Zi-Hao Xu, Wei-Yang Wang, Ren-Xin Xu

A numerical framework to calculate the height and potential of the vacuum inner gap is proposed here. The results show that small mountains on a pulsar's polar cap tend to significantly influence the properties of the inner vacuum gap, making it easier for sparks to form. In this scenario, the magnetospheric activity observed from the pulsars PSR J0250$+$5854 and PSR J2144$-$3933, which lie below the pulsar death line, would be reproduced, and the irregular discharge behaviour in other polar cap regions could also be understood. Furthermore, the presence of small mountains could provide a new way to probe the puzzling state of supranuclear matter inside pulsars. In order to have stable mountains on the surface, pulsars might be made of solid strangeon matter, which is favoured by both the charge neutrality and the flavour symmetry of quarks.