## Abstract

We have used the widths of Hβ and [O iii] emission lines to investigate the black hole–bulge relation in radio-loud active galactic nuclei (AGNs), radio-quiet AGNs and narrow-line Seyfert 1 galaxies (NLS1s). The central black hole mass, Mbh, is estimated from the Hβ linewidth and the optical luminosity, and the bulge velocity dispersion, σ, is directly estimated from the width of the [O iii] line. We have found that radio-quiet AGNs follow the established Mbh–σ relationship in nearby inactive galaxies, while radio-loud AGNs and NLS1s deviate from this relationship. There are two plausible interpretations for the deviation of radio-loud AGNs. One is that the size of broad-line regions (BLRs) emitting the Hβ line is overestimated because of the overestimation of optical luminosity. The other is that the dynamics of BLRs and/or narrow-line regions in radio-loud AGNs is different from that in radio-quiet AGNs. The deviation of NLS1s may be due to the small inclination of BLRs to the line of sight or the reliability of the [O iii] linewidth as the indicator of stellar velocity dispersion because of its complex multiple components.

## Introduction

Evidence shows that the evolution of black holes and that of their host galaxies appear to be closely coupled. It has been found that there is strong correlation between the central black hole masses, Mbh, and their bulge stellar velocity dispersion, σ. Tremaine et al. (2002) investigated this relationship in a sample of 31 nearby inactive galaxies and gave a better expression as

(1)

There are many methods to estimate the central black hole masses (Bian & Zhao 2003a, and references therein). In these methods, the reverberation method is thought to be more reliable. Using the reverberation mapping method, the sizes of broad-line regions (BLRs) and then the central black hole masses were obtained for 37 active galactic nuclei (AGNs; Ho 1998; Wandel, Peterson & Malkan 1999; Kaspi et al. 2000). For some AGNs with available bulge velocity dispersion and the reverberation mapping mass, Gebhardt et al. (2000) and Ferrarese et al. (2001) also found that these AGNs also follow the Mbh–σ relation founded in the nearby inactive galaxies. As we know, it is difficult to obtain the bulge velocity dispersion of AGNs. In order to investigate this relation in a larger sample of AGNs, Nelson (2001) used the width of the [O iii] line emitting from the narrow-line region (NLR) to indicate the bulge velocity dispersion, where σ= FWHM([O iii])/2.35, and found that these 37 AGNs with the reverberation mapping masses follow the Mbh–σ relation. Wang & Lu (2001) investigated this relation in a sample of narrow-line Seyfert 1 galaxies (NLS1s) from Veron-Cetty & Veron (2001). They used the B-band magnitude and the Hβ FWHM to estimate the black hole masses and the [O iii] FWHM to indicate the bulge velocity dispersion. They found that NLS1s also follow the Mbh–σ relation but with more scatter. We should notice that NLS1s deviated from the correlation defined in the nearby inactive galaxies if we think [O iii] FWHM is not overestimated because of the spectral resolution. Using the Sloan Digital Sky Survey (SDSS), Boroson (2003) investigated the relation between the black hole mass via the Hβ FWHM and the stellar velocity dispersion via [O iii] FWHM in a sample of 107 low-redshift radio-quiet AGNs. They have found that the correlation is consistent with that defined in nearby galaxies and the [O iii] FWHM can predict black hole mass to a factor of 5. There are only a few radio-loud AGNs in Boroson (2003). Shields et al. (2003) also investigated the Mbh–σ relation as a function of redshift for an assembled sample of quasars. They suggested that this correlation can be right out to redshift of z≈ 3. However, Shields et al. (2003) noticed that the radio-loud AGNs seem to deviate from this correlation.

The central black hole mass can be obtained from the Hβ FWHM and the optical luminosity, and the bulge velocity dispersion can be indicated by the [O iii] FWHM. This provides us with the opportunity to investigate the Mbh–σ relation in a larger sample of AGNs with available optical spectra. Moreover, we need to investigate this correlation in a larger sample of radio-loud AGNs and NLS1s. In the next section we present the method to estimate the black hole mass, and then our adopted data set. Our results and discussion are given in Section 3. A conclusion is presented in the final section. All of the cosmological calculations in this paper assume H0= 75 km s−1 Mpc−1, ΩM= 0.3, ΩΛ= 0.7.

## Method and Data

### Estimation of the black hole masses

For the reverberation mapping method, it takes a long time to simultaneously monitor the variability of the broad emission line and the continuum, and then to obtain the BLRs size. Up to now, there are only 37 AGNs with the reverberation mapping mass (Ho 1998; Wandel et al. 1999; Kaspi et al. 2000). Fortunately, with the study of the reverberation mapping method, Kaspi et al. (2000) found an empirical correlation between the BLR size and the monochromatic luminosity at 5100 Å

(2)
where λLλ (5100 Å) can be estimated from the optical magnitude by adopting an average optical spectral index of −0.3 and accounting for Galactic reddening and K-correction (Wang & Lu 2001). Assuming that the Hβ widths reflect the Keplerian velocity of the line-emitting BLR material around the central black hole, we can estimate the viral black hole mass
(3)
where G is the gravitational constant and V is the velocity of the line-emitting material. V can be derived from the FWHM of the Hβ width. Assuming the random orbits, Kaspi et al. (2000) related V to the FWHM of the Hβ line by .

This method to estimate the central black hole masses of AGNs has been discussed by several authors (Wang & Lu 2001; Bian & Zhao 2003b,c; Shields et al. 2003; Boroson 2003).

### Data of NLS1s

Williams, Pogge & Mathur (2002) presented a sample of 150 low-redshift NLS1s (z < 0.8) found within the SDSS. Using the SDSS Query Tool, we downloaded the spectra data and the photometry data of these 150 NLS1s. We used the Hβ FWHM from their table 1. The value of λLλ (5100 Å) is estimated from the r* magnitude. Fluxes were converted to luminosity using the Schlegel, Finkbeiner & Davis (1998) maps for correcting for Galactic absorption. We can obtain the central black hole masses in these 150 NLS1s through equations (2) and (3). Each spectrum was shifted to the rest frame and we performed a quadratic continuum fit. Using the splot tools in the iraf software, we measured the [O iii] FWHM through a Gaussian curve fit to each [O iii] line. The spectrum resolution R is about 1800, which is equivalent to 166 km s−1. The error of the measured [O iii] FWHM and Hβ FWHM is about 10 per cent. The [O iii] FWHM is used to estimate the host velocity dispersion. It is difficult to measure [O iii] FWHM in three NLS1s of SDSS J010226.31−003904.6, SDSS J013521.68−004402.2 and SDSS J15324.367−004342.5 because of their [O iii] line with irregular profile or low signal-to-noise ratio, which are omitted in our discussion. We list the NLS1 data in Table 1.

Table 1.

M bh and σ [oiii] for NLS1s in the SDSS. The columns give the following: (1) object name; (2) redshift; (3) FWHM of the broad Hβ line in units of km s−1; (4) log of continuum luminosity at 5100 Årest wavelength in units of erg s−1; (5) log of the black hole mass in units of solar mass; (6) log of the bulge velocity dispersion derived from the FWHM of the [O iii] line in units of erg s−1.

Table 1.

M bh and σ [oiii] for NLS1s in the SDSS. The columns give the following: (1) object name; (2) redshift; (3) FWHM of the broad Hβ line in units of km s−1; (4) log of continuum luminosity at 5100 Årest wavelength in units of erg s−1; (5) log of the black hole mass in units of solar mass; (6) log of the bulge velocity dispersion derived from the FWHM of the [O iii] line in units of erg s−1.

Table 2.

Mbh and σ[oiii] for AGNs. Teh columns give the following: (1) object name; (2) RQ denotes radio-quiet objects, SS denotes steep-spectrum objects and FS denotes flat-spectrum objects; (3) redshift; (4) FWHM of the broad Hβ line in units of km s−1 (5) log of continuum luminosity at 5100 Å rest wavelength in units of erg s−1; (6) log of the black hole mass in units of solar mass; (7) log of the bulge velocity dispersion derived from the FWHM of the [O iii] line in units of m s−1.

Table 2.

Mbh and σ[oiii] for AGNs. Teh columns give the following: (1) object name; (2) RQ denotes radio-quiet objects, SS denotes steep-spectrum objects and FS denotes flat-spectrum objects; (3) redshift; (4) FWHM of the broad Hβ line in units of km s−1 (5) log of continuum luminosity at 5100 Å rest wavelength in units of erg s−1; (6) log of the black hole mass in units of solar mass; (7) log of the bulge velocity dispersion derived from the FWHM of the [O iii] line in units of m s−1.

## Results and Discussion

### MHβ–σ[O III] relation

In Figs 1 and 2, we plot black hole masses estimated from the Hβ linewidth versus the bulge velocity dispersion obtained from the [O iii] linewidth for the samples of Marziani et al. (1996), Shields et al. (2003), Wang & Lu (2001), Nelson (2001), Boroson (2003) and Williams et al. (2002).

Figure 1.

Black hole masses derived from the Hβ linewidth and B-band magnitude versus the width of the [O iii] line for AGNs. The solid line shows the Mbh–σ relation from equation (1); open circles, radio-quiet AGNs in Shields et al. (2003); solid circles, radio-loud AGNs in Shields et al. (2003); solid triangles, radio-loud AGNs from Marziani et al. (1996); open triangles, radio-quiet AGNs from Marziani et al. (1996); plus signs, AGNs from Nelson (2001); crosses, AGNs from Boroson (2003).

Figure 1.

Black hole masses derived from the Hβ linewidth and B-band magnitude versus the width of the [O iii] line for AGNs. The solid line shows the Mbh–σ relation from equation (1); open circles, radio-quiet AGNs in Shields et al. (2003); solid circles, radio-loud AGNs in Shields et al. (2003); solid triangles, radio-loud AGNs from Marziani et al. (1996); open triangles, radio-quiet AGNs from Marziani et al. (1996); plus signs, AGNs from Nelson (2001); crosses, AGNs from Boroson (2003).

Figure 2.

Black hole masses derived from the Hβ linewidth and B-band magnitude versus the width of the [O iii] line for narrow-line AGNs. The solid line shows the Mbh–σ relation from equation (1); open squares, NLS1s from Wang & Lu (2001); solid squares, NLS1s from Williams et al. (2002).

Figure 2.

Black hole masses derived from the Hβ linewidth and B-band magnitude versus the width of the [O iii] line for narrow-line AGNs. The solid line shows the Mbh–σ relation from equation (1); open squares, NLS1s from Wang & Lu (2001); solid squares, NLS1s from Williams et al. (2002).

The sample of Shields et al. (2003) included 49 radio-quiet AGNs and 35 radio-loud AGNs. Shields et al. (2003) used the Hβ emission linewidth to investigate the Mbh–σ relation as a function of redshift for an assembled sample of quasars. They suggested that this correlation is not a function of redshift and can be right out to redshift of z≈ 3. They adopted the relation between BLR sizes and continuum luminosity suggested by the photoionization model, RL0.5. In order to be consistent with our calculation, we recalculated the black hole masses of AGNs in their sample using equations (2) and (3). The sample of Wang & Lu (2001) consisted of 59 NLS1s from Veron-Cetty & Veron (2001). The sample of Williams et al. (2002) included 147 NLS1s from the SDSS. Up to now, this is the largest sample of NLS1s.

From Figs 1 and 2, it is found that radio-quiet AGNs in Marziani et al. (1996), Shields et al. (2003) and Boroson (2003) follow the Mbh–σ relation defined in equation (1) with a larger scatter compared with that in Nelson (2001). However, the radio-loud AGNs in Marziani et al. (1996) and Shields et al. (2003), and the NLS1s in Wang & Lu (2001) and Williams et al. (2002) seemed not to follow this relation.

For radio-loud AGNs, the mean black hole mass estimated from the Hβ FWHM is larger than that from the [O iii] FWHM. For NLS1s, the mean black hole mass estimated from the Hβ FWHM is smaller than that from the [O iii] FWHM. In Figs 1 and 2, it is clear that radio-loud AGNS and NLS1s deviated from the relation defined in equation (1).

We also calculated the black hole mass, M[O III], directly from equation (1) using the [O iii] linewidth as the indicator of σ. Table 3 shows the distribution of log(M/M[O III]) for different AGN samples. The distribution of log(M/M[O III]) for radio-quiet AGNs in Marziani et al. (1996) is −0.36 ± 0.19 with a standard deviation of 0.81 (see Table 3). This shows that the mass estimated from the Hβ linewidth is consistent with that from the [O iii] linewidth but with a large scatter, which is consistent with the data of radio-quiet AGNs in Fig. 1. However, the distribution of log(M/M[O III]) for radio-loud AGNs in Marziani et al. (1996) is 0.51 ± 0.13 with a standard deviation of 0.73. This shows that the mass estimated from the Hβ linewidth is larger than that from the [O iii] linewidth, which is also consistent with the data of radio-loud AGNs in Fig. 1. The distributions of log(M/M[O III]) for radio-loud and radio-quiet AGNs in Shields et al. (2003) are listed in Table 3. The results for the sample of Shields et al. (2003) are consistent with those for the sample of Marziani et al. (1996).

Table 3.

The distributions of log(M/M[oiii]) for different types ofAGNs:RL(Marziani), radio-loudAGNs in Marziani Sulentic et al. (1996); FS (Marziani), flat-spectrum AGNs in Marziani Sulentic et al. (1996); SS (Marziani), steep-spectrumAGNsin Marziani Sulentic et al. (1996); RQ (Marziani), radio-quiet AGNs in Marziani Sulentic et al. (1996); RL (Shields), radio-loud AGNs in Shields et al. (2003); RQ (Shields), radio-quiet AGNs in Shields et al. (2003); RQ AGNs (Boroson), radio-quiet AGNs in Boroson (2003); NLS1s (Wang): NLS1s inWang & Lu (2001); NLS1s (Williams), NLS1s inWilliams et al. (2002).

Table 3.

The distributions of log(M/M[oiii]) for different types ofAGNs:RL(Marziani), radio-loudAGNs in Marziani Sulentic et al. (1996); FS (Marziani), flat-spectrum AGNs in Marziani Sulentic et al. (1996); SS (Marziani), steep-spectrumAGNsin Marziani Sulentic et al. (1996); RQ (Marziani), radio-quiet AGNs in Marziani Sulentic et al. (1996); RL (Shields), radio-loud AGNs in Shields et al. (2003); RQ (Shields), radio-quiet AGNs in Shields et al. (2003); RQ AGNs (Boroson), radio-quiet AGNs in Boroson (2003); NLS1s (Wang): NLS1s inWang & Lu (2001); NLS1s (Williams), NLS1s inWilliams et al. (2002).

### Uncertainties of black hole mass and stellar velocity dispersion

In our analysis, we used equations (2) and (3) to calculate the black hole masses and FWHM of the [O iii] line to indicate the bulge velocity dispersion. The errors of the calculated black hole masses using equations (2) and (3) are mainly from the accuracy of equations (2) and (3); the geometry and the dynamics of the BLRs, especially the disc inclination to the line of sight in NLS1s (Bian & Zhao 2002) and in flat-spectrum quasars (Jarvis & McLure 2002). The appropriate measurement of the Hβ linewidth for estimating the black hole mass has been discussed by some authors (Vestergaard 2002; Shields et al. 2003). The error in the mass estimation using equations (2) and (3) is about 0.5 dex (Wang & Lu 2001).

It is possible to measure the luminosity at 5100 Å (Lspec) for the 147 SDSS NLS1s spectrum. We compared the luminosity at 5100 Å estimated from r* (Lr) with that from the SDSS spectrum in Fig. 3. They are consistent and the distribution of log(Lr/Lspec) is 0.21 ± 0.01 with a standard deviation of 0.15. The mean mass estimation using Lr would be enhanced by 0.15 dex compared with that using Lspec.

Figure 3.

Monochromatic luminosity at 5100 Å measured from the spectra of the SDSS NLS1s versus that from r*-band magnitude.

Figure 3.

Monochromatic luminosity at 5100 Å measured from the spectra of the SDSS NLS1s versus that from r*-band magnitude.

McLure & Dunlop (2001) suggested that the assumption of random orbits of BLRs seems unrealistic for quasars, and that the BLR velocity should be related to the FWHM of Hβ as V= 1.5 × FWHM[Hβ]. It is equivalent to assume smaller inclination in quasars (McLure & Dunlop 2001). Gu, Cao & Jiang (2001) also used V= 1.5 × FWHM[Hβ] to estimate the velocity of BLRs in radio-loud AGNs. Jarvis & McLure (2002) investigated the relation between the black hole mass and radio luminosity in flat-spectrum quasars. Considering the Doppler boosting correction of the radio luminosity and the inclination correction of the BLR velocity, they found that flat-spectrum quasars follow the relation between radio luminosity and black hole mass found by Dunlop et al. (2003). Jarvis & McLure (2002) adopted a correction factor of 2 for the BLR velocity of flat-spectrum quasars as the effect of inclination, which would increase the black hole mass estimates by a factor of 4, ∼0.6 dex. Smaller inclination in radio-loud AGNs would enhance the value of BLR virial velocity derived from the Hβ linewidth and would make radio-loud AGNs deviate much from the line defined by equation (1) in Fig. 1.

The [O iii] linewidth may be overestimated by a factor of 1.3 because of the poor resolution spectrum (Veilleux 1991; Wang & Lu 2001). Considering the overestimation of the width of the [O iii] line, we found that NLS1s in Wang & Lu (2001) and SDSS NLS1s also deviate from the relation defined in equation (1) (see Fig. 2). The overestimation of bulge velocity dispersion derived from the observed [O iii] linewidth would also make radio-loud AGNs deviate much from the line defined in equation (1).

Radio-loud AGNs with significant Hβ blueshifts or redshifts have been observed (Marziani et al. 1996). The oversimple models involving pure rotation or radial motion are unlikely. There are many possible components of motion in the BLRs (Marziani et al. 1996). For luminous AGNs, bright emission lines would contribute to the optical continuum luminosity, which would overestimate the BLR sizes derived from equation (2). It is the use of a broad-band luminosity (optical magnitude) not being converted to the luminosity in 5100 Å properly that also accounts for the overestimate of BLR sizes (also see Fig. 3). The optical luminosity may be contaminated by the synchrotron emission from the jet for flat-spectrum quasars whose radio emission is beamed to us (Gu et al. 2001; Jarvis & McLure 2002). The overestimated optical continuum luminosity would overestimate BLR sizes, which would account for the overestimated black hole masses in radio-loud AGNs. This would lead to the deviation from the relation defined in equation (1) for radio-loud AGNs. If we think all types of galaxies follow the same Mbh–σ correlation, we should be cautious about using equations (2) and (3) to calculate the black hole masses for radio-loud AGNs.

## Conclusion

The correlation between the central black hole mass and the bulge velocity dispersion was investigated in radio-quiet AGNs, radio-loud AGNs and NLS1s. The main conclusions can be summarized as follows.

• Radio-quiet AGNs follow the Mbh–σ correlation defined by equation (1) founded in nearby inactive galaxies, while radio-loud AGNs and NLS1s seem not to follow this correlation.

• Small inclination or overestimated bulge velocity dispersion cannot account for the deviation of radio-loud AGNs from the correlation defined in equation (1). There are two possibilities to explain this deviation in radio-loud AGNs. One is that the size of the BLR emitting Hβ line is overestimated because of the overestimation of optical luminosity; the other is that the dynamics in BLRs and/or NLRs in radio-loud AGNs is different from that in radio-quiet AGNs.

• For NLS1s, small inclination may play a particular role in the deviation from the correlation defined in equation (1). We should consider the inclination effect in the black hole mass estimation using the Hβ FWHM.

### Acknowledgments

We thank the anonymous referee for valuable comments. This work has been supported by the NSFC (No. 10273007) and NSF of Jiangsu Provincial Education Department (No. 03KJB160060). The SDSS web site is http://www.sdss.org/. This research has made use of the NASA/IPAC Extragalactic Laboratory Database (NED), which is operated by the Jet Propulsion Laboratory, California Institute of Technology, under contract to NASA.

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