Lepto-hadronic $\gamma$-ray and neutrino emission from the jet of TXS 0506+056

The observation of IceCube-170922A event from the direction of TXS 0506+056 when it was in its enhanced $\gamma$-ray emission state offers a unique opportunity to investigate the lepto-hadronic processes in blazar jets. Here, the observed broadband emission of TXS 0506+056 is explained by boosted synchrotron/synchrotron self Compton emission from the jet whereas the $\gamma$-ray data observed during the neutrino emission- by inelastic interactions of the jet-accelerated protons in a dense gaseous target. The proton energy distribution is $\sim E_{p}^{-2.50}$, calculated straightforwardly from the data obtained by Fermi-LAT and MAGIC and if such distribution continues up to $E_{c,p}=10$ PeV, the expected neutrino rate is as high as $\sim0.46$ events during the long active phase of the source or $\sim0.15$ if the activity lasts 60 days. In this interpretation, the energy content of the protons above $>$ GeV in blazar jets can be estimated as well: the required proton injection luminosity is $\simeq2.0\times10^{48}\:{\rm erg\:s^{-1}}$ exceeding $10^3$ times that of electrons $\simeq10^{45}\:{\rm erg\:s^{-1}}$ which are in equipartition with the magnetic field. As the required parameters are physically realistic, this can be an acceptable model for explanation of the neutrino and $\gamma$-ray emission from TXS 0506+056.