The far-infrared (FIR) lines are key tracers of the physical conditions of the interstellar medium (ISM) and are becoming workhorse diagnostics for galaxies throughout the universe. Our goal is to explain the differences and trends observed in the FIR line emission of dwarf galaxies compared to more metal-rich galaxies. We present Herschel PACS spectroscopic observations of the CII157um, OI63 and 145um, OIII88um, NII122 and 205um, and NIII57um fine-structure cooling lines in a sample of 48 low-metallicity star-forming galaxies of the guaranteed time key program Dwarf Galaxy Survey. We correlate PACS line ratios and line-to-LTIR ratios with LTIR, LTIR/LB, metallicity, and FIR color, and interpret the observed trends in terms of ISM conditions and phase filling factors with Cloudy radiative transfer models. We find that the FIR lines together account for up to 3 percent of LTIR and that star-forming regions dominate the overall emission in dwarf galaxies. Compared to metal-rich galaxies, the ratios of OIII/NII122 and NIII/NII122 are high, indicative of hard radiation fields. In the photodissociation region (PDR), the CII/OI63 ratio is slightly higher than in metal-rich galaxies, with a small increase with metallicity, and the OI145/OI63 ratio is generally lower than 0.1, demonstrating that optical depth effects should be small on the scales probed. The OIII/OI63 ratio can be used as an indicator of the ionized gas/PDR filling factor, and is found ~4 times higher in the dwarfs than in metal-rich galaxies. The high CII/LTIR, OI/LTIR, and OIII/LTIR ratios, which decrease with increasing LTIR and LTIR/LB, are interpreted as a combination of moderate FUV fields and low PDR covering factor. Harboring compact phases of low filling factor and a large volume filling factor of diffuse gas, the ISM of low-metallicity dwarf galaxies has a more porous structure than that in metal-rich galaxies.
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