On the spin period distribution of millisecond pulsars

Spin period distribution provides important clues to understand the formation of millisecond pulsars (MSPs). To uncover the intrinsic period distribution, we analyze three samples of radio MSPs in the Galactic field and in globular clusters. The selection bias due to pulse broadening has been corrected but turns out to be negligible. We find that all the samples can be well described by a Weibull distribution of spin frequencies. Considering MSPs in the Galactic field or in globular clusters, and in isolation or in binary systems, we find no significant difference in the spin distribution among these subpopulations. Based on the current known population of MSPs, we find that sub-millisecond pulsars are unlikely to be discovered by the Square Kilometer Array, although up to $\sim10$ discoveries of pulsars that spin faster than the current record holder of $P=1.4$~ms are expected.