Spectrum and extension of the inverse-Compton emission of the Crab Nebula from a combined Fermi-LAT and H.E.S.S. analysis

¹ Dublin Institute for Advanced Studies, 31 Fitzwilliam Place, Dublin 2, Ireland
² Max-Planck-Institut für Kernphysik, PO Box 103980 69029 Heidelberg, Germany
³ Yerevan State University, 1 Alek Manukyan St, Yerevan 0025, Armenia
⁴ Landessternwarte, Universität Heidelberg, Königstuhl, 69117 Heidelberg, Germany
⁵ Kapteyn Astronomical Institute, University of Groningen, Landleven 12, 9747 AD Groningen, The Netherlands
⁶ Laboratoire Leprince-Ringuet, École Polytechnique, CNRS, Institut Polytechnique de Paris, 91128 Palaiseau, France
⁷ University of Namibia, Department of Physics, Private Bag 13301, Windhoek 10005, Namibia
⁸ Centre for Space Research, North-West University, Potchefstroom 2520, South Africa
⁹ Universität Hamburg, Institut für Experimentalphysik, Luruper Chaussee 149, 22761 Hamburg, Germany
¹⁰ Deutsches Elektronen-Synchrotron DESY, Platanenallee 6, 15738 Zeuthen, Germany
¹¹ Institut für Physik und Astronomie, Universität Potsdam, Karl-Liebknecht-Strasse 24/25, 14476 Potsdam, Germany
¹² Université de Paris, CNRS, Astroparticule et Cosmologie, 75013 Paris, France
¹³ Department of Physics and Electrical Engineering, Linnaeus University, 351 95 Växjö, Sweden
¹⁴ Institut für Physik, Humboldt-Universität zu Berlin, Newtonstr. 15, 12489 Berlin, Germany
¹⁵ Institut für Astronomie und Astrophysik, Universität Tübingen, Sand 1, 72076 Tübingen, Germany
¹⁶ Laboratoire Univers et Théories, Observatoire de Paris, Université PSL, CNRS, Université Paris Cité, 5 Pl. Jules Janssen, 92190 Meudon, France
¹⁷ Sorbonne Université, Université Paris-Diderot, Sorbonne Paris Cité, CNRS/IN2P3, Laboratoire de Physique Nucléaire et de Hautes Énergies, LPNHE, 4 Place Jussieu, 75252 Paris, France
¹⁸ IRFU, CEA, Université Paris-Saclay, 91191 Gif-sur-Yvette, France
¹⁹ University of Oxford, Department of Physics, Denys Wilkinson Building, Keble Road, Oxford OX1 3RH, UK
²⁰ Friedrich-Alexander-Universität Erlangen-Nürnberg, Erlangen Centre for Astroparticle Physics, Nikolaus-Fiebiger-Str. 2, 91058 Erlangen, Germany
²¹ Astronomical Observatory, The University of Warsaw, Al. Ujazdowskie 4, 00-478 Warsaw, Poland
²² Université Savoie Mont Blanc, CNRS, Laboratoire d’Annecy de Physique des Particules – IN2P3, 74000 Annecy, France
²³ Instytut Fizyki Jdrowej PAN, ul. Radzikowskiego 152, 31-342 Kraków, Poland
²⁴ Université Bordeaux, CNRS, LP2I Bordeaux, UMR 5797, 33170 Gradignan, France
²⁵ School of Physics, University of the Witwatersrand, 1 Jan Smuts Avenue, Braamfontein, Johannesburg 2050, South Africa
²⁶ Laboratoire Univers et Particules de Montpellier, Université Montpellier, CNRS/IN2P3, CC 72, Place Eugène Bataillon, 34095 Montpellier Cedex 5, France
²⁷ School of Physical Sciences, University of Adelaide, Adelaide 5005, Australia
²⁸ Aix-Marseille Université, CNRS/IN2P3, CPPM, Marseille, France
²⁹ School of Science, Western Sydney University, Locked Bag 1797, Penrith South DC, NSW 2751, Australia
³⁰ Universität Innsbruck, Institut für Astro- und Teilchenphysik, Technikerstraße 25, 6020 Innsbruck, Austria
³¹ Obserwatorium Astronomiczne, Uniwersytet Jagielloński, ul. Orla 171, 30-244 Kraków, Poland
³² Institute of Astronomy, Faculty of Physics, Astronomy and Informatics, Nicolaus Copernicus University, Grudziadzka 5, 87-100 Torun, Poland
³³ Nicolaus Copernicus Astronomical Center, Polish Academy of Sciences, ul. Bartycka 18, 00-716 Warsaw, Poland
³⁴ Department of Physics and Astronomy, The University of Leicester, University Road, Leicester LE1 7RH, UK
³⁵ GRAPPA, Anton Pannekoek Institute for Astronomy, University of Amsterdam, Science Park 904, 1098 XH Amsterdam, The Netherlands
³⁶ Yerevan Physics Institute, 2 Alikhanian Brothers St., 0036 Yerevan, Armenia
³⁷ Department of Physics, Konan University, 8-9-1 Okamoto, Higashinada, Kobe, Hyogo 658-8501, Japan
³⁸ 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
³⁹ RIKEN, 2-1 Hirosawa, Wako, Saitama 351-0198, Japan
⁴⁰ Theoretical Division, Los Alamos National Laboratory Los Alamos, Alamos, NM 87545, USA

Received: 17 November 2023
Accepted: 18 March 2024

Abstract

The Crab Nebula is a unique laboratory for studying the acceleration of electrons and positrons through their non-thermal radiation. Observations of very-high-energy γ rays from the Crab Nebula have provided important constraints for modelling its broadband emission. We present the first fully self-consistent analysis of the Crab Nebula’s γ-ray emission between 1 GeV and ∼100 TeV, that is, over five orders of magnitude in energy. Using the open-source software package GAMMAPY, we combined 11.4 yr of data from the Fermi Large Area Telescope and 80 h of High Energy Stereoscopic System (H.E.S.S.) data at the event level and provide a measurement of the spatial extension of the nebula and its energy spectrum. We find evidence for a shrinking of the nebula with increasing γ-ray energy. Furthermore, we fitted several phenomenological models to the measured data, finding that none of them can fully describe the spatial extension and the spectral energy distribution at the same time. Especially the extension measured at TeV energies appears too large when compared to the X-ray emission. Our measurements probe the structure of the magnetic field between the pulsar wind termination shock and the dust torus, and we conclude that the magnetic field strength decreases with increasing distance from the pulsar. We complement our study with a careful assessment of systematic uncertainties.