How long does a uniformly accelerated observer need to interact with a

quantum field in order to record thermality in the Unruh temperature?

In the limit of large excitation energy, the answer turns out to be

sensitive to whether (i) the switch-on and switch-off periods are

stretched proportionally to the total interaction time T, or whether

(ii) T grows by stretching a plateau in which the interaction remains

at constant strength but keeping the switch-on and switch-off

intervals of fixed duration. For a pointlike Unruh-DeWitt detector,

coupled linearly to a massless scalar field in four spacetime

dimensions and treated within first order perturbation theory, we show

that letting T grow polynomially in the detector's energy gap E

suffices in case (i) but not in case (ii), under mild technical

conditions. These results limit the utility of the large E regime as a

probe of thermality in time-dependent versions of the Hawking and

Unruh effects, such as an observer falling into a radiating black

hole. They may also have implications on the design of prospective

experimental tests of the Unruh effect.

Based on arXiv:1605.01316 (published in CQG) with Christopher J

Fewster and Benito A Juarez-Aubry.