Revised the $\gamma$-ray emission from SNR CTB 109 with Fermi-LAT

CTB 109 is a middle-aged shell-type SNR with bright thermal X-ray emission. We reanalyze the GeV $\gamma$-ray emission from CTB 109 using thirteen years of Pass 8 data recorded by the Fermi Large Area Telescope (Fermi-LAT). The $\gamma$-ray emission of CTB 109 shows a center bright morphology, which is well consistent with its thermal X-ray emission rather than the shell-type structure in the radio band. The spectral analysis shows an evident spectral curvature at $\sim$ several GeV for the GeV $\gamma$-ray spectrum, which can naturally explain the lack of TeV $\gamma$-ray emission from CTB 109. Although either a leptonic or a hadronic model could fit the multi-wavelength observations of CTB 109, the hadronic model is favored considering its $\gamma$-ray morphology and the spectral curvature of GeV spectrum. The unusual $\gamma$-ray spectrum of CTB 109 with other SNRs and the luminosity-diameter squared relation make CTB 109 to be distinguished both from the young-aged SNRs with hard GeV $\gamma$-ray spectra and several old-aged SNRs interacting with molecular clouds.