Polar Gap Dynamics and the Death Line of Millisecond Pulsars

Abstract

Pulsar polar gaps are considered in which the potential drop is a significant fraction of that induced by the rotation of the neutron star. Such gaps are required in order for the observed restriction in the distribution of magnetic field strengths (B) and periods (P) in normal pulsars to be attributed to a death line beyond which the pulsar emission mechanism ceases to operate. It is shown that in contrast to normal pulsars, in which curvature radiation determines the death line, for millisecond pulsars synchrotron radiation is the dominant emission mechanism. The resulting death line is shifted to shorter periods by a factor ~3, as compared to an extrapolation of the death line for normal pulsars. The magnitude of this shift is quite model independent, since it is determined by the diterent properties of the two emission mechanisms. The transition between these different parts of the death line is caused by radiative reaction and occurs for B ~ 109?1010 G. A hitherto neglected effect forces a steepening of the death line for B 1012 G. Although quite model dependent, the same effect can account for the lack of observed millisecond pulsars with B 108 G. Except for the transition region, the location of the death line is insensitive to whether the polar gap breaks down or not. On the other hand, it is argued that both observational and theoretical results are reconciled best with a gap that breaks down, albeit only over a limited portion of the polar cap. The resemblance of the derived death line to the limits of the observed distribution of millisecond pulsars suggests that the observed values of magnetic field strengths and periods are due to the dynamics of the polar gap and not to restrictions imposed during their formation process. Since a large fraction of millisecond pulsars lie close to the derived death line, a significant number of neutron stars may exist that are not observed as millisecond pulsars. This makes the birth rate discrepancy between millisecond pulsars and their assumed low-mass X-ray binary progenitors more acute.