Multi-spacecraft observations and transport simulations of solar energetic particles for the May 17th 2012 event
M. Battarbee, J. Guo, S. Dalla, R. Wimmer-Schweingruber, B. Swalwell, D. J. Lawrence
AAstronomy & Astrophysics manuscript no. aanda © ESO 2018January 26, 2018
Multi-spacecraft observations and transport simulations of solarenergetic particles for the May 17th 2012 event
M. Battarbee (cid:63) , J. Guo , S. Dalla , R. Wimmer-Schweingruber , B. Swalwell , and D. J. Lawrence Jeremiah Horrocks Institute, University of Central Lancashire, PR1 2HE, Preston, UKe-mail: [email protected] Institut fuer Experimentelle und Angewandte Physik, University of Kiel, Germanye-mail: [email protected] Johns Hopkins University Applied Physics Laboratory, MD, USAReceived 26th June 2017 / Accepted 25th January 2018
ABSTRACT
Context.
The injection, propagation and arrival of solar energetic particles (SEPs) during eruptive solar events is an important andcurrent research topic of heliospheric physics. During the largest solar events, particles may have energies up to a few GeVs andsometimes even trigger ground-level enhancements (GLEs) at Earth. These large SEP events are best investigated through multi-spacecraft observations.
Aims.
We study the first GLE-event of solar cycle 24, from 17th May 2012, using data from multiple spacecraft (SOHO, GOES, MSL,STEREO-A, STEREO-B and MESSENGER). These spacecraft are located throughout the inner heliosphere, at heliocentric distancesbetween 0.34 and 1.5 astronomical units (au), covering nearly the whole range of heliospheric longitudes.
Methods.
We present and investigate sub-GeV proton time profiles for the event at several energy channels, obtained via di ff erentinstruments aboard the above spacecraft. We investigate issues due to magnetic connectivity, and present results of three-dimensionalSEP propagation simulations. We gather virtual time profiles and perform qualitative and quantitative comparisons with observations,assessing longitudinal injection and transport e ff ects as well as peak intensities. Results.
We distinguish di ff erent time profile shapes for well-connected and weakly connected observers, and find our onset timeanalysis to agree with this distinction. At select observers, we identify an additional low-energy component of Energetic StormParticles (ESPs). Using well-connected observers for normalisation, our simulations are able to accurately recreate both time profileshapes and peak intensities at multiple observer locations. Conclusions.
This synergetic approach combining numerical modelling with multi-spacecraft observations is crucial for understand-ing the propagation of SEPs within the interplanetary magnetic field. Our novel analysis provides valuable proof of the ability tosimulate SEP propagation throughout the inner heliosphere, at a wide range of longitudes. Accurate simulations of SEP transportallow for better constraints of injection regions at the Sun, and thus, better understanding of acceleration processes.
Key words.
Sun: activity – Sun: magnetic field – Sun: particle emission – Sun: heliosphere – methods: numerical – Instrumentation:detectors
1. Introduction
The Sun releases vast amounts of energy through its activity,which mostly follows a periodic 11-year cycle. These eruptionscan accelerate protons, electrons and heavier ions to relativisticenergies and release them into interplanetary space. These so-lar energetic particles (SEPs) are guided by the interplanetarymagnetic field (IMF), and in some cases result in intensive parti-cle fluxes near the Earth. SEP events take place more frequentlyduring solar maximum, and can a ff ect atmospheric and space-related activities in many ways (see, e.g., Turner 2000 and ref-erences therein), and as such, their investigation has been recog-nized as extremely important.During extreme solar events, protons can be accelerated intothe GeV range, and, when directed at the Earth, may lead toneutron monitors (NMs) detecting events at the Earth’s surface.These ground-level enhancements (GLEs) are the most extremeof solar events, and thus are of special interest to the helio-physics community (see, e.g., Asvestari et al. 2017 and Nitta (cid:63) Currently at the Department of Physics, University of Helsinki, Fin-land et al. 2012). Our understanding of energetic solar events andspecifically GLEs increased dramatically during solar cycle 23(Gopalswamy et al. 2012) due to advances in instrumentationand an abundance of events to observe. Solar cycle 24, beingmuch quieter, has so far provided only two unambiguous GLEs,GLE71 on May 17th 2012 and GLE72 on September 10th 2017.Being able to observe this event from multiple vantage pointswithin the inner heliosphere provides us with an exciting oppor-tunity to increase our understanding the dynamics of strong solarevents. In such an analysis, three-dimensional modelling of par-ticle propagation is a crucial tool.We present sub-GeV proton observations of GLE 71, focus-ing on comparative analysis between observations from mul-tiple vantage points throughout the inner heliosphere to betterunderstand the spatial extent of SEP intensities in strong SEPevents. GeV-energy particles are thus excluded from our analy-sis due to observations at such energies being available only inthe vicinity of the Earth. We present new observations from theMars Science Laboratory (MSL) Radiation Assessment Detector(RAD) and the MESSENGER Neutron Spectrometer (NS), to-gether with energetic particle data from STEREO and near-Earth
Article number, page 1 of 12 a r X i v : . [ a s t r o - ph . S R ] J a n & A proofs: manuscript no. aanda missions. We use a fully three-dimensional test particle model tosimulate the transport of SEPs, originating from an accelerationregion in the solar corona, generating virtual time profiles at var-ious observer locations. The model includes, for the first time,the e ff ects of a wavy Heliospheric Current Sheet (HCS) betweentwo opposite polarities of the IMF. We compare intensity timeprofiles and peak intensities of data from both observations andsimulations, at the di ff erent observer locations.In section 2, we introduce the event along with previouslypublished analysis. In section 3, we introduce the instrumentsused in our multi-spacecraft observations. We then present inten-sity time profiles and solar release times, and discuss magneticconnectivity and energetic storm particles (ESPs). In section 4,we describe our particle transport simulation method. We thenproceed to present simulated intensity time profiles, and comparethem and deduced peak intensities with observations. Finally, insection 5 we present the conclusions of our work. In AppendixA, we discuss calibration of our MESSENGER NS observations.
2. The May 17th 2012 solar eruption
On May 17, 2012 at 01:25 UT, the NOAA active region 11476,located at N11 W76 in Earth view, produced a class M5.1 flarestarting, peaking, and ending at 01:25, 01:47, and 02:14 UT, re-spectively (e.g., Gopalswamy et al. 2013; Shen et al. 2013). Thetype II radio burst indicating the shock formation was reportedby Gopalswamy et al. (2013) to start as early as 01:32 UT us-ing the dynamic spectra from Hiraiso, Culgoora and Learmonthobservatories. Based on this, they also determined the coronalmass ejection (CME) driven shock formation height as 1.38 so-lar radii ( R (cid:12) , from the centre of the Sun). The CME reached apeak speed of ∼ − at 02:00 UT. They reasoned thatalthough the May 17th flare is rather small for a GLE event, theassociated CME was directed toward near-ecliptic latitudes, fa-cilitating good connectivity between the most e ffi cient particleacceleration regions of the shock front and the Earth. Despitethe flare exhibiting relatively weak x-ray flux, Firoz et al. (2014,2015) suggested that both the flare and the CME had a role inparticle acceleration. Ding et al. (2016) agreed with this, basedon velocity dispersion analysis (VDA) of proton arrival.Gopalswamy et al. (2013) further estimated, using NM data,that the solar particle release time was about 01:40, slightlylater than the shock formation time of 01:32. Papaioannou et al.(2014) reported the type III radio bursts which signified the re-lease of relativistic electrons into open magnetic field lines start-ing at around 01:33 UT and ending at 01:44 UT. Using a simpletime-shifting analysis, they derived the release of 1 GeV pro-tons from the Sun at about 01:37 UT, slightly earlier but broadlyagreeing with the onset time obtained by Gopalswamy et al.(2013).This event was later directly detected at Earth by severalNMs with slightly di ff erent onset times (between 01:50 and02:00), with the strongest signal detected at the South Pole (Pa-paioannou et al. 2014) where the rigidity cuto ff is the lowest.Within the magnetosphere, proton energy spectra were measuredby the PAMELA instrument (Picozza et al. 2007) as reportedby Adriani et al. (2015), indicating that protons with energiesof up to one GeV and helium of up to 100 MeV / nucleon wereaccelerated and transported to the vicinity of Earth. The GeVproton detection has also been corroborated later by Kühl et al.(2015) using an inversion technique exploring the response func-tions of the Electron Proton Helium Instrument (EPHIN, Müller- Mellin et al. 1995) aboard the SOHO spacecraft. The event wasalso detected aboard the international space station (Berrilli et al.2014). Analysis of NM and PAMELA observations, using com-parisons of peak and integral intensities, can be found in Asves-tari et al. (2017). Mishev et al. (2014) performed reverse mod-elling based on NM measurements of this event, finding evi-dence of anisotropic twin-stream SEP pitch-angle distributions.Utilizing lower particle energies for release time analysis,Li et al. (2013) compared Wind / / HED detector (Torsti et al. 1995) aboard SOHO detecteda strong event, but su ff ered from data gaps during the event,which poses additional challenges to analysis.During this event, the STEREO Ahead (STA) and STEREOBehind (STB) spacecraft were leading and trailing Earth by114.8 and 117.6 degrees, respectively, both at a heliocentricdistance of approximately 1 au. Lario et al. (2013) studied the15-40 MeV and 25-53 MeV proton channels of this event usingGOES and the high energy telescope (HET) on STB. For the15-40 MeV channel, they obtained an enhancement rate (peakintensity / pre-event intensity) of 2.64 × at GOES and only35.0 at STB. For the 25-53 MeV channel, they obtained an en-hancement rate of 1.94 × at GOES and only 13.4 at STB.Unfortunately they did not determine the peak intensity of thisevent as measured by STA. This event has previously been in-cluded in a STEREO event catalogue (Richardson et al. 2014),and multi-spacecraft observations of electrons have been anal-ysed in Dresing et al. (2014). Heber et al. (2013) included STAand STB proton time profiles for a single energy range in a fig-ure, displaying the longitudinal extent of the event.The event was also observed by the MESSENGER (MES)spacecraft orbiting around Mercury which, at the time of theevent, was at a heliocentric distance of 0.34 au (Lawrence et al.2016). The longitudinal connectivity of MES was similar to thatof STA, as shown in Figure 1. In this paper, we investigate thetime-series of proton measurements from MES using its neutronspectrometer (NS, Lawrence et al. 2016).Beyond 1 au, this event was also observed by the RadiationAssessment Detector (RAD, Hassler et al. 2012) on board theMars Science Laboratory (MSL) on its way to Mars (Zeitlin et al.2013). We derive the proton intensities measured by RAD at dif-ferent energy ranges and compare them with Earth-based obser-vations and simulated particle intensities at the same location.We note that the RAD detector did not measure original protonintensities in space, but rather a mix of primary and secondaryparticles due to primaries experiencing nuclear and electromag-netic interactions as they traverse through the inhomogeneousflight-time shielding of the spacecraft. To retrieve the originalparticle flux outside the spacecraft is rather challenging and isbeyond the scope of the current paper.
3. Multi-spacecraft observations
The heliospheric locations of five di ff erent spacecraft whosemeasurements are employed in the current study are shown inFigure 1 and also listed in Table 1. For this study, we estimatedthe average solar wind speed from measurements made by theCELIAS / MTOF Proton Monitor on the SOHO Spacecraft duringCarrington rotation 2123. The average radial solar wind speedvalue was 410 km s − , which was rounded down to 400 km s − for the purposes of this research. Table 1 also includes calculatedParker spiral lengths using this solar wind speed. Article number, page 2 of 12. Battarbee et al.: Multi-spacecraft observations and transport simulations of solar energetic particles
Table 1.
Heliospheric location, Parker spiral length and onset time of the event seen at di ff erent spacecraft. The flare source region at the Sun isNOAA active region 11476 with coordinate of N11 W76 and the flare onset time is 01:25 on 17th May 2012. HGI HGI distance Parker spiral shortest SEP estimated SRT Observed SEPlatitude longitude to the Sun length travel time onset time (1 GeV p) event typeSTA 7.3 ° 275.4 ° 0.96 au 1.11 au 631.4 s 10.18 10:07 slowly risingMES 2.1 ° 290.9 ° 0.35 au 0.36 au 204.8 s 03:14 03:11 slowly risingEarth -2.4 ° 160.7 ° 1.01 au 1.18 au 671.2 s 01:56 01:45 rapidly risingMSL -7.3 ° 121.8 ° 1.46 au 1.92 au 1092 s 02:04 01:46 rapidly risingSTB -4.7 ° 42.7 ° 1.00 au 1.16 au 659.8 s 11:06 10:55 slowly rising
EarthMSL STASTB MES
Fig. 1.
The heliospheric locations of MES, Earth, MSL, STA and STB.The Parker spiral configuration is calculated using a constant solar windspeed of u sw =
400 km s − . The 1 au distance is shown with a dashedcircle. The arrow is placed along the radial direction at the flare location. In order to e ff ectively analyse the heliospheric and tempo-ral extent of the May 17th 2012 solar eruption, we assess protontime profiles from multiple instruments throughout the inner he-liosphere. The energy-dependent time profiles of SEPs measuredat five di ff erent heliospheric locations are shown in Figure 2.For STA and STB, we analyse 1-minute resolution data fromHET of the In situ Measurements of Particles and CME Tran-sients (IMPACT) investigation aboard both STEREOs. The pro-tons are measured between 13 and 100 MeV in 11 di ff erentenergy channels. For our purpose of comparing the STEREOmeasurement to those at other locations, we combine the en-ergy channels into four di ff erent bins: 13–24 MeV, 24–40 MeV,40–60 MeV, and 60–100 MeV.For MES data at Mercury, we use the neutron spectrome-ter which contains one borated plastic (BP) scintillator sand-wiched between two Li glass (LG) scintillators. To account forthe shielding of particles by the magnetosphere of Mercury andby the geometric shadowing of the planet itself, we selectedonly observations where the orbit altitude of MES is greaterthan 5000 km. The energy thresholds for triggering each typeof charged particle were simulated and derived using particletransport codes (Lawrence et al. 2014) and are as follows: singlecoincidence, ≥
15 MeV protons (or ≥ ≥
45 MeV protons (or ≥
10 MeV electrons); andtriple coincidences, ≥
125 MeV protons (or ≥
30 MeV electrons).Since ≥
10 MeV electrons are fairly rare in SEPs, we assumethese channels measure mainly protons during the event. Forthe single-coincidence channel, contamination by many di ff er-ent sources such as electrons, gamma-rays and various chargedparticles is possible, and thus, care must be taken when draw- -3 -2 -1 S T E R E O - A -3 -2 -1 M E SS E N G E R -3 -2 -1 E A R T H / G O E S -3 -2 -1 E A R T H / E R N E -3 -2 M S L / R A D D o s e r a t e [ m G y / d a y ] -3 -2 S T E R E O - B Proton intensity I [s -1 cm -2 sr -1 MeV -1 ] Fig. 2.
The proton intensity time profiles, in units s − cm − sr − MeV − ,for di ff erent proton energy ranges at various spacecraft. The green verti-cal lines mark the onset times of the first arriving particles while the greyvertical lines mark the possible onsets of ESP events. SOHO / ERNEhas two large data gaps but is located close to GOES, allowing cross-comparison of the data. The 17th of May is DOY 138. ing conclusions from the flux. We converted single, double, andtriple coincidence counts into fluxes according to methods ex-plained in detail in Appendix A.We solve the intensity profile for 15–45 MeV and 45–125MeV protons in the following way: We subtract the ≥
45 MeVflux from the ≥
15 MeV flux, and the ≥
125 MeV flux fromthe ≥
45 MeV flux. These two fluxes, now bounded from both
Article number, page 3 of 12 & A proofs: manuscript no. aanda above and below in energy, are then divided with the energybin widths, i.e., 30 and 80 MeV, resulting in intensities in unitsprotons s − sr − cm − MeV − . The ≥
125 MeV flux is not shownin Figure 2, as it shows little enhancement for this time period.We emphasize that the 15–45 MeV flux calibration is uncertain.The time profiles in Figure 2 indeed show a very high intensityin the 15–45 MeV channel, likely due to non-proton backgroundcontamination.Close to the Earth, we employed two separate detectors.GOES 13, situated within the Earth’s magnetosphere, providedus with 15–40 MeV, 38–82 MeV, and 84–200 MeV protonchannels, with 32 second resolution. The SOHO / ERNE HED de-tector at L1 was used to construct energy channels with 1 minutetime resolution, matching the GOES channels with energyranges of 14.6–40.5 MeV, 40.5–86.7 MeV, and 86.7–140 MeV.GOES provided uninterrupted observations of the event, but thebackground levels were enhanced due to increased ambient par-ticle densities in the magnetosphere. ERNE / HED, located out-side the magnetosphere at the Lagrangian point L1, provideduncontaminated pre-event intensities, but with data gaps dur-ing the event. Additionally, the peak intensities observed byERNE / HED are suspected to be incorrect due to non-linear satu-ration artefacts and particles propagating through the detector inthe reverse direction.At MSL, during the cruise phase, the RAD instrument pro-vided radiation dose measurements with a high time resolutionof 64 seconds, and particle spectra with a time resolution of ∼
32 minutes. The radiation dose measurements were used to de-termine the event onset time. The particle spectra are providedby a particle telescope consisting of silicon detectors and plas-tic scintillators, with a viewing angle of ∼
60° (Hassler et al.2012), and providing proton detections up to a stopping energyof 100 MeV. The original energy of the particle, E , is solvedthrough analyzing E versus d E / d x correlations for each parti-cle. Since RAD transmits the deposited energy in each triggereddetector layer for almost all stopping protons, the particle iden-tification is done in post-processing and is very accurate. Pro-tons stopping inside RAD can thus be selected and their inten-sities have been obtained in four energy channels: 12–24 MeV,24–40 MeV, 40–60 MeV, and 60–100 MeV. The particles de-tected by RAD are a combination of primaries and secondariesresulting from spallation and energy losses as particles travelthrough the flight-time spacecraft shielding. The shielding distri-bution around RAD is very complex: most of the solid angle waslightly shielded with a column density smaller than 10 g / cm ,while the rest was broadly distributed over a range of depths upto about 100 g / cm (Zeitlin et al. 2013). Due to this shielding,deducing the exact incident energies of particles as they reachthe spacecraft is a challenging process. We briefly discuss cor-recting for these e ff ects in section 4.2.Celestial mechanics dictate that a spacecraft on a Hohmanntransfer to Mars remain magnetically well connected to Earthduring most of its cruise phase (Posner et al. 2013). This con-nection is also shown in Figure 1. Due to this reason, the inten-sity profiles seen at Earth and MSL are expected to show similartime evolutions. Intense energy release at the surface of the Sun or in the coronacan accelerate SEPs to relativistic energies, allowing them topropagate rapidly along the Parker spiral (Parker 1958) to helio-spheric observers. If the observer is magnetically well-connectedto the acceleration site and particle transport is unhindered, the arrival time of first particles can be used to infer the travel dis-tance, i.e., the Parker spiral length.As each heliospheric location will see the first arrival of en-ergetic protons at a di ff erent time, we have defined onset timesseparately for each spacecraft, listed in Table 1. In Figure 2, thegreen vertical lines mark the onset times of the highest-energychannel corresponding to the arrivals of fastest protons. For STAand MES observations, we also define onset times of possibleESP events in low-energy channels, marked by grey lines, as willbe discussed in more detail later. For STA, we find two distinctjumps, which may both be due to an ESP event. These timeswere defined from the raw data through subjective analysis ofrise over a background level.The nominal Parker spirals connecting the spacecraft to theSun are shown in Figure 1 assuming an average solar wind speedof 400 km s − and their lengths have also been calculated andlisted in Table 1. Given a Parker spiral length of 1.18 au for anobserver at Earth, 1 GeV protons (with a speed of ∼ . × km / s) propagating from the flare site without scattering wouldarrive after ∼
670 s or 11 minutes. A particle onset time at Earthat 01:56 would indicate a solar release time (SRT) of about 01:45UT for these protons, which is consistent with radio burst ob-servations (Gopalswamy et al. 2013; Papaioannou et al. 2014),considering the 8-min propagation time of radio signals fromthe Sun to the Earth. Table 1 also lists the 1 GeV proton traveltimes and estimated associated SRTs, for each of the locationconsidered, based on the calculated Parker spiral lengths. Theobserved MSL onset time is in good agreement with that atEarth and with the estimated proton release time, likely due tothe good magnetic connection between the acceleration regionand Earth / MSL. However, SRT values derived from MES, STA,and STB are very di ff erent from each other and hours later thanthe time of flare onset and shock formation. This indicates thatthese spacecraft were not magnetically well-connected to the so-lar acceleration site, and that particle transport to these locationswas not due to propagation parallel to the magnetic field linesbut was a ff ected by drift motion, co-rotation, cross-field di ff u-sion and turbulence e ff ects. The multi-spacecraft observations available for the SEP event onMay 17th 2012 provide an exemplary chance to investigate mag-netic connectivity between the Sun and observation platforms ata wide variety of longitudes and radial distances. We model mag-netic connectivity by assuming the IMF to follow a Parker spiral.We use a constant solar wind speed of 400 km s − for our mod-elling, based on the averaging described in Section 3.In Figure 3, we plot the Carrington Rotation 2123 solar syn-optic source surface map (Hoeksema et al. 1983) for r = . R (cid:12) ,resulting from potential field modelling, provided by the WilcoxSolar Observatory. The model assumes a radial magnetic fieldat the solar surface and at r = . R (cid:12) . The plot shows the loca-tion of the flare on May 17th 2012 (indicated by a triangle) rel-ative to the central meridian, along with estimated Parker spiralfootpoints for the five observation platforms. As the plot shows,Earth (labelled 1) and MSL (2) are connected to regions on theSun’s surface very close to each other, with STA (3) and MES(5) connected to more western longitudes, close to each other.STB (4) is connected to more eastern longitudes.Figure 3 also includes, as a thick white solid curve, a depic-tion of a potential field model neutral line between hemispheresof outward and inward pointing magnetic field. A model of asimple parametrized wavy neutral line, based on a tilted dipole Article number, page 4 of 12. Battarbee et al.: Multi-spacecraft observations and transport simulations of solar energetic particles formulation, is fitted to this neutral line using a least squares dis-tance fit method, as described in Battarbee et al. (2018). Thisneutral line parametrisation is the r = . R (cid:12) anchor point forour model wavy HCS, and the wavy HCS parameters are de-scribed in section 4. Finally, figure 3 shows a rectangular regionof width 180 ◦ , extending to latitudes ± ◦ , which we use as amodel injection region for SEPs. The width of the injection re-gion was iterated upon, until an agreement between observationsand simulations, for as many heliospheric observers as possible,was achieved.As the solar wind flows outward and the solar surface ro-tates, magnetic structures at a given heliocentric distance are co-rotated westward. In Figure 3, this would be described by the po-tential field polarity map including the HCS moving to the right.We validate the synoptic source and Parker spiral model throughsimple radial magnetic field observations. MES and STA are inregions of inward-pointing magnetic field throughout the anal-ysed time period, in agreement with the map. Up until the timeof the flare, Earth is connected to outward-pointing field lines,after which a strong interplanetary CME (ICME) is detected andthe field orientation flips. STB is initially connected to inward-pointing field lines, but from the 19th of May onward, the direc-tion points inward, in agreement with the spacecraft crossing theHCS. In addition to SEPs accelerated close to the Sun during the ini-tial, strong phase of the solar eruption, particle acceleration canhappen throughout the inner heliosphere at propagating inter-planetary (IP) shocks, driven by ICME fronts. Depending on theheliospheric location relative to the flare site and the ICME, dif-ferent spacecraft see di ff erent properties of the event. The timeprofiles of in-situ measurements in Figure 2 and estimated SRTsin Table 1 suggest that the particle intensities at Earth and MSL(with estimated SRTs of 01:45 and 01:46) are dominated bycoronally accelerated SEPs, but at MES and STA, there is anadditional population of energetic storm particles (ESPs) accel-erated by an IP shock. To identify and decouple the signal ofparticles accelerated at an IP shock from those accelerated earlyon in the corona, we turn to ICME and shock catalogues.For MES, the circum-Mercurial orbital period of only 8hours and related magnetospheric disturbances make identifica-tion of ICMEs challenging. Winslow et al. (2015) were able todetect an ICME at MES, lasting from 12:09 until 15:38 on May17th. The shock transit speed was identified as 1344 km s − .ESPs usually peak at lower energies than coronally acceleratedSEPs, and are found only in the vicinity of the IP shocks due toturbulent trapping. At MES shown in Figure 2, we notice a clearintensity peak, likely due to ESPs, starting around 12:10 markedby a grey line right after the arrival of the ICME.A comprehensive catalogue of ICMEs, IP shocks, andstreaming interactive regions (SIRs) for the STEREO spacecrafthas been compiled by Jian et al. (2013) . A shock was detectedat STA on May 18th at 12:43, followed by an ICME until 09:12on May 19th. The deka-MeV proton channels at STA show ma-jor enhancements starting at about 15:25 on May 18th (markedby a grey line), which can be attributed to IP shock acceleratedESPs. A smaller enhancement is seen at 04:52, possibly due to aforeshock of ESPs escaping in front of the IP shock. STB is reported to be within a SIR from 23:48 on May 18thuntil 16:35 on May 22nd, well after the weak increase in protonflux. Upon further inspection of relevant solar wind measure-ments at STB, the possibility of an IP shock passing the space-craft on between the 18th and 19th of May cannot be ruled out,but the data are ambiguous. An alternative explanation for theparticle enhancement at STB, which begins less than 12 hoursafter the flare, is for coronally accelerated particles to drift therealong the HCS, which co-rotates over the position of STEREO-B. We include this HCS drift in our simulations and assess thispossibility in section 4.1.Many spacecraft are available for observing near-Earth tran-sients. Both Wind and ACE databases report the Earth as withinan ICME already from the 16th of May, being thus unrelated tothe GLE 71 eruption. The Wind ICME list lists the ICME start-ing at May 16th 12:28, and ending at May 18th 02:11. ACE ob-servations by Richardson & Cane (2010) list an ICME startingon May 16th 16:00, and ending at May 17th 22:00 UT. The onlyassertion of an actual shock is from the ACE list of disturbancesand transients (see McComas et al. 1998 and Smith et al. 1998) ,with a shock at May 17th 22:00, but it is registered only in mag-netic field measurements. Thus, we find no suggestion that thereshould be a significant ESP signal at Earth.At the location of MSL, neither magnetic nor plasma mea-surements are available to identify ICMEs and IP shocks. NoESP structures are present in the RAD data. However, as RADmeasurements of low energy protons are a ff ected by nonuniformshielding, we cannot rule out the possibility of an ICME associ-ated shock passing at the location of MSL.
4. Particle transport simulations
In order to model heliospheric transport of SEPs accelerated dur-ing the May 17th event, we simulated the propagation of 3 · test particle protons, from the corona into interplanetary space,using the full-orbit propagation approach of Marsh et al. (2013)and Marsh et al. (2015). This model naturally accounts for parti-cle drifts and deceleration e ff ects, and allows for the generationof virtual time profiles at many heliospheric observer locations.Our model was newly improved by the inclusion of a HCS, nor-malised to a thickness of 5000 km at 1 au, as introduced in Bat-tarbee et al. (2017) and as extended to non-planar geometriesin Battarbee et al. (2018). We present here the first results ofthree-dimensional forward modelling of SEP propagation, ex-tending throughout the inner heliosphere, for this event. Becausewe focused on multi-spacecraft observations and the 3D spatialdistribution of particle fluxes, we have not performed compar-isons with 1D modelling e ff orts of large SEP events (see, e.g.,Kocharov et al. 2017)We inject energetic particles into our transport simulation as-suming acceleration to happen at a coronal shock-like structure.Acceleration e ffi ciency across a coronal shock front is a com-plex question in its own right, with applications to the event inquestion presented in Rouillard et al. (2016) and Afanasiev et al.(2017). Their analysis of CME expansion suggests a CME widthof 100 degrees in longitude with varying e ffi ciency along thefront. Using this width, our simulations had di ffi culty recreat-ing proton time profiles at many heliospheric observer locations. https://wind.nasa.gov/2012.php http://espg.sr.unh.edu/mag/ace/ACElists/obs_list.html Article number, page 5 of 12 & A proofs: manuscript no. aanda
Fig. 3.
Synoptic source surface map computed for r = . R (cid:12) using photospheric measurements for Carrington rotation 2123. The location of theflare on May 17th, 2012, is indicated with a triangle. The central meridian at the time of the flare is indicated with a star. The Parker spiral con-necting footpoints for each observer, assuming a solar wind speed of 400 km s − , are shown with squares, numbered as 1: Earth, 2: MSL, 3: STA,4: STB, 5: MES. Purple regions indicate outward-pointing magnetic fields, orange regions inward-pointing magnetic fields, and the boundary lineis shown as a solid black curve. The heliographic equatorial plane is shown as a solid white line. Contour values are given in microtesla. A fit fora simple wavy current sheet is shown as a black dashed curve, and the boundary of the injection region used in particle transport simulations isshown with a black rectangle. Potential field data is provided by the Wilcox Solar Observatory. Thus, we chose to assume additional spread of energetic parti-cles in the corona during the early phase of the event. We iter-ated the width of the injection area, finding one of 180 ◦ widthin longitude, centered at the flare location, to provide the bestresults when attempting to recreate observed time profiles. Thiswide injection region is in agreement with a very wide coronalshock acting as the source of accelerated particles. Injection wasperformed between equatorial latitudes of ± ◦ . The injectionregion is shown in Figure 3 as a black rectangle.In order to decouple injection and transport e ff ects, we choseto model particle injection through a simplified case. Thus, weinject isotropic protons from the aforementioned region with auniform source function at a heliospheric height of r = . R (cid:12) ,at the estimated solar particle release time of 1:40 (Gopalswamyet al. 2013). As most acceleration of particles is assumed to takeplace at low heliospheric heights of up to a few R (cid:12) , an instan-taneous injection is a fair approximation. Any ESPs acceleratedby the interplanetary shock are not modelled. Protons were in-jected according to a power law of γ = − .
0, distributed in theenergy range 10 −
600 MeV. The chosen power law is close tothe value derived by (Kühl et al. 2016) from in-situ observationsusing SOHO / EPHIN. As our focus was on multi-spacecraft ob-servations and modelling over a large spatial extent, we did notmodel protons in the GeV energy range due to comparison datafrom GeV-range observations being available only in the vicinityof the Earth. Extending our injection power law higher, whilstmaintaining adequate statistics, would have required computa-tional resources beyond the scope of this project. The total sim-ulation duration was set to 72 hours.During transport, we modelled particle scattering usingPoisson-distributed scattering intervals, with a mean scatter-ing time in agreement with a mean free path of λ mfp = . u sw =
400 km s − throughout. The magnetic field was scaled to B = .
85 nt at 1 au, consistent with observations. For the wind-ing of the magnetic field, we assumed an average solar rotationrate of Ω (cid:12) = . × − rad s − or 25.34 days per rotation.In order to model particle detection at spacecraft, we gath-ered simulated particle crossings across virtual observer aper-tures at the locations of STA, MES, Earth, MSL, and STB. Foreach virtual observer, we used energy bins in agreement withthose listed in section 3 and time binning of 60 minutes. Toincrease statistics, simulated protons propagating outward fromthe Sun were gathered over a 10 ◦ × ◦ angular window at eachobserver location. As the orbital period of Mercury is only 88days, we implemented longitudinal orbital motion of virtual ob-servers around the Sun. Due to the large time bins used, we havenot attempted to infer exact onset times from particle simula-tions, nor have we explicitly considered twin acceleration sce-narios (see, e.g., Ding et al. 2016 and Shen et al. 2013).For parametrization of the wavy current sheet, we used aleast squares sum method to fit the distance of the r = . R (cid:12) potential field neutral line to a wavy model neutral line, result-ing in a dipole tilt angle of α nl = ◦ , a longitudinal o ff set of φ nl = ◦ , and an peak count multiplier of n nl =
2. This sourceneutral line at r = . R (cid:12) , used as the anchor point of the currentsheet, is depicted in Figure 3 as a dashed black curve.Figure 4 shows the ecliptic distribution of accelerated pro-tons, 10 hours after injection (11:40 UT), along with observerlocations and Parker spiral connectivity assuming a solar windspeed of 400 km s − . Shaded contours show the scaled particledensity in units cm − between −
20 and +
20 degrees latitude. Ofparticular interest is the band of protons close to STB, whichhave experienced HCS drift.
Article number, page 6 of 12. Battarbee et al.: Multi-spacecraft observations and transport simulations of solar energetic particles
Fig. 4.
Filled contours of simulated particle density in units cm − in theinner heliosphere, close to the ecliptic, 10 hours after injection (11:40UT). The locations of five observer platforms are shown along withParker spiral connectivity using a solar wind speed of 400 km s − . The1 au distance is shown with a dashed circle. The arrow is placed alongthe radial direction at the flare location. As our simulations do not include a background intensity andprovided counts in arbitrary units, the particle densities and in-tensities had to be calibrated using a normalisation multiplier.Due to good magnetic connectivity at Earth, we decided to usea near-Earth peak intensity as the reference intensity. For thisnormalisation, we used the 38.0–82.0 MeV GOES energy chan-nel, as it had a clearly defined peak. Although the backgroundlevels at GOES were enhanced due to magnetospheric e ff ects,we assume that the peak values were not a ff ected significantly.Hereafter, for all time profile and peak intensity analysis, resultsfrom our simulations were multiplied by a single normalisationconstant, which resulted in agreement between peak intensitiesdeduced from the 38.0–82.0 MeV channels at Earth from bothsimulations and observations. In this section, we compare the intensity time profiles of simu-lations and observations. Figure 5 displays results of both obser-vations and simulations, with intensity time profiles for selectedenergy bins at each location, actual observations on the top rowand simulation results on the bottom row. For simulation timeprofiles, we include error bars calculating an estimate of uncer-tainty for the intensity using the square root of registered particlecounts. Panels are ordered according to observer footpoint lon-gitude, as shown in Figure 3. We first focus on the qualitativeshape of the time profiles, proceeding from west to east (right toleft) in observer footpoint longitude.At STA, observations show a gradually increasing flux, andSRTs calculated from onset times in Table 1 are many hours af-ter the flare time. This suggests that the location of STA doesnot have good magnetic connectivity to the injection region atthe start of the event. However, the numerical simulation is ableto provide a proton time profile in agreement with observations,using the 01:40 UT release time. Protons fill the well-connectedfield lines with a population which isotropizes, and this popula-tion is then co-rotated over the STA position, becoming magnet-ically well-connected later in the simulation. STA observations in the lowest two energy bins show an additional feature, withbumps in intensity at approximately 04:52 and 15:25 on DOY139. Both these bumps are designated with grey vertical lines inFigure 5. As described in section 3.3, an IP shock is detected atSTA, and these enhancement at low energies can be explained asESPs related to a passing IP shock. The first bump would indi-cate the arrival of an enhanced foreshock region, and the secondbump would occur during the actual shock crossing. The sim-ulated results do not show these bumps as ESP enhancementswere not modelled by the SEP transport simulations.At MES, the rapid increase in particle intensity of our sim-ulations does not agree with the observed delayed particle flux.The simulated time profile shows a simple abrupt event due to ane ffi cient connection to the injection region, although it does dropo ff fast as the observer is rotated westward around the Sun witha rapid 88 day orbital period. Observations seem to suggest thatcoronally accelerated particles were not propagated e ffi ciently toMES, as the enhancement over background intensities is smalland happens too late. Shielding e ff ects due to Mercury or itsmagnetic field were accounted for by masking out measurementswith altitudes below 5000 km. Thus, if an abrupt coronally ac-celerated component had been present at the position of MES,we should have detected it. A delayed enhancement, possiblydue to ESPs, has a good match with the reported ICME cross-ing at 12:09, preceded by a foot of particles accelerated at the IPshock. This enhancement appears stronger in the 45–125 MeVchannel, which might indicate that the signal at MES is stronglyinfluenced by particle drifts, as the magnitude of particle driftsscales with energy. Alternatively, the signal in the 15–45 MeVchannel might be hidden behind a strong background contami-nation signal. We note again that ESPs were not modelled in ourtransport simulations. We also note that although we only showderived 15–45 MeV and 45–125 MeV energy channels in figures2 and 5, the single coincidence channel for >
15 MeV detectiondid not show an abrupt rise, but rather a similar time profile asthe shown derived energy channels. This also rules out singlecoincidence channel contamination as a source of discrepancy.After discussing the observed and simulated time profiles atSTA and MES, it is appropriate to recall the assumed magneticconnectivity to these observers based on Figures 1 and 3. Themagnetic connectivity footpoint of MES is eastward of the STAconnectivity footpoint, i.e. closer to the flare location. Thus, as-suming a Parker spiral IMF and a simplistic injection region sur-rounding the flare location, a strong particle signal at STA shouldsuggest a strong signal also at MES. This is in agreement withour simulated results, but in clear disagreement with the obser-vations.One possible explanation for the discrepancies between ob-servations and simulations is that the IMF shape may di ff er fromthat of a Parker spiral. We find that STA was in a fast solar windstream prior to the event, and additionally a SIR was detectedat STA on May 16th (Jian et al. 2013), with a maximum solarwind speed of 660 km s − , well above the value of 400 km s − used in our simulations. Thus, the IMF might have been primedby this stream, providing STA with a connected footpoint signif-icantly east of the one used in our model. As we do not havesolar wind speed measurements at Mercury, we cannot makesimilar educated guesses about the longitudinal position of thewell-connected footpoint location for MES.Another possible explanation is that smaller-scale e ff ects ofthe IMF and particle propagation are taking place, invalidatingthe Parker spiral model. Recent research into field-line mean-dering (see, e.g., Laitinen et al. 2016 and Ru ff olo et al. 2012)and SEP cross-field propagation (see, e.g., Laitinen et al. 2013 Article number, page 7 of 12 & A proofs: manuscript no. aanda
STEREO-B10 -3 -2 -1 O b s e r v a t i o n
138 139 140DOY 201210 -3 -2 -1 S i m u l a t i o n MSL/RAD138 139 140DOY 2012 EARTH/GOES138 139 140DOY 2012 MESSENGER138 139 140DOY 2012 STEREO-A138 139 140DOY 2012
Proton intensity I [s -1 cm -2 sr -1 MeV -1 ] Fig. 5.
Top row: proton time profiles at five heliospheric locations. Bottom row: corresponding virtual time profiles generated through SEPtransport simulations. The locations are ordered according to connected footpoint longitude: STB, MSL, Earth, MES, and STA. MES and STAobservations are also marked with the onsets of ESP-related proton e ff ects with grey lines. For STA, the first grey line designates the estimatedonset of foreshock ESP flux. and references therein) has investigated this problem. New mis-sions going close to the Sun will provide key data to validatethese theories. Recent research, shown in in panel (a) of Figure6 in Laitinen et al. (2017), suggests, however, that the early-timecross-field variance of a particle distribution is strongly depen-dent on radial distance. Thus, if we assume a narrowed injectionregion, during the early phase of the event, STA could be con-nected to the injection region through widely meandering fieldlines, whereas MES at a distance of only 0 . R (cid:12) would remainoutside this region.At the location of Earth, we compare three GOES en-ergy channel time profiles with observations. The highest en-ergy channel at 84.0–200.0 MeV provides an excellent matchbetween simulations and observations, suggesting accelerationwas near-instantaneous in the corona, and that Earth was well-connected to the acceleration region. At the middle energy chan-nel of 38.0–82.0 MeV, the agreement between simulations andobservations is also good, although the observed time profilebegins to decrease slightly more rapidly than the simulatedone. This may be due to, e.g., di ff erences in particle scatter-ing rates early in the event. At the lowest energy channel of15.0–40.0 MeV, agreement is moderately good, although therate of intensity decay is slightly di ff erent for observations andthe simulation. Additionally, an enhancement in observed in-tensity is found about halfway through DOY 138. Althoughdatabases of interplanetary shocks showed only weak indicationsof a shock passing at earth, an IP-shock related ESP event is stillthe most likely explanation for this feature.At MSL, with a similar magnetic connection to Earth, timeprofiles agree moderately well with simulations. The observa-tions at MSL seem to show similar intensities for all the di ff erentchannels, resulting in a near-flat spectrum. The total intensitiesobserved at the detector are more than an order of magnitudelower than the simulated intensities. However, as the generalshape of the time profile agrees well with that of simulations,we suggest that transport and connectivity is not the primary cause of the disrepancy, but rather, that is due to the flight-timespacecraft shielding around MSL / RAD, causing particles to de-celerate, fragment, or be deflected away. Modelling this e ff ect indetail and performing inversion on the measured particle flux israther challenging. We present preliminary corrections account-ing for the energy loss of protons in section 4.2.Although the footpoint of STB is separated from the flare re-gion by almost 180 degrees, a weak enhancement in proton fluxis seen both in observations and in simulation results. There wasa SIR in the vicinity of STB in the time period following theevent (Jian et al. 2013). Due to this and complicated solar windobservations, a weak ICME-driven shock cannot be ruled out.However, the most likely candidate for explaining the SEP fluxenhancements at STB is coronally accelerated particles trans-ported along the HCS. The successful simulation of this signal atSTB is only possible through the results of our newly improvedSEP transport simulation, supporting an IMF with two magneticpolarities separated by a wavy HCS. Particles propagate alongthe HCS, which is co-rotated over the position of STB (see Fig-ure 3). The di ff erence in onset time and signal duration betweensimulations and observations can be explained by inaccuraciesin the exact position and tilt of the HCS at the position of STB. In order to further assess longitudinal accuracy of our SEP trans-port simulations, we gathered peak intensities for both simula-tions and observations for each channel and plotted them accord-ing to estimated footpoint location (see also Figure 3). The peakintensities for STB, MSL, GOES, MES, and STA are shown inFigure 6, along with peak intensities deduced from simulations.In determining observational peak intensities for STA and MES,we excluded time periods deemed to be enhanced by ESP e ff ects.For STA, this exclusion began at 04:52 UT on the 18th of May,corresponding with the foreshock region of the IP shock. This Article number, page 8 of 12. Battarbee et al.: Multi-spacecraft observations and transport simulations of solar energetic particles foreshock region is visible especially in the 13–24 MeV chan-nel, but somewhat also in the 24–40 MeV channel.Comparing the 15–40 MeV and 38–82, MeV observed andsimulated peak intensities at Earth results in a good match due tothe 38–82 MeV energy channel being used for the normalisationof simulation results. However, observations at 82–200 MeVshow smaller intensities than the respective simulation results.We discuss the e ff ects of the injection spectrum on peak intensi-ties at the end of this section.At STB, simulated peak intensities exceed observed inten-sites by approximately one order of magnitude, but all chan-nels show a similar intensity o ff set. All channels at STB showonly a weak increase over background intensities, which is mod-elled well by the HCS-transported particles in the simulation.The highest two observed energy channels are somewhat lowerthan the simulated ones, suggesting an injection spectrum relatede ff ect, similar to what was seen at Earth.At STA, after excluding all ESP-enhanced regions from ob-servations, observed and simulated peak intensities show a sim-ilar order-of-magnitude di ff erence as was noted at STB. Similarto STB, the observations in the two highest energy channels ex-hibit slightly weaker peak intensities, pointing to the injectionspectrum as the culprit.Neither the time profiles nor the peak fluxes of simulationsand observations at MES agree with each other, which indicatesthat the true magnetic connectivity to MES is more complicatedthan the one used in our simulations. Based on our calibrations,we believe that instrumental e ff ects cannot explain this discrep-ancy. The simulated injection region was set to a width of 180 ◦ in order to provide a good time profile match at STA, how-ever, CME modelling from observations produced shocks frontsof only 100 ◦ width. A narrower injection region might preventcoronally accelerated particles from reaching MES, but wouldalso result in a poor match for STA. The question of magneticconnectivity from the corona to STA and MES was explained indetail in section 4.1. If the CME were to transition to an ICME,and further from the Sun, expand in width, this could be seen asESPs at MES, thus explaining the observations.At MSL, the observed peak intensities are much lower thanthose of simulations, likely due to the in-flight shielding coveringmuch of the detector. As a first step toward correcting particlefluxes at MSL / RAD, we performed calculations of the energyloss of protons traversing a model of the spacecraft shielding.Proton energy losses in matter are primarily due to ionization,which is characterized by the Bethe-Bloch equation, which wasused in our calculations. We considered the distribution of alu-minium equivalent shielding depth within RAD’s viewing angle(Zeitlin et al. 2013). Due to the involved complexity, we did notaccount for generation of secondary particles, which play a ma-jor role at low energies. Thus, we produced a corrected peak in-tensity only for the 60-100 MeV channel, shown in Figure 6 as ablack square. This value appears to be a better match with bothsimulation results and GOES observations, showing a similar re-lationship to the simulated channel as was seen for the GOES82–200 MeV channel. Recreating original particle intensities atall channels of MSL / RAD will be the topic of future investiga-tions.In comparing peak intensities for observations and simula-tions, many things must be taken into account. At MSL, shield-ing weakens the observed intensity in a significant manner,which requires post-processing to correct for. Magnetic connec-tivity at MES provides contradicting time profiles and peak in-tensities. At STA and STB we are able to reproduce time profileshapes, but the peak intensities are over-estimated in our trans- port simulations. However, noting that our injection source wasuniform in longitude, which is not a realistic estimate, but allowsus to now draw conclusions from the peak intensity fits. At lon-gitudes close to the flare location, injection was as simulated andnormalised, but at longitudes far away from the flare, injectione ffi ciency drops, apparently an order of magnitude. This wouldbe unsurprising, considering our injection region was set at 180degrees. Thus, we now have indication that a strong injectiontakes place at the observed shock front with a width of ca. 100degrees, but early-time propagation e ff ects spread particles to aregion of up to 180 degrees with lesser intensity.A general trend was that simulated and observed fluxes forlow energy channels were in better agreement than those ofhigher energy channels. This suggests that our simulated injec-tion power law of γ = / MESSENGER shows that the inner heliosphereis a complicated environment and proper modelling of magneticconnectivity throughout it requires additional e ff ort. Observations of the pitch angle distribution of GeV-class par-ticles for GLE 71 have shown an unusual twin-beam distribu-tion (Adriani et al. 2015, Mishev et al. 2014). In our model, wehave used a simplified model of the scattering experienced bythe SEPs, by considering only large angle scattering events. Infigure 7 we show the derived 10-600 MeV proton pitch-angledistribution at Earth for the early phase of the simulation. Wegathered proton crossings across the 1 au sphere at the locationof Earth, gathering crossings over a 10 ◦ × ◦ angular windowand applied the same intensity scaling as for earlier plots. Wealso performed scaling to account for solid angle size for eachbin. The results indicate that our model is capable of reproduc-ing a twin-stream distribution without including additional mag-netic structures such as loops associated with preceding CMEs.We note that some qualitative similarities with figure 6 of Mi-shev et al. (2014) exist, but more detailed analysis would requirerefining our scattering model.
5. Conclusions
We have presented extensive, detailed multi-spacecraft observa-tions of proton intensities for the solar eruption of May 17th,2012. We have shown the event to encompass a large portion ofthe inner heliosphere, extending to a wide range of longitudes,with a strong detection at Earth, MSL, and STA. We were able
Article number, page 9 of 12 & A proofs: manuscript no. aanda
GOESMSL STASTB MES-150 -100 -50 0 50 100 150Footpoint longitudinal distance from flare site10 -3 -2 -1 P e a k p r o t o n i n t e n s i t y [ s - c m - s r - M e V - ] Legend
SimulationsObservations GOES15-40 MeV38-82 MeV82-200 MeVMSL12-24 MeV24-40 MeV40-60 MeV60-100 MeV STA13-24 MeV24-40 MeV40-60 MeV60-100 MeVSTB13-24 MeV24-40 MeV40-60 MeV60-100 MeV MES15-45 MeV45-125 MeV
Fig. 6.
Peak intensities of time profiles, recorded from observations (circles) and numerical simulations (diamonds). Observers are placed on thex-axis according to footpoint longitudinal distance from the flare. Peak intensities inferred from observations excluded time periods with ESPe ff ects. For MSL / RAD, in addition to the recorded intensities, we show as a black square a version of the 60-100 MeV proton channel, withpreliminary first-order corrections for energy losses due to spacecraft shielding. α I n t e n s i t y [ m − s − s r − M e V − ] Fig. 7.
Derived pitch-angle distribution for 10–600 MeV protons atEarth, using particle propagation simulation data for the early phaseof GLE 71. Time in UT refers to the start of each 10 minute binninginterval. to analyse SEP transport and magnetic connectivity based on anew improved 3D test particle model.Our SEP transport model solves the full-orbit 3D motionof test particle SEPs within heliospheric electric and magneticfields. The model naturally accounts for co-rotation, particledrifts and deceleration e ff ects (Marsh et al. 2013, Dalla et al.2013, and Dalla et al. 2015). Our new improved model includes,for the first time, e ff ects due to a solar magnetic field of twodi ff erent polarities, separated by a wavy HCS. We model pro-ton injection with a shock-like structure near the Sun, and modelinterplanetary transport in accordance with a particle mean freepath of λ mfp = . ff . We report howSTEREO-A observations are explained through a combinationof co-rotation of an SEP-filled flux tube across the spacecraft incombination with an ESP event, and how STEREO-B observa-tions can be explained through HCS drift of coronally acceler-ated protons.For four out of five observer locations, we are able to finda good match in both the qualitative intensity time profiles andthe quantitative peak intensities when comparing observationsand numerical simulations, if we assume that injection e ffi ciencyweakens as a function of longitudinal distance from the flare lo-cation. Our results suggest modern modelling of large-scale so-lar eruptions has improved, and has benefited greatly from theopportunities provided by the two STEREO spacecraft, as wellas other heliospheric and even planetary missions such as MES-SENGER and MSL. SEP forecast tools such as those presentedin Marsh et al. (2015) should play an important role in furtheringour understanding of solar activity.Our study shows that magnetic connectivity to the injectionregion as well as the perpendicular propagation of particles in in-terplanetary space are important factors when assessing the riskof SEP events. Solar wind streams, interacting regions, and con-current coronal mass ejections with associated magnetic struc-tures alter the IMF and particle transport conditions, yet mod-ern computation methods are capable of impressive modellingof SEP events. Further improvements in modelling of the back-ground conditions for SEP simulations are required, with 3Dmagnetohydrodynamic models a likely candidate for future stud-ies. Acknowledgements.
This work has received funding from the UK Science andTechnology Facilities Council (STFC; grant ST / M00760X /
1) and the Lever-
Article number, page 10 of 12. Battarbee et al.: Multi-spacecraft observations and transport simulations of solar energetic particles hulme Trust (grant RPG-2015-094). We acknowledge the International SpaceScience Institute, which made part of the collaborations in this paper throughthe ISSI International Team 353 "Radiation Interactions at Planetary Bod-ies". RAD is supported by the National Aeronautics and Space Administration(NASA, HEOMD) under Jet Propulsion Laboratory (JPL) subcontract 1273039to Southwest Research Institute and in Germany by DLR and DLR’s SpaceAdministration grant numbers 50QM0501, 50QM1201, and 50QM1701 to theChristian Albrechts University, Kiel. The RAD data used in this paper arearchived in the NASA Planetary Data Systems Planetary Plasma InteractionsNode at the University of California, Los Angeles. The PPI node is hosted athttp: // ppi.pds.nasa.gov / . The Solar and Heliospheric Observatory (SOHO) is amission of international collaboration between ESA and NASA. Data from theSOHO / ERNE (Energetic and Relativistic Nuclei and Electron) instrument wasprovided by the Space Research Laboratory at the University of Turku, Fin-land. Wilcox Solar Observatory data used in this study was obtained via theweb site http://wso.stanford.edu at 2017:01:12_05:40:05 PST courtesy ofJ.T. Hoeksema. The Wilcox Solar Observatory is currently supported by NASA.MESSENGER data were calibrated using measurements from Neutron monitorsof the Bartol Research Institute, which are supported by the National ScienceFoundation. Work from D. J. Lawrence is supported by the NASA’s MESSEN-GER Participating Scientist Program through NASA grant NNX08AN30G. Alloriginal MESSENGER data reported in this paper are archived by the NASAPlanetary Data System ( http://pdsgeosciences/wustl.edu/missions/messenger/index.htm ). The authors wish to thank Dr. Nina Dresing for herassistance in accessing and using STEREO data. The authors gratefully acknowl-edge the important comments and suggestions provided by the anonymous ref-eree.
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As the MESSENGER NS instrument was not originally de-signed with SEP proton measurements in mind, calibration andvalidation of derived fluxes is necessary. Absolute flux profilesof protons for the MES ≥
45 MeV and ≥
125 MeV energy thresh-olds were determined using the modelled response and validatedwith measures of the galactic cosmic ray (GCR) flux. Follow-ing Feldman et al. (2010), the measured count rate, C , is relatedto the proton flux, F , (in units of protons sec − sr − cm − ) us-ing C = GAF , where G is the geometry factor in sr, and A =
100 cm is the detector area. For the two highest energy ranges,the values for G are G ≥
125 MeV = . G ≥
45 MeV = .
25 sr(Lawrence et al. 2014). For borated plastic singles, the geometryfactor is approximately G singles ≈ π − G ≥
45 MeV . However, thesingles count rate likely contains a substantial fraction of con-tamination and non-proton background counts, such that its ab-solute calibration for energetic protons is highly uncertain. Themeasured count rates (Lawrence et al. 2016, 2017) are convertedto fluxes using the above relation with the appropriate geometryfactors.The derived fluxes for the ≥
45 MeV and ≥
125 MeV thresh-olds were validated based on a comparison with Earth-basedneutron monitor counts that were converted to particle flux usingthe process given by McKinney et al. (2006). Specifically, neu-tron monitor counts from McMurdo (Bieber et al. 2014) wereempirically converted to a solar modulation parameter, which isused as input to a GCR flux parameterization of Castagnoli &Lal (1980) and Masarik & Reedy (1996). The total GCR flux ac-counts for both protons and proton-equivalent alpha particles us-ing the formulation given by McKinney et al. (2006). When theNS-measured fluxes are compared to the fluxes derived throughthe neutron monitor data, we find an average absolute agreementof <
10% for the ≥
125 MeV flux and <
20% for the ≥
45 MeVflux, which validates the modelled response of Lawrence et al.(2014). The flux rates for the time period of March 26th 2011 toApril 30th 2015 are plotted in Figure A.1.The mean validation ratios of 1 .
07 for triple coincidences,1 .
15 for double coincidence channel LG1 and 1 .
17 for doublecoincidence channel LG2 were applied as correction coe ffi cientsto the extracted MES proton fluxes. Article number, page 11 of 12 & A proofs: manuscript no. aanda