Permitted luminosity of the magnetar wind and the corresponding age of the magnetar for a given M_c which varies from 0.1 M_⊙ to 100 M_⊙, at which the magnetar wind will interact with the companion wind with the generation of the bow shock. Different colors represent different values of P_orb, as indicated in the caption. The solid lines show the luminosity of the magnetar wind, while the dashed lines indicate the age of the magnetar. The colored areas show the permitted parameter for the scenario where the bow shock is generated from the interaction between the magnetar wind and the companion wind.