VALES: II. The physical conditions of interstellar gas in normal star-forming galaxies up to z=0.2 revealed by ALMA

We use new Band-3 CO(1-0) observations taken with the Atacama Large Millimeter/submillimeter Array (ALMA) to study the physical conditions in the interstellar gas of a sample of 27 dusty main-sequence star-forming galaxies at 0.03<$z$<0.2 present in the Valpara\'iso ALMA Line Emission Survey (VALES). The sample is drawn from far-IR bright galaxies over $\sim$160 deg$^{2}$ in the Herschel Astrophysical Terahertz Large Area Survey (HATLAS), which is covered by Herschel [CII] 158 $\mu$m spectroscopy and far-infrared (FIR) photometry. The [CII] and CO lines are both detected at >5$\sigma$ in 26 sources. We find an average [CII] to CO(1-0) luminosity ratio of 3500$\pm$1200 for our sample that is consistent with previous studies. Using the [CII], CO and FIR measurements as diagnostics of the physical conditions of the interstellar medium, we compare these observations to the predictions of a photodissociation region (PDR) model to determine the gas density, surface temperature, pressure, and the strength of the incident far-ultraviolet (FUV) radiation field, $G_{0}$, normalised to the Habing Field. The majority of our sample exhibit hydrogen densities of 4 < $\log n/\mathrm{cm}^{3}$ < 5.5 and experience an incident FUV radiation field with strengths of 2 < $\log G_0$ < 3 when adopting standard adjustments. A comparison to galaxy samples at different redshifts indicates that the average strength of the FUV radiation field appears constant up to redshift $z\sim$6.4, yet the neutral gas density increases with redshift by a factor of $\sim$100, that persists regardless of various adjustments to our observable quantities. This evolution could provide an explanation for the observed evolution of the star formation rate density with cosmic time, yet could arise from a combination of observational biases when using different suites of emission lines as diagnostic tracers of PDR gas.