The radio luminosity, black hole mass and Eddington ratio for quasars from the Sloan Digital Sky Survey

Abstract

We investigate the $\mbh- \sigma_*$ relation for radio-loud quasars with redshift $z<0.83$ in Data Release 3 of the Sloan Digital Sky Survey (SDSS). The sample consists of 3772 quasars with better model of H$\beta$ and \oiii lines and available radio luminosity, including 306 radio-loud quasars, 3466 radio-quiet quasars with measured radio luminosity or upper-limit of radio luminosity (181 radio-quiet quasars with measured radio luminosity). The virial supermassive black hole mass (\mbh) is calculated from the broad \hb line, the host stellar velocity dispersion ($\sigma_*$) is traced by the core \oiii gaseous velocity dispersion, and the radio luminosity and the radio loudness are derived from the FIRST catalog. Our results are follows: (1) For radio-quiet quasars, we confirm that there is no obvious deviation from the $\mbh- \sigma_*$ relation defined in inactive galaxies when \mbh uncertainties and luminosity bias are concerned. (2) We find that radio-loud quasars deviate much from the $\mbh- \sigma_*$ relation respect to that for radio-quiet quasars. This deviation is only partly due to the possible cosmology evolution of the $\mbh- \sigma_*$ relation and the luminosity bias. (3) The radio luminosity is proportional to $\mbh^{1.28^{+0.23}_{-0.16}}(\lb/\ledd)^{1.29^{+0.31}_{-0.24}}$ for radio-quiet quasars and $\mbh^{3.10^{+0.60}_{-0.70}}(\lb/\ledd)^{4.18^{+1.40}_{-1.10}}$ for radio-loud quasars. The weaker correlation of the radio luminosity dependence upon the mass and the Eddington ratio for radio-loud quasars shows that other physical effects would account for their radio luminosities, such as the black hole spin.

Full text

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arXiv:0803.3411v1 [astro-ph] 24 Mar 2008
The radio luminosity, black hole mass and Eddington ratio for
quasars from the Sloan Digital Sky Survey
Wei-Hao. Bian1,2, Yan-Mei. Chen1, Chen. Hu3, kai. Huang2and Yan. Xu2
1Key Laboratory for Particle Astrophysics, Institute of High Energy Physics, Chinese Academy of
Sciences, Beijing 100039, China
2Department of Physics and Institute of Theoretical Physics, Nanjing Normal University, Nanjing
210097, China
3National Astronomical Observatories, Chinese Academy of Sciences, Beijing 100012, China
Abstract We investigatethe MBH−σ∗relationforradio-loudquasars with redshiftz < 0.83
in Data Release 3 of the Sloan Digital Sky Survey (SDSS). The sample consists of 3772
quasars with better model of Hβ and [O III] lines and available radio luminosity, includ-
ing 306 radio-loud quasars, 3466 radio-quiet quasars with measured radio luminosity or
upper-limit of radio luminosity (181 radio-quiet quasars with measured radio luminosity).
The virial supermassive black hole mass (MBH) is calculated from the broad Hβ line, the
host stellar velocity dispersion (σ∗) is traced by the core [O III] gaseous velocity dispersion,
and the radio luminosity and the radio loudness are derived from the FIRST catalog. Our
results are follows: (1) For radio-quiet quasars, we confirm that there is no obvious devia-
tion from the MBH− σ∗relation defined in inactive galaxies when MBHuncertainties and
luminosity bias are concerned. (2) We find that radio-loud quasars deviate much from the
MBH−σ∗relation respect to that for radio-quiet quasars. This deviation is only partly due to
the possible cosmology evolution of the MBH− σ∗relation and the luminosity bias. (3) The
radio luminosity is proportional to M
BH
and M
BH
radio luminosity dependence upon the mass and the Eddington ratio for radio-loud quasars
shows that other physical effects would account for their radio luminosities, such as the black
hole spin.
1.28+0.23
−0.16
(LBol/LEdd)1.29+0.31
−0.24for radio-quiet quasars
3.10+0.60
−0.70
(LBol/LEdd)4.18+1.40
−1.10for radio-loud quasars. The weaker correlation of the
Key words: quasars: emission lines — galaxies: nuclei — galaxies: bulges — black hole
physics
1 INTRODUCTION
The relation between the supermassive black hole (SMBH) mass and the host stellar velocity dispersion
(hereafter MBH− σ∗relation) is one of the most important results in the study of supermassive black
holes (SMBHs) in these decades, implying the intimate correlation between the SMBHs and their host
galaxies (e.g. Gebhardt et al. 2000; Ferrarese & Merrit 2000; Tremaine et al. 2002; Lauer et al. 2007). This
correlation would provide strong constraints for the evolution of active galactic nuclei (AGNs) if we know
∗ Supported by the National Natural Science Foundation of China.
⋆ E-mail: bianwh@ihep.ac.cn

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2 W. Bian, et al.
AGNs follow this relation or not. However it is still under debate for different kind of AGNs, such as radio-
loud AGNs, narrow-line Seyfert 1 galaxies, intermediate supermassive black hole, et al. (e.g., Nelson 2001;
Boroson 2003; Shield et al. 2003; Bian & Zhao 2004; Grupe & Mathur 2004; Bonning et al. 2005; Greene
& Ho 2006; Woo et al. 2006; Zhou et al. 2006; Salviander et al. 2007; Komossa & Xu 2007; Shen et al.
2008). In order to study this relation for AGNs, we should calculate MBHand σ∗as accurately as possible.
The width of the broad emission line (e.g., Hβ , Hα , Mg II , C IV ) can be used to trace virial velocity
of the clouds in broad line regions (BLRs) when the line contribution from narrow-line regions (NLRs) is
reasonably removed, and the reverberation mapping method or the empirical luminosity-size relation can
be used to calculate the BLRs size (e.g., Kaspi et al. 2000; McLure & Dunlop 2004; Bian & Zhao 2004;
Peterson et al., 2004; Greene & Ho 2005b). The gas velocity dispersion of the narrow lines (e.g., [O III]
, [O II] , [S II] ) from NLRs are usually used to trace the host stellar velocity dispersion (e.g., Nelson &
Whittle 1996; Greene & Ho 2005a). We also can directly measure the host velocity dispersion from AGNs
host spectra (e.g., Kauffmann et al. 2003; Heckman et al. 2004; Greene & Ho 2005a; Bian et al. 2006). The
larger number of quasars found in the Sloan Digital Sky Survey (SDSS) provides the possibility to tackle
the MBH− σ∗relation in radio-loud quasars. (e.g. Bian & Zhao 2004; Salviander et al. 2007).
The dichotomy of the radio loudness in quasars is a long-time question since the discovery of quasars
(Sandage 1965; Strittmatter et al. 1980; Kellermann et al. 1989). The radio luminosity is assumed com-
ing from the relativistic electrons powered by a jet, which is intimately connected with the SMBH (e.g.,
Begelman et al. 1984; Blundell & Beasley 1998).For scale-free jet physics and accretion theories, the radio
luminosity is related to the central engines, such the SMBH mass, the SMBH spin, the Eddington ratio,
et al. (Heinz & Sunyaev 2003). For radio-loud or radio-quiet quasars, the dependence of the radio loud-
ness/luminosity upon the SMBH mass/Eddington ratio is discussed by many peoples, some support it and
some against it. (e.g., Franceschini et al. 1998; Laor 2000; Lacy et al. 2001; Ho 2002; Woo & Urry 2002;
McLure & Jarvis 2004; Wang et al. 2004; Greene et al. 2006; Liu et al. 2006; Sikora 2007; Panessa et al.
2007). Laor (2003) gave some comments on the origin of AGNs radio loudness and discussed the some
error SMBH mass estimation for radio-loud AGNs in the literature, which is mainly due to optical spectra
with low signal-to-noise ratios, no correction of Hβ contribution from narrow line regions (NLRs).
In this paper, we use larger number of quasars with redshifts z < 0.83 in SDSS Data Release 3 (DR3;
see Abazajian et al. 2005) to investigate the MBH−σ∗relation and the radio luminosity dependenceon the
SMBH mass and the Eddington ratio for radio-loud and radio-quiet quasars. In §2, we briefly introduce the
SDSS quasars Data Release 3 catalog of Schneider et al. (2005). §3 is the data analysis. §4 introduces the
methods to calculate the SMBH masses and the Eddingtonratios. Our results and discussions of MBH−σ∗
relation and the origin of radio luminosity are given in §5 and §6, respectively. The last section is our
conclusions.All of the cosmologicalcalculations in this paperassume H0= 70km s−1Mpc−1, ΩM= 0.3,
ΩΛ= 0.7.
2 SAMPLE AND DATA ANALYSIS
The sample used in this paper is selected from the SDSS quasars Catalog III, which covers a spectroscopic
area of 1360 sq. deg., about 40% of the proposed SDSS survey area (Schneider et al. 2003). This catalog
consists of 46,420 quasars in SDSS DR3 with Mi< −22. The catalog also contains radio emission proper-
ties from Faint Images of the Radio Sky at Twenty-cm (FIRST) survey within 2.0” of the quasars position
(see Col. 17 in their Table 1).
SDSS optical spectra cover the wavelength range 3800-9200˚ A with a resolution of 1800 < R < 2100.
In order to calculate SMBH mass from the broad Hβ line and the host stellar velocity dispersion from
the narrow [O III] line, we just consider the quasars with redshifts less than 0.83, which consists of 9753
quasars. Because whether the SMBH mass from Mg II linewidth is consistent with that from Hβ line width
is still a complex question (e.g., Salviander et al. 2007), here we don’t consider using Mg II linewidth to
calculate the SMBH mass.
The radio luminosity at 5GHz is calculated from the peak flux density listed in Col. 17 in Table 2
(Schneider et al. 2003), considering the spectral index of α = 0.5, where fν ∝ ν−α. The radio loudness
R is calculated from: R = f5GHz/fB, where f5GHzand fBare the rest-frame flux density at 5 GHz and

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Radio-loud and radio-quiet quasars from SDSS3
Fig.1 Sample of SDSS spectrum measurement for SDSS J113801.84+490506.5. In the top
panel, the black curve is the observed spectrum, the red line is the sum of the power-law contin-
uum, the Balmer continuum and Fe II multiples (blue curves). The green ranges are our fitting
windows. The bottom panel is the multi-Gaussian fit for Hβ and [O III] lines. The red line is the
sum of all multi-Gaussian (blue curves). The green curve is our fitting range of the pure Hβ and
[O III] emissions after the subtraction of the power-law continuum, the Balmer continuum and
Fe multiples.
4400˚ A, considering k correction. R = 10 is commonly used to define radio-loud quasars and radio-quiet
quasars (e.g., McLure & Jarvis 2004), as well as the radio luminosity at 5 GHz (e.g., Lacy 2001).
For 9573 quasars with z < 0.83 from SDSS DR3, 914 quasars are detected by FIRST, 7846 quasars
are under the FIRST flux limit, and 993 quasars are not in the region covered by FIRST. For these objects
with non-detection in FIRST, we only have the upper-limits of the radio luminosity and the radio loudness.
598 quasars with detection in FIRST and R ≥ 10 are classified as radio-loud quasars. 316 quasars with
detection in FIRST and R < 10 are classified as radio-quiet quasars. 5712 quasars with non-detection in
FIRST and R < 10 are classified as radio-quietquasars but with upper-limits of R and the radio luminosity.
As we know, NLRs can contribute Hβ emission in the total Hβ profile; [O III] usually shows non-
symmetric profile and its narrow/core component can trace the stellar velocity better (e.g., Greene & Ho
2005a); optical and ultraviolet Fe II multiples are often presented in quasars spectra; Balmer continuum is
required because of the existence of strong Balmer emission lines, therefore, we use following steps to do
the SDSS spectral measurements.
(1) First, we do the Galactic extinction in the observed spectra by using the extinction law of Cardelli,
Clayton & Mathis (1989) (IR band) and O’Donnell (1994) (optical band), then the spectra are transformed
into the rest frame defined by the redshifts given in their FITS headers.
(2) The optical and ultraviolet Fe II template from the prototype NLS1 I ZW 1 is used to subtract
the Fe II emission from the spectra (Boroson & Green 1992; Vestergaard & Wilkes 2001). The I ZW
1 template is broadened by convolving with a Gaussian of various linewidths and scaled by multiplying
a factor. A power-law continuum and the Balmer continuum are added in the fitting. We calculate the
Balmer continuum following Grandi (1982) and also add the high order Balmer lines at the red side of the
Balmer edge using the result in Storey & Hummer(1995).The best subtraction of the Fe II , power-law and
Balmer continuumis found when χ2minimized in the fitting windows: 3550-3645,4170-4260,4430-4770,
5080-5550, 6050-6200, 6890-7010˚A (see a sample fit in the top panel of Figure 1). The monochromatic
luminosity at 5100˚ A(λLλ(5100˚ A) ) is calculate from the power-law continuum.
(3) Two sets of two-Gaussian are used to model [O III] λλ4959,5007 lines. Three-Gaussian is used to
model Hβ line. For the doublet [O III] λλ4959,5007, we take the same linewidth for each component, and
fix the flux ratio of [O III] λ4959 to [O III] λ5007 to be 1:3. Two componentsof Hβ (supposed from NLRs)
are set to have the same linewidth of each component of [O III] λ5007 and their flux are constrained to be

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4W. Bian, et al.
less than 1/2 of each component of [O III] λ5007. The linewidth of the broad component of Hβ is used to
trace the virial velocity around central SMBH (see a sample fit in the bottom panel of Figure 1).
From above spectral measurement, we obtain the full width at half maximum (FWHM) of the broad
Hβ line and the narrow/core [O III] line (FWHMHβ, FWHMn
5100˚ A(λLλ(5100˚ A)),thetotalHβ luminosity(LHβ),as well asthe radioluminosityandtheradioloudness
for SDSS DR3 quasars with z < 0.83.
Objects without the Hβ or [O III] lines are eliminated. In order to obtain the reliable spectra fit, we
carefully select objects for analysis. The line equivalent width (EW) can show line signal-to-noise ratios.
The error of EW can be regard as a tracer to show the fitting goodness. Because the Hβ is usually strong,
we don’t constrain EW of Hβ line, only constrain the error of EW for Hβ line. We select objects by the
criterions of EW of [O III] larger than 1.5, the errors of EWs of Hβ and [O III] λλ4959,5007 less than
100%. It leads to 367 radio-loud quasars, 3677 radio-quiet quasars including 207 radio-quiet quasars with
measured radio luminosity. Then we visually check these spectra one by one.
At last,we obtaina sampleof3772quasarswith bettermulti-componentsmodelofHβ and[O III] lines,
including 3466 radio-quiet quasars (hereafter ”RQ total sample”), 306 radio-loud quasars (hereafter ”RL
sample”). Most objects in these 3466 radio-quiet quasars only have upper-limits of the radio luminosity
and the radio loudness, 181 radio-quiet quasars (hereafter ”RQ sample”) have the measurements of the
radio luminosity and the radio loudness. We use the radio-quiet sample as the control sample to discuss the
MBH− σ∗in radio-loud quasars.
[OIII]), the monochromatic luminosity at
3 SMBH MASS, EDDINGTON RATIO AND STELLAR VELOCITY DISPERSION
The BLRs size is calculated from the monochromatic luminosity at 5100˚ A (λLλ(5100˚ A) ) or the Hβ
luminosity by the following formulae (Kaspi et al. 2005):
RλLλ(5100˚ A)
BLR
= (22.3 ± 2.1)
?λLλ(5100˚ A)
1044erg s−1
?0.69±0.05
lt − days
(1)
RLHβ
BLR= (82.3 ± 7.0)
?
LHβ
1043erg s−1
?0.80±0.11
lt − days
(2)
We use the FWHM of the broad Hβ line (FWHMHβ) to trace the BLRs virial velocity vBLR=√f ×
FWHMHβ, f is the calibration factor. If BLRs cloud is disk-like with a inclination of θ (Wills & Browne
1986),
FWHMHβ= 2(v2
r+ v2
BLRsin2θ)1/2
(3)
where vr is the random isotropic component. We can then calculate the SMBH masses by MBH =
RBLRv2
BLR
G
(Kaspi et al. 2000; Kaspi et al. 2005):
MBH= f × 4.35 × 106
?FWHMHβ
103km s−1
?2?λLλ(5100˚ A)
1044erg s−1
?0.69
M⊙.
(4)
MBH= f × 1.61 × 107
?FWHMHβ
103km s−1
?2?
LHβ
1043erg s−1
?0.80
M⊙.
(5)
If assuming vr ≪ vBLR, and the random orbits of BLRs clouds, f = 0.75. Onken et al. (2004) did a
calibration by the MBH− σ∗relation and suggested f ≈ 1.4 (see also Collin et al. 2006; Dasyra et al.
2007). In our mass calculation, we adopt the random orbits of BLRs clouds and f = 0.75.

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Radio-loud and radio-quiet quasars from SDSS5
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Fig.2 The distributions of MBH, λLλ(5100˚ A), FWHMHβ, σn
with radio loudness (top), 306 radio-loudquasars with measured radio luminosity (middle), total
3466 radio-quiet quasars (bottom).
[OIII]for 181 radio-quiet quasars
We calculate the Eddington ratio, i.e., the ratio of the bolometric luminosity (Lbol) to the Eddington
luminosity(LEdd),whereLEdd= 1.26×1038(MBH/M⊙)erg s−1. Thebolometricluminosityis calculated
from the monochromatic luminosity at 5100˚ A , Lbol = cBλLλ(5100˚ A), where we adopt the correction
factor cBof 9 (Kaspi et al. 2000; Marconi et al. 2004; Richards et al. 2006; Netzer & Trakhtenbrot 2007).
We use the gas velocity dispersion of the narrow/core [O III] component from NLRs to trace the host
stellar velocity dispersion, σn
[OIII]=
?σ2
redshift (Bian et al. 2006). For SDSS spectra, the mean value of instrument resolution σinstis 60 km s−1
for [O III] (e.g. Greene & Ho 2005a).
In Figure 2, we present the distributions of the SMBH mass, λLλ(5100˚ A), FWHMHβ, σn
181 radio-quiet quasars with radio loudness (top), 306 radio-loud quasars with measured radio luminosity
(middle), total 3466 radio-quiet quasars (bottom). The mean of SMBH mass is 8.65±0.03 with a standard
deviationof 0.45 for RL sample of 306 radio-loudquasars, 8.36±0.04with a standarddeviationof 0.48 for
RQ sample of 181 radio-quiet quasars with reliable radio luminosity, 8.32±0.01 with a standard deviation
of 0.43 for total 3466 radio-quiet quasars. Radio-loud quasars have larger SMBH masses, and there is only
a few objects with mass less than 108M⊙(see Figure 3), which is consistent with the results of McLure &
Jarvis (2004). Radio-loud quasars have smaller Eddington ratios, respect to radio-quiet quasars (see Table
1). We find that, for radio-loud quasars, the mean of Hβ FWHM is 7493 ± 165 km s−1with a standard
deviation of 2882 km s−1, the mean of log λLλ(5100˚ A) is 44.86±0.03 erg s−1with a standard deviation
of 0.45; for radio-quiet quasars, the mean of Hβ FWHM is 5780 ± 176 km s−1with a standard deviation
obs− [σinst/(1 + z)]2, where σobs= FWHMn
[OIII]/2.35, z is the
[OIII]for