Is there emitted radiation in Unruh effect?

The thermal radiance felt by a uniformly accelerated detector/oscillator/atom--the Unruh effect-- is often mistaken to be some emitted radiation detectable by an observer/probe/sensor. Here we show by an explicit calculation of the energy momentum tensor of a quantum scalar field that, at least in 1+1 dimension, while a polarization cloud is found to exist around the particle trajectory, there is no emitted radiation from a uniformly accelerated oscillator in equilibrium conditions. Under nonequilibrium conditions which can prevail for non-uniformly accelerated trajectories or before the atom or oscillator reaches equilibrium, there is conceivably radiation emitted, but that is not what Unruh effect entails.