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 June 2009 , up to August 2012 .
The timing analysis allowed us to obtain the first measurement of the period derivative of SGR 0418 + 5729 : \dot { P } = 4 ( 1 ) \times 10 ^ { -15 } Â s s ^ { -1 } , significant at \sim 3.5 \sigma confidence level .
This leads to a surface dipolar magnetic field of B _ { dip } \simeq 6 \times 10 ^ { 12 } Gauss .
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 \sim 1200 days , we observe a gradual cooling of the tiny hot spot responsible for the X-ray emission , from a temperature of \sim 0.9 to 0.3 keV .
Simultaneously , the X-ray flux decreased by about 3 orders of magnitude : from about 1.4 \times 10 ^ { -11 } to 1.2 \times 10 ^ { -14 } Â erg s ^ { -1 } 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 \sim 550 kyr , and a dipolar magnetic field at birth of \sim 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 result in several other astrophysical contexts .