Time-Dependent Modeling of the Sub-Hour Spectral Evolution During the 2013 Outburst of Mrk 421
MAGIC Collaboration, K. Abe, S. Abe, J. Abhir, A. Abhishek, A. Aguasca-Cabot, I. Agudo, T. Aniello, S. Ansoldi, L. A. Antonelli, A. Arbet Engels, C. Arcaro, T. T. H. Arnesen, A. Babić, C. Bakshi, U. Barres de Almeida, J. A. Barrio, L. Barrios-Jiménez, I. Batković, J. Baxter, J. Becerra González, W. Bednarek, E. Bernardini, J. Bernete, A. Berti, C. Bigongiari, A. Biland, O. Blanch, G. Bonnoli, Ž Bošnjak, E. Bronzini, I. Burelli, A. Campoy-Ordaz, A. Carosi, R. Carosi, M. Carretero-Castrillo, A. J. Castro-Tirado, D. Cerasole, G. Ceribella, Y. Chai, A. Cifuentes, J. L. Contreras, J. Cortina, S. Covino, F. D'Ammando, P. Da Vela, F. Dazzi, A. De Angelis, B. De Lotto, R. de Menezes, J. Delgado, C. Delgado Mendez, F. Di Pierro, R. Di Tria, L. Di Venere, A. Dinesh, D. Dominis Prester, A. Donini, D. Dorner, M. Doro, L. Eisenberger, D. Elsaesser, J. Escudero, L. Fariña, L. Foffano, L. Font, S. Fröse, Y. Fukazawa, R. J. García López, S. García Soto, M. Garczarczyk, S. Gasparyan, J. G. Giesbrecht Paiva, N. Giglietto, F. Giordano, P. Gliwny, T. Gradetzke, R. Grau, D. Green, J. G. Green, P. Günther, A. Hahn, T. Hassan, L. Heckmann, J. Herrera Llorente, D. Hrupec, D. Israyelyan, J. Jahanvi, I. Jiménez Martínez, J. Jiménez Quiles, J. Jormanainen, S. Kankkunen, T. Kayanoki, J. Konrad, P. M. Kouch, G. Koziol, H. Kubo, J. Kushida, M. Laínez, A. Lamastra, E. Lindfors, S. Lombardi, F. Longo, M. López-Moya, A. López-Oramas, S. Loporchio, L. Lulić, E. Lyard, P. Majumdar, M. Makariev, M. Mallamaci, G. Maneva, M. Manganaro, S. Mangano, K. Mannheim, S. Marchesi, M. Mariotti, M. Martínez, P. Maruševec, S. Menchiari, J. Méndez Gallego, S. Menon, D. Miceli, J. M. Miranda, R. Mirzoyan, M. Molero González, E. Molina, H. A. Mondal, A. Moralejo, C. Nanci, A. Negro, V. Neustroev, L. Nickel, M. Nievas Rosillo, C. Nigro, L. Nikolić, S. Nozaki, A. Okumura, J. Otero-Santos, S. Paiano, D. Paneque, R. Paoletti, J. M. Paredes, M. Peresano, M. Persic, M. Pihet, G. Pirola, F. Podobnik, P. G. Prada Moroni, E. Prandini, W. Rhode, M. Ribó, J. Rico, A. Roy, N. Sahakyan, F. G. Saturni, K. Schmitz, F. Schmuckermaier, T. Schweizer, A. Sciaccaluga, G. Silvestri, A. Simongini, J. Sitarek, V. Sliusar, D. Sobczynska, A. Stamerra, J. Strišković, D. Strom, M. Strzys, Y. Suda, H. Tajima, R. Takeishi, F. Tavecchio, T. Terzić, M. Teshima, A. Tutone, S. Ubach, J. van Scherpenberg, M. Vazquez Acosta, S. Ventura, G. Verna, I. Viale, A. Vigliano, C. F. Vigorito, E. Visentin, V. Vitale, I. Vovk, R. Walter, F. Wersig, M. Will, T. Yamamoto, P. K. H. Yeung, M. Petropoulou, M. Polkas
公開日: 2025/9/10
Abstract
In April 2013, the TeV blazar Markarian~421 underwent one of its most powerful emission outbursts to date. An extensive multi-instrument campaign featuring MAGIC, VERITAS, and \textit{NuSTAR} provided comprehensive very-high-energy (VHE; $E > 100$\,GeV) and X-ray coverage over nine consecutive days. In this work, we perform a detailed spectral analysis of the X-ray and VHE emissions on sub-hour timescales throughout the flare. We identify several clockwise spectral hysteresis loops in the X-rays, revealing a spectral evolution more complex than a simple harder-when-brighter trend. The VHE spectrum extends beyond 10\,TeV, and its temporal evolution closely mirrors the behavior in the X-rays. We report the first evidence of VHE spectral hysteresis occurring simultaneously with the X-ray loops. To interpret these findings, we apply a time-dependent leptonic model to 240 broadband spectral energy distributions (SEDs) binned on a 15-minute scale, allowing us to self-consistently track the particle distribution's history. Our modeling shows that the majority of the sub-hour flux and spectral variations are driven by changes in the luminosity and slope of the injected electron distribution. The required variations in the electron slope are difficult to reconcile with magnetic reconnection but are consistent with a shock-acceleration scenario where the shock compression ratio evolves by a factor of $\sim2$. The model also points to a relatively stable magnetic field and emitting region size, favoring a scenario where the emission originates from a stationary feature in the jet, such as a recollimation shock. However, this scenario requires a jet Lorentz factor that significantly exceeds values from VLBI measurements to account for the high minimum electron energy implied by the lack of variability in the optical band.