We present synthetic Hi and CO observations of a simulation of decaying turbulence in the thermally bistable neutral medium. We first present the simulation, with clouds initially consisting of clustered clumps. Self-gravity causes these clump clusters to form more homogeneous dense clouds. We apply a simple radiative transfer algorithm, and defining every cell with <Av> > 1 as molecular. We then produce maps of Hi, CO-free molecular gas, and CO, and investigate the following aspects: i) The spatial distribution of the warm, cold, and molecular gas, finding the well-known layered structure, with molecular gas surrounded by cold Hi, surrounded by warm Hi. ii) The velocity of the various components, with atomic gas generally flowing towards the molecular gas, and that this motion is reflected in the frequently observed bimodal shape of the Hi profiles. This conclusion is tentative, because we do not include feedback. iii) The production of Hi self-absorption (HISA) profiles, and the correlation of HISA with molecular gas. We test the suggestion of using the second derivative of the brightness temperature Hi profile to trace HISA and molecular gas, finding limitations. On a scale of ~parsecs, some agreement is obtained between this technique and actual HISA, as well as a correlation between HISA and N(mol). It quickly deteriorates towards sub-parsec scales. iv) The N-PDFs of the actual Hi gas and those recovered from the Hi line profiles, with the latter having a cutoff at column densities where the gas becomes optically thick, thus missing the contribution from the HISA-producing gas. We find that the power-law tail typical of gravitational contraction is only observed in the molecular gas, and that, before the power-law tail develops in the total gas density PDF, no CO is yet present, reinforcing the notion that gravitational contraction is needed to produce this component. (abridged)
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