Left panel: expected integral number (all-sky) of radio halos as a function of redshift in EMU+WODAN. Right panel: expected number of RH (all-sky) in redshift intervals in EMU+WODAN. The reference set of model parameters (b = 1.5, B _⟨ M ⟩  = 1.9   μG,  ⟨ M ⟩   =  1.6  ×  10¹⁵   M_⊙ and η_t = 0.2) is assumed. In both panels black lines show the total number of halos (“turbulent”+“off-state” halos, solid) and of “turbulent” halos (dashed) obtained by considering Eq. (9) with ξ₁ = 3 to derive f_min(z); while red upper lines show the total number of halos (“turbulent”+“off-state” halos) obtained by adopting Eq. (11) with ξ₂ = 10. Points show the integral number of radio halos observed so far.