We have completed two years of photometric and spectroscopic monitoring of a large number of active galactic nuclei (AGNs) with very high accretion rates. In this paper, we report on the result of the second phase of the campaign, during 2013--2014, and the measurements of five new H$\beta$ time lags out of eight monitored AGNs. All five objects were identified as super-Eddington accreting massive black holes (SEAMBHs). The highest measured accretion rates for the objects in this campaign are $\dot{ \mathscr{ M}}\gtrsim 200$, where $\dot{ \mathscr{ M}}= \dot{ M}_{ \bullet}/L_{ \rm Edd}c^{ -2}$, $\dot{ M}_{ \bullet}$ is the mass accretion rates, $L_{ \rm Edd}$ is the Eddington luminosity and $c$ is the speed of light. We find that the H$\beta$ time lags in SEAMBHs are significantly shorter than those measured in sub-Eddington AGNs, and the deviations increase with increasing accretion rates. Thus, the relationship between broad-line region size ($R_{ _{ \rm H\beta}}$) and optical luminosity at 5100\AA, $R_{ _{ \rm H\beta}}-L_{ 5100}$, requires accretion rate as an additional parameter. We propose that much of the effect may be due to the strong anisotropy of the emitted slim-disk radiation. Scaling $R_{ _{ \rm H\beta}}$ by the gravitational radius of the black hole, we define a new radius-mass parameter ($Y$) and show that it saturates at a critical accretion rate of $\dot{ \mathscr{ M}}_c=6\sim 30$, indicating a transition from thin to slim accretion disk and a saturated luminosity of the slim disks. The parameter $Y$ is a very useful probe for understanding the various types of accretion onto massive black holes. We briefly comment on implications to the general population of super-Eddington AGNs in the universe and applications to cosmology.
Categories: astro-ph.GA astro-ph.CO astro-ph.HE