The birth properties of Galactic millisecond radio pulsars

We model the population characteristics of the sample of millisecond pulsars (MSPs) within a distance of 1.5 kpc. We find that for a braking index n=3, the birth magnetic field distribution of the neutron stars as they switch on as radio-emitting MSPs can be represented by a Gaussian in the logarithm with mean log B(G) = 8.1 and sigma(log B) =0.4 and their birth spin period by a Gaussian with mean P-0=4 ms and sigma(P0) = 1.3 ms. We assume no field decay during the lifetime of MSPs. Our study, which takes into consideration acceleration effects on the observed spin-down rate, shows that most MSPs are born with periods that are close to the currently observed values and with average characteristic ages that are typically larger by a factor of similar to 1.5 compared to the true age. The Galactic birth rate of the MSPs is deduced to be greater than or similar to 3.2 x 10(-6) yr(-1) near the upper end of previous estimates and larger than the semi-empirical birth rate similar to 10(-7) yr(-1) of the low-mass X-ray binaries (LMXBs), the currently favoured progenitors. The mean birth spin period deduced by us for the radio MSPs is a factor of similar to 2 higher than the mean spin period observed for the accretion and nuclear powered X-ray pulsars, although this discrepancy can be resolved if we use a braking index n= 5, the value appropriate to spin-down caused by angular momentum losses by gravitational radiation or magnetic multipolar radiation. We discuss the arguments for and against the hypothesis that accretion-induced collapse (AIC) may constitute the main route to the formation of the MSPs, pointing out that on the AIC scenario the low magnetic fields of the MSPs may simply reflect the field distribution in isolated magnetic white dwarfs which has recently been shown to be bi-modal with a dominant component that is likely to peak at fields below 10(3) G which would scale to neutron star fields below 10(9) G, under magnetic flux conservation.