Is the GeV-TeV emission of PKS 0447-439 from the proton synchrotron radiation?

Abstract

We study the multi-wavelength emission features of PKS 0447-439 in the frame of the one-zone homogeneous lepto-hadronic model. In this model, we assumed that the steady power-laws with exponential cut-offs distributions of protons and electrons are injected into the source. The non-linear time-dependent kinematic equations, describing the evolution of protons, electrons and photons, are defined; these equations self-consistently involve synchrotron radiation of protons, photon-photon interaction, synchrotron radiation of electron/positron pairs, inverse Compton scattering and synchrotron self-absorption. The model is applied to reproduce the multi-wavelength spectrum of PKS 0447-439. Our results indicate that the spectral energy distribution (SED) of PKS 0447-439 can be reproduced well by the model. In particular, the GeV-TeV emission is produced by the synchrotron radiation of relativistic protons. The physically plausible solutions require the magnetic strength $10~\text{G}\lesssim B \lesssim 100~\text{G}$. We found that the observed spectrum of PKS 0447-439 can be reproduced well by the model whether $z = 0.16$ or $z = 0.2$, and the acceptable upper limit of redshift is $z=0.343$.