On the Diversity of Compact Objects within Supernova Remnants. I: A   Parametric Model for Magnetic Field Evolution
  A wealth of X-ray and radio observations has revealed in the past decade a growing diversity of neutron stars (NSs) with properties spanning orders of magnitude in magnetic field strength and ages, and with emission processes explained by a range of mechanisms dictating their radiation properties. However, serious difficulties exist with the magneto-dipole model of isolated neutron star fields and their inferred ages, such as a large range of observed braking indices ($n$, with values often $<$3) and a mismatch between the neutron star and associated supernova remnant (SNR) ages. This problem arises primarily from the assumptions of a constant magnetic field with $n$=3, and an initial spin period that is much smaller than the observed current period. It has been suggested that a solution to this problem involves magnetic field evolution, with some NSs having magnetic fields buried within the crust by accretion of fall-back supernova material following their birth. In this work we explore a parametric phenomenological model for magnetic field growth that generalizes previous suggested field evolution functions, and apply it to a variety of NSs with both secure SNR associations and known ages. We explore the flexibility of the model by recovering the results of previous work on buried magnetic fields in young neutron stars. Our model fits suggest that apparently disparate classes of NSs may be related to one another through the time-evolution of the magnetic field. 
Adam Rogers and Samar Safi-Harb
astro-ph.HE