Can Reverberation-measured Quasars Be Used for Cosmology?

Our sample of Hβ reverberation-measured AGNs is a compilation of the results published earlier in the literature. It was previously used by Czerny et al. (2019): the luminosity (L₅₁₀₀), time delay (τ_obs), and FWHM are the same as considered by them. We have collected a total of 117 sources, plus two objects that have been discarded from the analysis (see details in Section 2.2). The first subsample is composed of 25 highly accreting AGNs observed by the SEAMBHs project (Du et al. 2014, 2015, 2016, 2018; Wang et al. 2014a; Hu et al. 2015). The SEAMBH project group has been monitoring super-Eddington sources since 2012, obtaining important results for this kind of object. The second subsample contains 44 objects from the recent Sloan Digital Sky Survey Reverberation Mapping (SDSS-RM) project (Grier et al. 2017); two sources of this sample have been discarded. This sample comes from a larger sample of Shen et al. (2015); recently, they published an update of the catalog with additional information, such as the variability properties (Shen et al. 2019). The third subsample is a collection of 48 sources from long-term monitoring projects, where the majority of the sources have been summarized by Bentz et al. (2013). We include in this sample other sources monitored in recent years (Bentz et al. 2009, 2014, 2016a, 2016b; Barth et al. 2013; Pei et al. 2014; Fausnaugh et al. 2017). This collective sample is hereafter referred to as the Bentz collection. The fourth subsample includes NGC 5548 and 3C 273 (PG 1226+023), monitored by Lu et al. (2016) and Zhang et al. (2019), respectively. Previously, 3C 273 was monitored by Kaspi et al. (2000) and Peterson et al. (2004); however, new results from the GRAVITY Collaboration (Gravity Collaboration et al. 2018) resolved the BLR with a much better angular resolution of 10⁻⁵ '', indicating a smaller BLR size (∼150 lt-day) than the reverberation mapping results. Almost at the same time, Zhang et al. (2019) reported a new value for BLR size from a monitoring performed for ∼10 yr, which is similar to the one given by Gravity Collaboration et al. (2018). We will use this new estimation for 3C 273 hereafter in the paper.

These sources do not form a uniform sample. Sources from the Bentz collection were selected to cover a broad range of redshift (0.002 ≲ z ≲  0.292), from nearby sources studied earlier by, for example, Peterson et al. (2004) to more distant PG quasar samples from Kaspi et al. (2000). The average luminosity and dimensionless accretion rate are log L₅₁₀₀ = 43.4 erg s⁻¹ and ${\dot{{\mathscr{M}}}}^{{\rm{c}}}$ ∼ 0.8 (see Section 2.3), respectively. Sources from the SDSS-RM sample are, on average, slightly more luminous, log L₅₁₀₀ = 43.9 erg s⁻¹, and cover systematically larger redshifts, 0.116 ≲ z ≲  0.89. On the other hand, the SEAMBH sample has been selected with the aim of studying super-Eddington sources; they are nearby objects (0.017 ≲ z ≲  0.4) but with the largest accretion rates, ${\dot{{\mathscr{M}}}}^{{\rm{c}}}$_mean ∼ 14.6 (see Section 2.3).

The full sample includes 117 sources and covers a large redshift range (0.002 ≲ z ≲  0.89), which is convenient in order to test cosmological models. A detailed description of the sample is shown in Table 1.

Table 1.  Sample Description

Object	z	log L5100	τobs	FWHM	References
		(erg s−1)	(days)	( km s−1)
(1)	(2)	(3)	(4)	(5)	(6)
SEAMBH Sample
Mrk 335	0.0258	43.764 ± 0.067	${14.0}_{-3.4}^{+4.6}$	2096 ± 170	(1)
Mrk 142	0.0449	43.594 ± 0.044	${6.4}_{-3.4}^{+7.3}$	1588 ± 58	(1)
IRAS F12397	0.0435	44.229 ± 0.054	${9.7}_{-1.8}^{+5.5}$	1802 ± 560	(1)
Mrk 486	0.0389	43.694 ± 0.050	${23.7}_{-2.7}^{+7.5}$	1942 ± 67	(2)
Mrk 382	0.0337	43.124 ± 0.085	${7.5}_{-2.0}^{+2.9}$	1462 ± 296	(2)
IRAS 04416	0.0889	44.467 ± 0.030	${13.3}_{-1.4}^{+13.9}$	1522 ± 44	(2)
MCG +06-26-012	0.0328	42.675 ± 0.106	${24.0}_{-4.8}^{+8.4}$	1334 ± 80	(2)
Mrk 493	0.0313	43.112 ± 0.075	${11.6}_{-2.6}^{+1.2}$	778 ± 12	(2)
Mrk 1044	0.0165	43.095 ± 0.102	${10.5}_{-2.7}^{+3.3}$	1178 ± 22	(2)
J080101	0.1396	44.270 ± 0.030	${8.3}_{-2.7}^{+9.7}$	1930 ± 18	(3)
J081456	0.1197	43.990 ± 0.040	${24.3}_{-16.4}^{+7.7}$	2409 ± 61	(3)
J093922	0.1859	44.070 ± 0.040	${11.9}_{-6.3}^{+2.1}$	1209 ± 16	(3)
J080131	0.1786	43.950 ± 0.040	${11.5}_{-3.7}^{+7.5}$	1290 ± 13	(4)
J085946	0.2438	44.410 ± 0.030	${34.8}_{-26.3}^{+19.2}$	1718 ± 16	(4)
J102339	0.1364	44.090 ± 0.030	${24.9}_{-3.9}^{+19.8}$	1733 ± 29	(4)
J074352	0.2520	45.370 ± 0.020	${43.9}_{-4.2}^{+5.2}$	3156 ± 36	(5)
J075051	0.4004	45.330 ± 0.010	${66.6}_{-9.9}^{+18.7}$	1904 ± 9	(5)
J075101	0.1209	44.240 ± 0.040	${30.4}_{-5.8}^{+7.3}$	1679 ± 35	(5)
J075949	0.1879	44.190 ± 0.060	${43.9}_{-19.0}^{+33.1}$	1783 ± 17	(5)
J081441	0.1626	43.950 ± 0.040	${25.3}_{-7.5}^{+10.4}$	1782 ± 16	(5)
J083553	0.2051	44.440 ± 0.020	${12.4}_{-5.4}^{+5.4}$	1758 ± 16	(5)
J084533	0.3024	44.520 ± 0.020	${18.1}_{-4.7}^{+6.0}$	1297 ± 12	(5)
J093302	0.1772	44.310 ± 0.130	${19.0}_{-4.3}^{+3.8}$	1800 ± 25	(5)
J100402	0.3272	45.520 ± 0.010	${32.2}_{-4.2}^{+43.5}$	2088 ± 1	(5)
J101000	0.2564	44.760 ± 0.020	${27.7}_{-7.6}^{+23.5}$	2311 ± 11	(5)
SDSS-RM Sample
J140812	0.1160	43.154 ± 0.013	${10.5}_{-2.2}^{+1.0}$	4345 ± 558	(6)
J141923	0.1520	43.122 ± 0.010	${11.8}_{-1.5}^{+0.7}$	2945 ± 20	(6)
J140759	0.1720	43.577 ± 0.009	${16.3}_{-6.6}^{+13.1}$	3662 ± 27	(6)
J141729	0.2370	43.291 ± 0.007	${5.5}_{-2.1}^{+5.7}$	9208 ± 269	(6)
J141645.15	0.2440	43.213 ± 0.007	${5.0}_{-1.4}^{+1.5}$	7409 ± 113	(6)
J142135	0.2490	43.475 ± 0.007	${3.9}_{-0.9}^{+0.9}$	3090 ± 66	(6)
J141625	0.2630	43.964 ± 0.019	${15.1}_{-4.6}^{+3.2}$	3515 ± 17	(6)
J142103	0.2630	43.636 ± 0.019	${75.2}_{-3.3}^{+3.2}$	2990 ± 48	(6)
J142038	0.2650	43.458 ± 0.006	${25.2}_{-5.7}^{+4.7}$	4700 ± 55	(6)
J142043	0.3370	43.400 ± 0.005	${5.9}_{-0.6}^{+0.4}$	4429 ± 105	(6)
J141041	0.3590	43.824 ± 0.005	${21.9}_{-2.4}^{+4.2}$	5034 ± 35	(6)
J141318	0.3620	43.941 ± 0.005	${20.0}_{-3.0}^{+1.1}$	3428 ± 37	(6)
J141955	0.4180	43.395 ± 0.005	${10.7}_{-4.4}^{+5.6}$	6789 ± 580	(6)
J141645.58	0.4420	43.679 ± 0.009	${8.5}_{-1.4}^{+2.5}$	2178 ± 44	(6)
J141324	0.4560	43.945 ± 0.004	${25.5}_{-5.8}^{+10.9}$	6076 ± 121	(6)
J141214	0.4580	44.397 ± 0.004	${21.4}_{-6.4}^{+4.2}$	2652 ± 302	(6)
J140518	0.4670	44.333 ± 0.004	${41.6}_{-8.3}^{+14.8}$	3406 ± 22	(6)
J141018	0.4700	43.584 ± 0.005	${16.2}_{-4.5}^{+2.9}$	4329 ± 298	(6)
J141123	0.4720	44.128 ± 0.004	${13.0}_{-0.8}^{+1.4}$	4106 ± 38	(6)
J142039	0.4740	44.141 ± 0.004	${20.7}_{-3.0}^{+0.9}$	4259 ± 90	(6)
J141724	0.4820	43.992 ± 0.004	${10.1}_{-2.7}^{+12.5}$	5230 ± 76	(6)
J141004	0.5270	44.224 ± 0.003	${53.5}_{-4.0}^{+4.2}$	2918 ± 62	(6)
J141706	0.5320	44.186 ± 0.003	${10.4}_{-3.0}^{+6.3}$	1682 ± 14	(6)
J142010	0.5480	44.088 ± 0.003	${12.8}_{-4.5}^{+5.7}$	6050 ± 541	(6)
J141712	0.5540	43.209 ± 0.012	${12.5}_{-2.6}^{+1.8}$	2226 ± 405	(6)
J141115	0.5720	44.313 ± 0.003	${49.1}_{-2.0}^{+11.1}$	3442 ± 51	(6)
J141112	0.5870	44.123 ± 0.003	${20.4}_{-2.0}^{+2.5}$	2765 ± 36	(6)
J141417	0.6040	43.397 ± 0.013	${15.6}_{-5.1}^{+3.2}$	6476 ± 793	(6)
J141031	0.6080	44.022 ± 0.003	${35.8}_{-10.3}^{+1.1}$	3495 ± 118	(6)
J141941	0.6460	44.522 ± 0.017	${30.4}_{-8.3}^{+3.9}$	2818 ± 48	(6)
J141135	0.6500	44.040 ± 0.004	${17.6}_{-7.4}^{+8.6}$	2515 ± 61	(6)
J140904	0.6580	44.147 ± 0.004	${11.6}_{-4.6}^{+8.6}$	10405 ± 1094	(6)
J142052	0.6760	45.059 ± 0.003	${11.9}_{-1.0}^{+1.3}$	3646 ± 14	(6)
J141147	0.6800	44.025 ± 0.004	${6.4}_{-1.4}^{+1.5}$	2338 ± 65	(6)
J141532	0.7150	44.136 ± 0.004	${26.5}_{-8.8}^{+9.9}$	1615 ± 38	(6)
J142023	0.7340	44.222 ± 0.006	${8.5}_{-3.9}^{+3.2}$	4446 ± 135	(6)
J142049	0.7510	44.446 ± 0.003	${46.0}_{-9.5}^{+9.5}$	4665 ± 97	(6)
J142112	0.8430	44.315 ± 0.008	${14.2}_{-3.0}^{+3.7}$	4428 ± 295	(6)
J141606	0.8480	44.801 ± 0.003	${32.0}_{-15.5}^{+11.6}$	7307 ± 213	(6)
J141859	0.8840	44.907 ± 0.003	${20.4}_{-7.0}^{+5.6}$	4999 ± 53	(6)
J141952	0.8840	44.246 ± 0.006	${32.9}_{-5.1}^{+5.6}$	7726 ± 319	(6)
J142417	0.8900	44.089 ± 0.060	${36.3}_{-5.5}^{+4.5}$	1721 ± 147	(6)
J141856	0.9760	45.382 ± 0.002	${15.8}_{-1.9}^{+6.0}$	3120 ± 58	(6)†
J141314	1.0260	44.524 ± 0.038	${43.9}_{-4.3}^{+4.9}$	1412 ± 183	(6)†
Bentz Collection
PG 0026+129	0.1420	44.970 ± 0.016	${111.0}_{-28.3}^{+24.1}$	1719 ± 495	(7)
PG 0052+251	0.1545	44.807 ± 0.025	${89.8}_{-24.1}^{+24.5}$	4165 ± 381	(7)
Fairall 9	0.0470	43.981 ± 0.041	${17.4}_{-4.3}^{+3.2}$	6901 ± 707	(7)
Mrk 590	0.0264	43.496 ± 0.212	${25.6}_{-5.3}^{+6.5}$	2220 ± 701	(7)
3C 120	0.0330	44.004 ± 0.100	${26.2}_{-6.6}^{+8.7}$	2372 ± 501	(7)
Ark 120	0.0327	43.867 ± 0.253	${39.5}_{-7.8}^{+8.5}$	5410 ± 360	(7)
Mrk 79	0.0222	43.677 ± 0.067	${15.6}_{-4.9}^{+5.4}$	4852 ± 1554	(7)
PG 0804+761	0.1000	44.910 ± 0.017	${146.9}_{-18.9}^{+18.8}$	2012 ± 845	(7)
Mrk 110	0.0353	43.658 ± 0.115	${25.6}_{-7.2}^{+8.9}$	1494 ± 802	(7)
PG 0953+414	0.2341	45.186 ± 0.013	${150.1}_{-22.6}^{+21.6}$	3002 ± 398	(7)
NGC 3227	0.0039	42.236 ± 0.106	${3.8}_{-0.8}^{+0.8}$	3578 ± 83	(7)‡
NGC 3516	0.0088	42.787 ± 0.205	${11.7}_{-1.5}^{+1.0}$	5175 ± 96	(7)‡
SBS 1116+583A	0.0279	42.138 ± 0.231	${2.3}_{-0.5}^{+0.6}$	3604 ± 1123	(7)
Arp 151	0.0211	42.548 ± 0.101	${4.0}_{-0.7}^{+0.5}$	2357 ± 142	(7)
NGC 3783	0.0097	42.558 ± 0.180	${10.2}_{-2.3}^{+3.3}$	3093 ± 529	(7)‡
Mrk 1310	0.0196	42.293 ± 0.145	${3.7}_{-0.6}^{+0.6}$	1602 ± 250	(7)
NGC 4051	0.0023	41.898 ± 0.152	${2.1}_{-0.7}^{+0.9}$	1034 ± 41	(7)‡
NGC 4151	0.0033	42.091 ± 0.207	${6.6}_{-0.8}^{+1.1}$	4711 ± 750	(7)‡
Mrk 202	0.0210	42.260 ± 0.144	${3.0}_{-1.1}^{+1.7}$	1354 ± 250	(7)
NGC 4253	0.0129	42.570 ± 0.122	${6.2}_{-1.2}^{+1.6}$	834 ± 1260	(7)
PG 1229+204	0.0630	43.697 ± 0.047	${37.8}_{-15.3}^{+27.6}$	3415 ± 320	(7)
NGC 4593	0.0090	42.621 ± 0.370	${4.0}_{-0.7}^{+0.8}$	4268 ± 551	(7)
NGC 4748	0.0146	42.556 ± 0.120	${5.5}_{-2.2}^{+1.6}$	1212 ± 173	(7)
PG 1307+085	0.1550	44.849 ± 0.015	${105.6}_{-46.6}^{+36.0}$	5058 ± 524	(7)
Mrk 279	0.0305	43.705 ± 0.074	${16.7}_{-3.9}^{+3.9}$	3385 ± 349	(7)
PG 1411+442	0.0896	44.563 ± 0.020	${124.3}_{-61.7}^{+61.0}$	2398 ± 353	(7)
PG 1426+015	0.0866	44.629 ± 0.024	${95.0}_{-37.1}^{+29.9}$	6323 ± 1295	(7)
Mrk 817	0.0315	43.743 ± 0.089	${19.9}_{-6.7}^{+9.9}$	4122 ± 1197	(7)
Mrk 290	0.0296	43.168 ± 0.057	${8.7}_{-1.0}^{+1.2}$	4270 ± 157	(7)
PG 1613+658	0.1290	44.774 ± 0.022	${40.1}_{-15.2}^{+15.0}$	7897 ± 1792	(7)
PG 1617+175	0.1124	44.391 ± 0.017	${71.5}_{-33.7}^{+29.6}$	4718 ± 991	(7)
PG 1700+518	0.2920	45.586 ± 0.007	${251.8}_{-38.8}^{+45.9}$	1846 ± 682	(7)
3C 390.3	0.0561	44.434 ± 0.576	${44.5}_{-17.0}^{+27.7}$	10415 ± 1971	(7)
NGC 6814	0.0052	42.120 ± 0.285	${6.6}_{-0.9}^{+0.9}$	3277 ± 297	(7)
Mrk 509	0.0344	44.193 ± 0.045	${79.6}_{-5.4}^{+6.1}$	2715 ± 101	(7)
PG 2130+099	0.0630	44.203 ± 0.028	${9.6}_{-1.2}^{+1.2}$	2097 ± 102	(7)
NGC 7469	0.0163	43.506 ± 0.108	${10.8}_{-1.3}^{+3.4}$	1066 ± 84	(7)
PG 1211+143	0.0809	44.728 ± 0.081	${93.8}_{-42.1}^{+25.6}$	2012 ± 37	(8)
PG 0844+349	0.0640	44.218 ± 0.071	${32.3}_{-13.4}^{+13.7}$	2436 ± 329	(8)
NGC 5273	0.0036	41.535 ± 0.160	${2.2}_{-1.6}^{+1.2}$	4615 ± 330	(9)‡
Mrk 1511	0.0339	43.162 ± 0.062	${5.7}_{-0.8}^{+0.9}$	4171 ± 137	(10)
KA 1858-4850	0.0780	43.428 ± 0.047	${13.5}_{-2.3}^{+2.0}$	1511 ± 68	(11)
MCG 6-30-15	0.0078	41.643 ± 0.108	${5.7}_{-1.7}^{+1.8}$	1422 ± 416	(12)
UGC 06728	0.0065	41.864 ± 0.081	${1.4}_{-0.8}^{+0.7}$	1145 ± 58	(13)
MCG +08-11-011	0.0205	43.330 ± 0.111	${15.7}_{-0.5}^{+0.5}$	1159 ± 8	(14)
NGC 2617	0.0142	42.667 ± 0.159	${4.3}_{-1.4}^{+1.1}$	5303 ± 49	(14)‡
3C 382	0.0579	43.835 ± 0.102	${40.5}_{-3.7}^{+8.0}$	3619 ± 282	(14)
Mrk 374	0.0426	43.774 ± 0.042	${14.8}_{-3.3}^{+5.8}$	3250 ± 19	(14)
Lu et al. (2016)
NGC 5548	0.0172	43.210 ± 0.120	${7.2}_{-0.4}^{+1.3}$	9912 ± 362	(15)‡
Zhang et al. (2019)
3C 273	0.1583	45.965 ± 0.016	${146.8}_{-12.1}^{+8.3}$	3314 ± 59	(16)

Note. Columns are as follows. (1) Object name. Discarded objects of the analysis are marked with a † symbol. Double-peak Hα profiles are marked with a ‡ symbol. (2) Redshift. (3) Luminosity at 5100 Å. (4) Delay time at rest frame. (5) FWHM of Hβ emission line. (6) References: (1) Du et al. (2014), (2) Wang et al. (2014a), (3) Du et al. (2015), (4) Du et al. (2016), (5) Du et al. (2018), (6) Grier et al. (2017), (7) Bentz et al. (2013), (8) Bentz et al. (2009), (9) Bentz et al. (2014), (10) Barth et al. (2013), (11) Pei et al. (2014), (12) Bentz et al. (2016a), (13) Bentz et al. (2016b), (14) Fausnaugh et al. (2017), (15) Lu et al. (2016), (16) Zhang et al. (2019).

Download table as:  ASCIITypeset images: 1 2 3

Two objects from the SDSS-RM sample have been discarded from the analysis: J141856 and J141314. In the case of J141856, there is no detection of the blue side of the Hβ line, destroying the profile and prohibiting any possibility of measurement. In J141314, the Hβ line is at the border of the spectrum, where the signal-to-noise ratio (S/N) is poor and the emission line cannot be observed.

Observational problems can cause an incorrect estimation in the time delay; see Section 3.2 and the Appendix. It is important to stress that ∼30% of the SDSS-RM sample has a contribution of the host galaxy luminosity >50% with respect to AGNs. In order to decompose the quasar and host galaxy contribution, Shen et al. (2015) applied a principal component analysis (PCA). This method could present some systematic uncertainties in the decomposition due to the limited S/N or insufficient host contribution. However, in all of the analyzed cases, PCA is successful in decomposing both components, even those where S/N and the equivalent width are low, e.g., J141123.

In addition, some objects from the Bentz collection show a large variability and seem to not follow the ${R}_{{\rm{H}}\beta }\mbox{--}{L}_{5100}$ relation. For example, the Hβ broad component in NGC 5548 appears and disappears over the years (e.g., Sergeev et al. 2007) and shows a steeper radius–luminosity relation (Peterson et al. 2004). However, variations in the measurements seem to be included in the intrinsic scatter of the ${R}_{{\rm{H}}\beta }\mbox{--}{L}_{5100}$ relation (Kilerci Eser et al. 2015). Therefore, we decided to keep these peculiar sources in our analysis. The location of NGC 5548 is marked in all the plots.

Some of the sources from the sample deviate from the classical R_Hβ–L₅₁₀₀ relation (Grier et al. 2017; Czerny et al. 2019), and our aim is to find properties that characterize their departure from the scaling law in the best way. Du et al. (2016) suggested that accretion rate is the key parameter from which we calculate the related parameters uniformly for our sample.

In order to have an agreement in the computations of AGN parameters, we recompute the values following the same methods and using the same constant factors. The black hole mass (M_BH) is estimated following the well-known relation

$$\begin{eqnarray}&&{M}_{\mathrm{BH}}={f}_{\mathrm{BLR}}\displaystyle \frac{{R}_{{\rm{H}}\beta }\,{v}^{2}}{G},\end{eqnarray} \tag{ 1 }$$

where G is the gravitational constant, f_BLR is the virial factor, R_Hβ is the BLR size, and v is the velocity field in the BLR, which is typically represented by the FWHM or the line dispersion (σ_line,rms) of the emission line measured in the rms spectrum.

The virial factor takes into account the geometry, kinematics, and inclination angle of the BLR. Many formalisms have been proposed for its description, for example, Peterson et al. (2004), Onken et al. (2004), Collin et al. (2006), Mejía-Restrepo et al. (2018), and Yu et al. (2019). The best method to calibrate the virial factor is through a comparison with an independent measurement of the black hole mass, for example, the one obtained from the relation between the M_BH and the bulge or spheroid stellar velocity dispersion (σ_*), the relation M_BH–σ_* (e.g., Woo et al. 2015). However, in some cases, it is hard to get a proper measurement of the stellar absorption features, particularly in high-redshift sources. Also, it has not been tested considering super-Eddington sources. The large uncertainties associated with the virial factor introduce an error in the M_BH determination by a factor of 2–3.

In this work, we are going to consider the FWHM as the velocity field in the BLR. Recently, Mejía-Restrepo et al. (2018) proposed that the virial factor is anticorrelated with the FWHM of broad emission lines. For the Hβ line, the relation is given by

$$\begin{eqnarray}&&{f}_{\mathrm{BLR}}^{{\rm{c}}}={\left(\displaystyle \frac{{\mathrm{FWHM}}_{\mathrm{obs}}}{4550\pm 1000}\right)}^{-1.17},\end{eqnarray} \tag{ 2 }$$

with FWHM_obs in units of km s⁻¹. A similar relation has recently been found by Yu et al. (2019) but with an exponent of −1.11. This representation could indicate a disklike geometry for the BLR and/or cloud motions or winds induced by the radiation force. In order to explore the effects of a different virial factor expression over the black hole mass and accretion parameters (Eddington ratio and dimensionless accretion rate), we have computed the M_BH using the typical value f_BLR = 1 and ${f}_{\mathrm{BLR}}^{{\rm{c}}}\propto$ FWHM^−1.17 (see Section 3.3). In Table 2, we report mass M_BH considering f_BLR = 1.

Table 2.  Observational Properties for the Full Sample

Object	log MBH	log $\dot{{\mathscr{M}}}$	${L}_{\mathrm{bol}}/{L}_{\mathrm{Edd}}$	log ${\rm{\Delta }}{R}_{{\rm{H}}\beta }$	fBLRc	Fvar
	(M⊙)
(1)	(2)	(3)	(4)	(5)	(6)	(7)
SEAMBH Sample
Mrk 335	${7.08}_{-0.13}^{+0.16}$	${0.97}_{-0.27}^{+0.33}$	${0.33}_{-0.13}^{+0.15}$	$-{0.25}_{-0.12}^{+0.15}$	2.48 ± 0.24	0.030 (1)
Mrk 142	${6.50}_{-0.23}^{+0.50}$	${1.88}_{-0.47}^{+0.99}$	${0.85}_{-0.50}^{+1.00}$	$-{0.50}_{-0.23}^{+0.50}$	3.43 ± 0.15	0.066 (1)
IRAS F12397	${6.79}_{-0.28}^{+0.37}$	${2.25}_{-0.57}^{+0.74}$	${1.89}_{-1.30}^{+1.65}$	$-{0.66}_{-0.09}^{+0.25}$	2.96 ± 1.07	0.041 (1)
Mrk 486	${7.24}_{-0.06}^{+0.14}$	${0.54}_{-0.14}^{+0.29}$	${0.19}_{-0.05}^{+0.08}$	${0.01}_{-0.07}^{+0.14}$	2.71 ± 0.11	0.034 (1)
Mrk 382	${6.50}_{-0.21}^{+0.24}$	${1.18}_{-0.44}^{+0.50}$	${0.29}_{-0.16}^{+0.18}$	$-{0.18}_{-0.13}^{+0.18}$	3.77 ± 0.89	0.041 (1)
IRAS 04416	${6.78}_{-0.05}^{+0.45}$	${2.63}_{-0.11}^{+0.91}$	${3.34}_{-0.82}^{+3.57}$	$-{0.65}_{-0.06}^{+0.46}$	3.60 ± 0.12	0.020 (1)
MCG 06	${6.92}_{-0.10}^{+0.16}$	$-{0.34}_{-0.26}^{+0.36}$	${0.04}_{-0.02}^{+0.02}$	${0.56}_{-0.12}^{+0.17}$	4.20 ± 0.29	0.092 (1)
Mrk 493	${6.14}_{-0.10}^{+0.05}$	${1.88}_{-0.23}^{+0.15}$	${0.65}_{-0.23}^{+0.19}$	${0.01}_{-0.11}^{+0.07}$	7.90 ± 0.14	0.031 (1)
Mrk 1044	${6.46}_{-0.11}^{+0.14}$	${1.22}_{-0.27}^{+0.31}$	${0.30}_{-0.12}^{+0.13}$	$-{0.02}_{-0.13}^{+0.15}$	4.86 ± 0.11	0.037 (1)
J080101	${6.78}_{-0.14}^{+0.51}$	${2.33}_{-0.29}^{+1.02}$	${2.12}_{-0.82}^{+2.51}$	$-{0.75}_{-0.15}^{+0.51}$	2.73 ± 0.03	0.039
J081456	${7.44}_{-0.29}^{+0.14}$	${0.59}_{-0.59}^{+0.29}$	${0.24}_{-0.17}^{+0.09}$	$-{0.14}_{-0.30}^{+0.14}$	2.10 ± 0.06	0.031
J093922	${6.53}_{-0.23}^{+0.08}$	${2.53}_{-0.46}^{+0.17}$	${2.37}_{-1.36}^{+0.67}$	$-{0.49}_{-0.23}^{+0.09}$	4.71 ± 0.07	0.036
J080131	${6.57}_{-0.14}^{+0.29}$	${2.27}_{-0.29}^{+0.57}$	${1.64}_{-0.64}^{+1.14}$	$-{0.44}_{-0.15}^{+0.29}$	4.37 ± 0.05	0.047
J085946	${7.30}_{-0.33}^{+0.24}$	${1.50}_{-0.66}^{+0.48}$	${0.88}_{-0.69}^{+0.52}$	$-{0.14}_{-0.30}^{+0.14}$	3.13 ± 0.03	0.048
J102339	${7.17}_{-0.07}^{+0.35}$	${1.29}_{-0.15}^{+0.69}$	${0.58}_{-0.15}^{+0.48}$	$-{0.18}_{-0.08}^{+0.35}$	3.09 ± 0.06	0.032
J074352	${7.93}_{-0.04}^{+0.05}$	${1.68}_{-0.09}^{+0.11}$	${1.88}_{-0.43}^{+0.45}$	$-{0.61}_{-0.07}^{+0.08}$	1.53 ± 0.02	0.060
J075051	${7.68}_{-0.06}^{+0.12}$	${2.14}_{-0.13}^{+0.24}$	${3.11}_{-0.78}^{+1.08}$	$-{0.41}_{-0.08}^{+0.13}$	2.77 ± 0.02	0.032
J075101	${7.22}_{-0.08}^{+0.11}$	${1.40}_{-0.18}^{+0.22}$	${0.71}_{-0.21}^{+0.23}$	$-{0.17}_{-0.09}^{+0.11}$	3.21 ± 0.08	0.065
J075949	${7.44}_{-0.19}^{+0.33}$	${0.90}_{-0.39}^{+0.66}$	${0.39}_{-0.19}^{+0.31}$	${0.01}_{-0.19}^{+0.33}$	2.99 ± 0.03	0.094
J081441	${7.20}_{-0.13}^{+0.18}$	${1.02}_{-0.27}^{+0.36}$	${0.39}_{-0.14}^{+0.18}$	$-{0.10}_{-0.13}^{+0.18}$	2.99 ± 0.03	0.051
J083553	${6.88}_{-0.19}^{+0.19}$	${2.40}_{-0.38}^{+0.38}$	${2.53}_{-1.22}^{+1.22}$	$-{0.67}_{-0.19}^{+0.19}$	3.04 ± 0.03	0.052
J084533	${6.78}_{-0.11}^{+0.14}$	${2.72}_{-0.23}^{+0.29}$	${3.82}_{-1.27}^{+1.49}$	$-{0.55}_{-0.12}^{+0.15}$	4.34 ± 0.05	0.040
J093302	${7.08}_{-0.10}^{+0.09}$	${1.79}_{-0.28}^{+0.26}$	${1.17}_{-0.50}^{+0.48}$	$-{0.41}_{-0.12}^{+0.12}$	2.96 ± 0.05	0.036
J100402	${7.44}_{-0.06}^{+0.59}$	${2.89}_{-0.11}^{+1.17}$	${8.29}_{-2.00}^{+11.32}$	$-{0.83}_{-0.08}^{+0.59}$	2.49 ± 0.001	0.048
J101000	${7.46}_{-0.12}^{+0.37}$	${1.71}_{-0.24}^{+0.74}$	${1.37}_{-0.47}^{+1.19}$	$-{0.49}_{-0.13}^{+0.37}$	2.21 ± 0.001	0.065
SDSS Sample
J140812	${7.59}_{-0.14}^{+0.12}$	$-{0.96}_{-0.29}^{+0.24}$	${0.03}_{-0.01}^{+0.01}$	$-{0.05}_{-0.10}^{+0.06}$	1.06 ± 0.16	0.043
J141923	${7.30}_{-0.06}^{+0.03}$	$-{0.43}_{-0.11}^{+0.06}$	${0.05}_{-0.01}^{+0.01}$	${0.01}_{-0.07}^{+0.05}$	1.66 ± 0.01	0.076
J140759	${7.63}_{-0.18}^{+0.35}$	$-{0.41}_{-0.35}^{+0.70}$	${0.06}_{-0.03}^{+0.05}$	$-{0.09}_{-0.18}^{+0.35}$	1.29 ± 0.01	0.038
J141729	${7.96}_{-0.17}^{+0.45}$	$-{1.49}_{-0.34}^{+0.90}$	${0.01}_{-0.01}^{+0.02}$	$-{0.41}_{-0.17}^{+0.45}$	0.44 ± 0.01	0.033
J141645.15	${7.73}_{-0.12}^{+0.13}$	$-{1.15}_{-0.24}^{+0.26}$	${0.02}_{-0.01}^{+0.01}$	$-{0.41}_{-0.13}^{+0.14}$	0.57 ± 0.01	0.068
J142135	${6.86}_{-0.10}^{+0.10}$	${0.98}_{-0.20}^{+0.20}$	${0.28}_{-0.09}^{+0.09}$	$-{0.66}_{-0.11}^{+0.11}$	1.57 ± 0.04	0.038
J141625	${7.56}_{-0.13}^{+0.09}$	${0.31}_{-0.27}^{+0.19}$	${0.17}_{-0.06}^{+0.05}$	$-{0.33}_{-0.14}^{+0.10}$	1.35 ± 0.01	0.058
J142103	${8.12}_{-0.02}^{+0.02}$	$-{1.30}_{-0.06}^{+0.05}$	${0.02}_{-0.005}^{+0.005}$	${0.54}_{-0.04}^{+0.04}$	1.63 ± 0.03	⋯
J142038	${8.04}_{-0.10}^{+0.08}$	$-{1.40}_{-0.20}^{+0.16}$	${0.02}_{-0.01}^{+0.01}$	${0.16}_{-0.10}^{+0.09}$	0.96 ± 0.01	0.065
J142043	${7.36}_{-0.05}^{+0.04}$	$-{0.12}_{-0.10}^{+0.07}$	${0.08}_{-0.02}^{+0.02}$	$-{0.44}_{-0.06}^{+0.05}$	1.03 ± 0.03	0.036
J141041	${8.04}_{-0.05}^{+0.08}$	$-{0.85}_{-0.10}^{+0.17}$	${0.04}_{-0.01}^{+0.01}$	$-{0.09}_{-0.06}^{+0.09}$	0.89 ± 0.01	0.074
J141318	${7.66}_{-0.07}^{+0.03}$	${0.08}_{-0.13}^{+0.05}$	${0.13}_{-0.03}^{+0.03}$	$-{0.19}_{-0.07}^{+0.04}$	1.39 ± 0.02	0.060
J141955	${7.99}_{-0.19}^{+0.24}$	$-{1.39}_{-0.39}^{+0.48}$	${0.02}_{-0.01}^{+0.01}$	$-{0.18}_{-0.18}^{+0.23}$	0.63 ± 0.06	0.066
J141645.58	${6.90}_{-0.07}^{+0.13}$	${1.21}_{-0.15}^{+0.26}$	${0.42}_{-0.11}^{+0.15}$	$-{0.43}_{-0.08}^{+0.13}$	2.37 ± 0.06	0.053
J141324	${8.27}_{-0.10}^{+0.19}$	$-{1.12}_{-0.20}^{+0.37}$	${0.03}_{-0.01}^{+0.02}$	$-{0.09}_{-0.10}^{+0.19}$	0.71 ± 0.02	0.046
J141214	${7.47}_{-0.16}^{+0.13}$	${1.15}_{-0.33}^{+0.26}$	${0.58}_{-0.25}^{+0.21}$	$-{0.41}_{-0.13}^{+0.09}$	1.88 ± 0.25	0.034
J140518	${7.98}_{-0.09}^{+0.15}$	${0.04}_{-0.17}^{+0.31}$	${0.16}_{-0.04}^{+0.06}$	$-{0.09}_{-0.09}^{+0.16}$	1.40 ± 0.01	0.072
J141018	${7.77}_{-0.13}^{+0.10}$	$-{0.68}_{-0.27}^{+0.20}$	${0.04}_{-0.02}^{+0.01}$	$-{0.10}_{-0.13}^{+0.08}$	1.06 ± 0.09	0.044
J141123	${7.63}_{-0.03}^{+0.05}$	${0.42}_{-0.06}^{+0.10}$	${0.22}_{-0.05}^{+0.05}$	$-{0.48}_{-0.04}^{+0.06}$	1.13 ± 0.01	0.071
J142039	${7.87}_{-0.07}^{+0.03}$	$-{0.03}_{-0.13}^{+0.05}$	${0.13}_{-0.03}^{+0.03}$	$-{0.29}_{-0.07}^{+0.04}$	1.08 ± 0.03	0.079
J141724	${7.73}_{-0.12}^{+0.54}$	${0.01}_{-0.23}^{+1.08}$	${0.12}_{-0.04}^{+0.16}$	$-{0.52}_{-0.12}^{+0.54}$	0.85 ± 0.01	0.064
J141004	${7.95}_{-0.04}^{+0.04}$	$-{0.08}_{-0.07}^{+0.08}$	${0.13}_{-0.03}^{+0.03}$	${0.08}_{-0.05}^{+0.05}$	1.68 ± 0.04	0.028
J141706	${6.76}_{-0.13}^{+0.26}$	${2.25}_{-0.25}^{+0.53}$	${1.83}_{-0.65}^{+1.17}$	$-{0.61}_{-0.13}^{+0.26}$	3.20 ± 0.03	0.052
J142010	${7.96}_{-0.17}^{+0.21}$	$-{0.30}_{-0.34}^{+0.42}$	${0.09}_{-0.04}^{+0.05}$	$-{0.47}_{-0.16}^{+0.20}$	0.72 ± 0.08	0.133
J141712	${7.08}_{-0.18}^{+0.17}$	${0.14}_{-0.36}^{+0.34}$	${0.09}_{-0.04}^{+0.04}$	$-{0.01}_{-0.10}^{+0.08}$	2.31 ± 0.49	0.189
J141115	${8.06}_{-0.02}^{+0.10}$	$-{0.15}_{-0.04}^{+0.20}$	${0.12}_{-0.03}^{+0.04}$	${0.003}_{-0.04}^{+0.10}$	1.39 ± 0.02	0.064
J141112	${7.49}_{-0.04}^{+0.05}$	${0.70}_{-0.09}^{+0.11}$	${0.30}_{-0.07}^{+0.07}$	$-{0.28}_{-0.05}^{+0.06}$	1.79 ± 0.03	0.037
J141417	${8.11}_{-0.18}^{+0.14}$	$-{1.63}_{-0.36}^{+0.28}$	${0.01}_{-0.01}^{+0.01}$	$-{0.01}_{-0.15}^{+0.10}$	0.66 ± 0.09	0.149
J141031	${7.93}_{-0.13}^{+0.03}$	$-{0.34}_{-0.26}^{+0.06}$	${0.08}_{-0.03}^{+0.02}$	${0.02}_{-0.13}^{+0.03}$	1.36 ± 0.05	0.053
J141941	${7.68}_{-0.12}^{+0.06}$	${0.92}_{-0.24}^{+0.12}$	${0.48}_{-0.17}^{+0.12}$	$-{0.32}_{-0.12}^{+0.07}$	1.75 ± 0.03	0.055
J141135	${7.34}_{-0.18}^{+0.21}$	${0.87}_{-0.37}^{+0.43}$	${0.35}_{-0.16}^{+0.18}$	$-{0.30}_{-0.19}^{+0.21}$	2.00 ± 0.06	0.096
J140904	${8.39}_{-0.19}^{+0.33}$	$-{1.07}_{-0.39}^{+0.67}$	${0.04}_{-0.02}^{+0.03}$	$-{0.54}_{-0.18}^{+0.32}$	0.38 ± 0.05	0.099
J142052	${7.49}_{-0.04}^{+0.05}$	${2.10}_{-0.07}^{+0.10}$	${2.54}_{-0.56}^{+0.58}$	$-{1.02}_{-0.06}^{+0.07}$	1.30 ± 0.01	0.022
J141147	${6.84}_{-0.10}^{+0.10}$	${1.86}_{-0.20}^{+0.21}$	${1.06}_{-0.32}^{+0.33}$	$-{0.73}_{-0.10}^{+0.11}$	2.18 ± 0.07	0.092
J141532	${7.13}_{-0.15}^{+0.16}$	${1.43}_{-0.29}^{+0.33}$	${0.70}_{-0.27}^{+0.30}$	$-{0.18}_{-0.15}^{+0.17}$	3.36 ± 0.09	0.274
J142023	${7.52}_{-0.20}^{+0.17}$	${0.79}_{-0.40}^{+0.33}$	${0.35}_{-0.18}^{+0.15}$	$-{0.72}_{-0.20}^{+0.17}$	1.03 ± 0.04	0.107
J142049	${8.29}_{-0.09}^{+0.09}$	$-{0.43}_{-0.18}^{+0.18}$	${0.10}_{-0.03}^{+0.03}$	$-{0.10}_{-0.10}^{+0.10}$	0.97 ± 0.02	0.097
J142112	${7.74}_{-0.11}^{+0.13}$	${0.49}_{-0.22}^{+0.25}$	${0.26}_{-0.08}^{+0.09}$	$-{0.54}_{-0.10}^{+0.12}$	1.03 ± 0.08	0.075
J141606	${8.52}_{-0.21}^{+0.16}$	$-{0.36}_{-0.42}^{+0.32}$	${0.13}_{-0.07}^{+0.05}$	$-{0.45}_{-0.21}^{+0.16}$	0.57 ± 0.02	0.071
J141859	${8.00}_{-0.15}^{+0.12}$	${0.85}_{-0.30}^{+0.24}$	${0.56}_{-0.22}^{+0.19}$	$-{0.70}_{-0.16}^{+0.13}$	0.90 ± 0.01	0.056
J141952	${8.59}_{-0.08}^{+0.08}$	$-{1.31}_{-0.15}^{+0.16}$	${0.03}_{-0.01}^{+0.01}$	$-{0.14}_{-0.07}^{+0.08}$	0.54 ± 0.03	0.166
J142417	${7.32}_{-0.10}^{+0.09}$	${0.98}_{-0.22}^{+0.20}$	${0.40}_{-0.13}^{+0.13}$	$-{0.01}_{-0.08}^{+0.07}$	3.12 ± 0.31	0.275
J141856†	${7.48}_{-0.05}^{+0.17}$	${2.60}_{-0.11}^{+0.33}$	${5.50}_{-1.31}^{+2.37}$	$-{1.06}_{-0.08}^{+0.17}$	1.56 ± 0.03	0.144
J141314†	${7.23}_{-0.12}^{+0.12}$	${1.81}_{-0.25}^{+0.25}$	${1.34}_{-0.47}^{+0.48}$	$-{0.16}_{-0.06}^{+0.06}$	3.93 ± 0.60	0.216
Bentz Collection
PG 0026+129	${7.81}_{-0.27}^{+0.27}$	${1.33}_{-0.55}^{+0.44}$	${1.00}_{-0.66}^{+0.65}$	${0.001}_{-0.12}^{+0.11}$	3.12 ± 1.05	0.173 (2)
PG 0052+251	${8.48}_{-0.14}^{+0.14}$	$-{0.27}_{-0.28}^{+0.43}$	${0.14}_{-0.06}^{+0.06}$	$-{0.004}_{-0.12}^{+0.13}$	1.11 ± 0.12	0.199 (2)
Fairall 9	${8.21}_{-0.14}^{+0.12}$	$-{0.96}_{-0.29}^{+0.50}$	${0.04}_{-0.02}^{+0.01}$	$-{0.28}_{-0.11}^{+0.09}$	0.61 ± 0.07	0.328 (2)
Mrk 590	${7.39}_{-0.29}^{+0.30}$	$-{0.05}_{-0.66}^{+0.43}$	${0.09}_{-0.07}^{+0.08}$	${0.15}_{-0.15}^{+0.16}$	2.32 ± 0.86	0.108 (2)
3C 120	${7.46}_{-0.21}^{+0.23}$	${0.58}_{-0.45}^{+0.40}$	${0.24}_{-0.14}^{+0.15}$	$-{0.11}_{-0.13}^{+0.16}$	2.14 ± 0.53	0.178 (2)
Ark 120	${8.36}_{-0.10}^{+0.11}$	$-{1.42}_{-0.43}^{+0.43}$	${0.02}_{-0.01}^{+0.01}$	${0.14}_{-0.16}^{+0.17}$	0.82 ± 0.06	0.072 (2)
Mrk 79	${7.86}_{-0.31}^{+0.32}$	$-{0.71}_{-0.63}^{+0.43}$	${0.05}_{-0.03}^{+0.04}$	$-{0.16}_{-0.14}^{+0.16}$	0.93 ± 0.35	0.091 (2)
PG 0804+761	${8.07}_{-0.37}^{+0.37}$	${0.72}_{-0.74}^{+0.43}$	${0.48}_{-0.42}^{+0.42}$	${0.16}_{-0.07}^{+0.07}$	2.60 ± 1.28	0.176 (2)
Mrk 110	${7.05}_{-0.48}^{+0.49}$	${0.88}_{-0.98}^{+0.43}$	${0.28}_{-0.32}^{+0.33}$	${0.06}_{-0.14}^{+0.17}$	3.68 ± 2.31	0.184 (2)
PG 0953+414	${8.42}_{-0.13}^{+0.13}$	${0.42}_{-0.27}^{+0.44}$	${0.40}_{-0.15}^{+0.14}$	${0.02}_{-0.08}^{+0.08}$	1.63 ± 0.25	0.136 (2)
NGC 3227	${6.98}_{-0.09}^{+0.09}$	$-{1.11}_{-0.25}^{+0.43}$	${0.01}_{-0.005}^{+0.005}$	$-{0.01}_{-0.13}^{+0.13}$	1.32 ± 0.04	0.094 (2)
NGC 3516	${7.79}_{-0.06}^{+0.04}$	$-{1.90}_{-0.33}^{+0.45}$	${0.01}_{-0.004}^{+0.004}$	${0.19}_{-0.13}^{+0.13}$	0.86 ± 0.02	0.289 (2)
SBS 1116+583A	${6.77}_{-0.29}^{+0.29}$	$-{0.84}_{-0.67}^{+0.43}$	${0.02}_{-0.01}^{+0.01}$	$-{0.17}_{-0.17}^{+0.18}$	1.31 ± 0.48	0.043(3)
Arp 151	${6.64}_{-0.09}^{+0.08}$	${0.03}_{-0.24}^{+0.48}$	${0.06}_{-0.02}^{+0.02}$	$-{0.15}_{-0.11}^{+0.10}$	2.16 ± 0.15	0.120(3)
NGC 3783	${7.28}_{-0.18}^{+0.20}$	$-{1.24}_{-0.45}^{+0.40}$	${0.01}_{-0.01}^{+0.01}$	${0.25}_{-0.15}^{+0.18}$	1.57 ± 0.31	0.192 (2)
Mrk 1310	${6.27}_{-0.15}^{+0.15}$	${0.39}_{-0.37}^{+0.43}$	${0.07}_{-0.04}^{+0.04}$	$-{0.05}_{-0.12}^{+0.12}$	3.39 ± 0.62	0.051(3)
NGC 4051	${5.64}_{-0.15}^{+0.19}$	${1.05}_{-0.38}^{+0.37}$	${0.12}_{-0.07}^{+0.07}$	$-{0.08}_{-0.18}^{+0.22}$	5.66 ± 0.26	0.059 (2)
NGC 4151	${7.46}_{-0.15}^{+0.16}$	$-{2.29}_{-0.43}^{+0.42}$	${0.003}_{-0.002}^{+0.002}$	${0.31}_{-0.14}^{+0.15}$	0.96 ± 0.18	0.058 (2)
Mrk 202	${6.03}_{-0.23}^{+0.29}$	${0.82}_{-0.50}^{+0.35}$	${0.12}_{-0.08}^{+0.09}$	$-{0.12}_{-0.19}^{+0.27}$	4.13 ± 0.89	0.027(3)
NGC 4253	${5.93}_{-1.31}^{+1.32}$	${1.49}_{-2.64}^{+0.43}$	${0.30}_{-0.92}^{+0.92}$	${0.03}_{-0.12}^{+0.14}$	7.28 ± 12.87	0.053(3)
PG 1229+204	${7.94}_{-0.19}^{+0.33}$	$-{0.84}_{-0.39}^{+0.26}$	${0.04}_{-0.02}^{+0.03}$	${0.21}_{-0.18}^{+0.32}$	1.40 ± 0.15	0.107 (2)
NGC 4593	${7.15}_{-0.14}^{+0.14}$	$-{0.89}_{-0.62}^{+0.43}$	${0.02}_{-0.02}^{+0.02}$	$-{0.19}_{-0.22}^{+0.22}$	1.08 ± 0.16	0.114 (2)
NGC 4748	${6.20}_{-0.21}^{+0.18}$	${0.93}_{-0.47}^{+0.51}$	${0.16}_{-0.09}^{+0.08}$	$-{0.02}_{-0.20}^{+0.15}$	4.70 ± 0.79	0.045(3)
PG 1307+085	${8.72}_{-0.21}^{+0.17}$	$-{0.68}_{-0.42}^{+0.53}$	${0.09}_{-0.05}^{+0.04}$	${0.04}_{-0.20}^{+0.15}$	0.88 ± 0.11	0.113 (2)
Mrk 279	${7.57}_{-0.14}^{+0.14}$	$-{0.10}_{-0.29}^{+0.43}$	${0.09}_{-0.04}^{+0.04}$	$-{0.15}_{-0.11}^{+0.11}$	1.41 ± 0.17	0.082 (2)
PG 1411+442	${8.15}_{-0.25}^{+0.25}$	${0.04}_{-0.50}^{+0.44}$	${0.18}_{-0.11}^{+0.11}$	${0.27}_{-0.22}^{+0.22}$	2.12 ± 0.36	0.105 (2)
PG 1426+015	${8.87}_{-0.25}^{+0.22}$	$-{1.31}_{-0.49}^{+0.48}$	${0.04}_{-0.02}^{+0.02}$	${0.12}_{-0.17}^{+0.14}$	0.68 ± 0.16	0.173 (2)
Mrk 817	${7.82}_{-0.29}^{+0.33}$	$-{0.54}_{-0.60}^{+0.38}$	${0.06}_{-0.04}^{+0.05}$	$-{0.09}_{-0.16}^{+0.22}$	1.12 ± 0.38	0.050 (4)
Mrk 290	${7.49}_{-0.06}^{+0.07}$	$-{0.74}_{-0.15}^{+0.40}$	${0.03}_{-0.01}^{+0.01}$	$-{0.14}_{-0.07}^{+0.08}$	1.08 ± 0.05	0.180 (4)
PG 1613+658	${8.69}_{-0.26}^{+0.26}$	$-{0.73}_{-0.51}^{+0.44}$	${0.08}_{-0.05}^{+0.05}$	$-{0.34}_{-0.17}^{+0.17}$	0.52 ± 0.14	0.123 (2)
PG 1617+175	${8.49}_{-0.27}^{+0.26}$	$-{0.91}_{-0.55}^{+0.46}$	${0.05}_{-0.04}^{+0.03}$	${0.12}_{-0.21}^{+0.18}$	0.96 ± 0.24	0.191 (2)
PG 1700+518	${8.23}_{-0.33}^{+0.33}$	${1.42}_{-0.66}^{+0.43}$	${1.58}_{-1.23}^{+1.24}$	${0.03}_{-0.09}^{+0.10}$	2.87 ± 1.24	0.060 (2)
3C 390.3	${8.98}_{-0.23}^{+0.32}$	$-{1.81}_{-0.98}^{+0.40}$	${0.02}_{-0.03}^{+0.03}$	$-{0.11}_{-0.35}^{+0.41}$	0.38 ± 0.08	0.343 (2)
NGC 6814	${7.14}_{-0.10}^{+0.10}$	$-{1.62}_{-0.47}^{+0.43}$	${0.01}_{-0.005}^{+0.005}$	${0.29}_{-0.18}^{+0.18}$	1.47 ± 0.16	0.068(3)
Mrk 509	${8.06}_{-0.04}^{+0.05}$	$-{0.34}_{-0.11}^{+0.42}$	${0.09}_{-0.02}^{+0.02}$	${0.27}_{-0.05}^{+0.05}$	1.83 ± 0.08	0.181 (2)
PG 2130+099	${6.92}_{-0.07}^{+0.07}$	${1.96}_{-0.14}^{+0.43}$	${1.33}_{-0.35}^{+0.35}$	$-{0.65}_{-0.06}^{+0.06}$	2.48 ± 0.14	0.086 (2)
NGC 7469	${6.38}_{-0.09}^{+0.15}$	${1.99}_{-0.24}^{+0.30}$	${0.92}_{-0.35}^{+0.44}$	$-{0.23}_{-0.09}^{+0.15}$	5.46 ± 0.50	0.150 (2)
PG 1211+143	${7.87}_{-0.20}^{+0.12}$	${0.84}_{-0.41}^{+0.66}$	${0.50}_{-0.26}^{+0.19}$	${0.06}_{-0.20}^{+0.13}$	2.60 ± 0.06	0.134 (2)
PG 0844+349	${7.57}_{-0.21}^{+0.22}$	${0.67}_{-0.44}^{+0.43}$	${0.30}_{-0.17}^{+0.17}$	$-{0.13}_{-0.19}^{+0.19}$	2.08 ± 0.33	0.105 (2)
NGC 5273	${6.96}_{-0.32}^{+0.24}$	$-{2.13}_{-0.69}^{+0.55}$	${0.003}_{-0.002}^{+0.002}$	${0.13}_{-0.34}^{+0.27}$	0.98 ± 0.08	0.059(5)
Mrk 1511	${7.29}_{-0.07}^{+0.07}$	$-{0.34}_{-0.17}^{+0.41}$	${0.05}_{-0.02}^{+0.02}$	$-{0.32}_{-0.08}^{+0.09}$	1.11 ± 0.04	0.150(6)
KA 1858-4850	${6.78}_{-0.08}^{+0.08}$	${1.07}_{-0.18}^{+0.48}$	${0.31}_{-0.09}^{+0.09}$	$-{0.09}_{-0.09}^{+0.08}$	3.63 ± 0.19	0.084(7)
MCG 6-30-15	${6.35}_{-0.28}^{+0.29}$	$-{0.75}_{-0.59}^{+0.43}$	${0.01}_{-0.01}^{+0.01}$	${0.49}_{-0.16}^{+0.17}$	3.90 ± 1.34	0.132(8)
UGC 06728	${5.56}_{-0.25}^{+0.22}$	${1.17}_{-0.52}^{+0.49}$	${0.14}_{-0.09}^{+0.08}$	$-{0.24}_{-0.26}^{+0.24}$	5.03 ± 0.30	0.090(9)
MCG +08-11-011	${6.62}_{-0.02}^{+0.02}$	${1.25}_{-0.17}^{+0.43}$	${0.36}_{-0.12}^{+0.12}$	${0.03}_{-0.07}^{+0.07}$	4.95 ± 0.04	0.100 (10)
NGC 2617	${7.37}_{-0.14}^{+0.11}$	$-{1.26}_{-0.36}^{+0.48}$	${0.01}_{-0.01}^{+0.01}$	$-{0.18}_{-0.17}^{+0.15}$	0.84 ± 0.01	0.090 (10)
3C 382	${8.02}_{-0.04}^{+0.11}$	$-{0.79}_{-0.17}^{+0.28}$	${0.05}_{-0.01}^{+0.02}$	${0.17}_{-0.07}^{+0.11}$	1.31 ± 0.12	0.090 (10)
Mrk 374	${7.49}_{-0.10}^{+0.17}$	${0.18}_{-0.20}^{+0.26}$	${0.13}_{-0.04}^{+0.06}$	$-{0.24}_{-0.10}^{+0.17}$	1.48 ± 0.01	0.030 (10)
Lu et al. (2016)
NGC 5548	${8.14}_{-0.04}^{+0.08}$	$-{1.98}_{-0.20}^{+0.25}$	${0.008}_{-0.003}^{+0.003}$	$-{0.25}_{-0.08}^{+0.11}$	0.40 ± 0.02	0.230 (11)
Zhang et al. (2019)
3C 273	${8.50}_{-0.04}^{+0.03}$	${1.44}_{-0.08}^{+0.06}$	${2.01}_{-0.45}^{+0.43}$	$-{0.41}_{-0.08}^{+0.08}$	1.45 ± 0.03	0.052 (2)

Note. Columns are as follows. (1) Object name. Discarded objects of the analysis are marked with a † symbol. (2) Black hole mass in units of solar masses. (3) Dimensionless accretion rate; see Equation (3). (4) Eddington ratio. (5) Deviations of BLR size from ${R}_{{\rm{H}}\beta }\mbox{--}{L}_{5100}$ relation. (6) Virial factor anticorrelated with the FWHM of Hβ; see Equation (2). (7) F_var value defined in Equation (5). In some cases, the origin of the estimation is specified: (1) Hu et al. (2015), (2) Peterson et al. (2004), (3) Bentz et al. (2009), (4) Denney et al. (2010), (5) Bentz et al. (2014), (6) Barth et al. (2013), (7) Pei et al. (2014), (8) Bentz et al. (2016a), (9) Bentz et al. (2016b), (10) Fausnaugh et al. (2017), (11) Lu et al. (2016). The F_var was estimated for the sources without references. Columns 2, 3, 4, and 5 were computed considering f_BLR = 1.

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In order to estimate the accretion rate, we use the dimensionless accretion rate introduced by Du et al. (2016),

$$\begin{eqnarray}&&\dot{{\mathscr{M}}}=20.1{\left(\displaystyle \frac{{l}_{44}}{\cos \theta }\right)}^{3/2}{m}_{7}^{-2},\end{eqnarray} \tag{ 3 }$$

where l₄₄ is the luminosity at 5100 Å in units of 10⁴⁴ erg s⁻¹, θ is the inclination angle of the disk to the line of sight, and m₇ is the black hole mass in units of 10⁷ M_⊙. We considered cos θ = 0.75, which is the mean disk inclination for type 1 AGNs. It is estimated considering a torus axis coaligned with the disk axis and a torus covering factor of 0.5 (Du et al. 2016). The justification for this assumption is discussed in Section 5.2. Sources with $\dot{{\mathscr{M}}}$ ≳ 3 are highly accreting AGNs and host a slim accretion disk (Wang et al. 2014c). The $\dot{{\mathscr{M}}}$ with f_BLR = 1 is reported in column 3 of Table 2.

The SEAMBH sample has, on average, the largest dimensionless accretion rate, $\dot{{\mathscr{M}}}$ $={139.5}_{-25.8}^{+96.8}$, which is expected due to the selection criteria of the sample. The SDSS-RM sample has the mean $\dot{{\mathscr{M}}}$ $={11.9}_{-2.7}^{+5.3}$, where one-third of the sources are classified as high accretors. The Bentz collection has the smallest mean value, $\dot{{\mathscr{M}}}$ $={7.9}_{-4.3}^{+4.5}$. As for the two remaining objects, 3C 273 is classified as a high accretor ($\dot{{\mathscr{M}}}$ $={27.4}_{-5.1}^{+3.9}$), and NGC 5548 is the source with the lowest accretion rate in the sample, $\dot{{\mathscr{M}}}$ $=\,{0.01}_{-0.005}^{+0.006}$.

We also consider the Eddington ratio, ${L}_{\mathrm{bol}}/{L}_{\mathrm{Edd}}$, as an estimation of the accretion rate, where L_bol is the bolometric luminosity and L_Edd is the Eddington luminosity defined by ${L}_{\mathrm{Edd}}=1.5\times {10}^{38}\left(\tfrac{{M}_{\mathrm{BH}}}{{M}_{\odot }}\right)$. In order to determine L_bol, we use the bolometric correction factor at 5100 Å proposed by Richards et al. (2006), BC₅₁₀₀ = 10.33. Although ${L}_{\mathrm{bol}}/{L}_{\mathrm{Edd}}$ depends upon the bolometric correction factor used, it has given good results in the identification of high accretion sources, which show ${L}_{\mathrm{bol}}/{L}_{\mathrm{Edd}}$ > 0.2 (Sulentic et al. 2017). The limit considered for $\dot{{\mathscr{M}}}$ and ${L}_{\mathrm{bol}}/{L}_{\mathrm{Edd}}$ in order to identify highly accreting sources is analogous, since both parameters are well correlated (e.g., Capellupo et al. 2016). Average ${L}_{\mathrm{bol}}/{L}_{\mathrm{Edd}}$ values are as follows: ${1.6}_{-0.2}^{+0.5}$, ${0.3}_{-0.03}^{+0.04}$, and 0.2±0.04 for SEAMBH, SDSS-RM, and the Bentz collection, respectively. An ${L}_{\mathrm{bol}}/{L}_{\mathrm{Edd}}$ with a virial factor equal to 1 is shown in the fourth column of Table 2.

Considering the virial factor anticorrelated with the FWHM of Hβ (${f}_{\mathrm{BLR}}^{{\rm{c}}}$), the dimensionless accretion rate and Eddington ratio change by a factor of ${({f}_{\mathrm{BLR}}^{{\rm{c}}})}^{-2}$ and ${({f}_{\mathrm{BLR}}^{{\rm{c}}})}^{-1}$, respectively, i.e.,

$$\begin{eqnarray}\begin{array}{rcl}{\dot{{\mathscr{M}}}}^{{\rm{c}}} & = & {({f}_{\mathrm{BLR}}^{{\rm{c}}})}^{-2}\,\dot{{\mathscr{M}}},\\ \displaystyle \frac{{L}_{\mathrm{bol}}}{{L}_{\mathrm{Edd}}^{{\rm{c}}}} & = & {({f}_{\mathrm{BLR}}^{{\rm{c}}})}^{-1}\left(\displaystyle \frac{{L}_{\mathrm{bol}}}{{L}_{\mathrm{Edd}}}\right).\end{array}\end{eqnarray} \tag{ 4 }$$

Therefore, new values for the accretion parameters can be estimated from the ones reported in Table 2. The virial factor selection changes considerably the accretion parameters and the dispersion associated with other physical parameters (see Section 3.3). We include a discussion of the uncertainties associated with the assumed virial factor and the implications for the presented analysis in Section 5.1.

In order to have an estimation of the optical continuum variability amplitude, we will consider the parameter F_var (Rodríguez-Pascual et al. 1997). It estimates the rms of the intrinsic variability relative to the mean flux,

$$\begin{eqnarray}&&{F}_{\mathrm{var}}=\displaystyle \frac{{({\sigma }^{2}-{{\rm{\Delta }}}^{2})}^{1/2}}{\langle f\rangle },\end{eqnarray} \tag{ 5 }$$

where σ² is the variance of the flux, Δ is the mean square value of the uncertainties (Δ_i) associated with each flux measurement (f_i), and $\langle f\rangle$ is the mean flux. Their definitions are as follows:

$$\begin{eqnarray}\begin{array}{rcl}{\sigma }^{2} & = & \displaystyle \frac{1}{1-N}\displaystyle \sum _{i=1}^{N}{({f}_{i}-\langle f\rangle )}^{2},\\ {{\rm{\Delta }}}^{2} & = & \displaystyle \frac{1}{N}\displaystyle \sum _{i=1}^{N}{{\rm{\Delta }}}_{i}^{2},\\ \langle f\rangle & = & \displaystyle \frac{1}{N}\displaystyle \sum _{i=1}^{N}{f}_{i}.\end{array}\end{eqnarray} \tag{ 6 }$$

The F_var parameter has been reported for all objects of the Bentz collection (Peterson et al. 2004; Bentz et al. 2009, 2014, 2016a, 2016b; Denney et al. 2010; Barth et al. 2013; Pei et al. 2014; Fausnaugh et al. 2017) and some SEAMBH objects (Hu et al. 2015). For the remaining SEAMBH sources, we estimate F_var from the light curves available in the literature (Du et al. 2015, 2016, 2018) following Equations (5) and (6). In the case of the SDSS-RM sample, we use the fractional rms variability provided by Shen et al. (2019; see their Table 2). Using the luminosities reported in Table 1, we can convert this quantity to F_var. The object J142103 shows σ² − Δ² < 0, indicating that it does not present a significant variability, such as the one that has been reported in other objects (e.g., Sánchez et al. 2017). The F_var values are reported in the last column of Table 2.

The radius–luminosity relation used in this paper is given by Bentz et al. (2013),

$$\begin{eqnarray}\begin{array}{rcl}\mathrm{log}\left(\displaystyle \frac{{R}_{{\rm{H}}\beta }}{1\ \mathrm{lt} \mbox{-} \mathrm{day}}\right) & = & (1.527\pm 0.31)\\ & & +\,{0.533}_{-0.033}^{+0.035}\,\mathrm{log}\left(\displaystyle \frac{{L}_{5100}}{{10}^{44}{L}_{\odot }}\right).\end{array}\end{eqnarray} \tag{ 7 }$$

With the information reported in Table 1, we are able to build an R_Hβ–L₅₁₀₀ diagram, which is shown in Figures 1 and 2. In both figures, the variations of the dimensionless accretion rate (left) and Eddington ratio (right) along the diagram, considering f_BLR = 1 (Figure 1) and f_BLR^c ∝ FWHM^−1.17 (Figure 2), are shown. Independent of the selected virial factor, there is a clear trend with the accretion parameters. Sources with high accretion rate values show the largest departures from the ${R}_{{\rm{H}}\beta }\mbox{--}{L}_{5100}$ relation (Du et al. 2015, 2018).

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On the other hand, we also explored whether the FWHM and the equivalent width of the Hβ line show a similar trend along the ${R}_{{\rm{H}}\beta }\mbox{--}{L}_{5100}$ diagram, but we cannot find any clear pattern.

The monitoring performed for the SDSS-RM sample is relatively short (only 180 days), taking into account that their sources are at relatively large redshift, and some of them are rather bright. An expected delay could be close to the duration of the campaign. In addition, the number of spectroscopic measurements is not very high (only 32). This may cast some doubts as to whether the estimated time delays are measured reliably. Thus, we performed simulations of the expected time delays assuming that the sources follow the standard ${R}_{{\rm{H}}\beta }\mbox{--}{L}_{5100}$ relation and using the observational cadence. The results are presented in the Appendix and they show that both the duration of the observation and the cadence should not strongly affect the measured delays.

The SEAMBH team made important progress in understanding the reverberation mapping in highly accreting sources (Wang et al. 2014a; Du et al. 2014, 2015, 2016, 2018; Hu et al. 2015), which have been scarcely included in previous RM samples. They found that AGNs with $\dot{{\mathscr{M}}}$ ≳ 3 have time delays (τ_obs) shorter than expected from the R_Hβ–L₅₁₀₀ relation (Bentz et al. 2013). The deviation can be estimated by the parameter

$$\begin{eqnarray}&&{\rm{\Delta }}{R}_{{\rm{H}}\beta }=\mathrm{log}\left(\displaystyle \frac{{R}_{{\rm{H}}\beta }}{{R}_{{\rm{H}}{\beta }_{{\rm{R}}-{\rm{L}}}}}\right)=\mathrm{log}\left(\displaystyle \frac{{\tau }_{\mathrm{obs}}}{{\tau }_{{\rm{H}}{\beta }_{{\rm{R}}-{\rm{L}}}}}\right),\end{eqnarray} \tag{ 8 }$$

where τ_HβR–L is the time delay corresponding to that expected from the ${R}_{{\rm{H}}\beta }\mbox{--}{L}_{5100}$ relation for the given L₅₁₀₀; see Equation (7). Figures 3 and 4 show ${\rm{\Delta }}{R}_{{\rm{H}}\beta }$ as a function of $\dot{{\mathscr{M}}}$ and ${L}_{\mathrm{bol}}/{L}_{\mathrm{Edd}}$ considering f_BLR and ${f}_{\mathrm{BLR}}^{{\rm{c}}}$. In all four cases, the largest ${\rm{\Delta }}{R}_{{\rm{H}}\beta }$ are associated with the highest $\dot{{\mathscr{M}}}$ and ${L}_{\mathrm{bol}}/{L}_{\mathrm{Edd}}$; the difference is the scatter along the relations. We perform an orthogonal linear fit in order to get the linear trend and estimate the Pearson coefficient (P) and rms error to measure the correlation and dispersion along the trend line. The general linear relation is given by

$$\begin{eqnarray}&&{\rm{\Delta }}{R}_{{\rm{H}}\beta ,X}=\alpha \,\mathrm{log}X+\beta ,\end{eqnarray} \tag{ 9 }$$

where X corresponds to the accretion parameter (dimensionless accretion rate or Eddington ratio) using a virial factor equal to 1 or the one anticorrelated with the FWHM. Coefficients of the fit (α and β), Pearson, and rms values are given in Table 3.

Table 3.  Orthogonal Linear Fit Parameters

	X	α	β	P	rms
(1)	(2)	(3)	(4)	(5)	(6)
fBLR	$\dot{{\mathscr{M}}}$	−0.143 ± 0.018	−0.136 ± 0.023	0.572	0.243
	${L}_{\mathrm{bol}}/{L}_{\mathrm{Edd}}$	−0.271 ± 0.030	−0.396 ± 0.032	0.605	0.626
fBLRc	${\dot{{\mathscr{M}}}}^{{\rm{c}}}$	−0.283 ± 0.017	−0.228 ± 0.016	0.822	0.172
	${L}_{\mathrm{bol}}/{L}_{\mathrm{Edd}}^{{\rm{c}}}$	−0.394 ± 0.030	−0.589 ± 0.036	0.744	0.199

Note. Columns are as follows. (1) Virial factor. (2) Accretion parameter: dimensionless accretion rate or Eddington ratio. (3) Slope of Equation (9). (4) Ordinate of Equation (9). (5) Pearson coefficient. (6) The rms value. Rows 1 and 2 correspond to the estimations for a virial factor equal to 1, f_BLR. Rows 3 and 4 correspond to the estimations for a virial factor anticorrelated with the FWHM, f_BLR^c.

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The information given by the Pearson coefficients and rms values indicates that the relations between ${\rm{\Delta }}{R}_{{\rm{H}}\beta }$ and accretion parameters are stronger when the virial factor anticorrelated with the FWHM is used; see Equation (9). We are able to propose a correction for the time delay based on the accretion parameters that recovers the expected value from the R_Hβ–L₅₁₀₀ relation. Since P and rms favor ${\dot{{\mathscr{M}}}}^{{\rm{c}}}$, the correction used will be based on it and not on ${L}_{\mathrm{bol}}/{L}_{\mathrm{Edd}}^{{\rm{c}}}$. The scattering of the Eddington ratio could be higher due to the large uncertainties associated with the bolometric correction factor.

The time delay corrected for the effect of the dimensionless accretion rate can be estimated by the relation

$$\begin{eqnarray}&&{\tau }_{\mathrm{corr}}({\dot{{\mathscr{M}}}}^{c})={10}^{-{\rm{\Delta }}{R}_{{\rm{H}}\beta }({\dot{{\mathscr{M}}}}^{{\rm{c}}})}\,\cdot {\tau }_{\mathrm{obs}}.\end{eqnarray} \tag{ 10 }$$

The quantities ${\dot{{\mathscr{M}}}}^{{\rm{c}}}$, ${\rm{\Delta }}{R}_{{\rm{H}}\beta }({\dot{{\mathscr{M}}}}^{{\rm{c}}})$, and ${\tau }_{\mathrm{corr}}({\dot{{\mathscr{M}}}}^{c})$ are listed in Table 4. The ${R}_{{\rm{H}}\beta }\mbox{--}{L}_{5100}$ relation with the correction for the dimensionless accretion rate is shown in Figure 5. If we compare this new diagram with the one shown in the left panel of Figure 2, it is clear that the scatter decreases significantly along the ${R}_{{\rm{H}}\beta }\mbox{--}{L}_{5100}$ relation, σ_obs = 0.684 versus ${\sigma }_{\mathrm{corr}}=0.396$ in log space. With this correction, we are able to build a better luminosity distance–redshift relation or Hubble diagram and compare them with the standard cosmological models (see Section 4).

Table 4.  Observational Properties Corrected by the Effect of Dimensionless Accretion Rate

Object	log ${\dot{{\mathscr{M}}}}^{{\rm{c}}}$	${\rm{\Delta }}{R}_{{\rm{H}}\beta ,{\dot{{\mathscr{M}}}}^{{\rm{c}}}}$	τcorr	DL,corr
			(days)	(Mpc)
(1)	(2)	(3)	(4)	(5)
SEAMBH Sample
Mrk 335	${0.19}_{-0.28}^{+0.34}$	$-{0.28}_{-0.08}^{+0.10}$	${26.7}_{-6.5}^{+8.8}$	136.1 ± 38.9
Mrk 142	${0.81}_{-0.47}^{+0.99}$	$-{0.46}_{-0.14}^{+0.28}$	${18.4}_{-9.8}^{+21.0}$	199.7 ± 167.0
IRAS F12397	${1.31}_{-0.65}^{+0.80}$	$-{0.60}_{-0.19}^{+0.23}$	${38.6}_{-7.2}^{+21.9}$	192.6 ± 72.5
Mrk 486	$-{0.32}_{-0.14}^{+0.29}$	$-{0.14}_{-0.04}^{+0.08}$	${32.5}_{-3.7}^{+10.3}$	271.9 ± 58.5
Mrk 382	${0.03}_{-0.49}^{+0.54}$	$-{0.24}_{-0.14}^{+0.15}$	${12.9}_{-3.4}^{+5.0}$	180.8 ± 59.1
IRAS 04416	${1.52}_{-0.12}^{+0.91}$	$-{0.66}_{-0.05}^{+0.26}$	${60.5}_{-6.4}^{+63.2}$	490.6 ± 282.2
MCG 06	$-{1.59}_{-0.26}^{+0.36}$	${0.22}_{-0.08}^{+0.11}$	${14.4}_{-2.9}^{+5.0}$	327.5 ± 90.1
Mrk 493	${0.09}_{-0.23}^{+0.15}$	$-{0.25}_{-0.07}^{+0.04}$	${20.8}_{-4.7}^{+2.1}$	268.0 ± 43.9
Mrk 1044	$-{0.15}_{-0.27}^{+0.31}$	$-{0.19}_{-0.08}^{+0.09}$	${16.1}_{-4.1}^{+5.1}$	114.9 ± 32.8
J080101	${1.46}_{-0.29}^{+1.02}$	$-{0.64}_{-0.09}^{+0.29}$	${36.4}_{-11.8}^{+42.5}$	602.2 ± 449.9
J081456	$-{0.05}_{-0.59}^{+0.29}$	$-{0.21}_{-0.17}^{+0.08}$	${39.7}_{-26.8}^{+12.6}$	767.7 ± 380.7
J093922	${1.18}_{-0.46}^{+0.17}$	$-{0.56}_{-0.13}^{+0.05}$	${43.6}_{-23.1}^{+7.7}$	1241.0 ± 438.1
J080131	${0.99}_{-0.29}^{+0.57}$	$-{0.51}_{-0.08}^{+0.16}$	${37.0}_{-12.0}^{+24.3}$	1159.0 ± 567.9
J085946	${0.51}_{-0.66}^{+0.48}$	$-{0.37}_{-0.19}^{+0.14}$	${82.0}_{-62.0}^{+45.2}$	2141.8 ± 1400.3
J102339	${0.31}_{-0.15}^{+0.69}$	$-{0.32}_{-0.05}^{+0.20}$	${51.6}_{-8.1}^{+41.1}$	1019.5 ± 485.2
J074352	${1.31}_{-0.09}^{+0.11}$	$-{0.60}_{-0.04}^{+0.04}$	${174.2}_{-16.7}^{+20.6}$	1563.7 ± 167.5
J075051	${1.25}_{-0.13}^{+0.24}$	$-{0.58}_{-0.05}^{+0.07}$	${254.6}_{-37.8}^{+71.5}$	4086.4 ± 877.5
J075101	${0.39}_{-0.18}^{+0.22}$	$-{0.34}_{-0.05}^{+0.06}$	${66.2}_{-12.6}^{+15.8}$	968.3 ± 208.2
J075949	$-{0.05}_{-0.39}^{+0.66}$	$-{0.21}_{-0.11}^{+0.19}$	${71.8}_{-31.2}^{+54.3}$	1803.4 ± 1072.6
J081441	${0.07}_{-0.26}^{+0.36}$	$-{0.25}_{-0.08}^{+0.10}$	${44.7}_{-13.3}^{+18.4}$	1264.3 ± 447.5
J083553	${1.43}_{-0.38}^{+0.38}$	$-{0.63}_{-0.11}^{+0.11}$	${53.4}_{-23.3}^{+23.3}$	1107.6 ± 482.4
J084533	${1.44}_{-0.23}^{+0.29}$	$-{0.64}_{-0.07}^{+0.09}$	${78.5}_{-20.5}^{+26.1}$	2307.1 ± 683.8
J093302	${0.85}_{-0.28}^{+0.26}$	$-{0.47}_{-0.08}^{+0.08}$	${55.9}_{-12.7}^{+11.2}$	1144.7 ± 244.0
J100402	${2.10}_{-0.11}^{+1.17}$	$-{0.82}_{-0.05}^{+0.33}$	${214.2}_{-28.0}^{+289.5}$	2182.5 ± 1616.9
J101000	${1.02}_{-0.24}^{+0.74}$	$-{0.52}_{-0.07}^{+0.21}$	${91.0}_{-25.0}^{+77.2}$	1677.6 ± 941.8
SDSS Sample
J140812	$-{1.00}_{-0.32}^{+0.27}$	${0.06}_{-0.09}^{+0.08}$	${9.2}_{-1.9}^{+0.9}$	450.4 ± 68.6
J141923	$-{0.87}_{-0.11}^{+0.06}$	${0.02}_{-0.04}^{+0.03}$	${11.3}_{-1.4}^{+0.7}$	767.1 ± 71.5
J140759	$-{0.63}_{-0.35}^{+0.70}$	$-{0.05}_{-0.10}^{+0.20}$	${18.3}_{-7.4}^{+14.7}$	843.3 ± 509.6
J141729	$-{0.78}_{-0.34}^{+0.90}$	$-{0.01}_{-0.10}^{+0.26}$	${5.6}_{-2.1}^{+5.8}$	513.3 ± 364.0
J141645.15	$-{0.66}_{-0.25}^{+0.26}$	$-{0.04}_{-0.07}^{+0.08}$	${5.5}_{-1.5}^{+1.7}$	571.3 ± 165.7
J142135	${0.58}_{-0.21}^{+0.21}$	$-{0.39}_{-0.06}^{+0.06}$	${9.6}_{-2.2}^{+2.2}$	756.9 ± 174.7
J141625	${0.05}_{-0.27}^{+0.19}$	$-{0.24}_{-0.08}^{+0.06}$	${26.3}_{-8.0}^{+5.6}$	1252.6 ± 323.5
J142103	$-{1.72}_{-0.06}^{+0.06}$	${0.26}_{-0.04}^{+0.04}$	${41.4}_{-1.8}^{+1.8}$	2868.9 ± 124.0
J142038	$-{1.36}_{-0.20}^{+0.16}$	${0.16}_{-0.06}^{+0.05}$	${17.5}_{-4.0}^{+3.3}$	1503.1 ± 310.2
J142043	$-{0.15}_{-0.10}^{+0.08}$	$-{0.19}_{-0.03}^{+0.03}$	${9.1}_{-0.9}^{+0.6}$	1096.8 ± 93.0
J141041	$-{0.74}_{-0.10}^{+0.17}$	$-{0.02}_{-0.03}^{+0.05}$	${22.8}_{-2.5}^{+4.4}$	1825.9 ± 275.1
J141318	$-{0.21}_{-0.13}^{+0.05}$	$-{0.17}_{-0.04}^{+0.02}$	${29.4}_{-4.4}^{+1.6}$	2080.1 ± 213.2
J141955	$-{0.98}_{-0.40}^{+0.49}$	${0.05}_{-0.11}^{+0.14}$	${9.5}_{-3.9}^{+5.0}$	1498.1 ± 700.0
J141645.58	${0.46}_{-0.15}^{+0.26}$	$-{0.36}_{-0.05}^{+0.08}$	${19.5}_{-3.2}^{+5.7}$	2352.9 ± 539.8
J141324	$-{0.83}_{-0.20}^{+0.37}$	${0.01}_{-0.06}^{+0.11}$	${25.1}_{-5.7}^{+10.7}$	2317.8 ± 759.0
J141214	${0.60}_{-0.35}^{+0.29}$	$-{0.40}_{-0.10}^{+0.08}$	${53.5}_{-16.0}^{+10.5}$	2950.6 ± 730.8
J140518	$-{0.26}_{-0.17}^{+0.31}$	$-{0.16}_{-0.05}^{+0.09}$	${59.5}_{-11.9}^{+21.2}$	3619.4 ± 1004.9
J141018	$-{0.73}_{-0.28}^{+0.21}$	$-{0.02}_{-0.08}^{+0.06}$	${17.0}_{-4.7}^{+3.0}$	2464.1 ± 562.8
J141123	${0.31}_{-0.06}^{+0.10}$	$-{0.32}_{-0.02}^{+0.03}$	${27.0}_{-1.7}^{+2.9}$	2101.4 ± 177.8
J142039	$-{0.10}_{-0.13}^{+0.06}$	$-{0.20}_{-0.04}^{+0.02}$	${32.8}_{-4.8}^{+1.4}$	2535.0 ± 238.8
J141724	${0.15}_{-0.23}^{+1.07}$	$-{0.27}_{-0.07}^{+0.30}$	${18.9}_{-5.0}^{+23.4}$	1763.9 ± 1327.3
J141004	$-{0.53}_{-0.08}^{+0.08}$	$-{0.08}_{-0.03}^{+0.03}$	${64.2}_{-4.8}^{+5.0}$	5113.1 ± 391.8
J141706	${1.24}_{-0.25}^{+0.53}$	$-{0.58}_{-0.08}^{+0.15}$	${39.4}_{-11.4}^{+23.9}$	3318.1 ± 1483.7
J142010	$-{0.01}_{-0.35}^{+0.43}$	$-{0.22}_{-0.10}^{+0.12}$	${21.5}_{-7.5}^{+9.6}$	2096.5 ± 835.3
J141712	$-{0.59}_{-0.41}^{+0.39}$	$-{0.06}_{-0.12}^{+0.11}$	${14.4}_{-3.0}^{+2.1}$	3916.2 ± 689.3
J141115	$-{0.44}_{-0.05}^{+0.20}$	$-{0.10}_{-0.02}^{+0.06}$	${62.4}_{-2.5}^{+14.1}$	4955.6 ± 661.1
J141112	${0.20}_{-0.09}^{+0.11}$	$-{0.28}_{-0.03}^{+0.04}$	${39.3}_{-3.8}^{+4.8}$	4003.1 ± 441.5
J141417	$-{1.27}_{-0.38}^{+0.30}$	${0.13}_{-0.11}^{+0.09}$	${11.5}_{-3.8}^{+2.4}$	2803.4 ± 745.8
J141031	$-{0.61}_{-0.26}^{+0.07}$	$-{0.06}_{-0.08}^{+0.03}$	${40.6}_{-11.7}^{+1.2}$	4857.2 ± 773.3
J141941	${0.44}_{-0.24}^{+0.12}$	$-{0.35}_{-0.07}^{+0.04}$	${68.4}_{-18.7}^{+8.8}$	4947.3 ± 992.8
J141135	${0.27}_{-0.37}^{+0.43}$	$-{0.30}_{-0.11}^{+0.12}$	${35.5}_{-14.9}^{+17.4}$	4509.7 ± 2049.9
J140904	$-{0.23}_{-0.40}^{+0.68}$	$-{0.16}_{-0.12}^{+0.19}$	${16.9}_{-6.7}^{+12.5}$	1923.8 ± 1094.6
J142052	${1.87}_{-0.07}^{+0.10}$	$-{0.76}_{-0.04}^{+0.05}$	${68.2}_{-5.7}^{+7.5}$	2810.9 ± 271.8
J141147	${1.18}_{-0.20}^{+0.21}$	$-{0.56}_{-0.06}^{+0.07}$	${23.4}_{-5.1}^{+5.5}$	3188.0 ± 722.4
J141532	${0.38}_{-0.29}^{+0.33}$	$-{0.34}_{-0.08}^{+0.09}$	${57.4}_{-19.0}^{+21.4}$	7326.8 ± 2585.2
J142023	${0.76}_{-0.40}^{+0.33}$	$-{0.44}_{-0.12}^{+0.10}$	${23.7}_{-10.9}^{+8.9}$	2827.5 ± 1181.0
J142049	$-{0.40}_{-0.18}^{+0.18}$	$-{0.11}_{-0.06}^{+0.06}$	${59.9}_{-12.4}^{+12.4}$	5688.3 ± 1174.8
J142112	${0.46}_{-0.23}^{+0.26}$	$-{0.36}_{-0.07}^{+0.08}$	${32.4}_{-6.9}^{+8.5}$	4128.8 ± 974.1
J141606	${0.12}_{-0.42}^{+0.32}$	$-{0.26}_{-0.12}^{+0.09}$	${58.7}_{-28.4}^{+21.3}$	4298.4 ± 1820.2
J141859	${0.95}_{-0.30}^{+0.24}$	$-{0.50}_{-0.09}^{+0.07}$	${64.0}_{-22.0}^{+17.6}$	4366.7 ± 1348.6
J141952	$-{0.77}_{-0.16}^{+0.17}$	$-{0.01}_{-0.05}^{+0.05}$	${33.6}_{-5.2}^{+5.7}$	4911.1 ± 798.6
J142417	$-{0.01}_{-0.23}^{+0.22}$	$-{0.22}_{-0.07}^{+0.06}$	${60.9}_{-9.2}^{+7.6}$	10753.6 ± 1481.3
Bentz Collection
PG 0026+129	${0.34}_{-0.62}^{+0.61}$	$-{0.32}_{-0.18}^{+0.17}$	${234.4}_{-59.8}^{+50.9}$	1761.2 ± 415.8
PG 0052+251	$-{0.36}_{-0.30}^{+0.30}$	$-{0.13}_{-0.09}^{+0.09}$	${120.2}_{-32.3}^{+32.8}$	1191.0 ± 322.3
Fairall 9	$-{0.54}_{-0.30}^{+0.27}$	$-{0.08}_{-0.09}^{+0.08}$	${20.8}_{-5.1}^{+3.8}$	151.1 ± 32.6
Mrk 590	$-{0.78}_{-0.73}^{+0.74}$	$-{0.01}_{-0.21}^{+0.21}$	${26.0}_{-5.4}^{+6.6}$	180.4 ± 41.6
3C 120	$-{0.09}_{-0.50}^{+0.53}$	$-{0.20}_{-0.14}^{+0.15}$	${41.9}_{-10.6}^{+13.9}$	206.4 ± 60.3
Ark 120	$-{1.24}_{-0.44}^{+0.44}$	${0.12}_{-0.13}^{+0.13}$	${29.7}_{-5.9}^{+6.4}$	171.3 ± 35.3
Mrk 79	$-{0.64}_{-0.71}^{+0.72}$	$-{0.05}_{-0.20}^{+0.20}$	${17.3}_{-5.4}^{+6.0}$	82.4 ± 27.2
PG 0804+761	$-{0.11}_{-0.85}^{+0.85}$	$-{0.20}_{-0.24}^{+0.24}$	${231.7}_{-29.8}^{+29.7}$	1278.3 ± 164.1
Mrk 110	$-{0.25}_{-1.12}^{+1.13}$	$-{0.16}_{-0.32}^{+0.32}$	${36.7}_{-10.3}^{+12.8}$	286.4 ± 90.1
PG 0953+414	${0.001}_{-0.30}^{+0.30}$	$-{0.23}_{-0.09}^{+0.09}$	${253.8}_{-38.2}^{+36.5}$	2587.7 ± 381.0
NGC 3227	$-{1.36}_{-0.25}^{+0.25}$	${0.16}_{-0.08}^{+0.08}$	${2.7}_{-0.6}^{+0.6}$	11.9 ± 2.5
NGC 3516	$-{1.77}_{-0.33}^{+0.32}$	${0.27}_{-0.10}^{+0.10}$	${6.2}_{-0.8}^{+0.5}$	33.3 ± 3.6
SBS 1116+583A	$-{1.07}_{-0.74}^{+0.75}$	${0.08}_{-0.21}^{+0.21}$	${1.9}_{-0.4}^{+0.5}$	68.9 ± 16.5
Arp 151	$-{0.63}_{-0.25}^{+0.22}$	$-{0.05}_{-0.07}^{+0.07}$	${4.5}_{-0.8}^{+0.6}$	74.3 ± 11.1
NGC 3783	$-{1.63}_{-0.48}^{+0.52}$	${0.23}_{-0.14}^{+0.15}$	${6.0}_{-1.3}^{+1.9}$	46.3 ± 12.7
Mrk 1310	$-{0.67}_{-0.41}^{+0.41}$	$-{0.04}_{-0.12}^{+0.12}$	${4.0}_{-0.7}^{+0.7}$	85.7 ± 13.9
NGC 4051	$-{0.45}_{-0.38}^{+0.44}$	$-{0.10}_{-0.11}^{+0.13}$	${2.6}_{-0.9}^{+1.1}$	8.7 ± 3.3
NGC 4151	$-{2.25}_{-0.46}^{+0.47}$	${0.41}_{-0.14}^{+0.14}$	${2.6}_{-0.3}^{+0.4}$	10.2 ± 1.5
Mrk 202	$-{0.42}_{-0.53}^{+0.65}$	$-{0.11}_{-0.15}^{+0.19}$	${3.9}_{-1.4}^{+2.2}$	89.5 ± 41.8
NGC 4253	$-{0.23}_{-3.05}^{+3.05}$	$-{0.16}_{-0.86}^{+0.86}$	${9.0}_{-1.7}^{+2.3}$	89.8 ± 20.3
PG 1229+204	$-{1.13}_{-0.40}^{+0.66}$	${0.09}_{-0.12}^{+0.19}$	${30.6}_{-12.4}^{+22.4}$	419.3 ± 237.9
NGC 4593	$-{0.95}_{-0.63}^{+0.64}$	${0.04}_{-0.18}^{+0.18}$	${3.6}_{-0.6}^{+0.7}$	23.6 ± 4.4
NGC 4748	$-{0.42}_{-0.49}^{+0.42}$	$-{0.11}_{-0.14}^{+0.12}$	${7.1}_{-2.9}^{+2.1}$	82.8 ± 28.8
PG 1307+085	$-{0.58}_{-0.44}^{+0.36}$	$-{0.07}_{-0.13}^{+0.10}$	${122.7}_{-54.1}^{+41.8}$	1165.7 ± 455.9
Mrk 279	$-{0.40}_{-0.31}^{+0.31}$	$-{0.11}_{-0.09}^{+0.09}$	${21.8}_{-5.1}^{+5.1}$	137.2 ± 32.0
PG 1411+442	$-{0.61}_{-0.52}^{+0.52}$	$-{0.06}_{-0.15}^{+0.15}$	${141.3}_{-70.1}^{+69.3}$	1038.8 ± 512.7
PG 1426+015	$-{0.97}_{-0.53}^{+0.50}$	${0.05}_{-0.15}^{+0.14}$	${85.1}_{-33.2}^{+26.8}$	559.4 ± 197.3
Mrk 817	$-{0.64}_{-0.67}^{+0.74}$	$-{0.05}_{-0.19}^{+0.21}$	${22.2}_{-7.5}^{+11.0}$	143.1 ± 59.7
Mrk 290	$-{0.81}_{-0.15}^{+0.16}$	${0.001}_{-0.05}^{+0.05}$	${8.7}_{-1.0}^{+1.2}$	101.7 ± 13.0
PG 1613+658	$-{0.17}_{-0.56}^{+0.56}$	$-{0.18}_{-0.16}^{+0.16}$	${60.8}_{-23.0}^{+22.7}$	515.3 ± 194.1
PG 1617+175	$-{0.87}_{-0.59}^{+0.56}$	${0.02}_{-0.17}^{+0.16}$	${68.3}_{-32.2}^{+28.3}$	773.7 ± 342.5
PG 1700+518	${0.50}_{-0.76}^{+0.76}$	$-{0.37}_{-0.21}^{+0.22}$	${590.8}_{-91.2}^{+107.8}$	4894.0 ± 824.1
3C 390.3	$-{0.97}_{-1.00}^{+1.09}$	${0.05}_{-0.28}^{+0.31}$	${40.0}_{-15.3}^{+24.9}$	207.4 ± 104.3
NGC 6814	$-{1.95}_{-0.48}^{+0.48}$	${0.32}_{-0.14}^{+0.14}$	${3.1}_{-0.4}^{+0.4}$	20.0 ± 2.7
Mrk 509	$-{0.87}_{-0.12}^{+0.12}$	${0.02}_{-0.04}^{+0.04}$	${76.5}_{-5.2}^{+5.9}$	312.7 ± 22.6
PG 2130+099	${1.17}_{-0.15}^{+0.15}$	$-{0.56}_{-0.05}^{+0.05}$	${34.9}_{-4.4}^{+4.4}$	266.8 ± 33.4
NGC 7469	${0.51}_{-0.25}^{+0.35}$	$-{0.37}_{-0.07}^{+0.10}$	${25.5}_{-3.1}^{+8.0}$	106.8 ± 23.2
PG 1211+143	${0.01}_{-0.41}^{+0.27}$	$-{0.23}_{-0.12}^{+0.08}$	${159.7}_{-71.7}^{+43.6}$	868.9 ± 313.6
PG 0844+349	${0.03}_{-0.46}^{+0.47}$	$-{0.24}_{-0.13}^{+0.13}$	${55.8}_{-23.2}^{+23.7}$	426.6 ± 179.0
NGC 5273	$-{2.12}_{-0.69}^{+0.55}$	${0.37}_{-0.20}^{+0.16}$	${0.9}_{-0.7}^{+0.5}$	9.4 ± 6.0
Mrk 1511	$-{0.43}_{-0.17}^{+0.18}$	$-{0.11}_{-0.05}^{+0.05}$	${7.3}_{-1.0}^{+1.1}$	97.5 ± 14.7
KA 1858-4850	$-{0.05}_{-0.19}^{+0.17}$	$-{0.21}_{-0.06}^{+0.05}$	${22.1}_{-3.8}^{+3.3}$	516.2 ± 82.6
MCG 6-30-15	$-{1.94}_{-0.66}^{+0.67}$	${0.32}_{-0.19}^{+0.19}$	${2.7}_{-0.8}^{+0.9}$	48.5 ± 14.7
UGC 06728	$-{0.23}_{-0.52}^{+0.46}$	$-{0.16}_{-0.15}^{+0.13}$	${2.0}_{-1.2}^{+1.0}$	21.1 ± 11.3
MCG +08-11-011	$-{0.14}_{-0.17}^{+0.17}$	$-{0.19}_{-0.05}^{+0.05}$	${24.3}_{-0.8}^{+0.8}$	164.0 ± 5.3
NGC 2617	$-{1.10}_{-0.36}^{+0.33}$	${0.08}_{-0.11}^{+0.10}$	${3.5}_{-1.1}^{+0.9}$	34.0 ± 9.7
3C 382	$-{1.02}_{-0.17}^{+0.28}$	${0.06}_{-0.06}^{+0.08}$	${35.1}_{-3.2}^{+6.9}$	376.6 ± 54.6
Mrk 374	$-{0.16}_{-0.20}^{+0.35}$	$-{0.18}_{-0.06}^{+0.10}$	${22.5}_{-5.0}^{+8.8}$	189.7 ± 58.3
Lu et al. (2016)
NGC 5548	$-{1.19}_{-0.20}^{+0.25}$	${0.11}_{-0.06}^{+0.08}$	${5.6}_{-0.3}^{+1.0}$	34.7 ± 4.1
Zhang et al. (2019)
3C 273	${1.12}_{-0.08}^{+0.07}$	$-{0.54}_{-0.03}^{+0.03}$	${514.1}_{-42.4}^{+29.1}$	1380.8 ± 96.0

Note. Columns are as follows. (1) Object name. (2) Dimensionless accretion rate. (3) Deviation of the expected ${R}_{{\rm{H}}\beta }\mbox{--}{L}_{5100}$ estimated from Equation (9). (4) Time delay corrected by the dimensionless accretion rate in units of days. (6) Luminosity distance in units of Mpc.

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As we show in the previous section, the relation between ${\rm{\Delta }}{R}_{{\rm{H}}\beta }$ and the dimensionless accretion rate (or Eddington ratio) can be represented by a linear fit, independent of the virial factor. However, Du et al. (2015, 2018) argued that around $\dot{{\mathscr{M}}}$ = 3, there is a break in the behavior of ${\rm{\Delta }}{R}_{{\rm{H}}\beta }$, where highly accreting sources would be characterized by optically thick and geometrically slim accretion (Wang et al. 2014c). Considering the deviation of the ${R}_{{\rm{H}}\beta }\mbox{--}{L}_{5100}$ relation, sources with $\dot{{\mathscr{M}}}$ < 3 would be associated with ${\rm{\Delta }}{R}_{{\rm{H}}\beta }$ ∼ 0, while sources with $\dot{{\mathscr{M}}}$ > 3 would show ${\rm{\Delta }}{R}_{{\rm{H}}\beta }$ with a decreasing trend as a function of $\dot{{\mathscr{M}}}$. This interpretation should correspond to the relation ${\rm{\Delta }}{R}_{{\rm{H}}\beta }$–$\dot{{\mathscr{M}}}$ assuming f_BLR = 1 (left panel of Figure 3), which was analyzed by Du et al. (2015, 2018). However, even in this case, there is a significant difference in our analysis that comes from the location of the SDSS-RM sample in the diagram. Du et al. (2018) included this sample in their analysis, but they used the M_BH estimated from Grier et al. (2017), who adopted f_BLR = 4.47, adequate for an M_BH estimation based on ${\sigma }_{\mathrm{line},\mathrm{rms}}$ (Woo et al. 2015). In our estimation, some SDSS-RM objects are located around $\dot{{\mathscr{M}}}$ = 3, covering the empty region shown in their Figure 3. In order to get a possible difference between the sources with $\dot{{\mathscr{M}}}$ < 3 and >3, we perform a two-sample Kolmogorov–Smirnov (K-S) test. We find a value of 0.344 with a probability of ${p}_{\mathrm{KS}}\sim 0.003$. A similar p_KS is reported by Du et al. (2015) that, according to them, is enough to demonstrate that ${\rm{\Delta }}{R}_{{\rm{H}}\beta }$ ∼ 0 for $\dot{{\mathscr{M}}}$ < 3. If we apply the K-S test for ${\rm{\Delta }}{R}_{{\rm{H}}\beta }$–${L}_{\mathrm{bol}}/{L}_{\mathrm{Edd}}$ with f_BLR = 1, we get a value of 0.392 and p_KS = 0.0004, which favors the difference at $\dot{{\mathscr{M}}}$ = 3. On the other hand, if we consider a virial factor anticorrelated with the FWHM of Hβ, ${\rm{\Delta }}{R}_{{\rm{H}}\beta }$ decreases progressively as a function of ${\dot{{\mathscr{M}}}}^{{\rm{c}}}$ or ${L}_{\mathrm{bol}}/{L}_{\mathrm{Edd}}^{{\rm{c}}}$ (Figure 4). It is confirmed by the K-S test; we get 0.771 with p_KS = 2.9 × 10⁻¹¹ and 0.663 with p_KS = 1.8 × 10⁻⁹ for ${\dot{{\mathscr{M}}}}^{{\rm{c}}}$ and ${L}_{\mathrm{bol}}/{L}_{\mathrm{Edd}}^{{\rm{c}}}$, respectively.

In all four cases, there is a different behavior around $\dot{{\mathscr{M}}}$ = 3. For all cases, the ${\rm{\Delta }}{R}_{{\rm{H}}\beta }$ median is 0.09 for $\dot{{\mathscr{M}}}$ < 3 (or ${L}_{\mathrm{bol}}/{L}_{\mathrm{Edd}}$ < 0.2); however, the scatter is higher with a virial factor equal to 1. For the high accretion rate, the ${\rm{\Delta }}{R}_{{\rm{H}}\beta }$ median is 0.26 and 0.31 for $\dot{{\mathscr{M}}}$ and ${L}_{\mathrm{bol}}/{L}_{\mathrm{Edd}}$ and 0.61 and 0.50 for ${\dot{{\mathscr{M}}}}^{{\rm{c}}}$ and ${L}_{\mathrm{bol}}/{L}_{\mathrm{Edd}}^{{\rm{c}}}$, respectively. However, from Figure 2, we see that very low accretion objects have ${\rm{\Delta }}{R}_{{\rm{H}}\beta }$ > 0 for a virial factor anticorrelated with the FWHM. As we have shown in the previous section, we can represent the relation between ${\rm{\Delta }}{R}_{{\rm{H}}\beta }$ and accretion parameters by a linear fit in the whole log space without any break, which is supported by the Pearson coefficient and rms value. We do not see any evidence of a break around $\dot{{\mathscr{M}}}$ = 3, especially in the cases with a virial factor anticorrelated with the FWHM of Hβ.

The virial factor is one of the most important uncertainties in the black hole mass determination and accretion parameters, as is emphasized in Sections 5.1 and 5.2. According to Mejía-Restrepo et al. (2018), the virial factor f_BLR^c includes a correction for the orientation effect, then ${\dot{{\mathscr{M}}}}^{{\rm{c}}}$ would show an accurate estimation that is reflected in the scattering of the measurement, particularly when it is compared with the other parameters. However, their results are based on a Shakura–Sunyaev (SS) disk (Shakura & Sunyaev 1973), which is appropriate for their sample, where ∼90% of the objects show a low accretion rate, and they can be perfectly presented by an SS model disk (Capellupo et al. 2016). One-third of our sample shows a high accretion rate ($\dot{{\mathscr{M}}}$ ≳ 3) and, according to Wang et al. (2014c), in high accretors, the slim disk produces an anisotropic radiation field, which divides the BLR into two regions with distinct incident ionizing photon fluxes. Using the code BRAINS, Li et al. (2018) demonstrated that two-region model is better than a simple one for Mrk 142, a typical high accretor source. Therefore, the incident radiation flux and geometry are more complex in highly accreting AGNs. New spectral energy distribution models for the slim disk are required in order to get a better estimation of the virial factor for this kind of object.

Studies of large quasar samples showed that the continuum amplitude of the variability is anticorrelated with the Eddington ratio (Wilhite et al. 2008; MacLeod et al. 2010; Simm et al. 2016; Rakshit & Stalin 2017; Li et al. 2018; Sánchez-Sáez et al. 2018). Here F_var measures the excess of variability above the noise level and can be used as an estimator of this effect. As we showed in the previous section, ${\rm{\Delta }}{R}_{{\rm{H}}\beta }$ is anticorrelated with the dimensionless accretion rate and Eddington ratio. In Figures 3 and 4, we show the change of F_var along the relation ${\rm{\Delta }}{R}_{{\rm{H}}\beta }$–$\dot{{\mathscr{M}}}$ and ${\rm{\Delta }}{R}_{{\rm{H}}\beta }$–${L}_{\mathrm{bol}}/{L}_{\mathrm{Edd}}$ using different virial factors. In all cases, the minimum F_var at 5100 Å values tends to be associated with the highest $\dot{{\mathscr{M}}}$ (and ${L}_{\mathrm{bol}}/{L}_{\mathrm{Edd}}$) and smallest ${\rm{\Delta }}{R}_{{\rm{H}}\beta }$ values.