# Constraining the age of a magnetar possibly associated with FRB 121102

## TL;DR

This paper estimates the age of a magnetar potentially linked to FRB 121102 by analyzing emission escape conditions, dispersion measures, and energy sources, providing constraints on magnetar models and properties.

## Contribution

It introduces a method to constrain magnetar age using emission escape and dispersion measure limits, integrating observational data with theoretical models.

## Key findings

- Lower age limits derived from emission escape conditions.
- Dispersion measure constraints support young magnetar hypothesis.
- Upper age limits discussed in context of energy sources.

## Abstract

The similarity of the host galaxy of FRB 121102 with those of long gamma-ray bursts and Type I super-luminous supernovae suggests that this FRB could be associated with a young magnetar. By assuming the FRB emission to be 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 rotational energy source.