  We model a sonic black hole analog in a quasi one-dimensional Bose-Einstein
condensate, using a Gross-Pitaevskii equation matching the configuration of a
recent experiment by Steinhauer [Nat. Phys. 10, 864 (2014)]. The model agrees
well with important features of the experimental observations, demonstrating
their hydrodynamic nature. We find that a zero-frequency bow wave is generated
at the inner (white hole) horizon, which grows in proportion to the square of
the background condensate density. The relative motion of the black and white
hole horizons produces a Doppler shift of the bow wave at the black hole, where
it stimulates the emission of monochromatic Hawking radiation. The mechanism is
confirmed using temporal and spatial windowed Fourier spectra of the
condensate. Mean field behavior similar to that in the experiment can thus be
fully explained without the presence of self-amplifying Hawking radiation.
