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 Hβ 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 areṀ 200, wherė M =Ṁ • /L Edd c −2 ,Ṁ • is the mass accretion rates, L Edd is the Eddington luminosity and c is the speed of light. We find that the Hβ 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 Hβ ) and optical luminosity at 5100Å, R Hβ − 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 Hβ 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 ofṀ c = 6 ∼ 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 -2for 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.

As one of the series of papers reporting on a large reverberation mapping campaign of super-Eddington accreting massive black holes (SEAMBHs) in active galactic nuclei (AGNs), we present the results of 10 SEAMBHs monitored spectroscopically during 2015-2017. Six of them are observed for the first time, and have generally higher 5100Å luminosities than the SEAMBHs monitored in our campaign from 2012 to 2015; the remaining four are repeat observations to check if their previous lags change. Similar to the previous SEAMBHs, the Hβ time lags of the newly observed objects are shorter than the values predicted by the canonical R Hβ -L 5100 relation of sub-Eddington AGNs, by factors of ∼ 2 − 6, depending on the accretion rate. The four previously observed objects have lags consistent with previous measurements. We provide linear regressions for the R Hβ -L 5100 relation, solely for the SEAMBH sample and for low-accretion AGNs. We find that the relative strength of Fe II and the profile of the Hβ emission line can be used as proxies of accretion rate, showing that the shortening of Hβ lags depends on accretion rates. The recent SDSS-RM discovery of shortened Hβ lags in AGNs with low accretion rates provides compelling evidence for retrograde accretion onto the black hole. These evidences show that the canonical R Hβ -L 5100 relation holds only in AGNs with moderate accretion rates. At low accretion rates, it should be revised to include the effects of black hole spin, whereas the accretion rate itself becomes a key factor in the regime of high accretion rates.

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 (t b H ) 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 Hβ -L 5100 relation. The five quasars have dimensionless accretion rates of Ṁ = 10-10 3 . Combining these with measurements of the previous SEAMBHs, we find that the reduction of Hβ lags depends tightly on accretion rates,, where t -R L is the Hβ lag from the normal R Hβ -L 5100 relation. Fitting 63 mapped AGNs, we present a new scaling relation for the broad-line region: . Implications of this new relation are briefly discussed.