  The Fourier transform of the density-density correlation function in a
Bose-Einstein condensate (BEC) analog black hole is a useful tool to
investigate correlations between the Hawking particles and their partners. It
can be expressed in terms of $\langle
^{\text{out}}\hat{a}_{\text{up}}^{\text{ext}}\
^{\text{out}}\hat{a}_{\text{up}}^{\text{int}} \rangle$, where
$^{\text{out}}\hat{a}_{\text{up}}^{\text{ext}}$ is the annihilation operator
for the Hawking particle and $^{\text{out}}\hat{a}_{\text{up}}^{\text{int}} $
is the corresponding one for the partner. This basic quantity is calculated for
three different models for the BEC flow. It is shown that in each model the
inclusion of the effective potential in the mode equations makes a significant
difference. Furthermore, particle production induced by this effective
potential in the interior of the black hole is studied for each model and shown
to be nonthermal. An interesting peak that is related to the particle
production and is present in some models is discussed.
