Contribution of accreting high-z BH sources to the present-day (z = 0) soft X-ray background (0.5–2 keV). The top row shows the cumulative evolution of the integrated background intensity, J_X, as a function of redshift z, for PBH masses of M_PBH = 1 M_⊙, 10 M_⊙, 33 M_⊙, and 100 M_⊙ in each column. Different values of f_PBH are represented by distinct colours, as indicated in the legend, ranging from 10⁻⁴ to 1. The grey shaded region corresponds to the observed excess X-ray background reported in Cappelluti et al. (2017). Three halo density profiles are considered: simple isothermal (dashed lines), the profile from Makino et al. (1998) (dashed-dotted lines), and the profile from Liu et al. (2022) (dotted lines). The bottom row illustrates the relative contributions of halos ($J_{\mathrm{X}}^{\mathrm{h}}$) and the IGM ($J_{\mathrm{X}}^{\mathrm{IGM}}$) to the total X-ray background intensity ($J_{\mathrm{X}}^{\mathrm{tot}}$). These are represented as $J_{\mathrm{X}}^{\mathrm{h}}/J_{\mathrm{X}}^{\mathrm{tot}}$ (dashed-dotted lines) and $J_{\mathrm{X}}^{\mathrm{IGM}}/J_{\mathrm{X}}^{\mathrm{tot}}$ (solid lines), respectively. The relative contributions are computed using the same PBH masses and density profile configurations as in the top row.