach number are lower by 50%(Bronarska & Michalek 2018) and we observe significant delaysin the SEPs. The SEP fluxes for eastern events are among thelowest in our sample, and probably much higher fluxes of ener-getic particles were produced earlier that could not be detecteddue to poor connectivity. We observe that the type II bursts startwhen the Mach number reaches 1 and end when the Mach num-ber goes back to 1 for all events. Therefore, type II bursts aregood indicators of production of large SEP fluxes. These delaysare discussed in detail in section 3.4. In addition, we observe thedecline of the >
10 MeV protons at the end of the type II burstsin the left panel, but in the right panel we see that the onset ofthe SEPs is well beyond the end of the radio bursts. This maybe due to the threshold of observations of the instrument mea-suring the DH type II bursts. The bursts may have prolonged fora longer time, but in the reduced intensity, which the instrumentwas unable to measure.Figure 3 shows the correlation between instantaneous veloc-ity and Mach number versus instantaneous fluxes of SEP in thethree energy bands, >
10 MeV, >
50 MeV, and >
100 MeV in red,blue, and green, respectively. Panels a and b represent the west-ern disk event on 13 March 2012, and panels c and d representthe eastern limb event on 22 September 2011; their correlationsare shown in the bottom left of the figure for the respective en-ergy bands. We observe perfect positive correlations in panelsa and b, and anticorrelation in panels c and d. Furthermore, thecorrelation and anticorrelation tends to 1 and -1, respectively,for the higher energy bands compared to the lower energy bandfor both the velocity and Mach number parameter with the SEPfluxes. These di ff erences in correlation for the two events are ob-served due to varying delays caused by magnetic connectivity ofthe Sun and Earth with respect to the longitude, as explained ear-lier. These delays can be clearly seen in figure 2, and is observedfor SEPs in all three considered energy bands. For this reason weobserve the western events showing positive correlation (panelsa and b) and the eastern events showing anticorrelation (pan-els c and d). Additionally, the correlation of the instantaneousMach number with SEP fluxes, shown in panels b and d, o ff ersimproved correlation compared to the instantaneous velocities.This shows that for studying the acceleration of particles drivenby the CME the Mach number is the best parameter to consider. A detailed analysis of this is dicussed in section 3.5. It is impor-tant to note that significant correlations are observed for > >
10 MeV SEP fluxes (panels a and b). This isdue to the larger delay between the SEP and maximum velocityor maximum Mach number for >
10 MeV compared to higherenergetic particles. Therefore, few points from the initial phaseof propagation decreases this correlation compared to higher en-ergies.The results presented in figures 3 and 4 are the basis ofour study, and are summarized in Table 6. In columns 2-6 wehave date and time, average velocity (V
AVG ), maximum velocity(V
MAX ), distance (R
MAX ), and time (T
MAX ) at V
MAX of a givenCME taken from the STEREO / SECCHI observations. Columns7-9 show the peak SEP fluxes in the three energy channels. Thenext three columns present CME speeds at peak SEP fluxes forthese energy channels. Columns 13-15 give the maximum Machnumber (M
MAX ) and distance (MR
MAX ) and time (MT
MAX ) atM
MAX of a given CME. Columns 16-18 show the Mach numberat maximum SEP peak flux in the three energy channels. The lo-cation of solar flares associated with CMEs from the GOES datais shown in column 19. The start and end times of the associatedtype II burst are shown in the last two columns.For all the considered correlation coe ffi cients in the studywe tested their significance. These tests confirmed (with a sig-nificance level of p = ff er-ence between a pair of correlation coe ffi cients. These tests con-firmed that (with a significance level of p = ffi cients are not significantly di ff erent from eachother. The statistical values are shown in Tables 1, 2, 3, 4, and 5.
3. Analysis and results
Our article focuses on recognizing how di ff erent kinematic pa-rameters of CME a ff ect the generation of SEP events. In ourstudy we use the STEREO instruments; they allow us to trackCMEs to very long distances from the Sun, which is importantbecause the SEPs are generated by the shocks driven by CMEsup to the orbit of the Earth and beyond. The results of the studyare presented in following sections. Article number, page 5 of 18 & Aproofs: manuscript no. 39537corr
200 400 600 800 1000 1200 1400 1600Average velocity [km/s ]0123456 F r a c t i on
500 1000 1500 2000 2500 3000Maximum velocity [km/s ]02468 a) b)
Min=345Max=1277Median=667Average=701 Min=524Max=2627Median=1598Average=1567
Fig. 4.
Distributions of average (panel a) and maximum (panel b) velocity and the time (T
MAX , panel c) and distance (R
MAX , panel d) when CMEsreach maximum velocity.
Fig. 5.
Distributions of time taken by SEPs to reach peak flux after the onset of the CME (panels a, b, and c) and distance at which the SEPs reachpeak flux (panels c, d, and e) in three energy channels ( >
10 MeV [SEP T MAX , R
MAX ], in red), ( >
50 MeV [SEP T MAX , R
MAX ], in blue), and( >
100 MeV [SEP T MAX , R
MAX ], in green).
The CME speeds can be determined in di ff erent ways. A linearfit of the height–time measurements can be useful for determin-ing an average CME speed, but will fail to capture the signifi-cant changes in velocity that can occur during CME expansion;therefore, in our considerations we use the speeds determined inour new approach. These speeds were described in section 2.2.In figure 4 we present histograms comparing the values of aver-age and maximum velocities in panels a and b, respectively. Theconsidered CMEs in our sample have an average speed range of345 to 1277 km s − and a maximum speed range of 524 to 2627km s − . On average, the maximum speeds in the STEREO fieldof view are 223% larger than the speed obtained from linear fitsto all height–time points (average speeds). This clearly showsthat the average speeds in the STEREO field of view are not prac-tical for studies. Panels c and d of figure 4 show the time (T MAX )and distance (R
MAX ) when CMEs reach maximum velocity, re-spectively. The CMEs in our sample have a range of 18 to 187minutes at a distance in the range 2.63–13.04 R sun to reach maxi-mum velocity. Therefore, on average, they take about 68 minutesat 6.38 R sun distance to reach maximum velocity. Instead, the re-sults obtained in Ravishankar & Michałek 2020a with 25 eventsshow that the CMEs, on average, take about 60 minutes at 7.61R sun distance to reach maximum velocity. It is worth noting that the CMEs achieve maximum velocity very close to the Sun, butSEP peak fluxes could be observed when CMEs have propagatedvery far away from the Sun. This discrepancy is described in thenext subsection. Thus, for the purposes of SEP generation, de-termining speeds closer to the Sun are more important for pre-dicting what is seen at the Earth.A comparison of the errors determined from the stan-dard deviation for average values of T
MAX and R
MAX for thesamples considered in our papers show < T MAX >= ± < R MAX >= ± < T MAX >= ± < R MAX >= ± The relationship between the CME onset and the SEP peakfluxes are shown in figure 5. Panels a, b, and c show the timetaken by the SEPs to reach peak flux after the onset of the CME
Article number, page 6 of 18nitha Ravishankar and Grzegorz Michałek: Relationship between solar energetic particle intensities and coronal mass ejection kinematics usingSTEREO / SECCHI field of view
Fig. 6.
Scatter plot of longitude of the solar flare associated with the respective CMEs vs SEP peak flux (left panel) and the time and distance atwhich SEPs reach peak flux (right panels). Colors are assigned to the SEPs in the energy channels: >
10 MeV (red), >
50 MeV (blue), and > and panels d, e, and f show the distance at which the SEP peakfluxes are observed. On average, all the events in our consid-ered sample take 655, 523, and 500 minutes and at a distanceof about 41.9, 35.0, and 32.6 R sun in the > >
50, and > sun in the > > >
100 MeV energy bands, respectively, to reach peak fluxes.Disk events, on average, take 626, 485, and 470 minutes and at adistance of about 40, 32, and 30 R sun in the > >
50, and > sun in the > >
50, and > ◦ < longitude < ◦ ), west limb (longitude > ◦ ), and east limb (longitude < -20 ◦ ). A modest trend is observed in the plot where the higher in-tensity SEPs seem to originate in the west limb and this intensitygradually reduces as we move towards the east limb. This grad-ual decrease in peak intensity is seen clearly for >
10 MeV pro-tons. The trend similar to >
10 MeV protons is also seen for > >
100 MeV protons at longitudes greater than 0 ◦ , but at lon-gitudes less than 0 ◦ ; their peak fluxes are constant and lie in therange 0.1-1 cm − s − sr − (i.e., moving towards the east). Theseare a consequence of the magnetic connectivity of Sun and Earth(i.e., Parker spiral IMF) (Marsh et al. 2013). West limb eventsare well connected to the Earth, and this connectivity decreasesas we move towards the east limb. In addition, Dalla et al. 2017aand Dalla et al. 2017b have pointed out that the SEP propagationis a ff ected, also due to the drifts caused by the gradient and cur-vation of the Parker spiral IMF, with their importance increasingwith the energy of the particle. The peak flux of >
50 and > >
100 MeV protons take less time and distanceto reach peak flux and >
10 MeV protons take more time andare observed at farther distances away from the Sun. The samedelays are represented in figure 6 (right panels) varying with lon-gitude. An explanation provided by Reames 2020 tells us that thedistinction between impulsive and gradual SEP events becomesunclear as the CME-driven shock waves can reaccelerate the im-pulsive ions pre-accelerated in the magnetic reconnection. Theimpulsive suprathermal seed ions are preferentially acceleratedby shock waves at active regions, and can even be dominatedand reaccelerated SEPs produced by weaker shocks (Desai et al.2003; Tylka et al. 2005; Tylka & Lee 2006). Thus, the higher en-ergy ions we observe are most likely pre-accelerated in the mag-netic reconnection close to the Sun and are further seeded intoreacceleration by CME-driven shocks at farther distances fromSun. For this reason, we observe the >
50 and >
100 MeV protonsreaching peak fluxes much earlier than >
10 MeV protons.
With the above introduction to the fundamental properties of theCMEs and the associated SEPs, we proceed to the main aim ofthe article, which is to investigate the best velocity parameterto study the acceleration of SEPs to their peak intensities. Wechose the average, the maximum, and the CME velocity at SEPpeak flux to analyze their correlation with SEP peak fluxes, asshown respectively in panels a, b, and c of figure 7. Linear fitsare suitable for all the scatter plots, and their formulae are shownin the left corner of the figures. In addition to dividing the sampleinto disk center, west, and east limb events, we also classify thesample into disk + west, disk + east, and disk-only events to studythe variation of their correlations. The correlation coe ffi cientsand their probability values (significance at p-value < > >
50, and >
100 MeV energy channels,respectively, for all events) and the least correlation compared topanels b and c. As explained in detail in the first paragraph ofsection 3.1, the average velocity may not be the best parameterto consider for correlation studies (Ravishankar and Michałek2019, Ravishankar & Michałek 2020a). Therefore, this leads toutilizing instantaneous velocities for accurate correlation studies
Article number, page 7 of 18 & Aproofs: manuscript no. 39537corr
400 600 800 1000 1200
Average velocity [km/s] −2 S o l a r E n r g t i c P a r t i c l s p a k f l − x ( / c m s s r ) a) y=-0.57+0.002xy=-1.57+0.002xy=-1.75+0.0001x Filled, West EventsUnfilled, Disk EventsVline, East Events
500 1000 1500 2000 2500
Maximum velocity [ m/s] −2 −1 b) y=-0.37+0.001xy=-1.49+0.001xy=-1.71+0.0007x Filled, West EventsUnfilled, Disk EventsVline, East Events
250 500 750 1000 1250 1500 1750 2000
CME velocity at SEP peak flux [km/s] −2 −1 c) −=-0.56+0.002xy=-1.20+0.001xy=-1.41+0.0001x Filled, West EventsUnfilled, Disk EventsVline, East Events Fig. 7.
Scatter plots of the average velocity (panel a), maximum velocity (panel b), and the CME velocity at SEP peak flux (panel c) vs SEP peakflux in the >
10 MeV (red), >
50 MeV (blue), and >
100 MeV (green) energy channels. The open symbols represent disk events (longitude -20 < L <
45) and the filled symbols represent west events (longitude >
45) and vertical lines represent east events (longitude < -20). Table 1.
Correlation coe ffi cients of CME velocities vs SEP peak flux and their probabilities (significance at p-value < a) Average velocity Energy channel All events(38) p-value Disk + West(31) p-value Disk + East(26) p-value Disk events(19) p-value East events(7) p-value >
10 MeV 0.69 .00001 0.68 .000026 0.74 .000016 0.74 .000292 0.71 .073861 >
50 MeV 0.61 .000048 0.63 .000146 0.67 .000181 0.76 .000159 0.0014 .997623 >
100 MeV 0.57 .000187 0.59 .000477 0.66 .000244 0.76 .000159 0.14 .764651b) Maximum velocity >
10 MeV 0.70 .00001 0.74 .00001 0.68 .000133 0.73 .000388 0.24 .604195 >
50 MeV 0.68 .00001 0.72 .00001 0.64 .00043 0.72 .000509 0.29 .528119 >
100 MeV 0.63 .000023 0.67 .000037 0.63 .000562 0.73 .000388 0.06 .898324c) CME velocityat SEP peak flux >
10 MeV 0.77 .00001 0.77 .00001 0.81 .00001 0.82 .00001 0.66 .106682 >
50 MeV 0.73 .00001 0.72 .00001 0.83 .00001 0.87 .00001 0.24 .604195 >
100 MeV 0.71 .00001 0.70 .00001 0.75 .00001 0.79 .000057 0.52 .231562 and also to studying SEP peak fluxes that are attained at fartherdistances away from the Sun.Figure 7, panel b, shows a good correlation (0.70, 0.68, and0.63 for the > >
50, and >
100 MeV energy channels, respec-tively, for all events) between CME maximum velocity and SEPpeak intensities. This parameter is good, but not the best to usewhile studying a sample comprising events originating at all lo-cations on the Sun. The west and disk events can be studied wellwith maximum velocity as they have good magnetic connectiv-ity to the Earth, but the CMEs originating in the eastern longi-tudes are poorly connected to Earth, which leads to a delay inSEP peak flux with respect to CME maximum speed (as shownin figure 2). Therefore, a better approach to studying all CMEs,irrespective of their location, is to use CME velocity at the SEPpeak flux. The fluxes of energetic particles are produced duringthe entire CME passage to the Earth, so it is also important todetermine their velocities during the same distance, if possible.Investigation of this parameter has improved the correlation asshown in panel c (0.77, 0.73, and 0.71 for the > >
50, and >
100 MeV energy channels, respectively, for all events).A comparison of the correlation coe ffi cients for the subdi-vided events according to their location, presented in Table 1,shows the best correlation for events located at disk center, thenext best for events located at disk + east, and last for disk + west events. These subdivisions give us an even more clear under-standing of the magnetic connectivity of the Sun and Earth atdi ff erent longitudes. In addition we observe that the correlationcoe ffi cient decreases with increasing energy band, meaning that >
10 MeV protons are best correlated and >
100 MeV protons areleast correlated for all the considered velocity parameters. Forall considered subsamples, the correlation coe ffi cient are highlysignificant (probability > > ffi cients shown in the figures.Ravishankar & Michałek (2020a) comprised a sample of 25events with 1 eastern event, whereas the current work comprises38 events with 7 eastern events. The number of eastern eventsare particularly highlighted here because significant delays inobservations of the peak fluxes are seen for these events due totheir poor magnetic connectivity. For this reason there are no-table changes to the overall correlation and the fits applied. Theaverage velocity versus SEP peak flux display the previous pa-per results (slope = = Article number, page 8 of 18nitha Ravishankar and Grzegorz Michałek: Relationship between solar energetic particle intensities and coronal mass ejection kinematics usingSTEREO / SECCHI field of view
Fig. 8.
Scatter plots showing distance at CME maximum velocity (left panel) and distance at CME maximum Mach number (right panel) vsdistance at SEP peak flux in the >
10 MeV (red), >
50 MeV (blue), and >
100 MeV (green) energy channels.
Table 2.
Correlation coe ffi cients of parameters and their probabilities (significance at p-value < SEP R
MAX vsCME velocity R
MAX
Energy channel All events(38) p-value Disk + West(31) p-value Disk + East(26) p-value Disk events(19) p-value East events(7) p-value >
10 MeV 0.15 .36872 0.24 .193445 0.21 .303165 0.34 .154372 0.22 .635489 >
50 MeV 0.02 .90513 0.09 .630171 0.07 .734011 0.17 .486556 0.11 .814386 >
100 MeV -0.03 .858099 0.03 .87272 0.03 .884332 0.13 .595802 0.11 .814386SEP R
MAX vs CME Mach R
MAX >
10 MeV 0.62 .000033 0.50 .004181 0.65 .000325 0.44 .059404 0.22 .635489 >
50 MeV 0.56 .000256 0.50 .004181 0.51 .007775 0.31 .196488 0.11 .814386 >
100 MeV 0.50 .001391 0.43 .015761 0.45 .021073 0.20 .411681 0.10 .831082 > > >
100 MeV, respectively) and the cur-rent paper results (slope = = -0.57, -1.57, -1.75 for > > >
100 MeV, respectively). Themaximum velocity versus SEP peak flux display the previouspaper results (the second order quadratic equation coe ffi cientsa = -7.205e-07 and b = = -2.846 for > = = > >
100 MeV, respectively) and the current paper results(slope = = -0.37, -1.49, -1.71for > > >
100 MeV, respectively). Lastly, the CME veloc-ity at SEP peak flux versus SEP peak flux show the previouspaper results (slope = = -0.34,-1.14, -1.35 for > > >
100 MeV, respectively) and the cur-rent paper results (slope = = -0.56, -1.20, -1.41 for > > >
100 MeV, respectively). Allthree comparisons show that the slopes do not exhibit much vari-ation, but the values at which the fit intercepts the y-axis are farlower in the current paper.
Mach number (M A ) is one of the most significant parametersdetermining the e ffi ciency of acceleration of particles in theshock vicinity (Li et al. 2012a, Li et al. 2012b). As explained byGopalswamy et al. (2010) and referenced in section 1, the for-mation of shock occurs when the velocity of the CME (V CME )exceeds the sum of Alfvén (V A ) and solar wind (V S W ) speed(i.e., V A + V S W ) in interplanetary space. The threshold valuefor the onset of SEP is, at M A , equal to 1, where the V CME and V A + V S W are equal. From this point of view, investigatingthe Mach number parameter with the associated SEP intensitiesmust provide better results than the velocities of CMEs. Theseparameters are represented in figure 2. The sum V A + V S W isrepresented as the dashed orange line and the instant at whichthe M A = A = V CME / (V A + V S W ), and mainly varies with thedistance parameter (r) away from the Sun; more specifically, theparameters decrease with distance from the Sun. Near the Sunthe corona holds dense streamers and tenuous regions that varythe magnetic field significantly; therefore, M A may vary signif-icantly (Gopalswamy et al. 2008a) compared to a much fartherdistance in the interplanetary medium away from the Sun. Thedescribed models for estimating the V A are not perfect, hence wemust consider the obtained M A only as an approximate value.In order to choose the Mach number parameter suitable forthe study, we first compared maximum velocity and maximumMach number, and investigated the outcome. In figure 8 wesee the relationship between distance at maximum velocity (leftpanel) and distance at maximum Mach number (right panel) ver-sus distance at SEP peak flux in the considered energy chan-nels. The correlation coe ffi cients and their probability values(significance at p-value < MAX for the three considered parameters should be approxi-mately same and must provide good correlation. But as we see inboth panels, the correlations are insignificant due to the contribu-tion by disk and east events which show delay at the distance at
Article number, page 9 of 18 & Aproofs: manuscript no. 39537corr
Fig. 9.
Distributions of maximum Mach number (panel a), time (Mach T
MAX , panel b), and distance (Mach R
MAX , panel c) at maximum Machnumber of CMEs.
Fig. 10.
Distribution showing the time di ff erence between SEP peak flux and maximum Mach number. Left: panel a for >
10 MeV (red), panel bfor >
50 MeV (blue), and panel c for >
100 MeV (green); Right: Variation of the time and distance delay with longitude. which the SEP attains peak flux. In the left panel we observe thebest correlation for disk events and least good for events locatedat longitudes less than 0, comprising a few disk + east events. Asignificant improvement is seen in the right panel. This is ev-idence that maximum Mach number o ff ers a better correlationfor all the considered events to study the SEP peak fluxes.Figure 9 shows the distribution of maximum Mach number(panel a), and the time (panel b) and distance (panel c) at whichthey reach maximum Mach number. The average value of maxi-mum Mach number of all the events in our sample is about 1.36and, on average, they take about 125 minutes at 12.1 R sun toreach the maximum. On comparing these results with figure 4,we observe that CMEs, on average, take about 68 minutes at 6.38R sun distance to reach maximum velocity. Hence, Mach numbertakes a longer time and farther distance to reach maximum afterthe CME eruption. Here, since the estimation of the Mach num-ber depends on the V A and V S W models along with V
CME , such di ff erences are seen. The CME speed and Mach number are in-dependent of magnetic connectivity. Therefore, it is obvious thatwe do not see any parity in these parameters with longitude. Wecan compare these parameters with similar indicator describingSEP peak fluxes. Panels a, b, and c in the left panel of figure 10show the time taken by the SEPs to reach peak fluxes after themaximum Mach number is attained. We observe that it takes, onaverage, 600, 468, and 445 minutes at a distance of about 41,35, and 32 R sun to reach peak intensities in the > >
50, and >
100 MeV energy bands, respectively. Panel c shows that the >
100 MeV protons take less time to reach peak fluxes comparedto the >
10 MeV protons, as shown in panel a. The same trendis observed for delay in distance. Similar conclusions to thoseshown in figure 5 can be drawn from these results. Based ontheir magnetic connectivity, as explained in detail in section 3.1,we observe the events located at the eastern limb exhibit moredelay in time and distance, and this decreases as we move to-
Article number, page 10 of 18nitha Ravishankar and Grzegorz Michałek: Relationship between solar energetic particle intensities and coronal mass ejection kinematics usingSTEREO / SECCHI field of view
Maximum Mach number −2 S o l a r E n e r g e t i c P a r t i c l e s p e a k l − x ( / c m s s r ) y=-0.38+1.18xy=-1.38+0.99xy=-1.58+0.73x Filled, West EventsUnfilled, Disk EventsVline, East Events 0.5 1.0 1.5 2.0 2.5 Mach number at SEP pea flux −2 −1 y=-0.41+1.60xy=-1.26+1.12xy=-1.43+0.78x Filled, West EventsUnfilled, Disk EventsVline, East Events Fig. 11.
Scatter plot of maximum Mach number (left panel) and Mach number at SEP peak flux (right panel) vs SEP peak flux in the >
10 MeV(red), >
50 MeV (blue), and >
100 MeV (green) energy channels. The open symbols represent disk events (longitude -20 < L < > < -20). Table 3.
Correlation coe ffi cients of parameters and their probability (significance at p-value < Maximum Mach number Energy channel All events(38) p-value Disk + West(31) p-value Disk + East(26) p-value Disk events(19) p-value East events(7) p-value >
10 MeV 0.83 0.00001 0.85 0.00001 0.82 0.00001 0.85 0.00001 0.53 0.221096 >
50 MeV 0.72 0.00001 0.75 0.00001 0.72 0.000034 0.80 0.000039 0.004 0.993209 >
100 MeV 0.65 0.00001 0.67 0.000076 0.64 0.00043 0.72 0.000509 0.24 0.604195Mach number at SEP peak flux >
10 MeV 0.85 0.00001 0.86 0.00001 0.83 0.00001 0.85 0.000034 0.71 0.073861 >
50 MeV 0.77 0.00001 0.78 0.00001 0.79 0.00001 0.86 0.00001 0.08 0.864622 >
100 MeV 0.71 0.00001 0.72 0.00001 0.72 0.000034 0.79 0.000057 0.34 0.455574 wards the western limb. This means that maximum Mach num-ber is not related very significantly with SEP peak flux, espe-cially for magnetically poorly connected events. Therefore, it isreasonable to analyze the instantaneous Mach number at SEPpeak fluxes. These parameters should be best correlated withSEP peak fluxes and should not depend on the source locationof CMEs.We restrict our analysis to using instantaneous parameters ofMach number to study their correlation with SEP intensities. Aspreliminary evidence seen in Ravishankar & Michałek (2020a),the properties of the Mach number shows better correlation withSEP peak intensities. We further investigate in detail this instan-taneous parameter with a larger number of events in our sample.We observe reduced correlation for maximum Mach number ver-sus SEP peak flux (left panel) compared to the Mach numberat SEP peak flux versus SEP peak flux (right panel) of figure11 as shown in Table 3. The reduction in correlation coe ffi cientand its significance is much more prominent while consideringeast events. This is an important result as the comparison showsthat in order to study the correlation between CMEs and the as-sociated SEP peak flux, the best parameter to consider is theMach number at SEP peak flux. The maximum Mach numberis suitable for events magnetically well connected to the Earth asthe delay between the peaks of Mach number and SEP flux arenot higher or rather are appropriate according to their propaga-tion. Hence the SEP peak flux that we observe is accurate. Butfor events originating in the eastern longitudes the instances atwhich we observe the peaks are not accurate as they are poorly connected. As a consequence, we observe significant delays be-tween peaks of Mach number and SEP flux. For such cases thebest parameter to consider is the Mach number at SEP peak flux,and we observe high correlations in the right panel of figure 11.The optimum correlation is observed for events located at diskcenter (i.e., -20 < longitude <
45) that are well connected to theEarth. Thus, the Mach number parameter does better than CMEvelocities for eastern SEP events with energies >
10 MeV. Thecoe ffi cients of the linear fits do not display notable di ff erences,but the fits are steeper in the right panel compared to the leftpanel of figure 11. The y-intercepts do not show any significantchange.While comparing the use of the instantaneous parameters,CME speed and Mach number at SEP peak flux, the latter provesto be a better parameter as it shows higher correlation coe ffi cient.This is evident as Mach number takes into account the major pa-rameters (V CME , V A , and V S W ) involved in the onset and influ-ence of particle acceleration, whereas CME speed alone lacksthe necessary information for a detailed study. In addition, weobserve in the left panel a Mach number of less than 1 for eightdisk events, which can also be seen in the histogram presentedin figure 9. These events are among the slowest events havingmaximum velocity of about 800 km s − , maximum Mach num-ber of about 0.7, and the associated SEP peak flux of about 5cm − s − sr − in the >
10 MeV band. Hence, the low speed mayhave contributed to the low Mach number. All these events weremeasured using the data from STEREO-A. With respect to therelative position of STEREO-A and the longitude of the event,
Article number, page 11 of 18 & Aproofs: manuscript no. 39537corr
Table 4.
Probability values (significance at p > ff erence between two correlation coe ffi cients presented in Tables 1 and 3. A probabilityvalue of more than 0.05 indicates that the two correlation coe ffi cients are significantly the same. a) Average velocityvsMach number at SEP peak flux Energy channel All events (38) Disk + West (31) Disk + East (26) Disk events (19) East events (7) >
10 MeV 0.08 0.08 0.83 0.38 1.00 >
50 MeV 0.19 0.25 0.69 0.40 0.91 >
100 MeV 0.31 0.38 0.82 0.83 0.76b) Maximum velocityvsMach number at SEP peak flux >
10 MeV 0.03 0.19 0.22 0.35 0.36 >
50 MeV 0.42 0.60 0.28 0.27 0.75 >
100 MeV 0.54 0.71 0.57 0.68 0.67c) Velocity at SEP peak fluxvsMach number at SEP peak flux >
10 MeV 0.32 0.30 0.83 0.77 0.89 >
50 MeV 0.70 0.60 0.69 0.91 0.81 >
100 MeV 1.00 0.88 0.82 1.00 0.75d) Maximum Mach numbervsMach number at SEP peak flux >
10 MeV 0.77 0.88 0.91 1.00 0.67 >
50 MeV 0.63 0.78 0.57 0.58 0.91 >
100 MeV 0.63 0.71 0.61 0.64 0.87 the projection e ff ect may have played a role in the decrease invelocity as the STEREO quadrature configuartion is not perfectfor disk events. An additional cause may be due to the the modelused to calculate the Alfvén speed.Table 4 shows the comparison of probabilty values of thedi ff erence between two correlation coe ffi cients of velocity pa-rameters (Table 1) and maximum Mach number (table 3) versusMach number at SEP peak flux. Inspecting table 4 we have toreject, at significance level p = ff erent. However, wecan consider 1-p, which is the probablility that the respectivecorrelation coe ffi cients are di ff erent. In a few examples (for > + West events in figure 7 panelc) this probability could be very high (1-p > ff erence is signif-icant). The results presented in this paper, showing importanceof Mach at SEP peak flux could be useful for future studies andspace weather prediction.In regards to space weather forecasting, the best CME kine-matic parameter that could be used to predict the SEPs is theMach number at SEP peak flux. As we observe that the Machnumber at SEP peak flux and SEP peak occur at the same time,and agrees with events originating at all longitudes, this could bebest utilized. Fortunately, SEPs are delayed by 69 ( >
10 MeV),31 ( >
50 MeV), and 22 ( >
100 MeV) minutes to reach the Earthwith respect to white light measurements by coronagraph. So atleast for the lower energetic particles that are comparatively slow( >
10 MeV), we can determine the Mach number one hour beforethe SEPs reach the Earth. In figure 2 we have shifted the profilesof the Mach number and the >
10 MeV SEP flux by about onehour to take into account the delay, but in reality we first observethe white light and then we measure the height–time data pointsto determine the Mach number. Therefore, predictions of the ar-rival of lower energetic SEPs to the Earth can be made by thismethod.However, accurate determination of the CME Mach numbermay be di ffi cult for a few reasons. First, the CMEs in consider-ation must be strictly non-interacting throughout their propaga-tion in the interplanetary space as in a CME-CME interaction thekinematics can vary significantly. Interacting CMEs are frequent during solar maximum, hence the application of our methodcould be inaccurate. Next, while the empirical models used inour analysis are satisfactory, the errors on the Mach number de-pend on the models of plasma density and magnetic field as theyare crucial for determining the Alfvén speed. To improve our re-sults we considered two di ff erent models for magnetic field, buta model never reflects perfectly the real scenario, especially formagnetic fields around active regions where most CMEs appear.Hence, a further investigation and better approach is required forthese parameters. Lastly, the SEP peak fluxes are observed tobe achieved at average distances of about R MAX = sun for > >
50, and >
100 MeV particles (figure 5). TheCME associated with the production of SEPs must be su ffi cientlystrong (or rather, not too weak) to be visible in the coronagraphs;farther away from the Sun the CMEs are poorer, making mea-surements di ffi cult and consequently a ff ecting the determinationof the Mach numbers. The errors on the measurements dependon the quality or brightness of the CMEs (Michalek et al. 2017).Hence, one must take into consideration these limitations in realtime prediction of CMEs and their associated SEPs.An important note on SEP fluxes is that it is impossible todetermine their peak flux until after the conclusion of an event at1 AU using the in situ observations, whereas the CME maximumMach number, on average, is attained at distance R MAX = sun (figure 9, panel c). With the help of the linear model pre-sented in figure 11 (left panel), which shows CME maximumMach number versus SEP peak flux, we can obtain the asso-ciated SEP peak flux and the time and / or distance of attainingpeak, which can be ultimately used for Mach number at SEPpeak flux versus SEP peak flux correlation. This proves to be animportant advantage in space weather forecasts, but the deter-mined values must be considered an underestimation due to thelimitations mentioned above. In this section we investigate whether the acceleration param-eters can influence the intensities of the associated SEPs. Fig-ure 12 shows an interesting trend in the variation of the CMEacceleration with heliocentric distance and time for the event
Article number, page 12 of 18nitha Ravishankar and Grzegorz Michałek: Relationship between solar energetic particle intensities and coronal mass ejection kinematics usingSTEREO / SECCHI field of view A cc e l e r a t i on [ m s - ] | | | | | | | 1 10 20 30 40 50 60Distance [R SUN ]S15W01 T
MAX =2012/07/12T16:39:00Acc
MAX = 757.m s -2 R MAX = 2.55R
SUN T MIN =2012/07/12T17:28:00Acc
MIN = -167.m s -2 R MIN = 7.60R
SUN T INF =2012/07/12T19:27:00Acc
INF = 1.20m s -2 R INF = 16.4R
SUN
Fig. 12.
12 July 2012 CME acceleration profile with the active region located at disk center (longitude = MAX , T
MAX , R
MAX ), minimum acceleration (Acc
MIN , T
MIN , R
MIN ), and acceleration at the point of inflection (Acc
INF , T
INF , R
INF ) arepresented in the top right corner. on 12 July 2012. The speed and acceleration of the CME af-ter its eruption increases rapidly as their dynamics are dom-inated by the propelling Lorentz force (e.g., Vršnak 2006;Bein et al. 2011; Carley et al. 2012). This expansion phase endswhen the CMEs reach maximum velocities leading to a dropin their acceleration to zero. At this point the forces actingon the CMEs (i.e., the propelling Lorentz force and the dragforce of the surrounding solar wind) are balanced. This firstphase of CME propagation is called the initial or main ac-celeration. After the maximum speed is reached, the CMEsare gradually slowed down by the ambient medium until theyreach the speed of the solar wind (e.g., Zhang & Dere 2006;Subramanian & Vourlidas 2007; Gopalswamy 2013). This phaseof expansion is called the residual acceleration. Using themethod described by Ravishankar et al. (2020b), the initial ormain acceleration is obtained from the formula
Acc
INI = V MAX
T ime
MAX − T ime
ONS ET , where V MAX is the maximum velocity of a given CME,
T ime
MAX is the time at maximum velocity, and
T ime
ONS ET is the onsettime of a given CME on the Sun. These parameters are obtainedfor each event as shown in figure 2. The initial acceleration isabout 3.7 m s − for the fastest and 145 m s − for the slowestCME, and on average the CMEs have Acc INI of 28 m s − untilthey reach V MAX .The maximum acceleration (Acc
MAX ) and the time and dis-tance at Acc
MAX (T MAX , R
MAX ), and the minimum acceleration(Acc
MIN ) and the time and distance at Acc
MIN (T MIN , R
MIN ) arerepresented by the first and second vertical dotted lines in figure12, respectively. On average, Acc
MAX is about 161 m s − and isachieved at about 30 minutes at 4 R sun , and Acc MIN is about -118 m s − and is achieved at about 80 minutes at 10 R sun afterthe CME onset. The point at which the CME ceases to decelerateas its kinematics is completely dominated by the interaction with the solar wind is called the point of inflection, and the accelera-tion at this point is represented by Acc INF . The CME accelera-tion from this point onwards is 0 m s − as it begins to travel atthe same velocity as the surrounding solar wind. The Acc INF andthe time and distance at Acc
INF (T INF , R
INF ) is represented bythe third vertical dotted line in figure 12. On average, Acc
INF isabout -10 m s − and is achieved at about 300 minutes at 25 R sun .We compare the correlation between the acceleration param-eters, Acc INI (left panel) and Acc
MAX (right panel), with the as-sociated SEP peak flux in figure 13. The correlation coe ffi cientsand their probability values are given in Table 5. Acc INI displaysa higher correlation compared to Acc
MAX . We can understandthat Acc
INI is in some sense the total acceleration of a CME inthe first or initial phase of expansion. Therefore, it is a betterindicator of SEP peak intensities compared to the instantaneouspoint of Acc
MAX . Although there is no significant correlation ob-served in the left panel, a general trend of increasing Acc
INI andSEP peak intensity is observed (i.e., higher initial accelerationleads to higher intensity peak fluxes of SEPs). Furthermore, thecorrelation shows a slight improvement for higher energy chan-nels of SEPs. In comparison, the best correlation is observed forevents originating at disk center.
CME-driven shocks accelerate not just protons, but alsothe electrons in the solar corona (Holman & Pesses 1983;Schlickeiser 1984; Kirk 1994; Mann et al. 1995; Mann et al.2001; Mann & Klassen 2005). These accelerated electron beamscan be observed as type II bursts in the solar radio radiation inthe metric wave range (Wild & McCready 1950; Uchida 1960).Type II bursts require electrons escaping from the shock front,and the lack of these bursts implicates the absence of acceler-ated electrons as type II bursts occur when 0.2-10 KeV electronsare accelerated in the shock front (see, e.g., Bale et al. 1999;
Article number, page 13 of 18 & Aproofs: manuscript no. 39537corr
Fig. 13.
Scatter plots of initial acceleration (left panel) and maximum acceleration (right panel) vs SEP peak flux in the >
10 MeV (red), >
50 MeV(blue), and >
100 MeV (green) energy channels. The open symbols represent disk events (longitude -20 < L < > < -20). Table 5.
Correlation coe ffi cients and their probabilities (significance at p-value < Initial acceleration Energy channel All events(38) p-value Disk + West(31) p-value Disk + East(26) p-value Disk events(19) p-value East events(7) p-value >
10 MeV 0.25 .130083 0.23 .213231 0.28 .165929 0.28 .245625 0.29 .528119 >
50 MeV 0.34 .036747 0.34 .061285 0.40 .042896 0.43 .066128 0.12 .797745 >
100 MeV 0.34 .036747 0.36 .046669 0.49 .011052 0.55 .014698 -0.01 .983024Maximum acceleration >
10 MeV -0.006 .971481 -0.07 .708265 0.05 .808343 -0.05 .83892 0.87 .010899 >
50 MeV -0.31 .058213 -0.32 .079269 -0.24 .237628 -0.26 .282375 -0.009 .984722 >
100 MeV -0.27 .10113 -0.27 .141844 -0.23 .258336 -0.25 .301953 -0.13 .781165
Knock et al. 2001; Mann & Klassen 2005). Energetic electronsare unstable to Langmuir waves, thus they are converted intoradio emission at the local plasma frequency and its harmonic(see Nelson & Melrose 1985). Therefore, type II radio burstshold crucial information of both the shock and the surround-ing ambient medium in which the CME-driven shock propa-gates (Gopalswamy et al. 2008a). Although almost every largeSEP event is accompanied by a type II radio burst (Gopalswamy2003; Cliver et al. 2004) that indicates CME-driven particle ac-celeration (Gosling 1993; Reames 1999), we have ten eventsin our sample that lack a type II burst: 14 August 2010, 03 Au-gust 2011, 04 March 2012, 26 May 2012, 27 May 2012, 14 June2012, 08 September 2012, 14 December 2012, 21 April 2013,and 06 November 2013. Of the ten events, two originate in thewest, three in the east, and five at the disk center. On average,these events have a maximum velocity of about 1000 km s − andmaximum Mach number of about 0.94. The protons acceleratedby these events have peak fluxes of about 23.2 cm − s − sr − inthe >
10 MeV band, making these events the slowest and weak-est SEPs in the sample. As the propagation of radio bursts doesnot depend on the magnetic connectivity, a possible explanationfor their absence could be that the path of the radio burst didnot coincide with the instrument on board the satellite or thatthe detection of the waves was below the range of the radio in-strument, hence missing the signature. Detailed investigation isrequired to understand the absence of DH type II radio bursts inthese events. In order to investigate the time taken to observe the start oftype II bursts after the onset of the associated CME, figure 14panel a, clearly shows their distribution. On average, shocks arise42 minutes after the onset of the CME. The time taken for theshock to accelerate the SEPs to peak fluxes is shown in panel b,c, and d for the >
10 MeV (red), >
50 MeV (blue), and >
100 MeV(green) energy channels, respectively. Again, the >
100 MeV pro-tons take less time to reach peak flux compared to the >
10 and >
50 MeV protons. Comparison with the results presented in fig-ure 2 for all events show that the Mach number is equal to 1at the same point when we observe the start of a type II burst,so our profiles seem to be correct. Similary, the burst disappearswhen again the Mach number decreases to approximately 1. Al-though we still observe the SEP flux, the type II burst disappearsdue to the threshold of the instruments. The instruments measurethe radio signal, but particles are observed in situ; therefore, thethreshold is much lower for SEP detection in comparison withthe radio signal coming from very far away.We also explore the relationship between the shock duration,i.e., type II Time
END - type II Time
S TART with the CME and SEPparameters. The scatter plots are presented in figure 15 show-ing CME maximum velocity (panel a) maximum Mach number(panel b) and SEP peak flux (panel c) versus shock duration.Although there are no significant correlations observed in theseparameters, a general trend of increasing Mach number and SEPpeak intensity in the >
10 MeV energy channel leads to the longerduration of shocks. An interesting conclusion that can be drawnfrom panel c is that the duration of the shock is closely correlated
Article number, page 14 of 18nitha Ravishankar and Grzegorz Michałek: Relationship between solar energetic particle intensities and coronal mass ejection kinematics usingSTEREO / SECCHI field of view
Fig. 14.
Distribution showing the time di ff erence between shock and CME onset (panel a), and time at SEP peak flux and shock onset (panels b,c, and d) in the energy channels: >
10 MeV (red), >
50 MeV (blue), and >
100 MeV (green), respectively.
Fig. 15.
Scatter plots showing maximum velocity (panel a), maximum Mach number (panel b), and SEP peak flux (panel c) vs duration of theshock. The SEPs are shown in the >
10 MeV (red), >
50 MeV (blue), and >
100 MeV (green) energy channels. The open symbols represent diskevents (longitude -20 < L < > < -20). The presented correlation coe ffi cient in the top left corner is for all events. with >
10 MeV protons, and less with >
50 and >
100 MeV pro-tons. The strength of the shock decreases with distance from theSun, and the reaccelerated suprathermal SEPs may not reach thespacecraft and the maximum fluxes may not be detected. In addi-tion, although shocks accelerate impulsive seed ions when theyare available, they can only result in a small fraction of the SEPsobserved (Mason et al. 1999). Due to this, the >
10 MeV protonspredominantly accelerated by CME-driven shocks exhibits thebest correlation compared to the higher energy protons.
4. Conclusions
To determine the best instantaneous kinematic parameter of aCME to conduct correlation studies with the intensities of en-ergetic particles, we conducted a statistical study of 38 non-interacting CMEs and their associated SEPs during the ascend- ing phase of solar cycle 24 (i.e., 2009-2013). On further in-vestigation the events were classified as halo and partial-haloevents. This particular period was chosen as the STEREO twinspacecraft were near quadrature configuration with respect to theEarth. This position o ff ered a big advantage in the accurate de-termination of the plane-of-sky speed, which is close to the trueradial speed of the halo CMEs. It is worth noting that the pre-sented sample of events is the complete list of non-interactinghalo or partial-halo CMEs that generate SEPs with flux values ≥ >
10 MeV, ≥ >
50 MeV, and ≥ >
100 MeV bands during the above-mentioned period. This workis a continuation of our previous paper Ravishankar & Michałek(2020a), where the main limitation was the small population ofthe considered CMEs (25 events). The comparative studies pre-sented in Ravishankar & Michałek (2020a) have also shown thatSTEREO / SECCHI o ff ers a wider range of observation (1.5 R sun Article number, page 15 of 18 & Aproofs: manuscript no. 39537corr – 318 R sun ) in contrast to the SOHO / LASCO C2 / C3 field of view(1.5 R sun – 32 R sun ). Therefore, in this paper we completely dedi-cated the kinematic study of CMEs with STEREO / SECCHI dataas we were able to study the CME evolution at large distancesfrom Sun during peak SEP intensities in the heliosphere. Manualmeasurements of height–time data points were employed to de-termine instantaneous velocities. Using the empirical models byDulk and McLean (1978), LeBlanc et al., (1998), Mann et al.(1999), Gopalswamy et al., (2001), Eselevich and Eselevich(2008), and Sheeley et al., (1997), for Alfvén and solar windspeed, we derived the instantaneous Mach number parametersfor the CMEs. The obtained Mach number was verified withthe start and end time of type II radio bursts, which are signa-tures of CME-driven shock in the interplanetary medium. Thestart and end times of type II radio bursts should be consis-tent with instances when the speeds of CMEs reach Mach Num-ber =
1. GOES-13 and Wind / WAVES data were used to study theSEPs (in the > >
50, and >
100 MeV energy channels) andshock profiles, respectively. Their properties are summarized inTable 6.Electromagnetic waves such as X-rays and radio bursts traveldirectly from the Sun to the Earth, but energetic ions and elec-trons propagate along the interplanetary magnetic field lines.Kinematic studies of SEPs are influenced by two uncertainties:1) the magnetic field may significantly vary for each event fromthe Parker spiral and 2) pitch angle scattering may occur due tointerplanetary turbulence, thus distorting the propagation profile.Therefore, studies of these energetic protons in varied energyranges is required for to determine the path length and propaga-tion times as accurately as possible (Tylka et al. 2003; Li et al.2012c). The key results of this article are summarized here.Of the 38 events in the sample, 19 events (50%) originateat the disk center (-20 ◦ < longitude < ◦ ), 12 events (31%)originate at the western limb (longitude > ◦ ), and 7 events(18%) originate at the eastern limb (longitude < -20 ◦ ). Thelocation of the event is the most important parameter that a ff ectsthe propagation of the particles. Western limb events have thebest connectivity, and SEPs reach peak fluxes quickly after theCME onset, but the connectivity becomes poor as we movetowards the east and to the farther western limb (longitude > ◦ ), causing delay as the CMEs must expand wide enough sothat their shock fronts are well connected magnetically to theEarth. Due to this variation in connectivity along the solar diskwe observe delays in the time at which the SEPs reach maximumintensity, as shown in figures 2 and 5. Additionally, we observein figure 6, left panel, a gradual decrease in peak intensity for >
10 MeV protons, but >
50 and >
100 MeV protons exhibitthis trend only at longitudes greater than 0 ◦ . At longitudes lessthan 0 ◦ (i.e., moving towards the east), their peak fluxes areconstant and lie in the range 0.1-1 cm − s − sr − . The peak fluxof >
50 and >
100 MeV particles occurs long before the instancewhen the associated shock gets connected to the Earth. Thus,though we observe these fluxes, they are very reduced and theinstruments miss detecting the maximum fluxes. Hence, themaximum SEP fluxes from the western longitudes can be moreaccurately measured in situ compared to eastern longitudes. Aconsequence of this can also be seen in figure 6, right panel,showing the delays in protons attaining peak flux after the CMEonset. The >
10 MeV protons take longer to reach peak fluxesand are observed at farther distances from the Sun comparedto the >
100 MeV protons which are observed close to the Sun(in the range 0-30 R sun ). As pointed out by Dalla et al. 2017aand Dalla et al. 2017b, the SEP propagation is also a ff ected bythe drifts caused by the gradient and curvation of the Parker spiral IMF, with their importance increasing with energy of theparticle.We also observe the delay in both time and distance de-creases with increasing energy bands of protons, i.e., >
100 MeVprotons take less time and distance to reach peak flux, and > >
50 and >
100 MeV protons reachingpeak fluxes much earlier than >
10 MeV protons (Desai et al.2003; Tylka et al. 2005; Tylka & Lee 2006; Reames 2020).The main objective of the paper was to determine the idealkinematic parameter of the CME that o ff ers the best correlationwith the associated SEP peak fluxes, irrespective of the locationof their origin. First, in figure 3 we compare instantaneous CMEspeed and Mach number versus SEP fluxes for the western andeastern events; we observed a high correlation for western eventsand an anticorrelation for eastern events. The anticorrelationis observed as the SEP peak intensties are achieved fartheraway from the Sun for poorly connected events. Of the twoparameters, the Mach number o ff ers higher correlation. Next,the comparative studies shown in figures 7 and 11 show that theCME velocity and Mach number at SEP peak flux o ff er highcorrelation of about 0.77 and 0.85, respectively, for the > ffi cients are highly significant (probability > > CME , V A , and V S W )involved in the onset and influence of particle acceleration,whereas CME speed alone lacks the necessary informationfor a detailed study. This good correlation is observed also foreastern limb events where the magnetic connectivity of theSun and the Earth are poor. The results support the works ofLiou et al. 2011 on their study of correlating fast-forward shockMach numbers with the intensity of SEPs. Inspecting Table 4,which shows the di ff erence between two correlation coe ffi cientspresented in Table 1 and 3, we have to reject (at significancelevel p = ffi cientsare significantly di ff erent. However, we can consider 1-p, whichis the probablility that the respective correlation coe ffi cients aredi ff erent. In a few examples (for >
10 MeV particles for All andDisk + West events in figure 7 panel c) this probability couldbe very high (1-p > ff erence is significant). And the resultspresented in this paper, showing the importance of Mach at SEPpeak flux, could be useful for future studies and space weatherprediction.For space weather forecasting the best CME kinematicparameter that could be used to predict SEPs is the Machnumber at SEP peak flux. As we observed that the Mach numberat SEP peak flux and SEP peak occur at the same time, and thatit agrees with events originating at all longitudes, this could bebest utilized. Fortunately, for the >
10 MeV particles that arecomparatively slow, we can determine the Mach number onehour before the SEPs reach the Earth with respect to white lightmeasurements by coronagraph. In figure 2 we have shifted the
Article number, page 16 of 18nitha Ravishankar and Grzegorz Michałek: Relationship between solar energetic particle intensities and coronal mass ejection kinematics usingSTEREO / SECCHI field of view profiles of Mach number and >
10 MeV SEP flux by about onehour to take into account the delay, but in reality we first observethe white light and then we measure the height–time data pointsto determine the Mach number. Therefore, a prediction of thearrival of the lower energetic SEPs to the Earth can be made bythis method.A thorough analysis of the active regions of five backsideevents in our sample allowed us to determine the source locationthat is responsible for the production of energetic particles. Twoof them (28 January 2011 and 23 July 2012) were located justover the edge of the solar disk, but the other three (21 March2011, 04 June 2011, and 08 November 2012) were located asfar as ≈ ◦ behind the western limb of the Sun. This meansthat SEPs can be produced from sources located not only onthe visible part of the Sun’s disk, but even very far ( ≈ ◦ )beyond the eastern (Gopalswamy et al. 2020) and western (ourstudy) limb of the disk. These results demonstrate the ability ofbacksided events to cause space weather e ff ects at Earth, andaccurate predictions of SEPs will therefore need to include suchevents.Ten events in our sample do not show the associated typeII burst. Additionally, for all events we observed that the Machnumber is equal to 1 at the same point when we observe thestart of the type II burst and that the burst disapears when againthe Mach number decreases to approximately 1. Even thoughwe still observe SEP flux, the type II burst disappears due tothreshold of instruments. The instrument measures radio signal,but particles are observed in situ; therefore, the threshold ismuch lower for SEP detection in comparison with radio signalscoming from a very great distance. Although no significantcorrelation is observed in these parameters, a general trend ofincreasing Mach number and SEP peak intensity in the > >
10 MeV protonscompared to >
50 and >
100 MeV protons. The shock strengthdecreases with distance from the Sun, and the reacceleratedsuprathermal SEPs may not reach the spacecraft and themaximum fluxes may not be detected. In addition, althoughshocks accelerate impulsive seed ions when they are available,they can only result in a small fraction of the SEPs observed(Mason et al. 1999). Consequently, the >
10 MeV protonspredominantly accelerated by CME-driven shocks exhibit thebest correlation compared to the higher energy protons.
Acknowledgements.
Anitha Ravishankar and Grzegorz Michałek were sup-ported by NCN through the grant UMO-2017 / / B / ST9 / / MNS / / SECCHI and GOES consortium who built theinstruments and provided the data used in this study.
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Article number, page 18 of 18 n it h a R a v i s h a nk a r a nd G r ze go r z M i c h a ł e k : R e l a ti on s h i pb e t w ee n s o l a r e n e r g e ti c p a r ti c l e i n t e n s iti e s a nd c o r on a l m a ss e j ec ti onk i n e m a ti c s u s i ng S TE R E O / S E CC H I fi e l do f v i e w Table 6.
Observational parameters of 38 CMEs and the associated SEPs and type II bursts during the period 2009-2013.
CME observations SEP peak flux CME speed at SEP peak flux Maximum Mach number Mach number at SEP peak flux Solar Flare Type II burst
AVG V MAX R MAX T MAX >
10 MeV >
50 MeV >
100 MeV >
10 MeV >
50 MeV >
100 MeV M
MAX MR MAX MT MAX >
10 MeV >
50 MeV >
100 MeV Location Start time End time[km / s] [km / s] [R SUN ] [Minute] [pfu] [pfu] [pfu] [km / s] [km / s] [km / s] [R SUN ] [Minute]1 20100814 10:06 744 825 8.33 107 14.17 0.45 0.12 792 825 782 1.12 3.53 34 0.92 0.86 1.00 N17W52 – –2 20110215 01:20 489 1064 4.56 67 2.58 0.24 0.10 477 543 543 0.91 20.01 292 0.76 0.86 0.86 S20W12 20110215 02:10 20110215 07:003 20110307 19:56 1147 1742 9.95 72 48.36 0.79 0.16 921 949 1031 1.79 29.55 245 1.63 1.66 1.70 N30W48 20110307 20:00 20110308 08:304 20110607 06:08 573 1406 3.88 43 72.86 14.40 4.52 425 587 587 1.11 3.87 43 1.69 1.80 1.80 S21W54 20110607 06:45 20110607 18:005 20110802 05:42 532 992 7.32 101 2.89 0.33 0.10 470 527 504 0.88 2.63 42 0.63 0.66 0.66 N14W15 20110802 06:15 20110802 07:306 20110803 12:36 380 684 7.66 125 1.08 0.19 0.09 464 464 439 0.62 8.75 144 0.56 0.56 0.55 N19W36 – –7 20110804 03:46 1277 2627 3.84 18 80.05 8.42 1.79 717 1121 1287 2.31 24.86 144 1.25 1.83 2.04 N17W69 20110804 04:15 20110805 17:008 20110808 17:58 615 1623 3.24 23 4.03 0.34 0.10 793 700 700 1.31 3.24 23 0.88 1.04 1.04 N14W07 20110808 18:10 20110808 20:109 20110809 08:02 993 1574 3.49 19 26.91 3.17 0.75 694 694 853 1.42 16.44 136 1.00 1.00 1.19 N14W18 20110809 08:20 20110809 08:3510 20110906 01:25 405 524 7.72 139 1.52 0.38 0.12 493 305 321 0.46 7.71 139 0.45 0.33 0.34 N11W47 20110906 02:00 20110906 23:4011 20110906 21:54 667 1598 3.65 45 8.84 1.61 0.41 659 778 771 1.26 3.64 45 1.12 1.17 1.21 S22W26 20110906 22:30 20110907 15:4012 20110922 10:19 550 1587 5.23 63 6.80 0.56 0.21 414 414 402 1.24 3.72 51 0.76 0.76 0.75 N27W71 20110922 11:05 20110922 24:0013 20111126 06:42 655 1044 3.50 39 80.26 0.11 0.11 652 623 623 1.35 33.91 447 1.22 1.18 1.18 N17W66 20111126 07:15 20111127 24:0014 20111225 17:54 345 647 2.63 47 3.23 0.26 0.07 293 298 298 0.57 2.63 47 0.35 0.37 0.37 N11W76 20111225 18:45 20111225 18:5515 20120119 13:31 467 972 8.95 187 3.51 0.17 0.06 436 461 480 0.91 8.95 187 0.81 0.80 0.82 S17E06 20120119 15:00 20120120 02:4516 20120123 02:48 956 2339 13.0 114 2243 60.59 2.38 1410 1455 1695 2.95 22.96 168 2.65 2.70 2.71 S13W59 20120123 04:00 20120124 15:0017 20120127 17:48 850 2562 11.1 78 795.5 47.19 11.8 904 940 1272 2.90 14.76 96 1.62 1.66 1.99 S15W01 20120127 18:30 20120128 04:4518 20120304 10:46 546 1012 4.99 71 2.26 0.15 0.07 430 430 430 0.92 3.66 54 0.62 0.62 0.62 S13W88 – –19 20120313 17:21 722 2397 12.3 61 468.7 17.86 1.88 1148 2092 2092 2.86 15.83 80 1.82 2.81 2.81 S19E42 20120313 17:35 20120313 24:0020 20120517 01:43 1009 1679 10.3 67 255.4 78.29 20.4 901 1587 1679 1.84 10.36 42 1.44 1.79 1.69 S06W34 20120517 01:45 20120517 17:2021 20120526 20:32 657 1479 3.27 34 6.94 0.21 0.08 566 605 605 1.19 3.26 34 0.76 0.78 0.78 N07E12 – –22 20120527 05:08 509 1070 4.98 67 14.77 0.22 0.08 528 578 466 0.96 3.77 53 0.78 0.78 0.70 N14W11 – –23 20120614 13:00 562 1327 4.46 41 0.95 0.20 0.06 457 457 457 1.12 7.46 68 0.84 0.84 0.84 N10W33 – –24 20120706 22:39 621 1890 3.65 46 25.24 1.82 0.36 496 499 475 1.50 3.64 46 0.78 0.76 0.68 S11W88 20120706 23:10 20120707 03:4025 20120712 16:10 712 1504 5.57 58 96.08 0.85 0.25 695 656 1176 1.28 4.27 47 1.07 0.90 1.36 S18E07 20120712 16:45 20120713 09:0026 20120719 05:01 898 2004 4.65 47 79.60 5.16 0.73 833 858 848 1.56 4.65 47 1.42 1.39 1.31 S13W59 20120719 05:30 20120719 06:2027 20120831 19:19 853 1590 4.33 50 47.44 0.20 0.06 654 684 684 1.65 44.05 450 1.35 1.36 1.36 S15W01 20120831 20:00 20120831 23:4528 20120908 09:48 482 773 2.91 39 1.16 0.22 0.09 414 414 434 0.65 2.90 39 0.55 0.55 0.54 S13W88 – –29 20120927 23:12 801 1610 12.3 114 28.43 0.79 0.15 818 808 676 1.76 12.34 114 1.24 1.27 1.16 S19E42 20120927 23:55 20120928 10:1530 20121214 01:35 596 1090 12.5 181 9.36 0.16 0.09 485 663 663 1.26 15.04 211 0.92 0.99 0.99 S06W34 – –31 20130116 17:57 544 1604 2.82 56 1.65 0.12 0.04 530 524 530 1.37 2.82 56 0.88 0.88 0.88 N07E12 20130116 22:00 20130117 01:3032 20130315 06:01 593 2039 3.95 61 7.43 0.19 0.08 406 406 406 1.61 3.95 61 0.79 0.79 0.79 N14W11 20130315 07:00 20130315 21:3033 20130411 06:53 695 1747 3.63 46 113.1 8.41 2.02 623 669 669 1.38 3.63 46 1.02 1.03 1.03 N10W33 20130411 07:10 20130411 15:0034 20130421 07:13 473 798 4.04 67 3.27 0.27 0.09 448 503 477 0.72 4.04 67 0.64 0.58 0.48 S11W88 – –35 20130929 21:29 715 1376 12.6 125 131.1 1.82 0.18 592 745 768 1.64 21.23 209 1.12 1.30 1.31 S18E07 20130929 21:53 20130930 21:0036 20131106 22:50 422 973 7.09 123 6.64 0.19 0.07 457 663 663 0.84 7.09 123 0.59 0.79 0.79 N10W33 – –37 20131119 10:00 402 1072 3.53 46 4.03 0.32 0.10 397 488 599 0.85 3.53 46 0.55 0.67 0.69 S11W88 20131119 10:39 20131119 20:2038 20131228 17:08 550 1062 6.97 82 29.27 1.51 0.27 593 708 841 1.09 11.97 138 0.87 1.00 1.00 S18E07 20131228 17:31 20131228 18:05 A r ti c l e nu m b e r , p a g e ff