Comparison between luminosity density–projected proper length relations for observed and simulated giants. Each dash-dotted curve denotes a family of giants at a given redshift, assuming f_Lν = 0.3 and f_l = 0.3, whose mean lobe surface brightnesses equal the LoTSS DR2 noise level and who are thus borderline-detectable. The grey band denotes the median-centred luminosity density range that contains 68% of giants. Top: 139 LoTSS DR1 giants (Dabhade et al. 2020b), alongside Alcyoneus, with redshift z_Alc. = 0.25 (Oei et al. 2022a). The solid green curve is similar to the dash-dotted green curve, but represents maximum instead of mean lobe surface brightness. Middle: 1000 simulated giants, assuming b_ν, ref = 1750 Jy deg⁻² and σ_ref = 1.3. Bottom: 1000 simulated giants, assuming b_ν, ref = 250 Jy deg⁻² and σ_ref = 1.3.