As onomy
&
As ophysics
A&A, 680, A66 (2023)
h ps://doi.o g/10.1051/0004-6361/202346927
© The Au ho s 2023
Pe o mance o he join LST-1 and MAGIC obse a ions
e alua ed wi h C ab Nebula da a
H. Abe1, K. Abe2, S. Abe1, V. A. Accia i3, A. Aguasca-Cabo 4, I. Agudo5, N. Al a ez C espo6, T. Aniello7,
S. Ansoldi8,9, L. A. An onelli10, C. A amo11, A. A be -Engels12, C. A ca o13, M. A e o14, K. Asano1, P. Aube 15,
D. Baack16, A. Babi´
c17, A. Bak ash18, A. Bamba19, A. Baque o La i a20,21, L. Ba oncelli22, U. Ba es de Almeida23,
J. A. Ba io20, I. Ba ko i´
c24, J. Bax e 1, J. Bece a González3, W. Bedna ek25, E. Be na dini24, M. I. Be na dos5,
J. Be ne e Med ano26, A. Be i12,⋆, J. Besen iede 12, P. Bha acha jee15, N. Biede beck16, C. Bigongia i10,
A. Biland27, E. Bissaldi28, O. Blanch14, G. Bonnoli29, P. Bo das4, Ž. Bošnjak17, A. Bulga elli22, I. Bu elli8,
L. Bu mis o 30, M. Buscemi31, G. Buse o13, A. Campoy O daz32, M. Ca dillo33, S. Ca o 15, A. Ca osi10,
R. Ca osi34, M. S. Ca asco35, M. Ca e e o-Cas illo4, F. Cassol35, A. J. Cas o-Ti ado5, D. Cauz8, D. Ce asole36,
G. Ce ibella12, Y. Chai12, K. Cheng1, A. Chia assa37, M. Chikawa1, L. Chy ka38, A. Ci uen es26, S. Ciko a17,
E. Colombo3, J. L. Con e as20, A. Co nelia24, J. Co ina26, H. Cos an ini35, S. Co ino7, G. D’Amico39, V. D’Elia7,
P. Da Vela34,40, M. Dalchenko30, F. Dazzi7, A. De Angelis13, M. de Bony de La e gne15, B. De Lo o8, M. De Lucia11,
R. de Menezes37, L. Del Pe al41, A. Del Popolo42, G. Deleglise15, M. Del ino14,43, C. Delgado Mendez26,
J. Delgado Mengual44, D. della Volpe30, M. Dellaie a15, D. Depaoli45, A. De Angelis24, A. Di Piano22,
F. Di Pie o37,⋆, A. Di Pila o30, R. Di T ia36, L. Di Vene e36, R. M. Dominik16, D. Dominis P es e 46, A. Donini10,
D. Do ne 47, M. Do o24, C. Díaz26, L. Eisenbe ge 47, D. Elsässe 16, G. Eme y35, J. Escude o5, V. Fallah Ramazani48,
L. Fa iña14, A. Fa o ini16, G. Fe a a31, F. Fe a o o49, A. Fiasson15,50, L. Fo ano33, L. Fon 32, L. F eixas Co omina26,
S. F öse16, S. Fukami1, Y. Fukazawa51, R. J. Ga cia López3, E. Ga cia15, M. Ga cza czyk52, R. J. Ga cía López3,
C. Gasba a53, D. Gaspa ini53, S. Gaspa yan54, M. Gaug32, D. Geye 16, J. G. Giesb ech Pai a23, N. Giglie o28,
F. Gio dano36, P. Gliwny25, N. Godino i´
c55, R. G au14, D. G een12, J. G. G een12, S. Gunji56, P. Gün he 47,
J. Hack eld48, D. Hadasch1, A. Hahn12, K. Hashiyama1, T. Hassan26, K. Hayashi1, L. Heckmann12, M. Helle 30,
J. He e a Llo en e3, K. Hi o ani1, D. Ho mann35, D. Ho ns18, J. Houles35, M. H abo sky38, D. H upec57,
D. Hui1, M. Hü en1, M. Ia lo i58, R. Imazawa51, T. Inada1, Y. Inome1, K. Ioka59, M. Io i49, R. Io o 47, K. Ishio25,
M. Jacquemon 15, I. Jiménez Ma ínez26, E. Jobs 12, J. Jo manainen60, J. Ju ysek61, M. Kagaya1, V. Ka as62,
H. Ka agi i63, J. Ka aoka64, D. Ke szbe g14, G. W. Kluge39,65, Y. Kobayashi1, K. Koh i66, A. Kong1, P. M. Kouch60,
H. Kubo1, J. Kushida2, M. Lainez20, G. Lamanna15, A. Lamas a10, T. Le Flou 15, F. Leone7, E. Lind o s60,
L. Linho 16, M. Linho 16, S. Lomba di7, F. Longo67, S. Lopo chio36, A. Lo ini68, J. Lozano Bahilo41,
P. L. Luque-Escamilla69, E. Lya d70, M. Láinez Lezáun20, R. López-Co o5, M. López-Moya20, A. López-O amas3,
B. Machado de Oli ei a F aga23, P. Majumda 1,71, M. Maka ie 72, D. Manda 61, G. Mane a72, M. Mangana o46,
S. Mangano26, N. Mang16, G. Manicò31, K. Mannheim47, M. Ma io i24, P. Ma quez14, G. Ma sella31,73, O. Ma inez6,
G. Ma ínez26, M. Ma ínez14, J. Ma í69, A. Mas-Aguila 20, G. Mau in15, D. Mazin1,12, S. Menchia i74, S. Mende 16,
E. Mes e Guillen69, S. Micano ic46, D. Miceli24, T. Miene 20, J. M. Mi anda6, R. Mi zoyan12, T. Mizuno75,
S. Mi´
cano i´
c46, M. Mole o González3, E. Molina4, H. A. Mondal71, T. Mon a uli30, I. Mon ei o15, A. Mo alejo14,
D. Mo cuende20, A. Mo selli53, V. Moya20, H. Mu aishi76, K. Mu ase1, S. Naga aki77, T. Nakamo i56, C. Nanci7,
A. Ne ono 78, V. Neus oe 79, L. Nickel16, M. Nie as Rosillo3, C. Nig o14, L. Nikoli´
c74, K. Nilsson60, K. Nishijima2,
T. Njoh Ekoume3, K. Noda1, D. Nosek80, S. Nozaki12, M. Ohishi1, Y. Oh ani1,⋆, T. Oka81, A. Okumu a82,83, R. O i o84,
J. O e o-San os3, S. Paiano7, M. Pala iello8, D. Paneque12, F. R. Pan aleo28, R. Paole i68, J. M. Pa edes4, L. Pa le i´
c46,
M. Pech61, M. Pecimo ika46, M. Pe esano37, M. Pe sic8,85, F. P ei le47, E. Pie opaolo58, M. Pihe 13, G. Pi ola12,
C. Pla d15, F. Podobnik68, V. Poi eau15, M. Polo26, E. Pons15, P. G. P ada Mo oni34, E. P andini24, J. P as 15,
G. P incipe67, C. P iyada shi14, M. P ouza61, R. Rando24, W. Rhode16, M. Ribó4, J. Rico14, C. Righi7, V. Rizi58,
G. Rod iguez Fe nandez53, M. D. Rod íguez F ías41, N. Sahakyan54, T. Sai o1, S. Saku ai1, D. A. Sanchez15,
K. Sa alecka60, M. Sa o15, Y. Sa o86, F. G. Sa u ni10, V. Sa chenko78, B. Schleiche 47, K. Schmid 16,
F. Schmucke maie 12, J. L. Schube 16, F. Schussle 87, T. Schweize 12, A. Sciaccaluga7, T. Siege 47, R. Sil ia36,
J. Si a ek25,⋆, V. Sliusa 70, D. Sobczynska25, A. Spolon24, A. S ame a7, J. S iško i´
c57, D. S om12, M. S zys1,
Y. Suda51,⋆, S. Suu a inen60, T. Ša i´
c55, H. Tajima82, H. Takahashi51, M. Takahashi82, J. Taka a1, R. Takeishi1,
P. H. T. Tam1, S. J. Tanaka86, D. Ta eishi88, F. Ta ecchio7, P. Temniko 72, Y. Te ada88, K. Te auchi81, T. Te zi´
c46,
⋆Co esponding au ho : e-mail: [email p o ec ed];[email p o ec ed]
A66, page 1 o 21
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Abe, H., e al.: A&A, 680, A66 (2023)
M. Teshima1,12, M. Tluczykon 18, F. Tokanai56, D. F. To es89, L. Tos i90, P. T a nicek61, S. T uzzi68, A. Tu one10,
S. Ubach32, M. Vacula38, P. Vallania37, J. an Sche penbe g12, M. Vazquez Acos a3, S. Ven u a74, V. Ve guilo 72,
I. Viale24, A. Vigliano8, C. F. Vigo i o37,91, E. Visen in37, V. Vi ale53, G. Vou sinas30, I. Vo k1, T. Vuillaume15,
M. Vázquez Acos a3, R. Wal e 70, Z. Wei89, M. Will12, T. Yamamo o92, R. Yamazaki86, T. Yoshida63,
T. Yoshikoshi1, and N. Zywucka25
(A ilia ions can be ound a e he e e ences)
Recei ed 17 May 2023 / Accep ed 1 Oc obe 2023
ABSTRACT
Aims. La ge-Sized Telescope 1 (LST-1), he p o o ype o he La ge-Sized Telescope a he upcoming Che enko Telescope A ay
Obse a o y, is concluding i s commissioning phase a he Obse a o io del Roque de los Muchachos on he island o La Palma. The
p oximi y o LST-1 o he wo MAGIC (Majo A mosphe ic Gamma Imaging Che enko ) elescopes makes i possible o ca y ou
obse a ions o he same gamma- ay e en s wi h bo h sys ems.
Me hods. We desc ibe he join LST-1+MAGIC analysis pipeline and used simul aneous C ab Nebula obse a ions and Mon e Ca lo
simula ions o assess he pe o mance o he h ee- elescope sys em. The addi ion o he LST-1 elescope allows o he eco e y o
e en s in which one o he MAGIC images is oo dim o su i e analysis quali y cu s.
Resul s. Thanks o he esul ing inc ease in he collec ion a ea and s onge backg ound ejec ion, we ound a signi ican imp o emen
in sensi i i y, allowing o he de ec ion o 30% weake luxes in he ene gy ange be ween 200 GeV and 3 TeV. The spec um o he
C ab Nebula, econs uc ed in he ene gy ange be ween ∼60 GeV and ∼10 TeV, is in ag eemen wi h p e ious measu emen s.
Key wo ds. ins umen a ion: de ec o s – me hods: da a analysis – gamma ays: gene al
1. In oduc ion
Ve y-high-ene gy (VHE ≳100 GeV) gamma ays canno be
obse ed di ec ly in an e icien way due o hei abso p ion by
he a mosphe e. In u n, obse a ions wi h space-bo n ins u-
men a e ma ed by ela i ely low luxes a hose ene gies. In he
las h ee decades, imaging a mosphe ic Che enko elescopes
(IACTs) ha e p o en use ul as sensi i e ins umen s in he s udy
o VHE gamma- ay emission om cosmic sou ces (see e.g.,
Si a ek 2022 o a ecen e iew). The combina ion o mul i-
ple elescopes a dis ances on he o de o 100 m (compa able
o he size o he gamma- ay Che enko ligh pool) allows o
join s e eoscopic analyses o he e en s, he eby imp o ing he
pe o mance o he sys em signi ican ly (Kohnle e al. 1996).
The Che enko Telescope A ay Obse a o y (CTAO) is an
upcoming nex -gene a ion gamma- ay acili y (Acha ya e al.
2013), composed o wo elescope a ays loca ed in he No h-
e n and Sou he n hemisphe es. In o de o co e a b oad ene gy
ange ( om a ew ens o GeVs up o a ew hund eds o TeVs),
i is o be composed o elescopes o h ee di e en sizes: La ge-
Sized Telescopes (LSTs), Medium-Sized Telescopes (MSTs),
and Small-Sized Telescopes (SSTs). The LSTs, wi h mi o
diame e s o 23m, will be he mos sensi i e pa o he sys-
em o he lowes ene gy ange o CTAO ( ens o GeV). The
cons uc ion o he i s LST elescope, named LST-1, was
comple ed in Oc obe 2018. Since 2019, i has been ecei ing
commissioning and enginee ing da a (CTA-LST p ojec 2021).
I is loca ed in Obse a o io Roque de los Muchachos, La Palma
(Spain), a he al i ude o 2200 m a.s.l.. I is se a a dis-
ance o only ∼100 m om he MAGIC (Majo A mosphe ic
Gamma Imaging Che enko ) elescopes, a pai o 17 m IACTs
(Aleksi´
c e al. 2016a). Bo h sys ems wo k independen ly, bu
hei p oximi y allows o o line sea ches o common e en s and
enables join LST-1+MAGIC analysis. A simila a ay con ain-
ing elescopes o di e en sizes is being ope a ed by he H.E.S.S.
Collabo a ion (Holle e al. 2015). Howe e , in ha case, he di -
e ence in mi o a ea (app oxima ely by a ac o o 5) causes a
simila di e ence in he ene gy h eshold. On he o he hand, in
he case o LST-1+MAGIC combina ion, he di e ence be ween
he mi o a ea o he LST-1 and ha o he MAGIC elescopes
is only a ac o o 2.
In his wo k, we epo he common analysis chain o bo h
ins umen s and i s achie ed pe o mance using bo h Mon e
Ca lo (MC) simula ions and obse a ions o he C ab Nebula. In
Sec . 2, we desc ibe bo h pa icipa ing ins umen s. The applied
da a and Mon e Ca lo (MC) simula ions a e desc ibed in Sec . 3.
We de i e a ious pe o mance pa ame e s o he join sys em
and p esen hem in Sec . 4. Ou concluding ema ks a e gi en
in Sec . 5.
2. Ins umen s and da a analysis
The ela i e loca ion o he LST-1 and he MAGIC elescopes,
along wi h hei basic pa ame e s a e compa ed in Fig. 1and
Table 1, espec i ely. While he elescopes ha e hei main
design concep s in common, he e a e some di e ences, such as
he la ge LST-1 mi o a ea, he highe quan um e iciency (QE)
o i s op ical de ec o s, and i s la ge ield o iew (FoV). Despi e
he same pa abolic dish shape (minimizing he ime sp ead o he
egis e ed Che enko pho ons) LST-1 has la ge /d and la ge
came a FoV. The highe e en a e in he case o LST-1 is a
sum o mul iple e ec s: lowe h eshold (due o highe QE and
mi o a ea), la ge size o he igge egion, and monoscopic
ope a ions.
2.1. MAGIC
MAGIC is a sys em made up o wo IACTs, sepa a ed by a
dis ance o 85m. The i s elescope, MAGIC-I (M1), was con-
s uc ed in 2003, while MAGIC-II (M2) was added in 2009.
Since hen, bo h elescopes ha e ope a ed in a s e eoscopic
obse a ion mode (Aleksi´
c e al. 2012). In he s anda d ope -
a ion mode, only e en s igge ing bo h elescopes a e sa ed.
The elescopes ha e unde gone a ew upg ades (wi h he mos
ecen in 2012) and since hen hey sha e a nea ly iden ical design
and compa able pe o mance. While he nominal came a FoV
is 3.5◦, he pa co e ed by he igge is limi ed only o he
A66, page 2 o 21
Abe, H., e al.: A&A, 680, A66 (2023)
100−80−60−40−20−0 20 40 60 80 100
Eas o se [m]
100−
80−
60−
40−
20−
0
20
40
60
80
100
No h o se [m]
LST-1
MAGIC-I
MAGIC-II
Fig. 1. Loca ion o he LST-1 and MAGIC elescopes. The Xand Yaxes
ep esen he geog aphical Eas and No h di ec ion, espec i ely. The
diame e o he ci cle is equal o he diame e o he elescope’s mi o
dish.
Table 1. Compa ison o LST-1 and MAGIC elescopes pa ame e s.
Pa ame e LST-1 MAGIC I/II
Diame e (d) 23 m 17 m
Focal leng h ( ) 28 m 17 m
Dish shape Pa abolic Pa abolic
Came a FoV 4.5◦3.5◦
Pixel FoV 0.1◦0.1◦
Numbe o pixels 1855 1039
Peak QE 41% 32–34%
Sampling speed 1 GHz 1.64 GHz
T igge ype Mono S e eo
Typical e en a e 104s−1300 s−1
Readou dead ime 7 µs 26 µs
inne hal o he ull came a a ea. A low zeni h angle dis ance,
he ene gy h eshold (de ined as he peak o he di e en ial ue
ene gy dis ibu ion) a igge le el o he MAGIC elescopes o
a sou ce wi h a −2.6spec al index is ∼50 GeV (Aleksi´
c e al.
2016b) o a s anda d digi al igge .
2.2. LST-1
LST-1 is he i s o he ou LSTs o be cons uc ed in he CTAO
No he n si e (CTA-LST P ojec 2022). The cons uc ion o
LST-1 was comple ed in Oc obe 2018, a e which i s commis-
sioning and alida ion pe iod s a ed. Cu en ly, he elescope
is pe o ming bo h commissioning and scien i ic obse a ions.
The mi o a ea being wice as la ge, as well as he imp o ed QE
o he op ical senso s (pho omul iplie s) compa ed o MAGIC,
enable LST-1 o achie e an ene gy h eshold o ∼20 GeV (Abe
e al. 2023). Howe e , as any IACT ope a ing s andalone, LST-1
su e s om a huge had onic backg ound, which is much mo e
e icien ly ejec ed in s e eoscopic sys ems. Simila ly, i also has
wo se accu acy in e ms o he econs uc ed showe geome-
y, which a ec s he angula and ene gy esolu ions. The e o e,
despi e he la ge ligh collec ion, a ene gies abo e 100 GeV,
he sensi i i y o LST-1 alone is a ac o ∼1.5wo se han ha o
MAGIC (Abe e al. 2023).
2.3. E en ma ching
Cu en ly MAGIC and LST-1 ope a e independen ly. Bo h sys-
ems a e howe e equipped wi h GPS clocks ha p o ide ime
s amps o each e en . Those ime s amps can be used o o line
ma ching o e en s ha o igina e om he same showe (simila
app oach has been used in he i s H.E.S.S. s e eoscopic da a,
H.E.S.S. Collabo a ion 2006). Due o he di e en elec onic
pa hways and di e en a el imes o he Che enko ligh o
indi idual elescopes, a poin ing-dependen ime delay be ween
he a i al imes a MAGIC and a LST-1 needs o be aken in o
accoun . Fo each sub un (co esponding o abou 10 s o LST-1
da a), we ma ch he e en s wi h a coincidence window o 0.6 µs.
The op imal delay is ob ained using an i e a i e p ocedu e. To
also allow o he analysis o LST-1+M1 o LST-1+M2 e en
ypes, he p ocedu e is done independen ly using ime s amps
in each o he MAGIC elescopes. Fo he ypical a e o LST-1
and MAGIC (see Table 1), his p ocedu e would esul in a neg-
ligible a e o acciden al coincidences o ≲1.8s−1. Anomalous
coincidence combina ions (e.g., ma ching wo LST-1 e en s o
one MAGIC e en o wo MAGIC e en s o one LST-1 e en )
we e excluded om he da a s eam; howe e , hey a e e y a e
due o LST-1 and MAGIC dead imes.
2.4. Da a analysis
In hei s andalone ope a ions, bo h MAGIC and LST-1 use inde-
penden analysis chains. The MAGIC da a analysis is based on
MARS (Mo alejo e al. 2009;Zanin e al. 2013), a C++, ROOT-
based lib a y, and a package o analysis p og ams. The aw da a
a e s o ed in a cus om bina y o ma and he da a a e gene a ed
a each p ocessing s ep a e s o ed using ROOT con aine s.
On he o he hand LST-1 is using c a-ls chain (Lopez-
Co o e al. 2022), a Py hon-based analysis lib a y exploi ing
c apipe (Kosack e al. 2022). The LST-1 aw da a consis o
pixel-wise wa e o ms and auxilia y in o ma ion. They a e s o ed
in a z i s o ma (Pence e al. 2012;Lya d e al. 2017) and
p ocessed da a a e s o ed in HDF5 iles (Nozaki e al. 2020).
Fo he da a ob ained by obse a ions, we pe o med he
i s s ages o he da a p ocessing, namely he signal ex ac-
ion om indi idual pixel wa e o ms and he calib a ion o he
esul ing images o pho oelec ons (p.e.) and indi idual pixel
iming, wi h he speci ic so wa e o each ins umen . Then
he MAGIC da a a e con e ed in o HDF5 o ma , compa ible
wi h he LST-1 da a using he dedica ed c apipe_io_magic
package1. The es o he analysis chain is pe o med wi h
he magic-c a-pipe2package using ls chain and c apipe
me hods. In pa icula , he magic-c a-pipe con ains analysis
sc ip s o, o example, apply he same image cleaning as in he
MARS package, bu wi hin a c apipe-like en i onmen and o
ma ch he e en s p oduced by he same showe in he h ee ele-
scopes. All he o he highe -le el analysis s eps a e pe o med
wi h he magic-c a-pipe package as well, wi h he help o
o he modules o speci ic asks (e.g., pyi ,Noe he e al. 2022,
o he calcula ion o ins umen esponse unc ion, IRF; and
1h ps://gi hub.com/c a-obse a o y/c apipe_io_magic
2h ps://gi hub.com/c a-obse a o y/magic-c a-pipe
A66, page 3 o 21
Abe, H., e al.: A&A, 680, A66 (2023)
MAGIC
Calib a ed
LST-1 R0
(wa e o m) LST-1 + MAGIC
Coinciden e en s
DL1 + s e eo
(image+geome y)
Random Fo es s
(ene gy, di ec ion,
classi ie )
sim_ ela ay MC DL0
(wa e o m)
sim_ ela ay MC
DL1 + s e eo
(image + geome y)
T ain samples
LST-1 DL1
(image)
MAGIC DL1a+b
(image +
pa ame e s)
LST-1 + MAGIC
Coinciden e en s
DL2 (ene gy,
di ec ion,
gammaness)
MC da a analysis:
ls chain
sim_ ela ay MC
DL2 (ene gy,
di ec ion,
gammaness)
LST-1 + MAGIC
Coinciden e en s
DL3 (e en lis ,
IRFs)
IRFs (e ec i e
a ea, ene gy
mig a ion, e c)
Apply
RFs
Calib a ion
Image pa ame iza ion
S e eo econs uc ion
sim_ ela ay MC
DL1 + s e eo
(image + geome y)
Tes samples
T ain RFs
Apply RFs
C ea e he IRFs
C ea e DL3 iles
MAGIC R0
(wa e o m)
MARS
Calib a ion
Image pa ame iza ion
MCP
gammapy
Fig. 2. Schema ic iew o MCP analysis chain. Blue, ed, iole , and g ay boxed ep esen di e en s ages o LST-1 da a, MAGIC da a, join da a,
and MC simula ions, espec i ely. Black boxes ma k he auxilia y iles.
gammapy,Deil e al. 2017, o lux es ima ion). Fo MC simu-
la ions, all he p ocessing (including he calib a ion) is ins ead
pe o med wi h magic-c a-pipe. The analysis chain p esen ed
in his pape is e e ed o as he MAGIC-c apipe (MCP) chain
(and summa ized in Fig. 2). Such a scheme allows us o ake
ad an age o he au oma ic p ocessing o he bulky, ea ly s ages
o da a and exploi he al eady implemen ed low-le el calib a-
ion co ec ions (see e.g., Si a ek e al. 2013 o he case o
MAGIC and Cassol e al., in p ep. o LST-1). A he same ime,
i allows o he u iliza ion o s a e-o - he-a so wa e de eloped
o CTAO, and in u n, he newly de eloped ools can also be
easily applied o CTAO analysis in he u u e.
A e he ini ial image cleaning (see Aleksi´
c e al. 2016b), he
images a e pa ame ized using he classical app oach o (Hillas
1985) and a quali y cu on “in ensi y” is applied (i.e., he o al
numbe o p.e. in he image should be a leas 50 p.e.)3. Nex ,
he e en s a e di ided in o di e en classes, depending on which
elescopes a e igge ed. We conside ed he ollowing combi-
na ions: M1+M2, LST-1+M1, LST-1+M2, and LST-1+M1+M2.
Howe e , i should be no ed, ha due o he s e eoscopic ig-
ge o he MAGIC elescopes, he e en ypes LST-1+M1 and
LST-1+M2 also co espond o e en s in which all h ee ele-
scopes had been igge ed. Though in hose e en s, one o he
MAGIC elescopes p o ided an image ha ei he did no su i e
he cleaning o had an in ensi y ha was oo low. In Table 2, we
epo he pe cen age o e en s o each kind o a ious da a and
MC samples ( he pa ame e s o he MC simula ions a e gi en
in Table 3). The domina ing ype o e en s a e h ee- elescope
e en s (3/4 o all gamma- ay e en s). The ac ion o LST-1+M2
e en s is abou wice as la ge as hose o LST-1+M1 and his is
ela ed o he p oximi y o LST-1 o he M2 elescope. While
3This is a s anda d cu bo h in MAGIC and LST-1 analysis chains, see
Aleksi´
c e al. (2016b); Abe e al. (2023).
Table 2. Pe cen age o di e en e en ypes in di e en ypes o MC
simula ions and in he obse a ions.
Type MC γMC γMC p Obse a ions
(0.4◦) (0−2.5◦)
M1+M2 6.2% 4.8% 20.4% 21.5%
LST-1+M1 7.1% 7.7% 6.2% 5.3%
LST-1+M2 12.5% 12.6% 11.9% 14.2%
LST-1+M1+M2 74.1% 74.8% 61.5% 59.0%
No es. Only images su i ing 50 p.e. cu in in ensi y a e consid-
e ed. Obse a ions and MC simula ions co e low zeni h dis ance
angle (<30◦). P o on MC a e weigh ed o −2.7spec al index, while
gamma- ay MC o −2.6. Values o gamma- ay simula ions a e p o ided
sepa a ed o showe s a ypical o se om he poin ing di ec ion (0.4◦)
and o iso opic dis ibu ion (wi hin 2.5◦ om he poin ing di ec ion).
he pe cen ages o di e en e en ypes in p o on simula ions
oughly ollow wha has been obse ed in he da a, he e a e
some mino di e ences a (absolu e) 1–2% le el. They a e likely
caused by he p esence o helium and highe elemen s in he
da a, as well as incomple eness o he simula ions due o e y
la ge impac and o se angle e en s. Addi ionally, he egula
sys ema ic e ec s (ligh yield, op ical poin s sp ead unc ion,
e c.) causing sligh MC-da a misma ches can also con ibu e o
hose small di e ences. The ac ion o MAGIC-only (wi hou
he LST-1 coun e pa ) e en s is signi ican ly la ge in he obse -
a ions and in he p o on MC simula ions (∼20%) compa ed o
he gamma- ay MC simula ions (∼5−6%, compa able o bo h
poin -like and di use gamma- ay simula ions). We in e p e his
as a esul o in insic di e ences be ween he Che enko ligh
A66, page 4 o 21
Abe, H., e al.: A&A, 680, A66 (2023)
Table 3. Summa y o he gene a ed MC samples and hei zeni h dis ance ange, ene gy ange, maximum impac pa ame e , and iewcone
(maximum o se angle om he came a cen e ).
Sample Pa icle ype Zd Emin Emax Impac max Viewcone
[◦][GeV] [TeV] [m] [◦]
T ain Gamma 6–52 5×cos−2.5Zd 50 ×cos−2.5Zd 900 ×cos−0.5Zd 0–2.5
P o ons 6–52 10 ×cos−2.5Zd min(100 ×cos−2.5Zd, 200) 1500 ×cos−0.5Zd 0–8 ×cos0.5Zd
Tes
Gamma 10–55 5×cos−2.5Zd 50 ×cos−2.5Zd 700 ×cos−0.5Zd 0.4
helium 10–43 20 ×cos−1.5Zd 200 ×cos−1.5Zd 1500 ×cos−1Zd 0–8
Elec ons 10-43 5×cos−2.5Zd 50 ×cos−2.5Zd 720–1200 0−7.5
No es. The i s h ee samples a e he same as hose used in Abe e al. (2023).
dis ibu ion on he g ound o showe s ini ia ed by di e en p i-
ma y pa icles. Gamma- ay-induced e en s ha e in gene al a
smoo h Che enko pho on dis ibu ion on he g ound. Fo such
“ egula ” e en s, i hey a e b igh enough o be de ec ed by
bo h MAGIC elescopes, he signi ican ly highe ligh yield o
LST-1 no mally also allows o he de ec ion o he showe by
he hi d elescope. Howe e , had onic e en s show i egula i-
ies in hei g ound dis ibu ion o Che enko ligh , caused by
indi idual high ans e se momen um sub-showe s. Such e en s
can p oduce a signi ican signal in MAGIC elescopes wi hou
an LST-1 e en coun e pa . Conside ing he small ac ion o
MAGIC-only e en s, and hei dominan backg ound o igin, we
excluded hose e en s om u he analysis.
Fo con enience, as well as o exploi he in o ma ion o ele-
scopes no con aining he image, he e en s we e hen di ided
in o he combina ion ypes (see Table 2). Fo each e en ype
and elescope pa icipa ing in he combina ion, he gamma-
had on sepa a ion pa ame e (i.e., “gammaness”, see Abe e al.
2023), es ima ed ene gy, and he es ima ed DISP pa ame e
(es ima ed dis ance o he sou ce posi ion p ojec ed on he cam-
e a o he cen oid o he image, Lessa d e al. 2001;Aleksi´
c
e al. 2010) we e compu ed. The aining was done using a an-
dom o es (RF) me hod (B eiman 2001), implemen ed in he
sciki -lea n package (Ped egosa e al. 2011). The RF eg es-
so s used o ene gy and DISP es ima ions used 150 es ima o s,
a maximum ee dep h o 50, he squa ed e o c i e ion o
selec ion o he bes cu om all he pa ame e s a each s ep
and di ision o lea es down o a single e en . The RF classi-
ie used o gamma-had on sepa a ion employed 100 es ima o s
wi h a maximum dep h o 100. In his case, he RF b anch-
ing was done using he Gini index c i e ion, bu a each s ep,
only he squa e oo o he o al numbe o pa ame e s is an-
domly selec ed. Indi idual elescope es ima es a e based on he
Hillas pa ame iza ion (in ensi y, leng h, wid h, skewness, ku -
osis, and ime slope compu ed along he main axis o he image,
and ac ion o o al image in ensi y in he wo ou e mos ings
o pixels) in he pa icula elescope. In each elescope, his
in o ma ion is combined wi h en a i e s e eoscopic pa ame e s
ob ained om he axis c ossing me hod (Ho mann e al. 1999)
(heigh o he showe maximum, impac pa ame e ) and poin -
ing di ec ion (azimu h and zeni h dis ance angles). In o de o
ob ain e en -wise classi ie s and es ima o s, he indi idual ele-
scope esponses a e weigh ed wi h he image in ensi y4. In his
way, b igh e and be e - econs uc ed images a e a o ed in he
inal es ima ion.
4O he possible weigh s, including in e se o a iance o he esponse
o indi idual ees, we e es ed and p o ed compa able, bu led o a
sligh ly wo se pe o mance.
A special a e aging p ocedu e was applied o he es ima-
ion o he a i al di ec ion o he showe . The a i al di ec ion
can be econs uc ed om an image using he DISP pa ame e ,
assuming ha i lies on he main axis o he image in he came a
plane. The e a e, howe e , wo di ec ions ha ul ill his condi-
ion, loca ed on opposi e sides o he image. The selec ion o he
co ec one ( he so-called head- ail disc imina ion), especially a
he lowe ene gies, may ail in a ac ion o e en s. Fo example,
Abe e al. 2023 epo s ha app oxima ely 20% o all gamma- ay
e en s ha e head and ail w ongly disc imina ed o a spec um
simila o he C ab Nebula5.
The e o e, we applied he S e eo DISP RF me hod (Aleksi´
c
e al. 2016b), adap ed o h ee- elescopes obse a ions. Speci i-
cally, we scanned all possible combina ions o pai s o possible
a i al di ec ions om indi idual images and selec he one ha
yields he smalles sp ead o econs uc ed posi ions. The sp ead
is quan i ied wi h he disp_di _mean pa ame e , de ined as he
sum o angula dis ances o econs uc ed di ec ions om all
pai s o elescopes, di ided by he numbe o such pai s. In o de
o enhance he angula esolu ion and p o ide addi ional ejec-
ion o had onic e en s (which a e mo e likely o ha e i egula
images), we apply an addi ional cu o disp_di _mean <0.22◦.
The same alue o he cu is used in he s anda d MARS analysis
chain. The change o collec ion a ea a di e en s ages o analy-
sis (including applica ion o he quali y cu s) is summa ized and
discussed in Appendix A.
2.5. Simula ions o he elescopes’ esponse o showe s
To ain he showe econs uc ion algo i hm and o e alua e
IRFs, he analysis o IACT da a equi es MC simula ions. In he
case o LST-1, he de elopmen o showe s is simula ed using
CORSIKA (Heck e al. 1998), while he esponse o he ele-
scope is simula ed wi h he sim_ ela ay p og am (Be nlöh
2008). On he o he hand, wi hin MAGIC, MC simula ions o
showe s a e gene a ed using a sligh ly modi ied e sion o COR-
SIKA, bu he esponse o he elescopes is ob ained using
MagicSo p og ams ( e lec o and came a;Majumda e al.
2005). Common LST-1+MAGIC obse a ions equi e he anal-
ysis chain o be pe o med wi hin he same amewo k, and he
same should happen o he simula ions.
We pe o med simula ions o he same showe s isible by
bo h MAGIC and LST-1, using he sim_ ela ay p og am.
To achie e his, we ansla ed he simula ion pa ame e s o he
5This ac ion was ob ained a e cleaning, an in ensi y cu o 50 p.e.,
and wi h he main image axis o ien ed wi hin 0.3◦o he nominal sou ce
posi ion. I is, howe e , s ongly dependen on ene gy, d opping below
5% abo e 200 GeV.
A66, page 5 o 21

Abe, H., e al.: A&A, 680, A66 (2023)
MAGIC elescopes om he e lec o and came a simula ion
p og ams in o he sim_ ela ay nomencla u e. Fo mos o
he pa ame e s (e.g., mi o dish geome y, angula dependence
o ligh guide e iciencies, a e age quan um e iciency o PMT,
ji e o single p.e. imes, elescope igge pa ame e s, and ead-
ou pulse shape), he ansla ion was di ec and he same alues
and cu es we e used in bo h simula ion chains. Fo some o he
pa ame e s, howe e , mino simpli ica ions o a e aging had o
be applied due o in insic di e ences be ween he wo so wa es.
Fo example, his was he case o he simula ion o he mi o s
e lec i i y and he noise wi hin he pulse in eg a ion window.
Thanks o he usage o sim_ ela ay, he LST-1 simula ion
pa ame e s could be aken di ec ly om he s anda d con ig-
u a ion, he so-called LSTP od2 (as in Abe e al. 2023). The
common pa ame e s (a mosphe ic model, geomagne ic ield)
ollow he LSTP od2 se ings. The le el o uni o m nigh sky
backg ound (NSB) was adjus ed a he analysis le el in he case
o LST-1, ollowing he p ocedu e desc ibed in Abe e al. (2023).
In he case o MAGIC, he adjus men was done acco ding o he
same p inciple (ma ching noise in emp y, he so-called pedes al,
and e en s), bu al eady a he elescope came a esponse simula-
ion le el. The alida ion p ocess o he MC simula ion se ings
on a dedica ed MC p oduc ion is desc ibed in Appendix B. As
a inal end- o-end check, we also compa ed he ene gies o
MAGIC e en s econs uc ed wi h bo h he MCP (based on he
sim_ ela ay MCs) and MARS (based on s anda d MAGIC
MCs) chains, achie ing simila accu acy (see Appendix C).
3. Obse a ion and simula ion samples
We de e mined he pe o mance o he join analysis chain in wo
ways: i s using obse a ion da a aken om he di ec ion o he
C ab Nebula and hen using dedica ed MC simula ions.
3.1. Obse a ions
In o de o e alua e he pe o mance o he join analysis, we
used 4h o good-quali y C ab Nebula da a aken simul aneously
by he LST-1 and MAGIC elescopes. The obse a ions span he
pe iod be ween Oc obe 2020 and Ma ch 2021, and aken in wob-
ble obse a ion mode, wi h he sou ce posi ion o se by 0.4◦
om he came a cen e . A e e e y 20-min long un, he di ec-
ion o he o se was lipped o main ain consis ency be ween he
sou ce and he backg ound con ol egion. Only da a in which
he poin ing di ec ion o bo h sys ems ma ched wi hin 0.1◦we e
used. The da a was aken a low and medium zeni h angles,
namely 0.8 h in be ween 12◦−30◦, 2.3 h in 30◦−45◦and 0.6 h
in be ween 45◦−53◦.
3.2. MC simula ions
Fo mos o he analysis chain we e-use he same MC simula-
ion samples o p o ons and gamma ays as in Abe e al. (2023).
Howe e , we also used addi ional simula ions o helium and
elec ons, wi h eop imized scaling o he simula ion pa ame e s
(maximum impac pa ame e and o se angle om he cam-
e a cen e ) wi h zeni h angle dis ance, o imp o e he sample
comple eness. The samples we e gene a ed a ixed poin ings
along he pa h o he sou ce in he sky ( aining samples), o
o co e he ull-sky on a g id o poin ings ( es samples), see
Abe e al. (2023) o de ails. All he MC samples a e gen-
e a ed wi h spec al index o −2and eweigh ed o speci ic
pa icle spec a. The p oduc ions a e summa ized in Table 3.
In he in e es o s udying he pe o mance wi h MC as well,
we di ided he “T ainP o on” sample in o aining and es ing
sub-samples.
3.3. Da a/MC compa isons
To ensu e he co ec ep oduc ion o obse ed da a by he MC
simula ions, we pe o med an end- o-end compa ison wi h he
da a. As he gamma- ay showe s a e mo e egula and (on a e -
age) less ex ended han had onic ones, compa isons pe o med
wi h gamma- ay e en s a e sensi i e o possible da a-MC mis-
ma ches. Hence, we p esen a compa ison wi h selec ed gamma-
ay e en s, which also e lec he pe o mance o gamma- ay
obse a ions. Ne e heless, o comple eness o he s udy and
o alida e he analysis h eshold, we also pe o med simila
compa isons wi h he backg ound e en s (see Appendix D).
We de i ed he pa ame e dis ibu ions ob ained om he
gamma- ay excess e en s. The dis ibu ions a e ex ac ed om
C ab Nebula obse a ions a e sub ac ion o he esidual back-
g ound using a backg ound con ol egion. We compa ed hese
excess dis ibu ions o he simula ed gamma ays weigh ed (and
no malized) acco ding o he spec um ha was measu ed by
Aleksi´
c e al. (2015). In his app oach, he gamma- ay e en s a e
domina ed by a backg ound o much mo e abundan had onic
showe s. Thus, o a oid la ge s a is ical (and sys ema ic) e o s,
some kind o backg ound supp ession needs o be applied. In
o de o pe o m he compa ison wi hou in oducing a la ge
bias, we applied so cu s co esponding o 95% “gammaness”
e iciency (in each es ima ed ene gy bin), and conside ed only
e en s wi h econs uc ed di ec ion up o 0.2◦away om he
nominal sou ce posi ion.
The esul s o he compa ison a e shown in Fig. 3. The
“in ensi y” dis ibu ion is oughly ep oduced. We no e ha
he MC simula ion shape o he dis ibu ion o hese pa ame-
e s (in pa icula , he in ensi y) is dependen on he assumed
spec al model o he C ab Nebula. The leng h dis ibu ion is
well ma ching be ween he da a and MCs. Howe e , con a y o
he backg ound case (c . Appendix D), he wid h pa ame e is
sligh ly unde es ima ed in he case o MAGIC-I and MAGIC-
II elescopes, which could be o ins ance due o insu icien ly
accu a e simula ions o he op ical PSF. Despi e his, he “gam-
maness” dis ibu ion, bo h o indi idual elescopes and a e age,
is s ill su icien ly well ep oduced in he simula ions o a oid
in oducing la ge sys ema ic e o s. The econs uc ed heigh o
he showe maximum is sligh ly shi ed owa ds highe alues in
MC simula ions han in he da a. This could be due o a combina-
ion o a ious e ec s, o ins ance: a sys ema ic unce ain y on
he ene gy scale o he elescopes, a misma ch be ween he zeni h
and azimu h dis ibu ions, which a e con inuous o he da a
and disc e e o he simula ions, o a sligh mispoin ing o he
elescopes. Finally, while he econs uc ion o he e en di ec-
ion is oughly consis en wi h he simula ions, a sligh inc ease
o he high- alues ail in he da a is p esen as well. Simila ly,
a sligh misma ch in such dis ibu ions has been obse ed in
LST-1-alone and MAGIC-alone obse a ions, and migh be
ela ed o a cmin-scale mispoin ing o he elescopes (Aleksi´
c
e al. 2016b;Abe e al. 2023).
4. Pe o mance pa ame e s
Using C ab Nebula da a and MC simula ions, we e alua ed a i-
ous pe o mance pa ame e s o he join analysis chain and com-
pa ed hose wi h he MAGIC-only analysis. We also compa ed
A66, page 6 o 21
Abe, H., e al.: A&A, 680, A66 (2023)
234
Log10 in ensi y, LST-1
101
102
Numbe o e en s
234
Log10 in ensi y, MAGIC-1
101
102
Numbe o e en s
234
Log10 in ensi y, MAGIC-2
101
Numbe o e en s
0.00 0.05 0.10 0.15 0.20 0.25
leng h [m], LST-1
101
102
Numbe o e en s
0.00 0.05 0.10 0.15 0.20 0.25
leng h [m], MAGIC-1
101
102
Numbe o e en s
0.00 0.05 0.10 0.15 0.20 0.25
leng h [m], MAGIC-2
101
102
Numbe o e en s
0.00 0.02 0.04 0.06
wid h [m], LST-1
101
102
Numbe o e en s
0.00 0.02 0.04 0.06
wid h [m], MAGIC-1
101
102
Numbe o e en s
0.00 0.02 0.04 0.06
wid h [m], MAGIC-2
101
102
Numbe o e en s
0.0 0.2 0.4 0.6 0.8 1.0
gammaness, LST-1
101
102
Numbe o e en s
0.0 0.2 0.4 0.6 0.8 1.0
gammaness, MAGIC-1
101
102
Numbe o e en s
0.0 0.2 0.4 0.6 0.8 1.0
gammaness, MAGIC-2
101
102
Numbe o e en s
5000 10000 15000
h_max [m]
101
102
Numbe o e en s
0.0 0.2 0.4 0.6 0.8 1.0
a _gammaness
101
102
Numbe o e en s
MC gamma
Da a (excess)
0.00 0.01 0.02 0.03 0.04
a _ he a2 [deg ee2]
101
102
Numbe o e en s
Fig. 3. Compa ison o image pa ame e s be ween he gamma- ay excess in he da a (blue) and MC simula ions o gamma ays (o ange). Only obse -
a ions wi h zeni h dis ance below 30◦a e used. The op ou ows o panels show in ensi y, leng h, wid h, and indi idual elescope “gammaness”
( om op o bo om) o LST-1 (le ), MAGIC-I (middle), and MAGIC-II ( igh ). The bo om ow shows s e eoscopic pa ame e s: heigh o he
showe maximum (le ), a e aged “gammaness” (middle) and squa ed econs uc ed dis ance o he sou ce ( igh ).
he sensi i i y and lux econs uc ion wi h he LST-1-only anal-
ysis. As he pe o mance o Che enko elescopes is s ongly
dependen on he zeni h dis ance o he poin ing, we in es iga ed
he case o Zd <30◦and 30◦<Zd <45◦sepa a ely o p o ide
a compa ison wi h he MAGIC-only pe o mance.
4.1. Ene gy h eshold
In Fig. 4, we p esen he di e en ial ue ene gy dis ibu ion o a
sou ce wi h a −2.6spec um. In he case o MAGIC-only e en s,
he ene gy h eshold (peak posi ion o ha dis ibu ion) a he
A66, page 7 o 21
Abe, H., e al.: A&A, 680, A66 (2023)
20 40 60 80 100 120 140 160 180
0
20000
40000
60000
80000
100000
120000
Weigh ed numbe o e en s [a.u.]
MAGIC+LST-1
MAGIC-only
20 40 60 80 100 120 140 160 180
Ene gy [GeV]
1.0
1.5
2.0
Ra io
Fig. 4. T ue ene gy dis ibu ion ob ained wi h MC simula ions
(weigh ed o a sou ce spec um o −2.6) o gamma ays o Zd <30◦a
he econs uc ion le el (a leas wo images wi h an in ensi y o >50).
Ve ical lines show he peak posi ion o he join analysis (blue) and
MAGIC-only analysis (o ange). Bo om panel shows he a io o he wo
cu es.
s e eoscopic econs uc ion le el o ∼70 GeV is consis en wi h
he alue ob ained in Aleksi´
c e al. (2016b). The addi ion o he
hi d elescope, while i canno p o ide addi ional e en s a he
igge le el, can eco e e en s in which one o he MAGIC
images displays an in ensi y le el ha is oo low o u he
s e eoscopic econs uc ion. As a esul , he ene gy h eshold a
he econs uc ion le el is educed o ∼60 GeV. Addi ionally, he
collec ion a ea below he ene gy h eshold is g ea ly imp o ed,
by a ac o o abou 2 a 30 GeV.
4.2. Flux econs uc ion
Since all he da a used in his wo k we e aken be o e Augus
2021, ollowing Abe e al. (2023), o he spec al analysis we
apply an inc eased cu o he in ensi y o >80 p.e. o LST-1
images. Due o he signi ican ly la ge ligh yield o LST-1
compa ed o MAGIC, he e ec o his cu on he s e eoscopic
analysis is e y small (e.g., o low zeni h angle obse a ions a
30 GeV only 10% o e en s a e emo ed). Fo MAGIC images, a
s anda d in ensi y o >50 p.e quali y cu was applied. To econ-
s uc he spec um o he C ab Nebula, we de i ed he IRFs
o a numbe o simula ed azimu h and zeni h poin ings close
o hose ollowed by he sou ce du ing he obse a ions. To e al-
ua e he IRFs co esponding o indi idual da a uns we employ
in e pola ion. We hen di ided he sample in o an ascending and
descending b anch (i.e., be o e and a e he culmina ion). Fo
each b anch sepa a ely, we pe o med a one-dimensional (1D)
in e pola ion (o e he cosine o zeni h dis ance angle) o he
IRFs. Subsequen ly a global, binned, join likelihood spec al i
was pe o med wi h gammapy 0.20.1 (Deil e al. 2017;Dona h
e al. 2022) o de e mine he bes pa ame e s o he spec al
model o a poin -like sou ce a he nominal posi ion o he
C ab Nebula. Nex , he same so wa e was used o de i e indi-
idual spec al poin s by i ing he no maliza ion o he global
10 1100101
Ene gy [TeV]
10 11
10 10
E
2
dN
/
dE
[e g cm 2 s 1]
MAGIC (Aleksi e al. 2015)
Meye e al. 2010
Model
LST-1 (Abe e al. 2023)
LST-1 + Fe mi-LAT (Abe e al. 2023)
LST-1 + MAGIC
10 1100101
Ene gy [TeV]
0.8
1.0
1.2
lux a io
MAGIC (Aleksi e al. 2015)
Meye e al. 2010
LST-1 (Abe e al. 2023)
LST-1 + Fe mi-LAT (Abe e al. 2023)
Fig. 5. Spec al ene gy dis ibu ion o C ab Nebula ob ained wi h join
LST-1+MAGIC analysis (blue poin s and i line, wi h he s a is ical
unce ain y o he i shown as shaded egion) compa ed o e e ence
measu emen s om MAGIC-alone (o ange dashed line, Aleksi´
c e al.
2015), LST-1-alone ( ed do -dashed, Abe e al. 2023), Fe mi-LAT+
LST-1 ( iole long-dashed, Abe e al. 2023), and Fe mi-LAT+IACT
(g een do ed line, Meye e al. 2010). The bo om panel shows he a io
o he spec al model de i ed wi h he join analysis o he indi idual
e e ence spec a (see he legend).
model in ene gy bands. In Fig. 5, we p esen he esul ing spec-
al ene gy dis ibu ion econs uc ed be ween ∼60 GeV and
∼10 TeV om he o al in es iga ed da a se . The spec um is
modeled in gammapy wi h a log pa abola spec um de ined as:
dN/dE=A(E/E0)−α−βln(E/E0),(1)
wi h A=(3.48 ±0.09s a )×10−11 cm−2s−1TeV−1,E0=1TeV,
α=2.49 ±0.03s a ,β=0.117 ±0.017s a 6. The esul ing spec-
um is consis en wi h p e ious MAGIC and LST-1 measu e-
men s wi hin ∼10%.
In o de o e alua e he s abili y o he lux econs uc ion,
we compu ed he ligh cu e o he obse ed lux abo e 300 GeV
(see Fig. 6). In he igu e, he plo ed da a a e binned nigh -by-
nigh , howe e , we also in es iga ed he s abili y o he lux a
he un-by- un (co esponding o ≤20 min pe bin) ime scales.
Simila ly o o he IACT measu emen s (Aha onian e al. 2006;
Aleksi´
c e al. 2016b;Abe e al. 2023), he esul ing C ab Neb-
ula ligh cu e is no consis en wi h a cons an i (χ2/Ndo =
39.5/15 o he un-by- un calcula ions and 13.1/5 o nigh -by-
nigh ). Such an obse ed ins abili y o he lux is likely due o he
sys ema ic e ec s ela ed o, o ins ance, he a mosphe e a y-
ing du ing he obse a ions. We in es iga ed how he χ2/Ndo
s a is ics changes when a gi en le el o sys ema ic unce ain ies
is added in quad a u e o he s a is ical unce ain y. To achie e
6No e: in Aleksi´
c e al. (2016b) he log pa abola is de ined using he
base 10 loga i hm, which explains he e y di e en alues epo ed o
he βpa ame e .
A66, page 8 o 21
Abe, H., e al.: A&A, 680, A66 (2023)
59180 59200 59220 59240 59260 59280
MJD
1.0
1.2
1.4
1.6
1.8
2.0
Flux > 300 GeV [cm 2s1]
1e 10
mean lux
nigh s
Fig. 6. In eg al lux o C ab Nebula ob ained wi h join LST-1+MAGIC
analysis binned day-by-day (blue emp y poin s). The ho izon al line
shows he co esponding a e age lux om he in eg a ed spec al
model.
he co esponding i p obabili y o 0.5, an addi ional 12.7% sys-
ema ic unce ain y is equi ed in he case o un-by- un analysis,
as well as 7.9% in he case o nigh -by-nigh , which is a he le el
o e en lowe han wha was es ima ed o MAGIC.
4.3. Di e en ial lux sensi i i y
Sensi i i y is a measu e o he minimum lux o a sou ce ha can
be de ec ed wi h an ins umen in a gi en ime exposu e. In he
case o di e en ial sensi i i y, he de ec ion should be achie ed
independen ly in a pa icula ene gy bin. We ollowed he de i-
ni ion ypically used in he IACT communi y, namely, he da a
a e di ided in o 5 bins pe decade o econs uc ed ene gy and
he e en s a is ics a e escaled o 50 h o obse a ion ime. The
sensi i i y in a gi en bin hen co esponds o he gamma- ay lux
om a poin -like sou ce ha p o ides 5σsigni icance signal, as
compu ed ia Eq. (17) o Li & Ma (1983), wi h addi ional wo
condi ions: he numbe o excess e en s should be g ea e han
en and also la ge han 5% o he esidual backg ound. In he
calcula ions o he signi icance, we assume ha he backg ound
can be compu ed om i e egions wi h he same accep ance o
he signal egion.
In o de o op imize he usage o s a is ics, we applied a
k- old c oss- alida ion p ocedu e (see e.g., Mos elle & T,ukey
1968). Speci ically, he sample is di ided in o ou sub-samples,
each o hem using e e y ou h e en in he sample. Fo each
o hem, we apply cu s in a i al di ec ion and “gammaness”,
compu ed using he emaining sub-samples and op imized o
p o ide he bes sensi i i y. We hen s ack he e en s om all
sub-samples and compu e he inal sensi i i y ha is no biased
by he cu selec ion.
We es ima ed he sensi i i y bo h wi h he C ab Nebula da a
and also wi h MC simula ions. In he la e case, we used he
spec um de i ed by Aleksi´
c e al. (2015) o con e he lux
in o C ab Nebula uni s (C.U.). In he calcula ions we assume
he p o on lux o Yue e al. (2019) and he elec on lux is
a pa ame ized combina ion o Fe mi-LAT and H.E.S.S. all-
elec on spec um applying he pa ame iza ion o Eq. (2) in
Ohishi e al. (2021).
We ollowed he app oach o Aleksi´
c e al. (2012) o include
he e ec o he o he elemen s. Speci ically, we used helium
simula ions and scaled he spec um o 0.8 o he p o on spec-
um o also oughly ake he hea ie elemen s in o accoun . I
should be no ed, howe e , ha helium and highe elemen s ha e
e y li le e ec on he sensi i i y. As i can be seen in Fig. D.1,
a high “gammaness” alues, hei con ibu ion o he es ima ed
backg ound is smalle by abou an o de o magni ude han he
one o p o ons (see also Si a ek e al. 2018). I also d ops e y
as wi h es ima ed ene gy. High ejec ion o p o on e en s ia
he “gammaness” cu a high ene gies esul s in se e ely educed
backg ound s a is ics. The e o e, we collec ed he backg ound
s a is ics om he inne 1◦ adius egion and apply an ene gy-
dependen co ec ion ac o be ween a e age p o on densi y in
his egion and he densi y a came a o se o 0.4◦. The co -
ec ion ac o is compu ed using a loose (co esponding o 94%
e iciency o gamma ays) “gammaness” cu and is ypically
∼1.4.
When calcula ing he sensi i i y using he C ab Nebula da a,
he backg ound is aken a ound a di ec ion in he sky wi h he
same angula o se om he came a cen e as he sou ce. Fo
ene gies below 400 GeV, whe e he backg ound is abundan , we
used only he e lec ed sou ce posi ion o minimize sys ema ic
unce ain ies, while abo e his alue we used i e backg ound
es ima ion egions. This app oach also p o ec s agains o e -
lapping backg ound es ima ion egions a he lowes ene gies.
Mo eo e , abo e 600 GeV, whe e he backg ound is e y sca ce,
and high angula esolu ion make he op imal angula dis ance
cu om he sou ce small, we inc ease he backg ound s a is-
ics by using a b oad cu o he backg ound es ima ion egion
(θ < 0.2◦) and scale he numbe o e en s o he ac ual θ-cu .
The esul ing sensi i i ies a e compa ed wi h he LST-1 s an-
dalone and MAGIC s e eoscopic sensi i i ies in Fig. 7. The
co esponding gamma- ay and backg ound a es a e p esen ed
in Fig. 8. The MAGIC-only sensi i i y cu e has been de i ed
om he same da ase as used o he join analysis. As expec ed,
he join analysis p o ides signi ican ly be e sensi i i y.
Using he LST-1+MAGIC join analysis in he medium
ene gy ange (i.e., excluding he i s and las wo ene gy bins)
allows o he de ec ion o abou 30% (40%) weake luxes han
wha can be de ec ed wi h MAGIC-only (LST-1-only) analy-
sis. This is ela ed o he addi ion o LST-1 a he han o he
di e en analysis chain as he MAGIC-only pe o mance is com-
pa ible wi h bo h chains (see Appendix C). Such a la ge gain in
pe o mance is expec ed om he s e eoscopic echnique when
using a small numbe o elescopes, and his is also in line wi h
he p e ious MC-based s udy (Di Pie o 2019), which claims a
50% imp o emen wi h espec o MAGIC. The gain is wo old:
i s , he addi ion o he hi d elescope imp o es he showe
econs uc ion, allowing o a mo e e icien ejec ion o he
backg ound e en s. Second, he numbe o de ec ed gamma- ay
e en s is also inc eased. Since he obse a ions a e pe o med
in so wa e-coincidence mode, he igge -le el collec ion a ea
canno be inc eased wi h he addi ion o he LST-1. Howe e ,
du ing he egula analysis o da a om MAGIC, a ac ion o
he images do no su i e he quali y cu s (small showe s p oduc-
ing <50 p.e. a e ypically ejec ed). In he MAGIC-only analysis
he ejec ion o ei he M1 o M2 image is equi alen o he
ejec ion o he whole e en , since i is no possible o pe o m
s e eoscopic econs uc ion wi h only one elescope. Howe e
he LST-1 image makes i possible o eco e hese kinds o
e en s (as LST-1+M1 o LST-1+M2 e en ). On a e age, abou
20% o he econs uc ed gamma e en s has only one image om
ei he M1 o M2 (see Table 2).
A66, page 9 o 21
Abe, H., e al.: A&A, 680, A66 (2023)
77 RIKEN, Ins i u e o Physical and Chemical Resea ch, 2-1 Hi osawa,
Wako, Sai ama, 351-0198, Japan
78 Labo a o y o High Ene gy Physics, École Poly echnique Fédé ale,
1015 Lausanne, Swi ze land
79 Finnish MAGIC G oup, Space Physics and As onomy Resea ch
Uni , Uni e si y o Oulu, 90014 Oulu, Finland
80 Cha les Uni e si y, Ins i u e o Pa icle and Nuclea Physics, V
Holešo iˇ
ckách 2, 180 00 P ague 8, Czech Republic
81 Di ision o Physics and As onomy, G adua e School o Science,
Kyo o Uni e si y, Sakyo-ku, Kyo o 606-8502, Japan
82 Ins i u e o Space-Ea h En i onmen al Resea ch, Nagoya Uni e -
si y, Chikusa-ku, Nagoya 464-8601, Japan
83 Kobayashi-Maskawa Ins i u e (KMI) o he O igin o Pa icles and
he Uni e se, Nagoya Uni e si y, Chikusa-ku, Nagoya 464-8602,
Japan
84 G adua e School o Technology, Indus ial and Social Sciences,
Tokushima Uni e si y, Tokushima 770-8506, Japan
85 INAF – Osse a o io as onomico di Pado a, Vicolo Osse a o io 5,
35122 Pado a, I aly
86 Depa men o Physical Sciences, Aoyama Gakuin Uni e si y,
Fuchinobe, Sagamiha a, Kanagawa, 252-5258, Japan
87 IRFU, CEA, Uni e si é Pa is-Saclay, Bâ . 141, 91191 Gi -su -Y e e,
F ance
88 G adua e School o Science and Enginee ing, Sai ama Uni e si y,
255 Simo-Ohkubo, Saku a-ku, Sai ama ci y, Sai ama 338-8570,
Japan
89 Ins i u e o Space Sciences (ICE, CSIC), and Ins i u d’Es udis
Espacials de Ca alunya (IEEC), and Ins i ució Ca alana de Rece ca I
Es udis A ança s (ICREA), Campus UAB, Ca e de Can Mag ans,
s/n 08193 Bella e a, Spain
90 INFN MAGIC G oup, INFN Sezione di Pe ugia, 06123 Pe ugia,
I aly
91 Dipa imen o di Fisica – Uni e si á degli S udi di To ino, Via Pie o
Giu ia 1, 10125 To ino, I aly
92 Depa men o Physics, Konan Uni e si y, Kobe, Hyogo, 658-8501,
Japan
A66, page 16 o 21

Abe, H., e al.: A&A, 680, A66 (2023)
Appendix A: Collec ion a ea a di e en s ages o
he analysis
10 210 1100
Ene gy [TeV]
100
101
102
103
104
105
Collec ion a ea [m2]
MAGIC igge ed
cleaning (>=2 el.)
S e eo, in ensi y>50 p.e.
disp_di _mean<0.022
< 0.2
10 210 1100
Ene gy [TeV]
0.0
0.2
0.4
0.6
0.8
1.0
Collec ion a ea a io
cleaning (>=2 el.)
S e eo, in ensi y>50 p.e.
disp_di _mean<0.022
< 0.2
Fig. A.1. Collec ion a ea a zeni h angle o 10◦ o gamma ays a wob-
ble o se o 0.4◦ o di e en s ages o analysis: e en s igge ed by bo h
MAGIC elescopes (blue), e en s wi h a leas wo images su i ing
cleaning (o ange), s e eoscopic econs uc ion wi h a leas wo images
wi h in ensi y abo e 50 p.e. (g een), cu in consis ency o econs uc ed
a i al di ec ion om di e en images ( ed), cu in angula dis ance
be ween he ue and econs uc ed showe di ec ion ( iole ). The bo -
om plo shows he a io o he collec ion a ea a di e en s ages o he
MAGIC one a igge le el, wi h he band wid h epo ing he s a is ical
unce ain y.
In Fig. A.1, we p esen he changes o he ene gy-dependen
collec ion a ea a di e en analysis s ages. Simila ly o Abe e al.
(2023) a la ge d op o he collec ion a ea a he lowes ene -
gies (≲70 GeV) and he esul ing shi o he ene gy h eshold,
occu s due o equi ed image cleaning and in ensi y quali y cu .
The second quali y cu in he ag eemen o econs uc ed posi-
ions om di e en elescopes esul s in u he d op o he
collec ion a ea, isible up o he le el o a ew hund ed GeVs.
Ne e heless, ha cu imp o es conside ably angula esolu ion,
such ha he e ec o he θ < 0.2◦cu is much milde .
Appendix B: Valida ion o he simula ion se ings
To alida e he pa ame e ansla ion p ocedu e and o assu e
ha he necessa y simpli ica ions do no signi ican ly a ec he
esul s, a compa ison o dedica ed MC samples (p oduced inde-
penden ly wi h MagicSo and sim_ ela ay) was pe o med.
Fo each p og am we gene a ed72000 e ical gamma- ay show-
e s o ene gy 100 GeV, a impac pa ame e s uni o mly dis-
ibu ed in he ange 30 – 180 m. In Fig. B.1, we p esen he
compa ison o ue numbe o p.e. ob ained wi h bo h chains.
The wo chains a e in ag eemen wi h espec o he o al
obse ed ligh yield wi hin ∼2% wi hin he ligh pool hump (i.e.
o impac s ≲120 m and wi hin 5% in he ail o he showe . Sim-
ila ly good ag eemen is also achie ed in he igge e iciency
( a io o igge ed and simula ed e en s, see Fig. B.2).
7Those special simula ions we e done no using he a ay geome y as
shown in Fig. 1, bu a “ i ual” a ay o MAGIC elescopes loca ed a
he dis ance, 30m, 60m, ..., 180m om a ixed showe axis impac poin .
Fo highe impac dis ances he igge e iciency d ops d ama ically.
A66, page 17 o 21
Abe, H., e al.: A&A, 680, A66 (2023)
0
50
100
150
200
250
300
350
400
Numbe o p.e.
MAGIC-I
MagicSo
sim_ ela ay
40 60 80 100 120 140 160 180
Impac pa ame e [m]
0.1
0.0
0.1
Rel. di .
0
50
100
150
200
250
300
350
400
Numbe o p.e.
MAGIC-II
MagicSo
sim_ ela ay
40 60 80 100 120 140 160 180
Impac pa ame e [m]
0.1
0.0
0.1
Rel. di .
Fig. B.1. Compa ison o he ue numbe o p.e. ob ained wi h MagicSo (blue) and sim_ ela ay (o ange) o 100 GeV gamma ays o
MAGIC-I (le ) and MAGIC-II ( igh ). In he bo om panel he ela i e di e ence o sim_ ela ay wi h espec o MagicSo is shown.
0.0
0.2
0.4
0.6
0.8
1.0
T igge e iciency
MAGIC-I
MagicSo
sim_ ela ay
40 60 80 100 120 140 160 180
Impac pa ame e [m]
0.1
0.0
0.1
Di e ence
0.0
0.2
0.4
0.6
0.8
1.0
T igge e iciency
MAGIC-II
MagicSo
sim_ ela ay
40 60 80 100 120 140 160 180
Impac pa ame e [m]
0.1
0.0
0.1
Di e ence
Fig. B.2. Compa ison o he igge e iciency ob ained wi h MagicSo (blue) and sim_ ela ay (o ange) o 100 GeV gamma ays o MAGIC-
I (le ) and MAGIC-II ( igh ). In he bo om panel, he di e ence o sim_ ela ay wi h espec o MagicSo is shown.
Appendix C: MAGIC-only pe o mance wi h MCP
MCP analysis chain can be also applied o MAGIC-only e en s.
Such a use case has limi ed p ac ical applica ions because he
high le el MAGIC-only analysis can also be pe o med in he
CTAO-like amewo k s a ing om he so-called DL3 da a le el
(Nig o e al. 2019); howe e i also u ned ou o be a use ul ool
in debugging and compa ing he pe o mance o he MAGIC
s anda d chain and MCP. To alida e he analysis p ocedu es,
we pe o med such an analysis o a MAGIC C ab Nebula sam-
ple. The da a we e aken on he same nigh s as he sample used
o join analysis. Howe e , because o lack o he simul anei y
condi ion hey amoun o a la ge du a ion o 6.6 h s o e ec-
i e ime (ou o which 2.2 h s a e aken in zeni h ange <30◦
and 3.5 h s in 30 −45◦). In Fig. C.1, we compa e he ene gy
es ima ion o he same gamma-like e en s p ocessed wi h MCP
and wi h he s anda d MARS analysis chains. The MCP chain
o MAGIC-only analysis uses he same (sim_ ela ay-based)
MC simula ions as o he join analysis, howe e only MAGIC
elescopes a e selec ed. The e is no isible bias be ween he wo
analysis chains: he a e age ene gy es ima e is consis en wi hin
∼2%.
In Fig. C.2, we p esen he di e en ial sensi i i y compa ison
wi h such a da a se . In he medium ene gy ange he pe o -
mance o bo h chains is simila down o he s a is ical e o s
(howe e a hin o possibly wo se pe o mance o MCP is seen
a he lowes ene gies). Compa ing he sensi i i ies compu ed
A66, page 18 o 21
Abe, H., e al.: A&A, 680, A66 (2023)
10 210 1100101102
MMc + MARS [TeV]
10 2
10 1
100
101
102
sim el MC + magic-c a-pipe [TeV]
Compa ison o econs uc ed ene gies
100
101
102
Numbe o e en s
1.00 0.75 0.50 0.25 0.00 0.25 0.50 0.75 1.00
Rela i e di e ence
0
250
500
750
1000
1250
1500
1750
Numbe o e en s
ON
median
(= 0.015)
Fig. C.1. Compa ison o he ene gy es ima e o he same MAGIC-only e en s wi h MARS and MCP chain. Le panel: Ene gy es ima ed wi h
MCP chain s ene gy es ima ed wi h MARS. Righ panel: Rela i e di e ence o MCP-es ima ed ene gy wi h espec o he MARS-es ima ed one.
Only gamma-like e en s wi h MARS had onness alue o <0.2and in ensi y o each image abo e 100 p.e. a e used.
100
101
sensi i i y [%C.U.]
MAGIC-only (Zd 0-30)
MAGIC(only), Da a(+MCP)
MAGIC(only), MC(+MCP)
MAGIC(only), Da a(+MARS)
10 1100
E [TeV]
0.0
0.5
1.0
1.5
2.0
2.5
sensi i i y a io
Da a MCP o MC MCP
Da a: MCP o MARS
100
101
sensi i i y [%C.U.]
MAGIC-only (Zd 30-45)
MAGIC(only), Da a(+MCP)
MAGIC(only), MC(+MCP)
MAGIC(only), Da a(+MARS)
10 1100
E [TeV]
0.0
0.5
1.0
1.5
2.0
2.5
sensi i i y a io
Da a MCP o MC MCP
Da a: MCP o MARS
Fig. C.2. Di e en ial sensi i i y o MAGIC-only obse a ions o MCP analysis chain (blue ci cles o da a and o ange squa es o MC) compa ed
wi h he s anda d MARS analysis o e he same da a sample (g een iangles) o he low-zeni h (le ) and medium-zeni h ( igh ) cases. The bo om
panel shows he sensi i i y a ios ( o isibili y o unce ain y ba s, he poin s a e shi ed in he X axis by ±1%).
using he da a ob ained by obse a ions and MC simula ions, he
di e ences o MAGIC-only analysis a e ypically ∼20 −30%,
excep a he highes ene gies o low-zeni h case, whe e he
MC sensi i i y unce ain y is e y la ge. Simila di e ences a
mid ene gies be ween he da a and MC a e also epo ed in he
in eg al sensi i i y o Aleksi´
c e al. (2012).
Appendix D: Da a and MC compa isons wi h
backg ound e en s
Simila ly o he compa isons using he gamma- ay excess, we
also compa ed he bulk o he obse ed e en s (cosmic ay back-
g ound) wi h he MC simula ions. While such a compa ison is
less sensi i e o he op ical elescope pa ame e s, i is mo e di ec
as i does no equi e any p eselec ion o e en s. The esul s
o he compa isons a e shown in Fig. D.1. The main con ibu-
ion in he backg ound e en s be o e gamma-selec ion cu s is
caused by p o ons, o which we adop ed he spec um om Yue
e al. (2019). Howe e , we also ake in o accoun helium (wi h
a co ec ion o hea ie elemen s; see Sec ion 4.3 o de ails)
and elec ons. Only e en s wi h econs uc ed di ec ion wi hin
1◦ om he came a cen e a e used. Mo eo e , o a oid con ami-
na ion om he C ab Nebula gamma ays, a egion wi h a adius
o 0.2◦a ound he nominal sou ce posi ion has been excluded.
We also excluded MAGIC-only e en s wi hou an LST-1 coun-
e pa . The ob ained no maliza ion o he dis ibu ions is in
ag eemen wi h he cosmic- ay measu emen s. The applied cu
o he in ensi y o >50 p.e. is su icien o ep oduce p op-
e ly he in ensi y dis ibu ion o bo h MAGIC elescopes. In he
case o LST-1 howe e a sligh misma ch ≲80 p.e. is isible,
which was also epo ed in Abe e al. (2023) and explained
as an e ec o less s able igge h esholds in he da a un il
Augus 2021. Bo h he wid h and leng h pa ame e dis ibu ions
a e closely ma ching be ween he da a and MC simula ions. The
A66, page 19 o 21
Abe, H., e al.: A&A, 680, A66 (2023)
1.5 2.0 2.5 3.0 3.5 4.0 4.5
Log10(In ensi y), LST-1
101
102
103
104
Numbe o e en s
Da a
MC p
MC He
MC e
MC (all)
1.5 2.0 2.5 3.0 3.5 4.0 4.5
Log10(In ensi y), MAGIC-1
101
102
103
104
Numbe o e en s
Da a
MC p
MC He
MC e
MC (all)
1.5 2.0 2.5 3.0 3.5 4.0 4.5
Log10(In ensi y), MAGIC-2
101
102
103
104
Numbe o e en s
Da a
MC p
MC He
MC e
MC (all)
0.0 0.1 0.2 0.3 0.4 0.5
Leng h[m], LST-1
101
102
103
104
Numbe o e en s
Da a
MC p
MC He
MC e
MC (all)
0.0 0.1 0.2 0.3 0.4 0.5
Leng h[m], MAGIC-1
101
102
103
104
Numbe o e en s
Da a
MC p
MC He
MC e
MC (all)
0.0 0.1 0.2 0.3 0.4 0.5
Leng h[m], MAGIC-2
101
102
103
104
Numbe o e en s
Da a
MC p
MC He
MC e
MC (all)
0.000 0.025 0.050 0.075 0.100 0.125 0.150 0.175 0.200
Wid h[m], LST-1
101
102
103
104
Numbe o e en s
Da a
MC p
MC He
MC e
MC (all)
0.000 0.025 0.050 0.075 0.100 0.125 0.150 0.175 0.200
Wid h[m], MAGIC-1
101
102
103
104
Numbe o e en s
Da a
MC p
MC He
MC e
MC (all)
0.000 0.025 0.050 0.075 0.100 0.125 0.150 0.175 0.200
Wid h[m], MAGIC-2
101
102
103
104
Numbe o e en s
Da a
MC p
MC He
MC e
MC (all)
0.0 0.2 0.4 0.6 0.8 1.0
Gammaness, LST-1
102
103
104
Numbe o e en s
Da a
MC p
MC He
MC e
MC (all)
0.0 0.2 0.4 0.6 0.8 1.0
Gammaness, MAGIC-1
102
103
104
Numbe o e en s
Da a
MC p
MC He
MC e
MC (all)
0.0 0.2 0.4 0.6 0.8 1.0
Gammaness, MAGIC-2
102
103
104
Numbe o e en s
Da a
MC p
MC He
MC e
MC (all)
0 2500 5000 7500 10000 12500 15000 17500 20000
Heigh o maximum [m]
101
102
103
104
Numbe o e en s
Da a
MC p
MC He
MC e
MC (all)
0.0 0.2 0.4 0.6 0.8 1.0
Gammaness (a e age)
102
103
104
Numbe o e en s
Da a
MC p
MC He
MC e
MC (all)
Fig. D.1. Compa ison o image pa ame e s be ween he Da a and MC simula ions ( o zeni h dis ance below 30◦). Top ou ows o panels show
in ensi y, leng h, wid h, and indi idual elescope “gammaness” ( om op o bo om) o LST-1 (le ), MAGIC-I (middle) and MAGIC-II ( igh ).
The bo om ow shows s e eoscopic pa ame e s: heigh o he showe maximum (le ) and a e aged “gammaness” ( igh ). In all he panels: he hick
blue line shows he da a, while he hick magen a line shows he sum o all MC componen s. Thin lines show he indi idual componen s: p o ons
(o ange), helium (wi h an addi ional co ec ion o hea ie elemen s (g een), and all-elec ons ( ed).
“gammaness” dis ibu ion o indi idual elescopes (as well as he
elescopes-a e aged alues) is ela i ely well ep oduced wi h MC simula ions. In he case o he heigh o he showe maxi-
mum, he dis ibu ion shape is ep oduced well, howe e , a small
shi is also p esen .
A66, page 20 o 21
Abe, H., e al.: A&A, 680, A66 (2023)
Appendix E: Addi ional ables
Fo con enience and possible compa isons wi h o he ins u-
men s in his sec ion we epo he nume ical alues o he
pe o mance pa ame e s. In Tables E.1 and E.2, we summa ize
he gamma- ay excess a es, backg ound a es, and de i ed sen-
si i i y om C ab Nebula da a sample and MC simula ions. In
Fig. E.3, we epo he ene gy esolu ion de i ed wi h di e en
de ini ions.
E0Gamma a e Backg ound a e Sensi i i y (da a) Sensi i i y (MC)
[TeV] (da a), [min−1](da a), [min−1][%C.U.] [10−12cm−2s−1e g]
0.0501 0.27±0.17 0.54±0.11 28.0±19.0 21.1±2.1
0.0794 2.59±0.34 1.50±0.18 4.81±0.82 4.41±0.22
0.126 2.68±0.29 0.65±0.12 3.08±0.51 2.41±0.11
0.2 2.07±0.23 0.272±0.075 2.61±0.54 1.237±0.089
0.316 2.13±0.21 0.021±0.021 0.77±0.4 0.946±0.084
0.501 1.23±0.16 0.025±0.010 1.44±0.36 0.882±0.086
0.794 0.81±0.13 0.0041±0.0017 1.03±0.27 0.610±0.073
1.26 0.458±0.098 0.0016±0.0011 1.29±0.54 0.537±0.087
2.0 0.271±0.075 0.00088±0.00088 1.8±1.0 0.69±0.13
3.16 0.164±0.059 0.0032±0.0023 4.6±2.4 0.82±0.21
5.01 0.104±0.047 – 3.2±1.4 0.96±0.32
7.94 0.021±0.021 – 16.0±16.0 0.80±0.14
Table E.1. Ra es and sensi i i y alues o C ab Nebula obse a ions and MC simula ions a zeni h dis ance <30◦, as plo ed in Figu es 7and 8
(le panels).
No e: Ra es a e in eg a ed in 0.2 decades cen e ed on E0 alue. Da a sensi i i ies a e p o ided in he pe cen age o C ab Nebula lux, while MC
sensi i i ies in SED uni s.
E0Gamma a e Backg ound a e Sensi i i y (da a) Sensi i i y (MC)
[TeV] (da a), [min−1](da a), [min−1][%C.U.] [10−12cm−2s−1e g]
0.0794 0.59±0.12 0.715±0.072 14.6±3.4 13.0±0.96
0.126 2.43±0.19 1.42±0.10 4.99±0.51 3.86±0.16
0.2 2.65±0.15 0.307±0.047 2.16±0.24 1.747±0.072
0.316 2.03±0.13 0.093±0.026 1.6±0.26 1.206±0.064
0.501 1.171±0.093 0.0229±0.0057 1.46±0.22 0.798±0.047
0.794 0.899±0.081 0.0093±0.0016 1.29±0.16 0.595±0.047
1.26 0.806±0.076 0.0096±0.0016 1.45±0.19 0.458±0.048
2.0 0.319±0.048 0.00264±0.00076 2.21±0.46 0.458±0.062
3.16 0.185±0.036 0.0007±0.00049 2.46±0.99 0.525±0.089
5.01 0.113±0.029 0.00138±0.00056 5.0±1.6 0.67±0.15
7.94 0.084±0.025 0.00148±0.00086 6.8±2.9 0.70±0.20
Table E.2. As in Table E.1 bu o zeni h dis ance 30 −45◦(see also Figu es 7and 8, igh panels).
E Res. 68% Res. (S.D.) Res. ( i )
[TeV] [%] [%] [%]
0.0794 19.2±0.1 20.27±0.06 16.16±0.05
0.126 16.26±0.07 17.32±0.04 15.63±0.04
0.2 15.83±0.08 16.82±0.04 15.34±0.04
0.316 14.68±0.08 15.91±0.04 14.5±0.04
0.501 13.82±0.08 15.7±0.05 13.99±0.04
0.794 13.54±0.09 16.24±0.06 13.84±0.05
1.26 13.5±0.1 17.32±0.07 13.87±0.06
2.0 13.3±0.1 18.18±0.09 13.57±0.07
3.16 12.7±0.1 19.5±0.1 13.63±0.08
5.01 13.9±0.2 20.9±0.2 14.4±0.1
7.94 15.6±0.3 20.4±0.2 15.0±0.1
12.6 15.9±0.4 20.4±0.2 15.2±0.2
Table E.3. Ene gy esolu ion a zeni h dis ance 23.6◦co esponding o Fig. 12.
No e: The columns epo : ue ene gy, 68% con ainmen esolu ion, s anda d de ia ion (S.D.), and ail-less i .
A66, page 21 o 21