2 Central mass estimates derived from host galaxy observations

Recent mass estimates using host galaxy observations mainly rely on the following two statistical correlations:

(1) Dynamical studies of nearby elliptical galaxies have revealed an apparent, almost linear correlation (albeit with significant intrinsic scatter) between the central BH mass and the B-band luminosity of the bulge part of the host galaxy, which is given by $M_H \simeq 0.78 \times 10^8 M_{\odot}\ (L_{B,\rm bulge}/10^{10} L_{\odot})^{1.08}$ (Magorrian et al. 1998; Kormendy & Gebhardt 2001, hereafter KG01).

(2) A much tighter correlation $M_H \propto \sigma^{\alpha}$ seems to exist between the BH mass M_H in nearby inactive galaxies and the stellar velocity dispersion $\sigma$ of their host bulge (Gebhardt et al. 2000; Ferrarese & Merritt 2000). However, up to now there is considerable debate over the true slope $\alpha$. Using different samples, Gebhardt et al. (2000) found $\alpha=3.75 \pm 0.3$, while Ferrarese & Merritt (2000) obtained $\alpha=4.8 \pm 0.54$ and $\alpha=4.72 \pm 0.36$ (Merritt & Ferrarese 2001a). Currently, further research is required to settle the question whether this difference is mostly caused by lower quality data and a less precise regression algorithm (cf. Merritt & Ferrarese 2001a) or by systematic differences in the velocity dispersions used by the different groups for the same galaxies (cf. Tremaine et al. 2002).

The results using reverberation mapping (RM) (e.g. Kaspi et al. 2000; Nelson 2000; Wandel 2002) indicate that the M_H-$\sigma$ correlation may also hold for nearby AGN. However, a critical test of this conclusion depends on both a secure measure of the BH mass and an accurate determination of the stellar velocity dispersion. So far, the quality of BH mass estimates from stellar or gas kinematical data (whether ground- or HST-based), which require the BH sphere of influence $r_H=G M_H/\sigma^2$ to be well-resolved, seems to increase only modestly (Merritt & Ferrarese 2001a), so that over-estimation may be quite possible. Further progress has been expected using RM methods (Ferrarese et al. 2001). Yet, the accuracy of RM may be strongly affected by systematic errors, e.g. due to uncertainties in the geometry and kinematics of the BLR or due to an unknown angular radiation pattern of the line emission, which may result in a systematic error up to at least a factor of 3 (cf. Krolik 2001). Moreover, only few accurate measurements of $\sigma$ seem to exist for AGN. Ferrarese et al. (2001) have recently analysed six AGN with well-determined RM BH masses by a careful measurement of their velocity dispersions and found a general consistency with the M_H-$\sigma$ relation for quiescent galaxies. However, only BH masses below $\simeq$ $10^8~M_{\odot}$ have been included so far, thus leaving out the high mass end of the correlation, and in addition, a large scatter is indicated. Besides providing a promising tool for the determination of BH masses in AGN, the current uncertainties in the correlations should be considered, if one tries to assess its implication for individual sources such as Mkn 501.

In the case of Mkn 501, Barth et al. (2002a) have recently determined the stellar velocity dispersion from the calcium triplet lines to be $\sigma =(372\pm18)$ km s^-1 (cf. also Barth et al. 2002b). Applying the M_H-$\sigma$ relations of KG01 and Merritt & Ferrarese (2001a), they derived a BH mass for Mkn 501 of $M_H \simeq$ (0.9-3.4) $\times 10^9~M_{\odot}$. This mass estimate was supported by the study of Wu et al. (2002), who estimated the velocity dispersions and BH masses from the fundamental plane for ellipticals for a large AGN sample including 63 BL Lac objects (but not Mkn 501). They derived BH masses up to $10^9~ M_{\odot}$, but with a potential error up to a factor of two. In particular, inspection of the fit in their Fig. 1 indicates a possible BH mass for Mkn 501 of $\sim$ $(4{-}7) \times 10^8~M_{\odot}$ for $M_R({\rm host})=-24.2$ mag (Pursimo et al. 2002). The general challenge of determining $\sigma$ accurately may be illustrated in more detail with reference to the recent work by Falomo et al. (2002), who provided a systematical study of the stellar velocity dispersion in seven BL Lacs. Using measurements in two spectral ranges, they found a velocity dispersion of $\sigma=(291\pm 13)$ km s^-1 for Mkn 501, which is significantly lower than the one derived by Barth et al. (2002a). Hence, if this value is used instead, the BH mass estimated by Barth et al. (2002a) is reduced by up to a factor of three, i.e. one obtains $M_H \simeq (3.6 {-} 10.7) \times 10^8~ M_{\odot}$. Additional support for such a low $\sigma$-value in Mkn 501 seems to be indicated by the original Faber & Jackson relation, which yields $\sigma \sim 270$ km s^-1 (see Fig. 2 in Falomo et al. 2002) for $M_R({\rm host})=-24.2$ mag. Future research is needed to test whether the discrepancy in $\sigma$ is mainly induced by the difference in the method deriving $\sigma$ (direct fitting versus Fourier quotient routine).

As noted above, an additional mass estimate for Mkn 501 can also be derived from the M_H- $L_{\rm bulge}$ correlation. The reported large uncertainties in this relation have recently been examined by McLure & Dunlop (2002) using R-band luminosities, which are less sensitive to extinction. By analysing the virial BH masses for a sample of 72 AGN, they found the scatter to be quite smaller than previously estimated and stressed its usefulness. For application to Mkn 501, we may exploit the absolute R-band luminosity of its host galaxy recently derived by Pursimo et al. (2002) (see also Nilsson et al. 1999). Assuming H₀=50 km s^-1 Mpc^-1, they obtained $M_R({\rm host})=-24.2$ mag. If we convert R- to B-band luminosity assuming B-R=1.56 (e.g. Goudfrooij et al. 1994; Fukugita et al. 1995; Urry et al. 2000), we have $M_B({\rm host})=-22.46$ mag, which results in $L(M_B({\rm host}))=1.406 \times 10^{11} ~L_{\odot}$. Using the KG01-relation for the B-band luminosity, the expected BH mass in Mkn 501 is $M_H \simeq 1.3 \times 10^9 ~M_{\odot}$, but with a potential error of up to at least a factor of three. Using the more recent McLure & Dunlop (2002)-relation $\log(M_H/M_{\odot})=-0.5 M_R - 2.96 (\pm 0.48)$, one finds $M_H \simeq (0.46{-}4.2) \times 10^9~M_{\odot}$. Uncertainties in the determination of M_R may further reduce the expected BH mass. For example, values from the literature presented in Table 4 of Nilsson et al. (1999) indicate that M_R might be up to 0.4 mag higher and therefore M_H correspondingly smaller. More importantly, if a Hubble constant H₀=70 km s^-1 Mpc^-1 is assumed, one finds M_R=-23.47, which results in $M_H \simeq 7.8 \times 10^8 ~M_{\odot}$ (KG01), again with substantial scatter of up to at least a factor of three, or $M_H \simeq (2{-}18) \times 10^8 ~M_{\odot}$ (McLure & Dunlop 2002), thus allowing for a central mass as low as $2 \times 10^8 ~M_{\odot}$.