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 to several key physical parameters of supermassive black holes (SMBHs), focusing on BH spin ($a_{\star}$) at the high BH-mass regime ($M_{BH} \geqslant10^9\, M_{\odot}$). We use a large grid of model spectral energy distribution, assuming geometrically-thin, optically-thick accretion discs, and spanning a wide range of five physical parameters: BH mass $M_{BH}$, BH spin $a_{\star}$, 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 $\sim 99.8\%$ of our models with $M_{BH} \leqslant 10^{9.5}\, M_{\odot}$ are selected as quasar candidates and thus would have been targeted for spectroscopic follow-up. However, in the extremely high-mass regime, $\geqslant 10^{10} M_{\odot}$, we identify a bias against slowly/retrograde spinning SMBHs. The fraction of SEDs that would have been selected as quasar candidates drops below $\sim50\%$ for $a_{\star} <0$ across $0.5<z<2$. For particularly massive BHs, with $M_{BH} \simeq 3\times10^{10}\, M_{\odot}$, this rate drops below $\sim20\%$, and can be yet lower for specific redshifts. We further find that the chances of identifying any hypothetical sources with $M_{BH} = 10^{11}\, M_{\odot}$ by colour selection would be extremely low at the level of $\sim 3\%$. 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.