THE MAGNETIC-FIELDS, AGES, AND ORIGINAL SPIN PERIODS OF MILLISECOND PULSARS

Accurate determination of the spin-down rates of millisecond pulsars r equires consideration of the apparent acceleration of the pulsars due to their high transverse velocities. We show that for several nearby p ulsars the neglect of this effect leads to substantial errors in infer red pulsar ages and magnetic fields. Two important ramifications follo w. (1) The intrinsic magnetic field strengths of all millisecond pulsa rs lie below 5 x 10(8) G, strengthening an earlier suggestion of a ''g ap'' between the magnetic field strengths of millisecond pulsars and o f high-mass binary pulsars such as PSR B1913+16, which are thought to have been formed by mass transfer in low-mass and high-mess X-ray bina ries, respectively This result suggests that the magnetic field streng ths of recycled pulsars are related to their formation and evolution i n binary systems. (2) The corrected characteristic ages of several mil lisecond pulsars appear to be greater than the age of the Galactic dis k. We reconcile this apparent paradox by suggesting that some millisec ond pulsars were born with periods close to their current periods. Thi s conclusion has important implications for the interpretation of the cooling ages of white dwarf companions, the birthrate discrepancy betw een millisecond pulsars and their X-ray binary progenitors, and the po ssible existence of a class of weakly magnetized (B much less than 10( 8) G), rapidly rotating neutron stars.