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 = 109M_⊙). 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~99.8 per cent of our models with M_BH ≤ 10^9.5M_⊙ are selected as quasar candidates and thus would have been targeted for spectroscopic follow-up. However, in the extremely high-mass regime,≥10¹⁰M_⊙, we identify a bias against slowly/retrograde spinning SMBHs. The fraction of SEDs that would have been selected as quasar candidates drops below ~50 per cent for a* < 0 across 0.5 < z < 2. For particularly massive BHs, with M_BH ≃ 3 × 10¹⁰M_⊙, this rate drops below ~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 = 10¹¹M_⊙ by colour selection would be extremely low at the level of ~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.