Constraints on the acceleration of ultra-high-energy cosmic rays in accretion-induced collapse pulsars

We have recently proposed that ultra-high-energy cosmic rays (UHECRs) obser ved above the Greisen-Zatsepin-Kuzmin (GZK) limit could be mostly protons a ccelerated in reconnection sites just above the magnetosphere of newborn mi llisecond pulsars originated by accretion-induced collapse (AIC). Although the expected rate of AIC sources in our own Galaxy is very small (similar t o 10(-5) yr(-1)), our estimates have shown that the observed total flux of UHECRs could be obtained from the integrated contribution of AIC pulsars in the whole distribution of galaxies located within the distance that is una ffected by the GZK cutoff (similar to 50 Mpc). We examine the potential acc eleration mechanisms in the magnetic reconnection site and find that first- order Fermi acceleration cannot provide sufficient efficiency. To prevent s ynchrotron losses, only very small deflection angles of the UHECRs would be allowed in the strong magnetic fields of a pulsar, which is contrary to th e requirements for efficient Fermi acceleration. This leaves one-shot accel eration via an induced electric field within the reconnection region as the only viable process for UHECR acceleration. We formulate the constraints o n both the magnetic field topology and strength in order to accelerate the particles and allow them to freely escape from the system. Under fast recon nection conditions, we find that AIC pulsars with surface magnetic fields 1 0(12) < B-* <less than or similar to> 10(15) G and spin periods 1 less than or similar to P-* <60 ms are able to accelerate particles to energies <gre ater than or equal to>10(20) eV, but the magnetic field just above the surf ace must be predominantly toroidal for the particles to be Alfven allowed t o escape from the acceleration zone without being deflected. Synchrotron lo sses bring potentially important constraints on the magnetic field geometry of any UHECR accelerators involving compact sources with strong magnetic f ields. compact sources with strong magnetic fields.