GeV $\gamma$-ray Emission of Compact Steep-Spectrum Source 4C +39.23B

Thirteen yr observation data of 4FGL J0824.9+3915 with the Large Area Telescope on board the Fermi Gamma Ray Space Telescope (Fermi/LAT) are analyzed for revisiting whether 4C +39.23B, a compact steep-spectrum (CSS) source closed to a flat-spectrum radio quasar (FSRQ) 4C +39.23A in the $\gamma$-ray emitting region of 4FGL J0824.9+3915, is a $\gamma$-ray emitter. We find that the time-integrated $\gamma$-ray emission of 4FGL J0824.9+3915 is overwhelmingly dominated by 4C +39.23A. It shows significant variability at a 6.7$\sigma$ confidence level and the average $\gamma$-ray flux in the 0.1--300 GeV energy band is $(1.60\pm 0.15)\times10^{-8}$ ph cm$^{-2}$ s$^{-1}$ with a power-law photon spectral index of $2.48\pm0.05$. During MJD 57500--58500, 4FGL J0824.9+3915 is in a low state with a steady $\gamma$-ray flux. Analyzed the Fermi/LAT observation data in this time interval, it is found that the TS values of the $\gamma$-ray emission from 4C +39.23A and 4C +39.23B are $\sim5$ and $\sim 31$, respectively, indicating that the $\gamma$-ray emission in this time interval is dominated by the CSS 4C +39.23B. The derived average flux in this time interval for 4C +39.23B is $(9.40\pm4.10)\times 10^{-9}$ ph cm $^{-2}$ s$^{-1}$ with $\Gamma_{\gamma}=2.45\pm0.17$. Attributing the spectral energy distribution (SED) of 4C +39.23B to the radiations from its core and extended region, we show that the SED can be represented with a two-zone leptonic model. Its $\gamma$-ray emission is contributed by the core region. The derived magnetic field strength and Doppler boosting factor of the core are 0.13 G and 6.5. Comparing 4C +39.23B with other $\gamma$-emitting CSSs and compact symmetric objects (CSOs) in the $\Gamma_{\gamma}-L_{\gamma}$ plane, it resembles CSSs.