Projected detection probability averaged over the ATHENA FoV, which is a weighted probability from on-axis to the edge of the detector as described in Sect. 3.2.3. The dashed blue horizontal line represents the projected detection probability at 0.8. Panel 1: baseline model with exposure times of 50 ks, 80 ks, and 130 ks. Panel 2: baseline model for different masses. Panel 3: assuming different surface brightness profile: r_c = 30%×r₅₀₀ and r_c = 45%×r₅₀₀. Panel 4: assuming there is no AGN in the center of galaxy groups, and assuming 40% flux of the groups to the central AGN. Panel 5: modified scaling relations of mass 10¹³ M_⊙. Panel 6: modified scaling relations of mass 5 × 10¹³ M_⊙. Panel 7: modified scaling relations of mass 10¹⁴ M_⊙. Panel 8: different ATHENA configurations used: without applying optical filter and with 19 mirror rows. The modified scaling relations are based on Reichert et al. (2011) and Truong et al. (2018).