#  First observation of MeV gamma-ray universe with bijective imaging
spectroscopy
using the Electron-Tracking Compton Telescope aboard SMILE-2+

Atsushi Takada  Taito Takemura  Kei Yoshikawa  Graduate School of Science,
Kyoto University
Kitashirakawa Oiwakecho, Sakyo, Kyoto, Kyoto, 606-8502, Japan  Yoshitaka
Mizumura  Institute of Space and Astronautical Science, Japan Aerospace
Exploration Agency
Yoshinodai 3-1-1, Chuou, Sagamihara, Kanagawa, 252-5210, Japan  Tomonori Ikeda
Yuta Nakamura  Ken Onozaka  Graduate School of Science, Kyoto University
Kitashirakawa Oiwakecho, Sakyo, Kyoto, Kyoto, 606-8502, Japan  Mitsuru Abe
Graduate School of Science, Kyoto University
Kitashirakawa Oiwakecho, Sakyo, Kyoto, Kyoto, 606-8502, Japan  Kenji Hamaguchi
Department of Physics, University of Maryland, Baltimore County
1000 Hilltop Circle, Baltimore, MD 21250, USA  Hidetoshi Kubo  Graduate School
of Science, Kyoto University
Kitashirakawa Oiwakecho, Sakyo, Kyoto, Kyoto, 606-8502, Japan  Shunsuke
Kurosawa  Institute of Materials Research, Tohoku University
Katahira 2-1-1, Aoba, Sendai, Miyagi, 980-8577, Japan  Kentaro Miuchi
Graduate School of Science, Kobe University
1-1 Rokkoudai-cho, Nada-ku, Kobe, Hyogo, 657-8501, Japan  Kaname Saito
Graduate School of Science, Kyoto University
Kitashirakawa Oiwakecho, Sakyo, Kyoto, Kyoto, 606-8502, Japan  Tatsuya Sawano
Graduate School of Natural Science and Technology, Kanazawa University
Kakuma, Kanazawa, Ishikawa, 920-1192, Japan  Toru Tanimori  Graduate School of
Science, Kyoto University
Kitashirakawa Oiwakecho, Sakyo, Kyoto, Kyoto, 606-8502, Japan

###### Abstract

MeV gamma-rays provide a unique window for the direct measurement of line
emissions from radioisotopes, but observations have made little significant
progress after COMPTEL/CGRO. To observe celestial objects in this band, we are
developing an electron-tracking Compton camera (ETCC), which realizes both
bijective imaging spectroscopy and efficient background reduction gleaned from
the recoil electron track information. The energy spectrum of the observation
target can then be obtained by a simple ON-OFF method using a correctly
defined point spread function on the celestial sphere. The performance of
celestial object observations was validated on the second balloon SMILE-2+
installed with an ETCC having a gaseous electron tracker with a volume of
30$\times$30$\times$30 cm3. Gamma-rays from the Crab nebula were detected with
a significance of 4.0$\sigma$ in the energy range 0.15–2.1 MeV with a live
time of 5.1 h, as expected before launching. Additionally, the light curve
clarified an enhancement of gamma-ray events generated in the Galactic center
region, indicating that a significant proportion of the final remaining events
are cosmic gamma rays. Independently, the observed intensity and time
variation were consistent with the pre-launch estimates except in the Galactic
center region. The estimates were based on the total background of
extragalactic diffuse, atmospheric, and instrumental gamma-rays after
accounting for the variations in the atmospheric depth and rigidity during the
level flight. The Crab results and light curve strongly support our
understanding of both the detection sensitivity and the background in real
observations. This work promises significant advances in MeV gamma-ray
astronomy.

Gamma-ray astronomy — Gamma-ray telescopes — High altitude balloons

##  1 Introduction

Various radiation process in the universe can be observed in the low-energy
gamma-ray band (0.1–100 MeV). Examples are line emissions from the
radioisotopes produced by nucleosynthesis in supernovae or neutron star
mergers (Matz et al.,, 1988; von Ballmoos,, 1995), the electron–positron
annihilation line in the Galactic center region (GCR) (Prantzos et al.,,
2011), synchrotron emissions and inverse Compton scattering with particle
acceleration in active galactic nuclei or gamma-ray bursts (GRBs) (Urry &
Padovani,, 1995; Briggs et al.,, 1999), pion-decay radiation in the strong
gravity fields around black holes (McConnell et al.,, 1996; Mahadevan et al.,,
1997), and de-excitation lines from nuclei excited by interactions between
cosmic-rays and the interstellar medium (Boggs et al.,, 2000; Strong et al.,,
2000). Population III stars are expected to be detected as long duration GRBs
(Mészáros & Rees,, 2010; Toma et al.,, 2011), because the universe is very
transparent in this energy band. Thermal emissions in the extragalactic
diffuse emission might confirm the existance of primordial black holes (PBHs)
with masses of $10^{16-17}$ g, which emit thermal emission in the MeV band
(Carr et al.,, 2010).

Although celestial MeV gamma-rays have been observed scince the dawn of high-
energy astrophysics, when GRBs were discovered by Vela and extragalactic
diffuse emission was detected by Apollo 15 (Trombka et al.,, 1973),
observations in this band stagnate. COMPTEL aboard CGRO (Schönfelder et al.,,
1993) discovered only $\sim$30 steady gamma-ray sources in the 0.75–30 MeV
band (Schönfelder et al.,, 2000), and SPI loaded on INTEGRAL discovered only
four steady celestial objects at energies above 0.6 MeV (Bouchet et al.,,
2008). The expected signatures of supernova explosions are line gamma-rays
emitted from fresh isotopes, but line gamma-rays of 56Ni/56Co have been
detected only from SN1987A (Matz et al.,, 1988) and SN2014J (Diehl et al.,,
2015; Chrazov et al.,, 2015). Various gamma-ray telescopes are being developed
and some balloon experiments have been performed, but none of the present
developments have surpassed the sensitivity of COMPTEL (Aprile et al.,, 2008;
Bandstra et al.,, 2011; Kamiya,, 2011). The NCT (predecessor of COSI) produced
some observational results using a wide-view Ge Compton Camera loaded on a few
balloon experiments. In 2009, COSI detected Crab at the 4$\sigma$ (Bandstra et
al.,, 2011) significance level. In 2016, they detected the annihilation line
from GCR at the 7$\sigma$ significance level (Kierans et al.,, 2020; Siegert
et al.,, 2020).

MeV observations have been bottlenecked by the huge background and difficulty
of imaging. Unlike visible light or X-rays, MeV gamma-ray wavelengths are is
too short to focus by a mirror or lens. Obtaining their total energy is also
difficult because whereas most incident photons deposit only part of their
energy via Compton scattering, Compton scattering domainates the interactions
between MeV gamma-rays and materials. In addition, observations are obstructed
by huge amounts of background photons produced by hadronic interactions
between cosmic rays and the material surrounding the detector (Weidenspointner
et al.,, 2001). The SPI spectrometer and other detectors based on coded
aperture imaging infer the intensity map of incident gamma-rays from the
pattern of the shadow image. Such detectors need many photons to obtain the
directions of celestial objects. Coded aperture imaging telescopes are usually
equipped with an active veto counter, but heavy anti-coincidence counters
scarcely improve the signal to noise ratio because the gamma rays produced by
cosmic-rays are delayed(Diehl et al.,, 2018). Conventional Compton cameras
such as COMPTEL can slightly suppress the contaminating background photons by
partially restricting the incident direction of each photon. However, this
type of camera measures only one of two angles representing the direction of
incident gamma-rays due to the lack of recoil direction. The signal-to-noise
ratio depends on the volume of the cone-shape response in the Compton data
space (Schönfelder et al.,, 1993), in which the information of recoil
directions degenerates. Therefore, the observations are obstructed by large
contamination of gamma-rays within the area spanned by a radius defined by the
average of the detectable scattering-angle. The detection sensitivity of a
non-bijection telescope based on coded aperture imaging or conventional
Compton imaging is inherently restricted by the principle confusion limit
caused by the overlapped responses of the surrounding sources. In fact,
Schönfelder, (2004) argued that above all abilities, next-generation MeV
gamma-ray telescopes must distinguish and reject the background based on sharp
point spread function (PSF) on the celestial sphere and additional event-
selection parameters. In early 2000, the MEGA group measured the tracks of
recoil electrons with enegies higher than 2 MeV using a Si-tracker and CsI
calorimeters. They reported worse angular resolution measures (ARMs) of
tracked events than untracked events because detecting a few sampling points
of the electron track requires a high recoil energy(Zoglauer et al.,, 2003).
Thus, a tracking detector must finely track electrons, even those with very
low energies ($\sim$10 keV) to obtain a sufficient PSF for MeV gamma-ray
astronomy.

As the next MeV gamma-ray telescope for deep sky surveying, we are developing
an electron-tracking Compton camera (ETCC), which applies a gaseous electron
tracker as the Compton-scattering target and pixel scintillator arrays as the
absorbers (Tanimori et al.,, 2004). The ETCC and conventional Compton camera
differ in their tracking of Compton-recoil electrons. The ETCC obtaines the
momentum of an incident gamma-ray by simply summing the momenta of the
scattered gamma-ray and the recoil electron event-by-event. In this way, it
completely reconstructs the Compton scattering process. Thus, (like other
wavelength telescopes) an ETCC is a bijection telescope, which obtains the
incident direction as the zenith and azimuthal angles and forms a proper PSF
on the celestial sphere. As the proper PSF defines the minimum size that
conserves the intensity of gamma rays, the spectroscopic information at many
points beyond the PSF can be independently obtained from one image. Therefore,
the ETCC can realize imaging spectroscopy in MeV gamma-ray astronomy. The
proper PSF on the celestial sphere enables the determination of the energy
spectrum of the observation target by a simple ON-OFF method (Tanimori et
al.,, 2017). Moreover, from the recoil-electron track, the background can be
rejected using two powerful tools (Tanimori et al.,, 2015): particle
identification based on the energy deposition rate $dE/dx$ in the gaseous
electron tracker, and a Compton-scattering kinematic test based on the angle
between the directions of scattered gamma-ray and recoil electron. These
background rejection tools enables ETCC observations without a heavy veto
counter; consequently, the ETCC has a large field of view (FoV). These unique
abilities of ETCC provide a real imaging spectroscopy to MeV gamma-ray
observations. In future observations with ETCCs loaded on a satellite
(Hamaguchi et al.,, 2019), we are planning balloon experiments, named Sub-
MeV/MeV gamma-ray Imaging Loaded-on-balloon Experiments (SMILE). As the first
step, we launched a small ETCC having an electron tracker with a sensitive
volume of 10$\times$10$\times$15 cm3 in 2006. This launch was intended as a
background study at high altitudes (SMILE-I) and confirmation of the
background rejection power of the ETCC (Takada et al.,, 2011). SMILE-I
successfully detected diffuse cosmic and atmospheric gamma-rays and performed
powerful background rejection based on particle identification. As the second
step, SMILE was tested on imaging-spectroscopy observations of bright
celestial objects. To this end, we set the Crab nebula and GCR as the
observation targets, and constructed a middle-size ETCC a sensitive volume of
30$\times$30$\times$30 cm3. Assuming a background of extragalactic diffuse and
atmospheric gamma rays, the Crab nebula should be detected at the 3–5$\sigma$
significance level. The second balloon SMILE-2+ was launched at Alice Springs,
Australia, on April 7 of 2018.

Herein, we assess the gamma-ray detection abilities of the ETCC from ground
calibrations, details of the SMILE-2+ flight, and the observation results of
the Crab nebula. We additionally discuss the detection sensitivities of next
ETCC observations by comparing the realized detection sensitivity with that
estimated from ground calibrations.

##  2 Instruments

###  2.1 SMILE-2+ ETCC and control system

At middle latitudes in the southern hemisphere, the large zenith angle ($>$45
degrees) reduces the flux of the Crab nebula by one half from that at low
zenith angles; consequently, the air mass is twice that at the zenith. Thus,
Crab nebula is difficult to detect even after several hours of balloon
observations. To detect the Crab nebula at the 3–5$\sigma$ significance level
within during a few hours in the 0.2–2 MeV energy band at 40 km altitude in
the southern hemisphere, the ETCC requires a minimum effective area of $\sim$1
cm2 (0.3 MeV). The required PSF is $\sim$30 degrees for 0.6 MeV detection at
the half power radius (HPR), and the instrumental background must be
suppressed to below the background of the diffuse cosmic and atmospheric
gamma-rays. Figure 1 is a schematic of SMILE-2+ ETCC.

Figure 1:  Schematic of the electron-tracking Compton camera (ETCC). The ETCC
comprises a gaseous electron tracker as the Compton-scattering target and
position-sensitive scintillation cameras that absorb the scattered gamma-rays.

The material of a Compton-scattering target should have a high electron
density to increase the Compton scattering probability and a low atomic-number
to suppress the photoabsorption. For this purpose, the electron tracker of
SMILE-2+ ETCC with a sensitive volume of $30\times 30\times 30$ cm3 is filled
with an argon-based gas (Ar : CF4 : iso C4H10; in pressure ratio = 95 : 3 : 2)
at a pressure of 2 atm. The approximate drift velocity of the electrons in
this gas is 3.7 cm $\mu$s-1. As the ETCC needs three-dimensional (3D) precise
electron tracks for the gamma-ray reconstruction, we adopted a time projection
chamber (TPC) with a micro pixel chamber ($\mu$-PIC) (Ochi et al.,, 2001;
Takada et al.,, 2005) and a gas electron multiplier (Sauli,, 1997; Tamagawa et
al.,, 2006) insulated by 100 $\mu$m liquid crystal polymer. To reduce the
power consumption, we combined two adjacent readout-strips of $\mu$-PIC into
one preamplifier. The readout pitch of the tracker is 800 $\mu$m and the
energy resolution of the tracker through the whole volume is 45.9% for 0.043
MeV (GdK$\alpha$) at full-width half maximum (FWHM).

As the gamma-ray absorber, we selected GSO (Gd2SiO5:Ce) pixel scintillator
arrays (PSAs) each containing $8\times 8$ pixels. The pixel size is $6\times
6$ mm2. The GSO scintillator is 26 and 13 mm thick at the bottom and sides of
the electron tracker, respectively. To efficiently absorb the scattered gamma-
rays, we placed 36 PSAs at the bottom and 18 PSAs at each side of the tracker.
The total number of scintillation pixels was 6912. For the photo readout, we
adopted the 4-channel (ch) charge division method with a resistor network
(Sekiya et al.,, 2006) and multi-anode photomultiplier tubes (Hamamatsu
Photonics, flat-panel H8500). The energy resolutions of the bottom and side
PSAs for 0.662 MeV are 13.4% and 10.9%, respectively, at FWHM. The PSAs are
placed in the TPC vessel, whereas the scintillators of the previous ETCC
(SMILE-I) were placed outside of the vessel. The total number of readouts of
TPC and PSAs are 768 ch for TPC and 432 ch, respectively. SMILE-2+ employs the
same data acquisition system as the middle-size ETCC prototype (Mizumoto et
al.,, 2015), but with the VMe bus replaced by a gigabit Ethernet link for fast
data transference. The top of the TPC vessel is installed with a 5 mm thick
plastic scintillator to reduce the number of triggers by charged particles.

The SMILE-2+ ETCC is set above the control system, as shown in Fig. 2.

Figure 2:  Cross-sectional view (upper) and photograph (lower) of SMILE-2+
system. Upper and lower halves are the ETCC and the control system,
respectively.

The control system includes a central processing unit (CPU) for communication
with the balloon control system, two CPUs with 1 TB solid-state drives for
data acquisition, a trigger control unit described in Mizumoto et al., (2015),
four high-voltage units for the TPC, a power management system with DC/DC
converters, and lithium batteries. SMILE-2+ also has a receiver with a global
positioning system, an atmospheric pressure gauge, two clinometers, and three
geomagnetic aspectmeters (GAs) for measuring the gondola attitude. However, it
lacks a feedback system for attitude control. The accuracy of posture
measurements is less than 5 degrees. The total power consumption is
approximately 250 W. Power is provided by the lithium batteries. The SMILE-2+
system is sealed in a pressured vessel maintained at 1 atm. The side of the
outer vessel is covered by multilayered insulators for temperature
maintenance, and the outer vessel is placed on the small aluminum gondola, as
shown in Fig. 3. The outer vessel is installed with an independent piggyback
sensor (Shoji,, 2019) that measures the attitude with three GAs, three
accelerometers, and a gyroscope. The gondola attitudes determinanted by the
SMILE-2+ sensors and the piggyback sensor were checked for consistency.
Without ballast, the SMILE-2+ gondola weights 511 kg in total.

Figure 3:  Photograph of the SMILE-2+ gondola.

###  2.2 ground calibration

The gaseous electron tracker on the ETCC obtains the 3D tracks and energies of
the Compton-recoil electrons, whereas the absorber detects the absorption
points and energies of the Compton-scattered gamma-rays. The momentum of the
incident gamma-rays is then obtained by summing the momenta of the recoil
electrons and the scattered gamma-rays:

$p_{0}^{\mu}=p_{\gamma}^{\mu}+p_{e}^{\mu},$ (1)

where $p_{0}^{\mu}$, $p_{\gamma}^{\mu}$, and $p_{e}^{\mu}$ are the four-
dimensional momenta of the incident gamma-ray, scattered gamma-ray, and recoil
electron, respectively. Using the measured values, the unit vector of the
incident gamma-ray ${\bf r}$ is described by

${\bf r}=\left(\cos\phi-\frac{\sin\phi}{\tan\alpha}\right){\bf
g}+\frac{\sin\phi}{\sin\alpha}{\bf e},$ (2)

where $\bf g$ and $\bf e$ are unit vectors in the directions of the scattered
gamma-ray and the recoil electron, respectively, in the laboratory system.
$\alpha$ is the angle between the scattering and recoil directions (see Fig.
1), and $\phi$ is the scattering angle given by

$\cos\phi=1-m_{e}c^{2}\left(\frac{1}{E_{\gamma}}-\frac{1}{E_{\gamma}+K_{e}}\right).$
(3)

In Eq. (3), $E_{\gamma}$, $K_{e}$, $m_{e}$, and $c$ denote the energy of the
scattered gamma-rays, kinetic energy of the Compton-recoil electrons, the
electron mass, and light speed, respectively.

The gamma-ray candidate events are reconstructed under the following criteria;

  1. 1.

Single pixel scintillator hits: When a Compton-scattered gamma-ray hits more
than one pixel in the absorber, the incident gamma-ray is difficult to
reconstruct because the sequence of interactions in the absorber become
confused. Therefore we select only the events with a single pixel scintillator
hit.

  2. 2.

Fully-contained electrons: The gamma-ray reconstruction requires the kinetic
energy of a recoil electron. If a recoil electron escapes the sensitive volume
of the TPC, the incident gamma-ray cannot be reconstructed because the recoil
energy measurement is incomplete. We thus set the TPC fiducial volume at
29$\times$29$\times$29 cm3 and require that the track length matches the
expected distance range of electrons depositing their energy in Ar gas
(Tanimori et al.,, 2015). Figure 4 plots the track length of the charged
particles detected in level flight versus the energy deposited in the TPC. The
gradient in this figure represents the energy loss $dE/dx$. The events in the
hatched area of this figure give rise to fully-contained electrons. The head-
tail of the recoil electrons is determined from the skewness of the track
image (Dujmic et al.,, 2008) and the recoil direction determined from the
time-over-threshold information (Tanimori et al.,, 2015). The angular
resolution of the recoil direction and the position resolution of the
scattering points are determined by a traditional method (see Ikeda et al.,
(2021)).

  3. 3.

Compton scattering kinematics: $\alpha$ is defined as

$\cos\alpha_{g}={\bf g}\cdot{\bf e},$ (4)

and can be calculated by Compton-scattering kinematics as follows:

$\cos\alpha_{k}=\left(1-\frac{m_{e}c^{2}}{E_{\gamma}}\right)\sqrt{\frac{K_{e}}{K_{e}+2m_{e}c^{2}}}.$
(5)

Therefore, we can select only Compton scattering events with the condition
described by

$\left|\cos\alpha_{g}-\cos\alpha_{k}\right|\leq\Delta_{\alpha},$ (6)

where $\Delta_{\alpha}$ is a cut parameter. For SMILE-2+ ETCC, we set
$\Delta_{\alpha}=0.5$.

Figure 4:  Track length of charged particles as a function of deposited energy
in SMILE-2+ TPC. We selected only the fully-contained electron events inside
the hatched green area.

The response function of parallel light, which is required for deconvoluting
the gamma-ray fluxes from celestial objects, was obtained in a simulator of
SMILE-2+ ETCC based on Geant4 (ver 10.04-patch02; Agostinelli et al.,, 2003).
Electromagnetic interactions were calculated in G4EmLivermorePhysics while
considering the Doppler broadening effect of Compton scattering. To confirm
the reliability of the SMILE-2+ ETCC simulator, we measured the effective
area, PSF, and energy resolution under irradiation by line gamma-rays from the
checking sources placed approximately 2 m from the center of SMILE-2+ ETCC.
The measured performances were compared with the simulated expectations.
Figure 5 plots the effective areas as functions of incident energy when the
checking sources were placed along on the center axis of the ETCC or when
parallel light was irradiated at a zenith angle of 0 degrees. The expected and
measured effective areas were consistent. In the energy-selected results, the
realized effective area was 1.1 cm2 at 0.356 MeV, which satisfies the
criterion for detecting the Crab nebula. The difference between all
reconstructed events and the energy-selected events (twice the FWHM of the
full-energy peak) increased at the higher energies. This difference is caused
by the scattered component, namely, the scattered gamma-rays in the
surrounding materials (e.g., the pressured vessel, TPC vessel, and PSA support
structures) before the radiation enters the ETCC. As the major interaction
between incoming rays and materials is Compton scattering, observations are
considered to be confused not only by PSF blurring of the surrounding sources
(the expected contamination) but also by components scattered from the
structures. Therefore, an accurate response function is critical for obtaining
the true fluxes of celestial objects.

Figure 5:  Effective areas as functions of incident energy. Filled and open
triangles represent the effective areas of all reconstructed events obtained
in the experiments and simulation, respectively. Filled circles and open
squares represent the experimental and simulated effective areas after
selection within the FWHM of the energy peak, respectively. Dashed and solid
lines plot the effective areas of all events and energy-selected events in the
parallel light case, respectively.

The zenith angle dependence of the effective area at 0.662 MeV is shown in
Fig. 6. As mentioned above, SMILE-2+ ETCC has a large FoV (3.1 sr). This FoV
is defined as the field covering more than half the effective area at the
zenith. In the ETCC simulator, the accuracy of the effective area was better
than 10% over the energy range 0.15–2.1 MeV within the FoV.

Figure 6:  Zenith angle dependence of the effective area at an incident energy
of 0.662 MeV. Symbols are described in the caption of Fig. 5.

Figure 7 plots the Half-power radius (HPR) of PSF as a function of incident
energy. The PSF size of SMILE-2+ ETCC is 30 degrees at the HPR for 0.662 MeV.
Furthermore, the angular resolution measure (ARM) and scatter plane deviation
(SPD) at the FWHM for 0.662 MeV, which define the accuracies of the scattering
angle and the scattering plane, respectively, are 10.5 and 148 degrees for
0.662 MeV at FWHM. The PSF of the ETCC depends on the energy resolution of the
PSAs, the position accuracy of the Compton-scattering point, and the angular
resolution of the direction of the Compton-recoil electrons. Although SMILE-2+
ETCC has poorer spatial resolution than the advanced telescopes that observe
other wavelengths, it satisfies the criteria for detecting the Crab nebula
with powerful background rejection capability.

Figure 7:  Half power radius (HPR) of the PSF as a function of incident
energy. The filled circles, open squares, and solid line represent the
measured HPR using the checking sources, the simulated HPR with a near point
source, and the simulated HPR for parallel light, respectively.

Figure 8 shows the energy resolutions of SMILE-2+ ETCC, TPC and PSA. The
fully-contained electron events are limited to recoil energies lower than 0.3
MeV because the TPC gas lacks any stopping power. Therefore the energy of the
scattered gamma-ray exceeds that of the recoil electron and the energy
resolution of the ETCC is dominated by that of PSAs.

Figure 8:  Energy resolutions of the ETCC, TPC, and PSAs as functions of
energy. The filled circles and solid line represent the energy resolutions of
the SMILE-2+ ETCC obtained via ground calibration and simulation,
respectively. The filled and open squares are the averaged energy resolutions
of the TPC and PSAs, respectively, measured via ground calibration. The dotted
and dashed lines represent the simulated energy resolutions of TPC and PSA,
respectively.

##  3 SMILE-2+ Balloon flight

The SMILE-2+ balloon was launched by ISAS/JAXA from the Australian balloon
launch station, Alice Springs, Australia, on April 7 of 2018. Three hours
before launching at 06:24 Australian Central Standard Time (ACST), the
SMILE-2+ system was switched on the data acquisition was running even during
the ascent. The time variations of the altitude and atmospheric pressure are
shown in the upper and lower panels of Fig. 9, respectively.

Figure 9:  Time variations of the altitude of SMILE-2+ gondola (upper panel)
and atmospheric pressure (lower panel). During the ’ON’ period, Crab nebula
was included in the FoV and was observed. ’OFF’ and ’(OFF)’ denote the period
of the background modeling when the atmospheric depth was the same and thinner
than that of during the ON periods, respectively. During those periods, the
Crab nebula was excluded from FoV of SMILE-2+.

At 08:44 ACST, the balloon reached an altitude of 39.6 km. SMILE-2+ performed
observations until 10:45 ACST on April 8 of 2018, and was switched off at
10:53 ACST. At 06:30 ACST on April 8 of 2018, the balloon slightly ascended
owing to sunrise. The duration of the level flight, in which the atmospheric
depth was maintained between 2.4–3.8 hPa (altitude 37.8–40.4 km), was
approximately 26 h. On April 9 of 2018, we approached and successfully
recovered the SMILE-2+ gondola, which had landed approximately 190 km from
Alice Springs.

Figure 10 shows the flight path of the SMILE-2+ balloon from the launch time
until turn-off of the SMILE-2+ system.

Figure 10:  Flight path of SMILE-2+. Open circle represents the position of
the Australian balloon launch station, and the contours outline the cutoff
rigidity calculated by PARMA (Sato et al.,, 2008).

The cutoff rigidity (marked by the contours in Fig. 10) were calculated by
PARMA (Sato et al.,, 2008) based on MAGNETOCOSMICS (Desorgher et al.,, 2005).
The time-averaged cutoff rigidity was 8.2$\pm$0.4 GV during the level flight,
and the $K_{p}$ index, which indicades an indicator of the disturbances in the
Earth’s magnetic field, was below 2111https://www.gfz-potsdam.de/en/kp-index.
The low $K_{p}$ index confirmed a stable and quiescent magnetic field
condition, under which the intensities of cosmic rays should cause negligible
fluctuations in the SMILE-2+ observation. In contrast, the intensity of
atmospheric gamma-rays is proportional to $zR_{\mathrm{cut}}^{-1.13}$
(Schönfelder et al.,, 1977; Thompson et al.,, 1981), where $z$ and
$R_{\mathrm{cut}}$ are the atmospheric depth and the cutoff rigidity,
respectively. Between 13:32 and 23:00 ACST on April 7 of 2018 (see Fig. 9),
the balloon altitude decreased with a concomitant 20% increase in atmospheric
depth. The intensity of atmospheric gamma-ray was expected to rise at this
time.

Figure 11:  Time variations of a) elevation angles and b) air mass during the
SMILE-2+ experiment. Red, blue, and black represent the Galactic center, the
Crab nebula, and the Sun, respectively. c) Count rates of PSAs (blue), TPC
(magenta), and ETCC (red) as functions of time; d) live time of the data
acquisition; e) light curve obtained after gamma-ray reconstruction and live-
time correction. This light curve is the total event rate of the final
remaining gamma-rays in all direction. The hatched area in b), c), d), and e)
represents the balloon ascending period.

The time variations of the elevation angles and air masses of the observation
targets are shown in panels a) and b) of Fig. 11, respectively. Panel c) of
this figure shows the count rates of PSAs, TPC, and ETCC. The live times of
SMILE-2+ observing the Crab nebula and the Galactic center were 5.1 h and 10.2
h, respectively. The data acquisition rate (red plots in Fig. 11) was 40
events s-1 on the ground, 700 events s-1 near the Pfotzer maximum (live time
45%), and approximately 450 events s-1 at 39.6 km altitude. After 06:45 ACST
on April 8 of 2018, the count rate of the TPC was raised by small discharges
occuring in the TPC. However, as these discharge events can be clearly
discriminated from the charged particle tracks in the track images, they do
not disturb the gamma-ray observations. During level flight, the live time of
the data-acquisition was maintained above 82% (Fig. 11 d)), sufficient for
observing the Crab nebula and Galactic center. Figure 12 represents the
exposure map with the definition of the observation area by the zenith angle
below 60 degrees.

Figure 12:  Exposure map of 0.3 MeV at zenith angles less than 60 degrees (in
the galactic coordinates). The solid line represents the tracked light axis of
SMILE-2+ ETCC and the open square indicates the Crab nebula.

##  4 Analysis

###  4.1 gamma-ray reconstruction

SMILE-2+ ETCC recorded $4.9\times 10^{7}$ events after turn-on. Typical tracks
detected during level flight are shown in Fig. 13. Single-electron events were
selected for the gamma-ray reconstruction as described in Section 2.2. The
measured track images clearly showed the occurrences in SMILE-2+ ETCC from
which select single-electron events were selected. Thus, the track image
itself provides a simple and powerful means of noise suppression.

Figure 13:  Typical tracks obtained by SMILE-2+ in the level flight. (top-
left: single-electron event, top-right: pair-production event, bottom-left:
cosmic-ray event, bottom-right: shower event) The hatched area represents the
active volume of the TPC, and the upper and lower sides of each image
represent the zenith and nadir directions, respectively.

At balloon altitudes, cosmic-rays interact with the structural materials to
produce positrons or gamma-rays. Because the ETCC is triggered by coincident
PSAs and TPC, many cosmic-ray induced events including the electron-positron
annihilation line absorbed in PSA were recorded. Using the cosmic-ray or
shower events in the flight data, we corrected the gain of the scintillators
by the annihilation line every 30 min and the TPC gain by the energy
deposition rate of the minimum ionizing particles every 10 min. Figure 14
shows the energy spectrum of each event selection during level flight, and the
spectrum obtained by selecting all events, when $2.4\times 10^{5}$ events
remained. After selecting the fully-contained electrons, the spectrum showed a
clear excess at 0.511 MeV.

Figure 14:  Total energy spectrum of each event selection during level flight
(see Section 2.2 for details). The black and magenta spectra were taken after
selecting single pixel scintillator hits and fully-contained electrons,
respectively, and the red spectrum was obtained by Compton scattering
kinematics.

Figure 11 e) shows the light curve obtained by the gamma-ray reconstruction in
all directions with the live-time correction. The gamma-ray event rate in all
directions was 2.7 events s-1 and remained stable during level flight. When
the air mass of the Galactic center is less than 4 g cm-2, the light curve
rises with increasing elevation angle of the Galactic center. The excess at
the culmination time of the Galactic center is 0.5 events s-1, so the
estimated intensity of the GCR is $\sim$0.15 photons s-1 cm-2 sr-1 MeV-1 with
an effective area of 1.1 cm2 and FoV of 3.1 sr. The intensity result is
roughly consistent with the intensity measured SPI/INTEGRAL (Bouchet et al.,,
2011).

Figure 15 shows the light curve at zenith angles below 60∘ in the 0.15–2.1 MeV
energy band. Plotted are the expected event rate at which SMILE-2+ detects the
extragalactic diffuse and atmospheric gamma-rays (blue curve) and the expected
instrumental background event rate induced by protons, neutrons, electrons and
positrons (magenta line), which was calculated by PARMA (Sato et al.,, 2008)
and Geant4. The intensity of atmospheric gamma-rays depends on the atmospheric
depth, cutoff rigidity $R$, and solar modulation. Here, we adopted the
semiempirical model by Ling, (1975) to the atmospheric depth dependence of
extragalactic diffuse and atmospheric gamma-rays. We additionally assumed that
the intensity of atmospheric gamma-rays is proportional to $1.2R^{-1.13}$, as
detailed in Section 5. The red line in Figure 15 plots the total event rate of
SMILE-2+ estimated independently of the observation results. Over most of the
level flight period, the observed rate 0.15–2.1 MeV events at a zenith angle
of 60∘ is explained by the sum of extragalactic gamma-rays, atmospheric gamma-
rays, and the instrumental background. The differential between the obtained
and estimated event rates (lower panel of Figure 15) shows a significant
excess around the culmination time of the Galactic center. The detector count
rates of SMILE-2+ clearly reveal an enhanced gamma-ray emission from the GCR.

Figure 15:  Light curve in the 0.15–2.1 MeV energy band at zenith angles below
60∘ during level flight. The vertical dotted line is the culmination time of
the Galactic center. The blue curve describes the expected event rate when
SMILE-2+ detected extragalactic diffuse and atmospheric gamma-rays. The
magenta curve is the simulated background event rate induced by protons,
neutrons, electrons and positrons. The red line describes the total estimated
event rate of SMILE-2+. The lower panel shows the difference between the
observed and expected event rates. Within the hatched area, the air mass of
Galactic center was less than 4 g cm-2.

In contrast, no clear excess appeared in Fig. 11 e) when the Crab nebula was
observed. This absence is explained by the low flux of the Crab nebula (only
$\sim$3% of the photon number of extragalactic diffuse gamma-rays in the FoV
of the ETCC in the energy range 0.2–2.1 MeV). During the ON-region of Crab
nebula observation, we considered that the Crab nebula ($l$ = 184.6∘, $b$ =
-5.8∘) was centered in a circle of radius 40 degrees, which defines the HPR of
the PSF at 0.3 MeV. The spectrum obtained in the ON-region is the red spectrum
in Fig. 16.

Figure 16:  Observed energy spectrum of the ON-region (red), estimated
background (hatched area, see text), and the subtraction (magenta).

###  4.2 background estimation

In celestial gamma-ray observations at balloon altitudes, the gamma-ray
background comprises extragalactic diffuse gamma-rays, atmospheric gamma-rays,
and instrumental gamma-rays. Although extragalactic diffuse gamma-rays are
isotropic at the top of the atmosphere, they are scattered and attenuated in
the atmosphere at balloon altitudes. The intensities of atmospheric gamma-rays
and the instrumental gamma-rays depend on the atmospheric depth, zenith angle,
and intensity of cosmic-rays. Unfortunately, the atmospheric depth increased
by 20% during observations of the Crab nebula. We thus defined an OFF-period
of 20:30–22:50 ACST on April 7 of 2018, when the balloon altitude decreased
over the Crab observation period (Fig. 9) and no bright celestial objects
appeared inside the FoV. Figure 17 maps the event intensity
$B(E^{\prime},\theta^{\prime})$ on the detected energy $E^{\prime}$ versus
zenith angle $\theta^{\prime}$ plane during the OFF period. This event
intensity map was assumed as the sky image of background gamma-rays in
horizontal coordinates.

Figure 17:  Event intensity map $B(E^{\prime},\theta^{\prime})$ in the
detected energy $E^{\prime}$ versus zenith angle$\theta$ during the OFF-
period.

Because the zenith angle of the ON-region avaried over time, we calculated the
average background energy spectrum $g(E^{\prime})$ over the Crab observation
period;

$g(E^{\prime})=\frac{1}{T_{\text{obs}}}\int_{\text{ON-
region}}B(E^{\prime},\theta^{\prime}(t))d\Omega dt,$ (7)

where $T_{\mathrm{obs}}$ is the live time of the Crab observation period
(hatched spectrum in Fig. 16). After subtracting the estimated background
$g(E^{\prime})$ from the ON-region events, we obtained $f(E^{\prime})$, the
energy spectrum of gamma-rays from the Crab nebula. The magenta spectrum in
Fig. 16 displays $f(E^{\prime})$ as a function of $E^{\prime}$. The convolved
significance is 4.0$\sigma$. Applying the same method to the observed data
from 08:44 ACST on April 7 of 2018 to 06:30 ACST on the following day, we
calculated the significance map shown in Fig. 18. Because the balloon altitude
varied in time, we defined $g(E^{\prime})$ in two time period: from 10:30 to
13:30 ACST on April 7 of 2018, when the atmospheric depth was less than 3.1 g
cm-2, and from 20:30 to 22:50 ACST on April 7 of 2018, when the atmospheric
depth exceeded 3.1 g cm-2. In addition to the light curve, SMILE-2+
significantly detected the GCR. A detailed study of the GCR will be described
elsewhere.

Figure 18:  Significance survey map in galactic coordinates. The open square
represents the Crab nebula.

###  4.3 calculation of flux

The background-subtracted spectrum in Fig. 16 includes the detector response
and attenuation by the atmosphere,

$f(E^{\prime})=\frac{1}{T_{\text{obs}}}\int
f_{c}(E)A(E,\theta,E^{\prime},\theta^{\prime})\exp\left(-\frac{z\tau_{\text{tot}}}{\cos\theta}\right)dEdt,$
(8)

where $E$ and $\theta$ are the true energy and true zenith angle of the
incident photons, respectively, $A$ is the response matrix of the ETCC, and
$z$, $\tau_{\mathrm{tot}}$, and $f_{c}$ denote the atmospheric depth, cross
section of total attenuation in the atmosphere, and photon flux of the
celestial object, respectively. $A(E,\theta,E^{\prime},\theta^{\prime})$ can
be estimated using the ETCC simulator described in Section 2.2. Because
$\theta$, $\theta^{\prime}$, and $z$ are temporally variable in balloon
observations, we calculated the time-averaged response matrix as follows:

$\bar{R}_{ij}=\frac{1}{T_{\text{obs}}}\int
A(E_{i},\theta,E^{\prime}_{j},\theta^{\prime})\exp\left(-\frac{z\tau_{\text{tot}}}{\cos\theta}\right)dt,$
(9)

where $i$ and $j$ are integers denoting specific energy bins. The resultant
spectrum is then described as

$f(E^{\prime}_{j})=\sum_{i}\bar{R}_{ij}f_{c}(E_{i}),$ (10)

where $f_{c}$ can be obtained thorough deconvolution. Assuming that $f_{c}$
follows a single power-law, the deconvolved photon flux was detemined as
$(1.82\pm 1.40)\times 10^{-2}\left(E/\text{MeV}\right)^{-2.19\pm 0.82}$
photons s-1 cm-2 MeV-1. This flux spectrum is shown in Fig. 19 together with
its 1$\sigma$ error band. The Swift/BAT transient monitor (Krimm et al.,,
2013) revealed no significant flares during the observation
time222https://swift.gsfc.nasa.gov/results/transients/index.html. Therefore,
as a consistency check, we can compare our result with other observations of
the Crab nebula. Our result is indeed consistent with previous observations of
the Crab nebula.

Figure 19:  Photon flux spectrum of the Crab nebula. Solid line and hatched
area are the best-fit and statistical error region (1$\sigma$), respectively,
obtained by SMILE-2+.

To investigate any time-dependence of the OFF-period, we calculated the photon
fluxes during two additional background periods. 10:30–13:30 ACST on April 7
of 2018 and the Crab observation period. During the first of these period, the
atmospheric depth was 3.01 g cm-2, 13% thinner than during the Crab
observation period (14:30–19:30 ACST on April 7 of 2018). Therefore, the
intensity of atmospheric gamma-rays should decrease and the resulting gamma-
ray flux of the Crab nebula based on this background period should be
overestimated. The selection of the Crab observation period is justified
because the Crab nebular’s flux is negligibly smaller than the intensity of
extragalactic diffuse and atmospheric gamma-rays within ETCC’s FoV. The single
power-law spectra within these additional two background periods were
calculated as described for the original background period. The obtained
parameters are listed in Table 1. As the parameters were quite simillar in
each case, the obtained photon flux little depended on the selection of the
OFF-period.

Table 1: Photon flux parameters obtained in different background periods BG timeaatime on April 7, 2018 in ACST | 20:30–22:50 | 10:30–13:30 | 14:30–19:30
---|---|---|---
normalizationbbunit in $10^{-2}$ photons s-1 cm-2 MeV-1 | $1.82\pm 1.40$ | $2.08\pm 1.38$ | $1.55\pm 1.37$
photon index | $2.19\pm 0.82$ | $2.28\pm 0.81$ | $2.05\pm 0.80$
significance | 4.0$\sigma$ | 6.6$\sigma$ | 2.9$\sigma$

##  5 Discussion

In general, the detection sensitivity $S(E)$ in some energy band is defined by
the detectable flux with a significance of 3$\sigma$, an observation time of
106 s, and an energy window of $\Delta E=E$. The background rate and the
detection sensitivity of SMILE-2+ are respectively estimated by Eq. (7) and by

$S(E)=\frac{3\sqrt{T_{\text{obs}}\int
B(E^{\prime},\theta^{\prime})dE^{\prime}d\Omega^{\prime}}}{T_{\text{obs}}\int
A(E,0^{\circ},E^{\prime},\theta^{\prime})dE^{\prime}d\Omega^{\prime}},$ (11)

in the zenith direction ($\theta$ = 0∘). When $d\Omega$ is defined by the HPR
(see in Fig. 7), the detection sensitivity of SMILE-2+ is the blue long-dashed
line in Fig. 20. The realized sensitivity, at which the Crab nebula was
detected within a few hours, was approximately ten times better than that of
SMILE-I.

Figure 20:  3 $\sigma$ detection sensitivity of SMILE-2+ for the continuum
spectrum at an observation time of $10^{6}$ s within an energy window of
$\Delta E=E$. The blue long-dashed line represents the realized sensitivity of
SMILE-2+ based on the actual background event intensity. The red solid line
plots the sensitivity of SMILE-2+ against the background photons comprising
extragalactic diffuse gamma-rays, atmospheric gamma-rays, and the instrumental
background. The blue hatched area represents the estimated detection
sensitivity of next observation (SMILE-3). The uncertainty in the SMILE-3
sensitivity depends on the cutoff rigidity, balloon altitude, and solar
modulation. The black lines represent the results of previous studies (Attwood
et al.,, 2009; Takahashi et al.,, 2013; Takada et al.,, 2011).

The background events comprise extragalactic diffuse gamma-rays, atmospheric
gamma-rays, instrumental gamma-rays, and other particles (such as neutrons).
Radioactivation is negligible because the duration time is too short in
balloon observation. Therefore the background event intensity
$B(E^{\prime},\theta^{\prime})$ will be described as

$B(E^{\prime},\theta^{\prime})=\int(I_{c}+I_{a})A(E,\theta,E^{\prime},\theta^{\prime})dEd\Omega+B_{\text{instr}},$
(12)

where $I_{c}$ and $I_{a}$ are intensities of extragalactic diffuse and
atmospheric gamma-rays, respectively, and
$B_{\mathrm{instr}}(E^{\prime},\theta^{\prime})$ is the event intensity of the
instrumental background. The intensity of extragalactic diffuse gamma-rays
depends on the zenith angle and changes with atmospheric attenuation and
scattering at balloon altitudes (Makino,, 1970; Horstman & Horstman-Moretti,,
1971; Schönfelder et al.,, 1977; Takada et al.,, 2011). In contrast, it is
uniform at the top of the atmosphere. Atmospheric gamma-rays, produced when
cosmic-rays interact with the atmosphere, depend on the atmospheric depth,
cutoff rigidity, and solar modulation. Among several models for atmospheric
gamma-rays is PARMA (Sato et al.,, 2008), an analytical model based on PHITS
simulations (Iwase et al.,, 2002). PARMA models the intensity of atmospheric
gamma-rays with respect to energy, zenith angle, atmospheric depth, solar
modulation, and cutoff rigidity, but does not consider the primary cosmic
electrons/positrons as the initial particles. Ling, (1975) and Ling et al.,
(1977) included extragalactic diffuse gamma-ray in a semiempirical model based
on balloon observations. Their model considers the gamma-ray energy, zenith
angle and atmospheric depth, but not consider the effect of cutoff rigidity
and solar modulation on gamma-ray intensity. Nevertheless, this model is often
cited in observational studies.

As the intensity model of extragalactic diffuse and atmospheric gamma-rays, we
adopted the Ling, (1975) and Ling et al., (1977) model and scaled by the
dependences of cutoff rigidity and solar modulation. To correct the cutoff
rigidity, we scaled the atmospheric component in the models by $(4.5\
\text{GV}/8.4\ \text{GV})^{1.13}$. Meanwhile, the balloons referred by Ling’s
models were launched around the solar maximum, whereas SMILE-2+ was launched
near the solar minimum. As the atmospheric gamma-ray intensity is around
1.2–2.0 times larger at the solar minimum than at the solar maximum (Morris,,
1984; Sazonov et al.,, 2007), we scaled the intensity of atmospheric gamma-
rays by a factor of1.2. Assuming the gamma-ray intensity at an atmospheric
depth of 3.0 g cm-2, we expected the SMILE-2+ ETCC spectrum represented by the
filled triangles in Fig. 21. To evaluate the instrumental background
$B_{\mathrm{intsr}}(E^{\prime},\theta^{\prime})$, we simulated the
reconstructed events of the ETCC simulator using the PARMA-calculated
intensities of the initial particles (protons, neutrons, electrons, and
positrons). The filled circles in Fig. 21 describe the estimated energy
spectrum of the instrumental background at the same altitude. The amount of
instrumental background was one-half that of the essential background composed
of extragalactic diffuse and atmospheric gamma-rays. Thus the instrumental
background negligibly affected the detection sensitivity of SMILE-2+. The
expected total background spectrum (indicated by the hatched area in Fig. 21)
approximately matched with the observed energy spectrum (described by the open
squares in Fig. 21). Against this estimated total background, we can obtain
the detection sensitivity independently of the sensitivities mentioned above.
The estimated detection sensitivity of SMILE-2+ (red solid line in Fig. 20)
was also consistent with the realized sensitivity.

Figure 21:  Energy spectra obtained within the zenith angle of 60 degrees at
an atmospheric depth of 3.0 g cm-2. Open squares plot the events detected
during 10:30–13:30 ACST on April 7 (ACST) of 2018. The filled circles, filled
triangles and hatched areas represent the estimated instrumental background,
summation of the extragalactic diffuse and atmospheric gamma-ray components
based on the Ling model (Ling,, 1975; Ling et al.,, 1977), and the total
estimated spectrum, respectively.

As confirmed in these results, the background spectrum and the detection
sensitivity of observations by an ETCC in space are well embodied in the
results of the ground calibrations. In contrast, the obtained sensitivities of
COMPTEL and most of the other conventional Compton cameras are several times
worse than the expected sensitivities (Schönfelder,, 2004; Bandstra et al.,,
2011). The above estimationis strongly and independently supported by the
enhanced light curve at the culmination time of the Galactic center. If the
instrumental background was several times more intense than the extragalactic
gamma-rays, such as COMPTEL, this enhancement could not be observed. The
instrumental background of ETCC observations is mainly contributed by gamma-
rays generated by interactions between cosmic rays and the instrumental
material. Other disturbances are diminished or removed by powerful background-
rejection tools such as particle identification, track image, and a Compton
kinematics test. The upward instrumental gamma-rays are intense because of the
instrumental material is below the ETCC. However, because the ETCC can
pinpoint the direction of an incident gamma-ray to a point in each event.
SMILE-2+ can suppress the instrumental background within the FoV to the
expected contamination level the PSF. Under this noise condition, the
detection sensitivity of the next observation (SMILE-3) can be estimated both
easily and realiably. After constructing a new TPC of volume $30\times
30\times 30$ cm3 filled with CF4 gas at a 3 atm pressure and optimizing the
structural design, the effective area of ETCC will be approximately 10 cm2 for
0.4 MeV and 1 cm2 for 2.5 MeV. To improve the PSF, we are developing an
analysis method based on machine learning. In the first trial, deep learning
of the recoil direction and scattering point improved the PSF to double that
of the present paper (Ikeda et al.,, 2021). If the direction accuracy of
Compton-recoil electrons could be improved to the limiting accuracy of
multiple scattering, the PSF of the ETCC will improve to 10 degrees and 2
degrees at HPR for 0.4 MeV and 2.5 MeV, respectively. The sensitivity of an
ETCC loaded on a long-duration balloon (SMILE-3)should exceed that of COMPTEL
by several times (indicated by the blue hatched area in Fig. 20). Recently, a
super-pressure balloon has been launched for over one month at middle
latitudes in the southern hemisphere (Kierans et al.,, 2017).
colorblueTherefore, if we can launch an updated ETCC on a long-duration
balloon in the SMILE-3 mission, we could significantly surpass the COMPTEL
observations because the large FoV of the ETCC enables observation times of
$\sim$106 s.

##  6 Summary

To advance MeV gamma-ray astronomy, we are developing an ETCC with imaging
spectroscopy ability. The ETCC is based on bijection imaging and utilizes
powerful background rejection tools (particle identification, Compton-
scattering kinematics test, and charged-particle track imaging). A proper PSF
is performed on the celestial sphere, enabling acquisition of the energy
spectrum of the observation target by simple ON-OFF method. In 2018, we
launched the second balloon (SMILE-2+) to confirm ETCC observations of
celestial objects. The effective area of the ETCC loaded on SMILE-2+ is 1.1
cm2 for 0.356 MeV, the PSF is 30 degrees at HPR for 0.662 MeV, and the FoV is
3.1 sr when a 30$\times$30$\times$30 cm3 TPC is filled with argon gas at 2 atm
pressure. The observed flux and energy spectrum during the level fight,
estimated independently of the experimental results, were well explained by a
background of extragalactic diffuse, atmospheric, and instrumental gamma-rays.
With this good understanding of the sensitivity and background, we achieved
the pre-launch expectations (a significance level of 4.0$\sigma$) of SMILE-2+
observations of gamma-rays from the Crab nebula. The obtained flux was also
consistent with other flux observations. In addition, the light curve and the
significance survey map show that the GCR is very bright with a significance
of $\sim$10$\sigma$ in the 0.2–2.1 MeV energy range. Thus, SMILE-2+ is the
first application of imaging spectroscopy based on a proper PSF and bijection
imaging to MeV gamma-ray astronomy. The observed energy spectrum during level
flight was explained by the background noise, which contains extragalactic
diffuse, atmospheric, and instrumental gamma-rays. The achieved detection
sensitivity of SMILE-2+ matched the sensitivity estimated from ground
calibrations, whereas the sensitivities of most conventional Compton cameras
are several times worse than their expected values. The instrumental gamma-
rays little affected the detection sensitivity of SMILE-2+, because they
constituted only one-third of the background. For this reason, the ETCC
overcomes the large background problem. When designing a Compton camera, the
sensitivity must be estimated with a PSF (not an ARM), similarly to telescopes
operating in the X-ray or GeV bands. In the near future, the ETCC will be
updated to an approximate effective area of 10 cm2 and a PSF of several
degrees at the HPR, and we will then launch a long-duration balloon flight
(SMILE-3) for scientific observations. The ETCC can become a unique pioneer
with deeper survey ability than COMPTEL in MeV gamma-ray astronomy.

The balloon-borne experiment was conducted by Scientific Ballooning (DAIKIKYU)
Research and Operation Group, ISAS, JAXA. This study was supported by the
Japan Society for the Promotion of Science (JSPS) Grant-in-Aid for Scientific
Research (S) (21224005), (A) (20244026, 16H02185), Grant-in-Aid for Young
Scientists(B) (15K17608), JSPS Grant-in-Aid for Challenging Exploratory
Research (23654067, 25610042, 16K13785, 20K20428), a Grant-in-Aid from the
Global COE program “Next Generation Physics, Spun from Universality and
Emergence” from the Ministry of Education, Culture, Sports, Science and
Technology (MEXT) of Japan, and Grant-in-Aid for JSPS Fellows (16J08498,
18J20107, 19J11323). Some of the electronics development was supported by KEK-
DTP and Open-It Consortium. And we thank Enago (www.enago.jp) for the English
language review.

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