of a swept BEC at 20 ms intervals with step $U_s/k=\text{ 6 nK}$, scaled by a common factor to match experiment, and viewed in the moving frame where $x=0$ defines the step edge; panel (h): $U_s/k =\text{ 3 nK}$ at 120 ms. Blue (dark gray): experiment [@nphys3104]; red (gray): present simulation. ](steinhauer_evolution_density_072417){width="3.5in"}

The density exhibits a standing-wave pattern behind the step, with amplitude growing in time. Considering that the experimental observations involve an average over any quantities that fluctuate from one run to another, the GP simulation qualitatively matches the overall evolution seen in the experiment. In particular, the growth, wavelength, and phase of the wave pattern are similar to each other.

Čerenkov mechanism {#sec:mechanism}
------------------

In the following, we present multiple lines of evidence showing that the standing wave results from the Bogoliubov-Čerenkov radiation (BCR) effect, in a process closely analogous to the flow past an obstacle studied in [@Carusotto]. This evidence is based on the wavevector and frequency spectra of the standing wave, and the growth rate of the standing wave, which we will show is due to the increasing BEC density. We also establish that the Hawking radiation is emitted by this system and that the partner 