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It is shown that the gray-body factor for a one-dimensional elongatedBose-Einstein condensate (BEC) acoustic black hole with one horizon does notvanish in the low-frequency ($\omega\to 0$) limit. This implies that the analogHawking radiation is dominated by the emission of an infinite number($\frac{1}{\omega}$) of soft phonons in contrast with the case of aSchwarzschild black hole where the gray-body factor vanishes as $\omega\to 0$and the spectrum is not dominated by low-energy particles. The infraredbehaviors of certain correlation functions are also discussed.

Gray-body factor and infrared divergences in 1D BEC acoustic black holes