Gas density PDFs at the onset of sink particle formation (top panel) and 4 Myr later (bottom panel). We show PDFs from the 10⁻² (red lines), 10⁻³ (green lines) and 10⁻⁴ Z_⊙ (blue lines) runs. We separately plot PDFs computed using all gas within the virial radius of the halo (dashed lines) and only gas with T < 200 K and n > 100 cm⁻³ (solid lines). For the all gas PDFs, the average density is n₀ ≈ 1 cm⁻³ at both times. In the bottom panel, we show lognormal fits to the 10⁻² and 10⁻³ Z_⊙ run cold gas PDFs which have widths of σ = 0.86 and 0.71, respectively. Power-law tails, evident in the top panel and in the 10⁻⁴ Z_⊙ run in the bottom panel, are an anticipated outcome of self-gravity. In the 10⁻³ Z_⊙ run, however, this power-law tail disappears within ∼2 Myr after the first sink particle formation as the sink particles deplete the cold, dense gas.