TeV pion bumps in the gamma-ray spectra of flaring blazars

(Abridged) Very high-energy (VHE, $E>100$ GeV) observations of the blazar Mrk 501 with MAGIC in 2014 provided evidence for an unusual narrow spectral feature at about 3 TeV during an extreme X-ray flaring activity. The one-zone synchrotron-self Compton scenario, widely used in blazar broadband spectral modeling, fails to explain the narrow TeV component. Motivated by this rare observation, we propose an alternative model for the production of narrow features in the VHE spectra of flaring blazars. These spectral features may result from the decay of neutral pions ($π^0$ bumps) that are in turn produced via interactions of protons (of tens of TeV energy) with energetic photons, whose density increases during hard X-ray flares. We explored the conditions needed for the emergence of narrow $π^0$ bumps in VHE blazar spectra during X-ray flares reaching synchrotron energies $\sim 100$ keV using time-dependent radiative transfer calculations. We focused on high-synchrotron peaked (HSP) blazars, which comprise the majority of VHE-detected extragalactic sources. We find that synchrotron-dominated flares with peak energies $\gtrsim100$ keV can be ideal periods for the search of $π^0$ bumps in the VHE spectra of HSP blazars. The flaring region is optically thin to photopion production, its energy content is dominated by the relativistic proton population, and the inferred jet power is highly super-Eddington. Application of the model to the spectral energy distribution of Mrk 501 on MJD 56857.98 shows that the VHE spectrum of the flare is described well by the sum of a synchrotron self-Compton (SSC) component and a distinct $π^0$ bump centered at 3 TeV. Spectral fitting of simulated SSC+$π^0$ spectra for the Cherenkov Telescope Array (CTA) show that a $π^0$ bump could be detected at a 5$σ$ significance level with a 30-min exposure.