Evolution of halos across snapshots. Top: sample of halos hosting clump at z = 18.8, left: halo virial mass vs redshift, right: halo H₂ abundance vs mass average gas temperature. The boundary between the solid line and dashed line corresponds to the snapshot at which a halo first host a cold gas clump. Bottom: same plot for a sample of halos that do not host cold gas clump. The gray rectangle shows the interval in the crirical value of M_vir and x_H2 identified in Sect. 3.4.