On the pumping of the CS($v=0$) masers in W51 e2e

We present the results of numerically solving the rate equations for the first 31 rotational states of CS in the ground vibrational state to determine the conditions under which the J=1-0, J=2-1 and J=3-2 transitions are inverted to produce maser emission. The essence of our results is that the CS($v=0$) masers are collisionally pumped and that, depending on the spectral energy distribution, dust emission can suppress the masers. Apart from the J=1-0 and J=2-1 masers the calculations also show that the J=3-2 transition can be inverted to produce maser emission. It is found that beaming is necessary to explain the observed brightness temperatures of the recently discovered CS masers in W51 e2e. The model calculations suggest that a CS abundance of a few times $10^{-5}$ and CS($v=0$) column densities of the order $10^{16}\,\mathrm{cm^{-2}}$ are required for these masers. The rarity of the CS masers in high mass star forming regions might be the result of a required high CS abundance as well as due to attenuation of the maser emission inside as well as outside of the hot core.