Two-photon annihilation in the pair formation cascades in pulsar polar caps

The importance of the photon-photon pair production process ($\gamma+ \gamma^{\prime}\to e^{+}+e^{-}$) to form pair production cascades in pulsar polar caps is investigated within the framework of the Ruderman-Sutherland vacuum gap model. It is found that this process is unimportant if the polar caps are not hot enough, but will play a non-negligible role in the pair formation cascades when the polar cap temperatures are in excess of the critical temperatures, $T_{cri}$, which are around $4\times 10^6K$ when $P=0.1$s and will slowly increase with increasing periods. Compared with the $\gamma-B$ process, it is found that the two-photon annihilation process may ignite a central spark near the magnetic pole, where $\gamma-B$ sparks can not be formed due to the local weak curvatures. This central spark is large if the gap is dominated by the ``resonant ICS mode''. The possible connection of these central sparks with the observed pulsar ``core'' emission components is discussed.