Understanding the TeV emission from a distant blazar PKS 1424+240 in a lepto-hadronic jet model

We investigate the formation of TeV spectrum of a distant blazar PKS 1424+240 residing at a redshift $z\ge 0.6$ in two scenarios in the frame of a lepto-hadronic jet model taking both the uncertainties of the extragalactic background light (EBL) and its redshift into account. In the first scenario, TeV emission is attributed to the synchrotron emission of pair cascades resulting from $p\gamma$ interaction; in the second scenario, TeV emission is attributed to the proton-synchrotron emission, and an internal absorption due to interaction with the photons around the jet is included. The results show that in the first scenario the 68% upper limit of its redshift within which this scenario can explain the VERITAS TeV spectrum in 2009 well is $\sim 0.75$; in the second scenario, this upper limit of the redshift becomes $\sim 1.03$. However, the second scenario can be excluded because it requires an unreasonable photon field around the jet with a luminosity of $\sim10^{43}\rm
erg\ s^{-1}$. In conclusion, the jet model can explain its TeV spectrum with a low EBL density if $0.6<z<0.75$.