Time-Dependent Modeling of the Sub-Hour Spectral Evolution During the 2013 Outburst of Mrk 421

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 $\sim 2$. 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.

Accepted in ApJ. Corresponding authors: A. Arbet-Engels, M. Polkas, M. Petropoulou, D. Paneque. All the broadband SEDs in 15-min bins are available at https://zenodo.org/records/17054582. The MAGIC data are also released in a Data Level 3 (DL3) format and can be downloaded from https://zenodo.org/records/17064461

References in corpus (64)

• The Large Area Telescope on the Fermi Gamma-ray Space Telescope Mission
• The Leiden/Argentine/Bonn (LAB) Survey of Galactic HI: Final data release of the combined LDS and IAR surveys with improved stray-radiation corrections
• The Swift X-ray Telescope
• The Nuclear Spectroscopic Telescope Array (NuSTAR) Mission
• The Swift Ultra-Violet/Optical Telescope
• The Spectral Energy Distribution of Fermi bright blazars
• The extragalactic optical-infrared background radiations, their time evolution and the cosmic photon-photon opacity
• Extragalactic Background Light Inferred from AEGIS Galaxy SED-type Fractions
• Relativistic Reconnection: an Efficient Source of Non-Thermal Particles
• The major upgrade of the MAGIC telescopes, Part II: A performance study using observations of the Crab Nebula
• Structured jets in TeV BL Lac objects and radiogalaxies
• Semi-analytic modeling of the EBL and consequences for extragalactic gamma-ray spectra
• The Fermi Large Area Telescope On Orbit: Event Classification, Instrument Response Functions, and Calibration
• Fast TeV variability in blazars: jets in a jet
• Constraints on the Physical Parameters of TeV Blazars
• A Proton Synchrotron Blazar Model for Flaring in Markarian~501
• Multiwavelength Observations of Strong Flares From the TeV-Blazar 1ES 1959+650
• Fermi-LAT Observations of Markarian 421: the Missing Piece of its Spectral Energy Distribution
• BeppoSAX Observations of Unprecedented Synchrotron Activity in the BL Lac Object Mkn 501
• VHE Gamma-Ray Observation of the Crab Nebula and its Pulsar with the MAGIC telescope
• The extent of power-law energy spectra in collisionless relativistic magnetic reconnection in pair plasmas
• Analytical solutions for energy spectra of electrons accelerated by nonrelativistic shock-waves in shell type supernova remnants
• MOJAVE XIII. Parsec-Scale AGN Jet Kinematics Analysis Based on 19 years of VLBA Observations at 15 GHz
• Reconnection-driven plasmoids in blazars: fast flares on a slow envelope
• Decelerating Flows in TeV Blazars: A Resolution to the BL Lac -- FR I Unification Problem
• Blazar spectral variability as explained by a twisting inhomogeneous jet
• The unprecedented optical outburst of the quasar 3C 454.3. The WEBT campaign of 2004-2005
• The WEBT BL Lac Campaign 2000
• Plasmoids in relativistic reconnection, from birth to adulthood: first they grow, then they go
• Blazar flares powered by plasmoids in relativistic reconnection
• The spectrum of particles accelerated in relativistic, collisionless shocks
• Particle acceleration and relativistic shocks
• Multiwavelength Study of Quiescent States of Mrk 421 with Unprecedented Hard X-Ray Coverage Provided by NuSTAR in 2013
• Multifrequency monitoring of the blazar 0716+714 during the GASP-WEBT-AGILE campaign of 2007
• Time-Dependent Stochastic Particle Acceleration in Astrophysical Plasmas: Exact Solutions Including Momentum-Dependent Escape
• Four Years Monitoring of Blazar PKS 2155-304 with BeppoSAX: Probing the Dynamics of the Jet
• MOJAVE XIX: Brightness Temperatures and Intrinsic Properties of Blazar Jets
• Gammapy: A Python package for gamma-ray astronomy
• The Steady Growth of the High-Energy Spectral Cutoff in Relativistic Magnetic Reconnection
• Correlation between the TeV and X-ray emission in high--energy peaked BL Lac objects
• The GASP-WEBT monitoring of 3C 454.3 during the 2008 optical-to-radio and gamma-ray outburst
• On the magnetization of BL Lac jets
• Observing Mkn 421 with XMM--Newton: the EPIC--PN point of view
• A multiwavelength view of the flaring state of PKS 2155-304 in 2006
• Observation of Markarian 421 in TeV gamma rays over a 14-year time span
• New hard-TeV extreme blazars detected with the MAGIC telescopes
• Status of the VERITAS Observatory
• Unravelling the complex behavior of Mrk 421 with simultaneous X-ray and VHE observations during an extreme flaring activity in April 2013
• Investigation of the correlation patterns and the Compton dominance variability of Mrk 421 in 2017
• Study of the variable broadband emission of Markarian 501 during the most extreme Swift X-ray activity
• Violent Hard X-ray Variability of Mrk 421 Observed by NuSTAR in 2013 April
• Dissecting the long-term emission behaviour of the BL Lac object Mrk 421
• Electron-proton co-acceleration on relativistic shocks in extreme-TeV blazars
• A search for spectral hysteresis and energy-dependent time lags from X-ray and TeV gamma-ray observations of Mrk 421
• Multiwavelength variability and correlation studies of Mrk 421 during historically low X-ray and $\gamma$-ray activity in 2015$-$2016
• X-Ray Spectral Variability of Extreme BL Lac AGN H1426+428
• VHE gamma-ray detection of FSRQ QSO B1420+326 and modeling of its enhanced broadband state in 2020
• H.E.S.S. detection of very-high-energy gamma-ray emission from the quasar PKS 0736+017
• Time-dependent modelling of PKS 2155-304 in a low state
• Probing an X-ray flare pattern in Mrk 421 induced by multiple stationary shocks: a solution to the bulk Lorentz factor crisis
• A numerical study of long-term multi-wavelength blazar variability
• Particle acceleration in thick parallel shocks with high compression ratio
• Quantitative comparisons of VHE gamma-ray blazar flares with relativistic reconnection models
• Suzaku observation of TeV blazar the 1ES 1218+304: clues on particle acceleration in an extreme TeV blazar

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