Extra light fermions in $E_6$-inspired models and the 3.5 keV X-ray line signal

We propose a scenario in which extra light fermions in an $E_6$-inspired U(1) extension of the standard model constitute the dark matter, as a simple variation of our model for dark radiation presented in 2010. Interestingly, for the light fermions of mass about 7 keV, they radiatively decay into active neutrinos and photons with a lifetime in the range of ${10}^{27}-{10}^{28}$ seconds, which naturally explains the recently discovered 3.5 keV X-ray line signal.