The magnetic fields, ages, and original spin periods of millisecond pulsars

Accurate determination of the spin-down rates of millisecond pulsars requires consideration of the apparent acceleration of the pulsars due to their high transverse velocities. We show that for several nearby pulsars the neglect of this effect leads to substantial errors in inferred pulsar ages and magnetic fields. Two important ramifications follow. (1) The intrinsic magnetic field strengths of all millisecond pulsars lie below 5 × 108 G, strengthening an earlier suggestion of a "gap" between the magnetic field strengths of millisecond pulsars and of high-mass binary pulsars such as PSR B1913+16, which are thought to have been formed by mass transfer in low-mass and high-mass X-ray binaries, respectively. This result suggests that the magnetic field strengths of recycled pulsars are related to their formation and evolution in binary systems. (2) The corrected characteristic ages of several millisecond pulsars appear to be greater than the age of the Galactic disk. We reconcile this apparent paradox by suggesting that some millisecond pulsars were born with periods close to their current periods. This conclusion has important implications for the interpretation of the cooling ages of white dwarf companions, the birthrate discrepancy between millisecond pulsars and their X-ray binary progenitors, and the possible existence of a class of weakly magnetized (B ≪ 108 G), rapidly rotating neutron stars.