Origin and evolution of magnetars

We present a population synthesis study of the observed properties of the magnetars investigating the hypothesis that they are drawn from a population of progenitors that are more massive than those of the normal radio pulsars. We assume that the anomalous X-ray emission is caused by the decay of a toroidal or tangled up field that does not take part in the spin-down of the star. Our model assumes that the magnetic flux of the neutron star is distributed as a Gaussian in the logarithm about a mean value that is described by a power law φ = φ₀ ^γG cm² (8M_⊙ ≤ M_p ≤ 45M_⊙), where M_p is the mass of the progenitor. We find that we can explain the observed properties of the magnetars for a model with φ₀ = 2 × 10²⁵ G cm² and γ = 5 if we suitably parametrize the time evolution of the anomalous X-ray luminosity as an exponentially decaying function of time. Our modelling suggests that magnetars arise from stars in the high-mass end (20 M_⊙ ≤ M_p ≤ 45 M_⊙) of this distribution. The lower mass progenitors are assumed to give rise to the radio pulsars. The high value of γ can be interpreted in one of two ways. It may indicate that the magnetic flux distribution on the main sequence is a strong function of mass and that this is reflected in the magnetic fluxes of the neutron stars that form from this mass range (the fossil field hypothesis). The recent evidence for magnetic fluxes similar to those of the magnetars in a high fraction (~25 per cent) of massive O-type stars lends support to such a hypothesis. Another possibility is that the spin of the neutron star is a strong function of the progenitor mass, and it is only for stars that are more massive than ~20M_⊙ that magnetar-type fields can be generated by the α-ω dynamo mechanism (the convective dynamo hypothesis). In either interpretation, it has to be assumed that all or a subset of stars in the mass range ~20-45 M_⊙, which on standard stellar evolution models lead to black holes via the formation of a fall-back disc, must give rise to magnetars. Unlike with the radio pulsars, the magnetars only weakly constrain the birth spin period, due to their rapid spin-down. Our model predicts a birthrate of ~ 1.5-3 × 10^-3 yr^-1 for the magnetars.