Formation of Millisecond Pulsars from Accretion‐induced Collapse and Constraints on Pulsar Gamma‐Ray Burst Models

Abstract

We study accretion-induced collapse of magnetized white dwarfs as an origin of millisecond pulsars. We apply magnetized accretion disk models to the precollapse accreting magnetic white dwarfs and calculate the white dwarf spin evolution. If the pulsar magnetic field results solely from the flux-frozen fossil white dwarf field, a typical millisecond pulsar is born with a field strength ~1011-1012 G. The uncertainty in the field strength is mainly due to the uncertain physical parameters of the magnetized accretion disk models. A simple correlation between the pulsar spin Ω* and the magnetic field B*, (Ω*/104 s-1) ~ (B*/1011 G)-4/5, is derived for a typical accretion rate ~5 × 10-8 M☉ yr-1. This correlation remains valid for a wide precollapse physical conditions unless the white dwarf spin and the binary orbit are synchronized prior to accretion induced collapse. We critically examine the possibility of spin-orbit synchronization in close binary systems. Using idealized homogeneous ellipsoid models, we compute the electromagnetic and gravitational wave emission from the millisecond pulsars and find that electromagnetic dipole emission remains nearly constant while millisecond pulsars may spin up rather than spin down as a result of gravitational wave emission. We also derive the physical conditions under which electromagnetic emission from millisecond pulsars formed by accretion-induced collapse can be a source of cosmological gamma-ray bursts. We find that relativistic beaming of gamma-ray emission and precession of gamma-ray-emitting jets are required unless the dipole magnetic field strengths are greater than 1015 G; such strong dipole fields are in excess of those allowed from the accretion-induced collapse formation process except in spin-orbit synchronization. Strong dipole fields greater than 1015 G could in principle be produced in situ. If the millisecond pulsars spin up while emitting gravitational waves, the required values for the shortest bursts are greater than 1016 G, which pushes the limits of suggested neutron star dynamos.