Constraining the Age of a Magnetar Possibly Associated with FRB 121102

The similarity of the host galaxy of FRB 121102 with those of long gamma-ray bursts and Type I superluminous supernovae suggests that this fast radio burst (FRB) could be associated with a young magnetar. By assuming the FRB emission is produced within the magnetosphere, we derive a lower limit on the age of the magnetar, after which GHz emission is able to escape freely from the dense relativistic wind of the magnetar. Another lower limit is obtained by requiring the dispersion measure contributed by the electron/positron pair wind to be consistent with the observations of the host galaxy. Furthermore, we also derive some upper limits on the magnetar age with discussions on possible energy sources of the FRB emission and the recently discovered persistent radio counterpart. As a result, some constraints on model parameters are addressed by reconciling the lower limits with the possible upper limits that are derived with an assumption of the rotational energy source.