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It is shown that the gray-body factor for a one-dimensional elongated Bose-Einstein condensate (BEC) acoustic black hole with one horizon does not vanish in the low-frequency (ω → 0) limit. This implies that the analog Hawking radiation is dominated by the emission of an infinite number (1/ω) of soft phonons in contrast with the case of a Schwarzschild black hole where the gray-body factor vanishes as ω → 0 and the spectrum is not dominated by low-energy particles. The infrared behaviors of certain correlation functions are also discussed. [ABSTRACT FROM AUTHOR]

We derive analytic expressions for the low-frequency properties of the analogue Hawking radiation in a general weak-dispersive medium. A thermal low-frequency part of the spectrum is expected even when dispersive effects become significant. We consider the two most common class of weak-dispersive media and investigate all possible anomalous scattering processes due inhomogeneous background flows. We first argue that under minimal assumptions, the scattering processes in near-critical flows are well described by a linearized Korteweg-de Vries equation. Within our theoretical model grey-body factors are neglected, that is, the mode comoving with the flow decouples from the other ones. We also exhibit a flow example with an exact expression for the effective temperature. We see that this temperature coincides with the Hawking one only when the dispersive length scale is much smaller than the flow gradient scale. We apply the same method in inhomogeneous flows without an analogue horizon. In this case, the spectrum coefficients decrease with decreasing frequencies. Our findings are in agreement with previous numerical works, generalizing their findings to arbitrary flow profiles. Our analytical expressions provide estimates to guide ongoing experimental efforts. [ABSTRACT FROM AUTHOR]