Cosmic-rays, gas, and dust in nearby anticentre clouds: II. Interstellar phase transitions and the dark neutral medium

Aims. H I 21-cm and (CO)-C-12 2.6-mm line emissions trace the atomic and molecular gas phases, respectively, but they miss most of the opaque H I and diffuse H-2 present in the dark neutral medium (DNM) at the transition between the H I-bright and CO-bright regions. Jointly probing H I, CO, and DNM gas, we aim to constrain the threshold of the H I-H-2 transition in visual extinction, AV, and in total hydrogen column densities, N-H(tot). We also aim to measure gas mass fractions in the different phases and to test their relation to cloud properties. Methods. We have used dust optical depth measurements at 353 GHz, gamma-ray maps at GeV energies, and H I and CO line data to trace the gas column densities and map the DNM in nearby clouds toward the Galactic anticentre and Chamaeleon regions. We have selected a subset of 15 individual clouds, from di ff use to star-forming structures, in order to study the different phases across each cloud and to probe changes from cloud to cloud. Results. The atomic fraction of the total hydrogen column density is observed to decrease in the (0.6-1) x 10(21) cm(2) range in N-H(tot) (A(V) approximate to 0.4 mag) because of the formation of H-2 molecules. The onset of detectable CO intensities varies by only a factor of 4 from cloud to cloud, between 0.6 x 10(21) cm(-2) and 2.5 x 10(21) cm(-2) in total gas column density. We observe larger H-2 column densities than linearly inferred from the CO intensities at AV > 3 mag because of the large CO optical thickness; the additional H-2 mass in this regime represents on average 20% of the CO-inferred molecular mass. In the DNM envelopes, we find that the fraction of di ff use CO-dark H-2 in the molecular column densities decreases with Increasing AV in a cloud. For a half molecular DNM, the fraction decreases from more than 80% at 0.4 mag to less than 20% beyond 2 mag. In mass, the DNM fraction varies with the cloud properties. Clouds with low peak CO intensities exhibit large CO-dark H-2 fractions in molecular mass, in particular the di ff use clouds lying at high altitude above the Galactic plane. The mass present in the DNM envelopes appears to scale with the molecular mass seen in CO as M-H(DNM) = (62 +/- 7)M-H2(CO) (0.51 +/- 0.02) across two decades in mass. Conclusions. The phase transitions in these clouds show both common trends and environmental di ff erences. These findings will help support the theoretical modelling of H-2 formation and the precise tracing of H-2 in the interstellar medium.