Using an empirical relation between the broad-line region size and optical continuum luminosity, we estimated the black hole mass and accretion rate for 135 active galactic nuclei (AGNs) with double-peaked broad emission lines in two samples, one from the Sloan Digital Sky Survey (SDSS) and the other from a survey of radio-loud broad emission line AGNs. With black hole masses ranging from 3; 107M to 5; 109M, these AGNs have dimensionless accretion rates (Eddington ratios) between 0.001 and 0.1 and bolometric luminosity between 1043 and 1046 ergs s[1]1, both values being significantly larger than those of several previously known low-luminosity (Lbol<1043 ergs s[1]1) double-peaked AGNs. The optical-X-ray spectra indices, OX, of these high-luminosity double-peaked AGNs are between 1 and 1.9, systematically larger than those of low-luminosity objects, which are around 1. Modest correlations (with a Spearman rank correlation coefficient of 0.60) of the OX value with the Eddington ratio and bolometric luminosity have been found, indicating that double-peaked AGNs with higher Eddington ratios or higher luminosity tend to have larger OX values. Based on these results, we suggested that the accretion process in the central region of some high-luminosity double-peaked emission line AGNs (especially those with Eddington ratios larger than 0.01) is probably different from that of low-luminosity objects, in which a well-known ADAF-like accretion flow was thought to exist. It is likely that the accretion physics in some high-luminosity doublepeaked AGNs is similar to that in normal type 1 AGNs, which is also supported by the presence of possible big blue bumps in the spectra of some double-peaked AGNs with higher Eddington ratios. We note that the prototype double-peaked emission line AGN, Arp 102B, which has a black hole mass of 108M and a dimensionless accretion rate of 0.001, may be an "intermediate" object between the high-and lowluminosity double-peaked AGNs. In addition, we found an apparent strong anticorrelation (with a Spearman rank correlation coefficient of [1] 0.79) between the peak separation of double-peaked profiles and Eddington ratios. However, such an anticorrelation is probably induced by a strong correlation between the peak separation and emission-line widths and needs to be confirmed by future work. If it is real, it may provide us another clue to understanding why double-peaked broad emission lines were hardly found in luminous AGNs with Eddington ratios larger than 0.1.

An empirical relation between the broad line region (BLR) size and optical continuum luminosity is often adopted to estimate the BLR size and then the black hole mass of AGNs. However, optical luminosity may not be a good indicator of photoionizing luminosity for extremely radio-loud AGNs because the jets usually contribute significantly to the optical continuum. Therefore, the black hole masses derived for blazar-type AGNs with this method are probably overestimated. Here we first derived a tight empirical relation between the BLR size and the Hβ emission line luminosity, R(light -days)=24.05(LHβ/1042 ergs s−1)0.68, from a sample of 34 AGNs with the BLR size estimated with the reverberation mapping technique. Then we applied this relation to estimate the black hole masses of some AGNs and found that for many extremely radioloud AGNs the black hole masses obtained with the R -LHβ relation are systematically lower than those derived previously with the R-L5100 Å relation, while for radio-quiet and slightly radio-loud AGNs the results obtained with these two methods are almost the same. The difference of black hole masses estimated with these two relations increases with the radio-loudness for extremely radio-loud AGNs, which is consistent with the fact that their equivalent widths of the Hβ emission line become smaller at greater radio-loudness. If the small Hβ equivalent widths of extremely radio-loud AGNs are indeed caused by the beaming effect, we argue that the optical emission line luminosity may be a better tracer of ionizing luminosity for blazartype AGNs and the black hole masses derived with the R-LHβ relation are probably more accurate.

The recently discovered tight correlation between supermassive black hole mass and central velocity dispersion for both inactive and active galaxies suggests a possibility to estimate the black hole mass from the measured central velocity dispersion. However, for most AGNs it is dicult to measure the central velocity dispersions of their host galaxies directly with spectroscopic studies. In this paper we adopt the fundamental plane for ellipticals to estimate the central velocity dispersion and black hole mass for a number of AGNs with morphology parameters of their elliptical host galaxies obtained by the Hubble Space Telescope imaging observations. The estimated black hole masses of 63 BL Lac objects, 10 radio galaxies, 10 radio-loud quasars and 9 radio-quiet quasars are mostly in the range of 107:5M to 109M. No signicant di erence in black hole mass is found for high-frequency peaked BL Lacs and low-frequency peaked BL Lacs, as well as for radio galaxies and radio-loud quasars. The Eddington ratios of radio galaxies are substantially smaller than those of quasars. This suggests that the di erent observational features of these radio-loud AGNs may be mainly dominated by di erent accretion rate rather than by the black hole mass, which is in agreement with some evolutionary scenarios recently proposed for radio-loud AGNs. Di erent to some previous claims, we found that the derived mean black hole mass for radio-loud quasars is only slightly larger than that of radio-quiet quasars. Though the black hole mass distributions between radio-loud and radio-quiet quasars are statistically di erent, their Eddington ratio distributions are probably from the same population. In addition, we noted that the relation between black hole mass and host galaxy luminosity we obtained using the fundamental plane provides further arguments for a nonlinear scaling law between supermassive black hole mass and galactic bulge mass.

A tight correlation between black hole mass (MBH) and central velocity dispersion (б) has been found recently for both active and quiescent galaxies. By applying this correlation, we develop a simple method to derive the inclination angles for a sample of 11 Seyfert 1 galaxies that have both measured central velocity dispersions and black hole masses estimated by reverberation mapping. These angles, with a mean value of 36 [1] that agrees well with the result obtained by fitting the iron Ka lines of Seyfert 1 galaxies observed with ASCA, provide further support to the orientation-dependent unification scheme of active galactic nuclei (AGNs). A positive correlation of the inclinations with observed FWHMs of the Hb line and a possible anticorrelation with the nuclear radio loudness have been found. We conclude that more accurate knowledge of inclinations and broad-line region dynamics is needed to improve the black hole mass determination of AGNs with the reverberation mapping technique.

We estimated black hole masses for 9 Seyfert 1 and 13 Seyfert 2 galaxies in the Palomar and CfA bright Seyfert samples using the tight correlation between black hole mass and bulge velocity dispersion. Combining other 13 Seyfert 1s and 2 Seyfert 2s in these samples but with black hole masses measured recently by reverberation mapping and stellar/gas dynamics, we studied the correlations of black hole masses with radio-loudness and bulge luminosities for a sample of 37 Seyfert galaxies. We found that if radio-loudness is measured using the optical and radio luminosities of the nuclear components, the black hole masses of radio-loud Seyfert 1s tend to increase with the radio-loudness. The black hole masses of all Seyfert galaxies increase with the radio power, but Seyfert galaxies have larger radio powers than nearby galaxies with the same black hole masses. In addition, the correlation between black hole masses and bulge V-band luminosities for Seyfert galaxies is consistent with that found for quasars and normal galaxies. The combined sample of 37 Seyfert galaxies, 15 quasars and 30 normal galaxies suggests a possible universal nonlinear relation between black hole and bulge masses, MBH/M1:74 0:14 bulge, which is slightly steeper than that found recently by Laor (2001) for a smaller sample. This nonlinear relation is supported by a larger sample including 65 Seyfert galaxies. The di rent MBH=Mbulge ratio for galaxies with di erent bulge luminosities or di erent black hole masses may be explained by this relation. These results are consistent with some theoretical implications and are important for understanding the nature of radio emissions and the formation and evolution of supermassive black holes and galaxies.