Supermassive black holes with high accretion rates in active galactic nuclei. V. A new size-luminosity scaling relation for the broad-line region

This paper reports results of the third-year campaign of monitoring super-Eddington accreting massive black holes (SEAMBHs) in active galactic nuclei (AGNs) between 2014 and 2015. Ten new targets were selected from the quasar sample of the Sloan Digital Sky Survey (SDSS), which have generally been more luminous than the SEAMBH candidates in the last two years. Hβ lags (${\tau }_{H\beta }$) in five of the 10 quasars have been successfully measured in this monitoring season. We find that the lags are generally shorter, by large factors, than those of objects with same optical luminosity, in light of the well-known R _{H β}–L ₅₁₀₀ relation. The five quasars have dimensionless accretion rates of $\dot{M}=10$–10³. Combining these with measurements of the previous SEAMBHs, we find that the reduction of Hβ lags depends tightly on accretion rates, ${\tau }_{H\beta }/{\tau }_{R-L}\propto {\dot{M}}^{-0.42}$, where ${\tau }_{R-L}$ is the Hβ lag from the normal R _{H β}–L ₅₁₀₀ relation. Fitting 63 mapped AGNs, we present a new scaling relation for the broad-line region: $R_{H\beta }={\alpha }_1{\ell }_{44}^{{\beta }_1}min$ $[1,{\left(\dot{M}/{\dot{M}}_c\right)}^{-{\gamma }_1}]$, where ${\ell }_{44}=L_{5100}/{10}^{44}erg{s}^{-1}$ is the 5100 Å continuum luminosity, and the coefficients are ${\alpha }_1={29.6}_{-2.8}^{+2.7}$ lt-day, ${\beta }_1={0.56}_{-0.03}^{+0.03}$, ${\gamma }_1={0.52}_{-0.16}^{+0.33}$, and ${\dot{M}}_c={11.19}_{-6.22}^{+2.29}$. This relation is applicable to AGNs over a wide range of accretion rates, from 10⁻³ to 10³. Implications of this new relation are briefly discussed.