CTA報告 171：小口径望遠鏡用
SiPMの光検出効率の入射角度依存性
奥村 曉 1, 2
黒田裕介 1、古田和浩 1、田島宏康 1、他 CTA Consortium
1 名古屋大学 宇宙地球環境研究所（ISEE）
2 名古屋大学 素粒子宇宙起源研究所 （KMI）

2020 年 9 月 15 日 @ 日本物理学会 2020 年秋季大会

oxon@mac.com

1 GeVCWI [84]2.17±0.21

1 GeV
Baksan [85]2.77±0.17

1 GeV
MACRO [86, 87]
2.29 ± 0.15

2 GeV
3 GeV
3 GeV
IMB [88, 89]
Kam [90]
SuperK [91]2.26±0.11
1.94±0.12
1.74±0.07
Galactic CRs ~3 × 1015 eV (3 PeV)
Modiﬁed Cronin+ (1997)

Cosmic-ray Hadron Spectrum
104

PDG 2020

cludes the surrounding
medium in the10This section focuses on neutrinos
1 particle (m belowsec)
10
on of atmospheric
neutrinos in the Tev–ompt component produced by charmed
103].
10
ntained eventsreflect neutrinos in theKneeegion where the product of increasing
1 particle (m year)10
ing flux is maximum. In the GeV reits angular10 distribution depend on thee detector and, to a lesser extent, on the10
aively, we expect‹µ /‹e = 2 from countavors coming from the chain of pion and
10o expectation, however, the numbers ofAncle
re similar rather
than differentby year)
a fac101 particle (kmderstood to be a consequence of neutrino
10ee the article
on neutrino properties in2KneeKnee
410-1-2Flux (m 2 sr s GeV) -1-5-82-1-11-14-17

E 2.6 F(E) [GeV1.6 m-2 s-1 sr -1]

2nd Knee

31010210HAWC
MSU
Tibet
Akeno
CASA-MIA
KascadeKascade Grande
IceTop

Ankle

Ankle

Extra Galactic

HiRes 1HiRes 2
Auger
Telescope Array-20-232-1

11310-269101010131011 1012 10151014 101610Energy (eV)181017 1019101014

101510161017

101810192010E [eV]2010Figure 30.8: The all-particle spectrum as a function of E (energyoperties of atmospheric cosmic rays pro[95–105]
parison of themeasurements of atmo- 20 per-nucleus) from air shower measurements
8-2.7-3.0~10eV(~100MeV)
to>
10eV,
withapower
lawofdN/dE=EtoEtation. These are the “sec ◊ effect” and]. The former refers originally to theWhat is the origin (PeVatron) ofGalacticCRs(<where~3 PeV)?
Supernova
remnants? witergy
E0 > 100TeV,
the low
flux makes measurementsof > 10 GeV muons (and neutrinos) atGalacticcenter? more in the small detectors in balloons and satellites difficult.
e the parent
pions propagate
Greisen [106] gives the following approximate analytic expres
phere where decay is enhanced relative2

A* is linked to this PeVatron. Sagittarius A* went through active
phases in the past, as demonstrated by X-ray outbursts5 and anoutflow from the Galactic Centre6. Although its current rate ofparticle acceleration is not sufficient to provide a substantial
contribution
to Galactic
cosmic rays, Sagittarius A* could have
LETTERRESEARCH
plausibly been more active over the last 106–107 years, and therefore
should be considered as a viable alternative to supernova remnants
as a source of petaelectronvolt Galactic cosmic rays.
30 photon statistics accumulated over the last 10 years ofThe large
observations with the High Energy Stereoscopic System (HESS),
H.E.S.S.improvements(2016) in the methods of data analysis, allow for
together with20
a deep study of the properties of the diffuse very-high-energy (VHE;

160.0

10 a

10–11+00.4

1/r

Galactic latitude (degrees)

6.0 × local cosmic-ray density+00.2

1/r 2+00.0+00.2

23.0+00.0

Sgr A*–00.2

Sgr A*

–00.4

0

20

40

60

80

100

120

Projected distance (pc)

140

160

180

200

7.8–12

10–00.2–00.4 2–00.6b
61.7+00.4

E2 × flux (TeV cm–2 s–1)

+00.6

1.9

Counts per pixel

wCR(≥10 TeV) (10–3 eV cm–3)

Galactic Center Region

spatial distribution of these cosmic rays which, together with the gas
distribution, shape the morphology of the central molecular zone
seen in VHE γ-rays. Figure 2 shows the radial profile of the E ≥ 10 TeV
cosmic-ray energy density wCR up to r ≈ 200 pc (for a Galactic Centre
distance of 8.5 kpc), determined from the γ-ray luminosity and theamount of target gas (see Extended Data Tables 1 and 2). This highenergy density in the central molecular zone is found to be an order ofmagnitude larger
10–10than that of the ‘sea’ of cosmic rays that universally
fills the Galaxy, while the energy density of low energy (GeV) cosmicrays in this region has a level comparable to it8. This requires the presence of one or more accelerators of multi-TeV particles operating in
the central molecular zone.

–0.5
Diffuse emission (×10)
Model (best fit): diffuse emission
Model: diffuse emission E 68%–1.4cut,p = 2.9 PeV
00.0
359.5
90%
Model: diffuse emission E cut,p = 0.6 PeV
Galactic longitude (degrees) 95%
Model: diffuse emission E cut,p = 0.4 PeV

00.0
359.5
359.0
Figure 2 | Spatial01.0
distribution00.5of the cosmic-ray
density versus
Galactic longitude (degrees)
10–13
projected distance from Sgr A*. The vertical and horizontal error bars
molecular gas, as traced by its HESS
CS lineJ1745–290
emission30. Black star, location ofFigure
1 | VHE
γ-ray
image plusof thesystematic
Galactic Centreshow
the 1σstatisticalerrorsregion.
and theThebincolour
size, respectively.
2
scaleFits
indicates
0.02°
× 0.02°a, Theblack lines
outline= 11.8/9),
a 1/r(blue line, Sgrχ2/ A*. Inset (bottom left), simulation of a point-like source. The part ofto thecounts
data ofpera 1/r(redline,pixel.
χ2/d.o.f.
the image shown boxed is magnified in b. b, Zoomed view of the inner
the regions
to calculate
the cosmic-ray(blackenergyline,density
throughout= 61.2/9) cosmicd.o.f. =used73.2/9)
and a homogeneous
χ2/d.o.f.
70 pc and the contour of the region usedof the1 to extract the spectrum 10
the central
molecular
A sectionof 66°alongis excluded
fromannuliray density
radialzone.
profileintegrated
the lineof thesightare shown.∼The
diffuse emission.
(see Methods). White
contour lines indicate the density distribution ofEnergy, E (TeV)
best fit of a 1/rα profile to the data is found for α = 1.10 ± 0.12 (1σ). TheFigure 3 | VHE γ-ray spectra of the diffuse emission and HESS
radial profile
isaffiliations
clearly appear
preferred
the*Lists1/rof participants
and theirat the forend oftheHESS
paper. data.
J1745−290.
The y axis shows fluxes multiplied by a factor E2, where E is the6 ⦿*in units of TeV cm−2 s−1. The vertical and horizontal
If the accelerator injects particles (here we consider protons through- energy on the0 0x axis,
M O N T H 2 0 1 6 | VO L 0 0 0 | NAT U R E | 1error
bars show the 1σ statistical error and the bin size, respectively. Arrows© distribution
2016 Macmillan Publishers
Limited.
reservedout) at a continuous rate, Q! p(E ), the radialof cosmic
raysAll rights
represent 2σ flux upper limits. The 1σ confidence bands of the best-fit
in the central molecular zone, in the case of diffusive propagation, is spectra of the diffuse and HESS J1745−290 are shown in red and blue
Q! (E )described9 as wCR(E , r , t ) = 4πDp (E)r erfc(r/rdiff ), where D(E) and rdiff are shaded areas, respectively. Spectral parameters are given in Methods. The
the diffusion coefficient and radius, respectively. For timescales t red lines show the numerical computations assuming that γ-rays result fromthe decay of neutral pions produced by proton–proton interactions. Thesmaller than the proton–proton interaction time (t pp ≈ fluxes of the diffuse emission spectrum and models are multiplied by 10 to

Massive black hole (4 × 10 M ) at Sgr A (bright radio source)Point source HESS J1745–290 at Str A* and diﬀuse gamma-ray emission

Diﬀuse component has a cutoﬀ energy of 2.9 PeV (68% conf.) → PeVatron?

3Cherenkov Telescope Array (CTA)

cherenkov
telescope
array

Small-Sized Telescope (SST)Dia. : 4 m
Energy : 5–300 TeVNTel : 0 @ North, 70 @ South

Image Credit: G. Pérez, IAC, SMM
4roduction to CTA Science

1.1 Key Characteristics & Capabi

High-energy Frontier by CTA SSTs
20,4(10y5–300 TeV(1ss8HALATPaW

HAW

MAGIC 5−1210CC51yeyearar0h

VEASTIh05R

thro

H.E.S.S. 50 h

ATCMSTLST

10−1htu50h

AT
C Longer Obs.

Differential flux sensitivity

10−2NSo

10−1350hwww.cta-observatory.org/science/cta-performance/ (prod3b-v1)0y(18PassLAT

E2 x Flux Sensitivity (erg cm-2 s-1)

10−11

SST Core Energy Band,(l,b)=,(l,b)=(05)),0))CTA Consortium arXiV:1709.07997

with SiPMs?

1
Energy E (TeV)

10102R5Three SST Designs → SST Harmonization
Compact High-Energy Camera (CHEC)

ASTRI

D=4m40 cm

Credit: Christian Föhr (MPIK)CTA had a design review process to “harmonize” the diﬀerent SST designs (3 cameras and 3telescopes) since May 2018
CHEC and ASTRI designs were finally chosen in June 2019 (to be further improved)
CTA Nagoya group will continue working on electronics, SiPM, software, and optics simulation
6

Crab Observations by an SST Prototype (CHEC–ASTRI)

https://www.cta-observatory.org/chec-achieves-first-light-on-astri/Two observation campaigns were held on Mt. Etna, Italy in 2019 (but with veryearly SiPM product)
Additional test observations canceled due to mirror re-coating and COVID-19
7

Schwarzschild–Couder Configuration with SiPM Camera
Segmented Primary

SiPM Camera

θ ~ 30–60°

Secondary

SiPM Channels (~0.16°)

Aspherical primary/secondary mirrors for wide FOV (< 10°) with good angular resolution
Wider FOV brings fast survey and wider eﬀective area for higher-energy photons
Large angular distribution (30–60°) of angles of incidence on SiPMs8

S14521-8649 (Coated) and S14521-8648 (Uncoated)
S14521-8649 (6 × 6 mm2, 75 µm, 16 ch × 4)

Measured by Hamamatsu (at normal incident)
60
50PDE (%)

40
302010Uncoated
Coated w/ Silicone Resin
sim_telarray (LVR3, 50 µm)

0300

400

500
600
Wavelength (nm)

700

800

Uncoated SiPMs (thin SiO2 and SiN layers only) is preferred for CTA to reduce theoptical crosstalk rate (See Nakamura et al. 2018)
But thin protection layers behave as multilayer coating, thus wavelength- and angulardependent photodetector eﬃciency (PDE) will appear (30–60° for SST)
9

Reflectance (%)

Measurement of Single APD-Cell Reflectance (50 µm, Normal Incidence)
50
45

L1T1 (×20)

4035302520151050300

400

500

600

700

800
Wavelength (nm)Bumpy reflectance was observed, explaining the bumpy PDE
Eight diﬀerent APD cells in the same channel show diﬀerent peak positions→ Can be explained if the SiO2 thickness is not uniform (typ. ±30 nm)
10Reflectance (%)

Measurement of Single APD-Cell Reflectance (50 µm, Normal Incidence)50
L1T1 (×20)

45

L2T1 (×20)

L1T2 (×20)

40

R3B1 (×20)

35

R1B3 (×20)
R2B2 (×20)

R1B2 (×20)

R2B1 (×20)

R1B1 (×20)

30
2520
15
10
50300

400

500

600

700

800
Wavelength (nm)Bumpy reflectance was observed, explaining the bumpy PDE
Eight diﬀerent APD cells in the same channel show diﬀerent peak positions→ Can be explained if the SiO2 thickness is not uniform (typ. ±30 nm)
11΄Ͳͷ͕ࠩ͋Δɻ͔͜͜ΒɺCr ͷ۶ં཰ͷจ‫ݙ‬஋ΛԾʹ৴༻Ͱ͖ͳ͍΋ͷͱͯ͠ɺͦΕΒ͕൓ࣹ཰ͷ‫ى‬෬ʹ

Multilayer Simulation
Reflectance (%)ͲͷΑ͏ʹӨ‫͢ڹ‬Δ͔Λߟ࡯ͨ͠ɻ

40
35

Cr : 1974

Cr : 1998

R1B2 (×20)

302520
1510
50300

400

500

600

700

800
Wavelength (nm)Measured the thickness of the layers and identified the materials (not allowed to make itਤ 12 Cr ͷ۶ં཰ͷจ‫ݙ‬஋͝ͱͷγϛϡϨʔγϣϯpublic)
Multilayer simulation by ROBAST (first talk after break) roughly reproduces the measurement
ਤ 12 ͸ɺCr ͷ۶ં཰ͷจ‫ݙ‬஋ΛมԽͤͨ࣌͞ͷγϛϡϨʔγϣϯͰ͋ΔɻCr ͷจ‫ݙ‬஋ΛมԽͤ͞Δͱɺ
Thickness
non-uniformity is not taken into account͋Δ൓ࣹ཰ͷ‫ۃ‬஋͕਺ % ϙΠϯτมԽ͍ͯ͠Δ৔ॴ͕‫ݟ‬ΒΕΔɻ͜Ε͸ Cr ͱ SiO2 ·ͨ͸ Si3 N4 ͷ۶ં཰ͷ

12PDE Measurement Rel. to Normal Incidence (635 nm)
Relative PDE

635 nm1.3Simulation
measurement #1

Schwarzschild–Couder

1.2

measurement #2
measurement #3

1.1
1±5%

0.9

Multilayer Simulation
0.80.7

・Measured・Measured・Measured

0.6
0.5
0.4

−80

−60

−40

−20020406080
Angle of Incidence (deg)Bumpy PDE vs angle was obtained as expected
Single multilayer simulation only roughly reproduce the measured PDE vs angle
Need to measure how uniform the SiO2 thickness is to reproduce the measurements
LED spectrum (Δλ ~ 15 nm) is convoluted in simulation
13PDE Measurement Rel. to Normal Incidence (635 nm)
Relative PDE

635 nm1.3

Simulation
Simulation+

Schwarzschild–Couder

1.2

Simulationmeasurement #1
measurement #2
measurement #3

1.1
1±5%

0.9

Multilayer Simulation
SiO2 += 100 nm
SiO2 −= 100 nm
・Measured・Measured・Measured

0.8
0.7
0.6
0.5
0.4

−80

−60

−40

−20

020

406080
Angle of Incidence (deg)Bumpy PDE vs angle was obtained as expected
Single multilayer simulation only roughly reproduce the measured PDE vs angle
Need to measure how uniform the SiO2 thickness is to reproduce the measurements
LED spectrum (Δλ ~ 15 nm) is convoluted in simulation
14

PDE Measurement Rel. to Normal Incidence (310 nm)
Relative PDE

310 nm1.3

Simulation
measurement #1

1.2

measurement #2
measurement #3

1.1
1
0.9
0.8
0.7
0.6
0.5
0.4

−80

−60

−40

−20

020

40

60
80
Angle of Incidence (deg)Peaks and valleys are smoothed out because the LED spectrum is wider than
the wavelength dependency
15PDE Measurement Rel. to Normal Incidence (830 nm)
Relative PDE

830 nm1.3

Simulation
measurement #1

1.2

measurement #2measurement #3

1.1
1
0.9
0.8
0.7
0.6
0.5
0.4

−80

−60

−40

−20020406080
Angle of Incidence (deg)16Summary and Plans“The” SST design has been chosen from 3 camera and 3optics designs after the “SST Harmonization” process in CTA
Prototype Schwarzschild–Couder (SC)telescopes for the CTA
Medium- and Small-sized Telescopes constructed (seebackup)
First realization of the SC configuration ever
SiPM PDE has non-negligible angular dependence whenresin coating is removed for CTA
Characterized by both measurement and ROBAST simulation
Angular-dependent PDE will be taken into account in future
CTA simulations and calibration
17