J/ApJ/963/30 Virial factor in SDSS AGNs from supermassive BH masses (Liu+, 2024)
Measuring the virial factor in SDSS DR7 active galactic nuclei with redshifted
Hβ and Hα broad emission lines.
Liu H.T., Feng H.-C., Li S.-S., Bai J.M., Li H.Z.
<Astrophys. J., 963, 30 (2024)>
=2024ApJ...963...30L 2024ApJ...963...30L
ADC_Keywords: Active gal. nuclei; Redshifts; Black holes; Surveys; Optical
Keywords: Active galactic nuclei ; Black hole physics ; Emission line galaxies ;
Quasars ; Supermassive black holes
Abstract:
Under the hypothesis of gravitational redshift induced by the central
supermassive black hole and based on line widths and shifts of
redward-shifted Hβ and Hα broad emission lines for more
than 8000 Sloan Digital Sky Survey DR7 active galactic nuclei (AGNs),
we measure the virial factor in determining supermassive black hole
masses. The virial factor had been believed to be independent of
accretion radiation pressure on gas clouds in broad-line regions
(BLRs) and only dependent on the inclination effects of BLRs. The
virial factor measured spans a very large range. For the vast majority
of AGNs (>96%) in our samples, the virial factor is larger than the
f=1 usually used in the literature. The f-correction makes the percent
of high-accreting AGNs decrease by about 100 times. There are positive
correlations of f with the dimensionless accretion rate and Eddington
ratio. The redward shifts of Hβ and Hα are mainly of
gravitational origin, confirmed by a negative correlation between the
redward shift and the dimensionless radius of the BLR. Our results
show that radiation pressure force is a significant contributor to the
measured virial factor, containing the inclination effects of the BLR.
The usually used values of f should be corrected for high-accreting
AGNs, especially high-redshift quasars. The f-correction increases
their masses by 1-2 orders of magnitude, which will make it more
challenging to explain the formation and growth of supermassive black
holes at high redshifts.
File Summary:
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FileName Lrecl Records Explanations
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ReadMe 80 . This file
table1.dat 136 9185 The relevant parameters for 9185 AGNs in SDSS DR7
for Sample 1
table2.dat 136 9271 The relevant parameters for 9271 AGNs in SDSS DR7
for Sample 2
table3.dat 178 8169 The relevant parameters for 8169 AGNs in SDSS DR7
for Sample 3
table7.dat 61 113 Quasars at z{~>}6 from Fan+ 2023ARA&A..61..373F 2023ARA&A..61..373F
table8.dat 53 62 62 SDSS AGNs in MBH-σ* map research
table9.dat 60 88 *88 SDSS quasars in MBH-σ* map research
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Note on table9.dat: The 88 SDSS quasars are taken from Table 1 in
Shen+ 2015, J/ApJ/805/96
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See also:
J/ApJ/613/682 : AGN central masses & broad-line region sizes (Peterson+, 2004)
J/ApJ/632/799 : NGC4395 light curves (Peterson+, 2005)
J/ApJ/687/78 : FeII emission in quasars (Hu+, 2008)
J/ApJ/705/L76 : AGNs with double-peaked [OIII] lines (Wang+, 2009)
J/ApJ/716/993 : LAMP: reverberation mapping of H and He lines (Bentz+, 2010)
J/ApJ/782/45 : SEAMBHs. I. Mrk 142, Mrk 335, and IRAS F12397+3333 (Du+, 2014)
J/ApJ/795/38 : Phot./spectroscopic measurements for KA1858+4850 (Pei+, 2014)
J/ApJ/793/108 : SEAMBHs. II. Continuum and Hbeta LCs (Wang+, 2014)
J/ApJS/217/26 : Lick AGN monitoring 2011: light curves (Barth+, 2015)
J/ApJ/806/22 : SEAMBHs IV. Hβ time lags (Du+, 2015)
J/ApJS/216/4 : SDSS-RM project: technical overview (Shen+, 2015)
J/ApJ/805/96 : SDSS-RM project: velocity dispersions of QSOs (Shen+, 2015)
J/ApJ/827/118 : A new reverberation mapping campaign on NGC 5548 (Lu+, 2016)
J/ApJ/818/30 : Lag measurements for z<0.8 QSOs from the SDSS-RM (Shen+, 2016)
J/ApJ/851/21 : SDSS RM project first year of observations (Grier+, 2017)
J/ApJS/228/9 : Physical parameters of ∼300000 SDSS-DR12 QSOs (Kozlowski, 2017)
J/ApJ/837/131 : Space telescope RM project. V. NGC5548 sp. (Pei+, 2017)
J/ApJ/869/142 : Monitoring AGNs with Hβ Asymmetry (MAHA). I. (Du+, 2018)
J/ApJ/856/6 : SEAMBHs IX. 10 new Hβ light curves (Du+, 2018)
J/ApJ/886/42 : Reverberation mapping & opt. spectra data of AGNs (Du+, 2019)
J/ApJS/243/21 : A complete sample of broad-line AGN from SDSS-DR7 (Liu+, 2019)
J/ApJS/241/34 : The SDSS Reverberation Mapping (SDSS-RM) project (Shen+, 2019)
J/ApJ/876/49 : A 10yr reverberation mapping campaign for 3C273 (Zhang+, 2019)
J/ApJ/905/75 : 3yrs spectroscopic light curves of PG0026+129 (Hu+, 2020)
J/MNRAS/491/5881 : Extended size-luminosity relation for RM AGNs (Yu+, 2020)
J/ApJ/909/18 : Reverberation mapping monitoring of NGC3516 (Feng+, 2021)
J/ApJ/912/92 : Lijiang/YFOSC light curves of NGC 2617 (Feng+, 2021)
J/ApJS/253/20 : SEAMBHs XII. Reberberation mapping for 15 PG QSOs (Hu+, 2021)
J/ApJ/920/9 : YFOSC light curves of PG 0923+201 and PG 1001+291 (Li+, 2021)
J/ApJ/918/50 : Reverberation mapping for Mrk 817 and NGC 7469 (Lu+, 2021)
J/ApJ/936/75 : Spectroscopy and photometry follow up for NGC 4151 (Li+, 2022)
J/ApJ/928/60 : Virial factor of SDSS DR5 QSOs (Liu+, 2022)
J/ApJ/944/29 : Reverberation mapping of IC 4329A (Bentz+, 2023)
Byte-by-byte Description of file: table1.dat
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Bytes Format Units Label Explanations
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1- 19 A19 --- SDSS SDSS DR7 object identifier
(JHHMMSS.ss+DDMMSS.s)
21- 27 F7.1 km/s FWHM [506/23540] Hbeta line Full-Width at
Half-Maximum (G1)
29- 34 F6.1 km/s e_FWHM [0/3675] Uncertainty in FWHM
36- 42 F7.5 --- zgHb [1e-05/0.017] Redward shift of broad
Hbeta emission line (G1)
44- 50 F7.5 --- e_zgHb [0/0.0022] Uncertainty in zgHb
52- 56 F5.2 [10-7W] logL5100 [40.58/45.6] Log luminosity at 5100Å;
erg/s (G1)
58- 61 F4.2 [10-7W] e_logL5100 [0/0.5] Uncertainty in logL5100
63- 66 F4.2 [Msun] logMbh [5.15/9.72] Log virial mass of black
hole, logMRM (G1)
68- 73 F6.3 [Lsun] logLb/LE [-3.13/0.13] Log ratio of bolometric to
Eddington luminosities (G1)
75- 79 F5.1 --- fHb [0.1/669] Hbeta virial factor
81- 85 F5.1 --- e_fHb [0/321] Uncertainty in fHb
87- 92 F6.3 [Msun/yr] logMdot [-1.71/1.55] Log dimensionless accretion
rate, logdM/dtfg=1
94- 101 F8.1 --- rBLR [162.9/306784] Dimensionless Broad-Line
Region radius (G2)
103- 110 F8.3 --- RFeII [0.002/296]?=-999 Line ratio of
FeII/Hbeta
112- 118 F7.2 [Msun] logMbhR [-95/9.7]?=-999 Estimated log virial
mass, logMRM (G3)
120- 127 F8.1 --- rBLRR [202/273885]?=-999 Estimated
dimensionless Broad-Line Region radius
(G2)(G3)
129- 136 F8.3 [Msun/yr] logMdotR [-1.5/104]?=-999 Estimated log
dimensionless accretion rate (G3)
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Byte-by-byte Description of file: table2.dat
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Bytes Format Units Label Explanations
--------------------------------------------------------------------------------
1- 19 A19 --- SDSS SDSS DR7 object identifier
(JHHMMSS.ss+DDMMSS.s)
21- 27 F7.1 km/s FWHM [506/19650] Hbeta line Full-Width at
Half-Maximum (G1)
29- 34 F6.1 km/s e_FWHM [0/3439] Uncertainty in FWHM
36- 42 F7.5 --- zgHa [2e-05/0.012] Redward shift of broad
Halpha emission line (G1)
44- 50 F7.5 --- e_zgHa [0/0.002] Uncertainty in zgHa
52- 61 F10.5 --- zHa(b-n) [2e-05/0.012]?=-999 Redward shift of broad
Halpha with respect to narrow Halpha (G1)
63- 72 F10.5 --- e_zHa(b-n) [1e-05/0.0016]?=-999 Uncertainty
in zHa(b-n)
74- 78 F5.2 [10-7W] logL5100 [40.58/45.6] Log luminosity at 5100Å;
erg/s (G1)
80- 83 F4.2 [10-7W] e_logL5100 [0/0.5] Uncertainty in logL5100
85- 88 F4.2 [Msun] logMbh [5.15/9.72] Log virial mass of black
hole (G1)
90- 95 F6.3 [-] logLb/LE [-3.27/0.85] Log ratio of bolometric to
Eddington luminosities (G1)
97- 101 F5.1 --- fHa [0.1/180.3] Halpha virial factor
103- 106 F4.1 --- e_fHa [0/67] Uncertainty in fHa
108- 113 F6.1 --- fHa(b-n) [0.1/150.5]?=-999 Broad Halpha virial
factor estimated by zHa(b-n)
115- 120 F6.1 --- e_fHa(b-n) [0/66.1]?=-999 Uncertainty in fHa(b-n)
122- 127 F6.3 [Msun/yr] logMdot [-1.85/2.27] Log dimensionless accretion
rate
129- 136 F8.1 --- rBLR [162.9/403063] Dimensionless Broad-Line
Region radius (G2)
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Byte-by-byte Description of file: table3.dat
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Bytes Format Units Label Explanations
--------------------------------------------------------------------------------
1- 19 A19 --- SDSS SDSS DR7 object identifier
(JHHMMSS.ss+DDMMSS.s)
21- 27 F7.1 km/s FWHMHb [506.8/23540] Hbeta line Full-Width at
Half-Maximum (G1)
29- 34 F6.1 km/s e_FWHMHb [0/3675] Uncertainty in FWHMHb
36- 42 F7.5 --- zgHb [4e-05/0.017] Redward shift of broad
Hbeta emission line (G1)
44- 50 F7.5 --- e_zgHb [0/0.0022] Uncertainty in zHb
52- 58 F7.1 km/s FWHMHa [506/19650] Halpha line Full-Widthat
Half-Maximum (G1)
60- 65 F6.1 km/s e_FWHMHa [0/3439] Uncertainty in FWHMHa
67- 73 F7.5 --- zgHa [2e-05/0.012] Redward shift of broad
Halpha emission line (G1)
75- 81 F7.5 --- e_zgHa [0/0.002] Uncertainty in zHa
83- 87 F5.2 [10-7W] logL5100 [40.58/45.6] Log luminosity at 5100Å;
erg/s (G1)
89- 92 F4.2 [10-7W] e_logL5100 [0/0.5] Uncertainty in logL5100
94- 97 F4.2 [Msun] logMbh [5.15/9.72] Log virial mass of black hole
(G1)
99- 104 F6.3 [-] logLb/LE [-3.13/0.13] Log ratio of bolometric to
Eddington luminosities (G1)
106- 110 F5.1 --- fHb [0.1/669] Hbeta virial factor
112- 116 F5.1 --- e_fHb [0/321] Uncertainty in fHb
118- 122 F5.1 --- fHa [0.1/181] Halpha virial factor
124- 127 F4.1 --- e_fHa [0/67] Uncertainty in fHa
129- 134 F6.3 [Msun/yr] logMdot [-1.71/1.55] Log dimensionless accretion
rate
136- 143 F8.1 --- rBLR [162.9/306784] Dimensionless Broad-Line
Region radius (G2)
145- 152 F8.3 --- RFeII [0.002/295.1]?=-999 Line ratio of
FeII/Hbeta (G1)
154- 160 F7.2 [Msun] logMR [-95/9.4]?=-999 Estimated log virial mass
(G3)
162- 169 E8.3 --- rBLRR [747/3.7e+31]?=-999 Estimated
dimensionless Broad-Line Region radius
(G2)(G3)
171- 178 F8.3 [Msun/yr] logMdotR [-1.5/104]?=-999 Estimated log
dimensionless accretion rate (G3)
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Byte-by-byte Description of file: table7.dat
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Bytes Format Units Label Explanations
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1- 20 A20 --- Name Quasar name (JHHMMSS.ss+DDMMSS.ss)
22- 26 F5.3 --- z [5.9/7.7] Spectroscopic redshift
28- 31 F4.2 [Msun] logMbh [7.58/10] Log virial mass of black hole
33- 37 F5.2 [10-7W] logL3000 [45/47.5] Log luminosity at 3000Å; erg/s
39- 43 F5.3 --- Lb/LE [0.08/2.7] Ratio of bolometric to Eddington
luminosities (1)
45- 49 F5.1 --- f [12/189.2] Virial factor (G4)
51- 55 F5.2 [Msun] logfMbh [9.5/12] Log virial mass of black hole
modified by f
57- 61 F5.3 --- Lb/fLE [0.007/0.014] Ratio of bolometric to
Eddington luminosities modified by f
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Note (1): Lbol=5.15L3000, where L3000 is the UV quasar continuum luminosity
at rest-frame wavelength 3000Å (Fan+ 2023ARA&A..61..373F 2023ARA&A..61..373F).
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Byte-by-byte Description of file: table8.dat
--------------------------------------------------------------------------------
Bytes Format Units Label Explanations
--------------------------------------------------------------------------------
1- 19 A19 --- SDSS SDSS DR7 object identifier
(JHHMMSS.ss+DDMMSS.s)
21- 25 F5.3 --- z [0.013/0.1] Spectroscopic redshift
27- 30 F4.2 [Msun] logM [5.97/7.3] Log virial mass
32- 36 F5.3 --- Lb/LE [0.02/0.4] Bolometric to Eddington
luminosities ratio
38- 41 F4.1 --- f [1/65] Virial factor
43- 45 I3 km/s sigma [38/169] Stellar velocity dispersion
from Table 1 in Woo+ 2015ApJ...801...38W 2015ApJ...801...38W
47- 48 I2 km/s e_sigma [1/24] Uncertainty in sigma
50- 53 F4.2 [Msun] logfMbh [6.8/8.62] Log virial mass of black hole
modified by f
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Byte-by-byte Description of file: table9.dat
--------------------------------------------------------------------------------
Bytes Format Units Label Explanations
--------------------------------------------------------------------------------
1- 19 A19 --- SDSS SDSS DR7 object identifier
(JHHMMSS.ss+DDMMSS.s)
21- 26 F6.4 --- z [0.1/1] Spectroscopic redshift
28- 31 F4.2 [Msun] logMbh [6.99/9.2] Log virial mass of black hole
33- 37 F5.2 [10-7W] logL5100 [42.73/44.72] Log luminosity at 5100Å;
erg/s
39- 43 F5.3 --- Lb/LE [0.001/0.3] Bolometric to Eddington
luminosities ratio (Lbol=9.8*L5100)
45- 48 F4.1 --- f [0.3/30.8] Virial factor (G4)
50- 52 I3 km/s sigma [44/379] Stellar velocity dispersion
54- 55 I2 km/s e_sigma [2/74] Uncertainty in sigma
57- 60 F4.2 [Msun] logfMbh [7.9/9.9] Log virial mass of black hole
modified by f
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Global notes:
Note (G1): Measurements taken from Table 2 of Liu+ (2019, J/ApJS/243/21)
or converted from the relevant quantities in Table 2 of Liu+ (2019).
Note (G2): In units of rg, where rg is the gravitational radius of the
black hole and rBLR=33.65L440.533 light-days with
L44=L5100/(1e44erg/s).
Note (G3): Estimated from Equation (6):
logrBLR(Hβ)=1.65+0.45logL44-0.35RFeII
where rBLR(Hβ) is rBLR in units of light-days for Hβ,
L44=L5100/(1044erg/s), and RFeII is the line ratio of
FeII to Hβ.
and Equation (7):
logMRM(RFeII)=logMRM-0.083logL44-0.35RFeII+0.123
A NULL value denotes no data for RFeII, which results in no data for
these columns.
In Table 3, the value "1.6E+106" in rBLRR has been set to NULL value by CDS.
Note (G4): f is estimated by log(f)=0.8+0.8log(Mdotfg=1_),
where Mdotfg=1_ is estimated by Lbol/LEdd/η and
η=0.038.
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History:
From electronic version of the journal
License: CC-BY-4.0
(End) Prepared by [AAS], Emmanuelle Perret [CDS] 21-May-2026