Exploring Axion-Like Particle from observation of FSRQ Ton 599 by Fermi-LAT

High energy photons traveling through astrophysical magnetic fields have the potential to undergo oscillations with axion-like particles (ALPs), resulting in modifications to the observed photon spectrum. High energy $\gamma-$ray sources with significant magnetic field strengths provide an ideal setting to investigate this phenomenon. Ton 599, a flat spectrum radio quasar with a magnetic field strength on the order of Gauss in its emission region, presents a promising opportunity for studying ALP-photon oscillations. In this study, we analyze the effects of ALP-photon oscillations on the $\gamma$-ray spectrum of Ton 599 as observed by Fermi-LAT. Our investigation considers the potential influences of the broad-line region and dusty torus on the $\gamma-$ray spectrum of Ton 599. We set the constraints on the ALP parameters at the $95\%$ confidence level, and find that the constraints on \(g_{a\gamma}\) can reach approximately \(2 \times 10^{-12}~\mathrm{GeV}^{-1}\) for \(m_a \sim 10^{9}~\mathrm{eV}\).