SGR 0418+5729, Swift J1822.3-1606, and 1E 2259+586 as massive, fast-rotating, highly magnetized white dwarfs

Following Malheiro et al. (2012) we describe the so-called low magnetic field magnetars, SGR 0418+5729, Swift J1822.3‐1606, as well as the AXP prototype 1E 2259+586 as massive fast rotating highly magnetized white dwarfs. We give bounds for the mass, radius, moment of inertia, and magnetic field for these sourc es by requesting the stability of realistic general relativ istic uniformly rotating configurations. Based on these parameters, we impr ove the theoretical prediction of the lower limit of the spin down rate of SGR 0418+5729; for a white dwarf close to its maximum stable we obtain the very stringent interval for the spindown rate of 4.1× 10 −16 < ˙ P < 6× 10 −15 , where the upper value is the known observational limit. A lower limit has been also set for Swift J1822.3-1606 for which a fully observationally accepted spin-down rate is still lacking. The white dwarf model provides for this source ˙ P≥ 2.13× 10 −15 , if the star is close to its maximum stable mass. We also present the theoretical expectation of the infrared, optical and ultraviolet emission of these objects and show their consistency with the current available observational data. We give in addition the frequencies at which absorption features could be present in the spectrum of these sources as the result of t he scattering of photons with the quantized electrons by the surface magnetic field.