  We explore the potential of imaging vibrationally excited molecular emission
at high angular resolution to better understand the morphology and physical
structure of the dense gas in Arp~220 and to gain insight into the nature of
the nuclear powering sources. Vibrationally excited emission of HCN is detected
in both nuclei with a very high ratio relative to the total $L_{FIR}$, higher
than in any other observed galaxy and well above what is observed in Galactic
hot cores. HCN $v_2=1f$ is observed to be marginally resolved in
$\sim60\times50$~pc regions inside the dusty $\sim100$~pc sized nuclear cores.
Its emission is centered on our derived individual nuclear velocities based on
HCO$^+$ emission ($V_{WN}=5342\pm4$ and $V_{EN}=5454\pm8$~\kms, for the western
and eastern nucleus, respectively). With virial masses within $r\sim25-30$~pc
based on the HCN~$v_2=1f$ line widths, we estimate gas surface densities (gas
fraction $f_g=0.1$) of $3\pm0.3\times10^4~M_\odot~\rm pc^{-2}$ (WN) and
$1.1\pm0.1\times10^4~M_\odot~\rm pc^{-2}$ (EN). The $4-3/3-2$ flux density
ratio could be consistent with optically thick emission, which would further
constrain the size of the emitting region to $>15$~pc (EN) and $>22$~pc (WN).
The absorption systems that may hide up to $70\%$ of the HCN and HCO$^+$
emission are found at velocities of $-50$~\kms~(EN) and $6$, $-140$, and
$-575$~\kms (WN) relative to velocities of the nuclei. Blueshifted absorptions
are the evidence of outflowing motions from both nuclei. The bright vibrational
emission implies the existence of a hot dust region radiatively pumping these
transitions. We find evidence of a strong temperature gradient that would be
responsible for both the HCN $v_2$ pumping and the absorbed profiles from the
vibrational ground state as a result of both continuum and self-absorption by
cooler foreground gas.
