Gamma-ray sources like V407 Cygni in Symbiotic Stars

Using a simple accelerating model and an assumption that $\gamma$-rays originate from $p-p$ collisions for a ${\pi }^0$ model, we investigate $\gamma$-ray sources like V407 Cygni in symbiotic stars. The upper limit of their occurrence rate in the Galaxy is between 0.5 and 5 yr${}^{-1}$, indicating that they may be an important source of the high-energy $\gamma$-rays. The maximum energies of the accelerated protons mainly distribute around ${10}^{11}$ eV, and barely reach ${10}^{15}$ eV. The novae occurring in D-type SSs with ONe WDs and long orbital periods are good candidates for $\gamma$-ray sources. Due to a short orbital period which results in a short acceleration duration, the nova occurring in symbiotic star RS Oph can not produce the $\gamma$-ray emission like that in V407 Cygni.