Spectral properties of a CRS assuming HD correlation. The left panel shows the free spectrum, the independent measurement of common power at each frequency bin, for the two versions of the EPTA-only data set. The right panel shows the 1σ, 2σ, and 3σ contours of the 2D posterior distribution of amplitude and spectral index, when modelling the spectrum with a power law. In both panels, results for DR2full are in blue, while those of DR2new are in orange. The solid lines in the left panel are the power law best-fits to the GWB (see main text for the parameters of the fit), while the vertical dashed line indicates the position of f = 1 yr⁻¹. The vertical dashed line in the right panel denotes γ = 13/3.