The Parkes multibeam pulsar survey: VII. Timing of four millisecond pulsars and the underlying spin period distribution of the Galactic millisecond pulsar population

We present timing observations of four millisecond pulsars discovered in the Parkes 20-cm multibeam pulsar survey of the Galactic plane. PSRs J1552-4937 and J1843-1448 are isolated objects with spin periods of 6.28 and 5.47 ms respectively. PSR J1727-2946 is in a 40-day binary orbit and has a spin period of 27 ms. The 4.43-ms pulsar J1813-2621 is in a circular 8.16-day binary orbit around a low-mass companion star with a minimum companion mass of 0.2 solar masses. Combining these results with detections from five other Parkes multibeam surveys, gives a well-defined sample of 56 pulsars with spin periods below 20 ms. We develop a likelihood analysis to constrain the functional form which best describes the underlying distribution of spin periods for millisecond pulsars. The best results were obtained with a log-normal distribution. A gamma distribution is less favoured, but still compatible with the observations. Uniform, power-law and Gaussian distributions are found to be inconsistent with the data. Galactic millisecond pulsars being found by current surveys appear to be in agreement with a log-normal distribution which allows for the existence of pulsars with periods below 1.5 ms.