Time-dependent leptohadronic modeling of Markarian 421

Abstract Due to its proximity, Markarian 421 is one of the most extensively studied jetted active galactic nuclei. Its spectral energy distribution and light curve are widely studied, serving as primary means for understanding jet radiation mechanisms. Numerous intriguing observational results have been discovered, some of which, such as the hard X-ray excess, and the associated variability between X-ray and very-high-energy (VHE) emissions, challenge the commonly adopted one-zone leptonic model. In this work, by establishing a time-dependent leptohadronic model, we explore whether the hard X-ray excess and the associated variability between X-ray and VHE emissions could be interpreted by emission from hadronic interactions. Our modeling finds that for the hard X-ray excess found in 2013, both of the secondary emissions from photohadronic and hadronuclear interactions could be a possible explanation for the hard X-ray excess without introducing a super-Eddington jet power. The emission from the photohadronic interactions contributes only to the hard X-ray band, while the hadronuclear interactions also predict VHE emissions associated with the hard X-rays. While for the hard X-ray excess found in 2016, only the secondary emissions from photohadronic interactions provide an interpretation at the cost of introducing a super-Eddington jet power. For the associated variability between X-ray and VHE emissions in 2017, we find that hadronic interactions fail to provide a possible interpretation.