Radial Evolution of the April 2020 Stealth Coronal Mass Ejection between 0.8 and 1 AU -- A Comparison of Forbush Decreases at Solar Orbiter and Earth
Johan L. Freiherr von Forstner, Mateja Dumbovi?, Christian Möstl, Jingnan Guo, Athanasios Papaioannou, Robert Elftmann, Zigong Xu, Jan Christoph Terasa, Alexander Kollhoff, Robert F. Wimmer-Schweingruber, Javier Rodríguez-Pacheco, Andreas J. Weiss, Jürgen Hinterreiter, Tanja Amerstorfer, Maike Bauer, Anatoly V. Belov, Maria A. Abunina, Timothy Horbury, Emma E. Davies, Helen O'Brien, Robert C. Allen, G. Bruce Andrews, Lars Berger, Sebastian Boden, Ignacio Cernuda Cangas, Sandra Eldrum, Francisco Espinosa Lara, Raúl Gómez Herrero, John R. Hayes, George C. Ho, Shrinivasrao R. Kulkarni, W. Jeffrey Lees, César Martín, Glenn M. Mason, Daniel Pacheco, Manuel Prieto Mateo, Ali Ravanbakhsh, Oscar Rodríguez Polo, Sebastián Sánchez Prieto, Charles E. Schlemm, Helmut Seifert, Kush Tyagi, Mahesh Yedla
AAstronomy & Astrophysics manuscript no. cme_fd_at_solo © ESO 2021February 25, 2021
Radial Evolution of the April 2020 StealthCoronal Mass Ejection between 0.8 and 1 AU
A Comparison of Forbush Decreases at Solar Orbiter and Earth
Johan L. Freiherr von Forstner , Mateja Dumbovi´c , Christian Möstl , Jingnan Guo , , , Athanasios Papaioannou Robert Elftmann , Zigong Xu , Jan Christoph Terasa , Alexander Kollho ff , Robert F. Wimmer-Schweingruber , JavierRodríguez-Pacheco , Andreas J. Weiss , Jürgen Hinterreiter , Tanja Amerstorfer , Maike Bauer , Anatoly V. Belov ,Maria A. Abunina , Timothy Horbury , Emma E. Davies , Helen O’Brien , Robert C. Allen , G. Bruce Andrews ,Lars Berger , Sebastian Boden , , Ignacio Cernuda Cangas , Sandra Eldrum , Francisco Espinosa Lara , Raúl GómezHerrero , John R. Hayes , George C. Ho , Shrinivasrao R. Kulkarni , , W. Je ff rey Lees , César Martín , , GlennM. Mason , Daniel Pacheco , Manuel Prieto Mateo , Ali Ravanbakhsh , , Oscar Rodríguez Polo , Sebastián SánchezPrieto , Charles E. Schlemm , Helmut Seifert , Kush Tyagi , and Mahesh Yedla , (A ffi liations can be found after the references) February 25, 2021
ABSTRACT
Aims.
We present observations of the first coronal mass ejection (CME) observed at the Solar Orbiter spacecraft on April 19, 2020, and theassociated Forbush decrease (FD) measured by its High Energy Telescope (HET). This CME is a multispacecraft event also seen near Earth thenext day.
Methods.
We highlight the capabilities of HET for observing small short-term variations of the galactic cosmic ray count rate using its singledetector counters. The analytical ForbMod model is applied to the FD measurements to reproduce the Forbush decrease at both locations. Inputparameters for the model are derived from both in situ and remote-sensing observations of the CME.
Results.
The very slow ( ∼
350 km / s) stealth CME caused a FD with an amplitude of 3 % in the low-energy cosmic ray measurements at HET and2 % in a comparable channel of the Cosmic Ray Telescope for the E ff ects of Radiation (CRaTER) on the Lunar Reconnaissance Orbiter, as well asa 1 % decrease in neutron monitor measurements. Significant di ff erences are observed in the expansion behavior of the CME at di ff erent locations,which may be related to influence of the following high speed solar wind stream. Under certain assumptions, ForbMod is able to reproduce theobserved FDs in low-energy cosmic ray measurements from HET as well as CRaTER, but with the same input parameters, the results do not agreewith the FD amplitudes at higher energies measured by neutron monitors on Earth. We study these discrepancies and provide possible explanations. Conclusions.
This study highlights that the novel measurements of the Solar Orbiter can be coordinated with other spacecraft to improve ourunderstanding of space weather in the inner heliosphere. Multi-spacecraft observations combined with data-based modeling are also essential tounderstand the propagation and evolution of CMEs as well as their space weather impacts.
Key words.
Sun: coronal mass ejections (CMEs) - Sun: heliosphere - cosmic rays
1. Introduction
On April 19, 2020, a coronal mass ejection (CME) passed theSolar Orbiter (SolO, Müller et al. 2020) spacecraft – the firstlarge-scale flux rope CME seen in situ at SolO. At this time,the spacecraft was closely aligned in heliospheric longitude withEarth (less than 4° separation), and it was located at a radialdistance of 0.8 AU from the Sun, as shown in Fig. 1. Conse-quently, the same slow CME ( v <
400 km / s) was also observednear Earth the next day, causing the first geomagnetic storm ofthe year with a Dst index of −
59 nT and Kp index of 5. Dur-ing the event, SolO was still in its Near Earth CommissioningPhase, which ended on June 15, 2020, but nevertheless, some ofthe in situ instruments, including the Energetic Particle Detectorsuite (EPD, Rodríguez-Pacheco et al. 2020) and the magnetome-ter (MAG, Horbury et al. 2020) were already taking continuousmeasurements and were able to observe signatures of the CME.In addition, the STEREO-A spacecraft had a su ffi cient longi-tudinal separation of ∼
75° from SolO and the Earth and thus was able to provide excellent remote sensing observations of theCME propagation from a side view. This event observed at bothSolO and Earth provides an excellent example for the coordi-nated science that is possible with SolO and other heliophysicsmissions in the solar system.CMEs, clouds of magnetized plasma ejected from the Sun,are one of the key phenomena in space weather research, as theycan cause severe geomagnetic storms (Kilpua et al. 2017) dis-rupting terrestrial infrastructure. The shocks driven by CMEs arealso partly responsible for energetic particles in the heliosphere(Reames 2013), which may pose radiation danger to astronautsand spacecraft. Consequently, two of the four main scientificquestions of the Solar Orbiter mission (Müller et al. 2013) arealso linked to the better understanding of CMEs.Forbush decreases (FDs), first observed by and later namedafter Scott E. Forbush (1937), are short-term decreases of thegalactic cosmic ray (GCR) flux, caused by the passage of mag-netic field structures in the solar wind, such as CMEs or streaminteraction regions (SIRs). Such magnetic structures can act as
Article number, page 1 of 16 a r X i v : . [ a s t r o - ph . S R ] F e b & A proofs: manuscript no. cme_fd_at_solo
Fig. 1.
Locations of planets and spacecraft in the inner solar system onApril 20, 2020, the day the CME arrived at Earth. The trajectory of So-lar Orbiter (SolO) is shown as an orange dashed line, and PSP denotesthe location of Parker Solar Probe. The large black arrow describes theapproximate propagation direction of the CME, and the colored seg-ments next to STEREO-A show the fields of view of the remote sensinginstruments COR1 / COR2 (green), HI1 (blue) and HI2 (red). The insetshows a zoomed-in view of the relative positions of Earth, the Moonand the Lagrange point L1, where the Wind spacecraft is located. a barrier for the propagation of GCRs, e.g. because the GCRsneed to di ff use across a strong field, so that the observed fluxis temporarily decreased at the locations these structures pass.The decrease phase usually takes less than 1 day, followed byan often slower recovery to the previous level (on the order of1 week). In the case of CMEs, FDs are driven by both the tur-bulent shock / sheath region (if present) as well as the followingmagnetic ejecta, two e ff ects which can sometimes be clearly sep-arated when a two-step decrease is observed (e.g. Cane 2000).The amplitude of a FD depends not only on the properties ofthe heliospheric structure, but also on the energy of the observedGCR particles: lower energy particles are modulated more easilyand thus typically show larger FDs (e.g. Lockwood 1971; Lock-wood et al. 1991; Cane 2000; Guo et al. 2020). In the past, thestudy of FDs was mainly based on data from neutron monitors onthe surface of the Earth, but nowadays, GCR measurements suit-able for FD studies are also available from many spacecraft inthe near-Earth space as well as on other solar system bodies, andthese have been routinely used for multi-spacecraft studies (e.g.Cane et al. 1994; Lockwood et al. 1991; Freiherr von Forstneret al. 2018, 2019, 2020; Witasse et al. 2017; Winslow et al.2018). In all cases, it is important to take into account the en-ergy dependence of the FD amplitude, as such instruments maybe sensitive to di ff erent GCR energies.In this work, we present the EPD observations of the FD as-sociated with the April 19 CME at SolO, as well as the corre-sponding observations at Earth. We describe which EPD dataproducts are best suited to make measurements of FDs, and weanalyze these data to see how the CME a ff ected the GCR flux atdi ff erent heliospheric locations and at di ff erent particle energies.We also employ the ForbMod model to reproduce the observedFD and gain insight into the how the large-scale evolution ofthe CME structure a ff ected the properties of the FD. A study A1 B1 C B2 A2 . Fig. 2.
Schematic diagram of the HET sensor head. Exemplary parti-cle trajectories ending up in di ff erent data products are shown by thearrows: stopping in B, stopping in C, penetrating, GCR channel, C sin-gle counter. A 3D graphic of the sensor head is shown in Rodríguez-Pacheco et al. (2020, Fig. 31). by Davies et al. (2021) complements this work by investigatingthe magnetic field measurements at both Solar Orbiter and Earthin more detail. In Sect. 2, we will introduce the di ff erent instru-ments used as data sources in this study, followed by an overviewof our modeling methods in Sect. 3. The measurement and mod-eling results will then be presented in Sect. 4, and discussed inmore detail in Sect. 5.
2. Data sources
As part of the Energetic Particle Detector suite (Rodríguez-Pacheco et al. 2020) onboard the Solar Orbiter mission (Mülleret al. 2013; Müller et al. 2020), the High Energy Telescope(HET) is a particle telescope covering the high-energy end ofthe solar energetic particle (SEP) spectrum as well as galacticcosmic rays (GCR). Its two double-ended telescopes each con-sist of four thin 300 µ m silicon solid state detectors (named theA1, B1, B2, and A2 detectors) and the C detector, a 2 cm thickBi Ge O (BGO) scintillator, in the center. This detector layoutis shown in Fig. 2. The C detector is read out using two photodi-odes placed on either side, named C1 and C2. HET is designedto measure the fluxes of electrons above 300 keV, protons above7 MeV as well as heavier ions, with one telescope (HET 1) pro-viding the sunward and antisunward viewing directions (paral-lel to the mean Parker spiral angle), and the other (HET 2) be-ing mounted perpendicular to that to measure particles comingfrom outside the ecliptic plane. The telescopes distinguish be-tween particles stopping in one of the B detectors (B1 or B2,e.g. red arrow in Fig. 2), particles stopping in the C (green ar-row) detector, and particles penetrating the whole telescope (bluearrow) to achieve a large energy coverage, and use the d E / d x - E -method to separate di ff erent particle species. This technique hasbeen in use by many previous space-borne charged particle de-tectors, including the Interplanetary Monitoring Platform-1 mis-sion in the 1960s (McDonald & Ludwig 1964) as well as morerecent instruments such as the Mars Science Laboratory Radia-tion Assessment Detector (Hassler et al. 2012) and the Chang’E4 Lunar Lander Neutrons and Dosimetry experiment (Wimmer-Schweingruber et al. 2020). For more details about the appli-cation of the d E / d x - E -method in HET, see Rodríguez-Pachecoet al. (2020, Sect. 7.2.5).While the nominal data products of HET are optimized forthe study of high intensity SEP events by choosing a rather smallopening angle to achieve a high energy resolution, these data arenot optimal for observing short-term variations of the GCR back-ground due to their low level of counting statistics. Alternatively,HET provides a separate “GCR channel”, which observes pen-etrating particles with an increased opening angle by omitting Article number, page 2 of 16ohan L. Freiherr von Forstner et al.: Radial Evolution of the April 2020 Stealth Coronal Mass Ejection between 0.8 and 1 AU the A detectors from the coincidence condition, i.e. counting allparticles that penetrate B1, C, and B2 (e.g. teal arrow in Fig. 2).This leads to an almost 20-fold increase in the geometric factorcompared to the nominal penetrating particle channel.For applications requiring even higher counting statistics, itis also possible to use single detector count rates without anycoincidence conditions, similar to the technique applied e.g. byRichardson et al. (1996) for the IMP 8 and Helios E6 instrumentsand Kühl et al. (2015) for SOHO-EPHIN. In this case, GCR par-ticles are measured from all directions (e.g. orange arrow in Fig.2), but without any energy resolution or species separation. TheHET C detectors are best suited for this purpose due to theirlarge size and nearly isotropic shielding by the aluminum hous-ing. For each HET telescope, four such counters are available— each of the two photodiodes has a high-gain channel (C1H,C2H) with a deposited energy threshold of E th = E th =
10 MeV. As theseC detector counters provide no directional information, the val-ues from HET 1 and HET 2 and from the two photodiodes ineach telescope can be simply summed up to achieve an evenhigher count rate, approximately 270 counts / s for the high-gainchannels (C1H + C2H × / s for the low-gain channels (C1L + C2L × / HET sensor head and thecorresponding electronics box, so that the the shielding by the in-strument housing and electronics box as well as the generation ofsecondary particles are taken into account. A simplified model ofthe Solar Orbiter spacecraft was also optionally included in thesimulation setup to consider the influence of the spacecraft bodyon the incoming particle flux. This may be important for the Cdetector counters, as they are sensitive to particles entering HETfrom any direction. The spacecraft was modeled as a cuboid withthe size of the main body (2 .
20 m × .
81 m × .
46 m) and totalmass of 1700 kg (which corresponds to the launch mass of SolarOrbiter, excluding its solar panels). Its composition was assumedto be 200 kg of hydrazine fuel, 750 kg of aluminum, represent-ing the structural components of the spacecraft, and 750 kg ofa printed circuit board (PCB)-like material, as defined by Ap-pel et al. (2018) and Appel (2018, Table 6.2), representing theelectronics components of the spacecraft and its payload. Thedevelopment of a more detailed Geant4 model of the spacecraftbody based on CAD models of its components is in progress,but was not possible within the time constraints of this study andis not expected to change the results significantly. Only protonsbetween 5 MeV and 100 GeV were used as input particles to re-duce the complexity of the simulation setup, as protons comprise90 % of primary GCR particles (Simpson 1983).The proton response function resulting from the simulationis shown in Fig. 3 (upper panel). Four curves are shown, corre-sponding to the simulation setup with and without the spacecraftmodel, and for the di ff erent threshold energies of the high- andlow-gain channels. It becomes clear that the low-energy cuto ff is mainly influenced by the threshold energy: 12 MeV for thehigh-gain channel and 16 MeV for the low-gain channel. Afterthe cuto ff follows a narrow plateau corresponding to particles G [ c m ² s r ] HET C detector counters E th = 4 MeV, spacecraftE th = 10 MeV, spacecraftE th = 4 MeV, no spacecraftE th = 10 MeV, no spacecraft10 primary energy [MeV]10 G [ c m ² s r ] CRaTER counters D2 single counter, h = 96 kmD2 single counter, h = 52 km to 133 kmGood events counter, h = 96 kmGood events counter, h = 52 km to 133 km
Fig. 3.
Upper panel:
Response functions of the SolO HET C detectorsingle counters as determined using a Geant4 simulation. The four linescorrespond to four di ff erent scenarios depending on the threshold ap-plied for the available counters. The derivation of the response functionis described in Sect. 2.1. Lower panel:
Response functions of the D2detector single counter (blue) and the good events counter (orange) ofthe LRO CRaTER instrument. Lines show the response for the mean al-titude of CRaTER during the event, while shaded areas mark the rangeof responses for the maximum and minimum altitudes. These responsefunctions were derived by Looper et al. (2013) and are described in Sect.2.2. entering C through the nominal field of view (i.e. through the Aand B detectors), followed by an increase related to particles en-tering from the sides through the HET housing. The spacecraftbody provides additional shielding ( ∼
20 %) for the detector inthe lower energy part, but generates additional secondary par-ticles above a primary proton energy of 1 GeV — up to a 2.5-fold increase of the geometric factor for 100 GeV particles. Onthe other hand, without the spacecraft body, the geometric factorfor high energies stays approximately constant above 1 GeV, at G = (128 ±
2) cm sr for E th = G = (106 ±
2) cm srfor E th =
10 MeV. As the GCR proton flux typically peaks at orbelow 1 GeV and decreases again for higher energies, the di ff er-ences caused by the spacecraft body only have a minor influenceon the observed count rates. By folding the response functionfor E th = Φ =
270 MV) and integrating over the primary energy, we ob-tained count rates of 48 / s without the spacecraft model and 53 / swith the spacecraft model, an increase on the order of 10 %. Thisis only about 80 % of the typically observed count rate (270 / s,divided by 4 channels), as only protons were simulated. We notethat the e ff ect of the spacecraft body may be larger for heav-ier ions, as they fragment more in the spacecraft and may thuscontribute more to the response function with the generated sec-ondaries. Article number, page 3 of 16 & A proofs: manuscript no. cme_fd_at_solo
The Cosmic Ray Telescope for the E ff ects of Radiation(CRaTER, Spence et al. 2010) is an instrument on the LunarReconnaissance Orbiter (LRO) mission measuring the radia-tion dose and linear energy transfer (LET) spectra in lunar or-bit. CRaTER consists of three pairs of thin (140 µ m) and thick(1000 µ m) silicon detectors, D1 through D6, separated by sec-tions of tissue-equivalent plastic serving as an absorber. The D1end of the telescope is pointed towards the zenith, while the D6end points towards the surface of the Moon. Similarly to HET,CRaTER uses multiple coincidence conditions between its de-tectors to measure particles of di ff erent energies. For example,the lowest energy particles are detected using the coincidenceof D1 and D2 (the uppermost two detectors), with a minimumenergy of 12 . . and on the CRaTER web site providesingle counters for each of the 6 detectors, similar to the HETcounters described in Sect. 2.1, as well as additional countersfor rejected events , good events and total events , where a goodevent is any valid event where an incoming particle triggered atleast one detector.This means that there are two di ff erent counters in theCRaTER data (D2 and good events ) measuring protons with en-ergies (cid:38) . good events counter was already used by Sohnet al. (2019b,a) to study Forbush decreases and energetic parti-cle events, and it has the best counting statistics (on the order of ∼ / s at the time of the event studied here). However, whilethe threshold is well-defined, the response function of the goodevents counter is slightly more complex, as it includes multi-ple detectors with di ff erent shielding conditions and measures ahigher amount of secondary particles coming from the lunar sur-face (the so-called albedo) than D2 alone. Looper et al. (2013,Appendix A) have derived the response functions of the singledetector count rates using a Geant4 (Agostinelli et al. 2003) sim-ulation. The response functions of the D2 detector single counteras well as the good events counter are plotted in 3 (lower panel).Similarly to the HET response function in the upper panel, stepsin the response function occur when di ff erent parts of the tele-scope are penetrated by particles.In addition to the count rate files, we have used the ancillarydata of the LRO to exclude time periods where the spacecraft isnot in its nominal orientation, e.g. due to orbit adjustment ma-neuvers. Any data where the LRO is more than 1° away fromthe nominal orientation, with CRaTER’s D2 detector pointingtowards the zenith, is excluded to make sure that the measuredcount rates are not a ff ected by these activities. This exclusiononly a ff ects few data points, as the LRO pointing is usually veryprecise to support its imaging instruments.As the LRO orbit is elliptical and relatively close to the lu-nar surface (between 54 km and 132 km above the surface in thetime period studied in this work), the Moon takes up a signifi-cant portion of the sky as viewed from CRaTER. Thus, the Moonshields CRaTER from part of the incoming GCR, but also pro-duces albedo particles. This means that the count rate of parti-cles measured using a single-detector counter (i.e. in a 4 π solid https://pds-ppi.igpp.ucla.edu/ http://crater-web.sr.unh.edu/ angle field of view) periodically varies with the current altitude,which is also shown in the altitude-dependent response functionsin Fig. 3 (lower panel). The plotted altitudes are slightly di ff erentfrom the actual values ( ± ff erence.The orbital period of the LRO is about 110 minutes, which de-termines the frequency of this periodic signal. Multiple methodshave been developed to correct for this e ff ect, such as the dosecorrection factor given by Schwadron et al. (2012) based on ge-ometrical calculation of the covered solid angle, or the Fourierseries method introduced by Winslow et al. (2018). In this study,we apply a simple empirical method in which we create a scat-ter plot of the time-dependent CRaTER count rate c ( t ) versus theLRO altitude h ( t ) for the time period of interest, apply a linear re-gression, and use the obtained slope m to calculate the correctedcount rate c corrected ( t ) = c ( t ) − m · (cid:16) h ( t ) − h (cid:17) (1)where h denotes the mean altitude of the LRO during the timeperiod investigated, which is 93 km for the event studied in thiswork. In this case, we have found this method to work aboutas well as the Fourier series method in suppressing the periodicsignal and better than the simple geometrical calculation, whichdoes not take into account the albedo particles generated by theMoon. However, short- or long-term variations of the GCR spec-trum, which influence the ratio between the counts of primaryGCR and albedo particles and thus the necessary correction fac-tor, are not accounted for by any of these methods and can stillcause the periodic component to appear in the corrected signal,albeit with a much lower amplitude. Due to these di ffi cultieswith the altitude correction, we additionally always plot orbit-averaged values of the CRaTER data. As stated above, neutron monitors have historically been themost important data source for the study of GCR variations ingeneral and FDs in particular. The global network of neutronmonitors, whose data are available from the Neutron MonitorDatabase (NMDB) , provides continuous measurements frommany locations around the globe. In contrast to deep space mea-surements, neutron monitors have an inherent cuto ff energy (of-ten given in terms of rigidity) determined by the Earth’s magne-tosphere and atmosphere, which depends on the latitude as wellas the altitude of the neutron monitor. At the poles, the influ-ence of the magnetosphere decreases to zero (see e.g. Smart &Shea 2008), leading to a cuto ff rigidity of 0 . ∼ ff dominates and results in a cuto ff energy of about450 MeV for protons Clem & Dorman (2000), i.e. a factor of ∼ ff erent lo-cations to calculate the main characteristics of cosmic-ray varia-tions outside of the atmosphere and magnetosphere of Earth haslong been proposed (see Krymsky 1964; Krymsky et al. 1966; Article number, page 4 of 16ohan L. Freiherr von Forstner et al.: Radial Evolution of the April 2020 Stealth Coronal Mass Ejection between 0.8 and 1 AU
Belov et al. 1973, 1974; Dorman 2009) and is still used nowa-days (e.g. Papaioannou et al. 2019, 2020; Abunina et al. 2020).This technique is called the global survey method (GSM). TheGSM separates the isotropic part of the variations of cosmic raysfrom the anisotropic part and uses spherical harmonics to expresstheir respective amplitudes: In the following, A Ax , Ay , and Az are the cor-responding amplitudes of the first harmonic (higher orders arenot considered). Ax and Ay denote the equatorial components ofthe anisotropy, with x pointing away from the Sun and y perpen-dicular to that, while z is the north-south component. However,in order to achieve this, first the atmospheric and instrumentalresponse functions, which couple the primary particles at the topof the atmosphere to the secondaries recorded by neutron mon-itors on the ground, and a backmapping of cosmic ray particlestraveling under the influence of Earth’s magnetic field are ap-plied. The historical development, scientific argumentation, andmathematical formulation of GSM can be found in the recentcomprehensive report of Belov et al. (2018). GSM incorporates apower-law dependence on the rigidity for the isotropic part of theCR variations (i.e. A
0) and thus can provide outputs for a set offixed rigidities (see for example Figure 2 in Belov 2000). How-ever, a fixed rigidity of 10 GV (corresponding to a proton energyof 9 . ff ective rigidity of NMs todetect GCRs (see e.g. Asvestari et al. 2017; Koldobskiy et al.2018), implying that a NM is mostly responsive to the variabil-ity of mid-rigidity CRs from several GV to several tens of GV inrigidity.
3. Methods
ForbMod (Dumbovi´c et al. 2018) is an analytical physics-basedmodel to describe Forbush decreases caused by flux rope CMEs.Its calculations are based on the self-similar expansion of a fluxrope, which is modeled as a (locally) cylindrical structure withan initial radius a close to the Sun that initially contains noGCRs at its center. While the flux rope propagates away fromthe Sun, it expands self-similarly: Both the increase of the fluxrope radius a and the decrease of the central magnetic field mag-nitude B c are assumed to follow power law expressions with theso-called expansion factors n a and n B used as power law indices: a ( t ) = a (cid:32) R ( t ) R (cid:33) n a , B c ( t ) = B (cid:32) R ( t ) R (cid:33) − n B , (2)where R ( t ) describes the radial distance of the flux rope from theSun, R the initial distance at time t =
0, and B the initial cen-tral magnetic field. As stated by Dumbovi´c et al. (2018), previousobservational studies (Bothmer & Schwenn 1998; Leitner et al.2007; Démoulin et al. 2008; Gulisano et al. 2012) constrainedthe power law indices to 0 . < n a < .
14 and 0 . < n B < . ff use into the flux rope slower than in the surround-ing solar wind, so that the GCR phase space density within theflux rope is decreased while it passes by an observer. ForbModthen describes the GCR phase space density within the flux ropeusing the following main equations, which are derived in detail by Dumbovi´c et al. (2018): U ( r , t ) = U (cid:32) − J (cid:32) α r ( t ) a ( t ) (cid:33) e − α f ( t ) (cid:33) , f ( t ) = D a (cid:32) vR (cid:33) x t x + x + U is the GCR phase space density outside the flux rope, J is the Bessel function of first kind and order zero, α is a con-stant corresponding to the first positive root of J , r is the radialdistance of the observer from the flux rope center (which may betime-dependent, hence r ( t )), D is the initial di ff usion coe ffi cientand v is the CME propagation speed. The function f ( t ) describesthe GCR di ff usion into the flux rope, where the di ff usion timeis equivalent to the propagation time t since the initial condi-tion ( t =
0) near the Sun. It is assumed that v is constant andthat the di ff usion coe ffi cient D is inversely proportional to thecentral magnetic field, D ∝ / B c , so that D ( t ) follows a powerlaw with the index n B (c.f. Eq. 2). This power law relation wasalready inserted to obtain the expression for f ( t ) given in Equa-tion 3. Additionally, the ambient GCR phase space density U is assumed to be constant to simplify the calculation; the knownradial gradient the GCR flux of about 3 % / AU (Webber & Lock-wood 1999; Gieseler & Heber 2016; Lawrence et al. 2016) is nottaken into account. The expansion type x = n B − n a (cid:44) − x = x > x < x = − ff erentfunctional form of f ( t ) in Equation 3 (for details, see Dumbovi´cet al. 2018). The influence of the value of x on the ForbMod re-sult can be understood as the interplay between the expansionand di ff usion e ff ects – when the di ff usion (which depends on themagnetic field, and thus, n B ) is very e ffi cient, the flux rope isquickly filled with GCR particles, but a fast increase of the fluxrope size (large n a ) can counteract this e ff ect by increasing thespace that needs to be filled with GCRs.In addition to its dependence on the magnetic field, the GCRdi ff usion coe ffi cient D also depends on the particle energy. E.g.,higher energy particles di ff use into the flux rope more easily andthus show a shallower FD. While the original model of Dum-bovi´c et al. (2018) describes only the FD profile of one specificGCR energy, for which D needs to be provided, Dumbovi´c et al.(2020) extended the model with empirical functions for the en-ergy dependence of the di ff usion coe ffi cient, so that the FD pro-file can be calculated for any GCR energy. By folding the result-ing spectrum with the response function of a particle detector,it is then possible to simulate the measurement of the FD bythis detector. In this version of ForbMod, the input GCR spec-trum and the energy dependence of the di ff usion coe ffi cient D areneeded as input parameters for the model. As described by Dum-bovi´c et al. (2020, Appendix B), the modified force-field approx-imation described by Gieseler et al. (2017) is used to calculatethe GCR spectrum based on the values of the solar modulationpotential Φ obtained from neutron monitor data by Usoskin et al.(2011) and from ACE / CRIS data by Gieseler et al. (2017). Forour event in April 2020, near the minimum between Solar Cy-cles 24 and 25, the corresponding measurements of Φ are notyet available, so we use the values from similar conditions for theprevious solar cycle in June 2009. The values from Usoskin et al. Article number, page 5 of 16 & A proofs: manuscript no. cme_fd_at_solo (2011) are derived based on data from the Oulu neutron monitor— as its count rates between April 2020 and June 2009 are com-parable, this supports our assumption that the solar modulationconditions are very similar. The energy-dependent di ff usion co-e ffi cient is calculated using the empirical formula given by Pot-gieter (2013), with parameters derived by Potgieter et al. (2014)for the period 2006–2009 from PAMELA data and by Corti et al.(2019) for the period 2011–2017 from AMS-02 measurements.In this case, data for 2020 are not yet available either, so we usethe values from 2009 with comparable solar cycle conditions.More detailed explanations about these parameters are given byDumbovi´c et al. (2020, Appendix A).To convert the U ( r , t ) dependence in Equation 3 into a func-tion that purely depends on the time t and thus can directly becompared to in situ GCR measurements, the observer location r with respect to the flux rope center needs to be defined. For this,we can use the in situ measured velocity profile v in situ ( t ) of theflux rope, i.e. the observer passes through the flux rope at thismeasured velocity: r ( t ) = (cid:12)(cid:12)(cid:12) a ( t ) − v in situ ( t ) · ( t − t CME ) (cid:12)(cid:12)(cid:12) (5)where t CME is the in situ arrival time of the CME. The conversionof U ( r ) into U ( t ) introduces some asymmetry into the FD profile,as the in situ measured velocity profile v in situ ( t ) is typically notconstant.Note that ForbMod only models the GCR modulation due toa flux rope CME, not the additional influence of a shock / sheathregion, although it may be combined with other models to takethis into account (see e.g. Dumbovi´c et al. 2020; Freiherr vonForstner et al. 2020).
4. Results
The April 19 CME was observed at Solar Orbiter using itsmagnetometer, showing a clear signature of a flux rope with asouth-east-north field rotation and a maximum field intensity of B max = . ff ected the sensor temperatures on that day.Solar wind plasma measurements from the Solar Wind Analyzerinstrument on SolO (SWA, Owen et al. 2020) are not availablefor this event, as it was not yet fully commissioned. EPD mea-sured the fluxes of suprathermal ions slightly above solar windenergies (5 . / s to 4000 km / s) us-ing the SupraThermal Electrons and Protons (STEP) instrument.As shown in the second panel of Fig. 4, STEP sees a clear en-hancement of suprathermal ions accelerated in the sheath region,and this is also confirmed by EPD’s Electron Proton Telescope(EPT, not shown here), which saw enhancements of ions upto 100 keV. No significant enhancements of energetic electronswere observed in EPT or STEP.The flux rope is followed by a separate structure with en-hanced levels of magnetic turbulence. By comparing with thesolar wind plasma observations near Earth (see Fig. 5 and itsdescription later in this section), where clear increases in solarwind speed and temperature are observed, we have identified this to be a stream interaction region (SIR), followed by a stream ofhigh speed solar wind. We have determined the onset times ofthe three SIR structures, the forward shock (F), stream interface(I), and reverse shock (R) at SolO by searching for shock sig-natures in the magnetic field data that are similar to those seenat Wind, though the identification is less reliable than at Earthdue to the missing SWA data. STEP and EPT also see anotherenhancement of energetic ions close to the stream interface.However, the main focus of this study is the signature in thehigh energy particles, where a clear Forbush decrease with a dropamplitude of around 3 % in both the GCR channel as well as theC detector counters is observed (bottom panels of Fig. 4). The Ccounter is plotted in 10 minute time averages, with an additionalcurve showing a smoothed version of these data (rolling mean),and the GCR channel is shown in a similar fashion with a 1 hourcadence. Due to the higher count rate, the FD is especially wellobserved in the C counters. The main part of the decrease occursduring the passage of the flux rope — the decrease within thesheath region is well below 1 %. This means that the assumptionof the ForbMod model (Sect. 3.1) that only the flux rope e ff ectis taken into account is fulfilled. A second GCR decrease is ob-served after the CME, coinciding with the passage of the SIR.Fig. 5 shows the in situ measurements of the CME arrivalnear Earth, including solar wind magnetic field and plasma datafrom the Magnetic Field Investigation (MFI, Lepping et al. 1995)and the Solar Wind Experiment (SWE, Ogilvie et al. 1995) on-board the Wind spacecraft, as well as GCR measurements fromthe South Pole neutron monitor (SoPo), the GSM outputs andthe CRaTER D2 counter. The measured speed of the CME atWind is very slow at a maximum of 370 km / s. The Wind andCRaTER measurements were shifted forward in time taking intoaccount the radial distance to Earth (1 h 7 min for Wind at L1,and 15 min for CRaTER at the Moon — cf. the inset in Fig.1). These time shifts were calculated using the abovementionedmaximum speed of 370 km / s, which is seen at the front of theCME flux rope. Considering this time shift, the shock arrivaltime at Earth is 02:40 UTC on April 20, and the flux rope arriveda few hours later at 09:01 UTC. In comparison to Solar Orbiter,the magnetic field strength of the flux rope has decreased to amaximum of B max = . B Z , or B N ) seen at the beginningof the flux rope is a feature which is typically associated withhigh geoe ff ectiveness (e.g. Gopalswamy 2008). The sheath du-ration increased by more than two hours ( ∼
60 %), which is prob-ably related to the accumulation of additional solar wind plasmain front of the CME as well as expansion due to the increasingvelocity profile of the sheath region (see e.g. Manchester et al.2005; Siscoe & Odstrcil 2008; Janvier et al. 2019; Freiherr vonForstner et al. 2020), while the expansion of the flux rope is moremoderate at a bit more than one hour ( ∼ / s for the flux rope front, which matches the in situmeasured front speed of 370 km / s very well.As mentioned before, the SIR following the CME is clearlyseen in the in situ data at Wind, showing signatures such asthe increases in temperature and velocity as well as a decreasein density. According to these signatures, the time of the for-ward shock (F), stream interface (I) and reverse shock (R) weremarked in Fig. 5. Even though the solar wind plasma data are notavailable at Solar Orbiter for this event (as described above), it Article number, page 6 of 16ohan L. Freiherr von Forstner et al.: Radial Evolution of the April 2020 Stealth Coronal Mass Ejection between 0.8 and 1 AU
Shock CME F I R B [ n T ] SolO MAG | B | B R B T B N E [ k e V ] SolO STEP ions c o un t r a t e [ s ] SolO HET (C counter) datasmoothed - - - - - - date0.580.590.600.610.62 c o un t r a t e [ s ] SolO HET (GCR) datasmoothed d J [ s mm ² s r k e V ] ¹ Fig. 4.
Measurements from MAG, STEP andHET on Solar Orbiter, showing the magneticstructure of the CME, suprathermal particle sig-natures, and the associated FD observations inthe GCR channel and the C detector counter ofHET. The MAG measurements are displayed inradial (R), tangential (T) and normal (N) coor-dinates. Black vertical lines and shaded regionsmark the time periods corresponding to di ff er-ent events: Shock arrival, CME (flux rope) startand end, as well as forward shock (F), streaminterface (I) and reverse shock (R) of the SIR. is clear from the magnetic field measurements that the SIR fol-lowed closely behind the CME at both locations, separated by aregion of high plasma density (seen in the Wind measurements).Assuming an average solar wind speed within the SIR of approx-imately 400 km / s, the separation of the Parker spiral footpointsof SolO and Earth is 16 . ff ected the evolution of the CME, e.g. bycompressing it from behind. We will discuss this further in Sect.5. Comparing the GCR measurements at SoPo and CRaTER,as well as the outputs of GSM, when utilizing measurements of ∼
35 neutron monitors, it can be seen that the relative amplitudesof the FD profiles induced by the CME at SoPo and from GSMare quite similar, whereas both are quite di ff erent compared toCRaTER. As discussed in Sect. 2.2, CRaTER covers a similarenergy range as the HET C counter at SolO, while neutron mon-itors have a larger cuto ff energy. The South Pole neutron mon-itor has much higher counting statistics than CRaTER, but theFD there only reaches an amplitude of 1 . . / sheath structure, dur-ing which only a small decrease is observed. On the other hand,the FD at CRaTER has an amplitude of 2 . ff erence is only less than one orbital period ofCRaTER, so this may also be an artifact of the altitude correc-tion (cf. Sect. 2.2). The slightly enhanced periodic variations ofthe CRaTER signal seen close to the minimum of the FD are alsoa sign that the altitude correction is not completely suppressingthe periodic signal due to the modulated GCR spectrum.Fig. 6 presents the density variations of cosmic rays at Earthobtained from GSM: A Axy (equatorial components) and Az (polar com-ponent). The characteristics of the cosmic ray anisotropy thatsignify the e ff ect of a MC on GCRs are summarized as follows: (a) the amplitude of Axy is higher within the MC, reaching amaximum of ∼ (b) the direction of the anisotropy vector (i.e. orange part of thevector diagram) changes abruptly when entering the MC (Belov Article number, page 7 of 16 & A proofs: manuscript no. cme_fd_at_solo
Shock CME F I R B [ n T ] WIND MFI (shifted) | B | B x B y B z v [ k m / s ] vfit10 n [ c m ] n c o un t r a t e [ s ] SoPosmoothed T [ M K ] WIND SWE (shifted) T A [ % ] South Pole neutron monitor / GSM
GSM - - - - - - - - - date22.622.823.023.223.423.6 c o un t r a t e [ s ] CRaTER D2 (shifted) dataorbit average
Fig. 5.
Measurements near Earth from MFI andSWE on Wind and neutron monitors on Earthas well as the CRaTER D2 counter, showingthe in situ signatures of the CME and the as-sociated FD, as well as a high speed streamfollowing afterwards. Wind data were shiftedforward in time by 1 hour and 7 minutes toaccount for the expected transit time betweenthe L1 Lagrange point and Earth, and CRaTERdata were shifted by 15 minutes, correspondingto the Moon–Earth radial distance. Black verti-cal lines and shaded regions mark the time pe-riods corresponding to di ff erent events: Shockarrival, CME start and end, as well as for-ward shock (F), stream interface (I) and reverseshock (R) of the SIR. Wind MFI measurementsare given in Heliocentric Earth Ecliptic (HEE)coordinates, with X pointing from the Sun toEarth and Z being perpendicular to the eclip-tic pointing north, and Y completing the righthanded triad. The general orientation of HEEis thus comparable to RTN, which is used forSolO data in Fig. 4, and the di ff erence to RTNis small. A linear fit to the velocity profile ofthe flux rope, which is used to determine theexpansion speed as explained by Gulisano et al.(2012), is shown in pink. The second to bot-tom panel shows both measurements from thesouth pole neutron monitor (gray, blue) and theGCR density variation at 10 GV (correspondingto 9 . et al. 2015); (c) there is a rotation of the Axy vector within theMC, and (d) the north-south component Az changes by 1 . B T component is positive for ashort while after 09:00 UT, which is inconsistent with its unipo- lar excursion to B T < B T cannot befitted with the 3DCORE flux rope model, and thus we choose tonarrow the fitting interval to what Davies et al. (2021) call the”unperturbed” inner part of the flux rope.The 3DCORE technique consists of a Gold-Hoyle uniformtwist magnetic field in an elliptical flux rope cross section placedin a 3D toroidal shape (Weiss et al. 2020). Here, we set the crosssection aspect ratio, otherwise a free parameter to be determinedfrom the fitting analysis, to a value of 2.0, which is consistentwith the angular width of the CME void in Heliospheric Imagerobservations (Davies et al. 2021). In Fig. 7a-c, a 3D visualizationof the 3DCORE envelope is presented from several viewpoints atthe time of the Forbush decrease onset at Earth. Fig. 7d demon-strates the ability of the model to fit the Solar Orbiter observa-tions. In Fig. 7e, we propagated the model to the Wind spacecraftself-similarly, where the power law exponents for the expansionof the diameter and magnetic field (as defined in Equation 2)were set to previously empirically derived values of n a = . n B = .
64, respectively. Those values are based on a powerlaw fit of the mean total magnetic field of a large sample of insitu measured CME flux ropes in the inner heliosphere (Leitneret al. 2007).
Article number, page 8 of 16ohan L. Freiherr von Forstner et al.: Radial Evolution of the April 2020 Stealth Coronal Mass Ejection between 0.8 and 1 AU
Fig. 6.
GCR density variation A . Axy of the anisotropy is displayed as a vectordiagram (teal and orange triangles), which are connected to the corre-sponding points in time on the A Az is shown as green vertical arrows ontop of A Ax and Ay that define the plane for the calculation of Axy are indicatedon the top right corner of the figure. Numbers at each anisotropy compo-nent on the figure indicate the scale used for the plotting of the relevantarrows.
The 3DCORE torus propagates according to a drag-basedmodel (see details in Weiss et al. 2020). The results show thatthe modeled magnetic field components are consistent at SolarOrbiter and Wind at L1, but as seen in Fig. 7e, there is a timeshift between the model and the observations of the flux ropemagnetic field at Wind (concerning all components and the totalfield). This points to a slight inconsistency of the Solar Orbiter fitresults when they are propagated to L1, which most likely arisesfrom the shape and direction of the 3DCORE torus being deter-mined with data from a single spacecraft, and it is expected thatdue to the model assumptions this does not exactly reproducethe observations at another spacecraft. This inconsistency can bealleviated with simultaneously fitting 3DCORE to Solar Orbiterand Wind in situ magnetic field data, but this is the subject offuture studies.In Fig. 7 we show a model which uses parameters represen-tative of the best fit, but with the fitting algorithm we use (Weisset al. 2020) we can derive distributions for each of the flux ropeparameters. The main results from the Solar Orbiter 3DCORE fitare, with the results stated as means ± standard deviations: theCME is directed at (13 ± − ± ± .
995 AU), the axial magneticfield strength in the model is (14 . ± .
9) nT, and the model fluxrope has a diameter of (0 . ± . .
809 AU this axial field is (20 . ± .
2) nT and the diameter is(0 . ± . Table 1.
CME and SIR parameters derived from the in situ measure-ments at Solar Orbiter and near Earth.
Solar Orbiter near EarthRadial distance R [AU] 0.809 0.995 a / b CME and SIR onset times t shock [UTC] 2020-04-19 05:06 2020-04-20 02:40 t CME [UTC] 2020-04-19 08:58 2020-04-20 09:01 t CME end [UTC] 2020-04-20 01:11 2020-04-21 02:32 t forward shock [UTC] 2020-04-20 05:22 c t stream interface [UTC] 2020-04-20 09:15 c t reverse shock [UTC] 2020-04-20 13:47 c ∆ t sheath [h] 3.9 6.4 ∆ t CME [h] 16.2 17.5In situ parameters B max [nT] 21.2 16.2 v CME [km / s] — 347 v exp [km / s] — 46 A FD [%] 2.9 2.0 Notes.
The listed Forbush decrease amplitudes A FD correspond to theHET C counter at Solar Orbiter and the CRaTER D2 counter near Earth. ( a ) L1 ( b ) Earth ( c ) Due to the missing plasma data, SIR onsettimes are less certain at SolO.be used to estimate the expansion factor n a , which describes theincrease of the flux rope radius a with the radial distance fromthe Sun (see definition in Sect. 3.1). From a linear fit, we cal-culate the expansion speed v exp , which is the velocity di ff erencebetween the front and rear end of the flux rope, to be 46 km / s,and together with the mean speed of v CME =
347 km / s we cal-culate: n a , in situ @ Wind = v exp ∆ t CME Rv = .
90 (6)where R is the radial distance of Wind at this time (see 1).It is also possible to calculate a value of n a for the propa-gation between SolO and Wind, using the two in situ measure-ments: n a , SolO-Wind = log (cid:32) ∆ t CME, Wind ∆ t CME, SolO (cid:33) (cid:30) log (cid:32) R Wind R SolO (cid:33) = . , (7)and, similarly, we can derive the expansion factor n B for the mag-netic field magnitude between SolO and Wind: n B , SolO-Wind = − log (cid:32) B max, Wind B max, SolO (cid:33) (cid:30) log (cid:32) R Wind R SolO (cid:33) = . , (8)The values for both n B , SolO-Wind and n a , in situ @ Wind are within thetypical ranges found in previous observational studies, as de-scribed in Sect. 3.1. The value n a , SolO-Wind is unusually low andquite di ff erent from the in situ measurement. This could be in-terpreted as a sudden change in the expansion rate of the CME,but may also be related to the di ff erence of the inherent assump-tions in the two methods: For example, the local determina-tion of the expansion factor at Wind (Eq. 6) assumes a quasi-undisturbed expansion of the CME following the current veloc-ity profile within the flux rope, while external influences are not Article number, page 9 of 16 & A proofs: manuscript no. cme_fd_at_solo
EarthSolar OrbiterVenus MercuryParker Solar ProbeBepi ColomboSTEREO-A B [ n T ] R T N | B | B R B T B N B [ n T ] H EE | B | B x B y B z - - - - - - - - E P D / H E T F D [ % ] - - - - - - - C R a T E R F D [ % ] (c) (d) (e)Solar Orbiter Earth Fig. 7.
Visualization of the results of the 3DCORE flux rope model fitted to the Solar Orbiter MAG observations, shown at the time of the onsetof the Forbush decrease at Earth. The reconstructed 3D flux rope structure is shown (a) looking down from the solar north pole onto the solarequatorial plane, (b) in a frontal view along the Sun–Earth line, and (c) in a side view at a 75 degree angle, the longitude of STEREO–A to Earth.A flux rope field line is highlighted as a solid blue line. The panels (d) and (e) show the in situ magnetic field data from Solar Orbiter and Windat Earth / L1 compared to the GCR variation as a percentage drop in the amplitude measured by EPD / HET and CRaTER. The Wind magnetic fieldcomponents are given here in Heliocentric Earth Ecliptic (HEE) coordinates, as in Fig. 5. The 3DCORE modeled magnetic field is overplotted inpanel (d) and propagated to Earth as shown in (e). An animation of this figure is available as an online movie . taken into account. Contrarily, the observation of a SIR that fol-lows closely behind the CME, as described above, suggest thatthere may have been some interaction between the two structuresthat may have a ff ected the expansion. This will be discussed inmore detail in Sec. 4.3 and 5. We also note that the derived val-ues of n a and n B are both lower than the fixed values assumedin the 3DCORE model, but this is partly due to the fact that the3DCORE modeling excludes the first part of the flux rope dura-tion (as explained above). Also, as stated above, a more detailed3DCORE analysis fitting the CME structure simultaneously atboth locations will be explored in future studies. Due to its 75° longitudinal separation from Solar Orbiter andEarth at the time (cf. Fig. 1), the STEREO-A spacecraft has pro-vided excellent remote-sensing observations of this CME event.Fig. 8 shows observations from the Sun Earth Connection Coro-nal and Heliospheric Investigation suite onboard STEREO-A(SECCHI, Howard et al. 2008), namely the COR2 white-lightcoronagraph, as well as from the Heliospheric Imagers (HI). TheCOR2 image shows two CMEs launched from the Sun in closesuccession on April 14–15 2020. The CME visible on the rightside of the COR2 image, which first appears at approximately19:30 UTC on April 14 and then slowly moves outward, is theone that headed towards SolO and Earth, while the larger CMEon the left side is backsided from the Earth point of view. To reconstruct the CME shape near the Sun, we have ap-plied the Graduated Cylindrical Shell model (GCS, Thernisienet al. 2006; Thernisien 2011) to the STEREO-A / COR2 andSOHO / LASCO C2 and C3 (Brueckner et al. 1995) coronagraphimages, which allows us to derive parameters such as latitudeand longitude as well as the flux rope height and radius. In theprocess of this study, we have developed a new implementationof the GCS model in Python , and verified its results against theexisting SolarSoft IDL version. During the reconstruction pro-cess, it became apparent that the structure seen on the east limbfrom SOHO / LASCO C3 cannot belong to the Earth-directedCME. To fit the GCS geometry to this structure, it would havebeen necessary to shift the CME longitude by more than 30°away from Earth and / or increase the flux rope height signifi-cantly, which contradicts the position of the clear flux rope struc-ture observed at STEREO-A / COR2 and the in situ observationat Earth and Solar Orbiter. Considering this, we suspect that thissignature is instead caused by the backsided CME, and we haveverified this by also approximately fitting the backsided CMEwith the GCS model (as plotted in orange in Fig. 8). The Earth-directed CME is not clearly seen in the LASCO C3 images, butshows a weak signature in C2 on the northwestern limb. Thisstructure was used in conjunction with the clear observations inthe STEREO-A COR2 data to reconstruct the CME (plotted inblue in Fig. 8). The GCS results show that the two CMEs partlyoverlap in the SOHO / LASCO observations due to the line of https://github.com/johan12345/gcs_python , https://doi.org/10.5281/zenodo.4443203 Article number, page 10 of 16ohan L. Freiherr von Forstner et al.: Radial Evolution of the April 2020 Stealth Coronal Mass Ejection between 0.8 and 1 AU
Table 2.
Results from the graduated cylindrical shell (GCS) model.
CME 1 a CME 2 b HEEQ Longitude [°] 18 ± ± − ± ±
11 15Height [ R (cid:12) ] 9 . ± . . κ . ± .
04 0 . R (cid:12) ] 1 . ± . . Notes.
GCS fitting was applied in the 2020-04-15 05:39:00 UTC imagefrom STEREO-A COR2 and the 2020-04-15 05:36:07 UTC image fromSOHO / LASCO C2. Results are plotted in Fig. 8. Error bars are givenonly for CME 1, as CME 2 is not further studied here. ( a ) Directed towards SolO and Earth ( b ) Backsided as seen fromSolO / Earthsight e ff ect, which is probably the reason why the Earth-directedCME is only seen from SOHO on the west limb. The fit parame-ters for both CMEs are listed in Table 2, where the uncertaintieswere derived by performing the GCS fit for the Earth-directedCME 40 times and then calculating the mean and standard devia-tion of each parameter. This was not done for the backsided CMEas its parameters are not needed for the further analysis in thisstudy. The GCS fit results for the latitude, longitude and tilt an-gle are also approximately consistent with the data derived fromthe 3DCORE reconstruction based on the in situ data (see Sect.4.1, though these are of course also associated with some uncer-tainties. We note that the 40 GCS fits of the Earth-directed CMEwere performed by a single person, which may decrease the un-certainties compared to a result produced using independent re-constructions from di ff erent scientists. Still, care was taken tosample a large range of possible values for each parameter andadjust the remaining parameters accordingly to fit the corona-graph images. Additionally, the data were compared to a singleindependent GCS reconstruction by another researcher, and theresults agree within the given uncertainty ranges.There is also no obvious signature of the CME in the lowcorona (low coronal signatures, LCS), as observed with theSDO / AIA (Lemen et al. 2012) 211 Å extreme ultraviolet (EUV)images, making it challenging to identify the CME source re-gion. A weak brightening is observed at approximately 2°N 8°E,but this is too far away from the GCS-reconstructed CME lon-gitude of (18 ± <
300 km / s according toMa et al. (2010)), and these signatures may be too weak to bedetected with the established observational and data processingtechniques (e.g. Alzate & Morgan 2017). A more detailed studyof the source region of this CME will be performed by O’Kaneet al. (2021, in preparation for A & A ).As a result of the GCS fit, we derived the initial height ofthe flux rope R = (9 . ± .
40) R (cid:12) and the initial radius at theapex a = (1 . ± .
15) R (cid:12) , calculated using the equation fromThernisien (2011). These parameters will be needed for the ap-plication of the ForbMod model in Sect. 4.3. Based on the GCS results, we can make a new calculationfor the expansion factor n a : The calculation in Equation 6 corre-sponds to the instantaneous expansion of the flux rope near 1 AU,which may not be the same as closer to the Sun. The average ex-pansion factor between the Sun and Earth can be calculated bycomparing the initial flux rope size a with the one measured insitu at Wind: n a , Sun-Wind = log (cid:32) a Wind a (cid:33) (cid:30) log (cid:32) R Wind R (cid:33) = .
70 (9)where R Wind is the radial distance of the Wind spacecraft fromthe Sun and a Wind = ∆ t CME · v CME / = . (cid:12) is the flux roperadius calculated from the in situ data (see Table 1). A similarvalue of n a = .
69 can be calculated from the SolO measure-ments, when assuming the CME speed to be the same as at Wind.STEREO-A HI observations clearly show the CME signa-ture out to elongation angles of approximately 35° (correspond-ing to a radial distance of ∼ . under theID HCME_A__20200415_01 . According to the self-similar ex-pansion fitting (SSEF) result (Davies et al. 2012) given in theHELCATS HIGeoCat catalog (Barnes et al. 2019), the CMEdirection in Heliocentric Earth Equatorial (HEEQ) coordinatesis −
6° in longitude and −
2° in latitude. The longitude does notmatch what we determined in our GCS reconstruction (Table 2)— but as the SSEF technique only uses data from a single space-craft and makes certain assumptions about the CME, such as aconstant speed and a fixed half-width of 30°, it is known to of-ten produce large uncertainties for the CME longitude (see e.g.Barnes et al. 2019). The SSEF results can also be used to calcu-late the arrival time at Solar Orbiter and Earth, as described byMöstl et al. (2017). The calculated arrival times available fromthe ARRCAT v2.0 are 2020-04-19 09:10 ± ± ±
17 hours.(Möstl et al. 2017). The arrival speed at Earth is predicted as(335 ±
11) km / s, which is also consistent with the in situ mea-sured CME speed (mean speed v =
347 km / s, see Table 1). In the previous sections 4.1 and 4.2, we have derived all in-put parameters necessary for applying the ForbMod model tothe Forbush decreases at Solar Orbiter and Earth. For the fluxrope radius expansion factor n a , multiple values were calcu-lated from measurements at di ff erent locations, with quite sig-nificant di ff erences: n a , SolO-Wind = . , n a , in situ @ Wind = .
90 and n a , Sun-Wind = .
70. Additionally, we have derived one value of themagnetic field expansion factor n B , SolO-Wind = .
30, based on theSolO and Wind in situ measurements of the magnetic field.While n B is also used separately to derive the radial depen-dence of the di ff usion coe ffi cient D , the key purpose of the twoexpansion factors within ForbMod, which makes the model verysensitive to these values, is to calculate the so-called expansiontype, a quantity defined as x = n B − n a (see equation 4). Itdescribes the evolution of the magnetic flux and is assumed tobe constant over the course of the CME propagation, i.e. themagnetic flux increases or decreases at the same rate. Thus, https://helioforecast.space/arrcat , https://doi.org/10.6084/m9.figshare.12271292 Article number, page 11 of 16 & A proofs: manuscript no. cme_fd_at_solo y [ a r c s e c ] COR2-A 2020-04-15 05:39:00 y [ a r c s e c ] LASCO-C3 2020-04-15 05:30:07 y [ a r c s e c ] LASCO-C2 2020-04-15 05:36:07 -10000" 0" 10000"10000"0"-10000" x [arcsec] y [ a r c s e c ] -10000" 0" 10000"10000"0"-10000" x [arcsec] y [ a r c s e c ] -4000" 0" 4000"4000"0"-4000" x [arcsec] y [ a r c s e c ] Fig. 8.
Remote sensing observations of the CME. In the STEREO-A COR2 and SOHO LASCO C2 and C3 running di ff erence images (top part),the GCS fitting was applied to derive the parameters R and a for the ForbMod model (see results in Table 2). The blue markings denote the Earth-directed CME we are investigating, while the CME fitted in orange is backsided and launched a few hours earlier. STEREO-A HI observations(bottom left) and time-elongation maps (bottom right) are provided by the HELCATS project. the inconsistency of the measured n a values suggests that n B must also have changed to keep x constant. So, we can derive x = n B , SolO-Wind − n a , SolO-Wind = .
55, and then, under the as-sumption that x = const., calculate a corresponding n B for eachof the measured n a values. The results of this calculation arelisted in Table 4. Of course, in the case of this event, x = const. isa quite bold assumption to make considering the observed vari-ation of n a , but due to the lack of additional observations of n B ,there is no other way to derive the necessary input parametersfrom observations. We will discuss the possible implications ofthis in more detail in Sect. 5.To summarize, we list all the parameters that are used forthe application of ForbMod again in Table 3. We have run Forb-Mod for each of the n a and n B pairs that we calculated (Table4), as well as for a “best fit” result reproducing the measured FDamplitudes at Solar Orbiter HET and CRaTER. Apart from theresponse functions, transit times and radial distances, the Forb-Mod input parameters were always the same for both locations. It also needs to be noted that following the observed variation of n a , the duration of the FD profile calculated with ForbMod wasnot derived from the a ( t ) power law assumed by ForbMod (equa-tion 2), but instead was fixed to the observed flux rope duration.The ForbMod best fit was obtained by calculating the FD am-plitudes across the whole reasonable parameter space of n a and n B (while keeping all other parameters fixed) and then selectingthe set of parameters that produced the lowest sum of squaredresiduals with respect to the two in situ measured amplitudes atHET and CRaTER (see Table 1).The ForbMod results for the “best fit” parameters are shownin Fig. 9, where the time profile calculated using Equation 5 isplotted in red and the measurements in blue / gray (as previouslyin Figures 4 and 5). It can be seen that for these parameters, thereis a good agreement between the model and observations: Forb-Mod describes well the relatively symmetric Forbush decreasecaused by the flux rope CME and reproduces the observed FDamplitudes. Of course, the second decrease caused by the SIR Article number, page 12 of 16ohan L. Freiherr von Forstner et al.: Radial Evolution of the April 2020 Stealth Coronal Mass Ejection between 0.8 and 1 AU
Table 3.
Input parameters for the ForbMod model
Parameter Source Section ValueGCR spectrum Force-field approximation, Gieseleret al. (2017) 3.1 Φ for June 2009Di ff usion coe ffi cient D Empirical function from Potgieter(2013) with parameters from Potgi-eter et al. (2014) 3.1 parameters for 2009Detector response function Geant4 simulation results 2.1, 2.2 See Fig. 3Magnetic field B c B max in Wind data 4.1 B c = . n a , n B Calculation assuming x = const.(Eq. 4) / best fit 4.3 see Table 4Flux rope parameters R , a GCS reconstruction 4.2 R = .
64 R (cid:12) , a = .
93 R (cid:12) Di ff usion time( ≈ transit time) In situ arrival time, Launch time:time of GCS fit 4.1, 4.2 t SolO =
99 h, t Earth =
123 hVelocity profile linear fit to in situ measurements atWind 4.1 see Table 1
Table 4.
Pairs of expansion factors n a , n B used for the ForbMod model,and resulting FD amplitudes at SolO HET, CRaTER and the South Poleneutron monitor. Calculation Sun → Wind SolO → Wind in situ@ Wind bestfit a n a n B b b x c -0.15 A FD, SolO [%] < < A FD, CRaTER [%] < < A FD, SoPo [%] < < Notes.
Each column in the table corresponds to one set of input parame-ters n a and n B that was used with ForbMod. The modeled FD amplitudefor the GSM data (10 GV) is < .
01 % for all four sets of input parame-ters and not shown here. ( a ) Best fit was obtained by constraining the FD amplitudes atSolO and CRaTER. ( b ) These quantities were calculatedassuming that x = .
55 (see discussion in Sect. 4.3). ( c ) Calculated using Equation 4.is not included in the model, which explains the obvious devi-ation of the measurements from the model after the flux ropepassage. The e ff ect of the spacecraft model included in the HETresponse function (see Sect. 2.1) is significant, applying Forb-Mod using the response function without the spacecraft wouldlead to a ∼
20 % larger FD (amplitude of 3 .
52 %, not shownhere).For the other parameters n a and n B derived from the ob-servations, ForbMod results for the FD amplitude at SolO andCRaTER are shown in Table 4. With all these parameter sets, itcan be seen that ForbMod underestimates the amplitude of theFD. The closest result is obtained using the in situ parametersmeasured at Wind, but even in this case the modeled FD ampli-tude is less than half of the measurement. For the other sets of parameters, ForbMod predicts the flux rope to already be com-pletely filled with GCRs by the time it reaches SolO and Earth,so that the FD amplitude is < .
01 %.In addition to SolO HET and CRaTER, we have appliedForbMod at Earth with di ff erent response functions to modelthe FDs observed at the South Pole neutron monitor (SoPo) andin the GSM data. For the latter, we have applied ForbMod mo-noenergetically at the fixed rigidity of 10 GV (corresponding to9 . ff energy of450 MeV (see Sect. 2.3). With these results, both the FDs at SoPoand GSM data are significantly underestimated, with a maximumamplitude of 0 .
44 % for SoPo and well below 0 .
01 % for GSMin all cases. To obtain the observed FD amplitude on the orderof 1 % from the model, especially for the higher energy of GSM,the parameters n a and / or n B would need to be increased evenmore, which is not supported by observations or the previousobservational constraints cited in Sect. 3.1.
5. Discussion and conclusions
In this study, we have shown in situ and remote sensing obser-vations of the first flux rope CME that hit Solar Orbiter on April19 and Earth on April 20, 2020, and studied the Forbush de-crease that it caused at both SolO and near Earth. This event isconsidered to be a “stealth CME” as it showed only weak sig-natures from the Earth point of view in the EUV observationsof the low corona. Remote sensing observations of this CMEwere only possible thanks to the ideal position of the STEREO-A spacecraft, which could track the CME from the outer coronauntil ∼ . ff ect of the shock-sheath region and the fol-lowing ejecta, both of which are necessary for deep GCR de-pressions (e.g. Papaioannou et al. 2020). Additionally, CMEsthat are characterized as magnetic clouds (MCs) are more of-ten associated with large FDs (Richardson & Cane 2011). How- Article number, page 13 of 16 & A proofs: manuscript no. cme_fd_at_solo - - - - - - - date321012 F D [ % ] Solar Orbiter
HET C counterHET C counter (smoothed)ForbMod - - - - - - - date CRaTER
CRaTER D2orbit averageForbMod
Fig. 9.
ForbMod model results at So-lar Orbiter and CRaTER, in comparisonwith the measured Forbush decreases atSolar Orbiter and CRaTER. The mea-surements are plotted in the same fash-ion as in Figures 4 and 5, but normalizedto their pre-onset values to reflect the rel-ative variation of the GCR count rate. In-put parameters for ForbMod are listed inTables 3 and 4. n a and n B were used fromthe “best fit” result. ever, although the CME studied in this work was associated witha shock and a clear MC observed at both SolO and Earth, theresulting amplitude of the FD at Earth was relatively low, espe-cially at higher GCR energies measured by neutron monitors andthe GSM (only ∼ / s led to a very weakshock and an extremely long propagation time of more than fivedays from the Sun to Earth, which made it possible for GCRsto di ff use into the MC and thus decrease the observed FD am-plitude. This explanation relates well to the concept of the Forb-Mod model, because the di ff usion of GCRs into the flux ropeover time is the basis for its calculations. Based on the timingof the FD, is seems that the shock only had a very weak e ff ecton the GCR modulation, with the main part being caused by theMC.Using input parameters derived from the CME observations,we have applied the ForbMod model to reproduce the FDsobserved by the SolO HET C detector counter and the LROCRaTER D2 counter. Most parameters were relatively straight-forward to derive. Only the expansion factors n a and n B , whichdescribe the evolution of the flux rope radius and its magneticfield and to which the model is quite sensitive, could not be un-ambiguously determined from observations, as they seem to varysignificantly depending on where and how they are measured. Inaddition, while n a could be measured for di ff erent locations, n B could only be measured based on SolO and Wind observations(i.e. there is no measurement of n B from the Sun to Earth). Aset of parameters derived assuming that the expansion type x is constant and using the n a value measured in situ near Earthonly produces a FD amplitude of 1 .
29 % at SolO compared tothe measurement of ∼ n a and n B , which closely reproduce the FD amplitudes measuredat CRaTER and HET, was also calculated, with an even highervalue of n a , i.e. a stronger expansion of the flux rope size notsupported by the observations, and a lower value of x closer tozero, corresponding to a conserved magnetic flux (see Dumbovi´cet al. 2018). In this case, the faster expansion (larger n a ) coun-teracts the di ff usion of GCRs into the flux rope, as described inSect. 3.1, so that the FD amplitude becomes larger. However,even with the “best fit” parameter values, the higher-energy FDmeasurements of the South Pole neutron monitor and the globalsurvey method (GSM) could not be reproduced with ForbMod. Using the observation of the flux rope evolution from SolOto Earth in ForbMod yields FDs which do not agree with the ob-servations. In addition, ForbMod best fit parameters yield globalflux rope Sun-to-Earth evolutionary parameters which are faraway from the values derived based on in situ measurement com-parison between SolO and Earth. This might indicate that Sun-to-Earth evolution of this CME was di ff erent from the SolO-to-Earth evolution. A similar event, a slow stealth CME followed bya high speed stream was studied by He et al. (2018). They haveshown that the CME was compressed by the fast solar wind be-hind it, which caused an enhanced magnetic field and thus an un-expectedly high geoe ff ectiveness. The same may have happenedfor this event — the inconsistent measured values of n a , whichcorrespond to a slower expansion of the flux rope between theSun and 1 AU than suggested by the in situ measured velocityprofile, can be a result of such a compression, and thus indicatethat the expansion behavior of this very slow CME may havechanged during its propagation time. E.g. at some point duringits propagation, the CME may have been slightly compressed bythe SIR, and expanded more freely at other times. Consequently,the assumption of ForbMod that the flux rope radius and its mag-netic field follow power laws with constant indices n a and n B and that the resulting expansion type x , which describes the evo-lution of the magnetic flux, is also constant may not be valid inthis more complex case. This may well be the reason why themodel is not able to reproduce the higher energy FD measure-ments, even with a set of input parameters that fits the lowerenergy measurements of HET and CRaTER.Another possible explanation for this discrepancy is that theenergy dependence of the ForbMod-modeled FD amplitude maysimply be overestimated for this event, resulting in too low FDamplitudes at higher energies. This could happen e.g. if the em-pirical input parameters for the GCR spectrum and the energydependence of the di ff usion coe ffi cient do not match the actualconditions at this time. This is an interesting result and shouldbe investigated in more detail in future studies. E.g., a statisticalvalidation of ForbMod against the results of the GSM, which hasalready been applied to a large catalog of FDs, may be helpfulto examine whether this is a systematic problem in the descrip-tion of the energy dependence for these higher GCR energies,or whether this disagreement is a specific attribute of this CMEevent due to its low speed, very long propagation time, and pos-sible influence of the following SIR.This study highlights the capabilities of the instruments on-board the Solar Orbiter spacecraft, such as the high counting Article number, page 14 of 16ohan L. Freiherr von Forstner et al.: Radial Evolution of the April 2020 Stealth Coronal Mass Ejection between 0.8 and 1 AU statistics of the HET C detector capable of detecting Forbush de-creases. In addition, it shows that coordinated observations withSolar Orbiter and other spacecraft will be extremely importantfor the better understanding of space weather in the inner helio-sphere. Spacecraft close to the Sun, such as Solar Orbiter andParker Solar Probe, can serve as an upstream monitor to pro-vide valuable information and early warning about CMEs. TheCME in this case study also serves as an excellent example for a“stealth CME” that was still geoe ff ective due to its strong mag-netic field even though it was not clearly seen in remote sens-ing observations from the Earth point of view. This again high-lights that the monitoring of Earth-directed CMEs requires insitu and remote sensing measurements at additional locations,such as at Solar Orbiter and Parker Solar Probe as well as fromSTEREO-A or a future L5 mission. As Solar Orbiter’s trajectorymoves closer to the Sun in the coming years and the solar activ-ity increases with the commencement of Solar Cycle 25, spaceweather events during conjunctions with Earth as well as otherspacecraft will become more probable, which will provide moreexciting science opportunities. Acknowledgements.
J. v. F. thanks L. Seimetz and N. Lundt for their assis-tance in simulating the HET detector response functions. Additionally, we thankM. D. Looper and J. Wilson from the CRaTER team for providing the re-sponse functions of their instrument and helpful suggestions about the anal-ysis of the CRaTER data. J. G. is supported by the Strategic Priority Pro-gram of the Chinese Academy of Sciences (Grant No. XDB41000000 andXDA15017300), the National Natural Science Foundation of China (Grant No.42074222) and the CNSA pre-research Project on Civil Aerospace Technolo-gies (Grant No. D020104). M. D. acknowledges support by the EU H2020Grant Agreement 824135 (SOLARNET) and the Croatian Science Foundationunder the Project 7549 (MSOC). A. P. acknowledges support by the TRACERproject ( http://members.noa.gr/atpapaio/tracer/ ) funded by the Na-tional Observatory of Athens (NOA) (Project ID: 5063) and from NASA / LWSproject NNH19ZDA001N-LWS. M. A. and A. B. (IZMIRAN) are supportedby the Russian Science Foundation under grant 20-72-10023. C. M., A. J. W.,J. H., T. A. and M. B. thank the Austrian Science Fund (FWF): P31521-N27,P31659-N27, P31265-N27. This work, as well as the development of EPD onSolar Orbiter were supported by the German Federal Ministry for EconomicA ff airs and Energy, the German Space Agency (Deutsches Zentrum für Luft-und Raumfahrt e.V., DLR) under grants 50OT0901, 50OT1202, 50OT1702, and50OT2002, by ESA under contract number SOL.ASTR.CON.00004, the Univer-sity of Kiel and the Land Schleswig-Holstein, as well as by the Spanish Ministe-rio de Ciencia, Innovación y Universidades under grants FEDER / MCIU – Agen-cia Estatal de Investigación / Projects ESP2105-68266-R and ESP2017-88436-R.The Solar Orbiter magnetometer was funded by the UK Space Agency (grantST / T001062 / http://soar.esac.esa.int/soar/ . We acknowledge theNMDB database ( ), funded under the European Union’sFP7 Programme (contract 213007), for providing data. The data from South Poleneutron monitor is provided by the University of Delaware with support from theU.S. National Science Foundation under grant ANT-0838839. LRO / CRaTERLevel 2 data are archived in the NASA Planetary Data System’s Plane-tary Plasma Interactions Node at https://pds-ppi.igpp.ucla.edu/ andalso available through the CRaTER website at https://crater-products.sr.unh.edu/data/inst/l2/ . The Wind spacecraft solar wind and mag-netic field data are provided on the Wind website at https://wind.nasa.gov/mfi_swe_plot.php . STEREO heliospheric imager observations and de-rived data are available on the HELCATS ( )and Helio4Cast ( https://helioforecast.space/arrcat ) websites. Grad-uated cylindrical shell reconstruction of CMEs was performed using ver-sion 0.2.0 of a new Python implementation of the GCS model ( https://doi.org/10.5281/zenodo.4443203 ) available at https://github.com/johan12345/gcs_python , which is based on version 2.0.3 ( https://doi.org/10.5281/zenodo.4065067 ) of the SunPy open source software package(The SunPy Community et al. 2020) and coronagraph images provided by theHelioviewer.org API (Müller et al. 2017).
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