Modelling of the Surface Emission of the Low-Magnetic Field Magnetar SGR 0418+5729

TL;DR

This paper models the surface emission of the low-magnetic-field magnetar SGR 0418+5729, using synthetic spectra and pulse profiles, and employs a novel MCMC approach to constrain system geometry and surface temperature distribution.

Contribution

It introduces a combined spectral and pulse profile modeling with MCMC analysis to constrain the geometry and surface features of a low-field magnetar, a novel approach in this context.

Findings

Angles are constrained to specific ranges for matching observations.

Surface temperature contrast must be at least a factor of 6.

Hot spot size ranges between 0.2 and 0.7 km.

Abstract

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=6x10^12 G 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. Nonetheless, the modelling allows us to place constraints on the system geometry (i.e. the angles $\psi$ and $\xi$ 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 $65\deg < \psi+\xi < 125\deg$ or $235\deg < \psi+\xi <295\deg$; (b) the temperature contrast between the poles and the equator must be at least a factor of $\sim6$, and (c) the size of the hottest region ranges between 0.2-0.7 km (including uncertainties on the source distance). Last, we interpret our findings within the context of internal and external heating models.