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We study accretion induced collapse of magnetized white dwarfs as an originof millisecond pulsars. We apply magnetized accretion disk models to thepre-collapse accreting magnetic white dwarfs and calculate the white dwarf spinevolution. If the pulsar magnetic field results solely from the flux-frozenfossil white dwarf field, a typical millisecond pulsar is born with a fieldstrength $\sim 10^{11}-10^{12}G$. The uncertainty in the field strength ismainly due to the uncertain physical parameters of the magnetized accretiondisk models. A simple correlation between the pulsar spin $\Omega_*$ and themagnetic field $B_*$, $(\Omega_*/10^4s^{-1})\sim (B_{*}/10^{11}G)^{-4/5}$, isderived for a typical accretion rate $\sim 5\times 10^{-8}M_{\sun}/yr$. Thiscorrelation remains valid for a wide pre-collapse physical conditions unlessthe white dwarf spin and the binary orbit are synchronized prior to accretioninduced collapse. We critically examine the possibility of spin-orbitsynchronization in close binary systems. Using idealized homogeneous ellipsoidmodels, we compute the electromagnetic and gravitational wave emission from themillisecond pulsars and find that electromagnetic dipole emission remainsnearly constant while millisecond pulsars may spin up rather than spin down asa result of gravitational wave emission. We also derive the physical conditionsunder which electromagnetic emission from millisecond pulsars formed byaccretion induced collapse can be a source of cosmological gamma-ray bursts. Wefind that relativistic beaming of gamma-ray emission and precession ofgamma-ray emitting jets are required unless the dipole magnetic field strengthsare $>10^{15}$G; such strong dipole fields are in excess of those allowed fromthe accretion induced collapse formation process except in spin-orbitsynchronization.Comment: 36 pages, AASLATEX, 4 ps figures, Ap

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