  We report numerical evidence of Hawking emission of Bogoliubov phonons from a
sonic horizon in a flowing one-dimensional atomic Bose-Einstein condensate. The
presence of Hawking radiation is revealed from peculiar long-range patterns in
the density-density correlation function of the gas. Quantitative agreement
between our fully microscopic calculations and the prediction of analog models
is obtained in the hydrodynamic limit. New features are predicted and the
robustness of the Hawking signal against a finite temperature discussed.
