A1 Refereed original research article in a scientific journal
The January 2010 flare of Mrk 421: Insights from a stochastic acceleration model; 
Authors: Abe, K.; Abe, S.; Abhir, J.; Abhishek, A.; Acciari, V. A.; Aguasca-Cabot, A.; Agudo, I.; Albanese, I.; Aniello, T.; Antonelli, L. A.; Arbet-Engels, A.; Arcaro, C.; Arnesen, T. T. H.; Babić, A.; Bakshi, C.; Barres de Almeida, U.; Barrio, J. A.; Barrios-Jiménez, L.; Batković, I.; Baxter, J.; Becerra González, J.; Bednarek, W.; Bernardini, E.; Bernete, J.; Berti, A.; Besenrieder, J.; Bigongiari, C.; Biland, A.; Blanch, O.; Bonnoli, G.; Bošnjak, Ž.; Bronzini, E.; Burelli, I.; Campoy-Ordaz, A.; Carosi, A.; Carosi, R.; Carretero-Castrillo, M.; Cerasole, D.; Ceribella, G.; Cerviño, A.; Chai, Y.; Chon, G.; Cifuentes, Santos, A.; Contreras, J. L.; Cortina, J.; Covino, S.; D’Amico, G.; Da Vela, P.; Dazzi, F.; De Angelis, A.; De Lotto, B.; de Menezes, R.; Delfino, M.; Delgado, J.; Delgado Mendez, C.; Di Pierro, F.; Di Tria, R.; Di Venere, L.; Dinesh, A.; Dominis Prester, D.; Donini, A.; Dorner, D.; Doro, M.; Eisenberger, L.; Elsaesser, D.; Foffano, L.; Font, L.; Frías García-Lago, F.; Fukazawa, Y.; García Soto, S.; Gasparyan, S.; Gaug, M.; Giesbrecht Paiva, J. G.; Giglietto, N.; Giordano, F.; Gliwny, P.; Gradetzke, T.; Grau, R.; Green, J. G.; Günther, P.; Hadasch, D.; Hahn, A.; Harutyunyan, G.; Hassan, T.; Herrera Llorente, J.; Hrupec, D.; Israyelyan, D.; Jahanvi, J.; Jiménez Martínez, I.; Jiménez Quiles, J.; Jormanainen, J.; Kankkunen, S.; Kayanoki, T.; Kluge, G. W.; Konrad, J.; Kouch, P. M.; Kubo, H.; Kushida, J.; Láinez, M.; Lamastra, A.; Lindfors, E.; Lombardi, S.; Longo, F.; López-Coto, R.; López-Moya, M.; López-Oramas, A.; Loporchio, S.; Lulić, L.; Lyard, E.; Majumdar, P.; Makariev, M.; Mallamaci, M.; Maneva, G.; Manganaro, M.; Mangano, S.; Mariotti, M.; Martínez, M.; Maruševec, P.; Mazin, D.; Menchiari, S.; Méndez Gallego, J.; Menon, S.; Miceli, D.; Miranda, J. M.; Mirzoyan, R.; Molero González, M.; Molina, E.; Mondal, H. A.; Moralejo, A.; Nanci, C.; Negro, A.; Neustroev, V.; Nievas Rosillo, M.; Nigro, C.; Nikolić, L.; Nilsson, K.; Nozaki, S.; Okumura, A.; Otero-Santos, J.; Paiano, S.; Paneque, D.; Paoletti, R.; Paredes, J. M.; Peresano, M.; Persic, M.; Pihet, M.; Pirola, G.; Podobnik, F.; Prada Moroni, P. G.; Prandini, E.; Rhode, W.; Ribó, M.; Rico, J.; Roy, A.; Sahakyan, N.; Saturni, F. G.; Schiavone, F.; Schmitz, K.; Schmuckermaier, F.; Sciaccaluga, A.; Silvestri, G.; Simongini, A.; Sitarek, J.; Sliusar, V.; Sobczynska, D.; Stamerra, A.; Strišković, J.; Strom, D.; Suda, Y.; Takahashi, M.; Takeishi, R.; Tartera Barberà, J.; Temnikov, P.; Terzić, T.; Teshima, M.; Tutone, A.; Ubach, S.; Vazquez Acosta, M.; Ventura, S.; Verna, G.; Viale, I.; Vigliano, A.; Vigorito, C. F.; Visentin, E.; Vitale, V.; Vorbrugg, M.; Vovk, I.; Walter, R.; Walther, C.; Wersig, F.; Yeung, P. K. H.; Perri, M.; Tramacere, A.
Publisher: EDP Sciences
Publication year: 2026
Journal: Astronomy and Astrophysics
Article number: A201
Volume: 710
ISSN: 0004-6361
eISSN: 1432-0746
DOI: https://doi.org/10.1051/0004-6361/202659090
Publication's open availability at the time of reporting: Open Access
Publication channel's open availability : Open Access publication channel
Web address : https://doi.org/10.1051/0004-6361/202659090
Self-archived copy’s web address: https://research.utu.fi/converis/portal/detail/Publication/527008560
Self-archived copy's licence: CC BY
Self-archived copy's version: Publisher`s PDF
Context. Mrk 421 displayed its highest flux state ever observed in February 2010 with very high tera-electronvolt fluxes and interesting cross-band correlations and a spectral energy distribution (SED) evolution not entirely consistent with the standard single zone leptonic synchrotron self-Compton model. The source was already in a high state in January 2010 and displayed strong variability in the days preceding the highest state. We study the temporal evolution of the spectra in January to extract information about the particle dynamics and the physical properties of the emission region.
Aims. We build on the temporal variability and correlations studied in our previous work and attempt to improve the SED model fits with a physics-oriented approach.
Methods. The The multi-wavelength data were processed and the SEDs were fit using JetSeT. The SED evolution and cross-band correlations were modelled using leptonic log-parabola with a low energy power-law branch (LPPL) and pile-up distributions that are predicted in a stochastic acceleration scenario. A simplified temporal evolution model was developed and fitted to the SEDs and the resulting trends and phenomenology were characterised in the context of the theoretical literature. An expanding emission region model was also tested.
Results. We find the spectral variability to be in good agreement with stochastic acceleration. Our analysis suggests that the standard LPPL distribution develops a Maxwellian pile-up component at the transition from the acceleration-dominated to the cooling-dominated phase on 3 nights in the dataset, as is also hinted at by the very-high energy and X-ray light curves. The resulting phenomenology of our sequential snapshot evolution SED model agrees well with theoretical and numerical simulation studies on temporal evolution using the diffusion equation approach. Curvature in the electron energy distribution (EED) anti-correlates with the synchrotron peak frequency, as was expected from stochastic acceleration. We tested an alternate model with expanding emission region and the resulting EED spectral index, expansion velocity, and magnetic field index agree with prior works using datasets collected in different flaring states of the source.
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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 BMFTR, MPG and HGF; the Italian INFN and INAF; the Swiss National Fund SNF; the grants 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 has also been supported by Centros de Excelencia “Severo Ochoa” y Unidades “María de Maeztu” program of the Spanish MCIN/AEI/ 10.13039/501100011033 (CEX2019-000918-M, CEX2021-001131-S, CEX2024001442-S), by AST22_00001_9 with funding from NextGenerationEU funds and by the CERCA institution and grants 2021SGR00426, 2021SGR00607 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 Science and Higher Education grant No. 2025/WK/04; by the European Union (ERC, MicroStars, 101076533); and by the Brazilian MCTIC, the CNPq Productivity Grant 309053/2022-6 and FAPERJ Grants E-26/200.532/2023 and E-26/211.342/2021. J.A. acknowledges support from the Swiss National Science Foundation (SNSF) Grant 200020_197007. A.A.-E. acknowledges support from the Deutsche Forschungs gemeinschaft (DFG, German Research Foundation) under Germany’s Excellence Strategy – EXC-2094 – 390783311.
