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Hyper-massive Black Holes have Faint Broad and Narrow Emission Lines

The EUV provides most of the ionization that creates the high equivalent width (EW) broad and narrow emission lines (BELs, NELs) of quasars. Spectra of Hypermassive Schwarzschild black holes (HMBHs, $M_{BH} \geq 10^{10} M_{\odot}$) with $α$-discs, decline rapidly in the EUV suggesting much lower EWs. Model spectra for black holes of mass $10^{6}-10^{12} M_{\odot}$ and accretion rates $0.03 \leq L_{bol}/L_{edd} \leq 1.0$ were input to the CLOUDY photoionization code. BELs become $\sim$100 times weaker in EW from $M_{BH} \sim 10^8 M_{\odot}$ to $M_{BH} \sim 10^{10} M_{\odot}$. The high ionization BELs (O VI 1034 $\overset{\circ}{\mathrm {A}}$, C IV 1549 $\overset{\circ}{\mathrm {A}}$, He II 1640 $\overset{\circ}{\mathrm {A}}$) decline in EW from ($M_{BH} \geq 10^6 M_{\odot}$, reproducing the Baldwin effect, but regain EW for $M_{BH} \geq 10^{10} M_{\odot}$). The low ionization lines (MgII 2798 $\overset{\circ}{\mathrm {A}}$, H$β$ 4861 $\overset{\circ}{\mathrm {A}}$ and H$α$ 6563 $\overset{\circ}{\mathrm {A}}$) remain weak. Lines for maximally spinning HMBHs behave similarly. Line ratio diagrams for the BELs show that high OVI/H$β$ and low CIV/H$α$ may pick out HMBH, although OVI is often hard to observe. In NEL BPT diagrams HMBHs lie among star-forming regions, except for highly spinning, high accretion rate HMBHs. In summary, the BELs expected from HMBHs would be hard to detect using the current optical facilities. From 100 to $10^{12} M_{\odot}$, the emission lines used to detect AGN only have high EW in the $10^6 - 10^9 M_{\odot}$ window, where most AGN are found. This selection effect may be distorting reported distributions of $M_{BH}$.