A&A, 700, A96 (2025) https://doi.org/10.1051/0004-6361/202555468 c© The Authors 2025 Astronomy &Astrophysics Testing the ubiquitous presence of very high energy emission in gamma-ray bursts with the MAGIC telescopes S. Abe1 , J. Abhir2 , A. Abhishek3 , V. A. Acciari4, A. Aguasca-Cabot5 , I. Agudo6 , T. Aniello7 , S. Ansoldi8,43 , L. A. Antonelli7, A. Arbet Engels9 , C. Arcaro10 , T. T. H. Arnesen11 , K. Asano1, A. Babic´12 , C. Bakshi13 , U. Barres de Almeida14 , J. A. Barrio15 , L. Barrios-Jiménez11 , I. Batkovic´10, J. Baxter1, J. Becerra González11, W. Bednarek16 , E. Bernardini10 , J. Bernete17, A. Berti9,?, J. Besenrieder9, C. Bigongiari7 , A. Biland2 , O. Blanch4 , G. Bonnoli7 , Ž. Bošnjak12 , E. Bronzini7 , I. Burelli4, A. Campoy-Ordaz18 , A. Carosi7, R. Carosi19 , M. Carretero-Castrillo5 , A. J. Castro-Tirado6, D. Cerasole20 , G. Ceribella9 , Y. Chai1, A. Cifuentes17, J. L. Contreras15 , J. Cortina17, S. Covino7,44 , G. D’Amico21, P. Da Vela7 , F. Dazzi7 , A. De Angelis10, B. De Lotto8 , R. de Menezes22 , M. Delfino4,45 , J. Delgado4,45 , C. Delgado Mendez17 , F. Di Pierro22 , R. Di Tria20 , L. Di Venere20, A. Dinesh15, D. Dominis Prester23, A. Donini7, D. Dorner24 , M. Doro10 , L. Eisenberger24, D. Elsaesser25 , J. Escudero6 , L. Fariña4, A. Fattorini25 , L. Foffano7 , L. Font18, S. Fröse25 , S. Fukami1 , Y. Fukazawa26, R. J. García López11 , S. García Soto17 , M. Garczarczyk27 , S. Gasparyan28, M. Gaug18 , J. G. Giesbrecht Paiva14, N. Giglietto20 , F. Giordano20, P. Gliwny16, N. Godinovic´29 , T. Gradetzke25 , R. Grau4 , D. Green9, J. G. Green9 , P. Günther24, D. Hadasch1 , A. Hahn9 , T. Hassan17, L. Heckmann9,46, J. Herrera Llorente11, D. Hrupec30, R. Imazawa26, S. Inoue1,38, D. Israyelyan28 , J. Jahanvi8 , I. Jiménez Martínez9 , J. Jiménez Quiles4 , J. Jormanainen31 , S. Kankkunen31, T. Kayanoki26 , J. Konrad25 , P. M. Kouch31 , H. Kubo1 , J. Kushida32, M. Láinez15 , A. Lamastra7 , E. Lindfors31, S. Lombardi7 , F. Longo8,47,? , R. López-Coto6, M. López-Moya15 , A. López-Oramas11, S. Loporchio20, L. Lulic´23 , E. Lyard33, P. Majumdar13, M. Makariev34, M. Mallamaci35, G. Maneva34 , M. Manganaro23, S. Mangano17 , K. Mannheim24 , S. Marchesi7 , M. Mariotti10 , M. Martínez4, P. Maruševec12 , A. Mas-Aguilar15, D. Mazin1,48, S. Menchiari6 , J. Méndez Gallego6, S. Menon7 , D. Miceli10,? , J. M. Miranda3, R. Mirzoyan9 , M. Molero González11, E. Molina11, H. A. Mondal13, A. Moralejo4 , E. Moretti4, T. Nakamori36, C. Nanci7 , L. Nava7,? , V. Neustroev37 , L. Nickel25, M. Nievas Rosillo11 , C. Nigro4, L. Nikolic´3, K. Nilsson31, K. Nishijima32 , K. Noda38, S. Nozaki1 , A. Okumura39 , J. Otero-Santos10, S. Paiano7 , D. Paneque9, R. Paoletti3, J. M. Paredes5 , M. Peresano9, M. Persic8,49, M. Pihet5, G. Pirola9, F. Podobnik3 , P. G. Prada Moroni19, E. Prandini10, M. Ribó5 , J. Rico4, C. Righi7, N. Sahakyan28, T. Saito1, F. G. Saturni7 , K. Schmitz25 , F. Schmuckermaier9, A. Sciaccaluga7 , G. Silvestri10, A. Simongini7 , J. Sitarek16, V. Sliusar33, D. Sobczynska16 , A. Stamerra7 , J. Striškovic´30, D. Strom9, M. Strzys1, Y. Suda26, H. Tajima39, M. Takahashi39, R. Takeishi1 , P. Temnikov34, K. Terauchi40, T. Terzic´23 , M. Teshima9,50 , A. Tutone7 , S. Ubach18 , J. van Scherpenberg9, M. Vazquez Acosta11, S. Ventura3, G. Verna3 , I. Viale22, A. Vigliano8, C. F. Vigorito22 , E. Visentin22, V. Vitale41, I. Vovk1 , R. Walter33, F. Wersig25, M. Will9 , T. Yamamoto42, and P. K. H. Yeung1 (Affiliations can be found after the references) Received 9 May 2025 / Accepted 27 June 2025 ABSTRACT Gamma-ray bursts (GRBs) are the most powerful transient objects in the Universe, and they are a primary target for the MAGIC Collaboration. Recognizing the challenges of observing these elusive objects with Imaging Atmospheric Cherenkov Telescopes (IACTs), we implemented a dedicated observational strategy that included an automated procedure for rapid re-pointing to transient sources. Since 2013, this automated procedure has enabled MAGIC to observe GRBs at a rate of approximately ten per year, which led to the successful detection of two GRBs at very high energies (VHE; E > 100 GeV). We present a comprehensive analysis of 42 non-detected GRBs (4 short GRBs) observed by MAGIC from 2013 to 2019. We derived upper limits (ULs) on the observed energy flux as well as on the intrinsic energy flux corrected for absorption by the extragalactic background light (EBL) from the MAGIC observations in selected energy and time intervals. We conducted a comprehensive study of their properties to investigate the reasons for these non-detections, including the possible peculiar properties of TeV-detected GRBs. We find that strong EBL absorption significantly hinders TeV detection for the majority of GRBs in our sample. For a subset of 6 GRBs with redshift z < 2, we compared the UL on the intrinsic flux in the VHE domain with the simultaneous X-ray flux, which is observed to be at the same level in the current population of TeV-detected GRBs. Based on these inferred MAGIC ULs, we conclude that a VHE component with a luminosity comparable to the simultaneously observed X-ray luminosity cannot be ruled out for this sample. Key words. radiation mechanisms: non-thermal – gamma-ray burst: general – gamma rays: general ? Corresponding authors: contact.magic@mpp.mpg.de Open Access article, published by EDP Sciences, under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. This article is published in open access under the Subscribe to Open model. Subscribe to A&A to support open access publication. A96, page 1 of 15 Abe, S., et al.: A&A, 700, A96 (2025) 1. Introduction Gamma-ray bursts (GRBs) represent one of the most enigmatic classes of transient sources (see e.g. Kumar & Zhang 2015, for an exhaustive review). In the past two decades, the knowledge and understanding of the GRB phenomenology and underlying physics has significantly improved, mainly based on observa- tions by the Neil Gehrels Swift Observatory (Swift hereafter; Gehrels et al. 2004) and Fermi (Band et al. 2009) satellites, and on the improved capabilities of ground-based facilities in per- forming fast follow-up observations. Moreover, a new observa- tional window has recently opened for the study of emission pro- cesses in GRBs through the first detections at ∼TeV energies by different ground-based facilities. The presence of emission in the GeV-TeV domain in GRBs has been discussed and theorised in several studies (e.g. Meszaros et al. 1994; Mészáros & Rees 1997; Zhang & Mészáros 2001; Sari & Esin 2001) well before ground- based facilities started to perform follow-up observations at these energies. In order to probe the TeV domain in GRBs, Imag- ing Atmospheric Cherenkov Telescopes (IACTs), such as the MAGIC telescope, have made a huge effort over the years to become ever more suitable for GRB observations. In particular, efforts were focused on: i) developing a fast repositioning sys- tem (able to move at about 7 deg per second) to promptly react to GRB alerts and start observations with delays of a few tens of seconds, and ii) lowering the energy threshold down to 50 GeV (in optimal conditions) to reduce the impact of the optical/IR photons of the diffuse extragalactic background light (EBL; Nikishov 1961; Gould & Schréder 1966) on the detection prob- ability of cosmological GRBs. In parallel, observations performed with the LAT instrument on board the Fermi satellite definitely proved that GeV emission (typically below 10 GeV) is produced and is a relatively com- mon feature in the brightest events detected by the GBM (see e.g., Ajello et al. 2019), the other instrument of the Fermi satellite. In the majority of LAT-detected GRBs, GeV emission starts with a short delay (seconds) and lasts much longer (hun- dreds or thousands of seconds) with respect to the sub-MeV prompt emission. In the time window of overlap between prompt (sub-) MeV emission and LAT emission, a variety of spectral behaviours were found. Sometimes, the LAT spectrum is con- sistent with being the extrapolation of the prompt keV-MeV spectra (Ackermann et al. 2010a), while in other cases, a sec- ond harder spectral component is clearly detected and is usu- ally well described as an additional power law (PL) that over- laps the Band function (Band et al. 1993), which describes the prompt emission spectrum and dominates the GBM band (see e.g., Ackermann et al. 2010b). It is still debated whether this second component in the GeV band belongs to the prompt phase or is instead the beginning of the afterglow phase. LAT emis- sion at later times is usually well described in terms of afterglow radiation and, in particular, synchrotron emission from electrons accelerated in forward shock (Kumar & Barniol Duran 2010; Ghisellini et al. 2010; Ghirlanda et al. 2010; Beniamini et al. 2015). In the notorious case of GRB 130427A, however, the late arrival (about four minutes after the GRB onset, i.e. well after the end of the prompt emission) of a nearly 100 GeV photon opened the concrete possibility that a component other than syn- chrotron emission is present (e.g. inverse-Compton or hadronic emission) in the afterglow phase of GRBs and might extend to the very high energy (VHE; >100 GeV) domain. Theoretical expectations in the TeV domain and the complex observational scenario described in the GeV band motivate GRB observations above 100 GeV, which have constituted one of the most ambi- tious targets for the current generation of IACTs. The MAGIC Collaboration identified the detection of VHE emission from GRBs as one of its primary targets. This key observing program resulted in the very much awaited detection of the first GRB at VHE gamma rays, namely GRB 190114C (MAGIC Collaboration 2019a), which led to the discovery of an additional spectral component that was detected up to 1 TeV and was successfully interpreted as synchrotron self-Compton (SSC) afterglow emission (MAGIC Collaboration 2019b). Additional detections have enlarged the sample of VHE GRBs (see Miceli & Nava 2022 for a review). The sample cur- rently consists of five events (all long GRBs, and all detected during the afterglow phase). In addition to GRB 190114C, MAGIC detected VHE gamma-rays (70–200 GeV from 56 s to ∼2400 s) from GRB 201216C (Abe et al. 2024), and H.E.S.S. detected VHE emission from GRB 180720B (100–440 GeV at ∼11 h; Abdalla et al. 2019) and GRB 190829A (up to 3.3 TeV; from 4 to 57 h, H.E.S.S. Collaboration 2021). More- over, LHAASO detected afterglow radiation up to ∼13 TeV from GRB 221009A that lasted for 3000 s (LHAASO Collaboration 2023; Cao et al. 2023). In all these cases, all the VHE data can be successfully described within the SSC scenario (see e.g. MAGIC Collaboration 2019b; Abe et al. 2024; Wang et al. 2019; Salafia et al. 2022; Ren et al. 2024) and carries a luminos- ity similar to that of the synchrotron component. The two GRBs detected by MAGIC are the result of the intense GRB follow-up programme that led to the obser- vation of a considerable number of GRBs over the past years. Several results about GRB follow-up were reported by MAGIC (Albert et al. 2007; Aleksic´ et al. 2010, 2014) and other IACTs (see e.g., Acciari et al. 2011). In this paper, we report the results for GRB observations achieved by MAGIC after the implementation of an improved GRB automatic observation pro- cedure in 2013 and before the changes that were introduced after the detection of GRB 190114C. The procedure introduced in 2013 allowed us to start the observation within few tens of sec- onds from the GRB onset. For the vast majority of observed GRBs, no gamma-ray sig- nal was detected, and hence, only upper limits (ULs) on the emission flux level could be derived. In this paper, we present these ULs and discuss them within the framework of the few VHE GRBs detected so far, with the aid of the available simul- taneous X-ray data. This discussion is conducted to understand how common VHE is in afterglow emission and to constrain its brightness compared to the synchrotron component. This study can be beneficial for the organization of GRB follow-up strate- gies for current and future IACTs. The paper is structured as follows: Sect. 2 introduces the MAGIC instrument and describes the GRB follow-up strategy. Sect. 3 describes the properties of the MAGIC GRB sample and the main selection criteria. Sect. 4 describes the data analysis we performed, and Sect. 5 focuses on a multi-wavelength view of a subsample of GRBs observed by MAGIC, in partic- ular comparing the results with X-ray data. Finally, we discuss and summarise the main results in Sect. 6. 2. The MAGIC telescopes and the GRB follow-up The MAGIC system consists of two 17 m dish IACTs located at the Roque de los Muchachos observatory (28.8◦ N, 17.9◦ W, 2200 m a.s.l.) on the Canary Island of La Palma, Spain. The MAGIC system is currently carrying out stereoscopic observa- tions with a sensitivity of <0.7% of the Crab Nebula flux for A96, page 2 of 15 Abe, S., et al.: A&A, 700, A96 (2025) energies above ∼220 GeV in 50 h of observation, and a trig- ger energy threshold of 50 GeV (Aleksic´ et al. 2016). Since the beginning of its operation, MAGIC was able to react to GRB alerts through a dedicated automatic alert system (AAS) that receives external triggers provided by the Gamma-ray Coor- dinates Network (GCN1) through a TCP/IP socket connec- tion. GRB observations are assigned the highest priority within MAGIC operations as soon as the alert is received and validated by the AAS according to predefined criteria. The event coordi- nates are communicated to the telescope central control, which stops the ongoing observation and starts the re-pointing to the GRB position. Their lightweight structure based on carbon fibre tubes enables the MAGIC telescopes to slew to a target using dedicated fast-slewing movements within few tens of seconds after the alert is received. This implies a remarkable re-pointing speed of about 7 deg per second in both zenith and azimuth2. To prevent possible failures and problems during the crucial phases of the follow-up of GRBs, an updated automatic procedure was implemented at the beginning of 2013. In particular, within the updated automatic procedure, the data-acquisition system is not stopped during the slewing of the telescopes, and a rate lim- iter avoids its saturation. This drastically reduces possible fail- ures when the observation of GRBs is started (see details in MAGIC Collaboration 2019a). Depending on the observational constraints, the follow-up of GRBs is usually carried out for a maximum observation time of 4 hours after the beginning of the visibility window. This observation time can be shortened or increased by the burst advocate on shift, who is informed by the local operators and decides the observational strategy based on incoming information on the GRB. Most of the GRB follow-ups performed by MAGIC are triggered by alerts sent by the BAT instrument on board the Swift satellite. While GBM alerts are more frequent, most of them are discarded either due to their large localisation uncer- tainty (several degrees) or their low significance. This filter is implemented within the AAS in order to avoid the follow-up of events that are less likely to be classified as a real GRB (e.g. terrestrial gamma-ray flashes or cosmic rays) to save valu- able observation time. BAT alerts instead provide a very good localisation at the arcminute level, and the probability that the trigger is of non-GRB origin (e.g. a background fluctuation or a flare from a Galactic source) is very low. An even lower number of follow-ups resulted from alerts by the INTEGRAL satellite (Winkler et al. 2003) because this instrument detects intrinsically few GRBs. The localisation is good enough to avoid adding additional filters in this case as well. Finally, a non-negligible number of follow-ups was triggered by GRBs detected by LAT, either as a follow-up of GBM detected bursts that were afterwards also detected by LAT, or as a late-time observation. In the latter case, the follow-up is performed even more than one day after the GRB onset. This observation strat- egy for LAT-detected alerts has a twofold explanation: on the one hand, it allows us to test for the presence of long-lasting emis- sion even hours after the GRB onset, and on the other hand, if the GRB is detected by GBM but not by BAT and is initially discarded, it allows us to search for a possible gamma-ray signal from a GRB exhibiting GeV and possibly VHE emission. To quantify the duty cycle of MAGIC (or of any Cherenkov telescope located at the Roque de los Muchachos) for the obser- vation of GRBs and to cross-check for systematic errors that can be nested in the follow-up procedure, we present here a calcula- 1 http://gcn.gsfc.nasa.gov/ 2 The normal pointing speed for MAGIC is about 4 deg per second. tion of the expected percentage of successfully followed alerts. We start our calculation from the constraints that are included in the automatic system that limit the number of alerts that can be followed. The criteria are listed below. – The Sun must be below the astronomical horizon (103 deg from zenith) to reduce the available time by 39%. – Alerts are followed if within 4 hours from the trigger time the position in the sky is 60 deg from zenith at most. This further reduces all observable alerts by 37.5% (25% of the alerts would have a zenith angle below 60 deg at the trig- ger time, and an additional 12.5% would satisfy the zenith requirement within 4 hours). – When the Moon is above the horizon, the angle between the GRB and the Moon must be larger than 30 deg in order to avoid pointing too close to the Moon, which would lead to a high-energy threshold and increased systematics. This has a small impact and excludes only 3.4% of the observable alerts. Moreover, we need to take into account the days in a year in which MAGIC does not perform GRB follow-up because oper- ations are stopped due to full-Moon conditions. These sum up to 21% of the total available night-time throughout the year. Finally, we need to account for the fraction of time in which operations are stopped due to weather above the operational safety limits or technical problems, which is 40% on average. When all the factors listed above are considered, the percentage of alerts that the MAGIC telescopes are expected to follow in a year is 6.7%. We then applied this percentage to the number of GRB alerts released between 2013 and 2019 and estimated the number of GRBs that MAGIC should have followed. Most alerts are pro- vided by Swift and Fermi. To the alerts coming from GBM, an additional requirement on the error on the GRB localization is applied. Only alerts with a statistical error smaller than 1 deg are processed by the automatic system. This additional con- straint is necessary because of the large localization uncertainty of GBM in comparison to other instruments (several degrees ver- sus arcminutes as provided e.g. by Swift-BAT). Given the rela- tively small field of view of MAGIC (3.5 deg in diameter), we need to maximise the probability that the actual location of the GRB falls within the effective field of view of the MAGIC cam- era. The number of GRB alerts that MAGIC is expected to fol- low up per year in the period 2013–2019 is about 6.7 from Swift and about 2.9 from Fermi, which means a total of 9.6 GRBs per year. In the 7 years considered in this manuscript, from 2013 to 2019, MAGIC performed 66 GRB observations, which agrees well with the expected number of observable alerts. We received a total of 46 alerts from Swift (6.6 per year) and 17 from Fermi (2.4 per year). The remaining 3 alerts were sent by INTEGRAL. Finally, after several years in which the updated automatic procedure was used and refined, we can assess its reliability. We took into account the number of times it was used after its introduction and the number of times it failed in the case of real alerts. From May 2013 to December 2019, the automatic pro- cedure took over 48 times, and it failed only twice. Therefore, the efficiency of the updated automatic procedure is about 96%. It has to be noted that the issue that occurred in the two failure cases is not specific to the automatic procedure, but occurs rarely during normal data taking. 3. The sample We focus on GRBs that were observed by MAGIC in the time period from 2013 to 2019. The choice of the starting year was A96, page 3 of 15 Abe, S., et al.: A&A, 700, A96 (2025) 102 103 104 105 Tdelay [s] 100 101 102 103 104 T d el ay /T 90 without redshift z>1 0.25 2, or Zd > 40 deg For the GRBs in our sample with an unknown redshift or with a redshift z ≥ 2 or observed at zenith angle Zd > 40 deg, we estimated night-wise ULs on the observed flux. This applied to 33 of the 39 GRBs considered for this analysis. We did not consider energies above 1 TeV. For a high redshift, the effect of EBL absorption above 1 TeV is extreme (see Fig. 2) and leads to huge uncertainties of the results that would be derived above this energy. The observed photon spectrum up to 1 TeV was assumed to be described by a power-law function dN/dE = E−α. We considered two possible values for the photon index α: 3.5 and 5.5. The first represents an optimistic scenario that is compat- ible with an event similar to GRB 190829A, and the second is compatible with the results obtained for GRB 190114C and GRB 201216C. The resulting ULs on the observed flux in sev- eral energy bins and time intervals are listed in Table B.1 in the appendix for this subsample of 33 GRBs. Only energy bins that ensured a systematic uncertainty below 30% are reported. In addition, the time window in which the ULs were computed was selected by excluding intervals of bad atmospheric conditions or problems during the data taking. As a result, the starting time for the UL calculation (Tstart in Table B.1) may differ with the time at which the telescopes started the follow-up observations (Tdelay reported in Table A.1). For three GRBs of the sample, namely GRB160910A, GRB190106B and GRB191004A, it was not possible to derive any ULs because none of the energy bins fulfilled the criteria for the systematics and the EBL absorption. The energy flux ULs3 estimated at 150 GeV and 250 GeV are plotted as a function of the exposure time in Fig. 3. The two considered reference energy values (150 GeV and 250 GeV) allowed us to be less sensible to EBL absorption and to include most of the GRBs of our sample. For comparison, we also report the fluxes or ULs for the TeV-detected GRBs in their corresponding exposure times. The flux values and correspond- ing time exposures were extracted from the papers of the TeV- detected bursts by MAGIC, HESS, and LHAASO. In a few cases (GRB190829A and GRB201216C), we estimated only an UL, rather than a flux point, for the selected reference energy value. We also plot the sensitivities at a 2σ level of the MAGIC and the Cherenkov Telescope Array Observatory (CTAO) northern array. The sensitivities at the 2σ level for the CTAO-North tele- scopes were derived from the official CTAO web page4, while those for MAGIC were derived from Fioretti et al. (2019). The sensitivity curves at a 5σ level were rescaled to those at a 2σ level assuming that the sensitivity, S , scales with significance σ as S (2σ)/S (5σ) ∝ 2/5. This is a simplified approach, but it can be provide a valid estimate for a background-dominated regime (Ambrogi et al. 2016). 4.2.2. GRBs with z < 2 and Zd < 40 deg For the GRBs in the sample with a redshift z < 2 and a zenith angle Zd < 40 deg, we estimated de-absorbed (i.e. corrected for the EBL absorption) ULs in selected energy and time intervals assuming a power-law function for the intrinsic gamma-ray dif- ferential photon spectrum dN/dE = E−α. This applied to 6 of the 39 GRBs considered for this analysis. Two values of the photon index α were considered: 1.6 and 2.2. This choice can be jus- tified from a phenomenological point of view because the val- 3 From now on, we refer to energy flux ULs simply as flux ULs. 4 https://www.cta-observatory.org/science/ ctao-performance/#1472563157332-1ef9e83d-426c A96, page 5 of 15 Abe, S., et al.: A&A, 700, A96 (2025) Fig. 3. Observed flux points or ULs for TeV-detected GRBs (empty markers) and most stringent ULs for catalog of GRBs non-detected by MAGIC (filled markers) vs. exposure time. The 2σ sensitivity level curves of the MAGIC and CTAO-North array are also displayed. Two reference energy values are shown: 150 GeV (left plot) and 250 GeV (right plot). Table 1. ULs at the 95% confidence level on the intrinsic flux (integrated from Emin to Emax) for the subsample of GRBs with z < 2 and Zd < 40 deg. GRB Tobs Emin Emax F18,1.6 F18,2.2 G12,1.6 G12,2.2 10−10 10−10 10−10 10−10 name [s] [GeV] [GeV] [erg cm−2 s−1] [erg cm−2 s−1] [erg cm−2 s−1] [erg cm−2 s−1] 130701A 403 100 696 4.45 2.70 11.4 6.57 130701A 1935 100 696 1.76 1.06 4.45 2.55 131030A 5795 120 654 1.64 1.00 5.72 3.30 141220A 314 75 647 4.10 2.39 10.7 5.85 141220A 2386 75 647 1.92 1.11 4.97 2.70 160623A 9324 165 1097 0.56 0.40 0.71 0.50 160623A 8388 140 1097 0.14 0.10 0.22 0.12 160625B 13968 200 625 7.58 5.11 56.3 35.9 160625B 8100 110 625 1.54 0.95 5.94 3.45 171020A 942 110 523 5.36 3.20 36.7 19.9 171020A 11906 110 523 5.42 3.32 41.1 23.3 Notes. Flux ULs are listed in units of 10−10 erg cm−2 s−1. The abbreviations refer to the EBL models (F18 and G12; see text) and to the assumed intrinsic photon indices (1.6 and 2.2). The table also lists the observation time and the lower and upper energy edge for the UL calculations. Multiple entries for the GRBs refer to different time intervals, as described in Sect. 4.2.2. ues correspond to the best-fit values obtained for GRB 180720B and GRB 190114C (Abdalla et al. 2019; MAGIC Collaboration 2019a). Moreover, they are also close to the photon indices expected in the SSC scenario: if the radiation is generated by electrons that are accelerated and result in a power-law distri- bution dN/dγ = γ−p with p ranging between 2.2 and 2.4, the photon indices α = 1.6 and α = 2.2 roughly correspond to the photon indices of the SSC spectrum assuming that the peak is above or below the GeV-TeV band. To estimate the effects of EBL absorption, we considered three different EBL mod- els: Domínguez et al. (2011) (D11), Franceschini & Rodighiero (2018) (F18), and Gilmore et al. (2012) (G12). The ULs com- puted with the EBL models D11 and F18 differ by no more than 30% up to E ∼ 200 GeV (see the bottom panel of Fig. 2), and we therefore decided to report only the latter ones. With these assumptions for each GRB, we calculated four values of the ULs in each energy bin. The results are reported in Table 1. In the following paragraphs, we explain some considerations related to the energy intervals and the time windows reported in Table 1. Energy intervals: The low-energy edge of the flux-integration window Emin is given by the energy threshold of each GRB, calculated as the peak of the MC reconstructed energy distribu- tion weighted for the observed spectrum, or by the lowest-energy value that ensures a total systematic uncertainty within 30%. In order to assess this condition, the corresponding estimated effec- tive area in the selected energy range was evaluated for different values of Emin starting from the GRB energy threshold. Given a value of Emin, the estimated effective area was calculated assum- ing Emin or a value shifted by ±15% as the low-energy edge of the flux-integration window. The estimated effective area calcu- lated for the shifted energy edges must vary by less than 30% with respect to the one computed for the nominal chosen Emin. If the GRB energy threshold did not fulfill this condition, an increased energy value that ensures that the variation in the total effective area was lower than 30% was chosen for the UL calcu- lation. The upper-energy edge Emax was fixed to 1.5 TeV in the rest frame. This value was chosen considering that the highest photon energies observed by MAGIC from GRB 190114C are ∼1 TeV (observer frame, corresponding to ∼1.5 TeV in the rest frame). Time intervals: For three GRBs of the subsample, namely GRB 130701A, GRB 141220A, and GRB 171020A, the MAGIC observation started with a short delay (shorter than ∼100 s) and covered several hours. Considering the typical rapid evolution of the afterglow flux, especially in the first hours after the trigger time, a single UL value cannot provide enough relevant infor- mation to be used in multi-wavelength studies, as we show in the following section. For this reason, we decided to estimate A96, page 6 of 15 Abe, S., et al.: A&A, 700, A96 (2025) the ULs by splitting the total observational interval into two time bins. For GRB 160623A and GRB 160625B, late-time observa- tions were performed for two nights. For this reason, the analyses were performed separately, and two different sets of ULs were computed for each night. For GRB 160625B, during the first night, in particular. from T0 + 2769 s to T0 + 8575 s, although a MAGIC observation was performed, it was not possible to derive ULs that fulfilled the criteria for the total systematic uncertainty explained above due to a combination of medium to large zenith angle (40 deg < Zd < 60 deg) and high night-sky background conditions due to the presence of the Moon. For this reason, we decided to focus on the data collected at zenith below 40 deg that were collected starting from T0 + 8575 s. For GRB 131030A, we removed the data that were collected in the first 20 minutes of observations from T0 + 27 s to T0 + 1260 s because they were strongly affected by poor atmosphere conditions. 5. Comparison with X-ray fluxes The current population of GRBs detected at VHE share one com- mon behaviour: the simultaneous EBL-corrected luminosities in the soft X-ray band and in the VHE band are comparable. In an SSC scenario, this roughly implies a similar amount of power in the synchrotron and in the inverse Compton components, assum- ing that the peak of the synchrotron component is approximately the soft X-ray band and the peak of the SSC is not far from the VHE band (see e.g. Figs. 2 and 3 in MAGIC Collaboration 2019b). Following these considerations, the question immedi- ately arises: do all GRBs have a VHE emission component with a luminosity similar to the simultaneous X-ray luminosity) If this is not the case, are the VHE-detected GRBs a peculiar popula- tion with particularly bright VHE emission? We partially investi- gated these open issues making use of the MAGIC ULs. Our aim was to understand how the ULs on the intrinsic VHE luminosity compare to simultaneous X-ray luminosities. We therefore com- pared the MAGIC de-absorbed flux ULs and the de-absorbed (i.e. corrected for Galactic and intrinsic absorption) flux in the soft X-ray band for a subsample of GRBs. For this comparison, we selected GRBs with a measured redshift, limiting the sample to redshift z < 2, and for which the total systematic uncertainty of the MAGIC ULs in the selected energy range was below 30%. For z > 2 and/or for energies above hundreds of GeV, the effect of EBL is so strong that the de-absorbed fluxes are much higher than the X-ray fluxes, and they do not provide meaningful con- straints. For the selected sample, we plot the de-absorbed flux light- curve integrated in the energy range 0.3–10 keV (observer frame, from https://www.swift.ac.uk/xrt_curves/) from the XRT instrument on board the Swift satellite together with MAGIC ULs on the intrinsic flux (i.e. de-absorbed by the EBL attenuation). The energy range over which the MAGIC ULs were calculated varies among the selected GRBs and is listed in Table 1. Since the XRT data points are typically derived on much shorter timescales, for a more reliable comparison, we esti- mated the XRT average flux over the same time interval where the MAGIC flux UL was extracted. To do this, we first fitted the X-ray light curves with a power-law function and then used the best fit to infer the average flux in the MAGIC time win- dow. The results are shown in Fig. 4. The XRT light curves are shown with blue data points, while the grey filled circles mark the XRT fluxes averaged over the same time-window of the MAGIC observations. In some cases, the total temporal window of MAGIC observations has been divided into two different time bins, for a more meaningful comparison. Arrows show the flux UL inferred from MAGIC observations. Four different estimates of the ULs are provided, inferred from two different assump- tions on the photon index of the intrinsic spectrum and for two different EBL models (see the legend). For GRB 160623A and GRB 160625B, LAT observations are available, but they unfor- tunately do not overlap in time with MAGIC observations. We added the estimated flux in the 0.1−100 GeV band as calculated by LAT (Ajello et al. 2019) (see the red data points in Fig. 4). For each GRB displayed in Fig. 4, we also included BAT data for completeness (black data points). These results show a few interesting cases in which the de- absorbed VHE flux UL lies very close to the average XRT flux or even below it, depending on the assumptions. Since this compar- ison is based on integrated fluxes, we chose the most promising cases (GRB130701A and GRB141220A) and performed a spec- tral analysis. XRT spectra and MAGIC differential ULs were extracted over the time ranges that included observations in both bands. XRT spectra were extracted with the online tool available at the online repository5 and were analysed with the XSPEC software. We modelled each analysed XRT spectrum with an absorbed power law accounting both for Galactic and intrinsic metal absorption using the XSPEC models tbabs and ztbabs, respectively. The Galactic contribution was fixed to the value reported in the automatic analysis tool, and the column den- sity in the host galaxy was a free parameter. The spectral data, rebinned for plotting purposes and de-absorbed for both Galactic and intrinsic absorption, are shown in Fig. 5. In conclusion, the comparison between MAGIC ULs with simultaneous XRT fluxes shows that VHE flux in many cases cannot be constrained to the same level as the X-ray flux. The comparison of energy-integrated flux light curves seemed to sug- gest a few cases in which MAGIC ULs can constrain the VHE flux to be lower than the X-ray flux. Nevertheless, a better com- parison of the SEDs leaves open the possibility of a VHE emis- sion at the same level or even brighter than the X-ray emission. This indicates that ULs by MAGIC cannot exclude a VHE emis- sion similar to the emission that was detected so far in a handful of GRBs for any of the GRBs presented in this paper, that is, a VHE emission with a luminosity that is comparable to that of the simultaneous X-ray luminosity. 6. Conclusion We presented the main results of the GRB follow-up campaign carried out by MAGIC from 2013 to 2019, which is the seven- year period that starts with an upgrade of the procedures for GRB searches and ends with the year in which the first GRBs at TeV energies were detected. During this period, 66 GRBs were followed-up by MAGIC, and the data taking in 42 cases was not affected by technical or observational problems. The best candidates for detecting a possible VHE component are those observed by MAGIC within the time window defined by T90 or, in general, with a short delay (Tdelay < 104 s). However, most of the events that fulfilled this criterion have an unknown red- shift or a redshift value z > 1 (see Fig. 1), which prevented us from inferring meaningful constraints on the presence of a VHE component. The only two cases of early observations of GRBs with z < 1 are GRB 190114C (detected by MAGIC) and GRB 160821B (showing a possible hint of a detection). We focused on the MAGIC data analysis of the 39 non- detected GRBs (excluding 3 events with a detection or a hint of a detection) that were followed-up from 2013 to 2019. We esti- 5 https://www.swift.ac.uk/xrt_curves/ A96, page 7 of 15 Abe, S., et al.: A&A, 700, A96 (2025) Fig. 4. Multi-wavelength light curves of the subsample of six GRBs described in Sect. 4.2.2 and Table 1. We show the flux light curves with X-ray data (black for BAT and blue for XRT), average X-ray flux in the MAGIC observational time windows (grey points), LAT data (red, if present), and MAGIC ULs assuming two different photon indices and EBL models for the subsample selected for the comparison with lower-energy bands. The time windows in which MAGIC ULs were computed are marked with vertical red and green stripes. mated the flux ULs at the 95% confidence level following a dif- ferent approach depending on the available information for the event. For the bursts with an unknown redshift, with a redshift z ≥ 2, or events that were observed at zenith angle Zd > 40 deg, which are 33 out of 39 GRBs, we computed the night-wise observed flux ULs and we compared these values with the pub- lished results of the GRBs detected in the VHE domain and the 2σ level sensitivities of the MAGIC and CTAO-North array at two reference energy values, 150 GeV and 250 GeV. The com- parison with the detected GRBs did not reveal any particular dif- ference in terms of their intrinsic properties. The observed ULs are well below the flux points derived from the detected GRBs, A96, page 8 of 15 Abe, S., et al.: A&A, 700, A96 (2025) 1016 1018 1020 1022 1024 1026 Frequency [Hz] 10−13 10−12 10−11 10−10 10−9 10−8 10−7 10−6 Flu x [ er g cm −2 s− 1 ] GRB130701A, z=1.155 92-285 s 1496-2257 s 1016 1018 1020 1022 1024 1026 Frequency [Hz] 10−14 10−12 10−10 10−8 Flu x [ er g cm −2 s− 1 ] GRB141220A, z=1.319 105-144 s 1589-2241 s Fig. 5. Simultaneous X-ray and MAGIC SEDs for GRB 130701A and GRB 141220A. The X-ray fluxes are corrected for dust extinction. The VHE flux ULs are corrected for EBL absorption. For each GRB, two different time intervals are considered. and they lie at the level of the 2σ sensitivity of MAGIC and above the CTAO-North one. This indicates that the non-detected GRBs are simply fainter or at larger distances and that they are thus more affected by EBL absorption than the detected GRBs. For the sample of GRBs with a redshift z < 2 and that were observed at a zenith angle Zd < 40 deg, which are 6 out of 39 GRBs, we computed EBL-corrected flux ULs in selected energy and time intervals and for different assumptions on the intrin- sic gamma-ray spectrum (a power law with photon indices 1.6 and 2.2) and EBL absorption models (D11, F18, and G12). We compared the MAGIC de-absorbed flux ULs with the flux in the soft X-ray band. This comparison provided relevant informa- tion to address the open questions of the possible universality of the GRB VHE emission component and the connection with the other lower-energy bands, especially with the X-ray band. We plotted the de-absorbed XRT flux light curves, the XRT average flux in the MAGIC observational time window, and the derived MAGIC flux ULs. For a few cases, we also added the available information on the LAT estimated flux in the 0.1–100 GeV band. This comparison showed that ULs are above the correspond- ing flux in the X-ray band. Only two cases (GRB130701A and GRB141220A) indicated that the VHE flux might be at the same level or below the average XRT flux. For these cases, we per- formed a refined spectral analysis of the X-ray and VHE simul- taneous data and displayed the SEDs in both bands. This further comparison showed that the VHE ULs do not constrain the TeV component at the same level as or below the X-ray one. In conclusion, these results confirm that MAGIC flux ULs cannot exclude the presence of a VHE emission component with properties similar to those detected in the current population of TeV GRBs. In particular, the possibility that the luminosity in the VHE domain is similar to that in the X-ray band is still open. For the most constraining cases of this study, we found that the VHE component in the MAGIC energy range was constrained to be no more than five to ten times brighter than the simultane- ous X-ray emission. Fig. 3 showed that the expected improved sensitivity of CTAO will allow us to fill this gap and lead to an increased number of detections, as well as to more constraining ULs providing crucially important information on a larger frac- tion of the GRB population. Acknowledgements. We 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 PID2019-107988GB-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, CNS2023-144504 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 Forschungs- gemeinschaft (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. LN acknowledges funding by the European Union-Next Generation EU, PRIN 2022 RFF M4C21.1 (202298J7KT – PEACE). Authors contributions. A. Berti: MAGIC data analysis, UL calculation, statistics on the triggers and AAS maintenance, paper editing; F. 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L., Di Cocco, G., et al. 2003, A&A, 411, L1 Zanin, R., Carmona, E., Sitarek, J., et al. 2013, Proceedings, 33rd International Cosmic Ray Conference (ICRC2013): Rio de Janeiro, Brazil, July 2–9, 2013, 0773 Zhang, B., & Mészáros, P. 2001, ApJ, 559, 110 1 Japanese MAGIC Group: Institute for Cosmic Ray Research (ICRR), The University of Tokyo, Kashiwa, 277-8582 Chiba, Japan 2 ETH Zürich, CH-8093 Zürich, Switzerland 3 Università di Siena and INFN Pisa, I-53100 Siena, Italy 4 Institut de Física d’Altes Energies (IFAE), The Barcelona Institute of Science and Technology (BIST), E-08193 Bellaterra (Barcelona), Spain 5 Universitat de Barcelona, ICCUB, IEEC-UB, E-08028 Barcelona, Spain 6 Instituto de Astrofísica de Andalucía-CSIC, Glorieta de la Astronomía s/n, 18008, Granada, Spain 7 National Institute for Astrophysics (INAF), I-00136 Rome, Italy 8 Università di Udine and INFN Trieste, I-33100 Udine, Italy 9 Max-Planck-Institut für Physik, D-85748 Garching, Germany 10 Università di Padova and INFN, I-35131 Padova, Italy 11 Instituto de Astrofísica de Canarias and Dpto. de Astrofísica, Uni- versidad de La Laguna, E-38200, La Laguna, Tenerife, Spain 12 Croatian MAGIC Group: University of Zagreb, Faculty of Electrical Engineering and Computing (FER), 10000 Zagreb, Croatia 13 Saha Institute of Nuclear Physics, A CI of Homi Bhabha National Institute, Kolkata 700064, West Bengal, India 14 Centro Brasileiro de Pesquisas Físicas (CBPF), 22290-180 URCA, Rio de Janeiro (RJ), Brazil 15 IPARCOS Institute and EMFTEL Department, Universidad Com- plutense de Madrid, E-28040 Madrid, Spain 16 University of Lodz, Faculty of Physics and Applied Informatics, Department of Astrophysics, 90-236 Lodz, Poland 17 Centro de Investigaciones Energéticas, Medioambientales y Tec- nológicas, E-28040 Madrid, Spain 18 Departament de Física, and CERES-IEEC, Universitat Autònoma de Barcelona, E-08193 Bellaterra, Spain 19 Università di Pisa and INFN Pisa, I-56126 Pisa, Italy 20 INFN MAGIC Group: INFN Sezione di Bari and Dipartimento Interateneo di Fisica dell’Università e del Politecnico di Bari, I- 70125 Bari, Italy 21 Department for Physics and Technology, University of Bergen, Bergen, Norway 22 INFN MAGIC Group: INFN Sezione di Torino and Università degli Studi di Torino, I-10125 Torino, Italy 23 Croatian MAGIC Group: University of Rijeka, Faculty of Physics, 51000 Rijeka, Croatia 24 Universität Würzburg, D-97074 Würzburg, Germany 25 Technische Universität Dortmund, D-44221 Dortmund, Germany 26 Japanese MAGIC Group: Physics Program, Graduate School of Advanced Science and Engineering, Hiroshima University, 739- 8526 Hiroshima, Japan 27 Deutsches Elektronen-Synchrotron (DESY), D-15738 Zeuthen, Germany 28 Armenian MAGIC Group: ICRANet-Armenia, 0019 Yerevan, Armenia 29 Croatian MAGIC Group: University of Split, Faculty of Electri- cal Engineering, Mechanical Engineering and Naval Architecture (FESB), 21000 Split, Croatia 30 Croatian MAGIC Group: Josip Juraj Strossmayer University of Osi- jek, Department of Physics, 31000 Osijek, Croatia 31 Finnish MAGIC Group: Finnish Centre for Astronomy with ESO, Department of Physics and Astronomy, University of Turku, FI- 20014 Turku, Finland 32 Japanese MAGIC Group: Department of Physics, Tokai University, Hiratsuka, 259-1292 Kanagawa, Japan 33 University of Geneva, Chemin d’Ecogia 16, CH-1290 Versoix, Switzerland 34 Inst. for Nucl. Research and Nucl. Energy, Bulgarian Academy of Sciences, BG-1784 Sofia, Bulgaria 35 INFN MAGIC Group: INFN Sezione di Catania and Dipartimento di Fisica e Astronomia, University of Catania, I-95123 Catania, Italy 36 Japanese MAGIC Group: Department of Physics, Yamagata Univer- sity, Yamagata 990-8560, Japan 37 Finnish MAGIC Group: Space Physics and Astronomy Research Unit, University of Oulu, FI-90014 Oulu, Finland 38 Japanese MAGIC Group: Chiba University, ICEHAP, 263-8522 Chiba, Japan 39 Japanese MAGIC Group: Institute for Space-Earth Environmental Research and Kobayashi-Maskawa Institute for the Origin of Parti- cles and the Universe, Nagoya University, 464-6801 Nagoya, Japan 40 Japanese MAGIC Group: Department of Physics, Kyoto University, 606-8502 Kyoto, Japan 41 INFN MAGIC Group: INFN Roma Tor Vergata, I-00133 Roma, Italy 42 Japanese MAGIC Group: Department of Physics, Konan University, Kobe, Hyogo 658-8501, Japan 43 also at International Center for Relativistic Astrophysics (ICRA), Rome, Italy 44 also at Como Lake centre for AstroPhysics (CLAP), DiSAT, Univer- sità dell’Insubria, via Valleggio 11, 22100 Como, Italy 45 also at Port d’Informació Científica (PIC), E-08193 Bellaterra (Barcelona), Spain 46 now at Université Paris Cité, CNRS, Astroparticule et Cosmologie, F-75013 Paris, France 47 also at Dipartimento di Fisica, Università di Trieste, I-34127 Trieste, Italy 48 Max-Planck-Institut für Physik, D-85748 Garching, Germany 49 also at INAF Padova, Padova, Italy 50 Japanese MAGIC Group: Institute for Cosmic Ray Research (ICRR), The University of Tokyo, Kashiwa, 277-8582 Chiba, Japan A96, page 10 of 15 Abe, S., et al.: A&A, 700, A96 (2025) Appendix A: GRBs observed by MAGIC between 2013 and 2019 Table A.1. List of GRBs observed by MAGIC (under acceptable conditions) between 2013 and 2019. GRB Redshift Instrument T90 T0 Tstart Tdelay Zenith angle name (position) [s] [UTC] [UTC] [s] [deg] 130502A Swift-BAT 3 17:50:30 20:57:03 11193 33.9-40.1 130504A Swift-BAT 50 02:05:34 02:13:09 455 44.7-56.5 130606A 5.913 Swift-BAT 277 21:04:39 21:15:28 649 1.7-46.1 130612A 2.006 Swift-BAT 5.6 03:22:22 03:23:08 46 38.0-53.0 130701A 1.155 Swift-BAT 4.4 04:17:43 04:18:32 49 15.9-22.6 130903A INTEGRAL 69 00:47:20 03:57:32 11412 51.9-62.8 131030A 1.295 Swift-BAT 41 20:56:19 20:56:45 26 33.7-39.7 140430A 1.60 Swift-BAT 174 20:33:36 20:52:06 1110 45.6-73.3 140709A Swift-BAT 98.6 01:13:41 03:22:13 7712 24.6-37.0 140930B Swift-BAT 0.84 19:41:42 21:10:05 5303 18.8-51.4 141026A 3.35 Swift-BAT 146 02:36:51 02:38:27 96 16.3-54.1 141220A 1.32 Swift-BAT 7.21 06:02:52 06:03:47 55 18.9-24.0 150213A Fermi-GBM 4.1 00:01:48 00:03:08 80 48.2-60.6 150428A Swift-BAT 53.2 01:30:40 01:32:11 91 27.0-57.7 150428B Swift-BAT 131 03:12:03 03:13:03 60 27.0-57.7 150819A Swift-BAT 52.1 00:50:08 02:11:51 4903 37.4-54.4 151118A Swift-BAT 23.4 03:06:30 03:07:14 44 42.8-57.4 151215A 2.59 Swift-BAT 17.8 03:01:28 03:01:58 30 15.8-58.0 160119A Swift-BAT 116 03:06:07 03:17:09 662 13.2-58.7 160310A Fermi-LAT 18.2 00:22:57 20:30:16 72439 35.5-40.9 160313A Swift-BAT 42.6 02:37:14 02:39:01 107 30.3-53.3 160504A Swift-BAT 53.9 19:30:36 20:56:29 5153 26.9-33.7 160509A 1.17 Fermi-LAT 370 08:59:04 21:21:07 (+2d) 217323 49.2-72.2 160623A 0.367 Fermi-LAT 50 05:00:34 02:05:31 75897 27.0-54.7 160625B 1.406 Fermi-LAT 460 22:43:24 23:29:38 2774 21.8-54.9 160821B 0.16 Swift-BAT 0.48 22:29:13 22:29:37 24 33.4-43.6 160910A Fermi-GBM 24.3 17:19:38 20:21:54 10936 45.4-72.9 160927A Swift-BAT 0.48 18:04:49 20:03:00 7091 32.0-58.8 161229A Fermi-GBM 33.5 21:03:48 23:05:54 7326 22.0-26.1 170728B Swift-BAT 47.7 23:03:19 23:03:58 39 41.8-52.7 170921B Fermi-GBM 39.4 04:02:11 04:48:04 2753 48.4-60.6 171020A 1.87 Swift-BAT 41.9 23:07:09 23:08:37 88 13.5-34.9 171210A Fermi-LAT 12 11:49:15 20:33:11 31436 30.9-61.9 180512A Swift-BAT 24.0 22:01:46 22:03:11 85 7.6-38.4 180715A Swift-BAT 0.68 18:07:05 21:27:24 12019 27.9-34.5 180720C Swift-BAT 124.2 22:23:57 22:25:44 107 55.3-55.4 180904A Swift-BAT 5.39 21:28:32 21:30:07 95 23.7-60.2 181225A Fermi-LAT 41.5 11:44:10 19:56:06 (+1d) 115916 46.7-62.6 190106B Fermi-GBM 11.8 20:47:10 20:49:13 123 60.0-60.4 190114C 0.425 Swift-BAT 25∗ 20:57:03 20:58:01 58 55.6-80.0 190829A 0.078 Swift-BAT 62.9 19:55:53 02:23:48 (+2d) 109624 37.7-59.6 191004A Swift-BAT 2.44 18:07:02 00:42:30 23728 65.4-69.9 Notes. The GRB redshift, when measured, is reported in the second column. The third column reports the name of the satellite which provided the sky coordinates (e.g. through GCN Notices or Circulars). The forth column reports the prompt emission duration T90. The fifth and sixth columns give the time of the trigger T0 and the time Tstart when MAGIC started the observations. The delay Tdelay(in seconds) is computed as the difference between the start time and the trigger time. The last column reports the zenith angle range related to each GRB observation. ∗Nominally, the T90 of GRB 190114C measured by and GBM is > 300 s. However, most of the emission recorded by and GBM was interpreted as afterglow radiation. The end of the prompt emission can be roughly identified with the end of flux variability, which occurs approximately at 25 s. Appendix B: Observed flux UL for GRBs with unknown z or z ≥ 2 or Zd > 40 deg A96, page 11 of 15 Abe, S., et al.: A&A, 700, A96 (2025) Table B.1. Night-wise flux ULs on the observed flux for the subsample of GRBs with unknown z or z ≥ 2 or Zd > 40 deg. GRB Tobs Tstart - Tstop E α = 3.5 α = 5.5 10−12 10−12 name [s] [s] [TeV] [TeV cm−2 s−1] [TeV cm−2 s−1] GRB130502A 1775 11769 - 13599 0.16 - 0.22 14.6 10.9 0.22 - 0.30 15.1 10.2 0.30 - 0.41 7.41 5.36 0.41 - 0.55 9.81 5.15 0.55 - 0.75 8.01 4.38 0.75 - 1.02 21.0 9.20 GRB130504A 10481 455 - 11487 0.22 - 0.30 4.31 2.95 0.30 - 0.41 4.06 2.89 0.41 - 0.55 2.48 1.64 0.55 - 0.75 2.02 1.07 0.75 - 1.02 1.86 1.02 GRB130606A 10704 1747 - 12868 0.12 - 0.16 5.26 3.88 0.16 - 0.22 4.24 3.23 0.22 - 0.30 5.66 4.40 0.30 - 0.41 2.95 2.31 0.41 - 0.55 2.34 1.62 0.55 - 0.75 1.74 0.93 0.75 - 1.02 4.82 2.54 GRB130612A 3822 688 - 4664 0.16 - 0.22 15.8 11.4 0.22 - 0.30 7.16 5.27 0.30 - 0.41 12.7 7.63 0.41 - 0.55 5.11 2.98 0.55 - 0.75 4.20 1.76 0.75 - 1.02 3.57 1.53 GRB130903A 2560 11412 - 14476 0.41 - 0.55 9.40 6.18 0.55 - 0.75 11.2 6.74 0.75 - 1.02 7.50 4.10 GRB140430A 1859 1110 - 3018 0.22 - 0.30 8.91 6.02 0.30 - 0.41 7.62 5.05 0.41 - 0.55 5.85 3.68 0.55 - 0.75 4.93 2.20 0.75 - 1.02 10.1 3.68 GRB140709A 5834 7712 - 13745 0.12 - 0.16 14.5 10.7 0.16 - 0.22 14.5 10.7 0.22 - 0.30 3.98 3.16 0.30 - 0.41 4.45 3.16 0.41 - 0.55 2.37 1.97 0.55 - 0.75 8.15 5.21 0.75 - 1.02 7.75 4.55 GRB140930B 7839 5690 - 14073 0.22 - 0.30 8.21 6.66 0.30 - 0.41 4.48 3.63 0.41 - 0.55 4.05 3.20 0.55 - 0.75 2.70 1.89 0.75 - 1.02 2.77 1.89 GRB141026A 6482 223 - 10818 0.16 - 0.22 5.39 3.95 0.22 - 0.30 4.00 3.02 0.30 - 0.41 3.57 2.50 0.41 - 0.55 2.55 1.81 0.55 - 0.75 1.90 1.09 0.75 - 1.02 5.41 1.93 GRB150213A 3727 80 - 5334 0.30 - 0.41 8.57 6.02 0.41 - 0.55 10.9 7.67 0.55 - 0.75 4.87 2.72 0.75 - 1.02 6.05 2.74 GRB150428A 3503 122 - 3713 0.22 - 0.30 4.94 3.34 0.30 - 0.41 2.84 2.15 0.41 - 0.55 6.67 3.67 A96, page 12 of 15 Abe, S., et al.: A&A, 700, A96 (2025) Table B.1. Continued. GRB Tobs Tstart - Tstop E α = 3.5 α = 5.5 10−12 10−12 name [s] [s] [TeV] [TeV cm−2 s−1] [TeV cm−2 s−1] 0.55 - 0.75 7.16 5.83 0.75 - 1.02 8.05 5.25 GRB150428B 7467 330 - 8200 0.16 - 0.22 3.83 2.80 0.22 - 0.30 3.34 2.44 0.30 - 0.41 2.40 1.77 0.41 - 0.55 2.40 1.77 0.55 - 0.75 4.74 3.04 0.75 - 1.02 5.06 1.26 GRB150819A 5103 4907 - 10211 0.22 - 0.30 7.99 5.46 0.30 - 0.41 11.2 7.65 0.41 - 0.55 4.61 2.64 0.55 - 0.75 4.99 2.84 0.75 - 1.02 7.56 3.17 GRB151118A 10689 44 - 11216 0.22 - 0.30 9.13 6.23 0.30 - 0.41 3.74 2.55 0.41 - 0.55 2.82 1.61 0.55 - 0.75 2.40 1.41 0.75 - 1.02 2.14 0.88 GRB151215A 10403 30 - 12434 0.12 - 0.16 8.52 6.07 0.16 - 0.22 4.79 3.54 0.22 - 0.30 7.40 5.43 0.30 - 0.41 5.52 3.79 0.41 - 0.55 2.81 1.72 0.55 - 0.75 2.29 1.29 0.75 - 1.02 2.24 0.76 GRB160119A 5858 1888 - 7954 0.16 - 0.22 11.0 7.99 0.22 - 0.30 7.29 5.30 0.30 - 0.41 3.84 2.42 0.41 - 0.55 3.25 2.15 0.55 - 0.75 3.83 2.46 0.75 - 1.02 3.26 1.79 GRB160310A 2343 72440 - 74847 0.12 - 0.16 30.2 19.8 0.16 - 0.22 15.4 9.59 0.22 - 0.30 8.91 6.65 0.30 - 0.41 9.05 5.76 0.41 - 0.55 8.50 5.45 0.55 - 0.75 4.72 2.52 0.75 - 1.02 12.4 7.72 GRB160310A 3495 159187 - 162841 0.12 - 0.16 13.6 8.62 0.16 - 0.22 8.81 6.71 0.22 - 0.30 6.69 5.55 0.30 - 0.41 6.74 5.14 0.41 - 0.55 3.61 2.87 0.55 - 0.75 3.66 2.45 0.75 - 1.02 10.0 5.27 GRB160310A 2687 332239 - 335312 0.16 - 0.22 8.69 5.74 0.22 - 0.30 8.11 5.70 0.30 - 0.41 6.93 4.75 0.41 - 0.55 4.51 2.84 0.55 - 0.75 3.65 2.39 0.75 - 1.02 9.51 5.93 GRB160313A 11622 107 - 12104 0.16 - 0.22 7.76 5.41 0.22 - 0.30 5.57 3.99 0.30 - 0.41 5.57 3.99 0.41 - 0.55 3.35 2.13 0.55 - 0.75 2.74 1.22 0.75 - 1.02 4.22 1.29 GRB160504A 8665 5153 - 14126 0.12 - 0.16 7.60 5.76 0.16 - 0.22 7.74 6.97 A96, page 13 of 15 Abe, S., et al.: A&A, 700, A96 (2025) Table B.1. Continued. GRB Tobs Tstart - Tstop E α = 3.5 α = 5.5 10−12 10−12 name [s] [s] [TeV] [TeV cm−2 s−1] [TeV cm−2 s−1] 0.22 - 0.30 7.74 6.97 0.30 - 0.41 3.42 2.75 0.41 - 0.55 3.34 2.90 0.55 - 0.75 2.39 1.95 0.75 - 1.02 2.19 1.84 GRB160509A 10647 315153 - 326820 0.30 - 0.41 5.74 3.28 0.41 - 0.55 3.93 2.37 0.55 - 0.75 2.70 1.37 0.75 - 1.02 2.28 1.12 GRB160509A 2218 407122 - 409400 0.30 - 0.41 21.7 12.9 0.41 - 0.55 7.65 4.15 0.55 - 0.75 9.09 3.91 0.75 - 1.02 5.29 2.24 GRB160927A 6773 7091 - 14145 0.16 - 0.22 8.63 5.12 0.22 - 0.30 7.78 5.17 0.30 - 0.41 5.99 4.40 0.41 - 0.55 4.15 3.21 0.55 - 0.75 3.56 2.48 0.75 - 1.02 2.99 1.79 GRB161229A 4207 7326 - 12275 0.09 - 0.12 8.93 6.19 0.12 - 0.16 6.74 4.94 0.16 - 0.22 6.45 5.12 0.22 - 0.30 3.89 2.86 0.30 - 0.41 3.53 2.82 0.41 - 0.55 6.08 4.20 0.55 - 0.75 3.34 2.61 0.75 - 1.02 4.32 3.37 GRB170728B 2774 39 - 3017 0.22 - 0.30 6.03 3.95 0.30 - 0.41 6.82 4.48 0.41 - 0.55 4.48 1.96 0.55 - 0.75 3.29 1.20 0.75 - 1.02 4.58 1.38 GRB170728B 5830 80279 - 86356 0.16 - 0.22 8.16 5.57 0.22 - 0.30 5.34 3.56 0.30 - 0.41 2.82 2.01 0.41 - 0.55 2.95 1.79 0.55 - 0.75 3.51 2.42 0.75 - 1.02 5.32 1.99 GRB170921B 2303 2792 - 6853 0.30 - 0.41 10.7 6.64 0.41 - 0.55 11.4 6.55 0.55 - 0.75 5.09 2.76 0.75 - 1.02 4.46 1.86 GRB171210A 8102 31436 - 39959 0.16 - 0.22 12.8 8.35 0.22 - 0.30 5.93 4.06 0.30 - 0.41 4.59 2.69 0.41 - 0.55 4.47 2.67 0.55 - 0.75 2.63 0.97 0.75 - 1.02 4.04 1.42 GRB180512A 13807 85 - 14519 0.09 - 0.12 9.72 6.35 0.12 - 0.16 7.28 5.21 0.16 - 0.22 3.34 2.57 0.22 - 0.30 2.49 1.91 0.30 - 0.41 2.30 1.74 0.41 - 0.55 2.23 1.61 0.55 - 0.75 1.48 0.98 0.75 - 1.02 3.62 2.36 GRB180715A 3498 12019 - 15675 0.12 - 0.16 8.92 6.03 0.16 - 0.22 6.58 4.99 0.22 - 0.30 5.14 3.68 A96, page 14 of 15 Abe, S., et al.: A&A, 700, A96 (2025) Table B.1. Continued. GRB Tobs Tstart - Tstop E α = 3.5 α = 5.5 10−12 10−12 name [s] [s] [TeV] [TeV cm−2 s−1] [TeV cm−2 s−1] 0.30 - 0.41 4.54 2.33 0.41 - 0.55 3.34 2.15 0.55 - 0.75 7.64 3.39 0.75 - 1.02 8.37 5.97 GRB180720C 2102 151 - 2507 0.75 - 1.02 8.22 6.38 GRB180904A 13834 212 - 14758 0.12 - 0.16 7.54 5.04 0.16 - 0.22 7.17 4.97 0.22 - 0.30 4.20 2.96 0.30 - 0.41 2.95 1.92 0.41 - 0.55 4.37 2.65 0.55 - 0.75 2.11 1.09 0.75 - 1.02 1.77 0.49 GRB181225A 5235 115916 - 121415 0.30 - 0.41 10.8 7.44 0.41 - 0.55 6.09 4.42 0.55 - 0.75 4.21 3.15 0.75 - 1.02 3.65 2.78 Notes. Flux ULs are in units of 10−12 TeV cm−2 s−1. The observed photon indices α assumed is mentioned (3.5 and 5.5). In the second and third column of the table, the total observation time Tobs and the time interval (Tstart and Tstop) in which ULs are estimated with respect to the burst trigger time T0 are reported. Multiple entries for the GRBs refer to different observational nights. A96, page 15 of 15