Does pulsar B1757-24 have a fallback disk?

Radio pulsars are thought to spin down primarily as a result of torque from magnetic dipole radiation (MDR) emitted by the time-varying stellar magnet ic field as the star rotates. This assumption yields a "characteristic age" for a pulsar, which has generally been assumed to be comparable to the act ual age. Recent observational limits on the proper motion of pulsar B1757-2 4, however, revealed that the actual age (>39 kyr) of this pulsar is much g reater than its MDR characteristic age (16 kyr), calling into question the assumption of pure MDR spin-down for this and other pulsars. To explore the possible cause of this discrepancy, we consider a scenario in which the pu lsar acquired an accretion disk from supernova ejecta and the subsequent sp in-down occurred under the combined action of MDR and accretion torques. A simplified model of the accretion torque involving a constant mass inflow r ate at the pulsar magnetosphere can explain the age and period derivative o f the pulsar for reasonable values of the pulsar magnetic field and inflow rate. We discuss testable predictions of this model.