Two possible approaches to form sub-millisecond pulsars

Pulsars have been recognized as normal neutron stars or quark stars. Sub-millisecond pulsars, if detected, would play an essential and important role in distinguishing quark stars from neutron stars. A key question is how sub-millisecond pulsars could form. Both sub-Keplerian (for neutron and quark stars) and super-Keplerian cases (only for quark stars, which are bound additionally by strong interaction) have been discussed in this paper in order to investigate possible ways of forming sub-millisecond pulsars. In the sub-Keplerian case, the equilibrium periods of both neutron and quark stars could be as low as ~0.4 ms when they are spun up through accretion in binary systems. In the super-Keplerian case, pulsars could very likely have an initial period of ~0.1 ms if quark stars with different mass could be formed from accretion-induced collapse (AIC) of white dwarfs. The timescale for a sub-millisecond pulsar to keep its period <1 ms is restricted due to gravitational wave radiation. We found that the timescales of neutron stars within sub-millisecond periods are approximately ~10 yr, but the timescales estimated (>10 Myr) for low-mass quark stars could be long enough for us to detect.