  The excitation of the filamentary gas structures surrounding giant elliptical
galaxies at the center of cool-core clusters, a.k.a BCGs (brightest cluster
galaxies), is key to our understanding of active galactic nucleus feedback, and
of the impact of environmental and local effects on star formation. We
investigate the contribution of the thermal radiation from the cooling flow
surrounding BCGs to the excitation of the filaments. We explore the effects of
small levels of extra-heating (turbulence), and of metallicity, on the optical
and infrared lines. Using the Cloudy code, we model the photoionization and
photodissociation of a slab of gas of optical depth AV{\leq}30mag at constant
pressure, in order to calculate self-consistently all of the gas phases, from
ionized gas to molecular gas. The ionizing source is the EUV and soft X-ray
radiation emitted by the cooling gas. We test these models comparing their
predictions to the rich multi-wavelength observations, from optical to
submillimeter. These models reproduce most of the multi-wavelength spectra
observed in the nebulae surrounding the BCGs, not only the LINER-like optical
diagnostics: [O iii]{\lambda} 5007 {\AA}/H\b{eta}, [N ii]{\lambda} 6583
{\AA}/H{\alpha} and ([S ii]{\lambda} 6716 {\AA}+[S ii]{\lambda} 6731
{\AA})/H{\alpha} but also the infrared emission lines from the atomic gas. The
modeled ro-vib H2 lines also match observations, which indicates that near and
mid-IR H2 lines are mostly excited by collisions between H2 molecules and
secondary electrons produced naturally inside the cloud by the interaction
between the X-rays and the cold gas in the filament. However, there is still
some tension between ionized and molecular line tracers (i.e. CO), which
requires to optimize the cloud structure and the density of the molecular zone.
