The correlation between $\gamma$-photon energy and synchrotron peak frequency for Fermi BL Lac objects

In this paper, the average energy of the \(\gamma\)-photon (\(E_{\mathrm {a},\mathrm{ph}}\)) is calculated and the correlation between \(\log E_{\mathrm{a},\mathrm{ph}}\) and the logarithm of the synchrotron peak frequency (\(\log\nu_{\mathrm{p}}\)) is discussed for a sample of 620 BL Lac objects. The results show that there exists a positive correlation between the \(\gamma\)-photon energy and the synchrotron peak frequency for BL Lac objects, which implies that the \(\gamma\)-ray emissions are related to the low-energy emissions of radio to X-ray bands, and the high energetic \(\gamma\)-ray emissions are only partially from the synchrotron self-Compton process (SSC) for BL Lac objects.