Evolution Of PSR J1734-3333 And PSR J1640-4631 Braked By A Fall-back Disk

The slow rotation of young isolated pulsars is closely related to the radiation mechanism and the braking index reflects the braking mechanism of pulsar.How to explain the observation performance of pulsars is a challenge to the theory of braking mechanism.The value of the braking index predicted by mainstream theory should be in the range of 1-3,however 12 young pulsars have observed a more accurate braking index,two of which are quite special.The braking indexes of PSR J1734-3333 and PSR J1640-4631 are n = 0.9 ± 0.2 and n = 3.15 ± 0.03,respectively.This paper mainly discusses the rotation evolution of these two pulsars under the action of the fall-back disk.After the supernova explosion,some materials may form a fall-back disk around the pulsar due to the larger angular momentum.The fall-back disk will be accreted by pulsar,which will interact with pulsar and produce an extra braking torque to affect the rotation evolution of the pulsar in the propeller phase.In this paper,a modified self-similar model of the fall-back disk is adopted.On the basis of this study,a final braking torque is obtained by considering the magnetic dipole radiation and the evolution path of PSR J1734-3333 and PSR J1640-4631 is fitted by using this torque.The results show that the evolution path fitted under this model is in good agreement with the observation performance of these two special pulsars.It is can be seen in the diagram,PSR J1734-3333 and PSR J1640-4631 may evolve into the area of AXP in the future.In this model,the observed braking index is used to limit the possible initial parameters,we found the initial period,magnetic field and the initial mass of the fall-back disk of these two pulsars respectively.The range is displayed in the three-dimensional diagram.The results show that the evolution path of the torque caused by the fall-back disk and the magnetic dipole radiation fit the observed braking indexes of PSR J1734-3333 and PSR J1640-4631.According to the change of the braking index with time,it can be seen that the observation performance of pulsars with braking index in the range of 1-3 is not contradictory.The evolutionary path gives a prediction that PSR J1734-3333 and PSR J1640-4631 may evolve into the AXP region in the future.The fall-back disk model is also helpful to explain the source of anomalous X-ray source in the process of the evolution.Then analyze the possible parameters space,the range of the magnetic field,the initial mass of the fall-back disk and the initial period are all in accordance with the parameters of ordinary pulsars.This may be a proof that ordinary pulsars have evolved into AXP.It was found that the range of the initial mass of the fall-back disk is consistent with the conclusion of other studies which the mass was less than 0.1 solar mass.The results of the future evolution of pulsars within this parameters range are predicted and the evolution may be consistent.It is expected that future observations will be tested and the theoretical model will be improved based on observations...