2 Data and analysis

A heterogeneous sample of 59 NLS1 galaxies were observed spectroscopically by Veron-Cetty et al. (2001) (hereafter VVG) with a moderate resolution of 3.4 Å. The measurement of the instrument-subtracted [OIII] and H$\beta$width as well as the optical magnitude at B band are listed in Table 1.

 

 

Table 1: Black hole mass estimates and narrow line cloud velocity dispersions. Column 1: name, Col. 2: B magnitude, Col. 3: redshift, Col. 4: the the Galactic hydrogen column density in units of 10²⁰ cm^-2, Col. 5: FWHM (in km s^-1) of the broad component of H$\beta$ line, Col. 6: FWHM (in km s^-1) of the broad component of [OIII] line, Col. 7: the estimated size of broad line region (in unit of day) using the empirical law (see Sect. 2.1) and Col. 8: the estimated black hole mass in unit 10⁷ $M_{\odot }$ (see Sect. 2.1). ^a the black hole mass has been measured in Kaspi et al. (2000) using reverberation mapping techniques.

Name	B	Z	NH	FWHM(H$\beta$)	FWHM([OIII])	$R_{\rm BLR}$	$M_{\rm BH}$
Mrk335a	13.7	0.025	3.8	$\cdots$	245	$\cdots$	0.63
IZW1	14.0	0.061	5.1	$\cdots$	1040	$\cdots$	$\cdots$
TonS180	14.4	0.062	1.5	1085	435	89.8	1.16
Mrk359	14.2	0.017	4.8	900	180	19.0	0.17
MS01442-0055	15.6	0.080	2.8	1100	240	63.7	0.85
Mrk1044	14.3	0.016	3.0	1010	335	15.0	0.17
HS0328+0528	16.7	0.046	8.9	1590	220	18.9	0.53
IRAS04312+40	15.2	0.020	34.5	860	380	52.2	0.42
IRAS04416+12	16.1	0.089	14.1	1470	650	92.8	2.20
IRAS04576+09	16.6	0.037	13.5	1210	380	18.5	0.30
IRAS05262+44	13.6	0.032	38.3	740	365	342.3	2.06
RXJ07527+261	17.0	0.082	5.1	1185	400	29.9	0.46
Mrk382	15.5	0.034	5.8	1280	155	23.0	0.41
Mrk705	14.9	0.028	4.0	1790	365	23.6	0.83
Mrk707	16.3	0.051	4.7	1295	315	23.2	0.43
Mrk124	15.3	0.056	1.3	1840	380	43.0	1.60
Mrk1239	14.4	0.019	4.1	1075	400	18.9	0.24
IRAS09571+84	17.0	0.092	3.9	1185	240	33.4	0.52
PG1011-040	15.5	0.058	4.5	1455	400	46.3	1.08
PG1016+336	15.9	0.024	1.6	1590	315	8.9	0.25
Mrk142	15.8	0.045	1.2	1370	260	22.7	0.47
KUG1031+398	15.6	0.042	1.4	935	315	23.6	0.23
RXJ10407+330	16.5	0.081	2.2	1985	460	35.3	1.53
Mrk734	14.6	0.049	2.7	1825	180	59.6	2.18
Mrk739E	14.1	0.030	2.2	1615	380	39.9	1.14
MCG06.26.012	15.4	0.032	1.9	1145	220	18.6	0.27
Mrk42	15.4	0.024	1.9	865	220	12.4	0.10
NGC4051a	12.9	0.002	1.3	1120	200	1.8	0.13
PG1211+143a	14.6	0.085	2.8	1975	410	132.6	4.05
Mrk766	13.6	0.012	1.8	1630	220	14.8	0.43
MS12170+0700	16.3	0.080	2.2	1765	365	39.4	1.35
MS12235+2522	16.3	0.067	1.8	800	240	29.9	0.21
IC3599	15.6	0.021	1.4	$\cdots$	280	8.8	$\cdots$
PG1244+026	16.1	0.048	1.9	740	330	21.2	0.13
NGC4748	14.0	0.014	3.6	1565	295	15.5	0.42
Mrk783	15.6	0.067	2.0	1655	430	47.4	1.43
R14.01	14.6	0.042	7.6	1605	430	60.5	1.71
Mrk69	15.9	0.076	1.1	1925	315	44.9	1.83
2E1346+2646	16.5	0.059	1.1	$\cdots$	180	21.2	$\cdots$
PG1404+226	15.8	0.098	2.0	1120	950	72.4	1.00
Mrk684	14.7	0.046	1.5	1150	1290	48.2	0.70
Mrk478	14.6	0.077	1.0	1270	365	105.3	1.87
PG1448+273	15.0	0.065	2.7	1050	155	69.1	0.84
MS15198-0633	14.9	0.084	12.4	$\cdots$	$\cdots$	170.4	$\cdots$
Mrk486	14.8	0.038	1.8	1680	400	34.9	1.08
IRAS15462-0450	16.4	0.100	12.5	1615	1600	83.9	2.40
Mrk493	15.1	0.031	2.0	740	315	21.7	0.13
EXO16524+393	16.7	0.069	1.7	1355	400	24.0	0.48
B31702+457	15.1	0.060	2.2	975	295	56.4	0.59
RXJ17450+480	15.9	0.054	3.1	1355	400	30.2	0.61
Kaz163	15.0	0.063	4.4	1875	480	71.7	2.77
Mrk507	15.4	0.053	4.3	1565	1025	43.0	1.16
HS1817+5342	15.2	0.080	4.9	1615	570	91.2	2.61
HS1831+5338	15.9	0.039	4.9	1555	240	20.7	0.55
Mrk896	14.6	0.027	4.0	1135	315	27.1	0.38
MS22102+1827	16.7	0.079	6.2	690	890	36.2	0.19
Akn564	14.2	0.025	6.4	865	220	35.4	0.29
HS2247+1044	15.8	0.083	6.2	1790	710	69.6	2.45
Kaz320	16.8	0.034	4.9	1470	260	9.5	0.23

VVG found that, in general, the [OIII] lines of those NLS1s have a relatively narrow Gaussian profile (with Full Width at Half Maximum, hereafter FWHM, of $\sim$200-500 km s^-1) with often, in addition, a second broad blueshifted Gaussian component (with FWHM of $\sim$500-1800 km s^-1). The blueshifted Gaussian component is proposed to be associated with those individual high-velocity clouds seen in the spatially resolved NLR of some nearby Seyfert galaxies, which is outflowing rather than virial bounded (e.g. NGC 4151: Kaiser et al. 2000). The width of the narrow component is then adopted as the velocity dispersion of the virial NLR clouds if the line is fitted by a narrow component and a blueshifted broad component.

2.1 Estimation of black hole masses

The size of the broad emission line region (BLR) can be estimated by the empirical relationship between the size and the monochromatic continuum luminosity at 5100 Å (Kaspi et al. 2000):

$$R_{\rm BLR} = 32.9 \left(\frac{\lambda L_{\lambda}(5100~{\rm\AA})} {10^{44}~{\rm erg~ s^{-1}}} \right)^{0.7} {\rm lt~day},$$ (1)

where $\lambda L_{\lambda}$ is estimated from the B-magnitude by adopting an average optical spectral index of -0.5 and accounting for Galactic reddening and K-correction (H₀=75 km s^-1 Mpc^-1, q₀=0.5). Assuming that the BLR is virialized, the MBH mass can be estimated by $M_{\rm BH} = R_{\rm BLR} V^2 G^{-1}$, where G is the gravitational constant, V can be estimated from the emission line width, $V=\sqrt{3}/2\,\,{\it FWHM}$, by assuming BLR clouds in random orbit motion. The estimated black hole masses are also listed in Table 1.

There are some uncertainties in the estimation of the MBH mass. First, a typical error of 0.2 mag in the B magnitude given in VVG would introduce an uncertainty of about 0.05 dex in the estimation of MBH mass. Second, the continua are likely to be variable, but generally this variation is not larger than a factor of 2 for most AGN (cf. Kaspi et al. 2000), which may introduce an uncertainty of 0.15 dex in the estimation of MBH mass. Third, using the empirical law of Eq. (1) to estimate the BLR size, the uncertainties are generally not much larger than a factor of 2 for those NLS1s in VVG sample (see Kaspi et al. 2000) with $\lambda L_{\lambda}(5100~{\rm\AA})$ range from 10⁴³ to 10⁴⁵ erg s^-1, if those NLS1s do follow this empirical relation. Finally, a significant fraction of optical light may come from host galaxies. To make a quantitative estimation of this effect in a NLS1, we notice that $L_{\rm AGN}/L_{\rm bulge}=L_{\rm AGN}/L_{\rm Edd}\times L_{\rm Edd}/M_{\rm BH} \times M_{\rm bulge}/L_{\rm bulge}\times M_{\rm BH}/M_{\rm bulge}$, and $L_{\rm Edd}/M_{\rm BH}\sim 3\times 10^4 L_{\odot}/M_{\odot}$. For NLS1, the typical value of $L_{\rm AGN}/L_{\rm Edd}$ should be around 0.5 (Puchnarewicz et al. 2001); the typical bulge mass to light ratio may be similar to nearby hot galaxies with $M_{\rm bulge}/L_{\rm bulge}~\sim~10 M_{\odot}/L_{\odot}$; and the MBH mass to bulge mass ratio may be similar to (or less than) nearby galaxies with $M_{\rm BH}/M_{\rm bulge}$ of about 0.0015-0.003 (by an order of magnitude) (Merritt & Ferrarese 2001b; Gebhardt et al. 2000a; Mathur et al. 2001). The fraction of light at the optical band $L_{\rm opt}/L_{\rm bol}$ is $\sim$0.1 for AGN and $\sim$1.0 for bulge. Adopting those values, one obtains -10, which suggests that the stellar contribution to the measured optical luminosity should be much less (or less) than that from the nuclear emission. Thus, the uncertainty in the mass estimation is small in comparison with the intrinsic scatter in the mass of the sample. Combining all those uncertainties, the estimation of the MBH mass would typically have an uncertainty of about 0.5 dex.

   
2.2 Estimation of the bulge velocity dispersion

The [OIII] width can be converted to the stellar velocity dispersion by $\sigma={\it FWHM}_{\rm [OIII]}/2.35$ (Nelson & Whittle 1995). Nelson (2000) has shown that the reverberation mapping measured MBH mass in AGN, for which the bulge velocity dispersion is derived from the [OIII] width, is in good agreement with the $M_{\rm BH}$-$\sigma$ relation defined by nearby hot galaxies, which may support the assertion that the narrow line [OIII] width serves as a good representation of the bulge velocity dispersion. The $\sigma$derived this way is systematically lower than the stellar velocity dispersion from the absorption line width by 0.1 dex, while the mean deviation to the best fit line is 0.13 dex (Nelson & Whittle 1995). This systematic difference will not affect the following statistical analysis significantly since it is much smaller than the intrinsic scatter in the [OIII] line width measurements.

The [OIII] width could be significantly over-estimated from the spectra with poor resolution (Veilleux 1991, hereafter V91). According to Fig. 3 in V91, this overestimation could be as large as a factor of 1.2-1.5 if the spectral resolution is close to the intrinsic [OIII] width of the object. Note that three objects in VVG, Mrk 359, NGC 4051, Mrk 766, were also observed by Veilleux (1991) at a resolution of 10 km s^-1, and the [OIII] line width (the width measured by VVG, the V91 width to the VVG width ratio) are 113 (180, 1.59), 162 (200, 1.23) and 180 (220, 1.22) km s^-1, respectively. These values clearly support that the [OIII] line width is overestimated by a factor of 1.2-1.5 for those objects with intrinsic widths close to or less than the spectral resolution, i.e. 204 km s^-1. As discussed by Whittle (1985), the detailed amount of the deviation is also sensitive to the line profile. This would suggest that the measured line width of less than 300 km s^-1 may be overestimated by such a factor. In the following analysis, we will keep in mind this uncertainty, and discuss its consequences wherever appropriate. Note also that the [OIII] widths for most objects in the Nelson (2000) sample were measured from the spectra with high resolution, <2 Å, corresponding to <120 km s^-1, which may not suffer from the overestimation due to spectral resolution, since measured [OIII] line widths are much larger than the spectral resolution.

2.3 M_BH to the bulge velocity dispersion relation

The relationship between the estimated MBH mass $M_{\rm BH}$ and the bulge velocity dispersion represented by the [OIII] width is shown in the left panel of Figs. 1 and 2 for NLS1s in VVG,

Figure 1: The estimated mass of MBHs versus the stellar velocity dispersion derived from the [OIII] line width: NLS1s from Veron-Cetty et al. (2001) (VVG) are shown as open stars. For comparison, NL AGN and BL AGN from Nelson (2000) (N00) are plotted as open squares and open triangles, respectively. The solid circles represent the nearby hot galaxies from Merritt & Ferrarese (2001a) (MF01). The dashed line is the best fitted line for nearby hot galaxies (MF01). The [OIII] width is corrected for the possible overestimation due to the low spectral resolution by a factor of 1.3 in the right panel, but not in the left panel. In the left panel, the dotted (solid) line is the best fitted line for NL AGN (NL + BL AGN, 78 objects in total by excluding those six objects which deviate from the others and have the largest [OIII] width, see also Sect. 2.3); in the right panel, the solid (dotted long-dashed) line is the best fitted line for the 78 NL + BL AGN (75 NL + BL AGN by excluding those three objects which deviate from the main trend but have the smallest [OIII] width, see also Sect. 2.3).

Figure 2: Legend as Fig. 1, but adopting the galaxies from Gebhardt et al. (2000a) (G00) for comparison. It is obviously that the best fit slope of AGN is consistent with the one derived by G00.

along with the same relationship for those BL AGN in Nelson (2000). Note that four objects, NGC 4051, Mrk 335, PG 1211+143 and Mrk 110, which have reverberation mapping measured MBH masses and high resolution ( ) [OIII] line widths, in the Nelson (2000) sample are NL Seyfert 1 galaxies or QSOs. The former three objects are also included in VVG. The high quality data in Nelson (2000) are adopted for these three objects instead of the estimated ones from VVG. The effectiveness of using the empirical law to estimate the mass of MBHs in NLS1s may also be supported by the fact that the other NL objects, whose masses are estimated from the empirical law, follow the trend of these four NL objects in Figs. 1 and 2. In the present paper, the stellar velocity dispersion derived from the [OIII] width is likely to represent the central velocity dispersion. For comparison, the nearby hot galaxies from Merritt & Ferrarese (2001a), for which values of $M_{\rm BH}$ and $\sigma$ (the central stellar velocity dispersion) are measured from dynamical modeling of HST data, are therefore also plotted in Fig. 1. Since there are different views on the slope of the M-$\sigma$ relation defined in nearby galaxies (see Merritt & Ferrarese 2001a; Gebhardt et al. 2000a), a similar figure is also plotted (see Fig. 2) for comparison with the galaxies from Gebhardt et al. (2000a), in which the brightness weighted stellar velocity dispersions within the effective radius of galaxies are adopted.

It is clearly shown in Figs. 1 and 2 that five NL objects, Mrk 507, Mrk 684, IRAS 15462-0450, MS 22102+1827, and PG 1404+226, having large [OIII] widths, deviate from other NL objects. Note that Mrk 507, Mrk 684, IRAS 15462-0450 are the three objects for which a narrow HII region contribution has been subtracted in the VVG sample. For spectra with a resolution of 3.4 Å used by VVG, the HII component may not be reliably separated from a narrow component of NLR with width 200-500 kms^-1 if an additional broad wing is present. Thus the widths of NLR in these three objects are likely to be significantly over-estimated. Only poor quality [OIII] profiles are available for MS 22102+1827 and PG 1404+226, and VVG mentioned that broad blueshifted [OIII] profiles should not be overlooked in PG 1404+226. These five objects will be excluded in the following statistic analysis. The galactic bulge mass of IC 4329A, which clearly deviates from other AGN in the Fig. 1 in Nelson (2000), is one of the smallest in the Wandel (1999) sample of about 10^10.6 solar mass. However, the bulge velocity dispersion derived from the [OIII] width of IC 4329A is one of the largest. The small bulge mass but large bulge velocity in this object compared with others in the Wandel (1999) sample is in contradiction with the Faber-Jackson relation. The high resolution radio map of IC 4329A consists of a compact core and with extended component to several kpc (Unger et al. 1987). If the extended component is the radio jet, then the large [OIII] width can be due to the non-virial component (Nelson & Whittle 1996). This object will also be removed from the sample in the following analysis.

Considering both the NL Seyfert 1 galaxies and NL QSOs in VVG and BL AGN in the Nelson (2000) sample, a Spearman rank correlation tests gives a strong correlation between $M_{\rm BH}$ and $\sigma$ for 78 AGN with a correlation coefficient of $R_{\rm s}=0.613$ corresponding to a probability of $P_{\rm s}=2.4\times 10^{-9}$ that the correlation is caused by a random factor, which can be fitted by a line with a slope of $3.64\pm0.21$ using an ordinary least-squares (OLS) bisector (Isobe et al. 1990) (represented by the solid line in the left panel of Figs. 1 and 2). This slope agrees well with the one defined in nearby hot galaxies derived by Gebhardt et al. (2000a), but deviates from the one derived by Merritt & Ferrarese (2001a), and the MBH mass in AGN seems smaller than the one in nearby hot galaxies by 0.5 dex. If we only consider NL Seyfert 1 galaxies and NL QSOs (51 objects), the correlation is also moderately significant with $R_{\rm s}=0.553$ ( $P_{\rm s}=2.6\times 10^{-5}$), which can be fitted by a line with a slope of $2.70\pm0.28$ using the OLS bisector (represented by the dotted line in the left panel of Figs. 1 and 2). Compared with the $M_{\rm BH}$-$\sigma$ relation defined by nearby hot galaxies (Gebhardt et al. 2000a), we find the MBH mass in NLS1s is smaller than that in nearby hot galaxies by $\sim$0.5 dex. However, we may not be able to draw a conclusion that the MBHs in NLS1s (or AGN) are systematically smaller than that in nearby hot galaxies at a given bulge velocity dispersion if the uncertainties in the estimation of MBH mass (about 0.5 dex) and possible overestimation of the [OIII] width (see following paragraph) are considered.

As discussed in Sect. 2.2, the low spectral resolution could introduce an overestimation of the [OIII] width, probably by a factor of 1.2-1.5. The relationship between $M_{\rm BH}$ and $\sigma$ are re-plotted in the right panel of Fig. 2 by correcting this overestimation of a moderate factor 1.3 for NLS1s in VVG. Now, the correlation between $M_{\rm BH}$ and $\sigma$ becomes very strong with a coefficient $R_{\rm s}=0.730$ ( $P_{\rm s}=3.8\times 10^{-14}$) for the combined sample (78 AGN), and can be fitted (using the OLS bisector) by

$$M_{\rm BH} = 10^{(7.78\pm0.005)}M_{\odot}\left( \frac{{\it FW... ...III]}/2.35}{200~{\rm km~ {\rm s}^{-1}}} \right)^{3.32\pm0.38},$$ (2)

as shown by the solid line in the right panel of Figs. 1 and 2. As seen in Figs. 1 and 2, three objects, Mrk 382, Mrk 734 and PG 1448+273, which have the smallest [OIII] widths, deviate from the other NL objects. The reason that they have somewhat larger MBHs than others is not known. However, if excluding them, the correlation becomes even stronger with $R_{\rm s}=0.762$ ( $P_{\rm s}=2.0\times 10^{-15}$), which can be fitted (using OLS bisector) by

$$M_{\rm BH} = 10^{(7.81\pm0.006)}M_{\odot}\left( \frac{{\it FW... ...III]}/2.35}{200~{\rm km~ {\rm s}^{-1}}} \right)^{3.70\pm0.51},$$ (3)

as shown by the dotted-long dashed line in the right panel of Figs. 1 and 2. The scatter is large for this relation, which should be due to large uncertainties in both variables. Whether we exclude Mrk 382, Mrk 734 and PG 1448+273 or not, the $M_{\rm BH}$-$\sigma$ relation for AGN (both NL and BL AGN) is consistent with that defined in nearby hot galaxies. It seems also that the slope of the fit agrees with the one found by Gebhardt et al. (2000a) for nearby hot galaxies and Nelson (2000) for AGN (see Fig. 2), but is different to the one derived by Merritt & Ferrarese (2001a) of 4.72 (see Fig. 1); more conclusive result needs precise measurement of both the MBH mass and bulge velocity dispersion. Again, the difference from the $M_{\rm BH}$-$\sigma$ relation (Gebhardt et al. 2000a) in Log₁₀ $M_{\rm BH}$ or Log₁₀$\sigma$ is about -0.5 or 0.1. The consistency of the MBH mass in NL Seyfert 1 galaxies and NL QSOs with the bulge velocity dispersion supports the result of Ferrarese et al. (2001) that the two NLS1s with measured MBH masses (by the reverberation mapping method) and bulge velocity dispersions (from stellar absorption lines) are consistent with $M_{\rm BH}$-$\sigma$ relation defined by nearby hot galaxies.