A Standard Ultraviolet Continuum Can Hide Supercritical Accretion in GN-z11

RESUMO

The ultraviolet continuum from a high-redshift accreting black hole is routinely used to infer its mass. GN-z11 offers a sharp test of whether that inference is secure. A thin-disk fit to its continuum gives an Eddington mass of $M_{\rm E}=1.12\times10^{7}\,\Msun$, an order of magnitude above the $\log(\Mbh/\Msun)=6.2\pm0.3$ inferred from broad N~\textsc{iv}. We show that this apparent tension is not imposed by the ultraviolet slope alone. We derive a closed-form criterion comparing the radius where observed photons are produced with the radius where a supercritical flow departs from efficient solution. For GN-z11, the criterion places the supercritical transition inside the ultraviolet-emitting region. Composite disks retaining the outer solution confirm this numerically, requiring $\Mdot_{\rm out}=3.1$--$4.4\,\Msun\,\mathrm{yr^{-1}}$ and placing $\Rsph=(1.2$--$1.8)\times10^{3}\,\rg$ inside $\Ruv=(2.6$--$2.9)\times10^{3}\,\rg$. Replacing the inner $\sim10^{3}\rg$ by a supercritical flow shifts the fitted slope by only $\Delta\betaUV=+0.08$ to $+0.11$, comparable to uncertainties from standard spectral modelling. Reversing the radial ordering requires the effective transition to move outward by a factor $1.7$--$2.1$. Within our composite models, the measured slope constrains black-hole mass only to around $10^{6}\,\Msun$, an order of magnitude below the continuum Eddington mass. Continuum Eddington masses should therefore be treated as model-dependent bounds that assume global thin-disk efficiency. The same hierarchy appears in three additional JWST sources under the disk-dominated interpretation, where separation masses are only $4$--$6$\% of continuum Eddington masses. This distinction can substantially weaken the seed-mass and early-growth demands inferred from ultraviolet continua at cosmic dawn for the first massive black holes.