  We theoretically study the entanglement of Hawking radiation pairs emitted by
an analogue black hole. We find that this entanglement can be measured by the
experimentally accessible density-density correlation function, vastly
simplifying the measurement. We find that while the Hawking radiation exiting
the black hole might be Planck-distributed, the correlations between the
Hawking radiation and the partner particles has a distribution which is weaker
but broader than Planckian. Thus, the high energy tail of the distribution of
Hawking radiation should be entangled, whereas the low energy part should not
be. This confirms a previous numerical study. The full Peres-Horodecki
criterion is considered, as well as a simpler criterion in the stationary,
homogeneous case. Our method applies to systems which are sufficiently cold
that the thermal phonons can be neglected.
