---
author:
- 'Jie-Ying Liu'
- 'B. F. Liu'
title: 'Investigating the Disk-Corona Relation in a Blue AGN Sample '
---

Introduction {#sect:intro}
============

The accretion onto the supermassive black hole is the key process to produce the spectral energy distribution in AGNs, including the Big Blue Bump, soft X-ray excess, Fe $K\alpha$ lines at 6.4 keV and hard X-ray tail.  These observed spectral properties indicate that the cold and hot gas coexist near the central supermassive black hole.  According to the commonly accepted theory the optical/UV radiations are emitted from a geometrically thin and optically thick disk (i.e. the cold gas) (e.g., Shakura & Sunyaev [@SS73], Lynden–Bell & Pringle [@lp74]), and the hard X-rays arise from hot optically thin and geometrically thick accretion flows, such as disk corona (Haardt & Maraschi 1991, 1993; Nakamura & Osaki 1993; Svensson & Zdziarski 1994; Kawaguchi et al.  2001, Cao 2009) or advection–dominated accretion flows (ADAF)(e.  g., Narayan & Yi [@ny94], 1995; Narayan et al.   [@na98]). 

The disk corona model was proposed by Liang & Price ([@lp77]) to explain the observed X-ray emission in Cyg X–1.  The accretion in the corona is supplied with material and energy through disk evaporation (e.g., Meyer & Meyer–Hofmeister [@mm94]; Liu et al.  [@liu99]) or magnetic process (e.g. Galeev et al.  [@gal79]; Stella et al.  [@stell84]; Liu et al.2002b, [@liu03]).  In AGNs a hot corona sandwiched by a disk is thought responsible to emit the X-rays (e.g. Haardt & Maraschi 1991; Nakamura & Osaki 1993; Kawaguchi et al.  2001; Liu et al.  2002b, 2003).  In the context of these studies it is often assumed that a fraction ($f$) of accretion energy is released in the corona in fits to individual AGN spectrum.  Questions arise as, is the fraction $f$ dependent on the Eddington ratio and black hole?  how does the relative strength of the corona to the disk vary with the Eddington ratio and black hole mass? 

In this work, we attempt to investigate these issues from observation.  We compile a large blue AGN sample of 240 objects derived from Dong et al.  [@dong08] (hereafter Dong08), in which the objects are selected from the Sloan Digital Sky Survey (SDSS) DR4 spectral data and less affected by dust extinction.  We investigate the correlation between the corona component and Eddington ratio.  We show how the coronal luminosity fraction varies with the Eddington ratio and black hole mass for radio-quiet (RQ) AGNs.  The results are compared with previous results of Wang et al. ([ @wang04]) for a sample of 56 RQ AGNs observed by ASCA and Yang et al. ([ @yang07]) for a combined sample from different observational satellites.  Our aim is to study the physical relation between the disk and corona. 

The outline of the paper is in the following.  In Sect.2 the black hole mass, the optical and X-ray luminosities are calculated.  In Sect.3 the overall properties of the sample and the correlation analyses are present.  In the Sect.4 the statistical results are interpreted by the disk corona model.  The discussion and conclusions are given in Sect.5 and Sect.6 respectively. 

The Sample and Data Reduction {#sect:sample}
=============================

Our sample is derived from a blue AGN sample in Dong08.  These blue AGNs are selected from the Sloan Digital Sky Survey (SDSS) DR4 spectral data, including Seyfert 1 galaxies and QSOs.  They are less affected by dust extinction.  In order to investigate the relation between the disk and the corona, whether and how the black hole mass and Eddington ratio affect this relation, we select the objects by the following criteria:

-   \(1) The objects are detected or covered by Faint Images of Radio Sky at Twenty Centimeters (FIRST) survey. 

-   \(2) The X-ray flux is available. 

-   \(3) Combining the radio with the optical data, we can determine the radio loudness and the RQ AGNs are selected. 

According to the above criteria, we analyze the sample in Dong08.  Given the upper limit to the radio flux, 404 AGNs are detected or covered by FIRST.  After matching to ROSAT bright and faint SRC Catalogue database ( ROSAT–SRC) with a distance criterion between the optical and X-ray source of $\Delta \leq 60''$ (Voges et al.  [@voges94]), we obtain a sample containing 258 AGNs. 

We use the radio–loudness definition (Ivezić et al.  [@Ive02]) to divide RQ and radio-loud(RL) AGNs, that is, $$R_{\rm i} \equiv \log(\frac{F_{\rm 20cm}}{F_{\rm i}})=0.4(i-t).$$ where $F_{\rm i}$ and $F_{\rm 20cm}$ are flux densities at I–band and 20cm respectively, $i$ is the I–band magnitude, and $t=-2.5\log(F_{\rm 20cm}/3631 \rm Jy)$. Objects with $R_{\rm i}> 1$ are RL and objects with $R_{\rm i}< 1$ are RQ.  According to this definition, 240 (93%) objects in the sample are RQ and 18 (7%) objects are RL.  We mainly analyze these 240 RQ objects in order to constraint the accretion mechanism. 

The black hole mass, $M_{\rm BH}$, is a fundamental parameter of AGNs.  Different methods have been developed to estimate the black hole mass (Woo & Urry [@woo02] and reference therein; Vestergaard & Peterson [@vest06]), of which the reverberation mapping is the most widely used method (Peterson  [@peterson93]; Peterson et al.  [@peterson04]).  In the reverberation mapping method, the distance of the broad line region (BLR) from the central black hole can be deduced from the time lag between continuum and emission lines.  By combining the distance with the mesaured emission line width, the black hole mass can be determined.  In our sample, we take the $FWHM(H\beta)$ as the circular velocity in BLR.  The size/distance of the BLR is given by an empirical relation with the continuum luminosity at $5100\AA$ (Vestergaard & Peterson 2006).  Thus, the mass of black hole for RQ AGNs can be estimated as $$\log M_{\rm BH}(H\beta)=\log\left\{\left[\frac{FWHM(H\beta)}{1000~{\rm km~s^{-1}}}\right]^2\left[\frac{\lambda~L_{\lambda}({\rm 5100\AA})}{10^{44}~{\rm ergs~s^{-1}}}\right]^{0.5}\right\}+(6.9\pm0.02).$$

The bolometric luminosity of AGNs is approximately calculated from optical continuum luminosity, $L_{\rm bol}\approx 9\lambda~L_{\lambda}({\rm 5100\AA})$ (Elvis et al.  [@elvis94]).  The Eddington ratio ($ L_{\rm bol}/L_{\rm Edd}$) is then calculated from the bolometric luminosity and black hole mass, $$L_{\rm bol}/L_{\rm Edd}=0.072{\lambda~L_{\lambda}({\rm 5100\AA})\over 10^{44}{\rm ergs~s^{-1}}}\left(M_{\rm BH}\over 10^8M_\odot\right)^{-1},$$ where the Eddington luminosity is $L_{\rm Edd}=1.25\times 10^{38}M_{\rm BH}/M_{\odot} ~\rm ergs~s^{-1}$.

We get the X-ray flux densities from the count rates using the energy to counts conversion factor (ECF) for power-law spectra and Galactic absorption, where the power-law photon indices and the corresponding absorption column densities ($N_H$) are estimated from the two hardness ratios given by the ROSAT-SRC.  With the integrated flux densities in 0.1–2.4 keV and power-law indices $\Gamma$ we deduce the monochromatic flux at 2keV. After deriving the flux at 2 keV we extrapolate X-ray flux ($F_{\rm int}$) in the range from 2 keV to 10 keV by assuming a constant hard X-ray photon index, $\Gamma=1.9$ (Pounds et al.  [@pounds90]; Reeves & Turner [@retu00]).  The X-ray luminosity is then calculated by the standard luminosity–flux relation, $$L=4\pi d_{\rm L}^2F_{\rm int}(1+z)^{-(1-\alpha)},$$ where $\alpha=\Gamma-1$ and $d_{\rm L}$ is the luminosity distance related to the redshift and cosmology model. 

Throughout this paper, we adopt the cosmology model with $H_0=70{\rm km~s^{-1}Mpc^{-1}}$, $\Omega_{\rm M}=0.3$, $\Omega_{\Lambda}=0.7$.

Our sample is listed in Table 1 of Appendix A, where column 1 is the object name, column 2 the redshift, column 3 the derived mass of black hole, column 4 the optical luminosity at 5100Å(in unit of $10^{44}$ ergs s$^{-1}$), column 5 the radio flux at 20cm, column 6 the radio–loudness, column 7 and 8 are the derived X-ray data in 0.1–2.4 keV and 2–10 keV respectively. 

Data Analysis and Results {#sect:analysis}
=========================

Properties of the Sample
------------------------

Fig.1 shows the histogram of black hole mass and the Eddington ratio of our sample.  It can be seen that the mass of black holes covers a large range from $10^{6}$ to $10^{10}M_{\odot}$. The center of the distribution of $M_{\rm BH}$ for the sources is greater than $10^{7} M_{\odot}$. The histogram of the Eddington ratio of the sample shows that the Eddington ratio ranges from $10^{-2.5}$ to 1.0, most of the objects are at high accretion rate.  If the accretion mode in AGNs is similar to that in black hole X-ray binaries, the high accretion rates of our sample indicate that the thin disk extends down to the innermost stable circular orbit, hence the hard X-ray arises from a disk corona rather than an ADAF. 

Correlation Analysis and Results
--------------------------------

We plot the ratio of X-ray luminosity to the bolometric luminosity vs. the mass of black holes and vs. the Eddington ratio for RQ sources in Fig.2.  In the upper two panels the vertical axis is logarithm of the fraction of hard X-ray luminosity to bolometric luminosity (log($L_{\rm 2-10 keV}/L_{\rm bol}$)).  While in the lower panels, the vertical axis is logarithm of the fraction of soft X-ray luminosity (0.1–2.4 keV) to the bolometric luminosity.  Comparing the upper and lower panels one can see that the distribution trends are different for soft X-ray and hard X-ray fraction. 

We test the correlations between log($L_{\rm 2-10 keV}/L_{\rm bol}$) and log($M_{\rm BH}$) and between log($L_{\rm 2-10 keV}/L_{\rm bol}$) and Eddington ratio by the method of Spearman’s rank correlation analysis (William et al.  [@will00]).  We calculate the Spearman’s rank correlation coefficient($\rho$) and the two-sided significance of its deviation from zero ($P_{\rm Null}$), representing the probability for randomness of the observed correlation of two variables.  Significant correlation of two variables is accepted if $P_{\rm null}$ is less than 0.05.  For our sample, the coefficient $\rho$ between log($L_{\rm 2-10
keV}/L_{\rm bol}$) and log$M_{\rm BH}$ is 0.001, and $P_{\rm Null}$ is 0.988.  This means that the fraction of hard X-ray is independent of black hole mass.  For the relation between the hard X-ray fraction and Eddington ratio, we get $\rho=-0.17$, $P_{\rm
Null}=0.008$. This indicates that for RQ AGNs the hard X-ray fraction correlates with Eddington ratio, with increase of the Eddington ratio, the hard X-ray fraction decreases.  This result is qualitatively consistent with the work of Wang et al. ( 2004). 

In addition, we analyze the correlation of soft X-ray fraction with the black hole mass and Eddington ratio.  It is found that the soft X-ray fraction in the bolometric luminosity depends on black hole mass ($\rho=-0.26$, $P_{\rm Null}=4.085e-5$), in contrast to the case of hard X-rays.  The soft X-ray fraction also positively correlated with the Eddington ratio ($\rho=0.18$, $P_{\rm Null}=0.005$), contrary to the trend of hard X-ray fraction. 

Interpretation of the Correlations with Disk Corona Model
=========================================================

The hard X-ray radiation from RQ AGNs with high Eddington ratio is commonly thought to be produced from a disk corona as a result of Comptonization of the softer photons arising from the accretion disk (e.g. Haardt & Maraschi 1993; Kawaguchi et al.  2001; Liu et al.  2003; Cao 2009).  If the bolometric luminosity is contributed dominantly by the disk ($L_d$) and corona ($L_c$), the fraction of hard X-ray luminosity in the total luminosity represents the strength of the corona relative to the disk.  Thus, the negative correlation between the fraction of hard X-ray and Eddington ratio for RQ AGNs indicates that the corona relative to the disk becomes weaker as the Eddington-scaled accretion rate increases. 

Theoretical calculation of radiations from the disk corona (Haardt & Maraschi 1991; 1993) shows that the spectral shape does not change with accretion rate.  In other words, ratio ($f$) of X-ray luminosity and bolometric luminosity is predicted to be independent on the accretion rate.  To explain the observational correlation between $f$ and Eddintong accretion rate, Wang et al. ( 2004), Yang et al. ( 2007) and Cao(2009) consider magnetic fields and different shear stress tensors.  Here we introduce the disk corona evaporation and/or condensation model (Liu et al.  2002a).  We show that even without magnetic fields the correlation can be simply a consequence of efficient condensation of coronal gas to the disk in the case of high accretion rates. 

Assuming that the energy of photons from the disk is amplified by a factor of $A\equiv \Delta \epsilon /\epsilon $ in the process of collisions with electrons when going through the corona, for non-relativistic thermal distributions of electrons $A$ is a function of electron temperature ($T_e$) and optical depth ($\tau_{es}$) of the corona, $$A={4kT_e\over m_ec^2}\tau_{es}.$$ The fraction of hard X-ray luminosity is expressed as, $$\label{X-farction}
{L_{2-10keV}\over L_{\rm bol}}={AL_d\over AL_d+L_d}={1\over 1+{1\over A}}.$$ In the case of high accretion rate, disk radiations are strong, which leads to efficient inverse Compton scattering in the corona.  As a consequence of over-cooling, part of the corona gas condenses into the disk, thereby the optical depth decreases and hence the amplification factor is low.  The higher the accretion rate, the lower density of the corona is.  Therefore, from Eq.\[X-farction\] one can see that the fraction of X-ray decreases at high accretion rates.  Thus, the negative correlation between the fraction of hard X-ray luminosity and the Eddington ratio can be explained by the corona condensation to the disk as a consequence of pressure and energy balance between the disk and corona. 

Detailed calculations of condensation rate and luminosity have been carried out by Liu et al. ( 2007) and Taam et al. ( 2008).  In this model, when the Compton scattering is the dominant cooling mechanism, the luminosities from the corona and disk are respectively as follows (Taam et al.  2008), $$\begin{aligned}
\label{lcom}
L_{\rm c}&=&\int_{3R_{s}}^{R_{out}}2\pi RH\frac{4kT_{\rm e}}{m_{\rm e}c^2}n_{\rm e}\sigma_{\rm T}4\sigma T^4_{\rm eff}(R)dR \nonumber\\
&=&4.11\times 10^{38}\alpha^{-\frac{7}{5}}m\dot{m_{\rm c}}^{\frac{7}{5}}\dot{m_{\rm d}}^{\frac{3}{5}}\int_{3}^{r_{out}}\left(\frac{3}{r}\right)^{\frac{23}{10}}\left[1-\left(\frac{3}{r}\right)^{\frac{1}{2}}\right]^{\frac{3}{5}}dr.\end{aligned}$$ $$\begin{aligned}
\label{ldisk}
L_{\rm d}&=&\int_{3R_s}^{R_{out}}\sigma T^4_{\rm eff}(R)4\pi RdR \nonumber\\
&=&\int_{3R_s}^{R_{out}}\frac{3GM\dot{M_{\rm d}}}{8\pi R^3}\left[1-\left(\frac{3R_s}{R}\right)^{\frac{1}{2}}\right]4\pi RdR \nonumber\\
&=&9.38\times 10^{38}m\dot{m_{\rm d}}\int_{3}^{r_{out}}\frac{1}{r^2}\left[1-\left(\frac{3}{r}\right)^{\frac{1}{2}}\right]dr.\end{aligned}$$ where $r=R/R_{s}$ ($R_{s}$ the Scwarzschild radius), $m=M_{\rm BH}/M_\odot$, $\dot m_c$ is the Eddington-scaled accretion rates in the corona and $\dot m_d$ the one in the disk.  Note that for a truncated inner disk lying under a corona, $\dot m_d$ comes only from the condensation of coronal gas; While in the case of a full disk coexisting with a corona for AGNs discussed here, the accretion rate in the disk is mainly from outer region, $\dot m_d=\dot m-\dot m_c$. We then derive the ratio of corona luminosity and disk luminosity, $$\label{lc/ld}
 L_{\rm c}/L_{\rm d}\propto \alpha^{-\frac{7}{5}}\dot{m_{\rm c}}^{\frac{7}{5}}\dot{m_{\rm d}}^{-\frac{2}{5}}=\alpha^{-\frac{7}{5}}\dot{m_{\rm c}}^{\frac{7}{5}}(\dot m-\dot{m_{\rm c}})^{-\frac{2}{5}}.$$ In the disk corona evaporation and/or condensation model, the coronal accretion flow is supplied by disk evaporation in the region around $300 R_s$. The coronal flow rate $\dot m_c$ can be as high as a few percent of Eddington value if the accretion rate exceeds a few percent of Eddington value.  However, the coronal flow can condense partially into the disk in the inner region as a result of Compton cooling, and the condensation rate is larger at higher accretion rate.  This means that the coronal flow ($\dot m_c$) is lower at higher accretion rate.  From Eq.(\[lc/ld\]) one can see that the ratio of corona luminosity and disk luminosity decreases with increasing accretion rate $\dot m$. Noting that the accretion rate in unit of Eddington value equals to the Eddington ratio, the disk corona evaporation and condensation model predicts that the ratio of X-ray luminosity and disk luminosity decreases with increasing Eddington ratio, which can explain the correlation obtained from our RQ AGN sample. 

If magnetic fields are also taken into account as additional heating (Liu et al.  2003; Cao 2009 ), the coronal accretion flow can be higher and the corona can be stronger than that without magnetic fields.  But the trend that condensation is stronger at higher accretion rates does not change by the magnetic fields.  Therefore, the variation of relative strength of the disk and corona with accretion rates keeps the same trend.  Thus, with inclusion of magnetic fields the model will still work in interpreting the correlations. 

Another important feature of the disk corona evaporation and condensation model is that the corona structure and evaporation/condensation properties are independent on the mass of black hole if scaled properly.  In fact, the model can be applied in both X-ray binaries and AGNs.  Eq.(\[lc/ld\]) shows that the luminosity ratio from the corona and disk indeed does not vary with the mass of black hole.  Therefore, the model can explain why for our sample the fraction of hard X-ray luminosity is independent on the mass of black hole. 

Discussion
==========

Implication to the Hard X-ray Bolometric Correction
---------------------------------------------------

The bolometric luminosity is either estimated from the measured luminosity at $5100\AA$ or from hard X-ray luminosity with fixed correction factors.  However, our data analysis shows that the hard X-ray fraction in the bolometric luminosity decreases with increasing Eddington ratio for RQ AGNs.  This means that bolometric correction factor from hard X-rays, $k_{\rm 2-10keV}=L_{\rm bol}/L_{2-10keV}$, should increase with increasing Eddington ratio.  This result is in good agreement with that of Vasudevan & Fabian (2007), which is drawn from 54 AGNs with available SEDs.  Note that in our study we calculate the bolometric luminosity from $9\lambda L_\lambda(5100\AA)$. If the bolometric correction factor for $L_{5100\AA}$ also tends to increase with Eddington ratio (see Fig.15 of Vasudevan & Fabian 2007), the hard X-ray fraction in bolometric luminosity would be even smaller at higher Eddington ratio for our sample.  Therefore, our statistical results support that the bolometric correction for hard X-rays increases with increasing Eddington ratio. 

The Constant Photon Index
-------------------------

In order to investigate the strength of corona ie.  to get the hard X-ray flux, we use the same photon indices for all objects in our sample to extrapolate the hard X-ray emissiong from 2keV flux.  From above analysis, we get a smaller absolute coefficient value ($\rho$) between the fraction of hard X-ray luminosity and Eddington ratio.  However, if we note that for some individual objects the spectra become softer when a source is brighter (e.g., Lu & Yu [@luyu99], Bian et al.  [@bian05], Middleton et al.  [@mid08]; Saez et al.  2008) and this effect is taken into account, the hard X-ray luminosity fraction should change with the Eddington ratio more steeply than our results since here we assume the photon index is constant in calculating the hard X-ray luminosity. 

The Origin of Soft X-rays in 0.1-2.4 keV 
-----------------------------------------

Our study also indicates that for the same RQ AGNs the fraction of soft X-ray luminosity in the ROSAT energy band ($0.1-2.4 \rm keV$) anticorrelates on the mass of black hole, as shown in Fig.2.  If the soft X-ray is also from the corona, the correlation should be similar to that for hard X-rays, that is, the fraction of soft X-ray is independent on the balck hole mass.  On the other hand, if the disk emits dominantly in the soft X-ray, the fraction of the soft X-ray to the total luminosity should also be independent on the mass of black hole since both the total luminosity and disk luminosity are proportional to the mass of black hole.  We note that the effective temperature of the disk decreases with the mass of black hole (e.g., Thorne K. S. [@thone74], Bonning et al.  [@bon07]), $\sigma T^4_{\rm eff}={3GM\dot M\over 8\pi R^3}\left[1-(3R_s/R)^{1/2}\right]$, reaching a maximum at $R=(49/36)(3R_S)$ (see Liu et al.  2007), $$T_{\rm eff,max}=1.3\times 10^5 (M_{\rm BH}/10^8M_\odot)^{-1/4}{\dot m}^{1/4}K.$$ For AGN with a high mass of black hole, the disk does not emit in the soft X-rays but in the optical/UV band.  With mass decreases, the high energy part of the disk spectrum could extend to soft X-ray.  Consequently, the fraction of disk contribution to the soft X-ray increases with decreasing of $M_{\rm BH}$. This could lead to a negative correlation between the fraction of soft X-ray and the mass of black hole, qualitatively consistent with the observational results shown in Section 3.  Therefore, the different correlations with black hole mass of the soft X-ray and hard X-ray may indicate that the soft X-rays are contributed from not only the corona but also the disk.  Zhou et al. ( 1997) separated two components in the soft X-ray region through statistic analyzing the Big Blue Bump. 

Conclusion {#sect:conclusion}
==========

We compile a blue AGNs sample containing Seyfert 1 galaxies and QSOs with 240 AGNs being RQ.  We mainly investigate the dependence of the fraction of hard X-ray luminosity in bolometric luminosity (log$(L_{\rm 2-10 keV}/L_{\rm bol})$) on the black hole mass and Eddington ratio in RQ AGNs by using the Spearman’s rank correlation.  We find that the fraction of hard X-ray luminosity in bolometric luminosity decreases with the increase of Eddington ratio for RQ AGNs.  While the fraction of hard X-ray luminosity in the bolometric luminosity is independent on black hole mass for a wide range of black hole mass.  The correlation between the hard X-ray and bolometric luminosity suggests that the hard X-ray bolometric correction increase at high Eddington ratio, confirming with a large sample Vasudevan & Fabian (2007)’s results.  These observational features support the disk corona model developed by Meyer et al. ( 2000) and Liu et al. ( 2002a).  Combining the theoretical model and the wide range of black hole mass in our sample, we suggest that the intrinsic accretion process in AGNs and black hole X-ray binaries be similar. 

We are grateful to the anonymous referee for constructive and enlightening comments.  Liu J. Y. greatly thanks Yuan W. for the instruction in X-ray data deducing and the statistical analysis.  We also acknowledge Dong X. B. for the SDSS data analysis.  This work is supported by the National Natural Science Foundation of China (grants 10533050 and 10773028) and National Basic Research Program of China-973 Program 2009CB824800. 

[99]{}

Bian W. H., 2005, ChJAS, 5, 289 Bonning E.W., Cheng L. et al.,  2007, ApJ, 659, 211 Cao Xinwu, 2009, MNRAS, 394, 207 Dong X.B., Wang T.G. et al.,  2008, MNRAS, 383, 581(Dong08) Elvis M., et al.,  1994, ApJS, 95, 1 Galeev A. A.,Rosner R., Vaiana G. S.,1979, ApJ, 229, 318 Haardt, F., & Maraschi, L., 1991, ApJ, 380, L51 Haardt, F., & Maraschi, L., 1993, ApJ, 413, 507 Ivezić Ž., et al.,  2002, AJ, 124, 2364 Kawaguchi, T., Shimura, T., & Mineshige, S., 2001, ApJ, 546, 966 Liang E. P. T., Price R. H., 1977, ApJ, 218, 247 Liu B. F., Yuan W., Meyer F., et al.,  1999, ApJ, 527, L17 Liu B. F., Mineshige S., Meyer F., et al.  2002, ApJ, 575, 117 (2002a) Liu B. F., Mineshige S., Shibata K., 2002, ApJ, 572, L173 (2002b) Liu B. F., Mineshige S., Ohsuga K., 2003, ApJ, 587, 571 Liu B. F., Taam Ronald E., Meyer-Hofmeister E., Meyer F., 2007, ApJ, 671, 695 Lu Y. & Yu Q., 1999, ApJ, 570, L47 Lynden–Bell D. & Pringle J.E., 1974, MNRAS, 168, 603 Meyer F. & Meyer–Hofmeister E., 1994, A&A, 288, 175 Meyer F., Liu B. F., et al. ,2000, A&A, 361, 175 Middleton M., Done C. and Schurch N., 2008, MNRAS, 383, 1501 Nakamura, K & Osaki, Y., 1993, PASJ, 45, 775 Narayan R. & Yi I., 1994, ApJ, 428, L13 Narayan R., Mahadevan R., & Quataert E., 1998, in The Thoery of Black Hole Accretion Discs, eds.  M. A. Abramowicz, G. Bjornsson, & J. E. Pringle (Cambridge University, Cambridge) Narayan R., & Yi, I. 1995, ApJ, 452, 710 Peterson B. M., 1 Narayan et al.993, PASP, 100, 18 Peterson B. M., Ferrarese L., et al.,  2004, ApJ, 613, 682 Pounds K. A., Nandran K., Stewart G. C. et al.,  1990, Nature, 344, 132 Reeves J. N., Turner M. J. L., 2000, MNRAS, 316, 234 Saez C., Chartas G., et al.  2008, ApJ, 135, 1505 Shakura N.I., Sunyaev R.A., 1973, A&A, 24, 337 Stella L., Rosner R., 1984, ApJ, 227, 312 Svensson R., Zdziarski A. A., 1994, ApJ, 436, 599 Taam, R.E, Liu, B. F, et al.,  2008, ApJ, 688, 527 Thorne K. S., 1974, ApJ, 191, 507 Vasudevan R .V., Fibian A. C., 2007, MNRAS,381, 1235 Vestergaard M., & Peterson B. M., 2006, ApJ, 641, 689 Voges W., Gruber R., Haberl F., et al.,  1994, ROSAT NEWS No.32 Wang J. M., Watarai K. Y., Mineshige, S., 2004, ApJ, 607, L107 William H.P., Saul A.T. et al.,  2000, Numerical Recipes in Fortran ( 2nd, Cambridge University Press, Cambridge) Woo J. H. & Urry C. M., 2002, ApJ, 578, 530 Yang F., Hu C. et al.,  2007, ChJAA, 7, 353 Zhou Y. Y., Yu K. N., et al.,  1997, ApJ, L9

Table
=====

        \[sample\]                                                                                                                                            
  ---------------------- --------- ----------------------- --------------------------- -------------------- ----------------- ------------------------------- ----------------------------
        **Object**         **Z**    **log($M_{\rm BH}$)**     **$L_{\rm 5100\AA}$**      **$F_{\rm 20cm}$**   **$R_{\rm i}$**  **log($L_{\rm 0.1-2.4keV}$)**   **log($L_{\rm 2-10keV}$)**
         **SDSS**                     ($\rm M_{\odot}$)     ($10^{44}$ ergs s$^{-1}$)                 (mJy)                         ($\rm ergs~s^{-1}$)           ($\rm ergs~s^{-1}$)
         **(1)**          **(2)**          **(3)**                   **(4)**                        **(5)**           **(6)**             **(7)**                       **(8)**
   000710.01$+$005329.0   0.31620           9.13                      3.85                             1.44              0.55             44.949                         44.238
   000834.72$+$003156.1   0.26303           7.71                      2.71                          $<$1.00              0.43             44.665                         42.915
   000943.14$-$090839.1   0.20958           8.52                      2.09                          $<$1.00              0.21             44.057                         43.225
   001247.93$-$084700.4   0.22006           8.01                      1.95                          $<$1.00              0.21             44.629                         43.965
   004319.74$+$005115.3   0.30807           9.36                      3.08                             1.60              0.80             44.425                         44.099
   010226.31$-$003904.6   0.29421           7.92                      9.63                          $<$1.00           $-$0.10             45.012                         43.656
   011254.92$+$000313.0   0.23855           8.14                      1.98                          $<$1.00              0.42             44.398                         43.816
   014017.07$-$005003.0   0.33424           8.92                      13.40                         $<$1.00              0.06             45.232                         44.927
   014234.40$-$011417.3   0.24453           7.14                      0.68                          $<$1.00              0.69             44.078                         44.060
   015530.01$-$085704.0   0.16465           8.48                      1.78                          $<$1.00           $-$0.04             44.212                         43.739
   015910.04$+$010514.6   0.21716           8.08                      1.99                          $<$1.00              0.22             44.164                         43.731
   022347.48$-$083655.5   0.26077           7.52                      0.97                             1.04              0.81             44.330                         43.631
   022417.16$-$092549.3   0.31148           8.79                      1.72                          $<$1.00              0.67             44.751                         43.763
   072937.04$+$375435.0   0.20364           7.23                      1.39                          $<$1.00              0.40             44.558                         43.179
   073503.49$+$431153.5   0.26246           8.11                      1.86                          $<$1.00              0.59             44.302                         43.979
   074645.05$+$314149.2   0.32696           7.55                      3.31                          $<$1.00              0.54             44.972                         43.504
   074820.97$+$340752.6   0.34304           8.09                      3.08                          $<$1.00              0.68             44.482                         43.986
   074948.26$+$345444.0   0.13181           7.71                      1.16                             0.82           $-$0.01             44.129                         43.526
   075217.84$+$193542.2   0.11723           9.43                      2.59                            22.95              0.84             43.173                         42.932
   075245.60$+$261735.7   0.08216           6.92                      0.46                             1.27              0.13             43.924                         42.985
   075819.68$+$421935.1   0.21125           7.97                      2.84                             1.81              0.36             44.958                         43.865
   075949.54$+$320023.9   0.18805           7.60                      1.92                          $<$1.00              0.35             44.488                         43.353
   080559.94$+$260602.3   0.13594           8.31                      1.34                          $<$1.00           $-$0.09             43.371                         42.525
   080644.65$+$384318.3   0.34539           7.98                      3.28                          $<$1.00              0.71             44.954                         44.363
   081054.73$+$501319.5   0.32184           9.13                      5.47                          $<$1.00              0.37             44.258                         43.940
   081317.91$+$435620.7   0.25455           8.30                      1.81                          $<$1.00              0.60             44.351                         43.472
   081427.69$+$433705.1   0.22418           7.61                      1.27                          $<$1.00              0.47             44.205                         43.334
   081738.33$+$242330.0   0.28259           8.20                      4.23                             4.45              0.86             44.599                         44.382
   082633.51$+$074248.4   0.31064           8.14                      7.54                          $<$1.00              0.12             44.876                         43.978
   082640.73$+$063041.5   0.17092           7.82                      0.80                          $<$1.00              0.50             44.165                         43.175
   083120.99$+$483154.4   0.33466           7.56                      3.30                          $<$1.00              0.62             45.087                         44.444
   083225.34$+$370736.1   0.09191           9.22                      1.20                            11.73              0.75             44.291                         43.776
   083417.91$+$491439.2   0.17315           7.40                      0.93                          $<$1.00              0.26             44.082                         43.225
   083443.80$+$382632.7   0.28822           8.59                      2.94                          $<$1.00              0.48             45.016                         43.780
   083553.46$+$055317.1   0.20438           7.49                      2.24                          $<$1.00              0.15             44.031                         43.165
   083658.91$+$442602.4   0.25443           8.74                      13.58                           10.25              0.64             45.314                         44.562
   084230.51$+$495802.3   0.30508           8.53                      2.88                          $<$1.00              0.54             44.447                         43.552
   084504.20$+$542612.0   0.30317           7.97                      1.53                          $<$1.00              0.88             44.427                         43.895
   084853.09$+$282411.8   0.19820           8.29                      0.81                          $<$1.00              0.60             44.265                         43.715
   085259.22$+$031320.6   0.29708           8.31                      8.80                          $<$1.00           $-$0.02             44.334                         43.979
   085632.39$+$504114.0   0.23471           8.20                      5.11                          $<$1.00           $-$0.10             44.005                         43.129
   085828.69$+$342343.8   0.25666           8.70                      6.43                          $<$1.00           $-$0.08             45.039                         43.989
   085900.48$+$383211.6   0.34551           7.73                      2.94                          $<$1.00              0.65             45.459                         43.663
   085915.65$+$011800.5   0.28206           8.40                      3.25                          $<$1.00              0.46             44.582                         43.603
   090137.99$+$532051.1   0.16165           7.11                      1.05                          $<$1.00              0.25             44.464                         43.359
   090151.14$+$103020.4   0.20093           7.92                      4.13                          $<$1.00           $-$0.14             44.572                         43.903
   090455.00$+$511444.6   0.22463           8.20                      2.55                          $<$1.00              0.10             44.364                         43.564
   090519.67$+$440139.1   0.34246           7.50                      1.64                          $<$1.00              0.80             44.898                         43.344
   090654.47$+$391455.4   0.24067           7.39                      1.85                          $<$1.00              0.51             44.593                         43.695
   090851.25$+$444611.2   0.32021           8.34                      3.66                          $<$1.00              0.42             44.130                         43.885

  ---------------------- --------- ----------------------- --------------------------- -------------------- ----------------- ------------------------------- ----------------------------
        **Object**         **Z**    **log($M_{\rm BH}$)**     **$L_{\rm 5100\AA}$**      **$F_{\rm 20cm}$**   **$R_{\rm i}$**  **log($L_{\rm 0.1-2.4keV}$)**   **log($L_{\rm 2-10keV}$)**
         **SDSS**                     ($\rm M_{\odot}$)     ($10^{44}$ ergs s$^{-1}$)                 (mJy)                         ($\rm ergs~s^{-1}$)           ($\rm ergs~s^{-1}$)
         **(1)**          **(2)**          **(3)**                   **(4)**                        **(5)**           **(6)**             **(7)**                       **(8)**
   090932.04$+$503019.6   0.26728           7.56                      1.14                          $<$1.00              0.79             43.933                         43.046
   091010.00$+$481341.7   0.11700           8.14                      0.86                          $<$1.00              0.00             44.297                         43.446
   091702.38$-$004417.5   0.32231           8.71                      8.21                          $<$1.00              0.15             45.337                         44.643
   091755.02$+$053749.7   0.34898           8.43                      1.86                          $<$1.00              0.74             44.573                         43.461
   091955.35$+$552137.1   0.12295           8.46                      2.33                          $<$1.00           $-$0.38             44.338                         43.412
   092309.87$+$453046.4   0.29238           7.63                      2.16                          $<$1.00              0.54             44.672                         43.779
   092554.44$+$453544.2   0.32948           7.97                      3.10                          $<$1.00              0.47             44.534                         43.631
   092909.79$+$464424.0   0.23996           8.64                      6.15                          $<$1.00           $-$0.12             43.833                         43.103
   092933.58$+$095617.0   0.23194           7.53                      0.95                          $<$1.00              0.70             44.199                         43.811
   093701.04$+$010543.7   0.05054           6.92                      0.30                          $<$1.00           $-$0.04             43.885                         43.308
   093939.69$+$375705.8   0.23127           7.79                      2.24                          $<$1.00              0.34             43.739                         42.863
   094621.27$+$471131.3   0.23049           7.67                      1.37                          $<$1.00              0.50             44.233                         43.890
   095048.38$+$392650.5   0.20564           8.41                      3.45                          $<$1.00           $-$0.16             44.807                         44.329
   095302.64$+$380145.2   0.27291           8.45                      2.60                          $<$1.00              0.45             44.740                         43.853
   095823.45$+$065506.5   0.34581           8.30                      5.20                          $<$1.00              0.53             44.715                         44.356
   095833.95$+$560224.4   0.21639           6.99                      0.74                             0.83              0.61             44.113                         42.926
   095915.65$+$050355.1   0.16230           7.88                      1.42                          $<$1.00              0.10             44.040                         42.836
   095931.67$+$504449.0   0.14323           7.54                      1.12                          $<$1.00              0.02             43.771                         42.984
   100033.88$+$104723.7   0.22648           7.99                      2.25                             2.17              0.29             44.776                         43.656
   100201.76$+$620816.3   0.13379           6.98                      0.35                          $<$1.00              0.49             44.093                         43.173
   100420.13$+$051300.4   0.16049           7.61                      2.61                          $<$1.00           $-$0.12             43.401                         42.547
   100541.86$+$433240.4   0.17843           7.79                      2.67                             2.81              0.47             44.844                         43.917
   100627.94$+$603043.6   0.21025           7.15                      1.00                          $<$1.00              0.56             44.164                         43.081
   100744.54$+$500746.6   0.21204           7.67                      2.51                          $<$1.00              0.18             44.594                         43.861
   101044.51$+$004331.3   0.17757           8.83                      3.15                             0.77           $-$0.36             44.556                         43.211
   101401.86$+$461953.7   0.32112           8.38                      5.56                          $<$1.00              0.22             44.707                         43.696
   101415.14$+$091839.3   0.25224           8.62                      1.18                          $<$1.00              0.58             44.500                         43.999
   101437.46$+$440639.1   0.20014           7.62                      1.38                          $<$1.00              0.31             44.251                         43.458
   101730.97$+$470225.0   0.33499           7.91                      3.62                          $<$1.00              0.48             44.629                         43.732
   101852.45$+$495800.3   0.15481           7.00                      0.41                          $<$1.00              0.63             43.931                         43.436
   102309.48$+$082602.1   0.34411           8.02                      2.69                          $<$1.00              0.60             44.492                         43.585
   102512.85$+$480853.2   0.33156           8.50                      2.35                          $<$1.00              0.66             44.289                         43.386
   102531.28$+$514034.8   0.04488           7.05                      0.29                             0.60           $-$0.43             44.038                         42.994
   102745.84$+$051558.9   0.31480           7.56                      3.02                          $<$1.00              0.45             44.648                         43.411
   103421.70$+$605318.1   0.22775           8.07                      1.97                          $<$1.00              0.29             44.158                         43.292
   103457.29$-$010209.0   0.32801           7.64                      3.20                          $<$1.00              0.51             44.791                         43.891
   104041.50$+$600239.3   0.29711           7.63                      2.53                          $<$1.00              0.54             44.318                         43.656
   104541.76$+$520235.5   0.28393           7.87                      5.73                          $<$1.00              0.16             44.855                         43.895
   105007.75$+$113228.6   0.13344           7.65                      2.50                             1.50           $-$0.10             44.264                         43.445
   105055.14$+$552723.2   0.33196           7.86                      5.20                          $<$1.00              0.33             45.165                         44.059
   105118.23$+$605008.2   0.27603           7.98                      1.97                          $<$1.00              0.61             44.031                         42.963
   105444.70$+$483139.0   0.28651           8.73                      10.08                            1.56           $-$0.00             45.219                         44.523
   105752.69$+$105037.9   0.22033           7.23                      1.20                          $<$1.00              0.48             44.458                         43.585
   105830.13$+$601600.3   0.14868           7.56                      1.40                          $<$1.00           $-$0.11             44.300                         43.041
   110016.19$+$393524.5   0.31265           7.71                      1.60                          $<$1.00              0.88             44.998                         43.979
   110540.09$+$064225.7   0.23046           8.36                      1.20                          $<$1.00              0.36             44.178                         44.159
   111006.95$+$612521.4   0.26234           7.60                      1.46                          $<$1.00              0.51             44.403                         43.527
   111706.39$+$441333.3   0.14382           8.73                      4.02                          $<$1.00           $-$0.45             43.323                         42.475
   111740.48$+$530151.3   0.15851           7.56                      0.83                          $<$1.00              0.36             43.783                         43.081
   111830.28$+$402554.0   0.15457           7.67                      3.16                             2.32              0.06             44.670                         43.826
   112114.21$+$032546.8   0.15203           7.62                      1.12                             2.20              0.59             43.858                         43.871
   112417.79$+$602026.7   0.20470           7.27                      1.06                          $<$1.00              0.49             44.288                         43.619
  ---------------------- --------- ----------------------- --------------------------- -------------------- ----------------- ------------------------------- ----------------------------

  ---------------------- --------- ----------------------- --------------------------- -------------------- ----------------- ------------------------------- ----------------------------
        **Object**         **Z**    **log($M_{\rm BH}$)**     **$L_{\rm 5100\AA}$**      **$F_{\rm 20cm}$**   **$R_{\rm i}$**  **log($L_{\rm 0.1-2.4keV}$)**   **log($L_{\rm 2-10keV}$)**
         **SDSS**                     ($\rm M_{\odot}$)     ($10^{44}$ ergs s$^{-1}$)                 (mJy)                         ($\rm ergs~s^{-1}$)           ($\rm ergs~s^{-1}$)
         **(1)**          **(2)**          **(3)**                   **(4)**                        **(5)**           **(6)**             **(7)**                       **(8)**
   112439.18$+$420145.0   0.22503           8.18                      7.01                          $<$1.00           $-$0.30             44.623                         43.072
   112646.43$-$013417.9   0.34095           8.32                      2.30                          $<$1.00              0.80             44.001                         43.866
   112941.93$+$512050.6   0.23385           7.47                      2.50                             1.26              0.36             44.719                         43.577
   113105.04$+$610405.0   0.33802           7.95                      3.64                          $<$1.00              0.46             44.206                         43.415
   113422.48$+$041127.6   0.10800           8.19                      1.04                          $<$1.00           $-$0.26             44.366                         43.591
   113706.84$+$013948.0   0.19262           8.73                      2.64                          $<$1.00              0.07             44.714                         44.322
   113738.04$+$103930.1   0.17454           8.06                      2.55                             1.65              0.20             44.405                         43.707
   113908.97$+$591154.8   0.06127           7.86                      0.76                          $<$1.00           $-$0.48             43.543                         43.303
   114039.86$+$414545.9   0.23833           7.87                      1.37                          $<$1.00              0.54             44.647                         43.770
   114105.71$+$024117.0   0.09313           7.55                      0.47                          $<$1.00              0.06             43.623                         43.092
   114327.21$+$431145.9   0.30505           8.05                      3.38                          $<$1.00              0.44             44.447                         43.550
   114341.97$-$014434.5   0.10522           7.52                      0.82                          $<$1.00              0.04             43.280                         42.444
   114408.90$+$424357.5   0.27248           7.74                      2.20                          $<$1.00              0.58             44.499                         43.612
   114559.00$+$040409.8   0.27359           7.69                      1.31                          $<$1.00              0.88             43.916                         43.889
   114954.99$+$044812.9   0.26951           7.53                      3.02                             1.76              0.62             44.474                         43.529
   115105.41$+$445309.3   0.34394           7.35                      1.99                          $<$1.00              0.75             44.455                         43.548
   115507.61$+$520129.6   0.15399           7.30                      1.12                             2.05              0.58             43.652                         42.801
   115549.43$+$502117.1   0.28443           8.05                      3.08                          $<$1.00              0.43             44.386                         43.495
   115558.97$+$593129.3   0.24081           7.98                      2.25                          $<$1.00              0.36             44.603                         43.579
   115632.24$+$112653.7   0.22582           7.52                      1.54                          $<$1.00              0.38             44.176                         43.302
   115758.73$-$002220.7   0.25984           8.42                      3.25                          $<$1.00              0.14             44.034                         44.029
   120118.43$+$060024.1   0.33555           8.79                      2.16                          $<$1.00              0.64             44.307                         43.402
   120233.08$+$022559.7   0.27287           8.51                      2.85                          $<$1.00              0.37             44.197                         43.366
   120347.70$+$520749.7   0.17760           8.50                      4.92                             0.68           $-$0.54             44.681                         43.957
   121018.35$+$015405.9   0.21589           8.40                      2.71                          $<$1.00              0.22             43.768                         43.174
   122420.28$+$435157.9   0.32172           8.44                      2.39                          $<$1.00              0.69             44.520                         43.880
   122549.28$+$472343.8   0.31883           7.56                      2.04                          $<$1.00              0.66             44.294                         43.394
   123054.12$+$110011.1   0.23596           8.29                      3.67                          $<$1.00           $-$0.02             44.503                         44.301
   123115.20$+$590707.2   0.32605           8.05                      3.14                          $<$1.00              0.48             44.461                         44.272
   123220.11$+$495721.7   0.26188           7.65                      2.94                          $<$1.00              0.50             45.082                         43.929
   123234.05$+$092815.2   0.34665           8.33                      2.35                          $<$1.00              0.74             44.614                         43.812
   123958.57$+$490540.1   0.23550           7.04                      1.08                          $<$1.00              0.59             43.941                         43.308
   124441.41$+$585626.8   0.19806           7.25                      0.75                          $<$1.00              0.54             44.667                         43.269
   124635.24$+$022208.7   0.04818           6.75                      0.31                             2.23              0.25             44.057                         43.159
   124931.72$+$523039.2   0.16228           8.00                      2.66                          $<$1.00           $-$0.14             44.447                         43.272
   125519.69$+$014412.3   0.34318           8.92                      15.52                            1.47              0.11             45.350                         44.548
   125719.56$+$442935.4   0.30025           8.25                      7.68                          $<$1.00              0.00             44.818                         44.084
   125824.57$+$540429.8   0.34769           8.12                      2.17                          $<$1.00              0.76             44.470                         43.562
   130250.51$+$111827.9   0.20284           7.47                      1.71                          $<$1.00              0.28             44.424                         43.334
   130416.99$+$020537.1   0.22854           7.67                      2.04                          $<$1.00              0.27             45.378                         43.966
   130421.84$+$560817.0   0.29830           7.82                      2.17                          $<$1.00              0.62             44.406                         43.823
   130604.48$+$453405.4   0.32709           7.52                      2.17                          $<$1.00              0.80             44.683                         44.095
   131308.67$+$542115.5   0.29798           8.45                      2.90                          $<$1.00              0.63             44.455                         43.872
   131404.97$+$153054.2   0.16517           7.94                      1.27                          $<$1.00              0.22             44.285                         43.363
   131651.70$+$630719.9   0.34724           8.65                      2.01                          $<$1.00              0.79             44.110                         44.246
   132144.96$+$033055.7   0.26889           8.70                      5.48                          $<$1.00              0.02             44.386                         43.765
   132242.47$-$022522.0   0.12115           7.69                      0.68                          $<$1.00              0.18             43.569                         43.592
   132447.65$+$032432.6   0.30578           8.25                      4.70                          $<$1.00              0.16             44.358                         43.461
   132643.62$+$015209.4   0.19670           7.68                      0.85                          $<$1.00              0.52             44.339                         43.680
   132802.54$+$441805.3   0.23155           8.13                      0.77                          $<$1.00              0.84             43.756                         42.880
   133051.24$+$412858.1   0.18174           7.70                      1.58                          $<$1.00              0.17             44.429                         43.511
   133300.83$+$451809.0   0.31974           8.36                      3.65                          $<$1.00              0.37             44.727                         44.267
  ---------------------- --------- ----------------------- --------------------------- -------------------- ----------------- ------------------------------- ----------------------------

  ---------------------- --------- ----------------------- --------------------------- -------------------- ----------------- ------------------------------- ----------------------------
        **Object**         **Z**    **log($M_{\rm BH}$)**     **$L_{\rm 5100\AA}$**      **$F_{\rm 20cm}$**   **$R_{\rm i}$**  **log($L_{\rm 0.1-2.4keV}$)**   **log($L_{\rm 2-10keV}$)**
         **SDSS**                     ($\rm M_{\odot}$)     ($10^{44}$ ergs s$^{-1}$)                 (mJy)                         ($\rm ergs~s^{-1}$)           ($\rm ergs~s^{-1}$)
         **(1)**          **(2)**          **(3)**                   **(4)**                        **(5)**           **(6)**             **(7)**                       **(8)**
   133423.30$+$434331.7   0.22551           7.65                      1.31                          $<$1.00              0.58             44.290                         43.751
   133636.65$+$420934.1   0.22328           8.23                      2.46                             3.55              0.73             43.559                         42.685
   134032.02$+$052158.5   0.27448           8.73                      2.26                          $<$1.00              0.63             44.668                         43.892
   134206.57$+$050523.8   0.26602           7.59                      3.48                             3.85              0.90             44.468                         43.582
   134251.60$-$005345.2   0.32581           8.37                      6.22                          $<$1.00              0.26             44.366                         43.364
   134444.17$+$630337.2   0.29218           7.80                      0.98                          $<$1.00              0.85             44.024                         43.327
   134459.45$-$001559.5   0.24490           7.55                      1.41                          $<$1.00              0.42             44.472                         43.475
   134845.44$+$451809.5   0.27653           8.90                      3.42                          $<$1.00              0.34             44.715                         43.930
   135829.58$+$010908.4   0.24392           8.30                      1.76                          $<$1.00              0.60             44.118                         43.240
   135946.91$+$581357.0   0.22391           7.44                      0.68                          $<$1.00              0.70             44.096                         43.716
   140050.21$+$532424.5   0.17466           7.25                      1.06                          $<$1.00              0.27             43.538                         42.678
   140104.18$+$635234.0   0.34386           8.44                      3.47                          $<$1.00              0.48             44.223                         42.802
   140604.25$+$572956.5   0.32581           8.57                      2.44                          $<$1.00              0.67             43.943                         43.040
   140824.76$+$543817.7   0.29106           7.63                      2.36                          $<$1.00              0.59             44.441                         43.548
   140827.51$+$142233.2   0.31766           7.48                      1.62                          $<$1.00              0.84             44.628                         43.795
   141046.46$+$465802.9   0.33409           7.38                      2.99                          $<$1.00              0.65             44.873                         43.164
   141758.25$+$360741.4   0.21180           7.62                      0.81                          $<$1.00              0.44             44.273                         43.558
   141942.46$+$591259.4   0.31988           8.37                      1.59                          $<$1.00              0.89             44.012                         43.318
   142424.22$+$595300.5   0.13495           8.75                      2.28                             2.51              0.08             44.091                         43.537
   142455.53$+$421407.6   0.31603           8.19                      7.32                          $<$1.00              0.17             44.661                         43.361
   142734.80$+$352543.4   0.34038           7.49                      1.69                          $<$1.00              0.78             44.084                         43.177
   142748.29$+$050222.0   0.10608           7.24                      1.27                          $<$1.00           $-$0.26             43.657                         42.900
   143039.30$+$493538.9   0.20355           7.82                      1.86                          $<$1.00              0.32             44.544                         43.403
   143204.60$+$394439.0   0.34848           9.05                      9.25                          $<$1.00              0.14             44.063                         43.154
   143704.12$+$000705.0   0.14036           7.45                      0.61                          $<$1.00              0.44             44.165                         43.270
   143919.31$+$551317.8   0.25720           8.52                      1.10                          $<$1.00              0.77             44.245                         43.807
   143940.27$+$030528.6   0.26856           7.23                      1.75                          $<$1.00              0.64             45.053                         43.949
   144012.76$+$615633.0   0.27547           7.54                      4.46                             2.88              0.69             44.860                         43.701
   144050.76$+$520445.9   0.31834           7.89                      3.73                          $<$1.00              0.46             44.684                         43.861
   144202.82$+$433708.7   0.23146           8.18                      3.54                          $<$1.00              0.20             44.584                         44.196
   144302.59$+$404525.1   0.24615           7.79                      3.16                          $<$1.00              0.11             44.231                         43.673
   144645.93$+$403505.7   0.26709           8.35                      11.37                         $<$1.00           $-$0.13             44.999                         44.073
   144751.79$+$505328.7   0.30565           7.56                      1.41                          $<$1.00              0.86             44.068                         43.173
   145006.93$+$581456.9   0.31520           7.72                      3.93                          $<$1.00              0.33             44.714                         43.755
   145254.74$+$395714.6   0.22528           7.31                      0.79                          $<$1.00              0.72             43.315                         43.261
   145307.63$+$380319.6   0.26191           7.32                      1.51                          $<$1.00              0.61             44.695                         43.416
   145439.39$+$465309.1   0.31645           8.45                      1.95                          $<$1.00              0.58             44.502                         44.050
   145440.39$+$455008.5   0.32471           7.92                      1.24                          $<$1.00              0.86             44.017                         43.115
   145817.42$+$455514.8   0.28575           7.79                      3.12                          $<$1.00              0.41             44.669                         43.422
   145824.46$+$363119.5   0.24637           7.91                      3.86                          $<$1.00              0.20             44.384                         43.474
   150049.15$+$343727.1   0.31794           7.52                      1.95                          $<$1.00              0.74             44.423                         43.423
   150114.45$+$393927.7   0.23072           7.51                      1.68                          $<$1.00              0.49             43.950                         43.074
   150155.24$+$563731.7   0.34338           7.54                      2.78                          $<$1.00              0.56             44.370                         42.992
   150242.39$+$395208.5   0.34185           8.19                      6.59                          $<$1.00              0.22             44.894                         43.976
   150437.67$+$541149.6   0.30519           8.39                      3.17                          $<$1.00              0.45             44.154                         43.128
   151304.56$+$304204.2   0.34801           8.14                      5.25                          $<$1.00              0.25             44.886                         43.997
   151557.75$+$302357.1   0.25171           7.60                      0.94                          $<$1.00              0.70             44.117                         43.235
   151940.87$+$320157.9   0.30132           8.35                      2.40                          $<$1.00              0.58             44.558                         43.896
   152153.81$+$594020.0   0.28599           8.10                      2.41                          $<$1.00              0.52             44.260                         44.001
   152524.16$+$523205.7   0.32755           8.28                      2.85                          $<$1.00              0.59             44.107                         43.125
   152628.19$-$003809.4   0.12333           7.40                      0.57                          $<$1.00              0.46             43.696                         42.856
   153941.49$+$504255.8   0.20315           7.40                      2.32                          $<$1.00              0.14             44.766                         43.774
  ---------------------- --------- ----------------------- --------------------------- -------------------- ----------------- ------------------------------- ----------------------------

  ---------------------- --------- ----------------------- --------------------------- -------------------- ----------------- ------------------------------- ----------------------------
        **Object**         **Z**    **log($M_{\rm BH}$)**     **$L_{\rm 5100\AA}$**      **$F_{\rm 20cm}$**   **$R_{\rm i}$**  **log($L_{\rm 0.1-2.4keV}$)**   **log($L_{\rm 2-10keV}$)**
         **SDSS**                     ($\rm M_{\odot}$)     ($10^{44}$ ergs s$^{-1}$)                 (mJy)                         ($\rm ergs~s^{-1}$)           ($\rm ergs~s^{-1}$)
         **(1)**          **(2)**          **(3)**                   **(4)**                        **(5)**           **(6)**             **(7)**                       **(8)**
   154004.24$+$355050.1   0.16361           8.16                      1.31                          $<$1.00              0.17             43.955                         43.126
   154344.27$-$001452.1   0.30189           8.16                      3.01                          $<$1.00              0.55             44.512                         43.620
   154348.62$+$401324.9   0.31826           8.60                      4.93                             2.75              0.84             44.885                         44.080
   155207.18$+$525347.0   0.33519           8.22                      2.50                          $<$1.00              0.65             44.313                         43.891
   155324.25$+$490726.9   0.25807           8.19                      1.88                          $<$1.00              0.59             44.297                         43.414
   155328.49$+$095102.0   0.19174           8.83                      3.31                          $<$1.00           $-$0.04             43.859                         42.996
   155837.88$+$282839.0   0.32336           8.54                      8.80                          $<$1.00              0.12             45.104                         44.163
   160518.50$+$375653.5   0.20087           7.55                      1.64                          $<$1.00              0.22             44.229                         43.314
   161118.82$+$291932.4   0.29364           8.29                      1.68                          $<$1.00              0.74             44.127                         43.757
   161849.25$+$442517.2   0.33521           8.46                      7.97                             3.09              0.63             44.636                         44.047
   162607.24$+$335915.2   0.20453           8.10                      5.54                             3.74              0.44             44.435                         43.243
   163111.28$+$404805.2   0.25751           8.03                      2.18                          $<$1.00              0.29             44.789                         44.152
   163631.58$+$461704.3   0.25170           7.64                      1.55                          $<$1.00              0.52             43.988                         43.086
   164343.24$+$405654.3   0.34375           7.04                      1.34                          $<$1.00              0.95             43.997                         43.089
   165338.69$+$634010.6   0.27897           7.54                      1.91                          $<$1.00              0.60             44.215                         41.701
   165352.82$+$384542.1   0.32302           7.64                      1.74                          $<$1.00              0.80             44.414                         43.383
   165737.30$+$604939.3   0.31316           7.67                      1.48                          $<$1.00              0.92             43.723                         43.004
   170231.06$+$324719.6   0.16333           7.76                      4.13                             1.52           $-$0.14             44.858                         43.879
   170302.88$+$191033.9   0.29045           7.86                      4.44                          $<$1.00              0.38             44.980                         44.210
   170525.54$+$194722.7   0.19392           8.42                      1.33                          $<$1.00              0.48             44.246                         43.436
   171013.42$+$334402.6   0.20749           8.67                      5.73                             4.60              0.40             44.590                         43.730
   171207.44$+$584754.5   0.26925           7.69                      1.55                          $<$1.00              0.64             44.551                         43.446
   171601.93$+$311213.8   0.11015           7.57                      1.76                             2.42           $-$0.06             44.301                         43.686
   171750.59$+$581514.0   0.31014           8.37                      4.19                          $<$1.00              0.42             44.428                         43.708
   171850.30$+$304201.6   0.28176           7.39                      2.03                             0.64              0.43             44.500                         43.400
   171902.29$+$593715.8   0.17852           7.49                      1.06                          $<$1.00              0.29             44.129                         43.018
   172711.81$+$632241.8   0.21736           9.17                      2.71                             1.23              0.23             44.482                         43.647
   173229.44$+$564811.3   0.30320           7.62                      1.87                          $<$1.00              0.67             44.309                         43.555
   211204.85$-$063535.2   0.20419           7.75                      1.71                          $<$1.00              0.34             44.239                         43.890
   213818.97$+$011222.4   0.34409           7.99                      3.98                          $<$1.00              0.48             44.584                         44.853
   215010.52$-$001000.7   0.33481           8.41                      1.90                          $<$1.00              0.80             44.719                         43.833
   215516.14$+$003250.8   0.27782           7.62                      2.11                          $<$1.00              0.59             44.648                         43.498
   231250.88$+$001719.0   0.25704           7.56                      2.02                          $<$1.00              0.56             44.201                         43.319
   233512.68$-$100040.3   0.24288           7.92                      0.50                          $<$1.00              0.83             44.095                         43.977
  ---------------------- --------- ----------------------- --------------------------- -------------------- ----------------- ------------------------------- ----------------------------

*Notes.*——\
Col.  1, object name in J2000.0.  Col.  2, redshift given by the SDSS spectroscopic pipeline.  Col.  3, logarithm of black hole mass .  Col.  4, luminosity at $5100\AA$ in unit of $10^{44}$ ergs s$^{-1}$. Col.  5, flux density at 20cm, ’$<$1’ represents that the object is covered yet not detected by FIRST.  Col.  6, the radio–loudness.  Col.  7–8, X-ray luminosity of 0.1–2.4 keV and 2–10 keV.\
\[lastpage\]
