The nature of the interstellar medium of the starburst low-metallicity
  galaxy Haro11: a multi-phase model of the infrared emission
  (abridged) Our goal is to describe the multi-phase ISM of the IR bright
low-metallicity galaxy Haro 11, dissecting the photoionised and
photodissociated gas components. We present observations of the mid- and far-IR
fine-structure cooling lines obtained with the Spitzer/IRS and Herschel/PACS
spectrometers. We use the spectral synthesis code Cloudy to methodically model
the ionised and neutral gas from which these lines originate. We find that the
mid- and far-IR lines account for ~1% of the total IR luminosity L_TIR. Haro 11
is undergoing a phase of intense star formation, as traced by the brightest
line [OIII] 88um, with L_[OIII]/L_TIR ~0.3%, and high ratios of [NeIII]/[NeII]
and [SIV]/[SIII]. Due to their different origins, the observed lines require a
multi-phase modeling comprising: a compact HII region, dense fragmented
photodissociation regions (PDRs), a diffuse extended low-ionisation/neutral gas
which has a volume filling factor of at least 90%, and porous warm dust in
proximity to the stellar source. For a more realistic picture of the ISM of
Haro 11 we would need to model the clumpy source and gas structures. We combine
these 4 model components to explain the emission of 17 spectral lines,
investigate the global energy balance of the galaxy through its spectral energy
distribution, and establish a phase mass inventory. While the ionic emission
lines of Haro 11 essentially originate from the dense HII region component, a
diffuse low-ionisation gas is needed to explain the [NeII], [NII], and [CII]
line intensities. The [OIII] 88um line intensity is not fully reproduced by our
model, hinting towards the possible presence of yet another low-density
high-ionisation medium. The [OI] emission is consistent with a dense PDR of low
covering factor, and we find no evidence for an X-ray dominated component. The
PDR component accounts for only 10% of the [CII] emission.
