Born to be recycled: A comprehensive population synthesis of the Galactic millisecond pulsars

Context. Millisecond pulsars (MSPs) are the oldest and fastest pulsars known to date. The first MSP to be discovered was PSR B1937+21 in 1982. To explain how these pulsars could be formed, a new hypothesis was formulated: the recycling of pulsars, i.e the fact that a pulsar could accrete matter from a companion and be spun up. Aims. In this study we develop a population synthesis algorithm for pulsars that belong to a binary in order to check whether most of the observed recycled pulsars were formed via an accretion mechanism, and we derive statistics about their properties that are difficult to obtain through observations. We also make predictions for future surveys. Methods. Towards the presented objectives, we used the code Stellar EVolution for N-body (SEVN) in order to take all the binary processes into account and our own code to evolve each pulsar self-consistently by considering the secular evolution of a force-free magnetosphere, the magnetic field decay, gravitational braking, and spatial evolution. Each pulsar was born in a binary with a main sequence companion and evolved to the present time. The radio and γ -ray emission locations were modelled using the polar cap geometry and striped wind model, respectively. Results. Our simulations reproduce well the population of radio and γ -ray pulsars observed in the selected surveys, as supported by Kolmogorov-Smirnov (KS) tests. We also found that there should be fewer than 220 unidentified recycled pulsars in the Fourth Fermi -LAT catalogue of γ -ray sources. Most of the pulsars accrete for typical durations of 10 8 − 9 yr. Moreover the typical timescale of alignment between the rotation axis and the normal to the orbital plane (angle α ) usually remains much shorter. As a consequence, ∼80% of the binary pulsar population has α close to 0°. Most of the recycled pulsars possess masses around 1.8 M ⊙ , and some have masses up to 2.7 M ⊙ , in agreement with recent observations of spider pulsars, which are massive. We estimate that ∼190 MSPs originally born in the Galactic spiral arms contribute to ∼5% of the γ -ray galactic center excess, reinforcing the fact that if this excess is entirely of pulsar origin, these MSPs must have come from globular clusters that migrated inwards to the Galactic centre or were born in the bulge. High values of the viewing angle, ζ , seem to be needed to be able to observe the recycled pulsars, and it also seems difficult to observe recycled pulsars with an aligned rotation axis and magnetic axis (i.e. χ ≤ 10°). We find that only a small fraction, approximately ∼7.6 × 10 −3 %, of oxygen-neon white dwarfs in binary systems appear to contribute to the population of mildly recycled pulsars through accretion-induced collapse.