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Resolving Be stars with the MAGIC+LST-1 SII: γ Cas first results and future prospects

Published online by Cambridge University Press:  09 November 2026

Alejo Cifuentes Santos Open the ORCID record for Alejo Cifuentes Santos [Opens in a new window] ,
Tarek Hassan ,
Irene Jiménez Martínez ,
Victor Acciari ,
Irene Burelli ,
Juan Cortina ,
Domenico della Volpe ,
Carlos Díaz Ginzo ,
Fernando Frías García-Lago  and
Iñigo Jorge
...Show all authors
Alejo Cifuentes Santos*
Affiliation:
Centro de Investigaciones Energéticas, Medioambientales y Tecnológicas (CIEMAT), Av. Complutense, 40, Madrid, Spain
Tarek Hassan
Affiliation:
Centro de Investigaciones Energéticas, Medioambientales y Tecnológicas (CIEMAT), Av. Complutense, 40, Madrid, Spain
Irene Jiménez Martínez
Affiliation:
Max-Planck-Institut für Physik, D-85748 Garching, Germany
Victor Acciari
Affiliation:
Institut de Física d’Altes Energies (IFAE), 08193 Bellaterra (Barcelona), Spain
Irene Burelli
Affiliation:
Institut de Física d’Altes Energies (IFAE), 08193 Bellaterra (Barcelona), Spain
Juan Cortina
Affiliation:
Centro de Investigaciones Energéticas, Medioambientales y Tecnológicas (CIEMAT), Av. Complutense, 40, Madrid, Spain Instituto de Astrofísica de Canarias (IAC), C. Vía Láctea, s/n, 38205 La Laguna, Santa Cruz de Tenerife
Domenico della Volpe
Affiliation:
Université de Genève, Quai Ernest-Ansermet 24, 1211 Genève, Switzerland
Carlos Díaz Ginzo
Affiliation:
Centro de Investigaciones Energéticas, Medioambientales y Tecnológicas (CIEMAT), Av. Complutense, 40, Madrid, Spain
Fernando Frías García-Lago
Affiliation:
Instituto de Astrofísica de Canarias (IAC), C. Vía Láctea, s/n, 38205 La Laguna, Santa Cruz de Tenerife Departamento de Astrofísica, Universidad de La Laguna, C. Vía Láctea, s/n, 38205 La Laguna, Santa Cruz de Tenerife
Iñigo Jorge
Affiliation:
Centro de Investigaciones Energéticas, Medioambientales y Tecnológicas (CIEMAT), Av. Complutense, 40, Madrid, Spain
Gustavo Martínez
Affiliation:
Centro de Investigaciones Energéticas, Medioambientales y Tecnológicas (CIEMAT), Av. Complutense, 40, Madrid, Spain
Ramik Mirzoyan
Affiliation:
Max-Planck-Institut für Physik, D-85748 Garching, Germany
Miguel Polo
Affiliation:
Centro de Investigaciones Energéticas, Medioambientales y Tecnológicas (CIEMAT), Av. Complutense, 40, Madrid, Spain
Aramis Raiola
Affiliation:
Université de Genève, Quai Ernest-Ansermet 24, 1211 Genève, Switzerland
Juan José Rodríguez-Vázquez
Affiliation:
Centro de Investigaciones Energéticas, Medioambientales y Tecnológicas (CIEMAT), Av. Complutense, 40, Madrid, Spain
Prasenjit Saha
Affiliation:
Physik-Institut, Universität Zürich, Winterthurerstrasse 190, 8057 Zürich, Switzerland
Thomas Schweizer
Affiliation:
Max-Planck-Institut für Physik, D-85748 Garching, Germany
Lucijana Stanic
Affiliation:
Physik-Institut, Universität Zürich, Winterthurerstrasse 190, 8057 Zürich, Switzerland
Álvaro García Lozano
Affiliation:
Centro de Investigaciones Energéticas, Medioambientales y Tecnológicas (CIEMAT), Av. Complutense, 40, Madrid, Spain
*
email: alejo.cifuentes@ciemat.es
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Abstract

Most stars have angular diameters of less than one milliarcsecond (mas), making optical interferometry essential for direct size and shape measurements. Historically, optical amplitude interferometers have dominated this field. However, OB main-sequence stars are not the ideal targets for these instruments: they are brighter in short wavelengths where amplitude interferometry becomes very technically challenging and generally have angular diameters beyond their typical resolution.

A new generation of optical intensity interferometers, capable of observing in the Blue band, are emerging by taking advantage of existing infrastructure of Imaging Atmospheric Cherenkov Telescopes (IACTs). Among those, the MAGIC+LST-1 Stellar Intensity Interferometer (SII) is the most sensitive. Once fully commissioned, it will be capable of resolving stars with angular diameters between 0.3 to 1 mas up to magnitude 6 in B in just a few hours. During its first year of operations, the MAGIC + LST-1 SII has been able to resolve the shape of the Be star $\gamma$ Cassiopeiae ($\gamma$ Cas). Additionally, new scientific cases, such as resolving massive close binaries are being studied.

Keywords

Optical Intensity InterferometryInstrumentation: High Angular ResolutionStars: Fundamental ParametersStars: Be starsStars: Fast RotatorsStars: Massive close binaries

Information

Type
Contributed Paper
Information
Proceedings of the International Astronomical Union , Volume 21 , Symposium S402: Massive Stars Across Redshifts in the Era of JWST and Large Surveys , January 2025 , pp. 150 - 161
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Copyright
© The Author(s), 2026. Published by Cambridge University Press on behalf of The International Astronomical Union

1. Introduction

Stellar Intensity Interferometry (SII), first demonstrated by Hanbury Brown & Twiss (Hanbury Brown 1956; Hanbury Brown & Twiss 1956) and implemented at the Narrabri Observatory (Hanbury Brown et al. 1974), measures correlations in the intensity fluctuations of light collected by separated telescopes. SII is more robust against atmospheric turbulence and optical imperfections than Amplitude Interferometry, allowing observations at short optical wavelengths and over long baselines (greater than 100 m$\gt100~m$) (Dravins et al. 2012). Imaging Atmospheric Cherenkov Telescopes (IACTs), designed for very-high-energy (VHE; upper E greater than 100 upper G e upper V$E\gt100~GeV$) gamma-ray observations, are built in arrays of telescopes with large light-collecting areas and photodetectors with nanosecond-level timing resolution, making them naturally well suited for the implementation of a cost-effective SII. In the recent years, VERITAS (Abeysekara et al. 2020), MAGIC (Acciari et al. 2020; Abe et al. 2024) and H.E.S.S (Zmija et al. 2024) collaborations have all demonstrated successful angular size measurements of massive stars using this technique.

2. The MAGIC+LST-1 SII

The MAGIC telescopes are a system of two IACTs of 17 m mirror dish diameter, with a separation of 87 m, located at the Roque de los Muchachos Observatory (ORM) in La Palma, Spain. Technical modifications were implemented to enable intensity interferometry observations and, since the system was fully commissioned in 2022, the MAGIC SII has been regularly observing during full Moon periods when the night-sky background light is too intense for VHE observations (Abe et al. 2024). The Large-Sized Telescopes (LSTs) will be the largest IACTs of the Cherenkov Telescope Array Observatory (CTAO), with a mirror dish diameter of 23 m. LST-1 is the first LST built in the CTAO North site at the ORM, with a separation of 95 m and 147 m to MAGIC-II and MAGIC-I respectively. The technical modifications described in Cifuentes et al. (2024), have allowed the LST-1 to perform SII observations jointly with MAGIC, since 2024. The SII observing mode has no impact on the VHE observations, but has rather effectively increased the scientific duty cycle of both MAGIC and CTAO LST-1. Observations with the MAGIC+LST-1 SII are carried out regularly during full Moon periods, mainly targeting calibration stars for the commissioning of the instrument (see preliminary results for calibration stars on Figure 1), and some scientific targets such as the Be star gamma$\gamma$ Cas.

Figure 1.

Measurements of the stellar angular diameter of 12 calibration stars, assuming a uniform disk profile, with the MAGIC+LST-1 SII. The measurements are represented as a function of their reference values from MAGIC SII (Blue band), when available, or from CHARA (Near-Infrared) otherwise. For the MAGIC+LST-1 SII, only statistical errors are shown.

Scatter plot showing measured angular diameter versus reference angular diameter with error bars.

3. Resolving Be stars with SII

Optical interferometry has become a key technique to study the effects of rapid rotation in stars and their circumstellar environments (van Belle 2012; Rivinius et al. 2013). Nevertheless, the presence of a decretion disk around active Be stars makes it very challenging to directly measure the photospheric oblateness of these objects with Amplitude Interferometry, due to the non-negligible contribution of the disk at the wavelengths where amplitude interferometers operate. The capability of SII to observe at short optical wavelengths (425-26 nm in the case of MAGIC+LST-1 SII), where the disk contribution is less significant, makes it a promising technique to resolve the photospheres of Be stars.

3.1. gamma$\gamma$ Cas results with the MAGIC+LST-1 SII

The Be star gamma$\gamma$ Cas (HD 5394, type B0.5IVe) has been observed with the MAGIC SII since 2022 and with the MAGIC+LST-1 SII since 2024. Preliminary results from the analysis of the MAGIC+LST-1 SII 2024 observations (see Figure 2), show that a uniform ellipse model is preferred over a uniform disk model, with a 3% statistical uncertainty on the axial ratio, consistent with a close-to-critical rotation velocity. Our preliminary best-fit values for the uniform ellipse model show a very good agreement with independent results obtained with the VERITAS SII (Archer et al. 2025), as shown in Table 1.

Figure 2.

Measurements of gamma$\gamma$ Cas with the MAGIC+LST-1 SII. Normalized squared visibilities are shown as a function of the baseline. The best fit for the uniform disk (blue) and uniform ellipse (orange) models are shown as well as the residuals for each fit (using the same colors). The color code of the visibility points indicates the position angle of each baseline, as shown on the inner figure showing the UV-plane coverage. The reduced chi squared$\chi ^2$ as well as the residuals show a preference for the uniform ellipse model.

A graph showing measurements of gamma Cas with different models and residuals.
Table 1.

Best-fit parameters for the uniform ellipse model of gamma$\gamma$ Cas obtained with two IACT-based SII systems: MAGIC+LST-1 SII and VERITAS SII.

A table comparing best-fit parameters for the uniform ellipse model of γ Cas using two IACT-based SII systems.
Table 1 Long description

A table comparing best-fit parameters for the uniform ellipse model of γ Cas using two IACT-based SII systems. The table has 2 columns and 4 rows. Column headers are Parameter, MAGIC+LST-1 SII, and VERITAS SII. Row 1: θmaj (mas), 0.59 ± 0.01 (stat), 0.55 ± 0.03 (stat) ±0.03 (sys). Row 2: θmin/θmaj, 0.76 ± 0.02 (stat), 0.78 ± 0.02 (stat) ±0.01 (sys). Row 3: Equatorial position angle (deg), 34 ± 3 (stat), 26 ± 5 (stat) ±7 (sys).

Although the uniform ellipse model provides a good first approximation, it fails to describe the full complexity of gamma$\gamma$ Cas’ photosphere, neglecting observable features such as the gravity darkening (von Zeipel 1924; Espinosa Lara & Rieutord 2011). Combining the MAGIC+LST1 SII results with those inferred from spectroscopic data, we aim to provide a more complete description of its photosphere in a future publication (in progress).

4. Future Prospects

Thanks to the improved sensitivity, angular resolution and UV-plane coverage enabled by the addition of LST-1 to the MAGIC SII, we are also exploring the possibility of resolving massive close binaries with the MAGIC+LST-1 SII. Simulations for Spica (alpha$\alpha$ Vir), a B1 III-IV + B2 V binary with a period of 4.0145 days and a maximum separation of 1.5 mas (Herbison-Evans & Cramer 1969; Tkachenko et al. 2016), show that we could constrain the angular separation, position angle and angular diameters of both components in just a few observing nights (Raiola et al. 2025). Further improvements are expected, as the remaining three LSTs of the CTAO North array will be added to the MAGIC+LST-1 SII, once they are operational. With 15 independent baselines of up to 260m the MAGIC+4LSTs SII will have an unprecedented angular resolution of 0.15 mas, together with an improved sensitivity and very dense UV-plane coverage (Jiménez Martínez et al. 2025).

A more dramatic breakthrough in sensitivity could be achieved by implementing an advanced IACT-based SII system, such as the “I3T concept” (Gori et al. 2021) or, more specifically for MAGIC and the CTAO LSTs: “The Butterfly’s Eye Camera for IACTs”, in which segments of the IACT mirror would be focused onto different pixels of its camera (J. Cortina et al., submitted).

5. Conclusions

The MAGIC+LST-1 SII provides a great tool for studying massive stars, thanks to its high angular resolution and sensitivity to blue wavelengths. Since the addition of LST-1 to the MAGIC SII, we have been able to increase the scientific capabilities of the system, allowing for the study of more complex systems than before, such as Be stars and massive close binaries. Preliminary results for gamma$\gamma$ Cas are very promising, showing the capabilities of our system to resolve the photosphere of Be stars with active decretion disks.

The addition of the remaining LSTs of CTAO North will greatly enhance the capabilities of the system in the near future, opening the possibility of studying a wider variety of targets. To increase the sensitivity of the system even more, further technical upgrades are under study.

Acknowledgements

The MAGIC collaboration would like to thank the Instituto de Astrofísica de Canarias for the excellent working conditions at the Observatorio del Roque de los Muchachos in La Palma. The financial support of the German BMBF, MPG and HGF; the Italian INFN and INAF; the Swiss National Fund SNF; the grants PID2019-104114RB-C31, PID2019-104114RB-C32, PID2019-104114RB-C33, PID2019-105510GB-C31, PID2019-107847RB-C41, PID2019-107847RB-C42, PID2019-107847RB-C44, PID2019-107988GB-C22, PID2022-136828NB-C41, PID2022-137810NB-C22, PID2022-138172NB-C41, PID2022-138172NB-C42, PID2022-138172NB-C43, PID2022-139117NB-C41, PID2022-139117NB-C42, PID2022-139117NB-C43, PID2022-139117NB-C44 funded by the Spanish MCIN/AEI/ 10.13039/501100011033 and “ERDF A way of making Europe”; the Indian Department of Atomic Energy; the Japanese ICRR, the University of Tokyo, JSPS, and MEXT; the Bulgarian Ministry of Education and Science, National RI Roadmap Project DO1-400/18.12.2020 and the Academy of Finland grant nr. 320045 is gratefully acknowledged. This work was also been supported by Centros de Excelencia “Severo Ochoa” y Unidades “María de Maeztu” program of the Spanish MCIN/AEI/ 10.13039/501100011033 (CEX2019-000920-S, CEX2019-000918-M, CEX2021-001131-S) and by the CERCA institution and grants 2021SGR00426 and 2021SGR00773 of the Generalitat de Catalunya; by the Croatian Science Foundation (HrZZ) Project IP-2022-10-4595 and the University of Rijeka Project uniri-prirod-18-48; by the Deutsche Forschungsgemeinschaft (SFB1491) and by the Lamarr-Institute for Machine Learning and Artificial Intelligence; by the Polish Ministry Of Education and Science grant No. 2021/WK/08; and by the Brazilian MCTIC, CNPq and FAPERJ.

The CTAO-LST project gratefully acknowledge financial support from the following agencies and organizations:

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq) Grant 309053/2022-6 and Fundação de Amparo à Pesquisa do Estado do Rio de Janeiro (FAPERJ) Grants E-26/200.532/2023 and E-26/211.342/2021, Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP), Fundação de Apoio à Ciência, Tecnologia e Inovação do Paraná - Fundação Araucária, Ministry of Science, Technology, Innovations and Communications (MCTIC), Brasil; Ministry of Education and Science, National RI Roadmap Project DO1-153/28.08.2018, Bulgaria; Croatian Science Foundation (HrZZ) Project IP-2022-10-4595, Rudjer Boskovic Institute, University of Osijek, University of Rijeka, University of Split, Faculty of Electrical Engineering, Mechanical Engineering and Naval Architecture, University of Zagreb, Faculty of Electrical Engineering and Computing, Croatia; Ministry of Education, Youth and Sports, MEYS LM2023047, EU/MEYS CZ.02.1.01/0.0/0.0/16_013/0001403, CZ.02.1.01/0.0/0.0/18_046/0016007, CZ.02.1.01/0.0/0.0/16_019/0000754, CZ.02.01.01/00/22_008/0004632 and CZ.02.01.01/00/23_015/0008197 Czech Republic; CNRS-IN2P3, the French Programme d’investissements d’avenir and the Enigmass Labex, This work has been done thanks to the facilities offered by the Univ. Savoie Mont Blanc - CNRS/IN2P3 MUST computing center, France; Max Planck Society, German Bundesministerium für Forschung, Technologie und Raumfahrt (Verbundforschung/ErUM), the Deutsche Forschungsgemeinschaft (SFB 1491) and the Lamarr-Institute for Machine Learning and Artificial Intelligence, Germany; Istituto Nazionale di Astrofisica (INAF), Istituto Nazionale di Fisica Nucleare (INFN), Italian Ministry for University and Research (MUR), and the financial support from the European Union – Next Generation EU under the project IR0000012 - CTA+ (CUP C53C22000430006), announcement N.3264 on 28/12/2021: “Rafforzamento e creazione di IR nell’ambito del Piano Nazionale di Ripresa e Resilienza (PNRR)”; ICRR, University of Tokyo, JSPS, MEXT, Japan; JST SPRING - JPMJSP2108; Narodowe Centrum Nauki, grant number 2023/50/A/ST9/00254, Poland; The Spanish groups acknowledge the Spanish Ministry of Science and Innovation and the Spanish Research State Agency (AEI) through the government budget lines PGE2022/28.06.000X.711.04, 28.06.000X.411.01 and 28.06.000X.711.04 of PGE 2023, 2024 and 2025, and grants PID2019-104114RB-C31, PID2019-107847RB-C44, PID2019-105510GB-C31, PID2019-104114RB-C33, PID2019-107847RB-C43, PID2019-107847RB-C42, PID2019-107988GB-C22, PID2021-124581OB-I00, PID2021-125331NB-I00, PID2022-136828NB-C41, PID2022-137810NB-C22, PID2022-138172NB-C41, PID2022-138172NB-C42, PID2022-138172NB-C43, PID2022-139117NB-C41, PID2022-139117NB-C42, PID2022-139117NB-C43, PID2022-139117NB-C44, PID2022-136828NB-C42, PID2024-155316NB-I00, PDC2023-145839-I00 funded by the Spanish MCIN/AEI/10.13039/501100011033 and by ERDF/EU and NextGenerationEU PRTR; CSIC PIE 202350E189; the “Centro de Excelencia Severo Ochoa” program through grants no. CEX2020-001007-S, CEX2021-001131-S, CEX2024-001442-S; the “Unidad de Excelencia María de Maeztu” program through grants no. CEX2019-000918-M, CEX2020-001058-M; the “Ramón y Cajal” program through grants RYC2021-032991-I funded by MICIN/AEI/10.13039/501100011033 and the European Union “NextGenerationEU”/PRTR and RYC2020-028639-I; the “Juan de la Cierva-Incorporación” program through grant no. IJC2019-040315-I and “Juan de la Cierva-formación” through grant JDC2022-049705-I; the “Viera y Clavijo” postdoctoral program of Universidad de La Laguna, funded by the Agencia Canaria de Investigación, Innovación y Sociedad de la Información. They also acknowledge the “Atracción de Talento” program of Comunidad de Madrid through grant no. 2019-T2/TIC-12900; “MAD4SPACE: Desarrollo de tecnologías habilitadoras para estudios del espacio en la Comunidad de Madrid” (TEC-2024/TEC-182) project, Doctorado Industrial (IND2024/TIC34250) and Ayudas para la contratación de personal investigador predoctoral en formación (PIPF-2023/TEC-29694) funded by Comunidad de Madrid; the La Caixa Banking Foundation, grant no. LCF/BQ/PI21/11830030; Junta de Andalucía under Plan Complementario de I+D+I (Ref. AST22_0001) and Plan Andaluz de Investigación, Desarrollo e Innovación as research group FQM-322; Project ref. AST22_00001_9 with funding from NextGenerationEU funds; the “Ministerio de Ciencia, Innovación y Universidades” and its “Plan de Recuperación, Transformación y Resiliencia”; “Consejería de Universidad, Investigación e Innovación” of the regional government of Andalucía and “Consejo Superior de Investigaciones Científicas”, Grant CNS2023-144504 funded by MICIU/AEI/10.13039/501100011033 and by the European Union NextGenerationEU/PRTR, the European Union’s Recovery and Resilience Facility-Next Generation, in the framework of the General Invitation of the Spanish Government’s public business entity Red.es to participate in talent attraction and retention programmes within Investment 4 of Component 19 of the Recovery, Transformation and Resilience Plan; Junta de Andalucía under Plan Complementario de I+D+I (Ref. AST22_00001), Plan Andaluz de Investigación, Desarrollo e Innovación (Ref. FQM-322). “Programa Operativo de Crecimiento Inteligente” FEDER 2014-2020 (Ref. ESFRI-2017-IAC-12), Ministerio de Ciencia e Innovación, 15% co-financed by Consejería de Economía, Industria, Comercio y Conocimiento del Gobierno de Canarias; the “CERCA” program and the grants 2021SGR00426 and 2021SGR00679, all funded by the Generalitat de Catalunya; and the European Union’s NextGenerationEU (PRTR-C17.I1). This work is funded/Co-funded by the European Union (ERC, MicroStars, 101076533). This research used the computing and storage resources provided by the Port d’Informació Científica (PIC) data center. State Secretariat for Education, Research and Innovation (SERI) and Swiss National Science Foundation (SNSF), Switzerland; The research leading to these results has received funding from the European Union’s Seventh Framework Programme (FP7/2007-2013) under grant agreements No 262053 and No 317446; This project is receiving funding from the European Union’s Horizon 2020 research and innovation programs under agreement No 676134; ESCAPE - The European Science Cluster of Astronomy & Particle Physics ESFRI Research Infrastructures has received funding from the European Union’s Horizon 2020 research and innovation programme under Grant Agreement no. 824064.

Full Author List: CTAO-LST Project

K. AbeSuperscript 1$^{1}$, S. Abesquared$^{2}$, A. Abhishekcubed$^{3}$, F. AceroSuperscript 4 comma 5$^{4,5}$, A. Aguasca-CabotSuperscript 6$^{6}$, I. AgudoSuperscript 7$^{7}$, C. AlispachSuperscript 8$^{8}$, D. AmbrosinoSuperscript 9$^{9}$, F. AmbrosinoSuperscript 10$^{10}$, L. A. AntonelliSuperscript 10$^{10}$, C. AramoSuperscript 9$^{9}$, A. Arbet-EngelsSuperscript 11$^{11}$, C. ArcaroSuperscript 12$^{12}$, T.T.H. ArnesenSuperscript 13$^{13}$, P. AubertSuperscript 14$^{14}$, A. BaktashSuperscript 15$^{15}$, M. BalboSuperscript 8$^{8}$, A. BambaSuperscript 16$^{16}$, A. Baquero LarrivaSuperscript 17 comma 18$^{17,18}$, U. Barres de AlmeidaSuperscript 19$^{19}$, J. A. BarrioSuperscript 17$^{17}$, L. Barrios JiménezSuperscript 13$^{13}$, I. BatkovicSuperscript 12$^{12}$, J. Baxtersquared$^{2}$, J. Becerra GonzálezSuperscript 13$^{13}$, J. BerneteSuperscript 20$^{20}$, A. BertiSuperscript 11$^{11}$, E. BissaldiSuperscript 21$^{21}$, O. BlanchSuperscript 22$^{22}$, G. BonnoliSuperscript 23$^{23}$, P. BordasSuperscript 6$^{6}$, A. BriscioliSuperscript 24$^{24}$, G. BrunelliSuperscript 25 comma 26$^{25,26}$, J. BucesSuperscript 17$^{17}$, A. BulgarelliSuperscript 25$^{25}$, I. BurelliSuperscript 27$^{27}$, L. BurmistrovSuperscript 28$^{28}$, M. CardilloSuperscript 29$^{29}$, S. CaroffSuperscript 14$^{14}$, A. CarosiSuperscript 10$^{10}$, R. CarraroSuperscript 10$^{10}$, F. CassolSuperscript 24$^{24}$, D. CerasoleSuperscript 30$^{30}$, A. Cerviño CortínezSuperscript 17$^{17}$, Y. ChaiSuperscript 11$^{11}$, G. ChonSuperscript 11$^{11}$, L. ChytkaSuperscript 31$^{31}$, G. M. CicciariSuperscript 32 comma 33$^{32,33}$, J. L. ContrerasSuperscript 17$^{17}$, J. CortinaSuperscript 20$^{20}$, H. CostantiniSuperscript 24$^{24}$, M. CroisonnierSuperscript 22$^{22}$, M. DalchenkoSuperscript 28$^{28}$, G. D’AmicoSuperscript 22$^{22}$, P. Da VelaSuperscript 25$^{25}$, F. DazziSuperscript 10$^{10}$, A. De AngelisSuperscript 12$^{12}$, M. de Bony de LavergneSuperscript 34$^{34}$, R. Del BurgoSuperscript 9$^{9}$, C. DelgadoSuperscript 20$^{20}$, J. Delgado MengualSuperscript 35$^{35}$, D. della VolpeSuperscript 28$^{28}$, B. De LottoSuperscript 27$^{27}$, L. Del PeralSuperscript 36$^{36}$, R. de MenezesSuperscript 37$^{37}$, G. De PalmaSuperscript 21$^{21}$, V. de SouzaSuperscript 38$^{38}$, C. DíazSuperscript 20$^{20}$, L. Di BellaSuperscript 39$^{39}$, A. Di PianoSuperscript 25$^{25}$, F. Di PierroSuperscript 37$^{37}$, R. Di TriaSuperscript 30$^{30}$, L. Di VenereSuperscript 40$^{40}$, D. Dominis PresterSuperscript 41$^{41}$, A. DoniniSuperscript 10$^{10}$, D. DornerSuperscript 42$^{42}$, L. EisenbergerSuperscript 42$^{42}$, D. ElsässerSuperscript 39$^{39}$, G. EmerySuperscript 7$^{7}$, L. FeligioniSuperscript 24$^{24}$, F. FerrarottoSuperscript 43$^{43}$, A. FiassonSuperscript 14 comma 44$^{14,44}$, L. FoffanoSuperscript 29$^{29}$, Y. FukazawaSuperscript 45$^{45}$, S. GallozziSuperscript 10$^{10}$, R. Garcia LópezSuperscript 13$^{13}$, S. Garcia SotoSuperscript 20$^{20}$, C. GasbarraSuperscript 46$^{46}$, D. GasparriniSuperscript 46$^{46}$, J. Giesbrecht PaivaSuperscript 19$^{19}$, N. GigliettoSuperscript 21$^{21}$, F. GiordanoSuperscript 30$^{30}$, N. GodinovicSuperscript 47$^{47}$, T. GradetzkeSuperscript 39$^{39}$, R. GrauSuperscript 22$^{22}$, J. GreenSuperscript 11$^{11}$, G. GrolleronSuperscript 14$^{14}$, S. GunjiSuperscript 48$^{48}$, P. GüntherSuperscript 42$^{42}$, J. HackfeldSuperscript 49$^{49}$, D. HadaschSuperscript 50$^{50}$, M. HashizumeSuperscript 45$^{45}$, T. HassanSuperscript 20$^{20}$, K. HayashiSuperscript 51 comma 2$^{51,2}$, L. HeckmannSuperscript 11 comma 52$^{11,52}$, M. HellerSuperscript 28$^{28}$, J. Herrera LlorenteSuperscript 13$^{13}$, N. Hiroshimasquared$^{2}$, D. HoffmannSuperscript 24$^{24}$, D. HornsSuperscript 15$^{15}$, J. HoulesSuperscript 24$^{24}$, D. HrupecSuperscript 53$^{53}$, R. ImazawaSuperscript 45$^{45}$, T. Inadasquared$^{2}$, S. InoueSuperscript 54 comma 2$^{54,2}$, K. IokaSuperscript 55$^{55}$, M. IoriSuperscript 43$^{43}$, T. Itokawasquared$^{2}$, A. IulianoSuperscript 9$^{9}$, J. JahanviSuperscript 27$^{27}$, I. Jimenez MartinezSuperscript 11$^{11}$, J. Jimenez QuilesSuperscript 22$^{22}$, I. Jorge RodrigoSuperscript 20$^{20}$, J. JurysekSuperscript 56$^{56}$, M. KagayaSuperscript 51 comma 2$^{51,2}$, V. KarasSuperscript 57$^{57}$, H. KatagiriSuperscript 58$^{58}$, D. KerszbergSuperscript 22 comma 59$^{22,59}$, T. KiyomotoSuperscript 60$^{60}$, Y. Kobayashisquared$^{2}$, K. KohriSuperscript 61$^{61}$, P. KorneckiSuperscript 7$^{7}$, H. Kubosquared$^{2}$, J. KushidaSuperscript 1$^{1}$, B. LacaveSuperscript 28$^{28}$, M. LainezSuperscript 17$^{17}$, A. LamastraSuperscript 10$^{10}$, L. LemoigneSuperscript 14$^{14}$, M. LinhoffSuperscript 39$^{39}$, S. LombardiSuperscript 10$^{10}$, F. LongoSuperscript 62$^{62}$, R. López-CotoSuperscript 7$^{7}$, A. López-OramasSuperscript 13$^{13}$, S. LoporchioSuperscript 30$^{30}$, J. Lozano BahiloSuperscript 36$^{36}$, F. LucarelliSuperscript 10$^{10}$, H. LucianiSuperscript 62$^{62}$, P. L. Luque-EscamillaSuperscript 63$^{63}$, M. MakarievSuperscript 64$^{64}$, M. MallamaciSuperscript 32 comma 33$^{32,33}$, D. MandatSuperscript 56$^{56}$, K. MannheimSuperscript 42$^{42}$, F. MariniSuperscript 12$^{12}$, M. MariottiSuperscript 12$^{12}$, P. MarquezSuperscript 65$^{65}$, G. MarsellaSuperscript 33 comma 32$^{33,32}$, J. MartíSuperscript 63$^{63}$, D. MartinSuperscript 17$^{17}$, O. MartinezSuperscript 66 comma 67$^{66,67}$, G. MartínezSuperscript 20$^{20}$, M. MartínezSuperscript 22$^{22}$, M. Massacubed$^{3}$, D. MazinSuperscript 2 comma 11$^{2,11}$, J. Méndez-GallegoSuperscript 7$^{7}$, S. MenonSuperscript 10 comma 68$^{10,68}$, E. Mestre GuillenSuperscript 69$^{69}$, D. MiceliSuperscript 12$^{12}$, T. MienerSuperscript 17$^{17}$, J. M. MirandaSuperscript 66$^{66}$, M. Molero GonzalezSuperscript 13$^{13}$, E. MolinaSuperscript 13$^{13}$, T. MontaruliSuperscript 28$^{28}$, A. MoralejoSuperscript 22$^{22}$, A. MorselliSuperscript 46$^{46}$, V. MoyaSuperscript 17$^{17}$, A. L. MüllerSuperscript 56$^{56}$, H. MuraishiSuperscript 70$^{70}$, S. NagatakiSuperscript 71$^{71}$, T. NakamoriSuperscript 48$^{48}$, A. NeronovSuperscript 72$^{72}$, D. Nieto CastañoSuperscript 17$^{17}$, M. Nievas RosilloSuperscript 13$^{13}$, L. Nikoliccubed$^{3}$, K. NodaSuperscript 54 comma 2$^{54,2}$, V. NovotnySuperscript 73$^{73}$, S. Nozakisquared$^{2}$, M. Ohishisquared$^{2}$, A. OkumuraSuperscript 74 comma 75$^{74,75}$, R. OritoSuperscript 76$^{76}$, L. Orsinicubed$^{3}$, J. Otero-SantosSuperscript 12$^{12}$, P. OttanelliSuperscript 77$^{77}$, M. PalatielloSuperscript 10$^{10}$, G. PanebiancoSuperscript 25$^{25}$, D. PanequeSuperscript 11$^{11}$, R. Paoletticubed$^{3}$, J. M. ParedesSuperscript 6$^{6}$, M. PechSuperscript 56 comma 31$^{56,31}$, M. PecimotikaSuperscript 22$^{22}$, M. PeresanoSuperscript 11$^{11}$, F. PerrottaSuperscript 78$^{78}$, F. PfeifleSuperscript 42$^{42}$, M. PihetSuperscript 7$^{7}$, G. PirolaSuperscript 11$^{11}$, C. PlardSuperscript 14$^{14}$, F. Podobnikcubed$^{3}$, M. PoloSuperscript 20$^{20}$, C. Pozo-GonzalézSuperscript 7$^{7}$, E. PrandiniSuperscript 12$^{12}$, S. RainòSuperscript 30$^{30}$, R. RandoSuperscript 12$^{12}$, W. RhodeSuperscript 39$^{39}$, M. RibóSuperscript 6$^{6}$, G. Rodriguez FernandezSuperscript 46$^{46}$, M. D. Rodríguez FríasSuperscript 36$^{36}$, A. RoySuperscript 45$^{45}$, A. RuinaSuperscript 12$^{12}$, E. Ruiz-VelascoSuperscript 14$^{14}$, T. Saitosquared$^{2}$, S. Sakuraisquared$^{2}$, D. A. SanchezSuperscript 14$^{14}$, H. SanoSuperscript 79 comma 2$^{79,2}$, E. Santos MouraSuperscript 38$^{38}$, T. ŠarićSuperscript 47$^{47}$, Y. SatoSuperscript 80$^{80}$, F. G. SaturniSuperscript 10$^{10}$, V. SavchenkoSuperscript 72$^{72}$, F. SchiavoneSuperscript 30$^{30}$, F. SchusslerSuperscript 34$^{34}$, T. SchweizerSuperscript 11$^{11}$, M. Seglar ArroyoSuperscript 22$^{22}$, G. SilvestriSuperscript 12$^{12}$, A. SimonginiSuperscript 10 comma 68$^{10,68}$, J. SitarekSuperscript 81$^{81}$, V. SliusarSuperscript 8$^{8}$, I. SofiaSuperscript 37$^{37}$, J. StriškovićSuperscript 53$^{53}$, M. Strzyssquared$^{2}$, Y. SudaSuperscript 45$^{45}$, A. SunnySuperscript 10 comma 68$^{10,68}$, H. TajimaSuperscript 74$^{74}$, M. TakahashiSuperscript 74$^{74}$, R. Takeishisquared$^{2}$, S. J. TanakaSuperscript 80$^{80}$, D. TateishiSuperscript 60$^{60}$, T. TavernierSuperscript 56$^{56}$, P. TemnikovSuperscript 64$^{64}$, Y. TeradaSuperscript 60$^{60}$, K. TerauchiSuperscript 82$^{82}$, T. TerzicSuperscript 41$^{41}$, M. TeshimaSuperscript 11 comma 2$^{11,2}$, M. TluczykontSuperscript 15$^{15}$, T. Tomurasquared$^{2}$, D. F. TorresSuperscript 50$^{50}$, F. Tramonticubed$^{3}$, P. TravnicekSuperscript 56$^{56}$, G. TripodoSuperscript 33$^{33}$, A. TutoneSuperscript 10$^{10}$, M. VaculaSuperscript 31$^{31}$, M. Vázquez AcostaSuperscript 13$^{13}$, G. Vernacubed$^{3}$, I. VialeSuperscript 12$^{12}$, A. VianaSuperscript 38$^{38}$, A. ViglianoSuperscript 27$^{27}$, C. F. VigoritoSuperscript 37 comma 83$^{37,83}$, E. VisentinSuperscript 37 comma 83$^{37,83}$, V. VitaleSuperscript 46$^{46}$, G. VoutsinasSuperscript 28$^{28}$, I. Vovksquared$^{2}$, T. VuillaumeSuperscript 14$^{14}$, R. WalterSuperscript 8$^{8}$, T. YamamotoSuperscript 84$^{84}$, R. YamazakiSuperscript 80$^{80}$, Y. YaoSuperscript 1$^{1}$, T. YoshidaSuperscript 58$^{58}$, T. Yoshikoshisquared$^{2}$, W. ZhangSuperscript 50$^{50}$, N. ZywuckaSuperscript 81$^{81}$

Superscript 1$^{1}$Department of Physics, Tokai University, 4-1-1, Kita-Kaname, Hiratsuka, Kanagawa 259-1292, Japan. squared$^{2}$Institute for Cosmic Ray Research, University of Tokyo, 5-1-5, Kashiwa-no-ha, Kashiwa, Chiba 277-8582, Japan. cubed$^{3}$INFN and Università degli Studi di Siena, Dipartimento di Scienze Fisiche, della Terra e dell’Ambiente (DSFTA), Sezione di Fisica, Via Roma 56, 53100 Siena, Italy. Superscript 4$^{4}$Université Paris-Saclay, Université Paris Cité, CEA, CNRS, AIM, F-91191 Gif-sur-Yvette Cedex, France. Superscript 5$^{5}$FSLAC IRL 2009, CNRS/IAC, La Laguna, Tenerife, Spain. Superscript 6$^{6}$Departament de Física Quàntica i Astrofísica, Institut de Ciències del Cosmos, Universitat de Barcelona, IEEC-UB, Martí i Franquès, 1, 08028, Barcelona, Spain. Superscript 7$^{7}$Instituto de Astrofísica de Andalucía-CSIC, Glorieta de la Astronomía s/n, 18008, Granada, Spain. Superscript 8$^{8}$Department of Astronomy, University of Geneva, Chemin d’Ecogia 16, CH-1290 Versoix, Switzerland. Superscript 9$^{9}$INFN Sezione di Napoli, Via Cintia, ed. G, 80126 Napoli, Italy. Superscript 10$^{10}$INAF - Osservatorio Astronomico di Roma, Via di Frascati 33, 00040, Monteporzio Catone, Italy. Superscript 11$^{11}$Max-Planck-Institut für Physik, Boltzmannstraße 8, 85748 Garching bei München, Germany. Superscript 12$^{12}$INFN Sezione di Padova and Università degli Studi di Padova, Via Marzolo 8, 35131 Padova, Italy. Superscript 13$^{13}$Instituto de Astrofísica de Canarias and Departamento de Astrofísica, Universidad de La Laguna, C. Vía Láctea, s/n, 38205 La Laguna, Santa Cruz de Tenerife, Spain. Superscript 14$^{14}$Univ. Savoie Mont Blanc, CNRS, Laboratoire d’Annecy de Physique des Particules - IN2P3, 74000 Annecy, France. Superscript 15$^{15}$Universität Hamburg, Institut für Experimentalphysik, Luruper Chaussee 149, 22761 Hamburg, Germany. Superscript 16$^{16}$Graduate School of Science, University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan. Superscript 17$^{17}$IPARCOS-UCM, Instituto de Física de Partículas y del Cosmos, and EMFTEL Department, Universidad Complutense de Madrid, Plaza de Ciencias, 1. Ciudad Universitaria, 28040 Madrid, Spain. Superscript 18$^{18}$Faculty of Science and Technology, Universidad del Azuay, Cuenca, Ecuador. Superscript 19$^{19}$Centro Brasileiro de Pesquisas Físicas, Rua Xavier Sigaud 150, RJ 22290-180, Rio de Janeiro, Brazil. Superscript 20$^{20}$CIEMAT, Avda. Complutense 40, 28040 Madrid, Spain. Superscript 21$^{21}$INFN Sezione di Bari and Politecnico di Bari, via Orabona 4, 70124 Bari, Italy. Superscript 22$^{22}$Institut de Fisica d’Altes Energies (IFAE), The Barcelona Institute of Science and Technology, Campus UAB, 08193 Bellaterra (Barcelona), Spain. Superscript 23$^{23}$INAF - Osservatorio Astronomico di Brera, Via Brera 28, 20121 Milano, Italy. Superscript 24$^{24}$Aix Marseille Univ, CNRS/IN2P3, CPPM, Marseille, France. Superscript 25$^{25}$INAF - Osservatorio di Astrofisica e Scienza dello spazio di Bologna, Via Piero Gobetti 93/3, 40129 Bologna, Italy. Superscript 26$^{26}$Dipartimento di Fisica e Astronomia (DIFA) Augusto Righi, Università di Bologna, via Gobetti 93/2, I-40129 Bologna, Italy. Superscript 27$^{27}$INFN Sezione di Trieste and Università degli studi di Udine, via delle scienze 206, 33100 Udine, Italy. Superscript 28$^{28}$University of Geneva - Département de physique nucléaire et corpusculaire, 24 Quai Ernest Ansernet, 1211 Genève 4, Switzerland. Superscript 29$^{29}$INAF - Istituto di Astrofisica e Planetologia Spaziali (IAPS), Via del Fosso del Cavaliere 100, 00133 Roma, Italy. Superscript 30$^{30}$INFN Sezione di Bari and Università di Bari, via Orabona 4, 70126 Bari, Italy. Superscript 31$^{31}$Palacky University Olomouc, Faculty of Science, 17. listopadu 1192/12, 771 46 Olomouc, Czech Republic. Superscript 32$^{32}$Dipartimento di Fisica e Chimica ’E. Segrè’ Università degli Studi di Palermo, via delle Scienze, 90128 Palermo, Italy. Superscript 33$^{33}$INFN Sezione di Catania, Via S. Sofia 64, 95123 Catania, Italy. Superscript 34$^{34}$IRFU, CEA, Université Paris-Saclay, Bât 141, 91191 Gif-sur-Yvette, France. Superscript 35$^{35}$Port d’Informació Científica, Edifici D, Carrer de l’Albareda, 08193 Bellaterrra (Cerdanyola del Vallès), Spain. Superscript 36$^{36}$University of Alcalá UAH, Departamento de Physics and Mathematics, Pza. San Diego, 28801, Alcalá de Henares, Madrid, Spain. Superscript 37$^{37}$INFN Sezione di Torino, Via P. Giuria 1, 10125 Torino, Italy. Superscript 38$^{38}$Instituto de Física de Sao Carlos, Universidade de Sao Paulo, Av. Trabalhador Sao-carlense, 400—CEP 13566-590, Sao Carlos, SP, Brazil Superscript 39$^{39}$Department of Physics, TU Dortmund University, Otto-Hahn-Str. 4, 44227 Dortmund, Germany. Superscript 40$^{40}$INFN Sezione di Bari, via Orabona 4, 70125, Bari, Italy. Superscript 41$^{41}$University of Rijeka, Department of Physics, Radmile Matejcic 2, 51000 Rijeka, Croatia. Superscript 42$^{42}$Institute for Theoretical Physics and Astrophysics, Universität Würzburg, Campus Hubland Nord, Emil-Fischer-Str. 31, 97074 Würzburg, Germany. Superscript 43$^{43}$INFN Sezione di Roma La Sapienza, P.le Aldo Moro, 2 - 00185 Rome, Italy. Superscript 44$^{44}$ILANCE, CNRS – University of Tokyo International Research Laboratory, University of Tokyo, 5-1-5 Kashiwa-no-Ha Kashiwa City, Chiba 277-8582, Japan. Superscript 45$^{45}$Physics Program, Graduate School of Advanced Science and Engineering, Hiroshima University, 1-3-1 Kagamiyama, Higashi-Hiroshima City, Hiroshima, 739-8526, Japan. Superscript 46$^{46}$INFN Sezione di Roma Tor Vergata, Via della Ricerca Scientifica 1, 00133 Rome, Italy. Superscript 47$^{47}$University of Split, FESB, R. Boškovića 32, 21000 Split, Croatia. Superscript 48$^{48}$Department of Physics, Yamagata University, 1-4-12 Kojirakawa-machi, Yamagata-shi, 990-8560, Japan. Superscript 49$^{49}$Institut für Theoretische Physik, Lehrstuhl IV: Plasma-Astroteilchenphysik, Ruhr-Universität Bochum, Universitätsstraße 150, 44801 Bochum, Germany. Superscript 50$^{50}$Institute of Space Sciences (ICE, CSIC), and Institut d’Estudis Espacials de Catalunya (IEEC), and Institució Catalana de Recerca I Estudis Avançats (ICREA), Campus UAB, Carrer de Can Magrans, s/n 08193 Bellatera, Spain. Superscript 51$^{51}$Sendai College, National Institute of Technology, 4-16-1 Ayashi-Chuo, Aoba-ku, Sendai city, Miyagi 989-3128, Japan. Superscript 52$^{52}$Université Paris Cité, CNRS, Astroparticule et Cosmologie, F-75013 Paris, France. Superscript 53$^{53}$Josip Juraj Strossmayer University of Osijek, Department of Physics, Trg Ljudevita Gaja 6, 31000 Osijek, Croatia. Superscript 54$^{54}$Chiba University, 1-33, Yayoicho, Inage-ku, Chiba-shi, Chiba, 263-8522 Japan. Superscript 55$^{55}$Kitashirakawa Oiwakecho, Sakyo Ward, Kyoto, 606-8502, Japan. Superscript 56$^{56}$FZU - Institute of Physics of the Czech Academy of Sciences, Na Slovance 1999/2, 182 21 Praha 8, Czech Republic. Superscript 57$^{57}$Astronomical Institute of the Czech Academy of Sciences, Bocni II 1401 - 14100 Prague, Czech Republic. Superscript 58$^{58}$Faculty of Science, Ibaraki University, 2 Chome-1-1 Bunkyo, Mito, Ibaraki 310-0056, Japan. Superscript 59$^{59}$Sorbonne Université, CNRS/IN2P3, Laboratoire de Physique Nucléaire et de Hautes Energies, LPNHE, 4 place Jussieu, 75005 Paris, France. Superscript 60$^{60}$Graduate School of Science and Engineering, Saitama University, 255 Simo-Ohkubo, Sakura-ku, Saitama city, Saitama 338-8570, Japan. Superscript 61$^{61}$Institute of Particle and Nuclear Studies, KEK (High Energy Accelerator Research Organization), 1-1 Oho, Tsukuba, 305-0801, Japan. Superscript 62$^{62}$INFN Sezione di Trieste and Università degli Studi di Trieste, Via Valerio 2 I, 34127 Trieste, Italy. Superscript 63$^{63}$Escuela Politécnica Superior de Jaén, Universidad de Jaén, Campus Las Lagunillas s/n, Edif. A3, 23071 Jaén, Spain. Superscript 64$^{64}$Institute for Nuclear Research and Nuclear Energy, Bulgarian Academy of Sciences, 72 boul. Tsarigradsko chaussee, 1784 Sofia, Bulgaria. Superscript 65$^{65}$Institut de Fisica d’Altes Energies (IFAE), The Barcelona Institute of Science and Technology, Campus UAB, 08193 Bellaterra (Barcelona), Spain. Superscript 66$^{66}$Grupo de Electronica, Universidad Complutense de Madrid, Av. Complutense s/n, 28040 Madrid, Spain. Superscript 67$^{67}$E.S.CC. Experimentales y Tecnología (Departamento de Biología y Geología, Física y Química Inorgánica) - Universidad Rey Juan Carlos. Superscript 68$^{68}$Macroarea di Scienze MMFFNN, Università di Roma Tor Vergata, Via della Ricerca Scientifica 1, 00133 Rome, Italy. Superscript 69$^{69}$Institute of Space Sciences (ICE, CSIC), Campus UAB, Carrer de Can Magrans, s/n 08193 Bellatera, Spain. Superscript 70$^{70}$School of Allied Health Sciences, Kitasato University, Sagamihara, Kanagawa 228-8555, Japan. Superscript 71$^{71}$RIKEN, Institute of Physical and Chemical Research, 2-1 Hirosawa, Wako, Saitama, 351-0198, Japan. Superscript 72$^{72}$Laboratory for High Energy Physics, École Polytechnique Fédérale, CH-1015 Lausanne, Switzerland. Superscript 73$^{73}$Charles University, Institute of Particle and Nuclear Physics, V Holešovičkách 2, 180 00 Prague 8, Czech Republic. Superscript 74$^{74}$Institute for Space-Earth Environmental Research, Nagoya University, Chikusa-ku, Nagoya 464-8601, Japan. Superscript 75$^{75}$Kobayashi-Maskawa Institute (KMI) for the Origin of Particles and the Universe, Nagoya University, Chikusa-ku, Nagoya 464-8602, Japan. Superscript 76$^{76}$Graduate School of Technology, Industrial and Social Sciences, Tokushima University, 2-1 Minamijosanjima,Tokushima, 770-8506, Japan. Superscript 77$^{77}$INFN Sezione di Pisa, Edificio C – Polo Fibonacci, Largo Bruno Pontecorvo 3, 56127 Pisa, Italy. Superscript 78$^{78}$Istituto Nazionale di Astrofisica - Osservatorio Astronomico di Capodimonte, Via Moiariello 16, 80131 Napoli (Italy). Superscript 79$^{79}$Gifu University, Faculty of Engineering, 1-1 Yanagido, Gifu 501-1193, Japan. Superscript 80$^{80}$Department of Physical Sciences, Aoyama Gakuin University, Fuchinobe, Sagamihara, Kanagawa, 252-5258, Japan. Superscript 81$^{81}$Faculty of Physics and Applied Informatics, University of Lodz, ul. Pomorska 149-153, 90-236 Lodz, Poland. Superscript 82$^{82}$Division of Physics and Astronomy, Graduate School of Science, Kyoto University, Sakyo-ku, Kyoto, 606-8502, Japan. Superscript 83$^{83}$Dipartimento di Fisica - Universitá degli Studi di Torino, Via Pietro Giuria 1 - 10125 Torino, Italy. Superscript 84$^{84}$Department of Physics, Konan University, 8-9-1 Okamoto, Higashinada-ku Kobe 658-8501, Japan.

Full Author List: MAGIC collaboration

K. AbeSuperscript 1$^{1}$, S. Abesquared$^{2}$, J. Abhircubed$^{3}$, A. AbhishekSuperscript 4$^{4}$, V. A. AcciariSuperscript 5$^{5}$, A. Aguasca-CabotSuperscript 6$^{6}$, I. AgudoSuperscript 7$^{7}$, T. AnielloSuperscript 8$^{8}$, S. AnsoldiSuperscript 9 comma 40$^{9,40}$, L. A. AntonelliSuperscript 8$^{8}$, A. Arbet EngelsSuperscript 10$^{10}$, C. ArcaroSuperscript 11$^{11}$, T. T. H. ArnesenSuperscript 12$^{12}$, A. BabićSuperscript 13$^{13}$, C. BakshiSuperscript 14$^{14}$, U. Barres de AlmeidaSuperscript 15$^{15}$, J. A. BarrioSuperscript 16$^{16}$, L. Barrios-JiménezSuperscript 12$^{12}$, I. BatkovićSuperscript 11$^{11}$, J. Baxtersquared$^{2}$, J. Becerra GonzálezSuperscript 12$^{12}$, W. BednarekSuperscript 17$^{17}$, E. BernardiniSuperscript 11$^{11}$, J. BerneteSuperscript 18$^{18}$, A. BertiSuperscript 10$^{10}$, J. BesenriederSuperscript 10$^{10}$, C. BigongiariSuperscript 8$^{8}$, A. Bilandcubed$^{3}$, O. BlanchSuperscript 5$^{5}$, G. BonnoliSuperscript 8$^{8}$, Ž. BošnjakSuperscript 13$^{13}$, E. BronziniSuperscript 8$^{8}$, I. BurelliSuperscript 5$^{5}$, A. Campoy-OrdazSuperscript 19$^{19}$, A. CarosiSuperscript 8$^{8}$, R. CarosiSuperscript 20$^{20}$, M. Carretero-CastrilloSuperscript 6$^{6}$, A. J. Castro-TiradoSuperscript 7$^{7}$, D. CerasoleSuperscript 21$^{21}$, G. CeribellaSuperscript 10$^{10}$, A. CerviñoSuperscript 16$^{16}$, Y. Chaisquared$^{2}$, A. ChilingarianSuperscript 22$^{22}$, G. ChonSuperscript 10$^{10}$, A. Cifuentes SantosSuperscript 18$^{18}$, E. ColomboSuperscript 5$^{5}$, J. L. ContrerasSuperscript 16$^{16}$, J. CortinaSuperscript 18$^{18}$, S. CovinoSuperscript 8 comma 41$^{8,41}$, G. D’AmicoSuperscript 23$^{23}$, P. Da VelaSuperscript 8$^{8}$, F. DazziSuperscript 8$^{8}$, A. De AngelisSuperscript 11$^{11}$, B. De LottoSuperscript 9$^{9}$, R. de MenezesSuperscript 15$^{15}$, M. DelfinoSuperscript 5 comma 42$^{5,42}$, J. DelgadoSuperscript 5 comma 42$^{5,42}$, C. Delgado MendezSuperscript 18$^{18}$, F. Di PierroSuperscript 24$^{24}$, R. Di TriaSuperscript 21$^{21}$, L. Di VenereSuperscript 21$^{21}$, A. DineshSuperscript 16$^{16}$, D. Dominis PresterSuperscript 25$^{25}$, A. DoniniSuperscript 8$^{8}$, D. DornerSuperscript 26$^{26}$, M. DoroSuperscript 11$^{11}$, L. EisenbergerSuperscript 26$^{26}$, D. ElsaesserSuperscript 27$^{27}$, J. EscuderoSuperscript 7$^{7}$, A. FattoriniSuperscript 27$^{27}$, L. FoffanoSuperscript 8$^{8}$, L. FontSuperscript 19$^{19}$, F. Frías García-LagoSuperscript 12$^{12}$, S. FröseSuperscript 27$^{27}$, Y. FukazawaSuperscript 28$^{28}$, R. J. García LópezSuperscript 12$^{12}$, S. García SotoSuperscript 18$^{18}$, M. GarczarczykSuperscript 29$^{29}$, S. GasparyanSuperscript 30$^{30}$, M. GaugSuperscript 19$^{19}$, J. G. Giesbrecht PaivaSuperscript 15$^{15}$, N. GigliettoSuperscript 21$^{21}$, F. GiordanoSuperscript 21$^{21}$, P. GliwnySuperscript 17$^{17}$, N. GodinovićSuperscript 31$^{31}$, T. GradetzkeSuperscript 27$^{27}$, R. Grausquared$^{2}$, D. GreenSuperscript 10$^{10}$, J. G. GreenSuperscript 10$^{10}$, P. GüntherSuperscript 26$^{26}$, A. HahnSuperscript 10$^{10}$, G. HarutyunyanSuperscript 30$^{30}$, M. HashizumeSuperscript 28$^{28}$, T. HassanSuperscript 18$^{18}$, J. Herrera LlorenteSuperscript 12$^{12}$, D. HrupecSuperscript 32$^{32}$, D. IsrayelyanSuperscript 30$^{30}$, T. Itokawasquared$^{2}$, J. JahanviSuperscript 9$^{9}$, I. Jiménez MartínezSuperscript 10$^{10}$, J. Jiménez QuilesSuperscript 5$^{5}$, J. JormanainenSuperscript 33$^{33}$, S. KankkunenSuperscript 33$^{33}$, T. KayanokiSuperscript 28$^{28}$, M. KhachatryanSuperscript 30$^{30}$, G. W. KlugeSuperscript 23 comma 43$^{23,43}$, J. KonradSuperscript 27$^{27}$, P. M. KouchSuperscript 33$^{33}$, G. KoziolSuperscript 34$^{34}$, H. Kubosquared$^{2}$, J. KushidaSuperscript 1$^{1}$, M. LáinezSuperscript 16$^{16}$, A. LamastraSuperscript 8$^{8}$, E. LindforsSuperscript 33$^{33}$, S. LombardiSuperscript 8$^{8}$, F. LongoSuperscript 9 comma 44$^{9,44}$, R. López-CotoSuperscript 7$^{7}$, M. López-MoyaSuperscript 16$^{16}$, A. López-OramasSuperscript 12$^{12}$, S. LoporchioSuperscript 21$^{21}$, L. LulićSuperscript 25$^{25}$, E. LyardSuperscript 34$^{34}$, P. MajumdarSuperscript 14$^{14}$, M. MakarievSuperscript 35$^{35}$, M. MallamaciSuperscript 36$^{36}$, G. ManevaSuperscript 35$^{35}$, M. ManganaroSuperscript 25$^{25}$, S. ManganoSuperscript 18$^{18}$, K. MannheimSuperscript 26$^{26}$, S. MarchesiSuperscript 8$^{8}$, M. MariottiSuperscript 11$^{11}$, M. MartínezSuperscript 5$^{5}$, P. MaruševecSuperscript 13$^{13}$, A. Mas-AguilarSuperscript 16$^{16}$, D. MazinSuperscript 2 comma 45$^{2,45}$, S. MenchiariSuperscript 7$^{7}$, J. Méndez GallegoSuperscript 7$^{7}$, S. MenonSuperscript 8 comma 46$^{8,46}$, D. MiceliSuperscript 11$^{11}$, J. M. MirandaSuperscript 4$^{4}$, R. MirzoyanSuperscript 10$^{10}$, M. Molero GonzálezSuperscript 12$^{12}$, E. MolinaSuperscript 12$^{12}$, H. A. Mondalsquared$^{2}$, A. MoralejoSuperscript 5$^{5}$, C. NanciSuperscript 8$^{8}$, L. NavaSuperscript 8$^{8}$, A. NegroSuperscript 24$^{24}$, V. NeustroevSuperscript 37$^{37}$, M. Nievas RosilloSuperscript 12$^{12}$, C. NigroSuperscript 5$^{5}$, L. NikolićSuperscript 4$^{4}$, K. NilssonSuperscript 33$^{33}$, S. Nozakisquared$^{2}$, A. OkumuraSuperscript 38$^{38}$, J. Otero-SantosSuperscript 11$^{11}$, S. PaianoSuperscript 8$^{8}$, D. PanequeSuperscript 10$^{10}$, R. PaolettiSuperscript 4$^{4}$, J. M. ParedesSuperscript 6$^{6}$, M. PeresanoSuperscript 10$^{10}$, M. PersicSuperscript 9 comma 47$^{9,47}$, M. PihetSuperscript 7$^{7}$, G. PirolaSuperscript 10$^{10}$, F. PodobnikSuperscript 4$^{4}$, P. G. Prada MoroniSuperscript 20$^{20}$, E. PrandiniSuperscript 11$^{11}$, A. RaiolaSuperscript 34$^{34}$, W. RhodeSuperscript 27$^{27}$, M. RibóSuperscript 6$^{6}$, J. RicoSuperscript 5$^{5}$, A. RoySuperscript 28$^{28}$, A. RuinaSuperscript 11$^{11}$, N. SahakyanSuperscript 30$^{30}$, F. G. SaturniSuperscript 8$^{8}$, F. SchiavoneSuperscript 21$^{21}$, K. SchmitzSuperscript 27$^{27}$, F. SchmuckermaierSuperscript 10$^{10}$, J. L. SchubertSuperscript 27$^{27}$, M. SchulzeSuperscript 29$^{29}$, T. SchweizerSuperscript 10$^{10}$, A. SciaccalugaSuperscript 8$^{8}$, G. SilvestriSuperscript 11$^{11}$, A. SimonginiSuperscript 8$^{8}$, J. SitarekSuperscript 17$^{17}$, V. SliusarSuperscript 34$^{34}$, D. SobczynskaSuperscript 17$^{17}$, A. StamerraSuperscript 8$^{8}$, L. Staniccubed$^{3}$, J. StriškovićSuperscript 32$^{32}$, D. StromSuperscript 10$^{10}$, M. Strzyssquared$^{2}$, Y. SudaSuperscript 28$^{28}$, M. TakahashiSuperscript 38$^{38}$, R. Takeishisquared$^{2}$, J. Tartera BarberàSuperscript 5$^{5}$, P. TemnikovSuperscript 35$^{35}$, T. TerzićSuperscript 25$^{25}$, M. TeshimaSuperscript 10 comma 48$^{10,48}$, A. TutoneSuperscript 8$^{8}$, S. UbachSuperscript 19$^{19}$, J. van ScherpenbergSuperscript 10$^{10}$, M. Vazquez AcostaSuperscript 12$^{12}$, S. VenturaSuperscript 4$^{4}$, G. VernaSuperscript 4$^{4}$, I. VialeSuperscript 24$^{24}$, A. ViglianoSuperscript 9$^{9}$, C. F. VigoritoSuperscript 24$^{24}$, E. VisentinSuperscript 24$^{24}$, V. VitaleSuperscript 39$^{39}$, M. VorbruggSuperscript 26$^{26}$, I. Vovksquared$^{2}$, R. WalterSuperscript 34$^{34}$, C. WaltherSuperscript 27$^{27}$, F. WersigSuperscript 27$^{27}$, P. K. H. Yeungsquared$^{2}$,

Superscript 1$^{1}$Japanese MAGIC Group: Department of Physics, Tokai University, Hiratsuka, 259-1292 Kanagawa, Japan squared$^{2}$Japanese MAGIC Group: Institute for Cosmic Ray Research (ICRR), The University of Tokyo, Kashiwa, 277-8582 Chiba, Japan cubed$^{3}$ETH Zürich, CH-8093 Zürich, Switzerland Superscript 4$^{4}$Università di Siena and INFN Pisa, I-53100 Siena, Italy Superscript 5$^{5}$Institut de Física d’Altes Energies (IFAE), The Barcelona Institute of Science and Technology (BIST), E-08193 Bellaterra (Barcelona), Spain Superscript 6$^{6}$Universitat de Barcelona, ICCUB, IEEC-UB, E-08028 Barcelona, Spain Superscript 7$^{7}$Instituto de Astrofísica de Andalucía-CSIC, Glorieta de la Astronomía s/n, 18008, Granada, Spain Superscript 8$^{8}$National Institute for Astrophysics (INAF), I-00136 Rome, Italy Superscript 9$^{9}$Università di Udine and INFN Trieste, I-33100 Udine, Italy Superscript 10$^{10}$Max-Planck-Institut für Physik, D-85748 Garching, Germany Superscript 11$^{11}$Università di Padova and INFN, I-35131 Padova, Italy Superscript 12$^{12}$Instituto de Astrofísica de Canarias and Dpto. de Astrofísica, Universidad de La Laguna, E-38200, La Laguna, Tenerife, Spain Superscript 13$^{13}$Croatian MAGIC Group: University of Zagreb, Faculty of Electrical Engineering and Computing (FER), 10000 Zagreb, Croatia Superscript 14$^{14}$Saha Institute of Nuclear Physics, A CI of Homi Bhabha National Institute, Kolkata 700064, West Bengal, India Superscript 15$^{15}$Centro Brasileiro de Pesquisas Físicas (CBPF), 22290-180 URCA, Rio de Janeiro (RJ), Brazil Superscript 16$^{16}$IPARCOS Institute and EMFTEL Department, Universidad Complutense de Madrid, E-28040 Madrid, Spain Superscript 17$^{17}$University of Lodz, Faculty of Physics and Applied Informatics, Department of Astrophysics, 90-236 Lodz, Poland Superscript 18$^{18}$Centro de Investigaciones Energéticas, Medioambientales y Tecnológicas, E-28040 Madrid, Spain Superscript 19$^{19}$Departament de Física, and CERES-IEEC, Universitat Autònoma de Barcelona, E-08193 Bellaterra, Spain Superscript 20$^{20}$Università di Pisa and INFN Pisa, I-56126 Pisa, Italy Superscript 21$^{21}$INFN MAGIC Group: INFN Sezione di Bari and Dipartimento Interateneo di Fisica dell’Università e del Politecnico di Bari, I-70125 Bari, Italy Superscript 22$^{22}$Armenian MAGIC Group: A. Alikhanyan National Science Laboratory, 0036 Yerevan, Armenia Superscript 23$^{23}$Department for Physics and Technology, University of Bergen, Norway Superscript 24$^{24}$INFN MAGIC Group: INFN Sezione di Torino and Università degli Studi di Torino, I-10125 Torino, Italy Superscript 25$^{25}$Croatian MAGIC Group: University of Rijeka, Faculty of Physics, 51000 Rijeka, Croatia Superscript 26$^{26}$Universität Würzburg, D-97074 Würzburg, Germany Superscript 27$^{27}$Technische Universität Dortmund, D-44221 Dortmund, Germany Superscript 28$^{28}$Japanese MAGIC Group: Physics Program, Graduate School of Advanced Science and Engineering, Hiroshima University, 739-8526 Hiroshima, Japan Superscript 29$^{29}$Deutsches Elektronen-Synchrotron (DESY), D-15738 Zeuthen, Germany Superscript 30$^{30}$Armenian MAGIC Group: ICRANet-Armenia, 0019 Yerevan, Armenia Superscript 31$^{31}$Croatian MAGIC Group: University of Split, Faculty of Electrical Engineering, Mechanical Engineering and Naval Architecture (FESB), 21000 Split, Croatia Superscript 32$^{32}$Croatian MAGIC Group: Josip Juraj Strossmayer University of Osijek, Department of Physics, 31000 Osijek, Croatia Superscript 33$^{33}$Finnish MAGIC Group: Finnish Centre for Astronomy with ESO, Department of Physics and Astronomy, University of Turku, FI-20014 Turku, Finland Superscript 34$^{34}$University of Geneva, Chemin d’Ecogia 16, CH-1290 Versoix, Switzerland Superscript 35$^{35}$Inst. for Nucl. Research and Nucl. Energy, Bulgarian Academy of Sciences, BG-1784 Sofia, Bulgaria Superscript 36$^{36}$INFN MAGIC Group: INFN Sezione di Catania and Dipartimento di Fisica e Astronomia, University of Catania, I-95123 Catania, Italy Superscript 37$^{37}$Finnish MAGIC Group: Space Physics and Astronomy Research Unit, University of Oulu, FI-90014 Oulu, Finland Superscript 38$^{38}$Japanese MAGIC Group: Institute for Space-Earth Environmental Research and Kobayashi-Maskawa Institute for the Origin of Particles and the Universe, Nagoya University, 464-6801 Nagoya, Japan Superscript 39$^{39}$INFN MAGIC Group: INFN Roma Tor Vergata, I-00133 Roma, Italy Superscript 40$^{40}$also at International Center for Relativistic Astrophysics (ICRA), Rome, Italy Superscript 41$^{41}$also at Como Lake centre for AstroPhysics (CLAP), DiSAT, Università dell?Insubria, via Valleggio 11, 22100 Como, Italy. Superscript 42$^{42}$also at Port d’Informació Científica (PIC), E-08193 Bellaterra (Barcelona), Spain Superscript 43$^{43}$also at Department of Physics, University of Oslo, Norway Superscript 44$^{44}$also at Dipartimento di Fisica, Università di Trieste, I-34127 Trieste, Italy Superscript 45$^{45}$Max-Planck-Institut für Physik, D-85748 Garching, Germany Superscript 46$^{46}$Please also add ’Dipartimento di Fisica, Università di Roma Tor Vergata, Via della Ricerca Scientifica, 1, Roma I-00133, Italy’ Superscript 47$^{47}$also at INAF Padova Superscript 48$^{48}$Japanese MAGIC Group: Institute for Cosmic Ray Research (ICRR), The University of Tokyo, Kashiwa, 277-8582 Chiba, Japan

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Figure 0

Figure 1. Measurements of the stellar angular diameter of 12 calibration stars, assuming a uniform disk profile, with the MAGIC+LST-1 SII. The measurements are represented as a function of their reference values from MAGIC SII (Blue band), when available, or from CHARA (Near-Infrared) otherwise. For the MAGIC+LST-1 SII, only statistical errors are shown.

Figure 1

Figure 2. Measurements of γ$\gamma$ Cas with the MAGIC+LST-1 SII. Normalized squared visibilities are shown as a function of the baseline. The best fit for the uniform disk (blue) and uniform ellipse (orange) models are shown as well as the residuals for each fit (using the same colors). The color code of the visibility points indicates the position angle of each baseline, as shown on the inner figure showing the UV-plane coverage. The reduced χ2$\chi ^2$ as well as the residuals show a preference for the uniform ellipse model.

Figure 2

Table 1. Best-fit parameters for the uniform ellipse model of γ$\gamma$ Cas obtained with two IACT-based SII systems: MAGIC+LST-1 SII and VERITAS SII.Table 1 long description.