stimulates emission of Hawking radiation at the BH horizon, i.e., “pair production" of an outgoing wave and partner radiation inside the horizon, as seen in Fig. \[fig:stimulated\_HR\](b). We verified that the partner has the same frequency as the Doppler-shifted BCR, using a temporal windowed Fourier transform, Figs. \[fig:stimulated\_HR\](c) and (d). This shows that only two frequencies are present: that of the background flow, and that of the BCR. It may be possible to perform a similar analysis on the experimental data.

We also explored trap parameters near those that roughly matched the experiment, seeking a regime that could yield a more distinct signal both for our analysis and in future experiments, We identified a slightly modified regime, in which all features are qualitatively the same as those in the experimental regime, only much sharper \[see Fig. \[fig:M20\](b)\]. In the modified regime we made a thorough spectral analysis of the condensate, using both temporal and spatial windowed Fourier transforms \[Figs. \[fig:STFT\_wt\](b) and (c)\]. This enabled us to establish that, despite the significant inhomogeneity in the system, the Bogoliubov–de Gennes dispersion relation gives a remarkably accurate prediction for the temporal and spatial spectral content of the BEC, with the only inputs being 