Testing the completeness of the SDSS colour selection for ultramassive, slowly spinning black holes

We investigate the sensitivity of the colour-based quasar selection algorithm of the Sloan Digital Sky Survey (SDSS) to several key physical parameters of supermassive black holes (SMBHs), focusing on BH spin (a(*)) at the high BH-mass regime (M-BH >= 10(9) M-circle dot). We use a large grid of model spectral energy distribution (SED), assuming geometrically thin, optically thick accretion discs, and spanning a wide range of five physical parameters: BH mass M-BH, BH spin a(*), Eddington ratio L/L-Edd, redshift z, and inclination angle inc. Based on the expected fluxes in the SDSS imaging ugriz bands, we find that similar to 99.8 per cent of our models with M-BH <= 10(9.5) M-circle dot are selected as quasar candidates and thus would have been targeted for spectroscopic follow-up. However, in the extremely high-mass regime, >= 10(10) M-circle dot, we identify a bias against slowly/retrograde spinning SMBHs. The fraction of SEDs that would have been selected as quasar candidates drops below similar to 50 per cent for a(*) < 0 across 0.5 < z < 2. For particularly massive BHs, with M-BH similar or equal to 3 x 10(10) M-circle dot, this rate drops below similar to 20 per cent, and can be yet lower for specific redshifts. We further find that the chances of identifying any hypothetical sources with M-BH = 10(11) M-circle dot by colour selection would be extremely low at the level of similar to 3 per cent. Our findings, along with several recent theoretical arguments and empirical findings, demonstrate that the current understanding of the SMBH population at the high M-BH, and particularly the low-or retrograde-spinning regime, is highly incomplete.