Supermassive Black Holes with High Accretion Rates in Active Galactic Nuclei. IX. 10 New Observations of Reverberation Mapping and Shortened Hβ Lags

Similar to SEAMBH2013–2014 (Papers IV and V), we selected SEAMBH candidates based on the dimensionless accretion rate estimator derived from the standard thin accretion disk model (Shakura & Sunyaev 1973). From the standard disk model, the dimensionless accretion rate is given by (see more details in Paper II and Appendix A in Paper V)

$$\begin{eqnarray}&&\mathop{{\mathscr{M}}}\limits^{\,.}=20.1{\left(\displaystyle \frac{{{\ell }}_{44}}{\cos i}\right)}^{3/2}{m}_{7}^{-2},\end{eqnarray} \tag{ 4 }$$

where m₇ = M_•/10⁷ M_⊙ and i is the inclination angle of the disk to the line of sight. We took $\cos i=0.75$ (see some discussions in Paper V), which is an average estimate for type I AGNs (e.g., Fischer et al. 2014; Pancoast et al. 2014). For BH masses, we adopted the virial factor f_BLR = 1 in our series of papers (see more discussions in Section 3.5 and in Paper IV).

In SEAMBH2013–2014, we fitted the spectra of all the quasars in Data Release 7 of the Sloan Digital Sky Survey (SDSS) using the fitting procedure in Hu et al. (2008a, 2008b), then estimated their BH masses and accretion rates by applying the normal R_Hβ–L₅₁₀₀ relation in Bentz et al. (2013). However, high-$\mathop{{\mathscr{M}}}\limits^{\,.}$ objects tend to have shortened Hβ time lags (Papers IV and V), which means the normal R_Hβ–L₅₁₀₀ relation may underestimate their accretion rates. Du et al. (2016c) discovered a bivariate correlation between $\mathop{{\mathscr{M}}}\limits^{\,.}$ and the profile of broad Hβ line (${{ \mathcal D }}_{{\rm{H}}\beta }=\mathrm{FWHM}/{\sigma }_{{\rm{H}}\beta }$), and the flux ratio of optical Fe ii to Hβ (${{ \mathcal R }}_{\mathrm{Fe}}$). This correlation provides a straightforward method to determine $\mathop{{\mathscr{M}}}\limits^{\,.}$ from single-epoch spectra of AGNs, and applies to a wide range of accretion rates ($\mathop{{\mathscr{M}}}\limits^{\,.}\approx {10}^{-2}\mbox{--}{10}^{3}$). We can easily estimate the accretion rates after we measure ${{ \mathcal R }}_{\mathrm{Fe}}$ and ${{ \mathcal D }}_{{\rm{H}}\beta }$ from the spectra of SDSS quasars by the multi-component fitting procedure in Hu et al. (2008a, 2008b). Therefore, instead of the accretion rates estimated from the traditional R_Hβ–L₅₁₀₀ relation and Equation (4), we adopted the $\mathop{{\mathscr{M}}}\limits^{\,.}$ estimated from ${{ \mathcal R }}_{\mathrm{Fe}}$ and ${{ \mathcal D }}_{{\rm{H}}\beta }$ to choose the targets in SEAMBH2015–2016.

After measuring $\mathop{{\mathscr{M}}}\limits^{\,.}$ for all of the SDSS quasars, we selected the objects with the highest $\mathop{{\mathscr{M}}}\limits^{\,.}$ and L₅₁₀₀ ≈ 10⁴⁴–10^45.5 erg s⁻¹. The coordinates of the targets should be appropriate for the site of the observatory. Furthermore, we constrained the redshift (z ≈ 0.2–0.4), and the SDSS r-band magnitude (r' < 17.5) in order to obtain a high enough signal-to-noise ratio (S/N). At the beginning, 10 objects were chosen as the observing targets. However, four of them were observed only in the first ∼2 months (with only a few epochs) because of poorer weather and the very limited observing time; these were rejected thereafter. The remaining six objects were observed for entirely two years. Besides the six objects with relatively high luminosities, we monitored four SEAMBHs that had been observed previously in SEAMBH2013–2014. The uncertainties of their Hβ lag measurements were larger than those of the other objects in SEAMBH2013–2014 because their light curves were shorter or the scatter of the points in the light curves was relatively larger. We observed them again in 2015–2017, in order to check their former measurements. In total, the 10 objects listed in Table 1 constitute the sample in the present paper.

The photometric and spectroscopic data used in this work were taken with the Lijiang 2.4 m telescope at the Yunnan Observatories of the Chinese Academy of Sciences. The telescope is equipped with the Yunnan Faint Object Spectrograph and Camera, which is a multi-functional instrument available both for photometry and spectroscopy. The images were taken using the SDSS r' filter. For spectroscopy, we used Grism 3, which has a sampling of 2.9 Å pixel⁻¹ (∼108 km s⁻¹ pixel⁻¹) and a wavelength coverage of 3800–9000 Å. To minimize the influence from atmospheric differential refraction, we employed a longslit with a width of 5''. For each object, we oriented the slit to simultaneously observe a nearby comparison star⁹ (listed in Table 1) as a calibration standard. This method provides highly accurate flux calibration (see Papers I–V).

Both the photometric and spectroscopic data were reduced with IRAF v2.16. The photometric light curves of the targets and the comparison stars were generated by differential photometry using several (5–8) other stars in the same fields. The radius of the aperture used for photometry is typically 4'', and the annulus for background determination is 85–17''. The comparison stars themselves are very stable given the photometric light curves shown in Figure 6 in Appendix A, and thus they can be used as standards for the spectral calibration.

The spectra were extracted using a uniform aperture of 85 and a background region of 74–14'' on both sides of the aperture. The fiducial spectra of the comparison stars were produced using data from nights with photometric conditions. The fluxes of the target spectra were calibrated by the comparison stars in the slit. More details for the photometry and spectroscopy can be found in Papers IV and V.

The [O iii]-based calibration approach (van Groningen & Wanders 1992; Fausnaugh 2017) is widely used in many RM works (e.g., Peterson et al. 1998; Bentz et al. 2009; Grier et al. 2012; Fausnaugh et al. 2017), but it does not apply to the SEAMBHs (Papers I, IV, and V). The [O iii] λ5007 emission lines in SEAMBHs are too weak to be used as a standard for flux calibration (see the mean spectra in Papers IV and V). Even worse, the Fe ii contribution beneath the [O iii] line, which is shown to also reverberate (Barth et al. 2013, Paper III), is relatively strong. Thus, the [O iii]-based calibration approach (van Groningen & Wanders 1992; Fausnaugh 2017) may give rise to large uncertainties in the flux calibration of the SEAMBHs in this paper. It has been demonstrated that the method based on the comparison star can provide accurate flux calibration: for the SEAMBHs with moderate [O iii] (in Paper I), the variation of the [O iii] fluxes in the calibrated spectra (by the comparison stars) is ∼3% (Paper I); for low-accretion rate AGNs (e.g., NGC 5548), the [O iii] fluctuation after the calibration is at a level of 2% (Lu et al. 2016). Therefore, we adopt the calibration approach based on comparison star as in Papers I–V. In Appendix B, as an example, we show that the scatter of [O iii] fluxes in the calibrated spectra of SDSS J075101 is ≲3%, which can be regarded as an estimate for the calibration precision in this paper.

After the data reduction and calibration, we can measure their continuum and Hβ light curves from the calibrated spectra. The light curves can be obtained by two different approaches: (1) the direct integration method and (2) the spectral decomposition method. The first approach, widely used in most RM studies (e.g., Peterson et al. 1998; Kaspi et al. 2000; Bentz et al. 2009; Grier et al. 2012; Fausnaugh et al. 2017, Papers I, IV, and V), simply integrates the flux in the Hβ band after subtracting the continuum determined by two nearby line-free windows. It applies to strong and isolated emission lines (e.g., Hβ) and works well both for the spectra with good or poor S/Ns. The second one measures the emission-line fluxes by multi-component spectral fitting, and has been gradually adopted in recent years (e.g., Barth et al. 2013, 2015, Paper III, and Lu et al. 2016). It can deblend and measure the fluxes of Fe ii or He ii lines, but has higher demand for the S/N of the spectra. The spectral decomposition approach can remove the contamination from Fe ii in the Hβ flux measurements. However, given the better robustness of the integration method for spectra with moderate S/Ns, we adopt the direct integration approach, as a first step, to measure the continuum and Hβ light curves in this paper. It should be noted that the two approaches do not give very different Hβ lag measurements for the AGNs with high accretion rates (see Figure 6 in Paper III). We will measure their Fe ii light curves using the spectral decomposition method in a separate paper in the future.

We choose the continuum and the Hβ windows that can avoid the contamination from the other emission lines (e.g., [O iii]λ4959, Fe ii, and He ii) as much as possible for each object (listed in Table 2). The continuum fluxes are set as the median values in the windows around 5100 Å in the rest frame. To measure the line light curves, we integrate the fluxes in the windows of Hβ after subtracting the background beneath, which is determined by interpolating two nearby bands (blue and red continuum windows, see also in Figure 8 in Appendix C). The uncertainties in the light curves consist of two components: statistical noises originated from the Poisson process of photons and systematic uncertainties caused by poor weather conditions, bright moon, telescope tracking inaccuracies, slit positioning, etc. The Poisson noises are demonstrated as the error bars of the points in the light curves (see Figure 1). The systematic uncertainties are estimated by the median filter method (see more details in Paper I), and are marked as gray error bars in the lower-left corners (for the light curves taken in 2015 October–2016 June) and lower-right corners (for the light curves taken in 2016 October–2017 June)¹⁰ of panels (b) and (c) in Figure 1. Both the two components of the uncertainties are taken into account in the analysis of the following sections. The photometric light curves of the targets, the continuum light curves at 5100 Å and Hβ light curves are provided in Table 3 and shown in Figure 1. We plot the photometric light curves to verify the calibration precision of the spectra. It is obvious that the calibration based on the comparison stars works fine, because the r'-band light curves are consistent with the 5100 Å light curves (Figure 1). In addition, the photometric light curves can also be used as a substitute of the continuum, if the quality of the 5100 Å light curve is not good enough (see Section 3.3).

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The interpolated cross-correlation function (ICCF; Gaskell & Sparke 1986; Gaskell & Peterson 1987) is adopted to determine the time delays of the Hβ emission lines to the variation of the continuum light curves. We use the centroid of the part higher than a threshold (80% used here) in CCF as the measurement (τ_cent) of the Hβ time lag. The uncertainties of the lags are provided by the "flux randomization/random subset sampling (FR/RSS)" method, which takes into account both the errors of the points in the light curves and the uncertainties caused by the sampling/cadence for each individual object (see more details in Peterson et al. 1998, 2004). We adopt τ_cent from the CCFs themselves instead of the median/mean values of the cross-correlation centroid distributions (CCCDs) produced by the FR/RSS method, to avoid any undiscovered bias to τ_cent introduced by this method (occasionally, it overestimates the uncertainties, e.g., Peterson et al. 1998). The CCCDs are only used to estimate the error bars. But it should be noted that, in the present sample, the τ_cent from the CCFs and the median/mean values of the CCCDs are highly consistent. Their differences are significantly smaller than the error bars (typically ≲10% of the error bars), and can be ignored.

The auto-correlation functions (ACFs), CCFs, and the distributions of the centroid time lags in the observed frame are shown in Figure 1. The time lags, their uncertainties, and the corresponding maximum correlation coefficients (r_max) are listed in Table 4. For the objects monitored for more than one year, we also measured the Hβ lags from the light curves only in 2015 October–2016 June or in 2016 October–2017 June. In some cases, the r_max measured from the light curves in a single year is significantly higher than the values calculated from all the light curves, or uncertainties of the Hβ lags are smaller because their ACFs are much narrower. We tend to use the time lags determined from the data in a single year, because the gaps in the light curves between the two years may introduce some uncertainties in the lag measurements. We discuss the light curves and the time delays for individual objects in Section 3.3. The Hβ time lags we used in the measurements of their BH masses are labeled by "√" in Table 4.

Table 4.  Time Lags

Object	Period	rmax	Observed	Rest-frame	Note
			Time Lag	Time Lag
			(days)	(days)
SDSS J074352	2015–2017	0.94	${68.6}_{-10.2}^{+4.7}$	${54.8}_{-8.1}^{+3.7}$
	2016–2017	0.79	${55.0}_{-5.2}^{+6.6}$	${43.9}_{-4.2}^{+5.2}$	√
SDSS J075051	2015–2017	0.69	${93.3}_{-13.9}^{+26.2}$	${66.6}_{-9.9}^{+18.7}$	√
SDSS J075101	2016–2017	0.96	${32.0}_{-7.6}^{+6.3}$	${28.6}_{-6.8}^{+5.6}$	√
SDSS J075949	2014–2017	0.74	${47.0}_{-12.1}^{+10.3}$	${39.5}_{-10.2}^{+8.7}$
	2015–2016	0.83	${31.3}_{-11.3}^{+13.8}$	${26.4}_{-9.5}^{+11.6}$	√
SDSS J081441	2016–2017	0.76	${31.2}_{-6.9}^{+8.4}$	${26.8}_{-5.9}^{+7.3}$	√
SDSS J083553	2015–2017	0.85	${42.6}_{-7.6}^{+7.1}$	${35.4}_{-6.3}^{+5.9}$
	2016–2017	0.86	${14.9}_{-6.6}^{+6.5}$	${12.4}_{-5.4}^{+5.4}$	√
SDSS J084533	2016–2017	0.78	${25.9}_{-5.1}^{+9.5}$	${19.9}_{-3.9}^{+7.3}$	√
SDSS J093302	2016–2017	0.66	${22.4}_{-5.0}^{+4.5}$	${19.0}_{-4.3}^{+3.8}$	√
SDSS J100402	2015–2017	0.84	${1.4}_{-19.0}^{+31.6}$	${1.0}_{-14.3}^{+23.8}$
	2016–2017	0.60	${42.8}_{-5.5}^{+57.7}$	${32.2}_{-4.2}^{+43.5}$	√
SDSS J101000	2015–2017	0.81	${48.1}_{-10.5}^{+19.0}$	${38.2}_{-8.4}^{+15.1}$
	2016–2017	0.61	${34.9}_{-9.6}^{+29.5}$	${27.7}_{-7.6}^{+23.5}$	√

Note. "√" means we use this time lag of the object to calculate its BH mass. The lag of SDSS J075051 is obtained from its photometric and Hβ light curves.

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SDSS J074352. Both the continuum and Hβ light curves show very clear dips during 2016–2017. In general, the time lag measured from the light curves in 2016–2017 is consistent with the lag measured from its entire light curves, within the uncertainties. However, the ACF generated solely from its continuum light curve in 2016–2017 is much narrower than the ACF obtained from its entire continuum light curve. Considering that the season gap between 2016 June to 2016 October may influence the Hβ lag measurement, we adopt the CCF analysis of the light curves in 2016–2017 as the final result of this object.

SDSS J075051. The quality of its photometric light curve is superior to the 5100 Å continuum light curve. The r_max of photometry versus Hβ is higher than the value (∼0.4) of 5100 Å versus Hβ. More observations are needed to improve its lag measurement in the future.

SDSS J075101. It was monitored previously in 2013 November–2014 May (Paper IV), yielding an Hβ time lag of ${33.4}_{-5.6}^{+15.6}$ days in the rest frame. The new measurement in the present paper is consistent with the previous observations, within the uncertainties, but the error bars are smaller. The peak around Julian date 550 (from the zero point of 2457300 in Figure 1, similarly hereinafter) is prominent, and its r_max is very high (0.96).

SDSS J075949. We have monitored it for three years, from 2014 to 2017. The result of the first year was published in Paper V, showing relatively large error bars in its Hβ time delay (${55.0}_{-13.1}^{+17.0}$ days in the rest frame). We also plot its old light curves in 2014–2015 in Figure 1 for comparison. The new observation in this paper gives better constraints on the Hβ lag. The light curves in 2015–2016 give a higher correlation coefficient (r_max = 0.83) than the value (r_max = 0.74) obtained from its entire light curves (including the data in 2014–2015). We thus use the CCF results from 2015–2016 in the analysis of the R_Hβ–L₅₁₀₀ relation. The new time lag is ${26.4}_{-9.5}^{+11.6}$ days in the rest frame. This is somewhat shorter than the previous value (Paper V), but considering the uncertainties, the difference is not significant.

SDSS J081441. Its light curves from 2013 November–2014 May were published in Paper IV. In the Hβ 2013–2014 light curve, there are only several points after the peak around Julian day 160 (see Figure 1 of Paper IV), because the altitude of the source was already too low to observe at the end. The new 2016–2017 light curves look more convincing, and the lag measurement is much better (with smaller error bars).

SDSS J083553. It is a little unfortunate that the primary peaks around Julian day ∼300 in the continuum and Hβ light curves are invisible. However, the small dip close to Julian day ∼450 is observed clearly. So, we adopt the CCF analysis from the 2016–2017 data to be the final result for this object. Its ACF is narrower and the r_max is a little higher than the analysis obtained from all of the light curves from 2015 to 2017.

SDSS J084533. The time lag in the present paper is consistent with the previous value from 2014 to 2015 (Paper V). Its light curves from 2016 to 2017 show two large structures, a dip around Julian day 430 and a peak around Julian day 480, yielding a very robust lag measurement.

SDSS J093302. The big dip and its response are very clear in the light curves. The lag measurement is pretty reliable.

SDSS J100402. The centroid of the peak of the CCF calculated from all of the light curves is nearly zero because of the gap between the two years and the very flat light curves in 2016–2017. Therefore, we adopt the light curves in 2015–2016 to measure the time lag. The uncertainty of its Hβ lag is the largest among all of the objects in this paper.

SDSS J101000. The scatter and the error bars of the Hβ light curve in 2016–2017 are smaller than those in 2015–2016. Thus, we select the lag measurement using the light curves in 2016–2017 as the final result. In general, the lags obtained from the light curves in 2015–2017 and in 2016–2017 are consistent with each other.

Generally, the contribution of host galaxies in the slit can be decomposed and removed from the 5100 Å luminosities of the objects by using the high-resolution image observations (e.g., from Hubble Space Telescope, HST). However, none of the objects, except SDSS J100402 (also known as PG 1001+291), have imaging observations from HST. As in Papers IV and V, we uniformly adopt the empirical relation proposed by Shen et al. (2011), to remove the host contribution in the 5100 Å luminosities. The luminosity ratio of host to AGN at 5100 Å can be expressed as ${L}_{5100}^{\mathrm{host}}/{L}_{5100}^{\mathrm{AGN}}=0.8052-1.5502x+0.912{x}^{2}-0.1577{x}^{3}$, for x < 1.053, where $x=\mathrm{log}({L}_{5100}^{\mathrm{tot}}/{10}^{44}\,\mathrm{erg}\,{{\rm{s}}}^{-1})$ and ${L}_{5100}^{\mathrm{tot}}$ is the total luminosity at 5100 Å. For x > 1.053, ${L}_{5100}^{\mathrm{host}}\ll {L}_{5100}^{\mathrm{AGN}}$, and the host contribution can be ignored. The fractions of host contamination in the total 5100 Å luminosities are 26.0%, 28.0%, 37.2%, 17.9%, 14.9%, 23.1%, and 6.8% for SDSS J075101, J075949, J081441, J083553, J084533, J093302, and J101000, respectively. The host contribution can be ignored for SDSS J074352, J075051, and J100402.

We use Equation (1) to calculate the BH masses of the objects observed in SEAMBH2015–2016. The widths of the Hβ emission lines can be obtained from the FWHM or σ_Hβ measured from their mean or rms spectra. Different works adopt different line width measurements (e.g., Peterson et al. 2004; Bentz et al. 2009; Denney et al. 2010; Grier et al. 2012; Kaspi et al. 2005, Papers I–V). In general, the BH masses produced by the different line width measurements are consistent, because their corresponding virial factors f_BLR are calibrated, in the same way, by comparing the RM objects with measurements of bulge stellar velocity dispersion (σ_*) with the M_•–σ_* relation of inactive galaxies (e.g., Onken et al. 2004; Woo et al. 2010; Park et al. 2012; Grier et al. 2013; Ho & Kim 2014; Woo et al. 2015, see a brief review in Du et al. 2017). The exact value of f_BLR is still a matter of some debate and has large uncertainties. Recently, Woo et al. (2015) found that narrow-line Seyfert 1 (NLS1) galaxies (the Hβ widths of most SEAMBHs conform to the definition of NLS1s) has a value of f_BLR = 1.12. On the other hand, Ho & Kim (2014) show that f_BLR is smaller than 1 for the AGNs with pseudobulges (NLS1s tend to host pseudobulges; e.g., Mathur et al. 2012). It is not clear what will be the final value of f_BLR. More observations are needed to calibrate f_BLR in the future. At this stage, as in the other papers in our series (Papers I–V), we adopt FWHM measured from the mean spectra and f_BLR = 1 to calculate the BH masses, but we acknowledge the large uncertainty of f_BLR.

In order to measure the FWHM of broad Hβ, the narrow component of the line should be removed. This is done by fixing the flux of narrow Hβ to 10% of the flux of [O iii] λ5007 (the typical value in AGNs; e.g., Kewley et al. 2006; Stern & Laor 2013), and the uncertainty is estimated by setting Hβ/[O iii] λ5007 to 0% and 20% as the lower and upper limits, respectively. Narrow Hβ and [O iii] are weak in SEAMBHs; thus, the influence of the narrow-component subtraction to the measurements is not very significant. We measure FWHM of Hβ from the mean spectra after removing the narrow component. For completeness, we also provide σ_Hβ measured from the mean spectra, and FWHM and σ_Hβ measured from the rms spectra. The widths are measured from the rms spectra after smoothing by a 9 pixel boxcar, and the uncertainties are obtained by comparing with the measurements from the profiles smoothed by a 3 pixel boxcar. The instrumental broadening (FWHM ≈ 1200 km s⁻¹), estimated from the spectra of the comparison stars, has been subtracted from the width measurements. The Hβ line width and their uncertainties are listed in Table 5.

As in Papers IV and V, the dimensionless accretion rates of the objects are estimated by Equation (4) because we cannot observe their entire spectral energy distributions (SEDs). Equation (4) is derived from the thin accretion disk model (Shakura & Sunyaev 1973; Frank et al. 2002; see more details in Paper II), and can be used as a substitute for the traditional estimate of the Eddington ratio (e.g., ${L}_{\mathrm{bol}}/{L}_{\mathrm{Edd}}=10{L}_{5100}/{L}_{\mathrm{Edd}}$, where L_bol is the bolometric luminosity and L_Edd is the Eddington Luminosity). Its validity has been discussed in the Appendix of Paper V, and it applies to $\mathop{{\mathscr{M}}}\limits^{\,.}\lesssim 3\times {10}^{3}\,{m}_{7}^{-1/2}$, where m₇ = M_•/10⁷ M_⊙. We list the BH masses, 5100 Å and Hβ luminosities, and the accretion rates in Table 6.

Table 6.  Results of Hβ Reverberation Mapping of the SEAMBHs in 2015–2017

Objects	τHβ	FWHM	$\mathrm{log}{M}_{\bullet }$	$\mathrm{log}\mathop{{\mathscr{M}}}\limits^{\,.}$	log L5100	$\mathrm{log}\,{L}_{{\rm{H}}\beta }$	EW(Hβ)
	(days)	(km s−1)	(M⊙)		(erg s−1)	(erg s−1)	(Å)
SDSS J074352	${43.9}_{-4.2}^{+5.2}$	3156 ± 36	${7.93}_{-0.04}^{+0.05}$	${1.69}_{-0.13}^{+0.12}$	45.37 ± 0.02	43.48 ± 0.01	65.8 ± 3.5
SDSS J075051	${66.6}_{-9.9}^{+18.7}$	1904 ± 9	${7.67}_{-0.07}^{+0.11}$	${2.14}_{-0.24}^{+0.16}$	45.33 ± 0.01	43.34 ± 0.03	51.9 ± 4.5
SDSS J075101	${28.6}_{-6.8}^{+5.6}$	1679 ± 35	${7.20}_{-0.12}^{+0.08}$	${1.45}_{-0.23}^{+0.30}$	44.24 ± 0.04	42.38 ± 0.04	70.4 ± 9.0
SDSS J075949	${26.4}_{-9.5}^{+11.6}$	1783 ± 17	${7.21}_{-0.19}^{+0.16}$	${1.34}_{-0.42}^{+0.48}$	44.19 ± 0.06	42.47 ± 0.04	98.9 ± 17.0
SDSS J081441	${26.8}_{-5.9}^{+7.3}$	1782 ± 16	${7.22}_{-0.11}^{+0.10}$	${0.97}_{-0.28}^{+0.28}$	43.95 ± 0.04	42.39 ± 0.02	140.4 ± 16.2
SDSS J083553	${12.4}_{-5.4}^{+5.4}$	1758 ± 16	${6.87}_{-0.25}^{+0.16}$	${2.41}_{-0.35}^{+0.53}$	44.44 ± 0.02	42.48 ± 0.02	56.1 ± 4.0
SDSS J084533	${19.9}_{-3.9}^{+7.3}$	1297 ± 12	${6.82}_{-0.10}^{+0.14}$	${2.64}_{-0.31}^{+0.22}$	44.52 ± 0.02	42.60 ± 0.03	61.7 ± 5.1
SDSS J093302	${19.0}_{-4.3}^{+3.8}$	1800 ± 25	${7.08}_{-0.11}^{+0.08}$	${1.79}_{-0.40}^{+0.40}$	44.31 ± 0.13	42.10 ± 0.05	31.8 ± 10.3
SDSS J100402	${32.2}_{-4.2}^{+43.5}$	2088 ± 1	${7.44}_{-0.06}^{+0.37}$	${2.89}_{-0.75}^{+0.13}$	45.52 ± 0.01	43.54 ± 0.01	53.6 ± 1.3
SDSS J101000	${27.7}_{-7.6}^{+23.5}$	2311 ± 1	${7.46}_{-0.14}^{+0.27}$	${1.70}_{-0.56}^{+0.31}$	44.76 ± 0.02	42.77 ± 0.02	52.6 ± 3.4

Note. τ_Hβ (in the rest-frame) and FWHM are the same as those in Tables 4 and 5; we list them here again for the convenience of inspection. L₅₁₀₀ are the luminosities corresponding to the light curves used for τ_Hβ measurements. The host contribution in L₅₁₀₀ has been removed (see Section 3.4). Galactic extinction has been corrected using the maps of Schlafly & Finkbeiner (2011).

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As described in Papers II and V, the criterion of $\mathop{{\mathscr{M}}}\limits^{\,.}$ for identifying SEAMBHs still has some uncertainties (Laor & Netzer 1989; Beloborodov 1998; Sa̧dowski et al. 2011). We can use $\eta \mathop{{\mathscr{M}}}\limits^{\,.}\geqslant 0.1$ as the criterion, because the accretion disk becomes slim and the radiation efficiency gets reduced (Sa̧dowski et al. 2011), where η is the mass-to-radiation conversion efficiency. To be conservative, we adopted the lowest η (0.038, for the retrograde disk with BH spin a = −1; see Bardeen et al. 1972). Thus, SEAMBHs are AGNs with $\mathop{{\mathscr{M}}}\limits^{\,.}\geqslant 2.63$. For simplicity, and as in other papers in this series, we use $\mathop{{\mathscr{M}}}\limits^{\,.}=3$ as the criterion to distinguish SEAMBHs from AGNs with low accretion rates.

Using the FITEXY algorithm as modified by Tremaine et al. (2002), we obtain the linear regression for the direct scheme

$$\begin{eqnarray}&&\mathrm{log}\displaystyle \frac{{R}_{{\rm{H}}\beta }}{\mathrm{ltd}}\\ \quad =\,\left\{\begin{array}{ll}(1.40\pm 0.03)+(0.43\pm 0.03)\mathrm{log}{{\ell }}_{44}, & (\mathrm{all}\ \mathop{{\mathscr{M}}}\limits^{\,.})\\ (1.53\pm 0.03)+(0.51\pm 0.03)\mathrm{log}{{\ell }}_{44}, & (\mathop{{\mathscr{M}}}\limits^{\,.}\lt 3)\\ (1.26\pm 0.04)+(0.45\pm 0.05)\mathrm{log}{{\ell }}_{44}, & (\mathop{{\mathscr{M}}}\limits^{\,.}\geqslant 3)\end{array}\right.\end{eqnarray} \tag{ 5 }$$

with intrinsic scatter σ_in = (0.21, 0.16, 0.22). For the averaged scheme, we find

$$\begin{eqnarray}&&\mathrm{log}\displaystyle \frac{{R}_{{\rm{H}}\beta }}{\mathrm{ltd}}\\ \quad =\,\left\{\begin{array}{ll}(1.39\pm 0.03)+(0.43\pm 0.03)\mathrm{log}{{\ell }}_{44}, & (\mathrm{all}\ \mathop{{\mathscr{M}}}\limits^{\,.})\\ (1.53\pm 0.04)+(0.51\pm 0.04)\mathrm{log}{{\ell }}_{44}, & (\mathop{{\mathscr{M}}}\limits^{\,.}\lt 3)\\ (1.27\pm 0.05)+(0.45\pm 0.05)\mathrm{log}{{\ell }}_{44}, & (\mathop{{\mathscr{M}}}\limits^{\,.}\geqslant 3)\end{array}\right.\end{eqnarray} \tag{ 6 }$$

with intrinsic scatter σ_in = (0.22, 0.17, 0.21). The intercepts of the correlations for the AGNs with high ($\mathop{{\mathscr{M}}}\limits^{\,.}\geqslant 3$) and low ($\mathop{{\mathscr{M}}}\limits^{\,.}\lt 3$) accretion rates are significantly different. On average, the Hβ lags of the $\mathop{{\mathscr{M}}}\limits^{\,.}\geqslant 3$ sources are shorter than the values of the $\mathop{{\mathscr{M}}}\limits^{\,.}\lt 3$ sources by a factor of ∼2 (0.26 dex). The slope of the SEAMBHs may be slightly smaller, although the difference is not very significant, considering the uncertainties. In view of the currently limited and nonuniform distribution, especially at low and high luminosities, it is premature to draw firm conclusions on the slopes of the correlations. At this stage, as a preliminary result, the slopes of high- and low-$\mathop{{\mathscr{M}}}\limits^{\,.}$ objects can be regarded as indistinguishable.

According to Papers IV and V, the shortening of the Hβ lags in SEAMBHs show a strong correlation with accretion rate. In order to test whether this correlation extends to SEAMBHs of even higher luminosities, we define, as in Papers IV and V, ${\rm{\Delta }}{R}_{{\rm{H}}\beta }=\mathrm{log}({R}_{{\rm{H}}\beta }/{R}_{{\rm{H}}\beta ,R-L})$ to quantify the deviation from the R_Hβ–L₅₁₀₀ relation of the subsample with $\mathop{{\mathscr{M}}}\limits^{\,.}\lt 3$ (i.e., ${R}_{{\rm{H}}\beta ,R-L}$ is the correlation for $\mathop{{\mathscr{M}}}\limits^{\,.}\lt 3$ in Equations (5) or (6)). Figure 3 shows the correlation between ΔR_Hβ and $\mathop{{\mathscr{M}}}\limits^{\,.}$, as well as the distributions of the AGNs with $\mathop{{\mathscr{M}}}\limits^{\,.}\geqslant 3$ and $\mathop{{\mathscr{M}}}\limits^{\,.}\lt 3$ in the direct and averaged schemes. The objects with $\mathop{{\mathscr{M}}}\limits^{\,.}\lt 3$ are located in both the two left quadrants of ΔR_Hβ ≥ 0 and ΔR_Hβ < 0. However, SEAMBHs ($\mathop{{\mathscr{M}}}\limits^{\,.}\geqslant 3$) only appear in the quadrant with ΔR_Hβ < 0, and their ΔR_Hβ values significantly correlate with $\mathop{{\mathscr{M}}}\limits^{\,.}$ (Pearson's correlation coefficient and null-probability are −0.84 and 4.8 × 10⁻¹³ for the direct scheme; the corresponding values are −0.82 and 1.4 × 10⁻⁹ for the average scheme). The objects in SEAMBH2015–2016 follow the same correlation as those SEAMBHs with lower luminosities observed in our campaign between 2012 and 2015. The dependence on accretion rate for SEAMBHs of the R_Hβ deviations from the R_Hβ–L₅₁₀₀ relation can be obtained by the regression for the objects with $\mathop{{\mathscr{M}}}\limits^{\,.}\geqslant 3$:

$$\begin{eqnarray}&&{\rm{\Delta }}{R}_{{\rm{H}}\beta }\\ \quad =\,\left\{\begin{array}{lc}(0.36\pm 0.08)-(0.44\pm 0.05)\mathrm{log}\mathop{{\mathscr{M}}}\limits^{\,.}, & (\mathrm{direct})\\ (0.30\pm 0.09)-(0.40\pm 0.06)\mathrm{log}\mathop{{\mathscr{M}}}\limits^{\,.}, & (\mathrm{averaged})\end{array}\right.\end{eqnarray} \tag{ 7 }$$

with intrinsic scatter σ_in = (0.04, 0.07).

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Principal component analysis has revealed that the main variance of quasar optical spectra is a strong correlation between the flux ratio of broad Fe ii to Hβ emission, the strength of [O iii] λ5007, and the width of Hβ (Boroson & Green 1992; Sulentic et al. 2000a). The so-called Eigenvector 1 has been demonstrated to be driven by the Eddington ratio ${L}_{\mathrm{bol}}/{L}_{\mathrm{Edd}}$ (Boroson & Green 1992; Sulentic et al. 2000a, 2000b; Marziani et al. 2003; Shen & Ho 2014). AGNs with high Eddington ratios/accretion rates, such as NLS1s, show very strong Fe ii emission compared with normal sources (Boroson & Green 1992; Hu et al. 2008a; Dong et al. 2011). And, at the same time, the Hβ profiles of NLS1s tend to be more Lorentzian (smaller values of ${{ \mathcal D }}_{{\rm{H}}\beta }$) than those of broader line AGNs, which probably have more normal accretion rates (Véron-Cetty et al. 2001; Zamfir et al. 2010; Kollatschny & Zetzl 2011).

Du et al. (2016c) recently investigated the correlation between the strength of Fe ii, the Hβ profile, and the accretion rates of the RM AGN sample. They found that both the relative strength of optical Fe ii lines (${{ \mathcal R }}_{\mathrm{Fe}}={F}_{\mathrm{Fe}}/{F}_{{\rm{H}}\beta }$) and the Hβ profile shape parameter (${{ \mathcal D }}_{{\rm{H}}\beta }$ = FWHM/σ_Hβ) indeed correlate with accretion rate $\mathop{{\mathscr{M}}}\limits^{\,.}$, where F_Fe is the flux of Fe ii in the region 4434–4684 Å and F_Hβ is the flux of broad Hβ. Combining ${{ \mathcal D }}_{{\rm{H}}\beta }$ and ${{ \mathcal R }}_{\mathrm{Fe}}$, they proposed a bivariate correlation of the form $\mathrm{log}\mathop{{\mathscr{M}}}\limits^{\,.}={\alpha }_{2}+{\beta }_{2}{{ \mathcal D }}_{{\rm{H}}\beta }+{\gamma }_{2}{{ \mathcal R }}_{\mathrm{Fe}}$, termed the "BLR fundamental plane." Thus, we can use ${{ \mathcal R }}_{\mathrm{Fe}}$ and ${{ \mathcal D }}_{{\rm{H}}\beta }$ as proxies of accretion rate to test the dependence of ΔR_Hβ on accretion rate.

Figure 4 shows the correlation between ΔR_Hβ and ${{ \mathcal R }}_{\mathrm{Fe}}$, ${{ \mathcal D }}_{{\rm{H}}\beta }$, or the $\mathop{{\mathscr{M}}}\limits^{\,.}$ derived from the fundamental plane. For comparison, the axis of ${{ \mathcal D }}_{{\rm{H}}\beta }$ is plotted inversely. In general, the objects with larger ${{ \mathcal R }}_{\mathrm{Fe}}$ and smaller ${{ \mathcal D }}_{{\rm{H}}\beta }$ deviate more extremely from the R_Hβ–L₅₁₀₀ relation. ${{ \mathcal R }}_{\mathrm{Fe}}$ and ${{ \mathcal D }}_{{\rm{H}}\beta }$ are purely observables; thus, using them as proxies of $\mathop{{\mathscr{M}}}\limits^{\,.}$ can avoid the implicit enhancement to the ΔR_Hβ–$\mathop{{\mathscr{M}}}\limits^{\,.}$ correlation caused by the fact that $\mathop{{\mathscr{M}}}\limits^{\,.}$ is a derived quantity. The scatter of the $\mathop{{\mathscr{M}}}\limits^{\,.}$–${{ \mathcal R }}_{\mathrm{Fe}}$ and $\mathop{{\mathscr{M}}}\limits^{\,.}$–${{ \mathcal D }}_{{\rm{H}}\beta }$ correlations is relatively large (see Figure 1 in Du et al. 2016c). So, the ΔR_Hβ–${{ \mathcal R }}_{\mathrm{Fe}}$ and ΔR_Hβ–${{ \mathcal D }}_{{\rm{H}}\beta }$ correlations in panels (a) and (b) of Figure 4 are not as good as the ΔR_Hβ–$\mathop{{\mathscr{M}}}\limits^{\,.}$ correlation in Figure 3. Panel (c) in Figure 4 shows ΔR_Hβ versus $\mathop{{\mathscr{M}}}\limits^{\,.}$ derived from the fundamental plane, which has smaller scatter than each of the single correlations ($\mathop{{\mathscr{M}}}\limits^{\,.}$–${{ \mathcal R }}_{\mathrm{Fe}}$ or $\mathop{{\mathscr{M}}}\limits^{\,.}$–${{ \mathcal D }}_{{\rm{H}}\beta }$). In consideration of the relatively large scatter in the $\mathop{{\mathscr{M}}}\limits^{\,.}$–${{ \mathcal R }}_{\mathrm{Fe}}$ and $\mathop{{\mathscr{M}}}\limits^{\,.}$–${{ \mathcal D }}_{{\rm{H}}\beta }$ correlations, and the fundamental plane, we do not attempt to apply linear regression to Figure 4. They are just used to demonstrate the validity of Equation (7) in different ways.

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It has been predicted that the self-shadowing effects of slim accretion disks leads to a shrinking of the ionization front of the BLR, so that the Hβ lag shortens with increasing accretion rate (Wang et al. 2014c). Because of radiation pressure, the inner part of the slim disk is not geometrically thin, a property that naturally leads to anisotropic ionizing continuum. The vertical thickness of the inner slim disk significantly suppresses the amount of the ionizing photons that can be received by the BLR clouds, although it does not change the continuum flux obtained by observers. If the ionization parameter remains constant for the Hβ line, the radius at which Hβ emits most efficiently will shrink significantly (see more details in Wang et al. 2014c). This was first evidenced in the SEAMBH2013–2014 samples (Papers IV and V). The current SEAMBH2015–2016 sample continues to lend support to the idea that the shortened Hβ lags arise from self-shadowing effects of a slim disk.

Self-shadowing effects also depend on BLR geometry. According to the opening angle of the slim disk (ΔΩ_disk), the BLR can be divided into two parts: (1) a shadowed region and (2) an unshadowed region (Wang et al. 2014c). If BLRs originate from inflows from the dusty torus to the central BH, as suggested by Wang et al. (2017), the BLR opening angle (ΔΩ_BLR) should follow the torus (ΔΩ_torus).¹² Namely, ΔΩ_BLR ∼ ΔΩ_torus. In the regime of the standard accretion disk, ΔΩ_disk > ΔΩ_BLR, and the entire BLR is illuminated by the radiation of the disk. In the case of a slim disk, for a simple consideration, the relative size of the shadowed and unshadowed regions depends on ΔΩ_disk and ${\rm{\Delta }}{{\rm{\Omega }}}_{\mathrm{torus}}$. The shadowed region receives less ionizing luminosity than the unshadowed region. This may give rise to shrinkage of the ionization front in the shadowed regions, thereby leading to shortened Hβ lags in SEAMBHs. This is a key prediction of the self-shadowing effects in SEAMBHs. Although shortened lags have been observed by the SEAMBH project, the relatively longer ones of the unshadowed regions have not yet been reported. A possible reason is that our current continuous period of monitoring is still not long enough because of the regular rainy season from June to October in the Lijiang site.

We note that the measurement of the Hβ lag may possibly be influenced by the characteristic continuum variability timescale (Goad & Korista 2014). The extremely short variability timescale (much shorter than the intrinsic Hβ lag or the centroid of the one-dimensional transfer function) may lead to shortening of the lag measurement (see more details in Goad & Korista 2014). However, the variation timescales of the objects in this paper are typically much larger than their Hβ time delays (the timescales are typically ∼100–300 days). Thus, the variation timescale is unlikely the dominant factor for the shortening of the Hβ lags.

The large sample size of the Sloan Digital Sky Survey RM (SDSS-RM) project (Shen et al. 2015) offers a promising opportunity to probe BHs with a large range of accretion rates and spins. Grier et al. (2017) recently reported Hβ time lags detected in the first year of SDSS-RM. They successfully measured Hβ lags for 44 SDSS targets mainly using the Bayesian-based modeling code JAVELIN (Zu et al. 2011) and the Continuum REprocessing AGN MCMC software (CREAM; Starkey et al. 2016) instead of the traditional ICCF.¹³ Interestingly, they, too, found shortened Hβ lags compared with the canonical R_Hβ–L₅₁₀₀ relation for a number of objects. We plot the 44 objects in the ΔR_Hβ–$\mathop{{\mathscr{M}}}\limits^{\,.}$ plane in Figure 5; the black and red points are the same objects in Figure 3. The time lags, luminosities, and BH masses are taken directly from Grier et al. (2017), and their accretion rates $\mathop{{\mathscr{M}}}\limits^{\,.}$ are calculated using Equation (4). There are two extreme cases (SDSS J142052.44+525622.4 and SDSS JJ141856.19+535845.0) that show ΔR_Hβ ≈ −1 and $\mathop{{\mathscr{M}}}\limits^{\,.}\approx {10}^{-0.4\sim -0.5}$. A couple of objects with $\mathop{{\mathscr{M}}}\limits^{\,.}\gtrsim 3$ are in the SEAMBH regime. These conform to our expectation that high $\mathop{{\mathscr{M}}}\limits^{\,.}$ leads to shortened Hβ lags. Surprisingly, some low-$\mathop{{\mathscr{M}}}\limits^{\,.}$ objects also have Hβ lags much shorter than the R_Hβ–L₅₁₀₀ relation. What is the physical explanation for these?

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One possible interpretation is that this is a signature of retrograde¹⁴ accretion onto the BH in low-accretion rate AGNs. In the accretion rate regime of the Shakura–Sunyaev disk ($\mathop{{\mathscr{M}}}\limits^{\,.}\lesssim 3$), the inner edge of the disk is fully determined by the last stable radius (Bardeen et al. 1972), since the dissipation of gravitational energy via viscosity can be neglected within this radius (Page & Thorne 1974). Different from the Shakura–Sunyaev disk, the inner edge of a slim disk is mostly determined by the accretion rate instead of the spin because the dissipation cannot be neglected (Watarai & Mineshige 2003). As a consequence, except for accretion rate, the ionizing luminosity highly depends on the spin and hence seriously influences the ionization front of the BLR (Wang et al. 2014b). In the Shakura–Sunyaev regime, the ionizing luminosity of Hβ shows a non-monotonic correlation with the 5100 Å luminosity if the quasar is undergoing retrograde accretion (see Figure 3 in Wang et al. 2014b). A cold disk in retrograde accretion leads to the inefficient generation of the ionizing continuum, causing the Hβ region to become smaller than the case of prograde accretion (Wang et al. 2014b). For the extreme case of retrograde accretion onto a maximally rotating BH, the Hβ lags are expected to be shortened by a factor of ∼10 (Wang et al. 2014b). The two extreme cases from the SDSS-RM campaign may be caused by retrograde accretion.

In Figure 5, we divide the regime of accretion rates by $\mathop{{\mathscr{M}}}\limits^{\,.}\approx 3$. Hβ lags are influenced jointly by the spin and the accretion rate below $\mathop{{\mathscr{M}}}\limits^{\,.}\approx 3$, and purely by accretion rate for $\mathop{{\mathscr{M}}}\limits^{\,.}\gtrsim 3$. The first regime is spin-driven, and the second is $\mathop{{\mathscr{M}}}\limits^{\,.}$-driven. The canonical R_Hβ–L₅₁₀₀ relation only holds for AGNs in the Shakura–Sunyaev regime. Our proposal should be tested by larger samples covering the widest possible range of accretion rates.

The discovery of retrograde accretion onto BHs in AGNs through RM campaigns, if confirmed by independent measurements (e.g., iron Kα observations from X-ray spectra), has important implications for the cosmological evolution of BHs. It has been suggested that the spin angular momentum of BHs originates from accretion if the mass of the BH gained through accretion is larger than one-third of its original mass (e.g., Thorne 1974). Therefore, the direction of ongoing accretion may be different from the current spins obtained from past accretion episodes. The cosmological evolution of the radiation efficiency of z ≲ 2 quasars (Wang et al. 2009; Li et al. 2012) suggests that BHs spinning down with cosmic time. This is confirmed by simulations of BH evolution (Volonteri et al. 2013; Tucci & Volonteri 2017). The SDSS-RM discovery of shortened lags for AGNs with low accretion rates supports spin-down evolution.

Additionally, the truncated accretion disk of a BH with low accretion rate is plausibly responsible for the shortened Hβ lag. In such an accretion disk, the linear ${L}_{5100}\mbox{--}{L}_{13.6\mathrm{eV}}$ relation will be broken since the ionizing photons are suppressed due to inefficient radiation in the evaporated part of the advection-dominated accretion flow, where ${L}_{13.6\mathrm{eV}}$ is the ionizing luminosity at 13.6 eV. Details will be presented in a forthcoming paper (B. Czerny & J.-M. Wang 2018, in preparation). Broadband SEDs are needed for these low-accretion AGNs with shortened lags in order to distinguish the two possible mechanisms.