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, often the characteristic age τ_ch=P/2Ṗ is used as a proxy. Here P is the spin period of the NS and Ṗ is the time derivative of P. Additional assumptions related to the initial properties and spin-down evolution are made to derive τ_ch. As a result, it is expected that τ_ch is an upper limit for the real age τ_real. Recently, Chrimes et al. presented measurements of kinematic ages τ_kin for several magnetars. Surprisingly, for the majority of these sources τ_kin>τ_ch. We present a simple model including a realistic approximation for the magnetic field decay in magnetars and a simple phenomenological description of the field re-emergence after an episode of fallback after the birth of a NS. We demonstrate that this simple model can explain the observed relation τ_kin>τ_ch for realistic sets of parameters.