THE OUTBURST DECAY OF THE LOW MAGNETIC FIELD MAGNETAR SGR 0418+5729

We report on the long-term X-ray monitoring of the outburst decay of the low magnetic field magnetar SGR 0418+5729 using all the available X-ray data obtained with RXTE, Swift, Chandra, and XMM-Newton observations from the discovery of the source in 2009 June up to 2012 August. The timing analysis allowed us to obtain the first measurement of the period derivative of SGR 0418+5729: Pdot=4(1)x10^{-15} s/s, significant at a ~3.5\u3c3 confidence level. This leads to a surface dipolar magnetic field of B dip ~ 6 7 10^12 G. This measurement confirms SGR 0418+5729 as the lowest magnetic field magnetar. Following the flux and spectral evolution from the beginning of the outburst up to ~1200 days, we observe a gradual cooling of the tiny hot spot responsible for the X-ray emission, from a temperature of ~0.9 to 0.3 keV. Simultaneously, the X-ray flux decreased by about three orders of magnitude: from about 1.4 7 10^{-11} to 1.2 7 10^{-14} erg/s cm^2. Deep radio, millimeter, optical, and gamma-ray observations did not detect the source counterpart, implying stringent limits on its multi-band emission, as well as constraints on the presence of a fossil disk. By modeling the magneto-thermal secular evolution of SGR 0418+5729, we infer a realistic age of ~550 kyr, and a dipolar magnetic field at birth of ~10^14 G. The outburst characteristics suggest the presence of a thin twisted bundle with a small heated spot at its base. The bundle untwisted in the first few months following the outburst, while the hot spot decreases in temperature and size. We estimate the outburst rate of low magnetic field magnetars to be about one per year per galaxy, and we briefly discuss the consequences of such a result in several other astrophysical contexts