Two possible approaches to form sub-millisecond pulsars

Pulsars have been recognized as normal neutron stars or quark stars. Submillisecond 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 be formed. Both sub-Keplerian (for neutron and quark stars) and super-Keplerian cases (only for quark stars, which are bound additionaly by strong interaction) have been discussed in this paper in order to investigate possible approaches 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 superKeplerian case, pulsars could very likely have an initial period of ∼ 0.1 ms if quark stars with different masses 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 by gravitational wave radiation. We found that the timescales of neutron stars in the phase of sub-millisecond periods are approximately ∼ 10 yr, but the timescales estimated (> 10 yr) for low mass quark stars could be long enough for us to detect. Subject headings: Stars: Pulsars: General, Stars: Neutron