11institutetext:  Dublin Institute for Advanced Studies, 31 Fitzwilliam Place,
Dublin 2, Ireland 22institutetext: Max-Planck-Institut für Kernphysik, P.O.
Box 103980, D 69029 Heidelberg, Germany 33institutetext: Laboratoire Leprince-
Ringuet, École Polytechnique, CNRS, Institut Polytechnique de Paris, F-91128
Palaiseau, France 44institutetext: University of Namibia, Department of
Physics, Private Bag 13301, Windhoek 10005, Namibia 55institutetext: Centre
for Space Research, North-West University, Potchefstroom 2520, South Africa
66institutetext: DESY, D-15738 Zeuthen, Germany 77institutetext: Université de
Paris, CNRS, Astroparticule et Cosmologie, F-75013 Paris, France
88institutetext: Department of Physics and Electrical Engineering, Linnaeus
University, 351 95 Växjö, Sweden 99institutetext: Institut für Physik,
Humboldt-Universität zu Berlin, Newtonstr. 15, D 12489 Berlin, Germany
1010institutetext: Institut für Astronomie und Astrophysik, Universität
Tübingen, Sand 1, D 72076 Tübingen, Germany 1111institutetext: Université
Savoie Mont Blanc, CNRS, Laboratoire d’Annecy de Physique des Particules -
IN2P3, 74000 Annecy, France 1212institutetext: IRFU, CEA, Université Paris-
Saclay, F-91191 Gif-sur-Yvette, France 1313institutetext: Astronomical
Observatory, The University of Warsaw, Al. Ujazdowskie 4, 00-478 Warsaw,
Poland 1414institutetext: Sorbonne Université, Université Paris Diderot,
Sorbonne Paris Cité, CNRS/IN2P3, Laboratoire de Physique Nucléaire et de
Hautes Energies, LPNHE, 4 Place Jussieu, F-75252 Paris, France
1515institutetext: Instytut Fizyki Ja̧drowej PAN, ul. Radzikowskiego 152,
31-342 Kraków, Poland 1616institutetext: School of Physics, University of the
Witwatersrand, 1 Jan Smuts Avenue, Braamfontein, Johannesburg, 2050 South
Africa 1717institutetext: Laboratoire Univers et Théories, Observatoire de
Paris, Université PSL, CNRS, Université de Paris, 92190 Meudon, France
1818institutetext: Aix Marseille Université, CNRS/IN2P3, CPPM, Marseille,
France 1919institutetext: School of Physical Sciences, University of Adelaide,
Adelaide 5005, Australia 2020institutetext: Friedrich-Alexander-Universität
Erlangen-Nürnberg, Erlangen Centre for Astroparticle Physics, Erwin-Rommel-
Str. 1, D 91058 Erlangen, Germany 2121institutetext: Laboratoire Univers et
Particules de Montpellier, Université Montpellier, CNRS/IN2P3, CC 72, Place
Eugène Bataillon, F-34095 Montpellier Cedex 5, France 2222institutetext:
Landessternwarte, Universität Heidelberg, Königstuhl, D 69117 Heidelberg,
Germany 2323institutetext: Université Bordeaux, CNRS, LP2I Bordeaux, UMR 5797,
F-33170 Gradignan, France 2424institutetext: University of Oxford, Department
of Physics, Denys Wilkinson Building, Keble Road, Oxford OX1 3RH, UK
2525institutetext: Institut für Astro- und Teilchenphysik, Leopold-Franzens-
Universität Innsbruck, A-6020 Innsbruck, Austria 2626institutetext:
Universität Hamburg, Institut für Experimentalphysik, Luruper Chaussee 149, D
22761 Hamburg, Germany 2727institutetext: Obserwatorium Astronomiczne,
Uniwersytet Jagielloński, ul. Orla 171, 30-244 Kraków, Poland
2828institutetext: Institute of Astronomy, Faculty of Physics, Astronomy and
Informatics, Nicolaus Copernicus University, Grudziadzka 5, 87-100 Torun,
Poland 2929institutetext: Nicolaus Copernicus Astronomical Center, Polish
Academy of Sciences, ul. Bartycka 18, 00-716 Warsaw, Poland 3030institutetext:
GRAPPA, Anton Pannekoek Institute for Astronomy, University of Amsterdam,
Science Park 904, 1098 XH Amsterdam, The Netherlands 3131institutetext:
Yerevan Physics Institute, 2 Alikhanian Brothers St., 375036 Yerevan, Armenia
3232institutetext: Institut für Physik und Astronomie, Universität Potsdam,
Karl-Liebknecht-Strasse 24/25, D 14476 Potsdam, Germany 3333institutetext:
Department of Physics, Konan University, 8-9-1 Okamoto, Higashinada, Kobe,
Hyogo 658-8501, Japan 3434institutetext: Kavli Institute for the Physics and
Mathematics of the Universe (WPI), The University of Tokyo Institutes for
Advanced Study (UTIAS), The University of Tokyo, 5-1-5 Kashiwa-no-Ha, Kashiwa,
Chiba, 277-8583, Japan 3535institutetext: RIKEN, 2-1 Hirosawa, Wako, Saitama
351-0198, Japan 3636institutetext: Department of Physics, University of the
Free State, PO Box 339, Bloemfontein 9300, South Africa 3737institutetext:
School of Physics, University of New South Wales, Sydney, NSW 2052, Australia
3838institutetext: Armagh Observatory and Planetarium, Armagh, BT61 7HT,
Northern Ireland, United Kingdom 3939institutetext: Western Sydney University,
Locked Bag 1797 Penrith South DC, NSW 2751, Australia

# A deep spectromorphological study of the $\gamma$-ray emission surrounding
the young massive stellar cluster Westerlund 1

F. Aharonian  A deep spectromorphological study of the $\gamma$-ray emission
surrounding the young massive stellar cluster Westerlund 1A deep
spectromorphological study of the $\gamma$-ray emission surrounding the young
massive stellar cluster Westerlund 1A deep spectromorphological study of the
$\gamma$-ray emission surrounding the young massive stellar cluster Westerlund
1A deep spectromorphological study of the $\gamma$-ray emission surrounding
the young massive stellar cluster Westerlund 1 H. Ashkar A deep
spectromorphological study of the $\gamma$-ray emission surrounding the young
massive stellar cluster Westerlund 1A deep spectromorphological study of the
$\gamma$-ray emission surrounding the young massive stellar cluster Westerlund
1 M. Backes A deep spectromorphological study of the $\gamma$-ray emission
surrounding the young massive stellar cluster Westerlund 1A deep
spectromorphological study of the $\gamma$-ray emission surrounding the young
massive stellar cluster Westerlund 1A deep spectromorphological study of the
$\gamma$-ray emission surrounding the young massive stellar cluster Westerlund
1A deep spectromorphological study of the $\gamma$-ray emission surrounding
the young massive stellar cluster Westerlund 1 V. Barbosa Martins A deep
spectromorphological study of the $\gamma$-ray emission surrounding the young
massive stellar cluster Westerlund 1A deep spectromorphological study of the
$\gamma$-ray emission surrounding the young massive stellar cluster Westerlund
1 Y. Becherini A deep spectromorphological study of the $\gamma$-ray emission
surrounding the young massive stellar cluster Westerlund 1A deep
spectromorphological study of the $\gamma$-ray emission surrounding the young
massive stellar cluster Westerlund 1A deep spectromorphological study of the
$\gamma$-ray emission surrounding the young massive stellar cluster Westerlund
1A deep spectromorphological study of the $\gamma$-ray emission surrounding
the young massive stellar cluster Westerlund 1 D. Berge A deep
spectromorphological study of the $\gamma$-ray emission surrounding the young
massive stellar cluster Westerlund 1A deep spectromorphological study of the
$\gamma$-ray emission surrounding the young massive stellar cluster Westerlund
1A deep spectromorphological study of the $\gamma$-ray emission surrounding
the young massive stellar cluster Westerlund 1A deep spectromorphological
study of the $\gamma$-ray emission surrounding the young massive stellar
cluster Westerlund 1 B. Bi A deep spectromorphological study of the
$\gamma$-ray emission surrounding the young massive stellar cluster Westerlund
1A deep spectromorphological study of the $\gamma$-ray emission surrounding
the young massive stellar cluster Westerlund 1 M. Böttcher A deep
spectromorphological study of the $\gamma$-ray emission surrounding the young
massive stellar cluster Westerlund 1A deep spectromorphological study of the
$\gamma$-ray emission surrounding the young massive stellar cluster Westerlund
1 M. de Bony de Lavergne A deep spectromorphological study of the $\gamma$-ray
emission surrounding the young massive stellar cluster Westerlund 1A deep
spectromorphological study of the $\gamma$-ray emission surrounding the young
massive stellar cluster Westerlund 1 F. Bradascio A deep spectromorphological
study of the $\gamma$-ray emission surrounding the young massive stellar
cluster Westerlund 1A deep spectromorphological study of the $\gamma$-ray
emission surrounding the young massive stellar cluster Westerlund 1 R. Brose A
deep spectromorphological study of the $\gamma$-ray emission surrounding the
young massive stellar cluster Westerlund 1A deep spectromorphological study of
the $\gamma$-ray emission surrounding the young massive stellar cluster
Westerlund 1 F. Brun A deep spectromorphological study of the $\gamma$-ray
emission surrounding the young massive stellar cluster Westerlund 1A deep
spectromorphological study of the $\gamma$-ray emission surrounding the young
massive stellar cluster Westerlund 1 T. Bulik A deep spectromorphological
study of the $\gamma$-ray emission surrounding the young massive stellar
cluster Westerlund 1A deep spectromorphological study of the $\gamma$-ray
emission surrounding the young massive stellar cluster Westerlund 1 C. Burger-
Scheidlin A deep spectromorphological study of the $\gamma$-ray emission
surrounding the young massive stellar cluster Westerlund 1A deep
spectromorphological study of the $\gamma$-ray emission surrounding the young
massive stellar cluster Westerlund 1 F. Cangemi A deep spectromorphological
study of the $\gamma$-ray emission surrounding the young massive stellar
cluster Westerlund 1A deep spectromorphological study of the $\gamma$-ray
emission surrounding the young massive stellar cluster Westerlund 1 S. Caroff
A deep spectromorphological study of the $\gamma$-ray emission surrounding the
young massive stellar cluster Westerlund 1A deep spectromorphological study of
the $\gamma$-ray emission surrounding the young massive stellar cluster
Westerlund 1 S. Casanova A deep spectromorphological study of the $\gamma$-ray
emission surrounding the young massive stellar cluster Westerlund 1A deep
spectromorphological study of the $\gamma$-ray emission surrounding the young
massive stellar cluster Westerlund 1 M. Cerruti A deep spectromorphological
study of the $\gamma$-ray emission surrounding the young massive stellar
cluster Westerlund 1A deep spectromorphological study of the $\gamma$-ray
emission surrounding the young massive stellar cluster Westerlund 1 T. Chand A
deep spectromorphological study of the $\gamma$-ray emission surrounding the
young massive stellar cluster Westerlund 1A deep spectromorphological study of
the $\gamma$-ray emission surrounding the young massive stellar cluster
Westerlund 1 S. Chandra A deep spectromorphological study of the $\gamma$-ray
emission surrounding the young massive stellar cluster Westerlund 1A deep
spectromorphological study of the $\gamma$-ray emission surrounding the young
massive stellar cluster Westerlund 1 A. Chen A deep spectromorphological study
of the $\gamma$-ray emission surrounding the young massive stellar cluster
Westerlund 1A deep spectromorphological study of the $\gamma$-ray emission
surrounding the young massive stellar cluster Westerlund 1 O. Chibueze A deep
spectromorphological study of the $\gamma$-ray emission surrounding the young
massive stellar cluster Westerlund 1A deep spectromorphological study of the
$\gamma$-ray emission surrounding the young massive stellar cluster Westerlund
1 P. Cristofari A deep spectromorphological study of the $\gamma$-ray emission
surrounding the young massive stellar cluster Westerlund 1A deep
spectromorphological study of the $\gamma$-ray emission surrounding the young
massive stellar cluster Westerlund 1 J. Damascene Mbarubucyeye A deep
spectromorphological study of the $\gamma$-ray emission surrounding the young
massive stellar cluster Westerlund 1A deep spectromorphological study of the
$\gamma$-ray emission surrounding the young massive stellar cluster Westerlund
1 A. Djannati-Ataï A deep spectromorphological study of the $\gamma$-ray
emission surrounding the young massive stellar cluster Westerlund 1A deep
spectromorphological study of the $\gamma$-ray emission surrounding the young
massive stellar cluster Westerlund 1 J.-P. Ernenwein A deep
spectromorphological study of the $\gamma$-ray emission surrounding the young
massive stellar cluster Westerlund 1A deep spectromorphological study of the
$\gamma$-ray emission surrounding the young massive stellar cluster Westerlund
1 K. Feijen A deep spectromorphological study of the $\gamma$-ray emission
surrounding the young massive stellar cluster Westerlund 1A deep
spectromorphological study of the $\gamma$-ray emission surrounding the young
massive stellar cluster Westerlund 1 G. Fichet de Clairfontaine A deep
spectromorphological study of the $\gamma$-ray emission surrounding the young
massive stellar cluster Westerlund 1A deep spectromorphological study of the
$\gamma$-ray emission surrounding the young massive stellar cluster Westerlund
1 G. Fontaine A deep spectromorphological study of the $\gamma$-ray emission
surrounding the young massive stellar cluster Westerlund 1A deep
spectromorphological study of the $\gamma$-ray emission surrounding the young
massive stellar cluster Westerlund 1 S. Funk A deep spectromorphological study
of the $\gamma$-ray emission surrounding the young massive stellar cluster
Westerlund 1A deep spectromorphological study of the $\gamma$-ray emission
surrounding the young massive stellar cluster Westerlund 1 S. Gabici A deep
spectromorphological study of the $\gamma$-ray emission surrounding the young
massive stellar cluster Westerlund 1A deep spectromorphological study of the
$\gamma$-ray emission surrounding the young massive stellar cluster Westerlund
1 Y.A. Gallant A deep spectromorphological study of the $\gamma$-ray emission
surrounding the young massive stellar cluster Westerlund 1A deep
spectromorphological study of the $\gamma$-ray emission surrounding the young
massive stellar cluster Westerlund 1 S. Ghafourizadeh A deep
spectromorphological study of the $\gamma$-ray emission surrounding the young
massive stellar cluster Westerlund 1A deep spectromorphological study of the
$\gamma$-ray emission surrounding the young massive stellar cluster Westerlund
1 G. Giavitto A deep spectromorphological study of the $\gamma$-ray emission
surrounding the young massive stellar cluster Westerlund 1A deep
spectromorphological study of the $\gamma$-ray emission surrounding the young
massive stellar cluster Westerlund 1 L. Giunti A deep spectromorphological
study of the $\gamma$-ray emission surrounding the young massive stellar
cluster Westerlund 1A deep spectromorphological study of the $\gamma$-ray
emission surrounding the young massive stellar cluster Westerlund 1A deep
spectromorphological study of the $\gamma$-ray emission surrounding the young
massive stellar cluster Westerlund 1A deep spectromorphological study of the
$\gamma$-ray emission surrounding the young massive stellar cluster Westerlund
1 D. Glawion A deep spectromorphological study of the $\gamma$-ray emission
surrounding the young massive stellar cluster Westerlund 1A deep
spectromorphological study of the $\gamma$-ray emission surrounding the young
massive stellar cluster Westerlund 1 J.F. Glicenstein A deep
spectromorphological study of the $\gamma$-ray emission surrounding the young
massive stellar cluster Westerlund 1A deep spectromorphological study of the
$\gamma$-ray emission surrounding the young massive stellar cluster Westerlund
1 P. Goswami A deep spectromorphological study of the $\gamma$-ray emission
surrounding the young massive stellar cluster Westerlund 1A deep
spectromorphological study of the $\gamma$-ray emission surrounding the young
massive stellar cluster Westerlund 1 M.-H. Grondin A deep spectromorphological
study of the $\gamma$-ray emission surrounding the young massive stellar
cluster Westerlund 1A deep spectromorphological study of the $\gamma$-ray
emission surrounding the young massive stellar cluster Westerlund 1 L.K. Härer
A deep spectromorphological study of the $\gamma$-ray emission surrounding the
young massive stellar cluster Westerlund 1A deep spectromorphological study of
the $\gamma$-ray emission surrounding the young massive stellar cluster
Westerlund 1 M. Haupt A deep spectromorphological study of the $\gamma$-ray
emission surrounding the young massive stellar cluster Westerlund 1A deep
spectromorphological study of the $\gamma$-ray emission surrounding the young
massive stellar cluster Westerlund 1 J.A. Hinton A deep spectromorphological
study of the $\gamma$-ray emission surrounding the young massive stellar
cluster Westerlund 1A deep spectromorphological study of the $\gamma$-ray
emission surrounding the young massive stellar cluster Westerlund 1 M. Hörbe A
deep spectromorphological study of the $\gamma$-ray emission surrounding the
young massive stellar cluster Westerlund 1A deep spectromorphological study of
the $\gamma$-ray emission surrounding the young massive stellar cluster
Westerlund 1 W. Hofmann A deep spectromorphological study of the $\gamma$-ray
emission surrounding the young massive stellar cluster Westerlund 1A deep
spectromorphological study of the $\gamma$-ray emission surrounding the young
massive stellar cluster Westerlund 1 T. L. Holch A deep spectromorphological
study of the $\gamma$-ray emission surrounding the young massive stellar
cluster Westerlund 1A deep spectromorphological study of the $\gamma$-ray
emission surrounding the young massive stellar cluster Westerlund 1 M. Holler
A deep spectromorphological study of the $\gamma$-ray emission surrounding the
young massive stellar cluster Westerlund 1A deep spectromorphological study of
the $\gamma$-ray emission surrounding the young massive stellar cluster
Westerlund 1 D. Horns A deep spectromorphological study of the $\gamma$-ray
emission surrounding the young massive stellar cluster Westerlund 1A deep
spectromorphological study of the $\gamma$-ray emission surrounding the young
massive stellar cluster Westerlund 1 M. Jamrozy A deep spectromorphological
study of the $\gamma$-ray emission surrounding the young massive stellar
cluster Westerlund 1A deep spectromorphological study of the $\gamma$-ray
emission surrounding the young massive stellar cluster Westerlund 1 V. Joshi A
deep spectromorphological study of the $\gamma$-ray emission surrounding the
young massive stellar cluster Westerlund 1A deep spectromorphological study of
the $\gamma$-ray emission surrounding the young massive stellar cluster
Westerlund 1 I. Jung-Richardt A deep spectromorphological study of the
$\gamma$-ray emission surrounding the young massive stellar cluster Westerlund
1A deep spectromorphological study of the $\gamma$-ray emission surrounding
the young massive stellar cluster Westerlund 1 E. Kasai A deep
spectromorphological study of the $\gamma$-ray emission surrounding the young
massive stellar cluster Westerlund 1A deep spectromorphological study of the
$\gamma$-ray emission surrounding the young massive stellar cluster Westerlund
1 K. Katarzyński A deep spectromorphological study of the $\gamma$-ray
emission surrounding the young massive stellar cluster Westerlund 1A deep
spectromorphological study of the $\gamma$-ray emission surrounding the young
massive stellar cluster Westerlund 1 U. Katz A deep spectromorphological study
of the $\gamma$-ray emission surrounding the young massive stellar cluster
Westerlund 1A deep spectromorphological study of the $\gamma$-ray emission
surrounding the young massive stellar cluster Westerlund 1 B. Khélifi A deep
spectromorphological study of the $\gamma$-ray emission surrounding the young
massive stellar cluster Westerlund 1A deep spectromorphological study of the
$\gamma$-ray emission surrounding the young massive stellar cluster Westerlund
1 W. Kluźniak A deep spectromorphological study of the $\gamma$-ray emission
surrounding the young massive stellar cluster Westerlund 1A deep
spectromorphological study of the $\gamma$-ray emission surrounding the young
massive stellar cluster Westerlund 1 Nu. Komin A deep spectromorphological
study of the $\gamma$-ray emission surrounding the young massive stellar
cluster Westerlund 1A deep spectromorphological study of the $\gamma$-ray
emission surrounding the young massive stellar cluster Westerlund 1 K. Kosack
A deep spectromorphological study of the $\gamma$-ray emission surrounding the
young massive stellar cluster Westerlund 1A deep spectromorphological study of
the $\gamma$-ray emission surrounding the young massive stellar cluster
Westerlund 1 D. Kostunin A deep spectromorphological study of the $\gamma$-ray
emission surrounding the young massive stellar cluster Westerlund 1A deep
spectromorphological study of the $\gamma$-ray emission surrounding the young
massive stellar cluster Westerlund 1 G. Kukec Mezek A deep
spectromorphological study of the $\gamma$-ray emission surrounding the young
massive stellar cluster Westerlund 1A deep spectromorphological study of the
$\gamma$-ray emission surrounding the young massive stellar cluster Westerlund
1 R.G. Lang A deep spectromorphological study of the $\gamma$-ray emission
surrounding the young massive stellar cluster Westerlund 1A deep
spectromorphological study of the $\gamma$-ray emission surrounding the young
massive stellar cluster Westerlund 1 S. Le Stum A deep spectromorphological
study of the $\gamma$-ray emission surrounding the young massive stellar
cluster Westerlund 1A deep spectromorphological study of the $\gamma$-ray
emission surrounding the young massive stellar cluster Westerlund 1 A. Lemière
A deep spectromorphological study of the $\gamma$-ray emission surrounding the
young massive stellar cluster Westerlund 1A deep spectromorphological study of
the $\gamma$-ray emission surrounding the young massive stellar cluster
Westerlund 1 M. Lemoine-Goumard A deep spectromorphological study of the
$\gamma$-ray emission surrounding the young massive stellar cluster Westerlund
1A deep spectromorphological study of the $\gamma$-ray emission surrounding
the young massive stellar cluster Westerlund 1 J.-P. Lenain A deep
spectromorphological study of the $\gamma$-ray emission surrounding the young
massive stellar cluster Westerlund 1A deep spectromorphological study of the
$\gamma$-ray emission surrounding the young massive stellar cluster Westerlund
1 F. Leuschner A deep spectromorphological study of the $\gamma$-ray emission
surrounding the young massive stellar cluster Westerlund 1A deep
spectromorphological study of the $\gamma$-ray emission surrounding the young
massive stellar cluster Westerlund 1 T. Lohse A deep spectromorphological
study of the $\gamma$-ray emission surrounding the young massive stellar
cluster Westerlund 1A deep spectromorphological study of the $\gamma$-ray
emission surrounding the young massive stellar cluster Westerlund 1 A.
Luashvili A deep spectromorphological study of the $\gamma$-ray emission
surrounding the young massive stellar cluster Westerlund 1A deep
spectromorphological study of the $\gamma$-ray emission surrounding the young
massive stellar cluster Westerlund 1 I. Lypova A deep spectromorphological
study of the $\gamma$-ray emission surrounding the young massive stellar
cluster Westerlund 1A deep spectromorphological study of the $\gamma$-ray
emission surrounding the young massive stellar cluster Westerlund 1 J. Mackey
A deep spectromorphological study of the $\gamma$-ray emission surrounding the
young massive stellar cluster Westerlund 1A deep spectromorphological study of
the $\gamma$-ray emission surrounding the young massive stellar cluster
Westerlund 1 J. Majumdar A deep spectromorphological study of the $\gamma$-ray
emission surrounding the young massive stellar cluster Westerlund 1A deep
spectromorphological study of the $\gamma$-ray emission surrounding the young
massive stellar cluster Westerlund 1 D. Malyshev A deep spectromorphological
study of the $\gamma$-ray emission surrounding the young massive stellar
cluster Westerlund 1A deep spectromorphological study of the $\gamma$-ray
emission surrounding the young massive stellar cluster Westerlund 1 V.
Marandon A deep spectromorphological study of the $\gamma$-ray emission
surrounding the young massive stellar cluster Westerlund 1A deep
spectromorphological study of the $\gamma$-ray emission surrounding the young
massive stellar cluster Westerlund 1 P. Marchegiani A deep
spectromorphological study of the $\gamma$-ray emission surrounding the young
massive stellar cluster Westerlund 1A deep spectromorphological study of the
$\gamma$-ray emission surrounding the young massive stellar cluster Westerlund
1 A. Marcowith A deep spectromorphological study of the $\gamma$-ray emission
surrounding the young massive stellar cluster Westerlund 1A deep
spectromorphological study of the $\gamma$-ray emission surrounding the young
massive stellar cluster Westerlund 1 G. Martí-Devesa A deep
spectromorphological study of the $\gamma$-ray emission surrounding the young
massive stellar cluster Westerlund 1A deep spectromorphological study of the
$\gamma$-ray emission surrounding the young massive stellar cluster Westerlund
1 R. Marx A deep spectromorphological study of the $\gamma$-ray emission
surrounding the young massive stellar cluster Westerlund 1A deep
spectromorphological study of the $\gamma$-ray emission surrounding the young
massive stellar cluster Westerlund 1 G. Maurin A deep spectromorphological
study of the $\gamma$-ray emission surrounding the young massive stellar
cluster Westerlund 1A deep spectromorphological study of the $\gamma$-ray
emission surrounding the young massive stellar cluster Westerlund 1 M. Meyer A
deep spectromorphological study of the $\gamma$-ray emission surrounding the
young massive stellar cluster Westerlund 1A deep spectromorphological study of
the $\gamma$-ray emission surrounding the young massive stellar cluster
Westerlund 1 A. Mitchell A deep spectromorphological study of the $\gamma$-ray
emission surrounding the young massive stellar cluster Westerlund 1A deep
spectromorphological study of the $\gamma$-ray emission surrounding the young
massive stellar cluster Westerlund 1A deep spectromorphological study of the
$\gamma$-ray emission surrounding the young massive stellar cluster Westerlund
1A deep spectromorphological study of the $\gamma$-ray emission surrounding
the young massive stellar cluster Westerlund 1 R. Moderski A deep
spectromorphological study of the $\gamma$-ray emission surrounding the young
massive stellar cluster Westerlund 1A deep spectromorphological study of the
$\gamma$-ray emission surrounding the young massive stellar cluster Westerlund
1 L. Mohrmann , Corresponding authors;
A deep spectromorphological study of the $\gamma$-ray emission surrounding the
young massive stellar cluster Westerlund 1A deep spectromorphological study of
the $\gamma$-ray emission surrounding the young massive stellar cluster
Westerlund 1<EMAIL_ADDRESS>A. Montanari A deep
spectromorphological study of the $\gamma$-ray emission surrounding the young
massive stellar cluster Westerlund 1A deep spectromorphological study of the
$\gamma$-ray emission surrounding the young massive stellar cluster Westerlund
1 E. Moulin A deep spectromorphological study of the $\gamma$-ray emission
surrounding the young massive stellar cluster Westerlund 1A deep
spectromorphological study of the $\gamma$-ray emission surrounding the young
massive stellar cluster Westerlund 1 J. Muller A deep spectromorphological
study of the $\gamma$-ray emission surrounding the young massive stellar
cluster Westerlund 1A deep spectromorphological study of the $\gamma$-ray
emission surrounding the young massive stellar cluster Westerlund 1 T. Murach
A deep spectromorphological study of the $\gamma$-ray emission surrounding the
young massive stellar cluster Westerlund 1A deep spectromorphological study of
the $\gamma$-ray emission surrounding the young massive stellar cluster
Westerlund 1 K. Nakashima A deep spectromorphological study of the
$\gamma$-ray emission surrounding the young massive stellar cluster Westerlund
1A deep spectromorphological study of the $\gamma$-ray emission surrounding
the young massive stellar cluster Westerlund 1 M. de Naurois A deep
spectromorphological study of the $\gamma$-ray emission surrounding the young
massive stellar cluster Westerlund 1A deep spectromorphological study of the
$\gamma$-ray emission surrounding the young massive stellar cluster Westerlund
1 A. Nayerhoda A deep spectromorphological study of the $\gamma$-ray emission
surrounding the young massive stellar cluster Westerlund 1A deep
spectromorphological study of the $\gamma$-ray emission surrounding the young
massive stellar cluster Westerlund 1 J. Niemiec A deep spectromorphological
study of the $\gamma$-ray emission surrounding the young massive stellar
cluster Westerlund 1A deep spectromorphological study of the $\gamma$-ray
emission surrounding the young massive stellar cluster Westerlund 1 S. Ohm
,11footnotemark: 1 A deep spectromorphological study of the $\gamma$-ray
emission surrounding the young massive stellar cluster Westerlund 1A deep
spectromorphological study of the $\gamma$-ray emission surrounding the young
massive stellar cluster Westerlund 1 L. Olivera-Nieto A deep
spectromorphological study of the $\gamma$-ray emission surrounding the young
massive stellar cluster Westerlund 1A deep spectromorphological study of the
$\gamma$-ray emission surrounding the young massive stellar cluster Westerlund
1 E. de Ona Wilhelmi A deep spectromorphological study of the $\gamma$-ray
emission surrounding the young massive stellar cluster Westerlund 1A deep
spectromorphological study of the $\gamma$-ray emission surrounding the young
massive stellar cluster Westerlund 1 M. Ostrowski A deep spectromorphological
study of the $\gamma$-ray emission surrounding the young massive stellar
cluster Westerlund 1A deep spectromorphological study of the $\gamma$-ray
emission surrounding the young massive stellar cluster Westerlund 1 S. Panny A
deep spectromorphological study of the $\gamma$-ray emission surrounding the
young massive stellar cluster Westerlund 1A deep spectromorphological study of
the $\gamma$-ray emission surrounding the young massive stellar cluster
Westerlund 1 M. Panter A deep spectromorphological study of the $\gamma$-ray
emission surrounding the young massive stellar cluster Westerlund 1A deep
spectromorphological study of the $\gamma$-ray emission surrounding the young
massive stellar cluster Westerlund 1 R.D. Parsons A deep spectromorphological
study of the $\gamma$-ray emission surrounding the young massive stellar
cluster Westerlund 1A deep spectromorphological study of the $\gamma$-ray
emission surrounding the young massive stellar cluster Westerlund 1 G. Peron A
deep spectromorphological study of the $\gamma$-ray emission surrounding the
young massive stellar cluster Westerlund 1A deep spectromorphological study of
the $\gamma$-ray emission surrounding the young massive stellar cluster
Westerlund 1 D.A. Prokhorov A deep spectromorphological study of the
$\gamma$-ray emission surrounding the young massive stellar cluster Westerlund
1A deep spectromorphological study of the $\gamma$-ray emission surrounding
the young massive stellar cluster Westerlund 1 G. Pühlhofer A deep
spectromorphological study of the $\gamma$-ray emission surrounding the young
massive stellar cluster Westerlund 1A deep spectromorphological study of the
$\gamma$-ray emission surrounding the young massive stellar cluster Westerlund
1 M. Punch A deep spectromorphological study of the $\gamma$-ray emission
surrounding the young massive stellar cluster Westerlund 1A deep
spectromorphological study of the $\gamma$-ray emission surrounding the young
massive stellar cluster Westerlund 1A deep spectromorphological study of the
$\gamma$-ray emission surrounding the young massive stellar cluster Westerlund
1A deep spectromorphological study of the $\gamma$-ray emission surrounding
the young massive stellar cluster Westerlund 1 A. Quirrenbach A deep
spectromorphological study of the $\gamma$-ray emission surrounding the young
massive stellar cluster Westerlund 1A deep spectromorphological study of the
$\gamma$-ray emission surrounding the young massive stellar cluster Westerlund
1 R. Rauth ,11footnotemark: 1 A deep spectromorphological study of the
$\gamma$-ray emission surrounding the young massive stellar cluster Westerlund
1A deep spectromorphological study of the $\gamma$-ray emission surrounding
the young massive stellar cluster Westerlund 1 P. Reichherzer A deep
spectromorphological study of the $\gamma$-ray emission surrounding the young
massive stellar cluster Westerlund 1A deep spectromorphological study of the
$\gamma$-ray emission surrounding the young massive stellar cluster Westerlund
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###### Abstract

Context. Young massive stellar clusters are extreme environments and
potentially provide the means for efficient particle acceleration. Indeed,
they are increasingly considered as being responsible for a significant
fraction of cosmic rays (CRs) accelerated within the Milky Way. Westerlund 1,
the most massive known young stellar cluster in our Galaxy is a prime
candidate for studying this hypothesis. While the very-high-energy
$\gamma$-ray source HESS J1646$-$458 has been detected in the vicinity of
Westerlund 1 in the past, its association could not be firmly identified.

Aims. We aim to identify the physical processes responsible for the
$\gamma$-ray emission around Westerlund 1 and thus to better understand the
role of massive stellar clusters in the acceleration of Galactic CRs.

Methods. Using 164 hours of data recorded with the High Energy Stereoscopic
System (H.E.S.S.), we carried out a deep spectromorphological study of the
$\gamma$-ray emission of HESS J1646$-$458\. We furthermore employed H I and CO
observations of the region to infer the presence of gas that could serve as
target material for interactions of accelerated CRs.

Results. We detected large-scale ($\sim$$2^{\circ}$ diameter) $\gamma$-ray
emission with a complex morphology, exhibiting a shell-like structure and
showing no significant variation with $\gamma$-ray energy. The combined energy
spectrum of the emission extends to several tens of TeV, and is uniform across
the entire source region. We did not find a clear correlation of the
$\gamma$-ray emission with gas clouds as identified through H I and CO
observations.

Conclusions. We conclude that, of the known objects within the region, only
Westerlund 1 can explain the bulk of the $\gamma$-ray emission. Several CR
acceleration sites and mechanisms are conceivable, and discussed in detail.
While it seems clear that Westerlund 1 acts as a powerful particle
accelerator, no firm conclusions on the contribution of massive stellar
clusters to the flux of Galactic CRs in general can be drawn at this point.

###### Key Words.:

Acceleration of particles – Radiation mechanisms: non-thermal – Shock waves –
Stars: massive – Galaxies: star clusters: individual: Westerlund 1 – Gamma
rays: general

##  1 Introduction

Young massive stellar clusters are environments of copious star formation, and
typically host a large number of very massive stars (Portegies Zwart et al.,
2010). For this reason, they have long been considered as potential sites of
cosmic-ray (CR) acceleration (Parizot et al., 2004). The acceleration may take
place at shock fronts of supernova remnants (SNRs) (which may collide with the
strong winds of massive stars in the cluster, see e.g. Bykov et al., 2020, and
references therein), or at the termination shock of the superbubble that is
excavated by the combined stellar winds of the cluster (e.g. Bykov, 2014;
Gupta et al., 2018; Morlino et al., 2021). Massive clusters form from
correspondingly massive molecular clouds, which are not very common in the
Milky Way but often found in starburst galaxies (Fujii & Portegies Zwart,
2016). Nevertheless, the notion that massive star clusters are responsible for
the bulk of hadronic CRs111 Here and in the following, the term “hadronic
cosmic ray” refers to cosmic-ray nuclei, as opposed to, e.g., cosmic-ray
electrons and positrons.  accelerated within our Galaxy represents a viable
alternative to the long-standing “SNR paradigm”, in which (isolated) SNRs are
the primary acceleration sites (Portegies Zwart et al., 2010; Aharonian et
al., 2019; Morlino et al., 2021).

Through interaction with ambient gas and radiation fields, high-energy
hadronic CRs produce high-energy $\gamma$ rays, which provides strong
motivation for the search for $\gamma$-ray emission from massive stellar
clusters (this has been realised already long ago, see e.g. Cesarsky &
Montmerle, 1983). Indeed, a bubble, or “cocoon” in the Cygnus X star-forming
region has been detected in _Fermi_ -LAT data in the
$\sim$$1\text{\,}\mathrm{GeV}$–few $100\text{\,}\mathrm{GeV}$ energy range
(Ackermann et al., 2011). Subsequently, _Fermi_ -LAT has detected diffuse
$\gamma$-ray emission in the same energy range around a number of other
massive stellar clusters in the Milky Way (Yang & Aharonian, 2017; Yang et
al., 2018; Yang & Wang, 2020; Sun et al., 2020a, b). Searches at higher
energies (i.e. at $1\text{\,}\mathrm{TeV}$ and above) with ground-based
instruments have also lead to several detections:

  * •

the Cygnus region harbours several sources of TeV-energy $\gamma$ rays (Abdo
et al., 2007; Abeysekara et al., 2018), and has recently been detected up to
energies of hundreds of TeV (Abeysekara et al., 2021; Cao et al., 2021);

  * •

the young stellar cluster Westerlund 2 within the star formation region RCW
49, which hosts with WR 20a an extraordinarily massive binary star system
(Aharonian et al., 2007; Abramowski et al., 2011);

  * •

the young stellar cluster Westerlund 1 (Abramowski et al., 2012), which will
be introduced in more detail below;

  * •

the super bubble 30 Dor C, whose detection is particularly noteworthy due to
its distant location in the Large Magellanic Cloud (Abramowski et al., 2015);

  * •

the stellar cluster Cl∗ 1806$-$20, which contains both a luminous blue
variable candidate, LBV 1806$-$20, and a magnetar, SGR 1806$-$20 (Abdalla et
al., 2018a).

However, the $\gamma$-ray emission can be linked directly to the stellar
clusters in only some of the above cases, the precise CR acceleration sites
are yet unidentified, and none of the detections constitutes unequivocal
evidence for the acceleration of hadronic CRs due to the respective clusters.
The assertion of the latter point is complicated by the fact that high-energy
$\gamma$ rays can be produced by CRs via two competing processes. Besides
their production in the decay of neutral pions (and other short-lived
particles), produced in turn in interactions of hadronic CRs with ambient
matter – the “hadronic scenario” – they may also be created through the
inverse Compton (IC) process, in which high-energy electrons and positrons222
Hereafter, we use the term “electrons” to refer to both electrons and
positrons.  can up-scatter low-energy photons from ambient radiation fields to
TeV energies – the “leptonic scenario”. These two scenarios can only be
distinguished by carrying out detailed spectromorphological studies of the
$\gamma$-ray emission, and combining the results with those obtained at other
wavelengths. In this article, we present such a study for the young massive
stellar cluster Westerlund 1.

Westerlund 1, named after its discoverer Bengt Westerlund (Westerlund, 1961)
and located at R.A.(2000)=$16^{\mathrm{h}}47^{\mathrm{m}}04.0^{\mathrm{s}}$,
Dec.(2000)=$-45^{\circ}51^{\prime}04.9^{\prime\prime}$ (Brandner et al.,
2008), is the most massive known young stellar cluster in the Milky Way, with
an estimated mass of around $10^{5}\,M_{\odot}$ (Clark et al., 2005; Brandner
et al., 2008; Portegies Zwart et al., 2010). It hosts a rich population of
evolved massive stars, including significant fractions of all known Galactic
Yellow Hypergiants (Clark et al., 2005) and Wolf-Rayet stars (Crowther et al.,
2006). The half-mass radius of the cluster is approximately
$1\text{\,}\mathrm{pc}$ (Brandner et al., 2008). Many estimates for the age of
the cluster and its distance from Earth have been put forward in the past.
Most age estimates agree with an age of $35\text{\,}\mathrm{Myr}$ (Clark et
al., 2005; Crowther et al., 2006; Brandner et al., 2008), although the single-
age paradigm has been questioned recently after finding that the observed
luminosities of cool supergiants are more consistent with an age of
$\sim$$10\text{\,}\mathrm{Myr}$ (Beasor et al., 2021). Early distance
estimates, using various techniques, find distances of around
$4\text{\,}\mathrm{kpc}$ (Clark et al., 2005; Crowther et al., 2006; Kothes &
Dougherty, 2007; Brandner et al., 2008). Recently, data from the _Gaia_
spacecraft were used to obtain new distance estimates. While most of them are
compatible with the old estimates (Davies & Beasor, 2019; Rate et al., 2020;
Beasor et al., 2021; Negueruela et al., 2022), closer distances of
$\sim$$2.7\text{\,}\mathrm{kpc}$ have also been obtained (Aghakhanloo et al.,
2020, 2021). Clark et al. (2019) have questioned the reliability of _Gaia_
(DR2) data in the Westerlund 1 field altogether, rendering the new estimates
somewhat uncertain. For this article, we adopted an age of
$4\text{\,}\mathrm{Myr}$ and a distance of $3.9\text{\,}\mathrm{kpc}$, as
these values are compatible with the majority of published results.
Additionally, we will need in the course of this paper estimates for the
properties of the collective cluster wind of Westerlund 1, which is formed as
a superposition of the strong winds of the massive stars in the cluster. Only
few estimates can be found in the literature; we assumed here for the kinetic
luminosity of the wind
$L_{\mathrm{w}}\sim$${10}^{39}\text{\,}\mathrm{erg}\text{\,}{\mathrm{s}}^{-1}$
(Muno et al., 2006b) and for the wind velocity
$v_{\mathrm{w}}\sim$$3000\text{\,}\mathrm{km}\text{\,}{\mathrm{s}}^{-1}$
(Morlino et al., 2021) as typical values. All parameter values for Westerlund
1 assumed in this work are summarised in Table 1.

Table 1: Parameter values for Westerlund 1 assumed in this work.

Par. | Description | Value | Ref.
---|---|---|---
$d$ | distance from Earth | $3.9\text{\,}\mathrm{kpc}$ | (1,2)
$\tau$ | cluster age | $4\text{\,}\mathrm{Myr}$ | (3,4)
$L_{\mathrm{w}}$ |  kinetic luminosity of cluster wind | ${10}^{39}\text{\,}\mathrm{erg}\text{\,}{\mathrm{s}}^{-1}$ | (5)
$v_{\mathrm{w}}$ | velocity of cluster wind | $3000\text{\,}\mathrm{km}\text{\,}{\mathrm{s}}^{-1}$ | (6)

(1) Kothes & Dougherty (2007); (2) Davies & Beasor (2019); (3) Clark et al.
(2005); (4) Brandner et al. (2008); (5) Muno et al. (2006b); (6) Morlino et
al. (2021).

Westerlund 1 has been studied extensively in the X-ray domain. Observations
with the _Chandra_ telescope have revealed diffuse hard X-ray emission from
the core of the cluster (Muno et al., 2006b), which was later identified as
likely being of thermal origin with _XMM-Newton_ observations (Kavanagh et
al., 2011). Additionally, Muno et al. (2006a) have identified an X-ray
magnetar, CXOU J164710.2$-$455216, which supposedly was created in the
explosion of a very massive ($>40\,M_{\odot}$) progenitor star (Clark et al.,
2008; Belczynski & Taam, 2008). Interestingly, CXOU J164710.2$-$455216 is the
only known remnant of a stellar explosion within Westerlund 1.

Moving to larger spatial scales (i.e. beyond the bounds of the cluster
itself), an analysis of _Fermi_ -LAT data between 3 and
$300\text{\,}\mathrm{GeV}$ by Ohm et al. (2013) revealed extended $\gamma$-ray
emission in the vicinity of Westerlund 1. With more data accumulated since
then, the latest _Fermi_ -LAT source catalogue (4FGL-DR2, Abdollahi et al.,
2020; Ballet et al., 2020) lists six sources within $1.1^{\circ}$ from the
cluster centre. Besides the stellar cluster and its members, several objects
that are located at relatively small angular separations from Westerlund 1
could potentially be contributing to the observed $\gamma$-ray emission. This
includes two energetic
($\dot{E}>$2\text{\times}{10}^{35}\text{\,}\mathrm{erg}\text{\,}{\mathrm{s}}^{-1}$$)
pulsars, PSR J1648$-$4611 and PSR J1650$-$4601 (Manchester et al., 2005), as
well as the low-mass X-ray binary (LMXB) 4U 1642$-$45 (Forman et al., 1978).
On the other hand, it is quite possible that some of the six sources listed in
the 4FGL catalogue share a common physical origin, and were separated into
distinct components only because the true source morphology is very complex.

Finally, at even higher energies, Abramowski et al. (2012) detected a large,
extended ($\sim$$2^{\circ}$ diameter) emission region centred on Westerlund 1,
named HESS J1646$-$458, between 0.45 and $\sim$$20\text{\,}\mathrm{TeV}$ with
the H.E.S.S. experiment. Based on the properties of the emission and taking
into account multi-wavelength data, the authors found Westerlund 1 to be the
most likely explanation of the $\gamma$-ray emission in a single-source
scenario, but were unable to draw definitive conclusions based on the data set
available at the time.

Since then, the exposure collected with H.E.S.S. on HESS J1646$-$458 has
almost quintupled, in large part thanks to a dedicated observation campaign in
2017. This, together with recent advances in analysis techniques, enabled a
new, detailed study of the $\gamma$-ray emission surrounding Westerlund 1,
which we present here. In Sect. 2.1, we introduce the H.E.S.S. data set and
provide a description of the data analysis. The results of the H.E.S.S. data
analysis are given in Sect. 2.2. Besides H.E.S.S. data, we have also analysed
data from H I and CO observations in the vicinity of Westerlund 1 and present
the results in Sect. 2.3. A detailed discussion of the results, considering
multiple explanations for the observed $\gamma$-ray emission, is presented in
Sect. 3, before we summarise our findings and provide an outlook in Sect. 4.

##  2 Observations and data analysis

###  2.1 H.E.S.S. data set and analysis

H.E.S.S. is an array of five imaging atmospheric Cherenkov telescopes (IACTs),
located in the Southern hemisphere in Namibia
($23^{\circ}16^{\prime}18^{\prime\prime}$ S,
$16^{\circ}30^{\prime}00^{\prime\prime}$ E) at an altitude of
$1800\text{\,}\mathrm{m}$ above sea level (Aharonian et al., 2006; Holler et
al., 2015). The array comprises four $12\text{\,}\mathrm{m}$-diameter
telescopes (CT1-4) that are arranged on a $120\text{\,}\mathrm{m}$-side square
and began operation in late 2003. A fifth telescope (CT5), with
$28\text{\,}\mathrm{m}$ diameter, was added in the centre of the array in
2012. The telescopes detect the Cherenkov light produced in atmospheric air
showers initiated by primary $\gamma$ rays, where the main background consists
of showers caused by hadronic CR. With the central telescope included, the
array is sensitive to $\gamma$ rays in the energy range between
$\sim$$0.1\text{\,}\mathrm{TeV}$ and $\sim$$100\text{\,}\mathrm{TeV}$; with
CT5 alone thresholds as low as $20\text{\,}\mathrm{GeV}$ have been achieved in
studies of pulsed emission (Abdalla et al., 2018d).

The H.E.S.S. data set for HESS J1646$-$458 comprises 362 observation runs
after quality selection, taken over the course of more than 13 years between
June 18, 2004 and October 11, 2017. The runs amount to a total observation
time of 164.2 hours, which represents a significant increase with respect to
the previous publication (Abramowski et al., 2012) (33.8 hours). We note that
not all of the observations have targeted HESS J1646$-$458 directly; some have
been taken as part of surveys, and some were primarily targeted at the nearby
sources HESS J1640$-$465 (Abramowski et al., 2014c) and HESS J1641$-$463
(Abramowski et al., 2014b), leading to a gradient in exposure across the HESS
J1646$-$458 region.

Only data from the four smaller telescopes (CT1-4) were considered in the
analysis presented here. For best performance, we restricted the maximum
zenith angle of the analysed observation runs to $<60^{\circ}$ and the maximum
offset angle between the reconstructed direction of events and the telescope
pointing direction to $<2^{\circ}$. With this selection, an energy threshold
of $0.37\text{\,}\mathrm{TeV}$ was achieved in the final analysis.
$\gamma$-like events were selected using the method described in Ohm et al.
(2009) and their energy and arrival direction were reconstructed with the
algorithm presented in Parsons & Hinton (2014). Subsequently, we converted our
data to the FITS-based data format described in Deil et al. (2018) and
performed the high-level data analysis using the Gammapy package (Deil et al.,
2017, 2020) (v0.17). All findings were confirmed with two cross-check
analyses: one based on a completely independent calibration and data analysis
chain (de Naurois & Rolland, 2009), and one based on the same calibration and
event reconstruction algorithms as those used in the main analysis, but
carried out with the ctools package (Knödlseder et al., 2016) (v.1.6.3); the
latter analysis is documented in Specovius (2021). Furthermore, results of
another, intermediate analysis of the data set, which has inspired parts of
the analysis presented here, can be found in Zorn (2019).

In the high-level analysis, we employed a concept that has only recently been
established for the analysis of IACT data: a 3-dimensional likelihood
analysis, in which the data can be modelled simultaneously in two spatial
dimensions and as a function of energy (Mohrmann et al., 2019). In this
method, contrary to more established ones, the residual background of CR-
induced air shower events (“hadronic” background) for a given observation run
is not directly estimated from source-free regions within the observed field
itself, but rather provided by a background model. This model was constructed
from archival observations and subsequently adjusted to the analysed
observations following the procedure outlined in Mohrmann et al. (2019). The
3-dimensional likelihood analysis method is especially suited for the analysis
of complex source regions and largely extended sources, and is thus a suitable
choice for the analysis of HESS J1646$-$458.

As a first step in the analysis, separate energy thresholds were determined
for each observation run, requiring that the energy reconstruction bias is
below 10% and that the background model is used only above its validity
threshold (Mohrmann et al., 2019). Aiming for sufficient exposure across the
entire region down to the lowest energies, a minimal energy threshold of
$0.37\text{\,}\mathrm{TeV}$ was enforced. We subsequently computed
3-dimensional maps of the observed number of events, predicted background, and
exposure, comprised of spatial pixels of $0.02^{\circ}\times 0.02^{\circ}$ and
an energy axis of 16 bins per decade of energy, with the $6^{\circ}\times
6^{\circ}$ region of interest centred on Westerlund 1. For each observation,
we adjusted the background model to the observed data by fitting a global
normalisation and a spectral tilt parameter, taking into account only regions
in the field of view that are free of $\gamma$-ray emission. In order to
safely exclude regions with $\gamma$-ray emission from the background fit, an
iterative procedure as described in Abdalla et al. (2018b) was employed to
generate an exclusion map.

###  2.2 H.E.S.S. analysis results

####  2.2.1 Maps and radial profiles

Figure 1:  Significance maps after background subtraction. The position of
Westerlund 1 is marked by the black star symbol; the grey, dashed line shows
the Galactic plane. (a) Map for the entire $6^{\circ}\times 6^{\circ}$ region
of interest, smoothed with a $0.07^{\circ}$ top-hat kernel. The final
exclusion map is shown in black, earlier iterations in blue, green, purple,
and orange. Locations of previously detected sources that are not connected to
HESS J1646$-$458 are indicated by black, open symbols. (b) Map with detail
view of the emission surrounding Westerlund 1, smoothed with a $0.22^{\circ}$
top-hat kernel. The colour scale is saturated at the maximum observed
significance value associated with the HESS J1646$-$458 region. Contour lines
corresponding to a significance of 4, 8, and 12 $\sigma$ are shown in blue.
Signal regions a–p used for spectrum extraction are overlaid (black), as are
segments 1–5 for the computation of radial profiles (white dashed).

We show in Fig. 1 the resulting residual significance maps after background
subtraction, where the significance was computed following Li & Ma (1983). For
the map in Fig. 1, a top-hat smoothing with a kernel of radius $0.07^{\circ}$
has been employed. The corresponding distribution of significance values – for
all pixels and those outside the exclusion map, displayed in black – is
presented in Fig. 2. As expected for the case of purely statistical
fluctuations, the distribution for pixels outside the exclusion map follows
very closely that of a Gaussian distribution with unit width, indicating a
good description of the hadronic background. Figure 1 shows a significance map
obtained with a correlation radius of $0.22^{\circ}$. Overlaid are 16 square
“signal regions” (of size $0.45^{\circ}\times 0.45^{\circ}$ each), labelled
a–p, that cover the $\gamma$-ray emission of HESS J1646$-$458, as well as 5
circular segments. These signal regions and segments are used in the further
characterisation of the $\gamma$-ray emission (see below).

Figure 2:  Significance entry distribution. The black histogram corresponds to
all pixels of the map shown in Fig. 1 with non-zero entries, the grey
histogram to all pixels outside of the final exclusion map. The green line
represents the fit of a Gaussian distribution to the grey histogram, the best-
fit mean and width are $\mu=-0.043\pm 0.005$ and $\sigma=1.008\pm 0.005$,
respectively. A Gaussian distribution with mean $\mu=0$ and width $\sigma=1$
is shown by the orange, dashed line for comparison.

Having obtained a satisfying description of the residual hadronic background,
we computed flux maps displaying the excess $\gamma$-ray emission (see Fig.
3). Focusing on the larger-scale structure of the emission of HESS
J1646$-$458, a top-hat smoothing with a kernel of radius $0.22^{\circ}$ – the
same value as already used in Abramowski et al. (2012) – has been applied for
the maps in panels 3(a), 3(c), and 3(d). Additionally, we show in panel 3(b) a
flux map smoothed with a Gaussian kernel of $0.07^{\circ}$ width, which
corresponds approximately to the size of the point-spread function for the
analysis configuration employed here.

(a) Smoothing kernel: $0.22^{\circ}$ top hat

(b) Smoothing kernel: $0.07^{\circ}$ Gaussian

(c) Smoothing kernel: $0.22^{\circ}$ top hat

(d) Smoothing kernel: $0.22^{\circ}$ top hat

Figure 3:  Flux maps of the HESS J1646$-$458 region. The position of
Westerlund 1 is marked by the black star symbol; the grey, dashed line shows
the Galactic plane. Coloured symbols indicate objects listed in the legend in
panel (a). Dark grey square markers denote positions of sources from the 4FGL-
DR2 catalogue (Abdollahi et al., 2020; Ballet et al., 2020), where those
sources that are still significant ($\sqrt{\mathrm{TS}}>3$) above
$30\text{\,}\mathrm{GeV}$ are shown with a diamond marker ($\Diamond$). Grey
circles labelled ‘A’ and ‘B’ mark regions defined in Abramowski et al. (2012);
region ‘C’ (at R.A. $16^{\mathrm{h}}49^{\mathrm{m}}4.8^{\mathrm{s}}$, Dec.
$-46^{\circ}06^{\prime}00^{\prime\prime}$) is newly defined here. The white
circle marker indicates the coordinate with respect to which the radial
profiles in Fig. 4 and 9 have been computed. The scale bar denotes a projected
distance of $40\text{\,}\mathrm{pc}$, for the nominal distance to Westerlund 1
of $3.9\text{\,}\mathrm{kpc}$. The maps are for different energy thresholds
(indicated at the bottom of each panel) and were computed using different
smoothing kernels (stated below each figure). Colour scales are saturated at
the maximum observed flux value associated with the HESS J1646$-$458 region.
Contour lines shown in blue are at flux levels of $F=(12.5/20/27.5)\times
10^{-9}${\mathrm{cm}}^{-2}\text{\,}{\mathrm{s}}^{-1}\text{\,}{\mathrm{sr}}^{-1}$$
for panels (a) and (b), at $F=(3/5.5/8)\times
10^{-9}${\mathrm{cm}}^{-2}\text{\,}{\mathrm{s}}^{-1}\text{\,}{\mathrm{sr}}^{-1}$$
for panel (c), and at $F=(1/1.5)\times
10^{-9}${\mathrm{cm}}^{-2}\text{\,}{\mathrm{s}}^{-1}\text{\,}{\mathrm{sr}}^{-1}$$
for panel (d).

Very strong $\gamma$-ray emission is observed from the known, nearby sources
HESS J1640$-$465 and HESS J1641$-$463\. Turning to HESS J1646$-$458, we
observe that its spatial morphology is very complex. Notably, the emission is
not peaked at the position of Westerlund 1, but rather exhibits a structure
resembling that of a shell, surrounding the stellar cluster. This global
structure is present in all of the displayed maps, and thus does not seem to
vary with $\gamma$-ray energy. On top of the large-scale structure, we
identify peaks of the emission in the circular regions labelled ‘A’ and ‘B’,
which correspond to regions with enhanced emission already found in Abramowski
et al. (2012), confirming these findings. Additionally, we find a peak –
visible in particular in the flux map above $4.9\text{\,}\mathrm{TeV}$ – in
region ‘C’, which encompasses the two energetic pulsars PSR J1648$-$4611 and
PSR J1650$-$4601, as well as an emission region extending beyond the shell-
like structure, to the east of region C. For future reference, we provide the
following source names for these regions: HESS J1645$-$455 (region A), HESS
J1647$-$465 (region B), HESS J1649$-$460 (region C), and HESS J1652$-$462
(emission east of region C). We stress, however, that we have found – as will
be detailed in the course of this paper – no indications that the $\gamma$-ray
emission in these regions is of a different origin than that of the rest of
the emission, and that the regions should therefore not be interpreted as
distinct sources. Rather, the regions have been labelled in order to ease the
discussion of the source morphology.

Because HESS J1646$-$458 is located along the Galactic plane, and towards the
inner Galaxy, it is safe to assume that diffuse $\gamma$-ray emission
contributes to the observed signal to some degree. This diffuse emission is
produced by CRs that propagate freely within the Galactic disc, and can be due
to bremsstrahlung or IC emission of CR electrons, or interactions of hadronic
CRs with gas. Due to its diffuse nature, the diffuse $\gamma$-ray emission
from the Galaxy is challenging to measure directly, and while it has been
detected over large scales in the TeV energy range (e.g., Abramowski et al.,
2014a; Amenomori et al., 2021), these measurements do not provide a good
constraint for the level of diffuse emission in the region of HESS
J1646$-$458\. Therefore, in order to assess the possible contamination with
diffuse emission of the $\gamma$-ray signal of HESS J1646$-$458, we have used
a prediction of the diffuse $\gamma$-ray flux based on the Picard CR
propagation code (Kissmann, 2014; Kissmann et al., 2015, 2017). This analysis
is described in more detail in Appendix A, where we show in Fig. 11 the same
flux maps as in Fig. 3, but with the predicted flux due to diffuse emission
subtracted. We conclude that, while the Galactic diffuse emission likely
contributes at a considerable level – $\sim$24% ($\sim$17%/$\sim$8%) above a
threshold energy of $0.37\text{\,}\mathrm{TeV}$
($1\text{\,}\mathrm{TeV}$/$4.9\text{\,}\mathrm{TeV}$), according to the Picard
template –, it cannot explain the bulk of the $\gamma$-ray emission, and does
not alter the source morphology in a significant way. For these reasons, and
because of the rather large uncertainties associated with any estimate of the
Galactic diffuse emission in a particular region of the sky, we have performed
the subsequent analysis without explicitly taking it into account, noting that
none of the conclusions drawn in this paper are affected by this.

In order to further characterise the morphology of the emission – and its
apparent invariance with respect to energy – we derived radial profiles of the
observed excess. Noting that Westerlund 1 is not located precisely at the
centre of the shell-like structure, the profiles were computed not with
respect to the stellar cluster position, but to a slightly shifted coordinate
(R.A. $16^{\mathrm{h}}46^{\mathrm{m}}36^{\mathrm{s}}$, Dec.
$-46^{\circ}01^{\prime}12^{\prime\prime}$), which corresponds to the
barycentre of the $\gamma$-ray excess. The asymmetry of the observed emission
with respect to the cluster position could for example be caused by
inhomogeneities in the ISM surrounding the stellar cluster. Fig. 4 shows the
profiles for different energy bands (upper panel), and for the five segments
defined in Fig. 1 (lower panel). The excess profiles:

  1. (i)

confirm the shell-like structure, with a peak at around $0.5^{\circ}$
(corresponding to a projected distance of $\sim$$34\text{\,}\mathrm{pc}$ for a
cluster distance of $3.9\text{\,}\mathrm{kpc}$), followed by a relatively slow
fall-off;

  2. (ii)

exhibit the same shape in all energy bands, that is, they show no indications
for an energy-dependent morphology of the excess;

  3. (iii)

are also largely compatible between the five segments, with only minor small-
scale deviations discernible.

In order to reinforce the second point above, we carried out $\chi^{2}$ tests
in which we compared the profile for each energy band with one computed using
all events outside this band (thus ensuring statistically independent sets).
The results, listed in Table 2, show that each of the profiles is compatible
with the total profile in terms of its shape within the statistical
uncertainties.

Figure 4:  Radial excess profiles. The upper panel shows exposure-corrected
excess counts per unit sky area for different energy bands, the lower panel
for different segments as defined in Fig. 1 – the black curve, showing the
total excess above threshold in all segments, is the same in both panels. All
profiles are normalised to equal area, to allow an easy comparison. The
profiles have been computed with respect to a centre point at R.A.
$16^{\mathrm{h}}46^{\mathrm{m}}36^{\mathrm{s}}$, Dec.
$-46^{\circ}01^{\prime}12^{\prime\prime}$, slightly shifted from the
Westerlund 1 position. In the calculation of the profiles, we discarded pixels
within $0.6^{\circ}$ of the position of HESS J1640$-$465\.  Table 2:
Morphological fit results.

Energy range | Excess | $\chi^{2}/N_{\mathrm{dof}}$ | $p_{\chi^{2}}$
---|---|---|---
(TeV) |  |  |
$>0.37$ | $15\,310\pm 440$ | – | –
0.37 – 0.65 | $5080\pm 300$ | 12.2 / 14 | 59.0%
0.65 – 1.2 | $3910\pm 230$ | 16.2 / 14 | 30.3%
1.2 – 4.9 | $5190\pm 220$ | 20.9 / 14 | 10.3%
$>4.9$ | $1130\pm 80$ | 19.5 / 14 | 14.6%
333 ‘Excess’ denotes the number of observed excess events within the white,
dashed circle in Fig. 1, excluding a circular region with $0.6^{\circ}$ radius
around HESS J1640$-$465\. The $\chi^{2}$ values and corresponding $p$-values
are a measure of the compatibility of the shape of the radial excess profile
of this energy band with the total radial excess profile (see text for
details).

####  2.2.2 Energy spectra

The complex morphology of HESS J1646$-$458 prohibits a simple extraction of an
energy spectrum by means of modelling the emission with a single spatial
model. We therefore considered the 16 signal regions indicated in Fig. 1 and
extracted energy spectra for each of these regions. To obtain the spectra, we
fitted (using a forward-folding likelihood fit; Piron et al., 2001) a power-
law (PL) model,

$\frac{\mathrm{d}N}{\mathrm{d}E}=\phi_{0}\cdot\left(\frac{E}{E_{0}}\right)^{-\Gamma}\quad,$
(1)

with $E_{0}=$1\text{\,}\mathrm{TeV}$$ kept fixed in the fit, to the observed
$\gamma$-ray excess in each signal region and subsequently derived flux points
based on this fitted model. Table 3 lists the observed $\gamma$-ray excess as
well as the fitted power-law model parameters. A comparison of the shapes of
the energy spectra is provided in Fig. 5. Finally, Fig. 6 shows the fitted
spectral index for each signal region as a function of its angular separation
from Westerlund 1.

Table 3: Spectral analysis results for signal regions.

Signal region | Excess events | Significance | Significance | $\phi_{0}$ | $\Gamma$ | $\sqrt{\Delta\mathrm{TS}}$
---|---|---|---|---|---|---
|  |  | $(E>$4.9\text{\,}\mathrm{TeV}$)$ | $(10^{-13}\,\mathrm{TeV}^{-1}\mathrm{cm}^{-2}\mathrm{s}^{-1})$ |  |
a | $396.1$ |  $5.3$$\sigma$ |  $0.9$$\sigma$ | $3.76\pm 0.66$ | $2.71\pm 0.18$ | $5.9$
b | $454.9$ |  $5.6$$\sigma$ |  $1.7$$\sigma$ | $4.34\pm 0.64$ | $2.53\pm 0.13$ | $7.5$
c | $901.8$ |  $10.3$$\sigma$ |  $2.8$$\sigma$ | $6.33\pm 0.58$ | $2.49\pm 0.08$ | $12.3$
d | $1014.0$ |  $10.8$$\sigma$ |  $7.7$$\sigma$ | $6.66\pm 0.58$ | $2.20\pm 0.06$ | $16.1$
e | $430.7$ |  $4.7$$\sigma$ |  $2.9$$\sigma$ | $2.84\pm 0.51$ | $2.35\pm 0.12$ | $6.7$
f | $648.9$ |  $7.7$$\sigma$ |  $4.0$$\sigma$ | $4.60\pm 0.64$ | $2.33\pm 0.11$ | $10.0$
g | $1238.5$ |  $13.5$$\sigma$ |  $6.0$$\sigma$ | $7.41\pm 0.54$ | $2.45\pm 0.07$ | $16.1$
h | $1409.2$ |  $14.5$$\sigma$ |  $4.6$$\sigma$ | $8.14\pm 0.54$ | $2.50\pm 0.06$ | $17.3$
i | $653.4$ |  $9.0$$\sigma$ |  $4.0$$\sigma$ | $6.65\pm 0.71$ | $2.41\pm 0.09$ | $11.4$
j | $1229.0$ |  $14.0$$\sigma$ |  $6.8$$\sigma$ | $9.07\pm 0.63$ | $2.39\pm 0.06$ | $17.7$
k | $1246.4$ |  $13.2$$\sigma$ |  $3.6$$\sigma$ | $7.73\pm 0.54$ | $2.48\pm 0.06$ | $16.5$
l | $1405.7$ |  $14.1$$\sigma$ |  $6.3$$\sigma$ | $7.95\pm 0.54$ | $2.51\pm 0.06$ | $16.9$
m | $469.5$ |  $6.8$$\sigma$ |  $1.7$$\sigma$ | $5.40\pm 0.73$ | $2.56\pm 0.13$ | $8.2$
n | $415.4$ |  $5.1$$\sigma$ |  $3.5$$\sigma$ | $3.49\pm 0.62$ | $2.33\pm 0.13$ | $7.4$
o | $1259.2$ |  $14.1$$\sigma$ |  $5.9$$\sigma$ | $8.23\pm 0.57$ | $2.39\pm 0.06$ | $17.7$
p | $996.7$ |  $10.5$$\sigma$ |  $4.0$$\sigma$ | $6.29\pm 0.55$ | $2.36\pm 0.07$ | $14.7$

444 See Fig. 1 for the definition of the signal regions. Significance values
were computed following Li & Ma (1983), assuming a perfect knowledge of the
background. $\phi_{0}$ and $\Gamma$ are the best-fit parameter values of the
power-law fit for each region (cf. Eq. (1)). $\sqrt{\Delta\mathrm{TS}}$
denotes the square root of the difference in test statistic
($\mathrm{TS}=-2\ln(\mathcal{L})$) between the best-fit power-law model and
the null hypothesis (corresponding to $\phi_{0}=0$).

Figure 5:  Comparison of signal region spectra. All spectra were divided (at a
reference energy of $1\text{\,}\mathrm{TeV}$) by a reference power-law
spectrum with spectral index $\Gamma=2.41$, corresponding to the weighted
average over all signal regions. Upper limits are at 95% confidence level, and
only two upper limits after the last significant (i.e., $>2\sigma$) flux point
are shown.  Figure 6:  Spectral index $\Gamma$ for the signal regions a–p, as
a function of angular separation between the centre point of each region and
the centre point of the total emission (white circle in Fig. 3). The red line
and band denote the weighted mean and uncertainty across all regions,
$\langle\Gamma\rangle=2.41\pm 0.02$, respectively.

The spectra in the signal regions are remarkably similar to each other, both
in terms of the fitted power-law indices (which show no dependence on the
separation of the region from the centre, see Fig. 6) and the shape of the
spectra as indicated by the extracted flux points (see Fig. 5). The only
significant deviation is observed in region ‘d’, where the fitted power-law
index deviates from the average of all other regions by $\sim 4\sigma$. We
have not been able to identify an issue in the analysis procedure that could
explain this deviation, and conclude that it either indicates that the
spectrum of the emission in this region is indeed harder, or that it is an
unexpectedly large statistical fluctuation. The similarity of the spectra
supports our previous finding of a lack of energy-dependent morphology of HESS
J1646$-$458, and motivates the extraction of a combined energy spectrum.

We computed combined flux points for HESS J1646$-$458 by adding up the flux
points from all 16 square regions, where we have used the best-fit flux for
each point and region also in cases where an upper limit was previously
derived. The result is shown in Fig. 7. Besides statistical uncertainties, the
displayed error bars contain a systematic uncertainty arising from the applied
background model. The systematic uncertainty is of the same magnitude as the
statistical one at the lowest energies considered here, and quickly becomes
negligible at higher energies. The combined flux points clearly show that the
$\gamma$-ray emission of HESS J1646$-$458 extends to at least several tens of
TeV. A comparison with the spectra of the individual signal regions (blue
lines in Fig. 7) shows that the total spectrum is not dominated by any single
signal region across the entire energy range.

Figure 7:  Combined energy spectrum. The black data points correspond to the
entire emission of HESS J1646$-$458; the solid orange, dashed green, and
dashed-dotted red lines show the result of fitting a power law with
exponential cut-off (ECPL), a hadronic ($pp$) model, and a leptonic (IC)
model, respectively, to these points. Fitted power-law models for each region
a–p are displayed by solid blue lines (with darker shades indicating closer
proximity to Westerlund 1), while the dashed blue line denotes their sum. All
power-law spectra are plotted up to $100\text{\,}\mathrm{TeV}$ for better
visibility, however, the observed $\gamma$-ray excess is not significant up to
this energy in any of the sub-regions. The bottom panel shows the ratio to the
ECPL model; note that the last flux point (with a ratio to the ECPL model of
$\sim$3.7$\pm$1.5) is beyond the vertical axis scale.

In order to characterise the combined spectrum, we fitted several spectral
models to the derived flux points. A simple PL model (cf. Eq. 1) does not lead
to a satisfactory fit ($p=0.06\%$). The solid orange line in Fig. 7 shows the
result for a power law with exponential cut-off (ECPL),

$\frac{\mathrm{d}N}{\mathrm{d}E}=\phi_{0}\cdot\left(\frac{E}{E_{0}}\right)^{-\Gamma}\cdot\exp\left(-\frac{E}{E_{c}}\right)\quad,$
(2)

for which we obtained (with $E_{0}=$1\text{\,}\mathrm{TeV}$$ kept fixed in the
fit) $\phi_{0}=$(1.00\pm
0.03)\text{\times}{10}^{-11}\text{\,}{\mathrm{TeV}}^{-1}\text{\,}{\mathrm{cm}}^{-2}\text{\,}{\mathrm{s}}^{-1}$$,
$\Gamma=2.30\pm 0.04$, and $E_{c}=(44^{+17}_{-11})\,\mathrm{TeV}$. This
corresponds to a total $\gamma$-ray luminosity of HESS J1646$-$458 between the
threshold energy of $0.37\text{\,}\mathrm{TeV}$ and $100\text{\,}\mathrm{TeV}$
of
$L_{\gamma}\sim$9\text{\times}{10}^{34}$\,(d/$3.9\text{\,}\mathrm{kpc}$)^{2}\,$\mathrm{erg}\text{\,}{\mathrm{s}}^{-1}$$,
where $d$ is the assumed distance to the source. We note that, while the ECPL
model yields an acceptable fit ($p=6.3\%$), the high-energy flux points do not
provide a clear indication of an exponential cut-off to the spectrum. Thus,
while the energy spectrum of HESS J1646$-$458 clearly extends to several tens
of TeV, its maximum energy cannot be determined reliably with the analysis
presented here, and may conceivably lie beyond
$100\text{\,}\mathrm{T}\mathrm{e}\mathrm{V}$. However, the last flux point
should not be regarded as a clear indication of an upward trend in the
spectrum, as it may be afflicted by unknown systematic uncertainties in the
high-energy response of the system, which is difficult to calibrate.

Assuming the $\gamma$-ray emission to be generated in collisions of CR protons
with ambient matter, we also fitted a primary proton spectral model (of the
same form as defined in Eq. 2) to the $\gamma$-ray flux points, employing the
Naima software package (Zabalza, 2015) for this task. For the parameters of
the primary proton spectrum we obtained a normalisation (at
$E_{0}=$1\text{\,}\mathrm{TeV}$$) of $\phi_{0}^{p}=$(1.28\pm
0.17)\text{\times}{10}^{38}$\,(d/$3.9\text{\,}\mathrm{kpc}$)^{2}\,(n/$1\text{\,}{\mathrm{cm}}^{-3}$)^{-1}\,${\mathrm{eV}}^{-1}$$
(with $n$ the assumed density of the ambient matter), a spectral index of
$\Gamma_{p}=2.33\pm 0.06$, and a cut-off energy of
$E_{c}^{p}=(400^{+250}_{-130})\,\mathrm{TeV}$; the dashed green line in Fig. 7
displays the corresponding $\gamma$-ray spectrum. The 95% confidence level
lower limit on the proton spectrum cut-off energy is
$E_{c}^{p}>$214\text{\,}\mathrm{TeV}$$. Extrapolating the proton spectrum down
to an energy of $1\text{\,}\mathrm{GeV}$, the required energy in primary
protons is
$W_{p}\sim$6\text{\times}{10}^{51}$\,(d/$3.9\text{\,}\mathrm{kpc}$)^{2}\,(n/$1\text{\,}{\mathrm{cm}}^{-3}$)^{-1}\,$\mathrm{erg}$$.

In a similar manner, now adopting with Naima a leptonic framework in which the
$\gamma$-ray emission is produced through IC scattering of CR electrons, we
also fitted a primary electron spectrum to the HESS J1646$-$458 flux points
(again assuming an ECPL model). Besides the cosmic microwave background, we
used as target radiation fields an infrared field
($T_{\mathrm{IR}}=$26\text{\,}\mathrm{K}$$,
$\rho_{\mathrm{IR}}=$0.74\text{\,}\mathrm{eV}\text{\,}{\mathrm{cm}}^{-3}$$)
and an optical field ($T_{\mathrm{opt}}=$2400\text{\,}\mathrm{K}$$,
$\rho_{\mathrm{opt}}=$1.4\text{\,}\mathrm{eV}\text{\,}{\mathrm{cm}}^{-3}$$) as
predicted by the Popescu et al. (2017) model, as well as an additional field
representing diffuse star light from the stellar cluster. For the latter, we
assumed $T_{\mathrm{SC}}=$40\,000\text{\,}\mathrm{K}$$ (Crowther et al., 2006)
and derived555 To derive the energy density, we used
$\rho_{\mathrm{SC}}=L\,/\,(4\pi r^{2}c)$, where $L$ is the total cluster
luminosity and $r$ the distance from the cluster. For a wind efficiency
$\eta=\dot{M}v_{\mathrm{w}}\,/\,(L/c)\simeq 1$ (Vink & Gräfener, 2012),
$L=2\,(v_{\mathrm{w}}/c)^{-1}L_{\mathrm{w}}\sim$2\text{\times}{10}^{41}\text{\,}\mathrm{erg}\text{\,}{\mathrm{s}}^{-1}$$
for the parameter values assumed in this work. Adding up the luminosities of
OB supergiant and Yellow Hypergiant stars listed in Clark et al. (2005) yields
$L\sim$6\text{\times}{10}^{40}\text{\,}\mathrm{erg}\text{\,}{\mathrm{s}}^{-1}$$,
which is consistent with our estimate. A slight reduction of the IC emission
due to the cluster radiation field is expected because of its anisotropy,
which we have not taken into account. However, since the contribution of this
component is suppressed due to the Klein-Nishina effect, the modification of
the total IC emission is negligible.  an energy density of
$\rho_{\mathrm{SC}}\sim$30\text{\,}\mathrm{eV}\text{\,}{\mathrm{cm}}^{-3}$$ at
a distance of $34\text{\,}\mathrm{pc}$ from the cluster, which approximately
corresponds to the distance at which the radial $\gamma$-ray excess profile
peaks (cf. Fig. 4). In this case, the best-fit parameters are
$\phi_{0}^{e}=$(4.7\pm
0.5)\text{\times}{10}^{35}$\,(d/$3.9\text{\,}\mathrm{kpc}$)^{2}\,${\mathrm{eV}}^{-1}$$,
$\Gamma_{e}=2.97\pm 0.07$, and $E_{c}^{e}=(180^{+200}_{-70})\,\mathrm{TeV}$,
with a 95% confidence level lower limit on $E_{c}^{e}$ of
$87\text{\,}\mathrm{TeV}$ – the resulting $\gamma$-ray spectrum is shown by
the red, dashed-dotted line in Fig. 7. Electrons down to energies of
$\sim$$0.4\text{\,}\mathrm{TeV}$ contribute to the $\gamma$-ray emission
detected with H.E.S.S.. Assuming that the spectrum of primary electrons
extends down to $0.1\text{\,}\mathrm{TeV}$, we obtained a total required
energy in primary electrons of
$W_{e}\sim$7.2\text{\times}{10}^{48}$\,(d/$3.9\text{\,}\mathrm{kpc}$)^{2}\,$\mathrm{erg}$$.
Dividing the required energy by the (energy-dependent) cooling time due to IC
scattering (Hinton & Hofmann, 2009) off the different target fields then
yields an estimate for the minimum total required power of
$L_{e}>$4.1\text{\times}{10}^{35}$\,(d/$3.9\text{\,}\mathrm{kpc}$)^{2}\,$\mathrm{erg}\text{\,}{\mathrm{s}}^{-1}$$.
The required power is larger if cooling due to synchrotron emission plays a
sizeable role, for example, in a magnetic field with
$B=$10\text{\,}\mathrm{\SIUnitSymbolMicro G}$$,
$L_{e}>$1.7\text{\times}{10}^{36}$\,(d/$3.9\text{\,}\mathrm{kpc}$)^{2}\,$\mathrm{erg}\text{\,}{\mathrm{s}}^{-1}$$.

The chosen analysis method and tools in principle also enable a three-
dimensional modelling of the $\gamma$-ray emission detected with H.E.S.S.,
that is, to decompose the emission into several components with separate
energy spectra and morphological models. However, owing to the complex
structure of the emission, a rather complicated model with multiple distinct
components is required to obtain a satisfactory description, and its
interpretation depends strongly on the chosen models for each of the
components. Considering furthermore the similarity of energy spectra extracted
in the signal regions, we do not present such a modelling here.

###  2.3 Analysis of radio line data

Attributing the $\gamma$-ray emission to interactions of accelerated cosmic-
ray nuclei requires sufficiently dense target material. The presence of such
target material can be estimated using radio observations, in particular of
the $21\text{\,}\mathrm{cm}$ H I emission line – indicating neutral, atomic
hydrogen – and of the CO ($J$=1–0) transition, which is a tracer for dense
clouds of molecular hydrogen, H2 (Heyer & Dame, 2015). We have therefore used
the H I Southern Galactic Plane Survey (SGPS; McClure-Griffiths et al., 2005)
and the Mopra Southern Galactic Plane CO Survey (Braiding et al., 2018) to
investigate the amount of hydrogen gas in the vicinity of Westerlund 1. The
analysis was repeated using the CO data from the (lower-resolution) survey by
Dame et al. (2001) instead of the Mopra CO data, leading to consistent
results.

The radio data analysis is hampered by the uncertainty on the distance to
Westerlund 1. We show in Fig. 8 the H I and CO maps for an interval in
velocity with respect to the local standard of rest of
$v=[-60,-50]\,$\mathrm{km}\text{\,}{\mathrm{s}}^{-1}$$, which corresponds to
the distance of $3.9\text{\,}\mathrm{kpc}$ that we adopted for this paper
(Kothes & Dougherty, 2007). As some measurements indicate smaller distances,
maps for two correspondingly chosen alternative velocity intervals,
$v=[-48.5,-38.5]\,$\mathrm{km}\text{\,}{\mathrm{s}}^{-1}$$
($d\approx$3.3\text{\,}\mathrm{kpc}$$) and
$v=[-37,-27]\,$\mathrm{km}\text{\,}{\mathrm{s}}^{-1}$$
($d\approx$2.7\text{\,}\mathrm{kpc}$$), are shown in Appendix B.

Figure 8:  Maps showing H I emission (McClure-Griffiths et al., 2005) (_top
panel_) and 12CO emission (Braiding et al., 2018) (_bottom panel_) in the
Westerlund 1 region. Both maps display the emission for an interval in
velocity with respect to the local standard of rest of
$v=[-60,-50]\,$\mathrm{km}\text{\,}{\mathrm{s}}^{-1}$$, which approximately
corresponds to a distance of $3.9\text{\,}\mathrm{kpc}$. The position of
Westerlund 1 is marked by the white star symbol and the grey, dashed line
shows the Galactic plane. The transparent, white circle marker denotes the
centre point with respect to which the radial CR density profiles in Fig. 9
have been computed; the dashed white line displays a circle with radius
$1^{\circ}$ – up to which the profiles have been computed – around this point.
The red lines are contour lines of the flux map shown in Fig. 3(a). Regions A,
B, and C are the same as in Fig. 3.

We find that the gas indicated by the radio observations at a distance of
$\sim$$3.9\text{\,}\mathrm{kpc}$ shows no spatial correlation with the
$\gamma$-ray emission that we observe with H.E.S.S.. In fact, both the H I and
CO maps indicate a particularly low atomic and molecular gas density in the
circular regions B and C, which are bright in $\gamma$ rays. Using an H I
intensity-mass conversion factor of
$X_{\mathrm{HI}}=$1.823\text{\times}{10}^{18}$\,\mathrm{cm}^{-2}\,/\,($\mathrm{K}\text{\,}\mathrm{km}\text{\,}{\mathrm{s}}^{-1}$)$
(Rohlfs & Wilson, 2004), we obtain for a circular region with radius
$1.1^{\circ}$, centred on Westerlund 1, a total enclosed mass as indicated
from H I of $M_{\mathrm{H\leavevmode\nobreak\
I,Wd1}}=$1.3\text{\times}{10}^{5}$\,M_{\odot}$. This translates into an
average density of $n_{\mathrm{H\leavevmode\nobreak\
I,Wd1}}=$3.2\text{\,}{\mathrm{cm}}^{-3}$$.666 Abramowski et al. (2012)
derived, for a similar region, a much smaller value of
$n_{\mathrm{H\leavevmode\nobreak\ I}}=$0.24\text{\,}{\mathrm{cm}}^{-3}$$. We
attribute this to the usage of an erroneous formula in that paper.  Similarly,
from the CO data we get777 Due to the more indirect nature of the estimate,
the CO-to-H2 conversion factor, $X_{\mathrm{CO}}$, is less well constrained
than $X_{\mathrm{H\leavevmode\nobreak\ I}}$. Here we used
$X_{\mathrm{CO}}=$1.5\text{\times}{10}^{20}$\,\mathrm{cm}^{-2}\,/\,($\mathrm{K}\text{\,}\mathrm{km}\text{\,}{\mathrm{s}}^{-1}$)$,
which Ackermann et al. (2012) indicate as an appropriate value for the
galactocentric radius of Westerlund 1, $R\approx$4.7\text{\,}\mathrm{kpc}$$
for a distance of $3.9\text{\,}\mathrm{kpc}$ (see their Fig. 25). This value
is also within the range of $(1.4-2.6)\times
10^{20}\,\mathrm{cm}^{-2}\,/\,($\mathrm{K}\text{\,}\mathrm{km}\text{\,}{\mathrm{s}}^{-1}$)$
recommended by Bolatto et al. (2013). We have neglected the possible
contribution of 4He, which could increase the mass estimate by $\sim$25%.
$M_{\mathrm{CO,Wd1}}=$4.3\text{\times}{10}^{5}$\,M_{\odot}$ and
$n_{\mathrm{CO,Wd1}}=$10.5\text{\,}{\mathrm{cm}}^{-3}$$, where
$n_{\mathrm{CO}}$ is the equivalent density for atomic hydrogen and can thus
be directly compared to $n_{\mathrm{H\leavevmode\nobreak\ I}}$. We stress,
however, that in particular the molecular material indicated by the CO
observations is not distributed homogeneously inside this region, but rather
concentrated in smaller-scale clouds. For instance, in the CO cloud located in
the Northern part of the H.E.S.S. emission region (cf. Fig. 8), we find –
assuming a spherical distribution of the gas – a density of
$n_{\mathrm{CO,cloud}}\sim$190\text{\,}{\mathrm{cm}}^{-3}$$.

Following Aharonian et al. (2019), we also derived a radial profile of the CR
density, assuming that the $\gamma$-ray emission is produced in interactions
of hadronic CRs with the gas indicated by the H I and CO data. Having used the
measured $\gamma$-ray flux above our threshold energy of
$0.37\text{\,}\mathrm{TeV}$ to compute the profiles, they indicate the density
of CRs above an energy about ten times higher, that is, above
$\sim$$4\text{\,}\mathrm{TeV}$. Density profiles for all three considered
velocity intervals are shown in Fig. 9, where we have used for the profiles in
panel 9 the same shifted centre point as for the radial excess profiles (cf.
Fig. 4), and for the profiles in panel 9 – for comparison with Aharonian et
al. (2019) – the position of Westerlund 1 as centre point. Regarding first
Fig. 9, for the interval corresponding to the nominal distance of
$d\approx$3.9\text{\,}\mathrm{kpc}$$ (blue curve with circle markers), we
observe a distinct peak at a radial distance from the centre of
$\sim$$0.4^{\circ}$, corresponding to the peak observed in the excess profiles
(cf. Fig. 4) at about the same distance. When choosing the cluster position as
centre point, the peak is smeared out, leading to a plateau at small radii.
The profile is then compatible with that derived in Aharonian et al. (2019),
and showing a gradual decline of the density moving away from the cluster. We
stress, however, that the $\gamma$-ray emission is not radially symmetric
around Westerlund 1, rendering the interpretation of radial profiles computed
with respect to this position difficult. Our profiles for the alternative
velocity intervals (i.e., distances; orange and green curves with triangle
markers in Fig. 9) exhibit approximately the same shape as the profile for the
nominal distance, but with a less distinct peak, and lower overall density.
This corresponds to the higher density of hydrogen gas observed for these
intervals (cf. Figs. 12, 13). Finally, we note that the shapes of the obtained
radial density profiles should be interpreted with care, owing to systematic
uncertainties associated with the determination of the gas distributions. For
instance, it is conceivable that a considerable amount of the CO molecules
have been photodissociated by the intense ultraviolet radiation from
Westerlund 1, implying that the CO line emission would no longer be an
accurate tracer of molecular hydrogen gas (e.g., Wolfire et al., 2010).

Figure 9:  Cosmic-ray density profiles above $4\text{\,}\mathrm{TeV}$ for
different velocity intervals. The profiles in the upper plot have been
computed with respect to the centre point shown by the circle marker in Fig. 8
(the same as for the excess profiles displayed in Fig. 4), whereas the
profiles in the lower plot have been computed with respect to the position of
Westerlund 1. The error bars denote the (statistical) uncertainty of the
measured $\gamma$-ray flux only, and in particular do not reflect systematic
uncertainties related to the gas distribution. The CR density at Earth,
indicated for comparison, was computed from the all-particle CR spectrum as
modelled in Breuhaus et al. (2022) (model ‘A’). The data points taken from
Aharonian et al. (2019), shown in the lower plot, have been derived using a
velocity interval of $v=[-60,-50]\,$\mathrm{km}\text{\,}{\mathrm{s}}^{-1}$$,
and should thus be compared to the blue curve with circle markers. The red,
solid line, from the same paper, shows a profile corresponding to a
$1/r$-distribution of the CRs, where $r$ is the distance to the cluster. Both
show the density above a slightly higher threshold energy of
$10\text{\,}\mathrm{TeV}$.

##  3 Discussion

In this section, we will discuss in turn the various possible sites for the
acceleration of CRs that could be responsible for the observed $\gamma$-ray
emission. Evidently, we can include in this discussion only those objects that
have been identified through observations at other wavelengths. While we
consider the association of the $\gamma$-ray emission with one of these
objects most likely, so far undiscovered objects (e.g. pulsars or SNRs) could
also contribute to it.

###  3.1 Objects not connected to Westerlund 1

####  3.1.1 4U 1642–45

The LMXB 4U 1642$-$45 lies close to the peak in $\gamma$-ray emission observed
in region A (cf. Fig. 3). However, despite this positional coincidence, we
consider an association of 4U 1642$-$45 with HESS J1646$-$458 – or even the
emission observed just in region A – highly unlikely: LMXBs are not known
emitters of $\gamma$ rays in the TeV energy range, in fact, Kantzas et al.
(2022) have recently shown that even the upcoming Cherenkov Telescope Array
(CTA) will be able to detect LMXB outbursts only under favourable
circumstances. Moreover, the observed emission is spatially extended, which
would be unexpected if it is produced inside a transient jet. Lastly,
Abramowski et al. (2012) reported no temporal variations of the observed
$\gamma$-ray flux, again disfavouring an association of HESS J1646$-$458 with
4U 1642$-$45\. While the deviation in spectral index observed in signal region
‘d’ (cf. Sect. 2.2.2), which partly coincides with the circular region A, is
intriguing, the lack of a plausible association leads us to conclude that it
is likely a statistical fluctuation, or due to an unidentified, hard-spectrum
source contributing to the emission in region d (but not to the entire region
A, as the signal regions c, g, and h, which also overlap with region A, do not
show deviating spectral indices).

####  3.1.2 PSR J1648–4611 & PSR J1650–4601

The two energetic pulsars PSR J1648$-$4611 (with spin-down power
$\dot{E}=$2.1\text{\times}{10}^{35}\text{\,}\mathrm{erg}\text{\,}{\mathrm{s}}^{-1}$$)
and PSR J1650$-$4601
($\dot{E}=$2.9\text{\times}{10}^{35}\text{\,}\mathrm{erg}\text{\,}{\mathrm{s}}^{-1}$$)
(Manchester et al., 2005) are located within region C (cf. Fig. 3), where we
observe enhanced $\gamma$-ray emission. Because pulsar wind nebulae (PWNe)
represent a large fraction of known Galactic $\gamma$-ray sources (e.g.,
Abdalla et al., 2018b), it seems likely that high-energy electrons provided by
one (or both) of the two pulsars contribute to the $\gamma$-ray emission
observed in region C. This remains true even though neither of the pulsar
locations fully coincides with the peak of the emission, as it is not uncommon
that $\gamma$-ray PWNe are observed offset from their respective pulsars. The
detection of diffuse, hard X-ray emission from the vicinity of PSR
J1648$-$4611 by Sakai et al. (2013) adds further support for this scenario.
However, while the 4FGL-DR2 catalogue (Abdollahi et al., 2020; Ballet et al.,
2020) contains sources associated with PSR J1648$-$4611 and PSR J1650$-$4601,
their $\gamma$-ray emission is detected as pulsed and exhibits a very steep
spectrum above $10\text{\,}\mathrm{GeV}$, implying that these sources are
directly connected to the pulsars rather than their putative PWNe.

On the other hand, viewing the entire emission of HESS J1646$-$458 as
resulting from one of the two pulsars would imply an unusually large PWN. For
instance, at the distance of PSR J1648$-$4611 of $5.7\text{\,}\mathrm{kpc}$
(Kramer et al., 2003), the emission region spans
$\sim$$200\text{\,}\mathrm{pc}$, which is twice the size of the largest known
$\gamma$-ray PWN, HESS J1825$-$137 (Abdalla et al., 2019). For such an
extended nebula, one would expect a considerable loss of energy due to
synchrotron cooling of the electrons when they propagate towards the edges of
the nebula, leading to softer $\gamma$-ray spectra in these regions (or,
equivalently, energy-dependent morphology). Because we observe very similar
energy spectra across the entire source, and no energy-dependent morphology,
we conclude that a PWN powered by PSR J1648$-$4611 or PSR J1650$-$4601 cannot
explain the entire $\gamma$-ray emission.

###  3.2 Distinct acceleration sites within Westerlund 1

Having established that other known objects in the region cannot explain the
bulk of $\gamma$-ray emission from HESS J1646$-$458, we assume next that the
CRs producing the emission are accelerated at one or multiple sites within the
stellar cluster Westerlund 1. Various scenarios can be considered, and will be
discussed in this section.

####  3.2.1 CXOU J164710.2–455216

At first sight, the magnetar CXOU J164710.2$-$455216 – the only known stellar
remnant inside the cluster – may be suspected to power a $\gamma$-ray PWN that
could potentially be associated to HESS J1646$-$458\. However, its measured
period and period derivative
($P=$10.6\text{\,}\mathrm{s}$,\,\dot{P}=$9.2\text{\times}{10}^{-13}\text{\,}\mathrm{s}\text{\,}{\mathrm{s}}^{-1}$$;
Israel et al., 2007) imply a rotational spin-down power of only
$\dot{E}=$3\text{\times}{10}^{31}\text{\,}\mathrm{erg}\text{\,}{\mathrm{s}}^{-1}$$,
which is orders of magnitude lower than for any of the pulsars associated with
PWN detected at TeV energies with H.E.S.S. (Abdalla et al., 2018c). Even
though the measured X-ray luminosity of
$L_{X}\approx$3\text{\times}{10}^{33}\text{\,}\mathrm{erg}\text{\,}{\mathrm{s}}^{-1}$$
(Muno et al., 2006a) exceeds the rotational spin-down power, implying another
source of energy (presumably connected to the high magnetic field of the
magnetar), it still appears very unlikely that CXOU J164710.2$-$455216 would
be able to sustain the observed $\gamma$-ray emission. Additionally, as is the
case for PSR J1648$-$4611 and PSR J1650$-$4601, the spatial extent of HESS
J1646$-$458 and the lack of energy-dependent morphology disfavour an
association of the $\gamma$-ray emission with CXOU J164710.2$-$455216.

####  3.2.2 Supernova remnants

The existence of CXOU J164710.2$-$455216 implies that at least one supernova
(SN) explosion took place within Westerlund 1. However, given the abundance of
massive stars in Westerlund 1, and its age of several Myr, it seems certain
that many more SNe have occurred already. Indeed, Muno et al. (2006b) have
argued that the number of SNe during the last $\sim$$1\text{\,}\mathrm{Myr}$
could be as high as 80–150, attributing the lack of identified SNRs to a
cavity in the interstellar medium (ISM), excavated by the stellar cluster.
Without detailed knowledge about the progenitor mass of CXOU
J164710.2$-$455216, or the SN rate in Westerlund 1, it is not straightforward
to estimate the energy output that SNRs in the stellar cluster may provide.
Nevertheless, assuming a canonical value for the kinetic energy released per
SN of ${10}^{51}\text{\,}\mathrm{erg}$ – possibly more in the case of CXOU
J164710.2$-$455216, if its progenitor was indeed as heavy as $40\,M_{\odot}$
(Muno et al., 2006a) – it seems plausible that one or several SNRs in
Westerlund 1 could be responsible for the $\gamma$-ray emission in terms of
the required energetics. For instance, in a hadronic scenario, assuming a
density of the ambient matter of $5\,m_{\mathrm{H}}\,${\mathrm{cm}}^{-3}$$
gives a required energy in protons of
$1.2\text{\times}{10}^{51}\text{\,}\mathrm{erg}$ (cf. Sect. 2.2.2). It would
take about 10 SNRs to reach this energy if the conversion efficiency from
kinetic energy into CRs is $\sim$10%.

####  3.2.3 SN-wind and wind-wind interactions

Another, related, possibility for the acceleration of CRs inside Westerlund 1
are interactions of SN shocks with winds of massive stars in the cluster, or
interactions between the winds of several stars. Indeed, for SN shocks
interacting with fast stellar winds, the efficiency for CR acceleration can be
as high as 30% (Bykov et al., 2020), and CR acceleration up to
$\geq$40\text{\,}\mathrm{PeV}$$ has been conjectured (Bykov et al., 2015).
Colliding winds of massive stars are also known to produce non-thermal
emission (Eichler & Usov, 1993; Reimer et al., 2006), and several searches for
$\gamma$-ray emission from colliding wind binaries have been performed in the
past (e.g. Werner et al., 2013; Pshirkov, 2016; Martí-Devesa & Reimer, 2021).
A well-known example is provided by the colliding wind binary $\eta$ Car,
which has indeed been detected up to $\sim$$100\text{\,}\mathrm{GeV}$ with the
_Fermi_ -LAT (Tavani et al., 2009; Abdo et al., 2010), and even up to
$\sim$$400\text{\,}\mathrm{GeV}$ with H.E.S.S. (Abdalla et al., 2020). These
considerations strengthen the conclusion that $\gamma$-ray emission at the
level observed with H.E.S.S. can in principle be produced by CRs accelerated
at shock fronts within Westerlund 1.

However, for the scenario of a central CR source, it is important to also take
into account the propagation of the CRs into the region where we observe
$\gamma$-ray emission with H.E.S.S.. In this case, the non-observation of a
peak in the $\gamma$-ray emission at the position of Westerlund 1 and the
large extent of HESS J1646$-$458 essentially rule out the leptonic scenario.
In a hadronic scenario, the complex morphology of HESS J1646$-$458 may in
principle be attributable to the distribution of target material – although a
clear correlation of the $\gamma$-ray emission with gas clouds as indicated by
H I and CO observations is lacking, and the inferred CR density does not peak
at the centre for any of the considered distances to the source (cf. Fig. 9),
as would be expected for a steady CR injection there (see Aharonian et al.
2019, but also Bhadra et al. 2022). Possible options to alleviate this problem
could be the presence of “dark” gas that is not traced by H I or CO (e.g.,
Wolfire et al., 2010), or the assumption that the CRs were provided by a
recent impulsive event (e.g., the SN explosion of the CXOU J164710.2$-$455216
progenitor star and/or other recent SNe), rather than being injected quasi-
continuously over the lifetime of the cluster. Another relevant constraint
comes from the maximum energy of the observed $\gamma$ rays, which implies the
presence of CRs with energies of several hundred TeV throughout the emission
region. If the acceleration sites are located exclusively within the compact
cluster, particles must pass through the wind zone. Taking reasonable limits
on the diffusion properties, adiabatic losses in the radial wind are
unavoidable. CRs that were injected at the cluster and have propagated to a
distance $R$ within the wind region would therefore need to be produced with
maximum energy $(R\,/\,R_{\mathrm{Wd1}})^{2/3}$ times larger (Longair, 1992),
where $R_{\mathrm{Wd1}}\sim$1\text{\,}\mathrm{pc}$$ is the radius of
Westerlund 1. For the nominal distance of $3.9\text{\,}\mathrm{kpc}$, we
observe a peak in the $\gamma$-ray emission at
$R\sim$34\text{\,}\mathrm{pc}$$, implying a need of multi-PeV CRs within
Westerlund 1. The H.E.S.S. observations thus provide a valuable constraint for
theoretical models of particle acceleration processes within a compact stellar
cluster (Bykov et al., 2020).

###  3.3 Acceleration by Westerlund 1 as a whole

Finally, there is the possibility that effects due to the entire stellar
cluster provide the means for efficient CR acceleration. In particular, we
consider in the following two scenarios related to the collective cluster
wind, in which the CR acceleration predominantly takes place outside of the
actual stellar cluster itself.

####  3.3.1 Turbulence in a superbubble

Due to the powerful collective cluster wind, as well as many SN explosions,
massive young stellar clusters are thought to create “superbubbles”, that is,
large cavities in the ISM, extending much beyond the boundaries of the cluster
itself. In the shocked medium inside the bubble, strong magnetohydrodynamic
(MHD) turbulences provide the conditions for particle acceleration via the
second-order Fermi mechanism (e.g., Bykov, 2014; Vieu et al., 2022). With a
maximum proton energy of $200\text{\,}\mathrm{TeV}$ and a source extent of
$\sim$$100\text{\,}\mathrm{pc}$, the Hillas criterion (Hillas, 1984) implies
for an average turbulent fluid velocity
$u=$100\text{\,}\mathrm{km}\text{\,}{\mathrm{s}}^{-1}$$ a minimum magnetic
field strength of $\sim$$13\text{\,}\mathrm{\SIUnitSymbolMicro G}$ in this
scenario. While the acceleration time scales are much longer compared to the
case of acceleration at shocks inside the cluster, the process could – under
favourable circumstances – generate CRs with up to PeV energies during several
Myr, the typical life time of young clusters (Bykov et al., 2020). For an
adiabatically expanding wind, and a density of the ambient ISM $\rho_{0}$, the
radius of the superbubble is given by
$R_{\mathrm{SB}}=0.76\,(L_{\mathrm{w}}\,/\,\rho_{0})^{1/5}\tau^{3/5}$ (Weaver
et al., 1977; Koo & McKee, 1992), or $R_{\mathrm{SB}}\sim
256\,(\rho_{0}\,/\,1\,m_{\mathrm{H}}\,${\mathrm{cm}}^{-3}$)^{-1/5}$\mathrm{pc}$$
for our assumptions (cf. Table 1). Adopting, for example,
$\rho_{0}=5\,m_{\mathrm{H}}\,${\mathrm{cm}}^{-3}$$, we obtain
$R_{\mathrm{SB}}\sim$185\text{\,}\mathrm{pc}$$ – a value more than two orders
of magnitude larger than the half-mass radius of the cluster. A superbubble
with a size of this order around Westerlund 1 has not yet been revealed at
other wavelengths. Because its dimensions also exceed the extent of the
$\gamma$-ray emission detected with H.E.S.S., an association of this emission
with the entire superbubble seems disfavoured. However, the assumption of a
homogeneous medium is an oversimplification, and bubbles in a structured and
possibly clumpy medium may have significantly different cooling rates and
dynamics (e.g., Chu, 2008). Moreover, more detailed models of superbubble
evolution indicate that the simple estimate for their radius given above often
over-predicts their true size (Yadav et al., 2017; Vieu et al., 2022). If this
is also the case for Westerlund 1, smaller-scale structures as for example the
bubble-like feature ‘B3’ in H I data reported by Kothes & Dougherty (2007)
could be associated with the cluster. Nevertheless, even in this case a
connection between the superbubble and the $\gamma$-ray emission is not
obvious (but conceivable, considering also that the $\gamma$-ray emission need
not be uniform from the superbubble volume).

####  3.3.2 Termination shock of collective cluster wind

Another possible site for the acceleration of CRs due to Westerlund 1, but
outside the stellar cluster itself, is the termination shock of the collective
cluster wind. The termination shock forms where the pressure of the outgoing
wind equals that of the ISM. Recently, Morlino et al. (2021) have proposed
that termination shocks of collective stellar cluster winds may be efficient
sites of particle acceleration, and demonstrated that CRs with PeV energies
could be produced in powerful clusters like Westerlund 1. Considering again as
above an adiabatic expansion, the radius of the termination shock is given by
$R_{\mathrm{TS}}=0.92\,(L_{\mathrm{w}}\,/\,\rho_{0})^{3/10}v_{\mathrm{w}}^{-1/2}\tau^{2/5}$
(Koo & McKee, 1992), or $R_{\mathrm{TS}}\sim
51\,(\rho_{0}\,/\,1\,m_{\mathrm{H}}\,${\mathrm{cm}}^{-3}$)^{-3/10}\,$\mathrm{pc}$$
with our adopted parameter values. Inserting
$\rho_{0}=5\,m_{\mathrm{H}}\,${\mathrm{cm}}^{-3}$$ yields a radius of
$R_{\mathrm{TS}}\sim$32\text{\,}\mathrm{pc}$$. Notably, this value coincides
well with the radial distance of $\sim$$34\text{\,}\mathrm{pc}$ at which we
observe a peak in the $\gamma$-ray excess profiles (cf. Sect. 2.2.1 and Fig.
4). The scenario of particle acceleration at the cluster wind termination
shock therefore provides a natural explanation for the shell-like structure
exhibited by the $\gamma$-ray emission detected with H.E.S.S., and can
furthermore reproduce its radial extent under reasonable assumptions. The
apparent asymmetry of the shell with respect to the position of Westerlund 1
could be caused, for example, by a gradient in the density of the surrounding
ISM, or by a SN that occurred within the cluster towards the direction of the
asymmetry.

Adopting the hadronic scenario, we find that the termination shock model is
also viable in terms of the required energetics: with
$L_{\mathrm{w}}\sim${10}^{39}\text{\,}\mathrm{erg}\text{\,}{\mathrm{s}}^{-1}$$
and $\tau\sim$4\text{\,}\mathrm{Myr}$$, the total available energy is
$\sim$$1.3\text{\times}{10}^{53}\text{\,}\mathrm{erg}$, which in principle
suffices to explain the required energy in CR protons,
$W_{p}\sim$6\text{\times}{10}^{51}$\,(n/$1\text{\,}{\mathrm{cm}}^{-3}$)^{-1}\,$\mathrm{erg}$$
– although, since the cooling time for protons exceeds the cluster lifetime,
the acceleration process would need to be rather efficient, or the target
density high. Furthermore, the energetics argument presupposes that the CRs
can be confined within the $\gamma$-ray emission region over a significant
fraction of the full cluster lifetime, which is not straightforward. For
instance, adopting Bohm diffusion, the diffusion length for protons is
$L\sim\sqrt{6Dt}\sim
81\,(E/$100\text{\,}\mathrm{TeV}$)^{1/2}\,(B/$10\text{\,}\mathrm{\SIUnitSymbolMicro
G}$)^{-1/2}\,(t/$1\text{\,}\mathrm{Myr}$)^{1/2}\,$\mathrm{pc}$$
(Chandrasekhar, 1943), where we have neglected projection effects. Hence, even
for slow diffusion, to confine protons with energy $200\text{\,}\mathrm{TeV}$
– our lower limit for the cut-off energy of the primary proton spectrum in a
hadronic scenario – within a region of radius $\sim$$50\text{\,}\mathrm{pc}$
for only $1\text{\,}\mathrm{Myr}$ already requires a rather large magnetic
field strength of $B\sim$50\text{\,}\mathrm{\SIUnitSymbolMicro G}$$.
Nevertheless, taking into account, for example, an additional smearing due to
the transformation from protons to $\gamma$ rays, the observed $\gamma$-ray
morphology can be reproduced with a not-too-extreme assumption on the magnetic
field, provided that the protons do not diffuse too fast. However, as already
mentioned in Sect. 3.2.3, the hadronic scenario is challenged further by the
absence of a correlation of the $\gamma$-ray emission with the gas observed in
the region.

Interestingly, the finding that the expected location of the termination shock
coincides with the shell-like structure of the measured $\gamma$-ray emission
also renders possible an interpretation within the leptonic scenario. This is
because the geometry of the acceleration site naturally explains the
relatively large extent of the emission region and its rather complex
structure, which are otherwise not easy to accommodate in a leptonic scenario.
The scenario is also feasible energetically; even in the presence of a
$10\text{\,}\mathrm{\SIUnitSymbolMicro G}$ magnetic field, the required power
of
$L_{e}\sim$1.7\text{\times}{10}^{36}\text{\,}\mathrm{erg}\text{\,}{\mathrm{s}}^{-1}$$
(cf. Sect. 2.2.2) is easily provided by the cluster wind if the acceleration
efficiency for electrons is of order 0.1%. However, as the accelerated
electrons emit synchrotron radiation, the scenario is subject to constraints
from observations at the corresponding wavelengths. For example, from
measurements by the Planck satellite at a frequency of
$30\text{\,}\mathrm{GHz}$888We have used the full-sky frequency map at
$30\text{\,}\mathrm{GHz}$ available through the Planck Legacy Archive,
http://pla.esac.esa.int/pla., at which the radiation is dominated by
synchrotron emission (Akrami et al., 2020), we infer an average intensity
within $1^{\circ}$ around Westerlund 1 of
$0.55\text{\,}\mathrm{MJy}\text{\,}{\mathrm{sr}}^{-1}$. For a magnetic field
of $10\text{\,}\mathrm{\SIUnitSymbolMicro G}$, electrons with energies around
$0.01\text{\,}\mathrm{TeV}$ emit synchrotron radiation at
$30\text{\,}\mathrm{GHz}$. Assuming that the electron spectrum extends down to
these energies, the predicted intensity at $30\text{\,}\mathrm{GHz}$ is
$\sim$0.3\text{\,}\mathrm{MJy}\text{\,}{\mathrm{sr}}^{-1}$$. Considering
furthermore that only part of the emission detected with Planck originates
from the vicinity of Westerlund 1, we conclude that the Planck measurements
imply either a magnetic field strength smaller than
$10\text{\,}\mathrm{\SIUnitSymbolMicro G}$ or a low-energy cut-off of the
primary electron spectrum. Finally, it is worth noting in this regard that for
another superbubble detected at TeV energies, 30 Dor C in the Large Magellanic
Cloud, a synchrotron shell has been detected using X-ray measurements, and a
leptonic scenario was found to be favoured to explain the TeV $\gamma$-ray
emission (Kavanagh et al., 2019, and references therein).

###  3.4 Escape of particles from the emission region

So far we have assumed that particles accelerated in or around Westerlund 1
are confined over the lifetime of the cluster. If a significant fraction of
accelerated particles can escape there are several important consequences:

  1. (i)

$\gamma$-ray emission would be expected outside the system, in the case of
hadronic CRs in particular in molecular clouds;

  2. (ii)

in the (most likely) case of energy-dependent escape, the inferred spectrum of
particles within the system would be softened with respect to the injection
spectrum by the energy-dependent escape probability;

  3. (iii)

the total energy requirements would be increased.

There is little evidence for (i) in the maps shown in Fig. 3 – with the
possible exception of the emission region east of region ‘C’, which, however,
does not coincide with a molecular cloud at the nominal distance of Westerlund
1 (cf. Fig. 8). The inferred injection indices for electrons and protons of
$\Gamma_{e}\sim$3.0999 The electron spectral index derived in the naima fit
corresponds to the present-time population of electrons, whose energy spectrum
is steepened with respect to the injection spectrum due to cooling.  and
$\Gamma_{p}\sim$2.3 seem broadly consistent with acceleration theory (e.g.,
Bell, 2013), so there seems to be no indication for (ii), although a modest
variation of the spectrum is tolerable within the precision of the H.E.S.S.
measurement. Finally, as the total energy requirement is already a challenge
in most acceleration scenarios under the assumption of confinement, there also
seems to be little room for (iii). Thus, while not entirely inconceivable, we
at least find no indications for particles escaping from the emission region.

In the absence of evidence for particle escape we need to consider if
confinement over the cluster lifetime is reasonable or not. As already
discussed in Sect. 3.3.2, this is not straightforward in the case of CR
protons, which in a disordered magnetic field would diffuse much too quickly.
A possible way to circumvent this problem would be a magnetic field topology
in which field lines are preferentially in the plane orthogonal to the radial
direction, which can substantially inhibit the radial diffusion.

##  4 Conclusion

We have presented a detailed analysis of HESS J1646$-$458, a very-high-energy
$\gamma$-ray source positionally coincident with the young massive stellar
cluster Westerlund 1. HESS J1646$-$458 is largely extended ($\sim$$2^{\circ}$
in diameter), and exhibits a complex, shell-like structure, with Westerlund 1
close to its centre. We found no indications for energy-dependent morphology.
The energy spectrum of HESS J1646$-$458 extends to at least several tens of
TeV, with a spectral index of $\sim$$-2.3$, and a gradual steepening above
$\sim$$10\text{\,}\mathrm{TeV}$. Energy spectra extracted within 16 signal
regions across the source region are very similar to each other, reinforcing
the observation that the morphology of HESS J1646$-$458 does not vary with
$\gamma$-ray energy.

In a hadronic scenario with CR protons producing the $\gamma$ rays, the
observed $\gamma$-ray spectrum implies proton energies in excess of several
hundred TeV. However, our analysis of the H I and CO emission around
Westerlund 1 indicates no clear correlation between hydrogen gas clouds and
the $\gamma$-ray emission, as would be expected to some degree within such a
scenario. Nevertheless, in particular due to uncertainties related to the
distribution of target gas, a hadronic scenario remains viable in principle.
On the other hand, the lack of significant energy-dependent morphology of the
$\gamma$-ray emission represents a challenge for an interpretation within an
IC-dominated, leptonic scenario.

Investigating the possible physical counterparts to HESS J1646$-$458, we found
that – while the energetic pulsars PSR J1648$-$4611 and PSR J1650$-$4601 may
be contributing to the emission in their immediate surroundings – no other
known object besides Westerlund 1 can be made responsible for the bulk of the
$\gamma$-ray emission. Particle acceleration due to the cluster may occur at
various possible sites: at wind-wind or SN-wind interaction shocks within the
cluster, at turbulences in the superbubble excavated by the collective cluster
wind, or at the termination shock of the cluster wind. Models in which the
acceleration takes place within the cluster generally need to overcome the
problem of transporting the accelerated CRs into the larger region from which
we observe the $\gamma$-ray emission without too severe energy losses, and
explain the fact that the $\gamma$-ray emission does not peak towards the
cluster position – in particular the latter argument rules out a leptonic
scenario with continuous injection for this case. Attributing the CR
acceleration to the superbubble as a whole seems disfavoured because HESS
J1646$-$458 – although largely extended – is still significantly smaller than
the expected size of the superbubble, which has, furthermore, so far eluded
its detection at other wavelengths. Therefore, we deem most attractive the
scenario of CR acceleration at the cluster wind termination shock, because it
provides a natural explanation for the shell-like morphology of HESS
J1646$-$458, and the wind is powerful enough to sustain the $\gamma$-ray
emission. Based on the available data, however, we are not able to firmly
identify the acceleration mechanism at work.

Our results further support massive stellar clusters as CR accelerators, and
motivate to investigate Westerlund 1 and other representatives of this class
of objects more deeply in the future. In particular, we encourage a deep and
broad coverage in X-ray observations of the region around Westerlund 1, which
may enable the identification of the cluster wind termination shock. On the
other hand, a more accurate measurement of the $\gamma$-ray emission in this
region will be provided by the upcoming Cherenkov Telescope Array (Acharya et
al., 2018), which is designed to be an order of magnitude more sensitive than
the H.E.S.S. experiment. Exploiting the data from this and other observatories
will be crucial in understanding the contribution of massive stellar clusters
to the sea of CRs in the Milky Way.

###### Acknowledgements.

The support of the Namibian authorities and of the University of Namibia in
facilitating the construction and operation of H.E.S.S. is gratefully
acknowledged, as is the support by the German Ministry for Education and
Research (BMBF), the Max Planck Society, the German Research Foundation (DFG),
the Helmholtz Association, the Alexander von Humboldt Foundation, the French