3 Discussion and conclusion

In this paper, we find that there is no clear difference in the relation between $M_{\rm BH}$ and $\sigma$ (the bulge velocity dispersion is represented by the [OIII] width for AGN) for both NL and BL AGN from the same relation defined by nearby hot galaxies (Gebhardt et al. 2000a; Ferrarese & Merritt 2000). Furthermore, the MBH masses and bulge velocity dispersions of NLS1s are consistent with the $M_{\rm BH}$-$\sigma$ relation for other galaxies if we consider the overestimation in the [OIII] line width. This consistency suggests that NLS1s have small MBHs compared with BL AGN with similar non-thermal luminosity simply due to their host galaxies having small bulges compared to that of BL AGN. This may support one of the competing model of NLS1s, i.e., the low-mass/high accretion rate interpretation.

A simple evolutionary scenario proposed by Mathur (2000) is that NLS1s are likely to represent a crucial early and more obscured phase in the evolution of active galaxies based on the observational properties of NLS1s, such as super-solar metallicities and are unusually luminous in the far-infrared band etc. This evolutionary view has also been frequently suggested by other authors (Law-Green et al. 2000). Although it is tentative that the $M_{\rm BH}$ and $\sigma$ of NLS1s is consistent with the $M_{\rm BH}$-$\sigma$ relation (Gebhardt et al. 2000a; Ferrarese & Merritt 2000), we cannot rule out the possibility that the MBHs in NLS1s are smaller than those in BL AGN or nearby hot galaxies at a given bulge velocity dispersion by a factor of several (say, 3), which means that Mathur's scenario cannot simply be ruled out by our results. However, the claim of Mathur et al. (2001) that NLS1s have a significantly smaller MBH to bulge velocity dispersion ratio, which may be caused by some non-virial component in their [OIII] line width measurements, is discredited by our results.

Now we have more confidence in applying the reverberation mapping method to measure the masses of MBHs in AGN, since the MBH masses from reverberation mapping are consistent with the $M_{\rm BH}$-$\sigma$ relation recently discovered for local galaxies (Gebhardt et al. 2000b; Ferrarese et al. 2001; Nelson 2000). Krolik (2000) pointed out, however, this consistence could be due to fortuitous mutual canceling of the systematic errors-including overestimation of the MBH mass by a fixed ratio by interpreting the emission line kinematics as gravitationally bound and underestimating the mass for planar-like BLR cloud distribution. If the narrowness of the permitted line width of NLS1s is due to a planar-like BLR viewed nearly "pole-on'' (the "orientation model'': Osterbrock & Pogge 1985; Goldrich 1989; Puchnarewicz et al. 1992), the estimated MBH masses would be systematically smaller than the real one. Since the orientation is a random effect, we would expect that the estimated MBH masses in BL AGN are systematically larger than those in NLS1 by a similar factor of 10, considering of NLS1s broad line width are around 1000 km s^-1 while BL objects are typically about 3000-5000 km s^-1 (which means that the velocity of broad-line-emitting clouds would be underestimated by a factor of about 3 if both NLS1s and BL objects have a similar central engine and a flat broad line geometry), at a given stellar velocity dispersion. As we can see in Figs. 1 and 2, masses of NL objects at a given bulge velocity dispersion are consistent with the trend of BL objects, which suggests that at least not all NLS1s can be regarded as "orientation'' dependent.

It is generally believed that the activity in galactic nuclei is closely linked with the galaxy and bulge formation. Silk & Rees (1998) proposed that the powerful wind from the central engine can blow away the cold gas from the galaxy and terminate the accretion process when the output kinetic energy is comparable with the bound energy of the total gas in the galaxy. This results in a relation of the MBH mass to the stellar velocity dispersion of the form $M_{\rm BH}\propto\sigma^5$. The typical duration of the bright QSOs phase is required to be only about few 10⁷ yr from fitting the optical QSOs luminosity function by the mass function of dark matter halos predicted by standard hierarchical cosmogonies (Haehnelt et al. 1998). It suggests that MBHs may grow at an accretion rate far above the Eddington rate before this brief optical bright phase and/or at a very low accretion rate via advection-dominated accretion flows lasting a Hubble time after this phase. Fabian (1999) further incorporated the Silk-Rees scenario in a model of obscured growth of MBHs. In his model, a MBH in the center of a galaxy accretes the surrounding material and emits a QSO/AGN-like spectrum which is absorbed by surrounding gas and dust. The wind from the central engine exerts a force on the gas and pushes it outwards. The central engine emerges when the Thomson depth in the surrounding gas has dropped to about unity. This model predicts a $M_{\rm BH}$-$\sigma$ relation for bright AGN or NL objects similar to that of the nearby galaxies. Our result of a consistent $M_{\rm BH}$-$\sigma$ relation in NLS1s favors the model of Fabian (1999).

Many works have been done on the relation between $M_{\rm BH}$ and $M_{\rm bulge}$. There is still controversy about whether Seyfert galaxies have a small $M_{\rm BH}$ to $M_{\rm bugle}$ ratio compared with local galaxies or not (Wandel 1999; McLure & Dunlop 2000). Czerny et al. (2000) claimed that NLS1s, at least, have a smaller $M_{\rm BH}$ to $M_{\rm bugle}$ ratio, which could be due to nuclear star burst (or stellar formation and evolution) in NLS1s leading to a small mass to light ratio of bulges.

In the present paper, there are some caveats for both the estimation of the MBH mass and the bulge velocity. First, the empirical $R_{\rm BLR}$-L relation is not fully tested for NLS1s. This relation is derived from a moderate-size sample of AGN, composed mainly of BL AGN (Kaspi et al. 2000). Three of the four NLS1s in this sample closely follow the $R_{\rm BLR}$-L relation. The lowest luminosity object, NGC 4051, shows a larger size of BLR than this empirical relation predicted. There is, at least, no obvious evidence against this empirical relation, although further confirmation is needed. Second, Nelson & Whittle (1996) identified two cases in which the [OIII] width can be significantly larger than the bulge velocity dispersion, i.e., presenting kpc linear radio sources or displaying distorting morphology. Though lacking in systematic study, NLS1s tend to possess similar radio properties to average radio-quiet Seyfert galaxies (Ulvestad et al. 1995). Zheng et al. (1999) found that NLS1s in their sample are morphology relaxed. We also note that two NL objects included in the sample of Nelson & Whittle (1995) do not show systematic deviation. Also, the non-virial component of [OIII] lines has been subtracted for VVG objects. Therefore, our results should not be affected by the possible linear radio source in some objects.

Acknowledgements

We thank the anonymous referee for helpful comments and suggestions. TW thanks the financial support from Chinese NSF through grant NSF-19925313 and from Ministry of Science and Technology. YL acknowledges the hospitality of the Department of Astrophysical Sciences, Princeton University.