On the formation of inner vacuum gaps in radio pulsars

The problem of formation of the Ruderman-Sutherland type inner vacuum gap in neutron stars with $\mathbf{\Omega }\cdot \mathbf{B}<0$ is considered. It is argued by means of the condition $T_i\mathrm{/}{T}_s>1$ (where $T_i$ is the critical temperature above which ${}_{26}^{56}$Fe ions will not be bound at the surface and $T_s$ is the actual temperature of the polar cap surface heated by the back-flow of relativistic electrons) that the inner vacuum gap can form, provided that the actual surface magnetic field is extremaly strong ($B_s\gtrsim {10}^{13}$ G) and curved ($\mathcal{R}<{10}^6$ cm), irrespective of the value of dipolar component measured from the pulsar spin down rate. Calculations are carried out for pulsars with drifting subpulses and/or periodic intensity modulations, in which the existence of the quasi steady vacuum gap discharging via ${\bf E}\times{\bf B}$ drifting sparks is almost unavoidable. Using different pair-production mechanisms and different estimates of the cohesive energies of surface iron ions, we show that it is easier to form the vacuum gap controlled by the resonant inverse Compton scaterring seed photons than by the curvature radiation seed photons.