OBSERVATIONS OF HIGH-ENERGY COSMIC-RAY ELECTRONS FROM 30 GeV TO 3 TeV WITH EMULSION CHAMBERS

Electrons⁸ in cosmic rays have unique features, complementary to cosmic-ray nuclear components, because of their low mass and leptonic nature. High-energy electrons lose energy by synchrotron radiation in the Galactic magnetic field and inverse Compton scattering with the interstellar photons in the Galaxy. High-energy cosmic-ray electrons cannot propagate far from their sources because the electrons lose energy rapidly with an energy loss rate of the square of energy through these radiative processes. These processes during propagation through the Galaxy without hadronic interactions simplify modeling of the propagation of electrons compared with other cosmic-ray components such as nucleons.

Evidence for non-thermal X-ray emission from supernova remnants (SNRs) indicates that high-energy electrons in the TeV region are accelerated in SNRs (e.g., Koyama et al. 1995). These observations strongly suggest that cosmic-ray electrons are accelerated in SNRs and that SNRs are the most likely primary sources of cosmic-ray electrons. Shen (1970) first pointed out that the electron spectrum in the TeV region depends on the age and distance of a few local sources. His proposed concept has been accepted in later calculations of cosmic-ray electrons (Kobayashi et al. 2004 and references therein). Kobayashi et al. (2004) suggest that the energy spectrum of cosmic-ray electrons has unique spectral structures in the TeV region due to the discrete effect of local sources. This means that we can identify cosmic-ray electron sources from the electron spectrum in the TeV region. In addition, some dark matter may produce negative electrons and positrons in the energy region around 100–10 TeV via dark matter annihilations or decaying dark matter (e.g., Kamionkowski & Turner 1991; Cheng et al. 2002). In particular, in the case of mono-energetic electrons from dark matter, although propagation through the Galaxy would broaden the line spectrum, the observed electron spectrum could still have distinctive features. Thus, observations of high-energy electrons provide unique information about sources and propagation of cosmic rays, and enable us to search for dark matter.

Although cosmic-ray electrons have been observed with many kinds of detectors since 1960 (Earl 1961), most observations are limited to below several 100 GeV (Daniel & Stephens 1965; Golden et al. 1984; Tang 1984; Grimani et al. 2002; Boezio et al. 2000; DuVernois et al. 2001; Torii et al. 2001; Aguilar et al. 2002). The first cosmic-ray electron observation with nuclear emulsions was achieved by Daniel & Stephens (1965). They indicated that nuclear emulsions are ideal for the detection of electrons among many background protons because of the excellent imaging capability with a high position resolution of 1 μm.

The reason for the difficulty observing electrons is that the electron flux itself is very low and decreases with energy much more rapidly than that of protons because of the electromagnetic energy loss. Electron energy spectra are represented by a power-law function with an index of −3.0 to −3.3, which is steeper than proton spectra with a power-law index of −2.7 (Haino et al. 2004 and references therein). The flux of cosmic-ray electrons is ∼1% of the protons at 10 GeV, and decreases very rapidly with increasing energy to be ∼0.1% of the protons at 1 TeV (e.g., Yoshida 2008). Therefore, there are few observations of electrons in the TeV region, since we need a long-duration exposure with a detector that has a large geometrical factor, sufficient thickness, and powerful background rejection powers.

Chang et al. (2008) performed the ATIC-2 balloon experiment in Antarctica and reported the energy spectrum in the energy region from 20 GeV up to 3 TeV. The instrument contained a deep, fully active, BGO calorimeter of 18 radiation lengths (r.l.). They found an excess of cosmic-ray electrons at energies of 300–800 GeV compared to a general electron spectrum calculated using GALPROP (Moskalenko & Strong 2010) and considered that the excess might indicate a nearby source of energetic electrons such as the annihilated electrons from dark matter particles. On the other hand, from the independent data analysis of ATIC-2 + ATIC-4, Panov et al. (2011) reported the electron spectrum from 30 GeV to 1 TeV and indicated that the electron spectrum in the region of the excess includes fine structure with a number of narrow peaks.

Torii et al. (2008) also observed cosmic-ray electrons from 10 GeV to 800 GeV from a long-duration balloon flight using Polar Patrol Balloon (PPB) in Antarctica. The PPB-BETS is an imaging calorimeter composed of scintillating-fiber belts and plastic scintillators inserted between lead plates with 9 r.l. They considered that the energy spectrum obtained with PPB-BETS might indicate signs of structure in the several 100 GeV region, which is similar to the ATIC-2 observations, although a single power-law spectrum is acceptable within statistical errors.

Ackermann et al. (2010b) presented the results of cosmic-ray electron observations from 7 GeV to 1 TeV using about 8 × 10⁶ electron candidates detected in the first 12 months on orbit of the Fermi Large Area Telescope (Fermi-LAT). Their electron spectrum can be described with a power law ∝E^{−3.08 ± 0.05} with no prominent features, accommodating a slight spectral hardening at around 100 GeV and a slight softening above 500 GeV. Fermi-LAT also searched for anisotropies of electrons from 60 GeV to 480 GeV with angular scale extending from ∼10° to 90°, resulting in null results (Ackermann et al. 2010a). They indicated that the upper limits for a dipole anisotropy range from ∼0.5% to ∼10%. Although Fermi-LAT has the long exposures of the electron observations, the detector thickness is insufficient to observe electrons in the TeV region. As a result, Fermi-LAT cannot separate electrons and protons one by one, but separates electrons from protons statistically based on Monte Carlo simulations and machine learning algorithms.

The H.E.S.S. ground-based imaging atmospheric Cherenkov telescopes measured the electron spectrum in the energy range of 340 GeV to 5 TeV (Aharonian et al. 2008, 2009). The H.E.S.S. data show no indication of structure in the electron spectrum, but rather a power-law spectrum with a spectral index of −3.0 which steepens to be around −4.0 above ∼1 TeV. While the H.E.S.S. team reported electron observations up to several TeV, the electron spectrum is provided by indirect observations. Thus, H.E.S.S. intrinsically has systematic errors in the reconstructed electron spectra arising from uncertainties in the simulation of hadronic interactions, the atmospheric model, and the absolute energy scale.

Adriani et al. (2009) reported a statistically significant increase in the positron fraction at energies above ∼10 GeV with the PAMELA satellite-borne experiment, which is completely inconsistent with standard models describing the secondary production of cosmic rays. The PAMELA positron data indicate the existence of primary positron sources such as annihilated dark matter particles in the vicinity of our Galaxy, nearby pulsars, and nearby micro-quasars. Adriani et al. (2011a) also presented the negatively charged cosmic-ray electron spectrum between 1 and 625 GeV performed by PAMELA, which is the first time that cosmic-ray negative electrons have been identified separately from positrons above 50 GeV. The negative electron spectrum can be described with a single power-law energy dependence with a spectral index of −3.18 ± 0.05 above 30 GeV and no significant spectral features.

We have observed high-energy cosmic-ray electrons from 30 GeV to 3 TeV with emulsion chambers at balloon altitudes, from 1968 to 2001, accumulating a total exposure of 8.19 m² sr  day. In the observations, we have carried out particle identification one event by one event with a proton rejection power larger than 1 × 10⁵ in the TeV region because of an excellent imaging detector with a position resolution of 1 μm, which is one of the outstanding capabilities of emulsion chambers. The performance of the emulsion chambers was examined with accelerator beam tests at CERN-SPS and Monte Carlo simulations. We also estimated the atmospheric electron spectra in a reliable way (Komori et al. 2012) and carried out on-board calibrations by using the flight data.

While we previously reported the results from 1968 to 1976 experiments (Nishimura et al. 1980 and some additional publications: see references in Kobayashi et al. 2004), in this paper we present the final cosmic-ray electron spectrum in the energy range from 30 GeV to 3 TeV observed with balloon-borne emulsion chambers up to 2001, combined with our previous results.

Emulsion chambers consist of nuclear emulsion plates, X-ray films, and lead plates (or tungsten plates in a few chambers). A nuclear emulsion plate is a methacrylate base 500–800 μm thick with a double coating of nuclear emulsion of a thickness of 50–100 μm. We used Fuji ET-7B and ET-7D for the nuclear emulsion. Nuclear emulsion plates are placed under lead plates. One or two X-ray films are inserted between a lead plate and a nuclear emulsion plate to allow rapid, naked-eye scanning for high-energy cascade showers, which produce dark spots in the films. Figure 1 shows a typical emulsion chamber configuration. The typical size and thickness of the detector are 40 cm × 50 cm and 8 cm (∼9 r.l.), respectively. Detailed configurations are described in Nishimura et al. (1980).

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The thickness of one lead plate in the upper layers is 0.5 mm (∼0.09 r.l.) to identify incident parent particles, determine the incident angles, and investigate the initial shower developments. In the bottom layers, the thickness of one lead plate is 5 mm (∼0.9 r.l.) and X-ray films are inserted to detect cascade showers, as shown in Figure 1.

Since high-energy electromagnetic showers above a few 100 GeV leave dark spots on X-ray films, these showers can be detected with the naked eye by scanning the X-ray films. The corresponding tracks in the adjacent emulsion plate are located using microscopes. The detection threshold of the X-ray film is 500 GeV for the Sakura type-N X-ray film used before 1984, 750 GeV for the Fuji #200 X-ray film, and 250 GeV, 200 GeV, and 150 GeV for the screen type X-ray films of Fuji G8-RXO, G12-RXO, and GS-RXO used from 1984 to 1988 (Kobayashi et al. 1991). After 1988 we used screen type X-ray films of HR8-HA30, HR12-HA30, and HR16-HA30. The experiment to determine the sensitivity of screen type X-ray films of the HR series was carried out at Research Center for Electron Photon Science of Tohoku University in 2001 using test chambers with multilayers of emulsion plates and X-ray films. The test chambers were exposed to 200 MeV electron beams. Figure 2 shows the result of the characteristic curves of different types of X-ray films. Since the detection threshold of the net darkness on the X-ray films with the naked eye is 0.1 (Kobayashi et al. 1991), the electron densities on the emulsion plates at the X-ray film detection threshold correspond to 0.9 × 10⁵ cm⁻² for HR16–HA30, 1.2 × 10⁵ cm⁻² for HR12–HA30, 2.6 × 10⁵ cm⁻² for HR8–HA30, and 4.0 × 10⁵ cm⁻² for Fuji #200 X-ray films. These electron densities are compatible with the shower track densities with emulsion chambers at the shower maximum of electrons with energies of 140 GeV, 180 GeV, 450 GeV, and 750 GeV, respectively (see Figure 6), which are the detection threshold energies of the X-ray films.

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Because of the simple configuration of the detector, the geometrical factor (SΩ) can be estimated very accurately, a difficult task for some electronic detectors. For electron observations, the effective geometrical factor is given by

$$\begin{equation} S\Omega _{e} = 2\pi S\eta \int _0^{\theta _0} \cos \theta \sin \theta d\theta = \pi S\eta \sin ^2{\theta _0}, \end{equation} \tag{ 1 }$$

where θ₀ is the upper limit of incident angles and η is the so-called edge effect. Some incident electrons near the edge at the top of the detector do not pass through the bottom of the detector. The edge effect is the efficiency of events that pass through the top and bottom emulsion plates. In the typical case of θ₀ = 60° and S = 0.40 × 0.50 m², SΩ_e is 0.39 m² sr with a η of 0.82 for a chamber thickness of 8.0 cm. In Appendix A, we summarize the area S, edge effect η, upper limit of incident angles θ₀, and SΩ_eT of the different emulsion chambers. As shown in Appendix A, S, η, θ₀, and SΩ_eT change depending on the electron energies.

We measure the shower particles within a circle of 100 μm radius from the shower axis. This means that we select shower particles with higher energies, which suffered less multiple scattering in the chamber. Hence, the number of shower particles selected decreases faster than that of all shower particles. The shower maximum in emulsion chambers for shower particles within a circle of 100 μm radius appears in ∼6 r.l. for 1 TeV electrons, while the maximum of the total number of shower particles appears in ∼12 r.l. for 1 TeV electrons. As a result, the energy of higher energy incident electrons can be determined with a thinner detector. Thus the emulsion chamber has the advantages of a wide field of view, small thickness, and a lightweight detector, compared to other instruments.

In order to verify the zenith angle dependence of the detection efficiency for the incident electrons, we present the zenith angle distribution of electrons observed with the balloon-borne emulsion chambers in Figure 3, which is compared to the expected distribution for primary cosmic-ray electrons. As shown in Figure 3, the zenith angle distribution of electrons is consistent with expectation.

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We have observed cosmic-ray electrons with balloon-borne emulsion chambers in 14 flights between 1968 and 2001. In order to reject background cosmic rays, the emulsion chambers are placed upside down in the balloon gondolas during ascent and descent of the balloons, and are flipped to a normal position during level flight. The pressure–altitude records for each flight correspond to residual atmospheric overburdens in the range from 4.0 g cm⁻² to 9.4 g cm⁻². In Table 1, we summarize the series of experiments since 1968 (the results for 1968–1976 observations were reported in Nishimura et al. 1980). The SΩ_eT in Table 1 are the effective exposure factors for primary electron observations in the energy range above 1 TeV within a zenith angle of 60°. Figure 4 shows the total cumulative effective exposure SΩ_eT for primary electrons, which is 8.19 m² sr day in the TeV region. In addition to the electron observations, we have simultaneously observed atmospheric gamma rays; the results are described in Yoshida et al. (2006).

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In the balloon observations, we identify electron events among incoming cosmic-ray events and determine their energies. In the following data analysis, we selected events with an incident zenith angle less than 60° and which passed all the way from the top to the bottom layer of the chambers.

4.1. Event Identification

High-energy electromagnetic showers above a few 100 GeV are detected with naked-eye scanning of dark spots left on the X-ray films. The corresponding tracks in the adjacent emulsion plate are located with microscopes and traced back through the stack to the shower starting points. As described in Section 2 and Appendix A, since we have improved the X-ray films to detect lower energy electrons, we have used different types of X-ray films that have different threshold energies. Hence, the total cumulative effective exposure SΩ_eT depends on electron energies, as shown in Figure 4. The detection efficiencies are 100% above the threshold energies and fall off rather rapidly below the thresholds (Nishimura et al. 1980). We also confirmed the threshold energy for each balloon flight by using the deviation from a single power-law spectrum of the observed atmospheric gamma rays. In this analysis, we used the electron events above the threshold energies to derive the electron energy spectrum. In order to detect the electromagnetic showers below a few 100 GeV, the emulsion plates were scanned directly with microscopes for a part of the 1968, 1969, 1970, 1973, and 1996 emulsion chambers. We successfully detected electron events down to 30 GeV with the microscope scanning. The detection efficiency is larger than 95% (Nishimura et al. 1980). The microscope scanning is carried out in the smaller rectangular area of the upper emulsion plates. Since the shower particles on the bottom emulsion plates are measured in the full area, the edge effect η of the microscope scanning has a larger value than that of the usual shower measurements. In the case of the scanning area within dtan θ₀ from the detector edge, where d is the thickness of the detector and θ₀ is the upper limit of incident angles, η is 1.00. For the larger scanning area, not within dtan θ₀ from the detector edge, η is smaller than 1.00, as described in Appendix A. In emulsion chambers, it is possible to measure the location of shower tracks in each emulsion plate with a precision of 1 μm. The incoming particles such as electrons, gamma-rays, protons, and heavier nuclei are identified by examining the details of shower development, especially around the shower starting points.

Since electron events start from a single charged track which produces an electron–positron pair within 1 r.l. of the top of the emulsion chamber with about 90% probability, they are identified by the existence of a single and a pair track with a spreading angle less than 1 × 10⁻³ rad at the interaction point, as described in Appendix B. Electron events also give an electro-magnetic shower without core structures. Gamma-ray events, which are also a pure electromagnetic shower, start from a pair with no visible primary track above the shower starting point. Although the incident track of a proton-induced shower shows a single charged track like an electron, proton-induced showers also have many secondaries at the shower starting point and often have multicore structures in the deep layers. Even in the case of proton-induced showers with few secondary tracks, it is possible to discriminate the proton-induced showers from electron-induced showers by the differences in the spreading angle between tracks at the shower starting points. As described in Appendix B, the proton rejection power is estimated to be larger than 1 × 10⁵, and is derived to be independent of Monte Carlo simulation codes and hadron interaction models. Hadron showers of heavier nuclei such as helium are easily distinguished because the grain density of the incident track is larger than a minimum ionizing particle.

In emulsion chambers, we can measure the depth of the first electron–positron pair of the electron-induced shower, the so-called shower starting point. The validity of event identification can be checked by comparison of the measured shower starting points with the expected values. Figure 5 presents the shower starting point distributions of the balloon observations for electrons above 400 GeV, gamma rays above 300 GeV, and protons compared to the expected distributions. For electrons, the shower starting point is compared to the Bethe–Heitler expectation and the Landau–Pomeranchuk–Migdal (LPM) expectation based on Migdal's formula (e.g., Baier & Katkov 2005). As shown in Figure 5, the shower starting point distributions within 3.0 r.l. show good agreement with the expectations, confirming the reliability of the particle identification, and the deviation of the proton distribution larger than 3.0 r.l. from the expectation shows the decrease in proton detection efficiency. In particular, the consistent result for electrons compared with the LPM expectation strongly suggests the accurate identification of electrons.

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4.2. Energy Determination

Electron energies were determined by counting the number of shower tracks in each emulsion plate within a circle of radius 100 μm centered on the shower axis. We derived the integral track length from these counted tracks in each layer. The integral track length is theoretically expected to be proportional to the shower energy, as discussed in detail in Nishimura et al. (1980). Our chamber structures are slightly different in each flight because of slight differences in lead thicknesses and the insertion of different types of X-ray films and phosphoric screen films. Since the differences in the chamber structure affect the integral track lengths, we calculated the shower developments for each chamber one by one using a Monte Carlo simulation code called Epics (Kasahara 2012). Epics has been used for cosmic-ray experiments (e.g., Torii et al. 2001; Amenomori et al. 2009), and also used for very forward single-photon energy spectra from 0.1 TeV to 3.6 TeV in the Large Hadron Collider forward experiments (Adriani et al. 2011b). The incident electron energies are determined by these track lengths compared with the values estimated from the Monte Carlo simulations for each chamber.

For the calibration of the detector, we carried out beam tests of electrons in 2004 at CERN-SPS. The detector configuration is the same as the balloon-borne emulsion chambers, except for the detector size of 10.0 cm × 12.5 cm. Results calculated using the Epics code were confirmed by emulsion chambers exposed to 50 GeV and 200 GeV electron beams at CERN-SPS. In order to evaluate the possible systematic errors at energies greater than 200 GeV, we also compared two independent Monte Carlo simulation codes; Epics and Geant4 (Agostinelli et al. 2003; Allison et al. 2006). Figure 6 shows the longitudinal development of the average number of shower tracks from the Monte Carlo simulations compared with the results of 50 GeV and 200 GeV electron beams. As shown in Figure 6, the simulations represent the experimental data well. The differences between the integral track lengths of Epics and Geant4 are ∼2% in the energy range of 30 GeV–3 TeV, which is negligibly small compared to the statistical errors of our cosmic-ray electron spectrum as described in Section 4.3. Figure 7 shows the energy distributions for 50 GeV and 200 GeV electron beams. The energies determined with the simulations for 50 GeV and 200 GeV electrons are consistent with the experimental data. The energy resolutions are 14.5% at 50 GeV and 10.6% at 200 GeV, respectively. Figure 8 presents the energy resolutions of the simulations compared with the experimental data. The energy resolution for the emulsion chamber is well represented by the form

$$\begin{eqnarray} &&\frac{\sigma }{E} = \left[ 8.6\%^{2}\! \left(\frac{E}{100{\rm \,GeV}}\right)^{-1}\!\! + 6.9\%^{2} + 2.4\%^{2}\! \left(\!\frac{E}{100{\rm \,GeV}}\!\right) \right]^{1/2}\!\!,\nonumber \\ \end{eqnarray} \tag{ 2 }$$

where E is the electron energy and σ is the standard deviation of the energy determination. The first term in the right-hand side root represents statistics-related fluctuations of the number of shower particles, while the last term represents fluctuations due to shower particles escaping from the finite thickness of the detector.

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4.3. Electron Energy Spectrum

In balloon flight experiments, it is necessary to correct the observed cosmic-ray electron spectrum because of the residual overlying atmosphere. We corrected for the energy lost by primary electrons due to bremsstrahlung radiation in the overlying atmosphere. The average bremsstrahlung energy loss for each electron is given by

$$\begin{equation} E_{0} = E e^{ \frac{A(s)}{s} {\cdot } \frac{t}{\cos \theta } }, \end{equation} \tag{ 3 }$$

when the incident electron spectrum is a power-law function with an index of −(s + 1). Here, E₀ is the energy of the primary electron at the top of the atmosphere, E is the measured energy in the detector, t is the vertical thickness of the overlying atmosphere in r.l., θ is the zenith angle of the incident electron to the detector, and A(s) refers to the function used in electro-magnetic shower theory,⁹ described by Nishimura (1967). In the case of s = 2.3, A(2.3) is 1.674. For example, in the case of a power-law index of −3.3 (s = 2.3), an atmospheric thickness of 6.0 g cm⁻², and a zenith angle of 45°, the energies of incident electrons are reduced by 16%, and hence the electron flux decreases by 32%. This energy loss formula is different from the simple energy loss of E₀ = Ee^t/cos θ, since the energy losses of electrons have broad distributions and the incident electron spectrum is steeply sloped. In the case of E₀ = Ee^t/cos θ with the same parameters, the energies are reduced by 21% and the electron flux decreases by 41%, which correspond to monochromatic electrons.

In addition to primary cosmic-ray electrons, atmospheric electrons are also produced by hadronic interactions of primary cosmic rays with nuclei in the atmosphere. Since almost all atmospheric electrons are produced via atmospheric gamma rays from neutral pion decay, the atmospheric electron spectrum is estimated by using the simultaneously observed atmospheric gamma-ray spectrum with the emulsion chambers (Yoshida et al. 2006). Komori et al. (2012) derived the atmospheric electron spectrum in the upper atmosphere less than 10 g cm⁻² from the observed gamma-ray spectrum using electro-magnetic shower theory. Their derived atmospheric electron spectrum is substantively free from the uncertainties of the cosmic-ray nuclear spectra and hadronic interaction models. The contributions of the atmospheric electrons to primary electrons increase with electron energies and with the thickness of the overlying atmosphere. Table 2 shows the number of atmospheric electrons, which ranges from 0% to 50% of the observed electrons.

Table 2. The Number of Observed Electrons and the Fluxes of Primary Cosmic-ray Electrons

Energy	$\overline{E}$	SΩeT	Nob	Nsec	Npri	Flux (J)	E3 × J
(GeV)	(GeV)	(m2 s sr)				(m−2 s−1 sr−1 GeV−1)	(GeV2 m−2 s−1 sr−1)
30–50	3.82 × 101	69.8	6	0	6	(3.94 ± 1.61) × 10−3	220 ± 90
60–100	7.64 × 101	682	9	0	9	(3.15 ± 1.05) × 10−4	141 ± 47
100–150	1.21 × 102	1.679 × 103	8	1.00	7.00	(8.08 ± 3.31) × 10−5	143 ± 59
150–200	1.72 × 102	5.613 × 103	7	1.43	5.57	(1.92 ± 0.93) × 10−5	98 ± 47
200–300	2.43 × 102	9.718 × 103	7	1.96	5.04	(5.03 ± 2.71) × 10−6	72 ± 39
300–400	3.45 × 102	4.8368 × 104	15	4.37	10.63	(2.14 ± 0.80) × 10−6	88 ± 33
400–600	4.86 × 102	1.3374 × 105	35	6.44	28.56	(1.05 ± 0.22) × 10−6	120 ± 25
600–800	6.90 × 102	3.2148 × 105	29	7.16	21.84	(3.35 ± 0.85) × 10−7	110 ± 28
800–1000	8.92 × 102	5.9088 × 105	20	6.54	13.46	(1.13 ± 0.39) × 10−7	80 ± 27
1000–1500	1.214 × 103	7.0795 × 105	15	7.73	7.27	(2.03 ± 1.14) × 10−8	36 ± 20
1500–3000	2.068 × 103	7.0795 × 105	15	5.31	9.69	(9.04 ± 3.74) × 10−9	80 ± 33

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We observed electrons at each balloon altitude and derived the cosmic-ray electron spectrum using the following formula:

$$\begin{equation} J_{\rm e}(E) = \frac{ N_{\rm e} - N_{\rm 2nd} }{ S\Omega _{e} T {\Delta } E C_{\rm eff} C_{\rm enh} } ({\rm m}^{-2}\,{\rm s}^{-1}\,{\rm sr}^{-1}\,{\rm GeV}^{-1}). \end{equation} \tag{ 4 }$$

Here, N_e is the number of observed electron events, N_2nd is the number of atmospheric electrons, C_eff is the electron detection efficiency, and C_enh is the enhancement factor due to the energy resolution.

The efficiency C_eff for detecting electromagnetic showers in emulsion chambers has been found to be essentially 100% above the threshold energy for naked-eye scanning of X-ray films (Kobayashi et al. 1991 and references therein). The detection efficiency for HR16–HA30 was also tested by using emulsion chambers exposed to the 200 GeV electron beam at CERN-SPS. Simultaneously with primary electrons, we have also observed atmospheric gamma rays to check the performance of the emulsion chambers in each balloon experiment (Yoshida et al. 2006). We also confirmed the detection efficiency of each emulsion chamber from the atmospheric gamma-ray spectra. The uncertainty of the energy determination has the effect of enhancing the absolute flux of electrons, in particular for a steep power-law spectrum. The enhancement factor C_enh due to the energy resolution has values from 1.01 to 1.09 depending on electron energies (see Yoshida et al. 2006 for more detail).

The total number of observed electrons is 166 events with the balloon-borne emulsion chambers exposed from 1968 to 2001 in the energy range of 30 GeV–3 TeV. After the corrections described above, we derived the primary cosmic-ray electron energy spectrum. Figure 9 shows the observed electron spectrum, which is well represented by the power-law function

$$\begin{eqnarray} J_{\rm e}(E) &=& (1.39 \pm 0.23)\nonumber\\ && \times 10^{-4} (E/100{\rm \,GeV})^{-3.28 \pm 0.10} ({\rm m}^{-2}\,{\rm s}^{-1}\,{\rm sr}^{-1}\,{\rm GeV}^{-1}).\nonumber\\ \end{eqnarray} \tag{ 5 }$$

The flux values and numbers of electrons in each energy bin are listed in Table 2. Compared with our previous electron spectrum in the energy range of 30–1000 GeV (Nishimura et al. 1980), the total number of observed electrons increased threefold, and the highest energy was extended up to 3 TeV.

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The cosmic-ray electrons observed with balloon-borne emulsion chambers (ECC) extend up to 3 TeV with no cutoff in the form of a power-law spectrum with an index of −3.28. In order to confirm the lower limit of the high-energy cutoff in the TeV region, we fitted the observed electron spectrum with an exponentially cutoff power law. With the fixed power-law index of −3.28, the lower limit (90% CL) of the exponential cutoff energy is 2.1 TeV.

This observed electron spectrum in the energy region below 1 TeV is very similar to the electron spectrum by PAMELA (Adriani et al. 2011a), and shows agreement with the electron observations by Fermi-LAT (Ackermann et al. 2010b). Our electron spectrum observed with the emulsion chambers does not exhibit significant spectral excesses. The result of our electron spectrum compared with the ATIC electron spectrum (Chang et al. 2008) is inconsistent, with a statistical significance level of 5% (a reduced χ² value of 1.834 for 11 degrees of freedom (dof)), although it is acceptable with a statistical significance level of 1%. Above the 1 TeV region, the comparison of our result with the electron spectra by H.E.S.S. is consistent, with a reduced χ² value of 1.121 for dof = 7, while H.E.S.S. data have large systematic errors (Aharonian et al. 2008, 2009).

We calculated an electron spectrum using the GALPROP code and a standard file, galdef_50p_599278 (Moskalenko & Strong 2010). As shown in Figure 10, this spectrum is consistent with the electron spectrum observed with the emulsion chambers. We also compared the observed electron energy spectrum with an electron spectrum calculated by Kobayashi et al. (2004), in which parameters are set as follows: diffusion coefficient D₀ = 2.0 × 10²⁹ cm² s⁻¹ at 1 TeV, supernova rate of 1/40 yr⁻¹ in the Galaxy, electron output energy of 1 × 10⁴⁸ erg above 1 GeV, 20 TeV cutoff energy of the electron injection spectrum, and the burst-like release at τ = 5 × 10³ yr after the explosion. The "distant component" in Figure 10 indicates the contributions from continuously distributed distant SNRs with distance larger than 1 kpc or age older than 1 × 10⁵ yr. As shown in Figure 10, our observed spectrum is consistent with the calculated spectra of the distant component + nearby component by Kobayashi et al. (2004), giving strong evidence for a non-zero flux in the TeV region, by the definite identification of electron events one by one. Figure 10 also shows that the electron energy spectrum observed with emulsion chambers has a significantly larger flux in the TeV region than that of the distant component. This suggests that nearby electron sources such as SNRs exist within a distance of 1 kpc and an age of 1 × 10⁵ yr.

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We have carried out cosmic-ray electron observations with balloon-borne emulsion chambers since 1968. The emulsion chamber is an excellent imaging detector with a high position resolution of 1 μm. This imaging capability enables the emulsion chamber to identify electrons with a high rejection power against gamma rays and protons; this proton rejection power of 1 × 10⁵ is the highest among existing cosmic-ray electron detectors. It also permits the determination of electron energies by using only the central part of the electromagnetic shower. This leads to the emulsion chamber being thin, having a lower mass, and a wider field of view compared to other detectors. Hence, emulsion chambers, even comparatively lightweight instruments, successfully observed electrons above several 100 GeV in the late 1960s and electrons above 1 TeV in the 1980s. Further, these electron observations initiated discussions about the investigation of propagation mechanisms in the Galaxy and the identification of nearby cosmic-ray electron sources. Recognized for their significance, high-energy electron observations opened up and have recently been carried out by ATIC, Fermi-LAT, H.E.S.S., PAMELA, and so on. In order to identify nearby cosmic-ray electron sources and search for dark matter signals, there are also some ongoing and new experiments for high-energy electron observations including AMS-02 and CALET on the International Space Station (ISS; Battiston 2008; Torii 2011). AMS-02 is ongoing to observe positrons and negative electrons up to 1 TeV. CALET is being developed to be installed on the ISS, preserving the excellent imaging characteristics of the emulsion chamber.

We sincerely thank the late Professor J. J. Lord and the late Professor T. Taira who started up this experimental program, brought us to many successful balloon observations, and worked on the development of the experiments. We are also grateful to a number of collaborators who have carried out the experiments since 1968. We thank the crews of the Sanriku Balloon Center (SBC) of ISAS/JAXA and the NASA Columbia Scientific Balloon Facility (CSBF) for their excellent and successful balloon flights. We acknowledge the staffs of Institute for Cosmic Ray Research (ICRR), University of Tokyo for their kind support of emulsion experiments. We also appreciate the excellent work and kind support of the staffs in Research Center for Electron Photon Science of Tohoku University and the H4 beam line of CERN-SPS. We are grateful to Y. Sato for his kind support at CERN for the beam tests.

The flux of cosmic-ray electrons is much smaller than that of cosmic-ray protons. The observed flux ratio of electrons to protons is around 1% for 10 GeV and 0.1% for 1 TeV. Therefore, in order to observe high-energy electrons above 1 TeV, the proton rejection power is required to be at least larger than 1 × 10⁴. We estimate the proton rejection power with the emulsion chamber in the following.

B.1. Mean Free Path for Hadronic Interactions

B.2. Energy Shift of Proton-induced Shower

B.3. Shower Starting Point

Electrons produce gamma rays via bremsstrahlung radiation, and then the gamma rays produce e⁻e⁺ pairs. Therefore, the almost electron-induced shower at the starting point in the emulsion chamber is composed of three tracks (one electron + one e⁻e⁺ pair) or five tracks (one electron + two e⁻e⁺ pairs). The mean spreading distance r of a parent electron and an e⁻e⁺ pair by Coulomb scattering is given approximately by

$$\begin{equation} r \simeq \frac{1}{\sqrt{3}}\frac{E_{\rm s}}{E} \left(\frac{x}{X_{0}}\right)^{1/2} L, \end{equation} \tag{ B1 }$$

where x is a traversing thickness of the electron in the material, X₀ is an r.l. of the material, L is a path length of the electron, E is the electron energy, and E_s is the scattering constant of ∼20 MeV. In the case of x = X₀ (i.e., 0.56 cm for lead) and L = 1 cm, the spreading distance r is 2 μm for a primary electron energy of 100 GeV and 0.2 μm for 1 TeV, taking the electron energy E to be half of the incident electron energy because of the energy loss by bremsstrahlung radiation.

Among hadronic interactions of high-energy protons with nuclei, possible candidates to mimic electron events are the following events. The forward produced charged secondary particles are narrowly collimated without heavily ionizing tracks, which are recorded by low-energy recoil protons and nuclei, and the number of charged secondary particles is just 1, 3, or 5, accompanied by one neutral pion. In addition, they have no multistructures in their cascade showers. In fact, there are phenomena such that the momentum transfer to the target nuclei is relatively low and hence the number of secondary particles is relatively small; this is called diffraction dissociation.

In order to study diffractive coherent production in hadronic interactions of protons with nuclei, experiments with nuclear emulsions have been performed for 400 GeV and 800 GeV proton beams by Boos et al. (1978) and Abduzhamilov et al. (1988), respectively. They selected events with the number of secondary charged particles 1, 3, or 5, with being relatively low momentum transfer to the target nuclei, and without heavily ionizing tracks. According to their results, the fractions of these selected events to the total hadronic interaction events are 3% for 400 GeV protons and 2% for 800 GeV protons.

Given that the spreading angle of the forward produced secondary particles is 1 × 10⁻³ rad, the radial distance between the secondary particles is 10 μm with a path length of 1 cm. Since this distance is one order of magnitude larger than the typical distance between a parent electron and an electron–positron pair, proton events with a spreading angle larger than 1 × 10⁻³ rad are readily identifiable from electron events. Adding the condition of a spreading angle less than 1 × 10⁻³ rad, the residual events are less than 4% of the measured diffraction dissociation events, that is the fraction of the selected events to the total hadronic interaction events is less than 3% × 4% = 0.12% for 400 GeV protons and 2% × 4% = 0.08% for 800 GeV protons.

For electron-like events of protons, since there are also further conditions that the selected events should be accompanied by one neutral pion and have no multistructures in the shower developments, the above fraction gives us just the upper limit. Hence, the proton rejection power for the shower starting point is estimated to be larger than 1/0.1% = 1 × 10³.

B.4. Total Proton Rejection Power