The unprecedented flaring activities around Mrk 421 in 2012 and 2013: The test for neutrino and UHECR event connection

Since its mission, Fermi Collaboration reported the highest flux observed during July - September 2012 for the BL Lac Markarian 421 (Mrk 421). The integrated flux was eight times greater than the average flux reported in the second Fermi catalog. During April 2013, Mrk 421 exhibited the highest TeV $\gamma$-ray and optical fluxes recorded. The Telescope Array (TA) collaboration reported the arrival of 72 ultra-high-energy cosmic rays (UHECRs), two in temporal and positional coincidence with the flaring activity observed in 2012 and one with the flaring activity in 2013. The IceCube collaboration has reported around 100 neutrino events in the High-Energy Starting Events (HESE) catalog. Although no neutrino track-like event has been associated with this source, a neutrino shower-like event (IC31) is in temporal and positional coincidence with the flare in 2012. Describing the broadband spectral energy distribution during the flaring activities exhibited in 2012 and 2013 with one- and two-zone lepto-hadronic scenarios and one-zone SSC model, we study a possible correlation between the neutrino event IC31 and the three UHECRs. We estimate the number of neutrino and UHECR events generated from the proposed models, and show that while the neutrino events are low to associate the event IC31 with Mrk 421, the number of UHECRs are similar to those reported by TA collaboration.