A Phenomenological Model of the Magnetic Field Re-Emergence in Magnetars and Discrepancy Between the Kinematic and Characteristic Ages

Robust age measurements for isolated neutron stars (NSs) are not easily available. That is why the characteristic age τch=P/2P˙ is often used as a proxy. Here, P is the spin period of the NS and P˙ is the time derivative of P. Additional assumptions related to the initial properties and spin-down evolution are made to derive τch. As a result, it is expected that τch is an upper limit for the real age τreal. Recently, Chrimes et al. presented measurements of kinematic ages τkin for several magnetars. Surprisingly, for the majority of these sources, τkin>τch. We present a simple model that includes a realistic approximation for magnetic field decay in magnetars and a simple phenomenological description of field re-emergence following fallback after the birth of an NS. We demonstrate that this simple model can explain the observed relation τkin>τch for a realistic set of parameters.