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

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The importance of the photon-photon pair production process (γ+ γ′→ 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, Tcri, which are around 4× 10⁶K when P=0.1s and will slowly increase with increasing periods. Compared with the γ-B process, it is found that the two-photon annihilation process may ignite a central spark near the magnetic pole, where γ-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.