Searching for the 3.5 keV Line in the Deep Fields with Chandra: The 10 Ms Observations

In this paper we report a 3$\sigma$ detection of an emission line at $\sim$3.5 keV in the spectrum of the Cosmic X-ray Background using a total of $\sim$10 Ms Chandra observations towards the COSMOS Legacy and CDFS survey fields. The line is detected with an intensity is $8.8\ \pm\ {2.9}\times10^{-7}$ ph cm$^{-2}$s$^{-1}$. Based on our knowledge of $Chandra$, and the reported detection of the line by other instruments, an instrumental origin for the line remains unlikely. We cannot though rule out a statistical fluctuation and in that case the current data allows us to place a 3$\sigma$ upper limit at 0.8$\times$10$^{-6}$ ph cm$^{-2}$s$^{-1}$. We discuss the interpretation of this observed line in terms of the iron line background; S {\sc XVI} charge exchange as well as potentially from sterile neutrino decay. We note that our detection is consistent with previous measurements of this line toward the Galactic center, and can be modeled as the result of sterile neutrino decay from the Milky Way for the dark matter distribution modeled as an NFW profile. For this case, we estimate a mass m$_{\nu}\sim$7.01 keV and a mixing angle sin$^2$(2$\theta$)= 0.83--2.75 $\times 10^{-10}$. These derived values are in agreement with independent estimates from galaxy clusters; the Galactic center and M31.