Modelling of the surface emission of the low magnetic field magnetar SGR 0418+5729

We perform a detailed modelling of the post-outburst surface emission of the low magnetic field magnetar SGR 0418+5729. The dipolar magnetic field of this source, B=6×1012G estimated from its spin-down rate, is in the observed range of magnetic fields for normal pulsars. The source is further characterized by a high pulse fraction and a single-peak profile. Using synthetic temperature distribution profiles, and fully accounting for the general-relativistic effects of light deflection and gravitational redshift, we generate synthetic X-ray spectra and pulse profiles that we fit to the observations. We find that asymmetric and symmetric surface temperature distributions can reproduce equally well the observed pulse profiles and spectra of SGR 0418. None the less, the modelling allows us to place constraints on the system geometry (i.e. the angles ψ and ξ that the rotation axis makes with the line of sight and the dipolar axis, respectively), as well as on the spot size and temperature contrast on the neutron star surface. After performing an analysis iterating between the pulse profile and spectra, as done in similar previous works, we further employed, for the first time in this context, a Markov-Chain Monte Carlo approach to extract constraints on the model parameters from the pulse profiles and spectra, simultaneously. We find that, to reproduce the observed spectrum and flux modulation: (a) the angles must be restricted to 65° ≲ ψ + ξ ≲ 125° or 235° ≲ ψ + ξ ≲ 295°; (b) the temperature contrast between the poles and the equator must be at least a factor of ∼6, and (c) the size of the hottest region ranges between 0.2 and 0.7 km (including uncertainties on the source distance). Lastly, we interpret our findings within the context of internal and external heating models.

Constraining the GRB-Magnetar Model by Means of the Galactic Pulsar Population

A large fraction of Gamma-ray bursts (GRBs) displays an X-ray plateau phase within <105 s from the prompt emission, proposed to be powered by the spin-down energy of a rapidly spinning newly born magnetar. In this work we use the properties of the Galactic neutron star population to constrain the GRB-magnetar scenario. We re-analyze the X-ray plateaus of all Swift GRBs with known redshift, between 2005 January and 2014 August. From the derived initial magnetic field distribution for the possible magnetars left behind by the GRBs, we study the evolution and properties of a simulated GRB-magnetar population using numerical simulations of magnetic field evolution, coupled with Monte Carlo simulations of Pulsar Population Synthesis in our Galaxy. We find that if the GRB X-ray plateaus are powered by the rotational energy of a newly formed magnetar, the current observational properties of the Galactic magnetar population are not compatible with being formed within the GRB scenario (regardless of the GRB type or rate at z = 0). Direct consequences would be that we should allow the existence of magnetars and "super-magnetars" having different progenitors, and that Type Ib/c SNe related to Long GRBs form systematically neutron stars with higher initial magnetic fields. We put an upper limit of ≤16 "super-magnetars" formed by a GRB in our Galaxy in the past Myr (at 99% c.l.). This limit is somewhat smaller than what is roughly expected from Long GRB rates, although the very large uncertainties do not allow us to draw strong conclusion in this respect.