On low mass X-ray binaries and millisecond pulsar

The detection, in 1998, of the first Accreting Millisecond Pulsar, started an exiciting season of continuing discoveries in the fashinating field of compact binary systems harbouring a neutron star. Indeed, in these last three lustres, thanks to the extraordinary performances of astronomical detectors, on ground as well as on board of satellites, mainly in the radio, optical, x-ray, and gamma-ray bands, astrophysicists had the opportunity to thoroughly investigate the so-called Recycling Scenario: the evolutionary path leading to the formation of a Millisecond Radio Pulsar. The most intriguing phase is certainly the spin-up stage during which, because of the accretion of matter and angular momentum, the neutron star accumulates an extraordinary amount of mechanical rotational energy, up to 1% of its whole rest-mass energy. These millisecond spinning neutron stars are truly extreme physical objects: General and Special Relativity are fully in action, since their surfaces, attaining speeds close to one fifth of the speed of light, are located just beyond their Schwartzscild Radius, and electrodynamical forces, caused by the presence of huge surface magnetic fields of several hundred million Gauss, display their spectacular properties accelerating electrons up to such energies to promote pair creation in a cascade process responsible for the emission in Radio and Gamma-ray. The rotational energy is swiftly converted and released into electromagnetic power which, in some cases, causes the neutron star to outshine with a luminosity of one hundred suns. Along these fifteen years, a fruitful collaboration was established, at the Rome Astronomical Observatory, between my group and Franca D'Antona: her profound knowledge of the complex phases of stellar evolution, in particular of low-mass stars in close binary systems, was the key ingredient which boosted our theoretical and experimental studies of different evolutionary stages of these intriguing and fashinating systems. In this paper we review some of the most recent discoveries on (accreting) millisecond pulsars, highlighting the role played by our proficuous collaboration.