We report on the analysis of two deep XMM-Newton observations of the magnetar Swift J1834.9-0846 and its surrounding extended emission taken in March 2014 and October 2014, 2.5 and 3.1 years after the source went into outburst. The magnetar is only weakly detected in the first observation with an absorption corrected flux $F_{rm 0.5-10 keV}approx4times10^{-14}$ erg s$^{-1}$ cm$^{-2}$, and a $3sigma$ upper limit during the second observation of about $3times10^{-14}$ erg s$^{-1}$ cm$^{-2}$. This flux level is more than 3 orders of magnitude lower than the flux measured at the outburst onset on September 2011. The extended emission, centered at the magnetar position and elongated towards the south-west, is clearly seen in both observations; it is best fit by a highly absorbed power-law (PL), with a hydrogen column density of $N_{rm H}=8.0times10^{22}$ cm$^{-2}$ and PL photon index $Gamma=2.2pm0.2$. Its flux is constant between the two observations at $F_{rm 0.5-10 keV}=1.3times10^{-12}$ erg s$^{-1}$ cm$^{-2}$. We find no statistically significant changes in the spectral shape or the flux of this extended emission over a period of 9 years from 2005 to 2014. These new results strongly support the extended emission nature as a wind nebula and firmly establish Swift J1834.9-0846 as the first magnetar to show a surrounding wind nebula. Further, our results imply that such nebulae are no longer exclusive to rotation-powered pulsars and narrow the gap between these two sub-populations of isolated neutron stars. The size and spectrum of the nebula are compatible with those of pulsar-wind nebulae but its radiative efficiency $eta_{rm X}=L_{rm X}/dot{E}approx0.1$ is markedly high, possibly pointing to an additional wind component in Swift J1834.9-0846.
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