Constraints of Flat Spectrum Radio Quasars in the hadronic model: the case of 3C 273

Understand

We present a method of constraining the properties of the $\gamma$-ray emitting region in flat spectrum radio quasars (FSRQs) in the one-zone proton synchrotron model, where the $\gamma$-rays are produced by synchrotron radiation of relativistic protons.

• We show that for low enough values of the Doppler factor $\delta$, the emission from the electromagnetic (EM) cascade which is initiated by the internal absorption of high-energy photons from photohadronic interactions may exceed the observed $\sim$GeV flux.
• We use that effect to derive an absolute lower limit of $\delta$; first, an analytical one, in the asymptotic limit where the external radiation from the broad line region (BLR) is negligible, and then a numerical one in the more general case that includes BLR radiation.
• As its energy density in the emission region depends on $\delta$ and the region's distance from the galactic center, we use the EM cascade to determine a minimum distance for each value of $\delta$.