1 Introduction

Massive Black Holes (MBHs) are believed to exist in the centers of all active and many or most normal galaxies. High-resolution observations of various kinematic tracers of the central gravitational potential have resulted in the detections of numerous MBHs in nearby galaxies over the past decade (e.g. Kormendy & Richstone 1995; Ferrarese & Merritt 2000; Gebhardt et al. 2000a; Sarzi et al. 2000; Ho 1999, and references therein). A relationship between the MBH mass and the mass of the spheroidal component was suggested by Kormendy (1993) and later quantified by Kormendy & Richstone (1995) and Magorrian et al. (1998). This correlation appears also in Seyfert 1 galaxies and QSOs, in which the MBH masses are measured either using reverberation mapping techniques (Wandel 1999) or using the empirical relation between the size of the Broad Line Region (BLR) and nuclear luminosity (Laor 1998). Laor (1998) found that the MBH mass-to-bulge mass ratio for a sample of PG QSOs is the same as that for nearby galaxies. In contrast, Wandel (1999) obtained a substantially lower MBH mass-to-bulge mass ratio for Seyfert 1 galaxies. This could be due to an overestimation of the bulge mass in Seyfert galaxies, e.g., a larger luminosity-to-mass ratio in the host galaxies, or an underestimation of central black hole masses using the reverberation mapping method (McLure & Dunlop 2000; Krolik 2000), or an intrinsic difference in the MBH mass-to-bulge mass ratio for Seyfert galaxies and normal galaxies.

For nearby hot galaxies (ellipticals and spiral bulge), recent works by Gebhardt et al. (2000a) and Ferrarese & Merritt (2000) have demonstrated that the mass of a MBH is tightly correlated with the stellar velocity dispersion, which is obtained within a large aperture extending to the galaxy effective radius and thus with little influence of the MBH, with remarkably small scatter. Note that Gebhardt et al. (2000b) included also seven AGN, in which the MBH masses are obtained by the reverberation mapping method, and they found that these objects follow the same correlation with small scatter. Ferrarese et al. (2001) reached the same conclusion by making an accurate measurement of stellar velocity dispersions for 6 Seyfert galaxies, for which the masses of MBHs have been measured using reverberation mapping techniques.

The good correlation between the [OIII] width and the stellar velocity dispersion (Nelson & Whittle 1996) indicates that the narrow-line width is primarily virial in origin and the Narrow Line Region (NLR) kinematics are mainly controlled by the gravitational potential of the galaxy bulge. For a sample of 32 AGN and QSOs in which the MBH masses have been measured from reverberation mapping, Nelson (2000) demonstrated a good relation between the MBH mass and the bulge velocity dispersion derived from the [OIII] width, which is consistent with the results of Gebhardt et al. (2000b) but with somewhat larger scattering. This agreement can be taken as evidence in support of the reverberation mapping method to measure the MBH masses in AGN.

The tight $M_{\rm BH}$-$\sigma$ relation supports the theoretical arguments of a close link between the growth of MBHs and the galaxy or spheroidal formation. Several theoretical scenarios have been proposed to explain the $M_{\rm BH}$-$\sigma$ or $M_{\rm BH}$- $M_{\rm bulge}$ relation (e.g. Silk & Rees 1998; Fabian 1999; Ostriker 2000; Haehnelt & Kauffmann 2000). Silk & Rees (1998) predicted $M_{\rm BH}\propto\sigma^5$, based on the back-reaction mechanism such that the kinetic energy associated with the output wind from the central BH-accretion disk system will evacuate the fueling gas when it is comparable to the bound energy of the gas in the bulge or host galaxy. Fabian (1999) further incorporated the Silk-Rees scenario into an obscured growth of MBHs model, and a consequent result is that most MBHs grow very fast in an obscured phase before they clean the surrounding dust and cold gas and appear as QSOs or AGN. This scenario can also explain both the $M_{\rm BH}$-$\sigma$ and $M_{\rm BH}$- $M_{\rm bulge}$ relation.

It is of particular interest to investigate the time evolution (or accretion history) of MBHs and thus reveal the physical link between the bulge formation and the MBH growth. One approach is to measure the masses of MBHs and bulge properties in high redshift QSOs and AGN and compare them with low redshift QSOs, AGN and nearby galaxies. Narrow Line Seyfert 1 galaxies (NLS1s) are suggested to be due to accretion rates close to the Eddington limit and have small BHs compared to normal Seyfert 1 galaxies at a given luminosity, and much evidence suggests that NLS1s might be normal Seyfert galaxies at an early stage of evolution (Mathur 2000, and references therein). If this is true, NLS1s could be an ideal class of objects, together with normal Seyfert galaxies and QSOs, to study the accretion history and growth of MBHs. Therefore, it is also interesting to measure the masses of MBHs and bulge properties in NLS1s and compare them with those in Broad Line (BL) Seyfert 1 galaxies and nearby galaxies. Using the MBH mass estimated from spectra fitting by an accretion disk model and the virial mass of the broad line region, Mathur et al. (2001) found that NLS1s show systematically lower $M_{\rm BH}$ than BL AGN with the same bulge luminosity or [OIII] width of host galaxies. However, two NLS1s in the Ferrarese et al. (2001) sample follow the same relation as BL Seyfert 1 galaxies. The conflicting results in the literature suggest that further study is required. In the present paper, we investigate the correlation between the MBH mass and the [OIII] line width for a large sample of NLS1s (Veron-Cetty et al. 2001) and find that NLS1s consistently follow the well-known $M_{\rm BH}$-$\sigma$ relation defined in nearby galaxies.