  Motivated by a recent experiment of J.~Steinhauer, we reconsider the spectrum
and the correlations of the phonons spontaneously emitted in stationary
transonic flows. The latter are described by "waterfall" configurations which
form a one-parameter family of stable flows. For parameters close to their
experimental values, in spite of high gradients near the sonic horizon, the
spectrum is accurately planckian in the relevant frequency domain, where the
temperature differs from the relativistic prediction by less than $10 \%$. We
then study the density correlations across the horizon and the non-separable
character of the final state. We show that the relativistic expressions provide
accurate approximations when the initial temperature is not too high. We also
show that the phases of the scattering coefficients introduce a finite shift of
the location of the correlations which was so far overlooked. This shift is due
to the asymmetry of the flow across the horizon, and persists in the
dispersion-less regime. Finally we show how the formation of the sonic horizon
modifies both local and non-local density correlations.
