Evolving into Magnetars from Normal Pulsars with a Low Braking Index

Anomalous x-ray pulsars (AXPs) and soft gamma-ray repeaters (SGRs) are believed to be candidates for magnetars, and they are powered by the decay of ultra-strong magnetic fields of >10¹⁴G. From the modified spin-down relation of pulsars ^・P∝P^2-n, we find that the Vela pulsar would evolve into the classes of magnetars under some assumptions that pulsars lose their rotational energy only by magnetic dipole radiation and the braking index is a constant. Our rough calculation indicates that only pulsars with n~1.3-1.6 can evolve into magnetars. Pulsars like Vela with a low braking index may be the progenitors of AXPs and SGRs. Regarding the mechanism evolved into magnetars, we suggest that pulsars' surface magnetic field component may be increased by frequent glitches.