  We consider the quasi-one-dimensional (quasi-1D) model of a sonic black hole
in a dilute Bose-Einstein condensate. It is shown that an accurate treatment of
the dimensional reduction to quasi-1D leads to a finite condensate quantum
depletion even for axially infinite systems, and an intrinsic nonthermality of
the black hole radiation spectrum. By calculating the depletion, we derive a
{\em first-order} many-body signature of the sonic horizon, represented by a
distinct peak in the depletion power spectrum. This peak constitutes a readily
experimentally accessible tool to detect quantum sonic horizons even when a
negligible Hawking radiation flux is created by the black hole.
