Comparison of hydrogen number density profiles n_H(r) within DM halos of different masses (M_h = 10⁴ M_⊙, 10⁶ M_⊙, and 10⁸ M_⊙) at redshifts z = 6 (solid lines), z = 10 (dashed-dotted lines), and z = 40 (dotted lines). The three density profiles examined include a simple isothermal profile (magenta), the profile derived by Makino et al. (1998) (blue), and the rescaled profile from Liu et al. (2022) (green). The vertical grey lines denote the virial radii of the corresponding halos at each redshift.