Measurement of low-energy cosmic-ray electron and positron spectra at 1 AU with the AESOP-Lite spectrometer
Sarah Mechbal, Pierre-Simon Mangeard, John M. Clem, Paul A. Evenson, Robert P. Johnson, Brian Lucas, James Roth
DDraft version September 9, 2020
Typeset using L A TEX default style in AASTeX63
Measurement of low-energy cosmic-ray electron and positron spectra at 1 AU with the AESOP-Litespectrometer
Sarah Mechbal, Pierre-Simon Mangeard, John M. Clem, Paul A. Evenson, Robert P. Johnson, Brian Lucas, and James Roth Santa Cruz Institute for Particle Physics,University of California Santa Cruz,Santa Cruz, CA 95064, USA Bartol Research Institute,University of Delaware,Newark, DE 19716, USA (Received June 1, 2019; Revised January 10, 2019; Accepted September 9, 2020)
Submitted to ApJABSTRACTWe report on a new measurement of the cosmic ray (CR) electron and positron spectra in the energyrange of 20 MeV – 1 GeV. The data were taken during the first flight of the balloon-borne spectrometerAESOP-Lite (Anti Electron Sub Orbital Payload), which was flown from Esrange, Sweden, to EllesmereIsland, Canada, in May 2018. The instrument accumulated over 130 hours of exposure at an averagealtitude of 3 g.cm − of residual atmosphere. The experiment uses a gas Cherenkov detector and amagnetic spectrometer, consisting of a permanent dipole magnet and silicon strip detectors (SSDs),to identify particle type and measure the rigidity. Electrons and positrons were detected againsta background of protons and atmospheric secondary particles. The primary cosmic ray spectra ofelectrons and positrons, as well as the re-entrant albedo fluxes, were extracted between 20 MeV – 1GeV during a positive solar magnetic polarity epoch. The positron fraction below 100 MeV appearsflat, suggesting diffusion dominated solar modulation at low rigidity. The all-electron spectrum ispresented and compared with models from a heliospheric numerical transport code. INTRODUCTIONPositrons and electrons constitute only 1% of galactic cosmic rays (GCRs). Although their contribution is smallcompared to that of cosmic ray nuclei, the leptonic component is nevertheless important in understanding the origin andpropagation of cosmic rays in the Galaxy and the Heliosphere. Electrons and positrons undergo energy loss processesthat nuclei do not, such as synchrotron radiation in magnetic fields, bremsstrahlung energy loss with interstellar gases,and inverse Compton scattering with ambient photons. Their measurement thus provides additional information abouttheir transport and origin that cannot be known from the hadronic component.Both electron and positron cosmic rays can be produced in the interaction between cosmic ray nuclei and theinterstellar matter: that contribution is then referred to as
GCR secondary . The
GCR primary contribution of cosmicray electrons has been known since their discovery in the 1960s (Earl 1961; Meyer & Vogt 1961), their origin mostlikely pointing to an acceleration in astrophysical shocks in supernova remnants (Abdo et al. 2010; Ackermann et al.2013). Before the paradigm-shifting measurements made by PAMELA, AMS-02 and Fermi-LAT (Adriani et al. 2009;Aguilar et al. 2013; Fermi-LAT collaboration 2012), it was long believed that all positrons were of purely secondaryorigin (Moskalenko & Strong 1998). However, the discovery of an excess at energies above 10 GeV seriously challengedthat assumption, pointing to possible new sources, such as pulsars or dark matter particles (Hooper et al. 2009; Choliset al. 2009). To the knowledge of the authors, the positron fraction has only been measured below 100 MeV during a
Corresponding author: Sarah [email protected] a r X i v : . [ a s t r o - ph . H E ] S e p Mechbal et al negative heliospheric polarity period in the 1960’s (Beuermann et al. 1969).In order to interpret any simultaneous measurements of electron and positron cosmic rays done at 1 AU at a givensolar epoch, we study these results through the lens of the dynamical heliosphere structure. As cosmic rays enter theboundary of the heliosphere, at ∼
120 AU (Stone et al. 2013, 2019), they encounter the turbulent outward flowingsolar wind embedded with the Suns heliospheric magnetic field (HMF). As particles propagate along magnetic fieldlines, they undergo some major modulation mechanisms: convection and adiabatic energy loss in the expanding solarwind, particle diffusion, and drifts due to the HMF (Jokipii et al. 1977). The lower the rigidity of the particle, themore susceptible to the mechanisms of solar modulation it will be (the effects of solar modulation are negligible abovea few tens of GV). Moreover, because of the well-established 11-year solar cycle, the intensity of CRs on Earth changeswith solar activity: when a solar cycle reaches its maximum activity, so do the tilt angle of the heliospheric currentsheet (HCS) and the magnitude of the HMF, thus maximizing the suppression of cosmic rays reaching Earth. Theinverse scenario occurs during solar minimum activity.On top of the time-varying nature of the solar modulation, GCRs also encounter gradients and curvatures in thelarge scale HMF, and the effect of the HCS, causing them to drift based of the magnetic polarity of Sun and the chargesign of the GCR. During so-called A > ◦ ◦ ∼ ), zero pressure, longduration balloon. The balloon floated at an average altitude of 135 kft ( ∼
41 km), which corresponds to ∼ − of atmospheric overburden, collecting data for roughly 133 hours. The northerly trajectory of the payload (Fig. 1)allowed the apparatus to survey regions of low geomagnetic cutoff (below 200 MV). We present here our measurementof the primary electron and positron spectra between 20 MeV and 1 GeV, as well as the re-entrant albedo fluxes inthe same energy range. We describe the detector system in §
2, the data analysis in §
3, and the results are presentedand discussed in § THE DETECTOR SYSTEMThe AESOP-Lite apparatus is the successor to the LEE (Low Energy Electrons) payload (Hovestadt et al. 1970),which retired after 23 successful flights, having contributed to important measurements of low-energy electrons overmany solar cycles (Fulks 1975; Evenson et al. 1983; Evenson & Clem 2009). The measurements from the final LEEflights, which occurred in 2009 and 2011 (“LEE09” and “LEE11”), were analyzed using the same method outlinedin Fulks (1975). The results, used in this analysis, are presented for the first time in Appendix A. The LEE instrumentwas modified by replacing the original calorimeter with a magnetic spectrometer, making it possible to resolve charge-sign. The original entry telescope was preserved. Since the pulse height analyzers (PHA) and front-end electronics ow energy electron and positron cosmic ray spectra Figure 1.
Trajectory of the first flight. The first 90 hours of the flight surveyed latitudes where diurnal variations of thegeomagnetic field are still present, as indicated by the color-coded legend. of each counter-photomultiplier tube (PMT) system were used in past LEE flights, we are provided with a mean ofcross-calibrating the absolute electron fluxes with previous measurements. Fig. 2 presents a diagram of the instrument.2.1.
The entry telescope
Detectors T1, T2, T3, T4, and the guard are all read out by PMTs. The entry telescope consists of three NE102 A plastic scintillators (T1, T3 and Guard) and a gas Cherenkov detector (T2). T3 identifies singly chargedrelativistic particles, while T2 serves as a hadron discriminator. The Cherenkov counter is filled with C F gas to anabsolute pressure of 1.8 atm, rejecting all particles with γ =E/mc ≤ . ∼
18 cm sr, without taking into accountthe important loss in fiducial volume incurred by the presence of the magnetic field. The guard counter (G), strictlyused offline in anti-coincidence, serves to flag particles produced by showers inside the apparatus, whereas the plasticscintillator T4, placed at the very bottom, selects particles that have exited the bottom of the instrument.2.2. Tracking spectrometer
The tracking system consists of seven planes of silicon strip detectors (SSD) and a Halbach ring dipole magnet (Hal-bach 1980). The average field is 0.3 T, though its known non-uniformity must be accounted for. The SSDs are arrangedin an xy-configuration, with 4 layers in the bending plane to measure the particle deflection, and 3 layers to view theirtrajectory in the non-bending plane. The magnet design allows the placement of a tracker in the bending-view at thecenter of the field. The silicon wafers were custom designed and manufactured for the Large Area Telescope (LAT)of the NASA Fermi mission (Atwood et al. 2007). Each SSD is a 8.95 × , 400 µ m thick single-sided detector,with strip pitch 228 µ m and spatial resolution 66 µ m (228 / √ Mechbal et al
X (cm)25 - - - - - Z ( c m ) - - - - T1T2T3GuardT4
Y (cm)25 - - - - - Z ( c m ) - - - - T1T2T3GuardT4
Figure 2.
Cross section of the AESOP-Lite instrument as viewed from the event display software. Shown is an electroncandidate recorded during the 2018 flight. The triggers T1, T2, T3 and T4 were fired (in green), whereas no signal was seen inthe guard (in red). The active layers in each view (non-bending on the left, bending on the right) are shown in red.
In flight, coincidences T1–T2–T3 and T1–T2–T4 were alternately used as an online trigger in flight (the “GO”signal). The tracker system self-triggers with a logical OR of two triggers: one from the bending plane, the other fromthe non-bending, requiring in each view a coincidence of at least one strip hit in each of the top 3 layers. The dataare stored in each board until a “GO” signal is received. If a “GO” signal fails to arrive within 5 µ s the data arediscarded. ANALYSISTo identify electrons and positrons from the total data sample collected in flight, a set of selection criteria isestablished. The level of background atmospheric particles is then estimated in order to derive the primary spectra.This analysis work relies on two Monte Carlo (MC) simulations performed with the FLUKA 2011 software (Ferrariet al. 2005; Bhlen et al. 2014).The first simulation studies the instrument’s response to fluxes of electrons, positrons, and protons. Due to theacceptance of the entry telescope, particles are generated with an incident angle θ < ◦ . The simulation includes themagnetic field map provided by the magnet manufacturer. The efficiency of each selection is calculated using the MCresults and/or the flight data when possible. ow energy electron and positron cosmic ray spectra Particle Identification
Tracking
The spectrometer measures the rigidity of a particle that has successfully passed the online trigger requirement. Theevent is first processed with a pattern recognition routine, which selects hits belonging to the same track. We imposea set of conditions on the fitted track to obtain a reliable reconstruction: • We restrict the allowed range of hit positions in the first three tracking layers to eliminate events that havescattered near or in the magnet walls, or produced electromagnetic showers in the upper-half of the spectrometer.All dimensions are given as measured from the center of the layer: – In L : | x | < – In L : | y | < – In L : | y | < • At least 6 (of 7) tracking layers must have a hit, with a maximum of 9 hits. We demand that all 4 layers inthe bending view record a hit, and that at least 2 (of 3) layers in the non-bending view do so. This conditioneliminates multi-track and δ -rays events.This selection helps to exclude events that have interacted in the tracking volume, or crossed a region of weakmagnetic field. In the non-bending view, the algorithm fits all possible lines between hits in the top-most and bottom-most layers, and chooses the track that minimizes the χ to derive the dip angle θ NB . In the bending view, a secondorder polynomial function is fit to all possible configurations of hits in the four layers, and the best fit is chosen. Theradius of curvature is calculated for all 4 bending planes, and the mean is taken to infer the transverse momentum p T .Fig. 2 illustrates the parabola and straight line fits as seen in solid blue lines in the event display. The dashed lines inthe bending plane indicate the incoming and outgoing directions of the particle, assuming no scattering or interactionhas occurred in the detector.Results from the pattern recognition are then used to initialize a fourth-order Runge-Kutta numerical integration:this method can follow a charge-particles changing momentum through an arbitrarily changing magnetic field, as longas multiple scattering in the silicon can be neglected; it serves as the final track fit method. A track is characterizedby five parameters: x , y , the position of the particle at the first spectrometer layer, cx , cy , its directional cosines at atthat point, and transverse momentum p T . The track parameters are iteratively adjusted by a Nelder-Mead ”simplex”algorithm (Nelder & Mead 1965) until a minimum is found with respect to the numerically integrated trajectory.The resulting maximum detectable rigidity at 3 σ is ∼
900 MV, with a reconstruction resolution of ∼
9% at 20 MeV/cand ∼
18% at 300 MeV/c, based on MC results obtained from fitting the 1/p reco distribution to a Gaussian function.The mean and resolution of the reconstruction at each momentum are derived from the mean and the width of thefitted Gaussian. The validity of the charge-sign capabilities of the spectrometer and the momentum reconstructionwas verified using ground-level muons.In addition to the tracking requirements listed above, a good quality of fit is demanded, as given by the value of themean square deviation of the fit. 3.1.2.
Scintillator and Cherenkov selection
The coincidence signal T1-T2-T3 is used as the main trigger in flight. Offline, we add the guard in anti-coincidence,as a way to remove events that have produced an electromagnetic shower above the spectrometer. A sequence of cutsis applied to identify electrons and positrons from the raw data sample. The scintillators T1 and T3 efficiently detectparticles with | Z | = 1, whereas the main purpose of the Cherenkov detector T2 is to discriminate against the highbackground of protons and muons present in the atmosphere. Finally, a particle must also cross the bottom-mostscintillator T4 to be considered an electron or positron candidate.A cut on the signal in T3 is applied to discriminate against alpha particles, as the energy deposited grows propor-tionally to Z , as shown in Fig. 3 (left). Alpha particles with a kinetic energy below ∼
54 GeV will not produce a
Mechbal et al
Cherenkov signal in T2, but they can produce a signal through scintillation. We fit the total distribution of the signalin T3 for the reconstructed tracks passing all the other selection criteria. The fit function is the sum of two Landau-Gaussian functions, one for the signal from singly charge particles and one for that from double charge particles. Thefit values of the Landau MPV (Most Probable Value) are ∼
83 ADC and ∼
327 ADC for the alphas, about 4 times thevalue of a Z =1 particle, as expected. The upper-limit cut of 200 ADC counts was chosen to remove the contaminationfrom alphas. The residual alpha contamination is negligible. Figure 3.
Left: PHA distribution of the scintillator T3 during the 2018 flight. The vertical line shows the upper-limit cut.The global fit (sum of two Laundau-Gaussian) is shown in black, the contribution from Z =1 particles is shown with the dashedblue line, and that from Z =2 particle with the dotted dashed red line. Right: PHA distribution of T2 during the 2018 flightfor tracks with a reconstructed momentum between 271 and 419 MeV/c. The purple vertical line is the offline lower thresholdapplied to the T2 signal (See the text for more details). In T2, the Lorentz threshold γ is set to a value γ = 15.7, such that protons with kinetic energy below 13.8 GeVand muons below 1.5 GeV do not trigger the detector. The online threshold applied on the PMT signal of T2 is setbelow the 1 photo-electron (PE) signal. Fig. 3 (right) shows the T2 signal for all tracks with reconstructed momentumbetween 271 and 419 MeV/c after the full sets of selection was applied. Two contributions can be observed. The largepeak at 1 PE ( ∼
42 ADC) and the smaller peaks at 2 and 3 PE are attributed to scintillation produced by low energyprotons in the C F gas, fit with a function that is the sum of 3 Gaussians (black line). The signal above the peaksis associated with the Cherenkov light produced by the electrons and positrons, fit to a Poisson distribution (blueline). For this range of reconstructed momentum, an average signal is estimated to be 8 PE. The total fit, which isthe contribution of the scintillation and the Cherenkov signal is shown in red.We apply a cut on the PHA value of T2 at an ADC count value of 160 to remove the contamination (which isnegligible after this cut). With this selection, the AESOP-Lite and LEE count rates agree within 5% during the ascentphase of the flight, when the temporal variation of cosmic rays flux is less relevant than at float altitude. For each binin reconstructed momentum, the efficiency losses due to this selection are calculated assuming a Poisson distributionfor the number of Cherenkov PE. The signal losses are ∼
11% at 25 MeV/c, ∼
7% at 45 MeV/c, and ∼ Detection efficiency
The total detection efficiency of the final event sample (cid:15) can be divided in two components: the trigger efficiency (cid:15) trigger and the particle selection efficiency (cid:15) sel . The former is defined as (cid:15) trigger = (cid:15) GO × (cid:15) tkrtrig , with (cid:15) GO the efficiencyof the main trigger (T1-T2-T3 or T1-T2-T4), estimated to be ∼ (cid:15) tkrtrig the tracking system trigger efficiency.The latter is the efficiency of the tracker trigger, which is an “OR” of the trigger signal in the bending and non-bendingplanes. To evaluate it, we have used a combined analysis of MC and flight data to estimate the inefficiencies eachview’s trigger, which were above 50% in the bending plane in flight, due to faulty connections between trackers, and ∼
80% in the non-bending view. In total, we estimate (cid:15) tkrtrig to be 94%.The efficiency (cid:15) sel of the particle’s selections of Sec. § (cid:15) T T T and (cid:15) T T T , using MC simulations only. They are shown in red in Fig. 4. The ow energy electron and positron cosmic ray spectra (cid:15) T , is excluded from what is presented in Fig. 4, as (cid:15) T is derivedfrom flight data.The two geometry factors are shown in blue in Fig. 4. The total efficiency times geometry factor (cid:15)G , expressedin cm sr, is represented by the dashed line. It is identical for both trigger configurations, as the increased geometryfactor of T1-T2-T4 compensates for the smaller selection efficiency. The small differences in the geometry factor andselection efficiency that exist between electrons and positrons (especially at low energy) have been studied and takeninto account in the analysis. Momentum (MeV/c) −1 E ff i c i en cy o f s e l e c t i on T1T2T3T1T2T4 10 G eo m e t r y F a c t o r ( c m s r) εGT1T2T3T1T2T4 Figure 4.
The selection efficiencies (cid:15) sel and geometry factor for trigger modes T1-T2-T3 and T1-T2-T4 for electrons.
Interplanetary fluxes
Once these selections have been completed, several steps are needed to extract the interplanetary, or primary, electronand positron differential flux spectra from a sample of event candidates. We describe our method in this section.3.2.1.
Time selection
Although the northerly trajectory of the payload allowed us to survey latitudes of low rigidity cutoff E c (below200MV), the diurnal variations between geomagnetic day and night were still present (Jokipii et al. 1967) until theballoon reached latitude ∼ ◦ N after 90 hours of flight. The particle rate rises during geomagnetic day when upward-going secondary “splash” albedo particles produced in the interaction of primary cosmic rays with atmospheric nuclei,lacking the energy to escape the geomagnetic field lines, spiral along them to reach their conjugate point, at theopposite latitude. These downward-going electrons are then called “re-entrant” albedo particles, overwhelming theprimary electron signal by this trapped secondary component (Israel 1969; Verma 1967). During geomagnetic night,however, as the field lines extend, the geomagnetic cutoff becomes essentially null: “splash” albedo particles can safelyescape, and primary cosmic-ray particles of all energies are able to enter the atmosphere.The instrument recorded ∼
70 hours of data during geomagnetic night. To separate our events in periods of “day-time” (DT) and “nighttime” (NT), we compare the time series of reconstructed electrons and positrons at the lowestenergy bin with calculated variation of the vertical geomagnetic cutoff (Fig. 5), based on measurements of the Kp in-dex (Bartels 1949), indicating the level of geomagnetic disturbances at the time of flight. To compute the geomagneticcutoff, we use a code (Lin et al. 1995) that calculates the trajectory of particles based on the IGRF (International
Mechbal et al C oun t R a t e / m n e − e + Nighttime periodDaytime periodExcluded period
Time from launch (in hours) V e r t i c a l C u t o ff ( M V ) e − e + Simulated transitions
Figure 5.
Top: Time series of reconstructed electrons and positrons at the lowest momentum bin (20-30 MeV/c). The diurnalvariations between geomagnetic day and night are clearly visible. Bottom: Simulated variation of the vertical geomagneticcutoff.
Geomagnetic Reference Field) for the internal geomagnetic field and the Tsyganenko model of the magnetosphere(Tsyganenko 1987). Apparent jumps in the cutoff calculation occur because the Kp index is only defined in three hoursinterval. Daytime and nighttime time zones are selected when the transitions in the flight data and the simulationagree with one another. When they do not, the region is excluded from the analysis (the black hatched section in Fig. 5).Within daytime and nighttime sets, we further section the event sample into 23 time bins ∆ T , ranging from 15minutes intervals, to capture the ascent, to ∼ d inthe time bin, the spectra of electrons and positrons as a function of reconstructed momentum are calculated. Thesespectra are then ready to be unfolded.3.2.2. Electron and Positron fluxes at the Top of Payload
Before reaching the spectrometer, a minimum ionizing particle will lose about 4 MeV in the shell and scintillatorsof the entry telescope. To contend with the biases, inefficiencies, and finite resolution of the energy reconstruction,we simulate a response matrix that encodes the smearing of the desired true quantity into the measured observable.A deconvolution, called unfolding, is performed to estimate the true variable. An iterative statistical procedure,based on Bayes’ theorem, was developed by D’Agostini (1995). For this work, we have used the Python package
PyUnfold , which was developed for the HAWC cosmic–ray experiment and implements the aforementioned unfoldingalgorithm (Bourbeau & Hampel-Arias 2018).We generate a set of MC electrons in the energy range 10-1500 MeV, following a P − power-law distribution inmomentum P , and select particles that have passed the full flight criteria.The simulated response matrix, whose elements represent the probability for an electron of momentum P true to bereconstructed with a momentum P reco , is shown in Fig. 6 (left). We observe that its diagonal elements dominate,while deviations from the diagonal represent the bias and resolution of the reconstruction. Prior to being used on theflight data, the method was tested with an independent distribution of simulated electrons, to be unfolded using theresponse matrix. For each time bin, the response matrix is weighted with the expected background spectrum at thatgiven altitude. For instance, Fig. 6 (right) shows the comparison of the simulated true counts (blue), the observedcounts (orange), the unfolded counts (red) and the counts determined without unfolding (black) for one time bin. The ow energy electron and positron cosmic ray spectra True Momentum (MeV/c) R e c on s t r u c t ed M o m en t u m ( M e V / c ) −5 −4 −3 −2 −1 ( P r e c o | P t r u e ) S i m u l a t ed c oun t s TrueObserved SimpleUnfolded Momentum (MeV/c) R a t i o Figure 6.
Left: Example of the normalized response matrix weighted for one of the time bin at float altitude. The true andreconstructed momenta are plot on the x and y axis, respectively. Right: Simulated true, observed and unfolded counts as afunction of momentum expected during the same time bin. The bottom shows the ratios between the reconstructed counts andthe expected true counts with (red) and without (black) unfolding. The presented results are for electrons and are based onMonte-Carlo only. unfolding procedure was found to improve the accuracy of the reconstructed distribution by as much as 20 % for lowerenergy bins, compared to a reconstruction sans unfolding, as illustrated by the bottom panel of Fig. 6 (right).For each time bin the data are unfolded by normalizing the response matrix to the calculated efficiency (cid:15) sel of thefinal selection. The unfolding procedure is carried through to yield the corrected count N e − ,e + . The differential fluxΦ e − ,e + ( P ) can then be derived: Φ e − ,e + ( P ) = N e − ,e + ∆ T × (cid:15) trigger × G ( P ) × ∆ P , (1)with Φ e − ,e + ( P ) in m − sr − s − (MeV/c) − , ∆ T the time interval in s, and (cid:15) trigger the trigger efficiency described inSec. 3.1.3. G ( P ) is the geometry factor in m sr, and ∆ P is the width of the momentum bin in MeV/c. An exampleof these fluxes is shown in Fig. 7, in which the edge bin 1–1.5 GeV/c is unfolded but not used.Once all time-separated spectra are unfolded, the data set is organized by momentum bins chosen in uniformlogarithmic space between 20 MeV/c to 1 GeV/c. We then produce growth curves for each bin, that is, a profile of theflux of particles as a function of the atmospheric depth. The first 2.5 hours are used to obtain the points during theascent, where the low energy cosmic ray electron and positron signal is assumed to be atmospheric secondaries. Fig. 8presents the growth curves for 3 ranges of energy: 30–47 MeV/c (left), 113–175 MeV/c (center), and 271–419 MeV/c(right). The ascent and the first 17 hours of the flight occurred during geomagnetic daytime. The corresponding dataare presented with filled markers in the figure. The nighttime data set is shown with open markers. As seen in thebottom panel of Fig. 5, the vertical geomagnetic cutoff varies within the range 0–300 MV during the first daytimeperiod such that we expect to observe a much larger contribution of re-entrant albedo secondary particles at lowenergy (below the cutoff) than at higher energies closer to the cutoff ( ∼
300 MV). This is indeed the case in thedata presented in the left and right panels Fig. 8. The bin 113–175 MeV/c represents the transition region of thegeomagnetic variation: since the ascent occurred at ∼
160 MV during a transition from nighttime to daytime, thedaytime points represent a mixture of trapped albedo and primary cosmic rays, hence the vertical spread of the filledmarkers.From this point onward in the analysis, we express all spectra in terms of kinetic energy (in MeV) instead ofmomentum (in MeV/c), to follow the convention used in other cosmic ray experiments.0
Mechbal et al Momentum (MeV/c) −3 −2 −1 F l u x ( m − s − s r − ( M e V / c ) − ) e − secondariese + secondaries e − e + Figure 7.
Unfolded electron (blue) and positron (red) spectra at the top of the payload and the simulated atmosphericsecondary electrons and positrons (dashed lines) at 2.5 g cm − of residual atmosphere. Atmospheric depth (g cm −2 )10 −1 F l u ( m − s − s r − ( M e V / c ) − )
30 - 47 MeV/c
NT e − NT e + DT e − DT e + Atmospheric depth (g cm −2 )10 −2 −1 F l u ( m − s − s r − ( M e V / c ) − )
113 - 175 MeV/c
NT e − NT e + DT e − DT e + Atmospheric depth (g cm −2 )10 −2 −1 F l x ( m − s − s r − ( M e V / c ) − )
271 - 419 MeV/c
NT e − NT e + DT e − DT e + Figure 8.
Daytime (DT) and nighttime (NT) growth curves for 3 ranges of momentum. In the range 30-47 MeV/c, the fluxof re-entrant albedo particles at float altitudes is clearly visible during daytime (left), whereas the difference between nighttimeand daytime is hardly visible for the range 271-419 MeV/c (right). This is in agreement with our estimation that the verticalcutoff during the flight did not exceed 300 MV. The middle panel shows the daytime and nighttime points in the geomagnetictransition zone.
Flux at the top of the atmosphere
For each energy bins, we distinguish three separate contributions to the flux measured at depth d , all derived fromMC atmospheric simulations: ow energy electron and positron cosmic ray spectra • The “ primaries ”: primary electrons and positrons that remained in the same energy bins at the top of payload(ToP) as they belonged to at the top of the atmosphere (ToA). This contribution is normalized to a flux of 1particle m − sr − s − MeV − . • The “ secondaries ”: secondary background contribution from the interactions of GCR nuclei, mostly of H andHe, with the atmosphere. . • The “ spillover ”: the contribution of primary electrons and positrons that belonged to a higher energy bin atToA than that they populate at ToP. 3.3.1.
Atmospheric simulations
During the 5 days of data taking, the balloon floated at an atmospheric depth between 2 and 4 g.cm − . The dashedcurves shown in Fig. 7 are the predicted electron and positron spectra, at float altitude, of the background electronsand positrons produced in the spallation of GCR with the nuclei of the residual atmosphere. These interactionsproduce short-lived mesons, such as pions and kaons, which in turn decay into electrons and positrons.To estimate this background, we implement an atmospheric simulation using a 3D profile of the atmosphere atEsrange, Sweden taken from the day of launch, following the method of Mangeard et al. (2016). The air showerdevelopment induced by H and He, as well as primary electrons and positrons, is simulated. Secondary particles fluxesare extracted at 19 atmospheric depths from 998 to 0.87 g.cm − .The “ secondaries ” contribution is estimated by normalizing the simulated spectra to H and He local interstellarfluxes derived by Ghelfi et al. (2016, 2017a). We apply a force-field approximation of the solar modulation (Gleeson &Axford 1968), using a parameter φ = 438 ±
50 MV as calculated from neutron monitor data taken at the time of theflight, using the method of Ghelfi et al. (2017b). The heavy nuclei are assumed to produce showers similar to thosefrom He, and are taken into account by applying a scale factor F hn = 1 .
445 to the He spectrum, as done in Ghelfiet al. (2016).We fit a 7 th degree log polynomial function to the MC results of electrons and positrons produced by protonsand alpha particles. At the Regener-Pfotzer maximum ( ∼
100 g.cm − ) (Regener & Pfotzer 1934), where the flux ofelectrons is highly dominated by atmospheric secondaries, the MC agrees with the data by within less than ∼ ∼
40% (seeTable 1). This general trend of b with energy is observed for all the hypothesis used in the systematic analysis, althoughthe value of b increases depending on the chosen LIS at the top of the atmosphere.In their propagation from the top of the atmosphere to the top of the payload, electrons and positrons experienceionization and bremsstrahlung losses, which give rise to bin migration. The simulation of the air shower developmentinduced by primary electrons and positrons provides the “ primaries ” and “ spillover ” contributions. Past analyses ofballoon-borne cosmic ray data have used empirical tables of energy losses of electrons and positrons from Berger &Seltzer (1964), or solved the theoretical coupled cascade equations describing the propagation of electrons, positrons,and secondary gamma rays (Boezio et al. 2000). 3.3.2. Fit method
To extract the flux at ToA at each energy bin, we implement a simple linear least squares fit, slightly modifiedfrom Fulks (1975), in which we consider the three contributions to the data:data( d ) = a × primaries( d ) + b × secondaries( d ) + spillover( d ) , (2)where d is the atmospheric depth, and a and b the parameters of the fit, and the spillover contribution is iterativelycalculated in the analysis. We proceed with an iterative method of fitting the daytime growth curves first. Sincethe balloon was ascending through the atmosphere during geomagnetic day, and the background dominates at highatmospheric depths (low altitudes), a fit to the entire atmospheric range at daytime is necessary to evaluate thecontribution b of the secondaries. For that same energy bin, we then fit the nighttime growth curve, for float altitudesonly, fixing the contribution b to the daytime derived value. For energy bins above ∼
300 MeV, the daytime andnighttime points are combined since they are above the maximum geomagnetic cutoff. The left panel of Fig. 9 illustratesthis fit method: the three growth curve contributions are fitted to the DT data growth curves from 2 to 900 g.cm − ,2 Mechbal et al Atmospheric depth (g cm ) F l u x ( m s r s M e V ) e + Secondaries: e + Spillover e + fitdata: e + Atmospheric depth (g cm ) F l u x ( m s r s M e V ) e + Secondaries: e + Spillover e + fitdata: e + Figure 9. (Left) Growth curves fit for positrons in the energy bin 73–113 MeV at daytime. The filled circles represent the flightdata, and the dotted, solid and dash-dotted lines contributions from primary, atmospheric secondary and spillover positrons,respectively. (Right) Nighttime growth curves for positrons for the same energy bins. and the parameters a and b are estimated. The right panel of Fig. 9 shows the fit performed for a nighttime bin,for points ranging from 2–4 g.cm − , with parameter b fixed. The fit value of parameter a then corresponds, in MeVm sr − s − , to the flux at ToA for the given energy bin.The fits are done in descending order of energy. At the first iteration (647 MeV–1 GeV), the “ spillover ” contributionis calculated assuming a specific spectrum above 1 GeV. We initialize the fit to the LEE09 flux Evenson & Clem (2009)for electrons and positrons combined (all electrons), and scale the flux assuming a positron fraction e + e + + e − = 0.2.Once the flux at ToA is extracted for the first energy bin, the “ spillover ” contribution into the lower bins is updated,and the fit routine iterated. Table 1.
Fit values of parameter b Mean Energy at ToA (MeV) be − e + ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± This method allows us simultaneously to extract the re-entrant albedo (daytime) and primary cosmic ray spectraflux (nighttime) for electrons and positrons. We present and discuss our results in the next section. ow energy electron and positron cosmic ray spectra RESULTS AND DISCUSSION4.1.
Systematic uncertainties
The determination of the extraterrestrial electron and positron fluxes with a balloon-borne instrument at our energyrange is complicated by two factors: the residual layer of atmosphere above the payload, and the fact that the balloonwas launched during a transition phase in the diurnal geomagnetic cutoff variations. Thus, depending on their energy,ascent points can be of trapped secondary particles.The main systematic errors arise from uncertainties on the secondary production in the atmosphere. As was shownin Fig. 8, MC simulations of protons and alpha particles gave a good agreement with the data at Regener-Pfotzermaximum. However, any deviation in shape of the secondary growth curves can have an important effect on the finalspectrum, considering that the primary signal is very close to the background at float altitudes. This is particularlytrue for positrons in energy bins near 100 MeV, as evident from Fig. 7. Three parameters of the secondary productionare studied: the choice of H and He LIS, the value of the solar modulation parameter φ , and the scale factor F hn applied to the He spectrum to estimate the contribution of heavier nuclei. Our “baseline” spectrum was derivedusing the LIS parametrized from Voyager data (column 6, Table 3 of Ghelfi et al. (2016)), assuming φ = 438 MVand F hn =1.445. We first calculate the systematic errors stemming from the choice of LIS, testing the median flux(without Voyager data) from the same reference, as well as the LIS constructed from Vos & Potgieter (2015). Giventhe strong correlation between the choice of an interstellar spectrum and the determination of φ (Herbst et al. 2010),we must apply a different modulation potential to the LIS taken from Vos & Potgieter (2015). We take the calibratedvalue from Usoskin et al. (2017), φ Uso = 446 MV . For electrons, the systematic uncertainty on the chosen LIS is ofthe order of 6% at 25 MeV to 14% at 145 MeV. For positrons, the effect is equally as important in the energy binsclosest to the background of secondaries. This highlights the delicate task of extracting the spectra in the regions ofthe “turn-up”, around 100 MeV, at float altitudes. We then vary the modulation parameter φ = 438 MV by ± F hn is studied, taken as a rough estimate of theuncertainty on the parameter: this effect changes the spectra by less than 1% for both electrons and positrons.The effects of the initial hypotheses of the fit are also taken into consideration in the systematic uncertainties: theelectron flux as well as the initial value of the positron fraction above 1 GeV were modified using the LEE11 andPAMELA 2009 results, and varying the positron fraction by ± ∼ (cid:15) sel are already included inthe unfolding procedure, in addition to any systematic error related to the algorithm’s iterations until the convergencecriterion is met. As was explained in § Re-entrant albedo spectra below 100 MeV
The spectra of re-entrant albedo electrons and positrons at ToA are presented in the left panel of Fig. 10. Theanalysis of the daytime portion of the flight yields a flux of the re-entrant albedo electrons and positrons below 160MeV (left panel of Fig. 10). This limit comes from the value of the geomagnetic cutoff at the time of the ascent.Below the 160 MeV cutoff mark (range 1 in the right panel), the measurements in the first hours of flight wereprimarily of trapped albedo particles. Electrons and positrons above that energy bin, however, were of primary origins(range 3). Range 2 constitutes the transition region of the geomagnetic time, a zone where the origin of the measuredparticle is somewhat blurrier, in part due to the uncertainties in the geomagnetic simulation performed. These threeregions and their spectral implications were already presented in the growth curves of Fig. 8.We fit a simple power-law to the electron and positron spectra below 100 MeV, of the form f ( E ) = AE − γ (3) http://cosmicrays.oulu.fi/phi/phi.html Mechbal et al E k (MeV) −3 −2 −1 F l u x ( m − s − s r − M e V − ) e + This work e − This work e + Fit e − Fit e − MC splash e + MC splash E k (MeV) e + / ( e + + e − ) Figure 10. (Left) “Daytime” spectra of electrons and positrons between 20 MeV and 1 GeV. (Right) “daytime” positronfraction at the top of the atmosphere. The energy range 1, below 100 MeV, is dominated by the re-entrant albedo particles.The range 2, between 100 and 300 MeV, is the transition around the geomagnetic cutoff. The range 3 is dominated by primaryparticles.
Table 2.
Flux of re-entrant albedo electron and positron at the top of the atmosphereMean Energy Flux at ToA (m sr s MeV) − at ToA (MeV) e − e + . ± . × − . ± . × − . ± . × − . ± . × − . × − ± . × − . × − ± . × − . × − ± . × − . × − ± . × − Both fits give a spectral index γ = 1 . ± .
1, which differs from the results from Verma (1967), who found the re-entrantalbedo spectrum to be well fitted with a power-law index γ = 1 . ± .
09. We note that that previous measurementhad only one data point below 100 MeV, with the highest energy bin extending to 1250 MeV.The flux of splash albedo particles from the MC simulation are also visible in the left panel of Fig. 10. As expectedfrom measurements (Verma 1967), the spectral index differs from that of the re-entrant component, with γ ∼ .
3. Weobserve in the right panel of Fig. 10 the clear presence of two regimes of the positron fraction, above and below thecutoff. At higher energies, in range 3, the positron fraction is close to ∼ Electron and positron spectra
The primary electron and positron spectra measured by the AESOP-Lite instrument are shown in the two panels ofFig. 11, from 30 MeV to 1 GeV. The points at the lowest energy bin are shown in gray because of inconsistencies foundwhen unfolding the spectra using two different reconstruction algorithms: this reflects the difficulty of extracting theflux at ToA during nighttime, while normalizing the secondary growth curve to the daytime ascent. The low statisticsof the ascent phase in the 20–30 MeV edge bin cause greater uncertainties in the unfolding procedure and the growthcurve fit.Both of the electron and positron spectra display a “turn-up”, the name we give to the transition region around 80–100 MeV where the spectral index changes and becomes negative at lower energies: this had previously been observed ow energy electron and positron cosmic ray spectra E k (MeV) −4 −3 −2 −1 E l e c t r on F l u x ( m − s − s r − M e V − ) Beuermann et al. (1968)PAMELA 2006bPAMELA 2009bThis work25 MeV 10 E k (MeV) −4 −3 −2 −1 P o s i t r on F l u x ( m − s − s r − M e V − ) Beuermann et al. (1968)PAMELA 2006bPAMELA 2009bThis work25 MeV
Figure 11. (Left) Primary spectrum of cosmic ray electrons between 20 MeV and 1 GeV. (Right) Primary spectrum of cosmicray positrons in the same energy range. The index ”b” corresponds to measurements made during the second semester of theyear. PAMELA electron and positron data are taken from Adriani et al. (2015), and Aslam et al. (2019), respectively. in the all electron spectrum measured by the LEE payload (Fulks 1975; Evenson et al. 1983; Evenson & Clem 2009),and had been hinted at in PAMELA data down to 80 MeV (Adriani et al. 2016; Aslam et al. 2019). This behavior isalso revealed in our positron spectrum, despite the uncertainties in the data points, as explained above.The comparison between AESOP-Lite’s and PAMELA’s electron and positron measurements is qualitatively con-sistent with the knowledge we have of charge-sign dependent solar modulation. In the second semester of the year2009 (“2009b”), the solar modulation parameter φ as measured by the methodology of Ghelfi et al. (2017b) was φ ∼
439 MV, while it was φ ∼
539 MV in 2006b. The lower solar modulation environs of 2009 help explain the higheramplitude in the electron and positron fluxes that PAMELA measured in 2009 compared to 2006, during the sameA- solar polarity cycle, taking into consideration the well-known anti-correlation between the solar activity and thecosmic ray flux at 1 AU. Our 2018 flight took place during a very low solar minimum, with φ ∼
438 MV, a value similarto that present during PAMELA’s data taking. However the solar epoch had changed from an A- polarity in 2009 toan A+ one in 2018. This has a notable impact on the propagation of charged particles: in a positive cycle, positronsreach the Earth with greater ease than electrons, having traveled via the polar regions of the heliosphere, whereaselectrons encounter more of the gradient and curvature of the wavy HCS present in the helio-equatorial regions theytraversed (Jokipii et al. 1977), their flux thus more suppressed. We notice that at energies above 100 MeV, the electronflux measured by AESOP-Lite is lower than that reported by PAMELA in 2009, which can likely be explained by thepolarity reversal. Conversely, the positron flux recorded by our instrument is higher in amplitude than PAMELA’s,consistent with the fact that the A+ epoch favors positively charged particles more so than the A- epoch does.At lower energies, the only comparable separate measurements of electrons and positrons are from Beuermann et al.(1969), in which a balloon-borne magnetic spectrometer measured particles down to 12 MeV; their data suggests asimilar power-law form.The positron fraction of the primary cosmic ray spectrum is presented in Fig. 12. Above 200 MeV, the frac-tion suggests a rise with decreasing energy, a trend previously displayed in results from the PAMELA, AESOP andCAPRICE94 experiments (Adriani et al. 2016; Clem et al. 1996; Boezio et al. 2000), to name a few. The solar polaritycycle appears to have an effect on the positron fraction: for instance, the measurement by AESOP-Lite at 1 GeV ina A+ epoch is significantly higher than the one made by PAMELA in A-. This temporal variation caused by thecharge-sign dependent solar modulation had previously been observed by PAMELA and AMS-02 (Adriani et al. 2016;Aguilar et al. 2018), and reproduced at higher energy using numerical transport codes (Potgieter 2014). We note that6
Mechbal et al the fraction we measured at higher energy is also significantly greater than the one observed by PAMELA in a similarpolarity cycle, presumably because the Sun’s activity was at a minimum in 2018.At first glance, the positron fraction appears to be flat from 30 MeV to 200 MeV, plateauing at ∼ E k (MeV) −3 −2 −1 e + / ( e + + e − ) Be)ermann e( al. (1968, A)CAPRICE (1994, A+)AESOP (1999, A+)PAMELA (2015, A+)PAMELA (20112013, A)This work (2018, A+)
Figure 12.
Positron fraction of primary cosmic rays.
Fig. 13 shows the all-electron spectrum, alongside the two last measurements completed by LEE09 and LEE11. Below50 MeV, the Jovian magnetosphere also becomes an important source of electrons (Vogt et al. 2018), as detected bythe ISEE-3 satellite mission at 1 AU (red circles in the figure) (Moses 1987). Elaborate 3D numerical transport codeshave been developed over the past decades (Potgieter et al. 2015; Vos & Potgieter 2015; Aslam et al. 2019; Bisschoffet al. 2019), in which the different processes of the theory of solar modulation are included: namely, the convection,adiabatic deceleration, drift and diffusion of charged particles in the solar wind. The dashed blue lines representsthe model of Potgieter et al. (2015), showing the LIS Voyager 1 spectra (solid black line) propagated through theheliosphere. PAMELA electron observations were used to tune model parameters. In dashed black is the prediction ofthe modulated Jovian spectrum, whereas the red solid line projects the expected electron spectrum at Earth for a givensolar epoch and modulation potential (Nndanganeni & Potgieter 2018). The crossover between the GCR electronsand the Jovian electrons is estimated to happen at 30 MeV, according to Nndanganeni & Potgieter (2018). The finalprediction of the all electron flux at 1 AU notably involves a “turn-up” around 80 MeV, and a negative power-lawbehavior below. From the combined study of AESOP-Lite and LEE data, the energy at which the minimum occurs isshifting, as LEE11 results coincidence with the model, whereas AESOP-Lite and LEE09 results do not.In fact, a dedicated study of the solar modulation of electrons and positrons is needed in order to characterize theinterplay of Galactic and Jovian of electron sources as well as drift and diffusion effects below 100 MeV. Diffusion anddrift coefficients are proportional to the mean free paths (MFP). For electrons, the parallel and perpendicular MFPs,which govern the diffusive process, are assumed to be rigidity-independent below a yet vague threshold ( ∼
100 MeV)Bieber et al. (1994); Drge (2003); Potgieter et al. (2015). The addition of our data set can offer a glimpse into the ow energy electron and positron cosmic ray spectra E k (MeV) −3 −2 −1 A ll E l e c ( r on F l ) x ( m − s − s r − M e V − ) LISGalac(ic 1 AUJovian 1 AUJovian + Galac(icV1 LEE09LEE11PAMELA 2009bISEE3 (11/1978)This +ork25 MeV
Figure 13.
Primary spectrum of cosmic ray the all electrons between 20 MeV and 1 GeV, shown with Voyager all electronsoutside the heliosphere.
Table 3.
Primary electron and positron flux at the top of the atmosphereMean Energy Flux at ToA (m sr s MeV) − at ToA (MeV) e − e + . × − ± . × − . × − ± . × − . × − ± . × − . × − ± . × − . × − ± . × − . × − ± . × − . × − ± . × − . × − ± . × − . × − ± . × − . × − ± . × − . × − ± . × − . × − ± . × − . × − ± . × − . × − ± . × − . × − ± . × − . × − ± . × − . × − ± . × − . × − ± . × − behavior of electron and positron cosmic rays in a poorly observed energy regime. The contemporary measurements ofVoyager 1 and 2, progress in the numerical modeling, and the planned future missions of the AESOP-Lite instrumentcreate a unique opportunity to finally resolve the origin of the low-energy electron and positron spectra on Earth.8 Mechbal et al
Table 4.
Positron fractionMean Energy at ToA (MeV) e + e + + e − . × − ± . × − . × − ± . × − . × − ± . × − . × − ± . × − . × − ± . × − . × − ± . × − . × − ± . × − . × − ± . × − . × − ± . × − ACKNOWLEDGMENTSThe authors would like to thank Matthew Collins, Forest Martinez-McKinney, Serguei Kachiguine, and Yang Zhoufor their help in the design, construction and integration of the instrument. We thank Chris Field and CSBF fortheir support during the integration period in Palestine, Texas, and for the successful balloon flight. We thankEsrange for their support during the flight campaign. This work is supported by NASA awards NNX15AL32G and80NSSC19K0746, and the Bartol Research Institute. ow energy electron and positron cosmic ray spectra A. FULL ELECTRON SPECTRA OF LEE INSTRUMENT FROM 2009 AND 2011 FLIGHTSTwo balloon flights carrying the LEE instrument took place during the dates May 16-21, 2009 and May 26-31, 2011from the Esrange Space Center near Kiruna, Sweden. Upon reaching the stratosphere the balloons rode the summerArctic polar vortex across the Atlantic Ocean, Greenland and the Baffin Bay into the northern regions of Canada wherethe flights were terminated. While both flights occurred during A- solar minimum, the 2009 flight took place duringexceptionally low solar modulation level, the lowest during the history of the neutron monitors. The long durationexposure combined with low modulation level allowed the complete electron spectrum from 20 MeV to 5 GeV to beobserved for the very first time. Flight data were analyzed using the same method outlined in Fulks (1975).
Table 5.
Full electron spectra of LEE instrument from 2009 and 2011 flightsMean Energy Flux e + + e − at ToA (m sr s MeV) − at ToA (MeV) May 16-21, 2009 May 26-31, 20112 . × . ± . × − . × − ± . × − . × . × − ± . × − . × − ± . × − . × . × − ± . × − . × − ± . × − . × . × − ± . × − . × − ± . × − . × . × − ± . × − . × − ± . × − . × . × − ± . × − . × − ± . × − . × . × − ± . × − . × − ± . × − . × . × − ± . × − . × − ± . × − . × . × − ± . × − . × − ± . × − . × . × − ± . × − . × − ± . × − . × . × − ± . × − . × − ± . × − . × . × − ± . × − . × − ± . × − . × . × − ± . × − . × − ± . × − . × . × − ± . × − . × − ± . × − . × . × − ± . × − . × − ± . × − REFERENCES
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