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Fast spinning neutron stars, recycled in low mass binaries, may have accreteda substantial amount of mass. The available relativistic measurements ofneutron star masses, all clustering around 1.4 M_sun, however refer mostly toslowly rotating neutron stars which accreted a tiny amount of mass duringevolution in a massive binary system. We develop a semi-analytical model forstudying the evolution of the spin period P of a magnetic neutron star as afunction of the baryonic mass load M_{ac}; evolution is followed down tosubmillisecond periods and the magnetic field is allowed to decay significantlybefore the end of recycling. We use different equations of state and includerotational deformation effects, the presence of a strong gravitational fieldand of a magnetosphere. For the non-magnetic case, comparison with numericalrelativistic codes shows the accuracy of our description. The minimum accretedmass requested to spin-up a magnetized 1.35M_sun-neutron star at a fewmillisecond is 0.05 M_sun, while this value doubles for an unmagnetized neutronstar. Below 1 millisecond the request is of at least 0.25 M_sun. There mayexist a yet undetected population of massive submillisecond neutron stars. Thediscovery of a submillisecond neutron star would imply a lower limit for itsmass of about 1.7M_sun.Comment: To appear in the Astrophysical Journal, June 199

Neutron Stars with Submillisecond Periods: A Population of High‐Mass Objects?