A CATALOG OF QUASAR PROPERTIES FROM SLOAN DIGITAL SKY SURVEY DATA RELEASE 7

For Hα we use the optical iron template from Boroson & Green (1992), and we fit for objects with z ⩽ 0.39. The continuum+iron fitting windows are [6000,6250] Å and [6800,7000] Å.

For Hα line fitting, we fit the wavelength range [6400,6800] Å. The narrow components of Hα, [N ii] λλ6548,6584, [S ii] λλ6717,6731 are each fit with a single Gaussian. Their velocity offsets from the systemic redshift and line widths are constrained to be the same, and the relative flux ratio of the two [N ii] components is fixed to 2.96. We impose an upper limit on the narrow line FWHM <1200 km s⁻¹ (e.g., Hao et al. 2005). The broad Hα component is modeled in two different ways: (1) a single Gaussian with an FWHM >1200 km s⁻¹ and (2) multiple Gaussians with up to three Gaussians, each with an FWHM >1200 km s⁻¹. The second method yields similar results to the fits with a truncated Gaussian–Hermite function (e.g., van der Marel & Franx 1993). During the fitting, all lines are restricted to be emission lines (i.e., positive flux).

For Hβ we use the optical iron template from Boroson & Green (1992), and we fit for objects with z ⩽ 0.89. The continuum+iron fitting windows are [4435,4700] Å and [5100,5535] Å. For the Hβ line fitting, we follow a similar procedure as Hα to fit for Hβ and [O iii] λλ4959,5007, where the line fitting wavelength range is [4700,5100] Å. Since the [O iii] λλ4959,5007 lines frequently show asymmetric blue wings (e.g., Heckman et al. 1981; Greene & Ho 2005a; Komossa et al. 2008) and sometimes even more dramatic double-peaked profiles (e.g., Liu et al. 2010b; Smith et al. 2009; Wang et al. 2009a), we model each of the narrow [O iii] λλ4959,5007 lines with two Gaussians, one for the core and the other for the blue wing. The flux ratio of the [O iii] doublet is not fixed during the fit, but we found that the fitting results show good agreement with the theoretical ratio of about 3. The velocity offset and FWHM of the narrow Hβ line are tied to those of the core [O iii] λλ4959,5007 components,¹⁰ and we impose an upper limit of 1200 km s⁻¹ on the narrow line FWHM. As in the Hα case, the broad Hβ component is modeled in two ways: either by a single Gaussian, or by multiple Gaussians with up to three Gaussians, each with an FWHM >1200 km s⁻¹.

The single Gaussian fit to the broad component is essentially the same to the procedure in Shen et al. (2008a), and is somewhat similar to the procedure in McLure & Dunlop (2004).¹¹ However, in many objects the broad Hα/Hβ component cannot be fit perfectly with a single Gaussian; and FWHMs from the single Gaussian fits are systematically larger by ∼0.1 dex than those from the multiple Gaussian fits (e.g., Shen et al. 2008a). The additional multiple Gaussian fits for the broad Hα/Hβ component provide a better fit to the overall broad line profile, and the FWHM measured from the model flux can be used in customized virial calibrations. It is unclear, however, which FWHM is a better surrogate for the true virial velocity, that is, the one that yields the smallest scatter in the calibration against RM black hole masses.

For Mg ii we use the UV iron template from Vestergaard & Wilkes (2001), and we fit for objects with 0.35 ⩽ z ⩽ 2.25. The continuum+iron fitting windows are [2200,2700] Å and [2900,3090] Å. We then subtract the pseudo-continuum from the spectrum, and fit for the Mg ii line over the [2700,2900] Å wavelength range, with a single Gaussian (with FWHM < 1200 km s⁻¹) for the narrow Mg ii component, and for the broad Mg ii component with (1) a single Gaussian and (2) multiple Gaussians with up to three Gaussians. Again, the multiple-Gaussian fits often provide a better fit to the overall broad Mg ii profile; but we have retained the FWHMs from a single Gaussian fit in order to use the Mg ii virial mass calibrations in McLure & Jarvis (2002) and McLure & Dunlop (2004). Some Mg ii virial estimator calibrations (e.g., McLure & Jarvis 2002; McLure & Dunlop 2004; Wang et al. 2009b) do subtract a narrow Mg ii component while others (e.g., Vestergaard & Osmer 2009) do not. To utilize the Mg ii calibration in Vestergaard & Osmer (2009), we also measure the FWHMs from the broad+narrow Mg ii fits (with multiple Gaussians for the broad component), where any Gaussian component having flux less than 5% of the total line flux is rejected when computing the FWHM—this step is to eliminate artificial noise spikes which can bias the FWHM measurements. During our fitting, we mask out 3σ outliers below the 20 pixel boxcar-smoothed spectrum to reduce the effects of narrow absorption troughs.

Unlike the cases of Hα and Hβ, it is somewhat ambiguous whether it is necessary to subtract a narrow line component for Mg ii and if so, how to do it. On one hand, for some objects, such as SDSSJ002209.95+001629.3 and SDSSJ130101.94+130227.1 (e.g., Figure 2), the spectral quality is sufficient to see the bifurcation of the Mg ii doublet around the peak. The locations of the two peaks indicate that they are associated with the Mg ii λλ2796,2803 doublet, and the fact that they are resolved means that the FWHM of each component is ≲ 750 km s⁻¹, hence they are most likely associated with the narrow-line region. On the other hand, such cases are rare and most SDSS spectra do not have adequate S/N to unambiguously locate the narrow Mg ii doublet. Associated narrow Mg ii absorption troughs can further complicate the situation by mimicking two peaks. Hence although our approach of fitting a single Gaussian to the narrow Mg ii component is not perfect, it nevertheless accounts for some narrow Mg ii contamination. Figure 3 compares our broad Mg ii FWHM measurements with those from Wang et al. (2009b) for the objects in both studies. Although we have used a different approach, our results are consistent with theirs, with a mean offset ∼0.05 dex. This systematic offset between our results and theirs is caused by the fact that they are treating the broad Mg ii line as a doublet as well, while we (and most studies) are treating the broad Mg ii line as a single component.

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For C iv we fit for objects with 1.5 ⩽ z ⩽ 4.95. Iron emission is generally weak for C iv, and most of our objects do not have the spectral quality sufficient for a reliable iron template subtraction (e.g., Shen et al. 2008a). The power-law continuum fitting windows are [1445,1465] Å and [1700,1705] Å. We found fitting C iv with iron subtraction does not change the fitted C iv FWHM significantly, but does systematically reduce the C iv EW by ∼0.05 dex because the iron flux under the wings of the C iv line is accounted for. At the same time, fitting iron emission increases the uncertainty in the fitted continuum slope and normalization, due to imperfect subtraction of the iron flux. Therefore we report our C iv measurements without the iron template fits, and emphasize that the C iv EWs may be overestimated by ∼0.05 dex on average.

The continuum subtracted line emission within [1500,1600] Å was fitted with three Gaussians (e.g., Shen et al. 2008a), and we measure the line FWHM from the model fit. To reduce the effects of noise spikes, we reject any Gaussian component having flux less than 5% of the total model flux when computing the FWHM. However, unlike some attempts in the literature (e.g., Bachev et al. 2004; Baskin & Laor 2005; Sulentic et al. 2007; Zamfir et al. 2010), we do not subtract a narrow C iv component because: (1) it is still debatable if a strong narrow C iv component exists for most quasars, or if it is feasible to do such a subtraction; (2) existing C iv virial estimators are calibrated using the FWHMs from the entire C iv profile (Vestergaard & Peterson 2006).

Many C iv lines are affected by narrow or broad absorption features. To reduce the effects of such absorption on the C iv fits, we mask out 3σ outliers below the 20 pixel boxcar-smoothed spectrum during our fits (to remedy for narrow absorption features); we also perform a second fit excluding pixels below 3σ of the first model fit, and replace the first one if statistically justified (to account for broad absorption features). We found these recipes can alleviate the impact of narrow or moderate absorption features, but the improvement is marginal for objects severely affected by broad absorption.

Our spectral fits were performed in an automatic fashion. Upon visual inspection of the fitting results we are confident that the vast majority (≳ 95%) of the fits to high S/N spectra were successful, and comparisons with independent fits by others also show good agreement. However, the reliability of our spectral fits drops rapidly for low-quality spectra. Figure 4 shows the distributions of the median S/N per pixel around the line-fitting region for objects that have line measurements, for Hα, Hβ, Mg ii, and C iv, respectively. Although the bulk of objects have median S/N >5 for the line-fitting regions, there are many objects that have lower median S/N, especially for C iv at high redshift. The effects of S/N on the measurements depend on both the properties of the lines (i.e., line profile, line strength, degree of absorption features, etc.), and the line-fitting technique itself (i.e., what functional form was used, how to deal with absorption troughs, etc.).

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To investigate the impact of S/N on our fitting parameters we ran a series of Monte Carlo simulations. We select representative real spectra with high S/N, then degrade the spectra by adding Gaussian noise and measure the line properties using the same line-fitting routine. For each line (Hβ, Mg ii, or C iv), we study several objects with various line shapes and EWs. We simulate 500 trials for each S/N level and take the median and the 68% range as the measurement result and its error.

Figures 5–8 show several examples of our investigations for Hα, Hβ, Mg ii and C iv, respectively. As expected, decreasing the S/N increases measurement scatter. In all cases the fitted continuum is unbiased as S/N decreases. The FWHMs and EWs are biased by less than ±20% for high-EW objects as S/N is reduced to as low as ∼3. For low-EW objects, the FWHMs and EWs are biased low/high by >20% for S/N ≲ 5. Since the median EWs for the three lines are >30 Å (see Section 4.1), we expect that the measurements for most objects are unbiased to within ±20% down to S/N ∼3. But for many purposes, it would be more conservative to impose a cut at S/N >5 for reliable measurements.

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To estimate the uncertainties in the measured quantities in our fits, we generate 50 mock spectra by adding Gaussian noise to the original spectrum using the reported flux density errors, and fit for those mock spectra with the same fitting routines. We estimate the measurement uncertainties from the 68% range (centered on the median) of the distributions of fitting results of the 50 trials. This approach gives more reasonable error estimation than using the statistical errors resulting from the χ² fits, in the sense that it not only takes into account the spectral S/N but also the ambiguity of subtracting a narrow line component in many cases (for Hα, Hβ and Mg ii). We estimate the spectral measurement uncertainties for all the 105,783 quasars in our sample in this way.

Given the automatic nature and specifics of our fitting recipe, there will undoubtedly be bad fits for noisy spectra or peculiar objects. We recommend using the reported measurement errors to remove suspicious measurements, e.g., Err >0 AND Err< some threshold. Our fitting recipe was optimized for the vast majority of quasars in our sample, and it may fail badly for rare objects with peculiar continuum and emission line properties. These objects include severe BALQSOs, disk emitters, and objects such as J094215.12+090015.8, which has extremely broad lines that exceed our line fitting range. One should pay attention to our fitting ranges and these special objects upon usage of the cataloged quantities. For various reasons, one may want to check the quality assessment (QA) plot for individual fits to make sure that the fitting results are robust. Such QA plots are provided along with this catalog.

Finally, we note that we imposed an FWHM limit of 1200 km s⁻¹ for the narrow line components when fitting Hα, Hβ and Mg ii. This choice is motivated by the results in Hao et al. (2005), but is still somewhat arbitrary; narrow lines broader than this threshold are not unusual. On the other hand, if a Gaussian component with FWHM <1200 km s⁻¹ can be fit to Hα, Hβ and Mg ii, it will be considered as a narrow line component and subtracted off. For these reasons, we urge caution regarding objects for which the measured narrow line FWHM reaches the 1200 km s⁻¹ limit (∼ a few percent). Upon visual inspection of the QA plots for these objects, even though the FWHM parameter reaches the limit, most of the fits still yield reasonable measurements of total line flux, line centroid and narrow line subtraction.

For the vast majority of objects in our catalog with z ≳ 0.5, host galaxy contamination is negligible. However, for the z ≲ 0.5 low-luminosity quasars in our sample, the continuum luminosity at rest-frame 5100 Å may be contaminated by light from the host galaxies. Unfortunately the spectral quality of the majority of individual objects does not allow a reliable galaxy continuum subtraction. Here we estimate the effects of host contamination with stacked spectra.

We take all quasars with measurable rest-frame 5100 Å continuum luminosity, L₅₁₀₀, and bin them on a grid of Δlog L₅₁₀₀ = 0.1 for log (L₅₁₀₀/erg s⁻¹) = 44.1–45.5. Following Vanden Berk et al. (2001), we generate geometric mean composite spectra for objects in each luminosity bin. The composite spectra are shown in Figure 9, where the flux gradually flattens at long wavelengths due to increasing host contamination at fainter quasar luminosities. This trend is accompanied by the increasing prominence of stellar absorption features and narrow line emission toward fainter luminosities. The inset shows the fractional host contamination at 5100 Å assuming that the highest luminosity bin (log L₅₁₀₀ = 45.5) is not affected by the host and that the intrinsic AGN power-law continuum slope does not change over the luminosity range considered. The host contamination is substantial at log L₅₁₀₀ < 44.5, and becomes negligible toward higher luminosities. The median value of log L₅₁₀₀ for quasars in this low-redshift sample is ∼44.6, and therefore the host contamination on average is ∼15%, which leads to a ∼0.06 dex overestimation of the 5100 Å continuum luminosity and thus ∼0.03 dex overestimation of the Hβ-based virial masses for the median object. While we do not correct the measured 5100 Å continuum luminosity (and other quantities depending on it) in the catalog, we provide an empirical fitting formula of the average host contamination based on the stacked spectra (dashed line in the inset of Figure 9):

$$\begin{equation} \frac{L_{\rm 5100,host}}{L_{\rm 5100,QSO}}=0.8052-1.5502x + 0.9121x^2-0.1577x^3 \end{equation} \tag{ 1 }$$

for x + 44 ≡ log (L_{5100, total}/erg s⁻¹) < 45.053; no correction is needed for luminosities above this value.

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We suspect that host contamination is largely responsible for the apparent anti-correlation between L₅₁₀₀ and spectral slope α_λ, and the "negative" Baldwin effect (e.g., Baldwin 1977) between the broad Hβ EW and L₅₁₀₀ below L₅₁₀₀ ∼ 10⁴⁵ erg s⁻¹ (see Section 4.1).

It has become common practice to estimate quasar/AGN BH masses based on single-epoch spectra (hereafter virial mass in short). This approach assumes that the broad-line region (BLR) is virialized, the continuum luminosity¹² is used as a proxy for the BLR radius, and the broad line width (FWHM or line dispersion) is used as a proxy for the virial velocity. The virial mass estimate can be expressed as

$$\begin{equation} \log \left({M_{\rm BH,vir} \over M_\odot }\right) =a+b\log \left({\lambda L_{\lambda } \over 10^{44}\,{\rm erg\,s^{-1}}}\right)+2\log \left({\rm FWHM\over km\,s^{-1}}\right)\, \end{equation} \tag{ 2 }$$

where the coefficients a and b are empirically calibrated against local AGNs with RM masses or internally among different lines. Hβ, Mg ii, C iv, and their corresponding continuum luminosities are all frequently adopted in such virial calibrations. Although it is straightforward to calibrate and use these virial estimators, one must bear in mind the large uncertainties (≳ 0.4 dex) associated with these estimates and the systematics involved in the calibration and usage, which will potentially lead to significant biases of these BH mass estimates (e.g., Collin et al. 2006; Shen et al. 2008a; Marconi et al. 2008; Denney et al. 2009; Kelly et al. 2009; Shen & Kelly 2010).

The virial BH mass calibrations used in this paper are from McLure & Dunlop (2004, Hβ and Mg ii), Vestergaard & Peterson (2006, Hβ and C iv), and Vestergaard & Osmer (2009, Mg ii). These calibrations have parameters:

$$\begin{eqnarray} (a,b)&=&(0.672,0.61), \qquad {\rm MD04;\ }{\hbox{H{$\beta $}}\ } \end{eqnarray} \tag{ 3 }$$

$$\begin{eqnarray} (a,b)&=&(0.505,0.62), \qquad {\rm MD04;}\,{{{\rm Mg}\,\mathsc{ii}}} \end{eqnarray} \tag{ 4 }$$

$$\begin{eqnarray} (a,b)&=&(0.910,0.50), \qquad {\rm VP06;\ }{\hbox{H{$\beta $}}\ } \end{eqnarray} \tag{ 5 }$$

$$\begin{eqnarray} (a,b)&=&(0.660,0.53), \qquad {\rm VP06;}\,{{\rm {C}\,\mathsc{iv}}} \end{eqnarray} \tag{ 6 }$$

$$\begin{eqnarray} (a,b)&=&(0.860,0.50), \qquad {\rm VO09;}\,{{\rm {Mg}\,\mathsc {ii}}.} \end{eqnarray} \tag{ 7 }$$

In using each of these relations we choose the proper FWHM definition adopted in these calibrations. In order to utilize our new Mg ii FWHM measurements (e.g., multiple-Gaussian fits with narrow line subtraction, see Section 3.3), we adopt the b = 0.62 slope in the BLR radius–luminosity relation in McLure & Dunlop (2004), and recalibrate the coefficient a such that the Mg ii-based estimates are consistent with the Hβ-based (VP06) estimates on average. We choose this particular slope b because it was re-calibrated in McLure & Dunlop (2004) using a subsample of reverberation mapping AGNs that occupy the high-luminosity regime in the local RM AGN sample, arguably better than using the whole RM sample. We choose the VP06 Hβ formula to calibrate our Mg ii formula because the FWHMs of broad Hβ and Mg ii were measured in a similar fashion (as opposed to the single-Gaussian or Lorentzian profile adopted in McLure & Dunlop 2004). This new Mg ii calibration is

$$\begin{equation} (a,b)=(0.740,0.62), \qquad {\rm S10;}\,{{\rm{Mg}\,\mathsc{ii}}}. \end{equation} \tag{ 8 }$$

In some cases a particular line may be unavailable in the spectrum, or the continuum is too faint to measure. Below we provide several alternative empirical recipes to estimate a virial BH mass. These recipes are calibrated using correlations among continuum and emission line properties, and are only valid in the average sense. We recommend to use them only when the above estimators are unavailable.

Following Greene & Ho (2005b), a virial BH mass can be estimated based on the FWHM and luminosity of the broad Hα line. We found a correlation between the FWHMs (using multiple-Gaussian fits) of the broad Hα and Hβ lines similar to that found in previous work (e.g., Greene & Ho 2005b; Shen et al. 2008b), with the broad Hβ FWHM systematically larger than the broad Hα FWHM:

$$\begin{eqnarray} \log \left(\frac{{\rm FWHM_{H\beta }}}{{\rm km\,s^{-1}}}\right)&=&(-0.11\pm 0.03)+(1.05\pm 0.01)\nonumber\\ &&\times\log \left(\frac{{\rm FWHM_{H\alpha }}}{{\rm km\,s^{-1}}}\right), \end{eqnarray} \tag{ 9 }$$

where the slope and intercept are determined using the BCES¹³ bisector linear regression estimator (e.g., Akritas & Bershady 1996) for a sample of ∼2400 quasars with both Hα and Hβ FWHM measurements and FWHM errors less than 500 km s⁻¹. Our continuum luminosities at 5100 Å have a narrow dynamical range and suffer from host contamination at the low-luminosity end, hence instead of fitting a new relation using our measurements, we adopt the relation between 5100 Å continuum luminosity and Hα line luminosity in Greene & Ho (2005b, their Equation (1)). The virial mass estimator based on Hα therefore reads

$$\begin{eqnarray} \log \left({M_{\rm BH,vir} \over M_\odot }\right)_{\rm H\alpha }&=&0.379 + 0.43\log \left(\frac{L_{\rm H\alpha }}{\rm 10^{42}\, erg\,s^{-1}}\right)\nonumber\\ &&+ 2.1\log \left(\frac{{\rm FWHM_{H\alpha }}}{{\rm km,s^{-1}}}\right), \end{eqnarray} \tag{ 10 }$$

where L_Hα is the total Hα line luminosity. For quasars in our sample, Equation (10) yields virial BH masses consistent with the VP06 Hβ results, with a mean offset ∼0.08 dex and a dispersion ∼0.18 dex.

Similarly, we can substitute the continuum luminosity in the above recipes for Hβ, Mg ii and C iv with the luminosity of the particular line used, given that for broad line quasars the line luminosity correlates with the continuum luminosity to some extent. We determine these correlations using subsamples of quasars for which both luminosities were measured with an uncertainty <0.03 dex. For the same reason as Hα, we do not fit a new relation between the Hβ line luminosity and continuum luminosity at 5100 Å, and we refer to Equation (2) of Greene & Ho (2005b) for such a relation. The following relations are determined again using the BCES linear regression estimator (for both the bisector fit and the Y|X fit, where the latter refers to "predict Y as a function of X"), where the line luminosity refers to the total line luminosity¹⁴:

$$\begin{eqnarray} \log \left(\frac{L_{\rm Mg\,\mathsc{ii}}}{\rm erg\,s^{-1}}\right)&=&(2.22\pm 0.09)+ (0.909\pm 0.002)\nonumber\\ &&{\times}\,\log\left(\frac{L_{3000}}{\rm erg\,s^{-1}}\right),\quad {\rm bisector}, \end{eqnarray} \tag{ 11 }$$

$$\begin{eqnarray} \log \left(\frac{L_{3000}}{\rm erg\,s^{-1}}\right)&=&(1.22\pm 0.11)+(1.016\pm 0.003)\nonumber\\ &&{\times}\,\log \left(\frac{L_{\rm Mg\,\mathsc{ii}}}{\rm erg\,s^{-1}}\right),\quad {\rm (Y|X)}, \end{eqnarray} \tag{ 12 }$$

where the scatter of this correlation is ∼0.15 (0.16) dex for ∼44,000 quasars, and

$$\begin{eqnarray} \log \left(\frac{L_{\rm C\,\mathsc{iv}}}{\rm erg\,s^{-1}}\right)&=&(4.42\pm 0.27)+(0.872\pm 0.006)\nonumber\\ &&{\times}\,\log \left(\frac{L_{1350}}{\rm erg\,s^{-1}}\right),\quad {\rm bisector}, \end{eqnarray} \tag{ 13 }$$

$$\begin{eqnarray} \log \left(\frac{L_{1350}}{\rm erg\,s^{-1}}\right)&=&(7.66\pm 0.41)+(0.863\pm 0.009)\nonumber\\ &&{\times}\,\log \left(\frac{L_{\rm C\,\mathsc{iv}}}{\rm erg\,s^{-1}}\right),\quad {\rm (Y|X)}, \end{eqnarray} \tag{ 14 }$$

where the scatter of this correlation is ∼0.18 (0.2) dex for ∼10,000 quasars. Using our measurements, one can also estimate these correlations with other linear regression algorithms. If we substitute log L₃₀₀₀ and log L₁₃₅₀ using Equations (12) and (14) in the Mg ii and C iv estimators, we obtain virial BH masses consistent with the original recipes with no mean offset (<0.02 dex) and negligible scatter (∼0.1 dex).

There are systematic differences among different versions of virial calibrations. For instance, the calibrations for Hβ and Mg ii in McLure & Dunlop (2004) used the old RM masses and virial coefficient, while those in Vestergaard & Peterson (2006) and Vestergaard & Osmer (2009) used the updated RM masses and virial coefficient (Onken et al. 2004). Significant uncertainties of the virial coefficient still remain (e.g., Woo et al. 2010; Graham et al. 2011). Moreover, different versions of virial calibration for the same line have different dependence on luminosity, and they usually measure the line FWHM differently (even though occasionally different approaches to measure the FWHM yield the same value during the multi-parameter fits), or prefer an alternative proxy (e.g., line dispersion) for the virial velocity (e.g., Collin et al. 2006; Rafiee & Hall 2011). Currently there is no consensus on which version of calibration is better. It is important to explore various systematics with RM AGN samples and statistical quasar samples to determine which is the best approach to estimate quasar BH masses with the virial technique, and this is work in progress (e.g., Onken & Kollmeier 2008; Denney et al. 2009; Wang et al. 2009b; Rafiee & Hall 2011). In the mean time, there is strong need to increase the sample size and representativity of AGNs with RM measurements, which anchor these single-epoch virial estimators.

Here we simply settle on a fiducial virial mass estimate: we use Hβ (VP06) estimates for z < 0.7, Mg ii (S10) estimates for 0.7 ⩽ z < 1.9 and C iv (VP06) estimates for z ⩾ 1.9. Figure 10 shows the comparison between these virial estimates between two lines for the subset of quasars for which both line estimates are available and the median line S/N >6. There is negligible mean offset (<0.01 dex) between these virial estimates (half by design), which motivated our choice of these three calibrations. However, as noted in Shen et al. (2008a), there is a strong trend of decreasing the ratio of $\log (M_{\rm BH}^{\rm Mg\,\mathsc{ii}}\!/M_{\rm BH}^{\rm C\,\mathsc{iv}})$ with increasing C iv–Mg ii blueshifts, indicating a possible non-virialized component in C iv. Richards et al. (2011) further developed a unified picture in which the C iv line has both a non-virial wind component and a traditional virial component, and it is plausible that the BH mass scaling relation based on C iv is only relevant for objects dominated by the virial component.

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We have tabulated all the measured quantities from the spectral fitting in the online catalog of this paper, along with other properties.¹⁵ The current compilation extends our earlier SDSS Data Release 5 (DR5) compilation (Shen et al. 2008a) by including the post-DR5 quasars, as well as measurements based on new multiple-Gaussian fits to the lines (as discussed above). The format of the catalog is described in Table 1. Objects are in the same order as the DR7 quasar catalog in Schneider et al. (2010). Below we describe the specifics of the cataloged quantities. The SDSS terminology can be found on the SDSS Web site.¹⁶ Flux measurements were corrected neither for intrinsic extinction/reddening, nor for host contamination. We only report FWHM and velocity shift values for detectable line components (i.e., the fitted line flux is non-zero), except for cases where the line FWHM and velocity offset can be inferred from other lines (such as the narrow Hβ line, whose FWHM and velocity offset are tied to those of the [O iii] doublet).

Table 1. FITS Catalog Format

Column	Format	Description
1...	STRING	SDSS DR7 designation hhmmss.ss+ddmmss.s (J2000.0)
2...	DOUBLE	Right ascension in decimal degrees (J2000.0)
3...	DOUBLE	Declination in decimal degrees (J2000.0)
4...	DOUBLE	Redshift
5...	LONG	Spectroscopic plate number
6...	LONG	Spectroscopic fiber number
7...	LONG	MJD of spectroscopic observation
8...	LONG	Target selection flag (TARGET version)
9...	LONG	Number of spectroscopic observations
10...	LONG	Uniform selection flag
11...	DOUBLE	Mi(z = 2) [h = 0.7, Ω0 = 0.3, $\Omega _\Lambda =0.7$, K-corrected to z = 2, following Richards et al. (2006b)]
12...	DOUBLE	Bolometric luminosity [log (Lbol/erg s−1)]
13...	DOUBLE	Uncertainty in log Lbol
14...	LONG	BAL flag (0 = nonBALQSO or no wavelength coverage; 1 = C iv BALQSO; 2 = Mg ii BALQSO; 3 = both 1 and 2)
15...	LONG	FIRST radio flag (−1 = not in FIRST footprint; 0 = FIRST undetected; 1 = core-dominant; 2 = lobe-dominant)
16...	DOUBLE	Observed radio flux density at rest-frame 6 cm fν, 6 cm [mJy]
17...	DOUBLE	Observed optical flux density at rest-frame 2500 Å [log (fν, 2500/erg s−1 cm−2 Hz−1)]
18...	DOUBLE	Radio loudness R ≡ fν, 6 cm/fν, 2500
19...	DOUBLE	Monochromatic luminosity at 5100 Å [log (L5100/erg s−1)]
20...	DOUBLE	Uncertainty in log L5100
21...	DOUBLE	Monochromatic luminosity at 3000 Å [log (L3000/erg s−1)]
22...	DOUBLE	Uncertainty in log L3000
23...	DOUBLE	Monochromatic luminosity at 1350 Å [log (L1350/erg s−1)]
24...	DOUBLE	Uncertainty in log L1350
25...	DOUBLE	Line luminosity of broad Hα [log (L/erg s−1)]
26...	DOUBLE	Uncertainty in log LHα, broad
27...	DOUBLE	FWHM of broad Hα (km s−1)
28...	DOUBLE	Uncertainty in the broad Hα FWHM
29...	DOUBLE	Rest-frame equivalent width of broad Hα (Å)
30...	DOUBLE	Uncertainty in EWHα, broad
31...	DOUBLE	Line luminosity of narrow Hα [log (L/erg s−1)]
32...	DOUBLE	Uncertainty in log LHα, narrow
33...	DOUBLE	FWHM of narrow Hα (km s−1)
34...	DOUBLE	Uncertainty in the narrow Hα FWHM
35...	DOUBLE	Rest-frame equivalent width of narrow Hα (Å)
36...	DOUBLE	Uncertainty in EWHα, narrow
37...	DOUBLE	Line luminosity of [N ii] λ6584 [log (L/erg s−1)]
38...	DOUBLE	Uncertainty in $\log L_{{\rm [\rm N\,\mathsc{ii}]6584}}$
39...	DOUBLE	Rest-frame equivalent width of [N ii] λ6584 (Å)
40...	DOUBLE	Uncertainty in ${\rm EW_{[\rm N\,\mathsc{ii}]6584}}$
41...	DOUBLE	Line luminosity of [S ii] λ6717 [log (L/erg s−1)]
42...	DOUBLE	Uncertainty in $\log L_{\rm [S\,\mathsc{ii}]6717}$
43...	DOUBLE	Rest-frame equivalent width of [S ii] λ6717 (Å)
44...	DOUBLE	Uncertainty in EW[SII]6717
45...	DOUBLE	Line luminosity of [S ii] λ6731 [log (L/erg s−1)]
46...	DOUBLE	Uncertainty in $\log L_{\rm [S\,\mathsc{ii}]6731}$
47...	DOUBLE	Rest-frame equivalent width of [S ii] λ6731 (Å)
48...	DOUBLE	Uncertainty in EW[SII]6731
49...	DOUBLE	Rest-frame equivalent width of Fe within 6000–6500 Å (Å)
50...	DOUBLE	Uncertainty in EWFe, Hα
51...	DOUBLE	Power-law slope for the continuum fit for Hα
52...	DOUBLE	Uncertainty in αHα
53...	LONG	Number of good pixels for the rest-frame 6400–6765 Å region
54...	DOUBLE	Median S/N per pixel for the rest-frame 6400–6765 Å region
55...	DOUBLE	Reduced χ2 for the Hα line fit; −1 if not fitted
56...	DOUBLE	Line luminosity of broad Hβ [log (L/erg s−1)]
57...	DOUBLE	Uncertainty in log LHβ, broad
58...	DOUBLE	FWHM of broad Hβ (km s−1)
59...	DOUBLE	Uncertainty in the broad Hβ FWHM
60...	DOUBLE	Rest-frame equivalent width of broad Hβ (Å)
61...	DOUBLE	Uncertainty in EWHβ, broad
62...	DOUBLE	Line luminosity of narrow Hβ [log (L/erg s−1)]
63...	DOUBLE	Uncertainty in log LHβ, narrow
64...	DOUBLE	FWHM of narrow Hβ (km s−1)
65...	DOUBLE	Uncertainty in the narrow Hβ FWHM
66...	DOUBLE	Rest-frame equivalent width of narrow Hβ (Å)
67...	DOUBLE	Uncertainty in EWHβ, narrow
68...	DOUBLE	FWHM of broad Hβ using a single Gaussian fit (km s−1)
69...	DOUBLE	Line luminosity of [O iii] λ4959 [log (L/erg s−1)]
70...	DOUBLE	Uncertainty in $\log L_{\rm [\rm O\,\mathsc{iii}]4959}$
71...	DOUBLE	Rest-frame equivalent width of [O iii] λ4959 (Å)
72...	DOUBLE	Uncertainty in ${\rm EW_{[\rm O\,\mathsc{iii}]4959}}$
73...	DOUBLE	Line luminosity of [O iii] λ5007 [log (L/erg s−1)]
74...	DOUBLE	Uncertainty in $\log L_{\rm [\rm O\,\mathsc{iii}]5007}$
75...	DOUBLE	Rest-frame equivalent width of [O iii] λ5007 (Å)
76...	DOUBLE	Uncertainty in ${\rm EW_{[\rm O\,\mathsc{iii}]5007}}$
77...	DOUBLE	Rest-frame equivalent width of Fe within 4435–4685 Å (Å)
78...	DOUBLE	Uncertainty in EWFe, Hβ
79...	DOUBLE	Power-law slope for the continuum fit for Hβ
80...	DOUBLE	Uncertainty in αHβ
81...	LONG	Number of good pixels for the rest-frame 4750–4950 Å region
82...	DOUBLE	Median S/N per pixel for the rest-frame 4750–4950 Å region
83...	DOUBLE	Reduced χ2 for the Hβ line fit; −1 if not fitted
84...	DOUBLE	Line luminosity of the whole Mg ii [log (L/erg s−1)]
85...	DOUBLE	Uncertainty in $\log L_{\rm Mg\,\mathsc{ii},\rm whole}$
86...	DOUBLE	FWHM of the whole Mg ii (km s−1)
87...	DOUBLE	Uncertainty in the whole Mg ii FWHM
88...	DOUBLE	Rest-frame equivalent width of the whole Mg ii (Å)
89...	DOUBLE	Uncertainty in ${\rm EW_{\rm Mg\,\mathsc{ii},whole}}$
90...	DOUBLE	Line luminosity of broad Mg ii [log (L/erg s−1)]
91...	DOUBLE	Uncertainty in $\log L_{\rm Mg\,\mathsc{ii},\rm broad}$
92...	DOUBLE	FWHM of broad Mg ii (km s−1)
93...	DOUBLE	Uncertainty in the broad Mg ii FWHM
94...	DOUBLE	Rest-frame equivalent width of broad Mg ii (Å)
95...	DOUBLE	Uncertainty in ${\rm EW_{\rm Mg\,\mathsc{ii},broad}}$
96...	DOUBLE	FWHM of broad Mg ii using a single Gaussian fit (km s−1)
97...	DOUBLE	Rest-frame equivalent width of Fe within 2200–3090 Å (Å)
98...	DOUBLE	Uncertainty in ${\rm EW_{Fe,\rm Mg\,\mathsc{ii}}}$
99...	DOUBLE	Power-law slope for the continuum fit for Mg ii
100...	DOUBLE	Uncertainty in $\alpha _{\rm Mg\,\mathsc{ii}}$
101...	LONG	Number of good pixels for the rest-frame 2700–2900 Å region
102...	DOUBLE	Median S/N per pixel for the rest-frame 2700–2900 Å region
103...	DOUBLE	Reduced χ2 for the Mg ii line fit; −1 if not fitted
104...	DOUBLE	Line luminosity of the whole C iv [log (L/erg s−1)]
105...	DOUBLE	Uncertainty in $\log L_{\rm C\,\mathsc{iv}}$
106...	DOUBLE	FWHM of the whole C iv (km s−1)
107...	DOUBLE	Uncertainty in the C iv FWHM
108...	DOUBLE	Rest-frame equivalent width of the whole C iv (Å)
109...	DOUBLE	Uncertainty in ${\rm EW_{\rm C\,\mathsc{iv}}}$
110...	DOUBLE	Power-law slope for the continuum fit for C iv
111...	DOUBLE	Uncertainty in $\alpha _{\rm C\,\mathsc{iv}}$
112...	LONG	Number of good pixels for the rest-frame 1500–1600 Å region
113...	DOUBLE	Median S/N per pixel for the rest-frame 1500–1600 Å region
114...	DOUBLE	Reduced χ2 for the C iv fit; −1 if not fitted
115...	DOUBLE	Velocity shift of broad Hα (km s−1); 3d5 if not measurable
116...	DOUBLE	Uncertainty in VHα, broad
117...	DOUBLE	Velocity shift of narrow Hα (km s−1); 3d5 if not measurable
118...	DOUBLE	Uncertainty in VHα, narrow
119...	DOUBLE	Velocity shift of broad Hβ (km s−1); 3d5 if not measurable
120...	DOUBLE	Uncertainty in VHβ, broad
121...	DOUBLE	Velocity shift of narrow Hβ (km s−1); 3d5 if not measurable
122...	DOUBLE	Uncertainty in VHβ, narrow
123...	DOUBLE	Velocity shift of broad Mg ii (km s−1); 3d5 if not measurable
124...	DOUBLE	Uncertainty in $V_{\rm Mg\,\mathsc{ii},\rm broad}$
125...	DOUBLE	Velocity shift of C iv (km s−1); 3d5 if not measurable
126...	DOUBLE	Uncertainty in $V_{\rm C\,\mathsc{iv}}$
127...	DOUBLE	Virial BH mass based on Hβ [MD04, log (MBH, vir/M☉)]
128...	DOUBLE	Measurement uncertainty in log MBH, vir (Hβ, MD04)
129...	DOUBLE	Virial BH mass based on Hβ [VP06, log (MBH, vir/M☉)]
130...	DOUBLE	Measurement uncertainty in log MBH, vir (Hβ, VP06)
131...	DOUBLE	Virial BH mass based on Mg ii [MD04, log (MBH, vir/M☉)]
132...	DOUBLE	Measurement uncertainty in log MBH, vir (Mg ii, MD04)
133...	DOUBLE	Virial BH mass based on Mg ii [VO09, log (MBH, vir/M☉)]
134...	DOUBLE	Measurement uncertainty in log MBH, vir (Mg ii, VO09)
135...	DOUBLE	Virial BH mass based on Mg ii [S10, log (MBH, vir/M☉)]
136...	DOUBLE	Measurement uncertainty in log MBH, vir (Mg ii, S10)
137...	DOUBLE	Virial BH mass based on C iv [VP06, log (MBH, vir/M☉)]
138...	DOUBLE	Measurement uncertainty in log MBH, vir (C iv, VP06)
139...	DOUBLE	The adopted fiducial virial BH mass [log (MBH, vir/M☉)]
140...	DOUBLE	Uncertainty in the fiducial virial BH mass (measurement uncertainty only)
141...	DOUBLE	Eddington ratio based on the fiducial virial BH mass [log (Lbol/LEdd)]
142...	LONG	Special interest flag

Notes. Objects are in the same order as in the DR7 quasar catalog Schneider et al. 2010. K-corrections are the same as in Richards et al. 2006a. Bolometric luminosities computed using bolometric corrections in Richards et al. 2006b using one of the 5100 Å, 3000 Å,  or 1350 Å monochromatic luminosities depending on redshift. Uncertainties are measurement errors only. Unless otherwise stated, null value (indicating unmeasurable) is zero for a quantity and −1 for its associated error.

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1. SDSS DR7 designation: hhmmss.ss+ddmmss.s (J2000.0; truncated coordinates)

2–4. R.A. and decl. (in decimal degrees, J2000.0), redshift. Here the redshifts are taken from the DR7 quasar catalog (Schneider et al. 2010). Hewett & Wild (2010) provided improved redshifts for SDSS quasars. These improved redshifts are particularly useful for generating co-added spectra, but the cataloged DR7 redshifts are fine for most of the purposes considered here.

5–7. Spectroscopic plate, fiber, and Modified Julian date (MJD): the combination of plate–fiber–MJD locates a particular spectroscopic observation in SDSS. The same object can be observed more than once with different plate–fiber–MJD combinations either on a repeated plate (same plate and fiber numbers but different MJD number), or on different plates. The DR7 quasar catalog typically lists the spectroscopic observation with the highest S/N.

8. TARGET_FLAG_TARGET: the target selection flag (TARGET version).

9. N_spec: number of spectroscopic observations. While we only used the default spectrum in our spectral fitting, this flag indicates if there are multiple spectroscopic observations for each object.

10. Uniform flag. 0 = not in the uniform sample¹⁷; 1 = uniformly selected using the target selection algorithm in Richards et al. (2002b), and flux limited to i = 19.1 at z < 2.9 or i = 20.2 at z > 2.9; 2 = selected by the QSO_HiZ branch only in the uniform target selection (Richards et al. 2002b) and with measured spectroscopic redshift z < 2.9 and i > 19.1. Objects with uniform flag = 2 are selected by the uniform quasar target algorithm, but should not be included in statistical studies; the fraction of such uniform objects is low (<1%; red dots in Figure 1).

11. M_i(z = 2): absolute i-band magnitude in the current cosmology, K-corrected to z = 2 following¹⁸ Richards et al. (2006b).

12–13. Bolometric luminosity L_bol and its error: computed from L₅₁₀₀ (z < 0.7), L₃₀₀₀ (0.7 ⩽ z < 1.9), L₁₃₅₀ (z ⩾ 1.9) using the spectral fits and bolometric corrections¹⁹ BC₅₁₀₀ = 9.26, BC₃₀₀₀ = 5.15 and BC₁₃₅₀ = 3.81 from the composite spectral energy distribution (SED) in Richards et al. (2006a).

14. BAL flag: 0 = nonBALQSO or no wavelength coverage; 1 = C iv HiBALQSO; 2 = Mg ii LoBALQSO; 3 = both 1 and 2. The LoBALQSO selection is very incomplete as discussed in Section 2.

15. FIRST radio flag: −1 = not in FIRST footprint; 0 = FIRST undetected; 1 = core dominant; 2 = lobe dominant (for details, see Jiang et al. 2007, and discussion in Section 2). Note these two classes of radio morphology do not necessarily correspond to the FR I and FR II types (see Lin et al. 2010 for more details).

16–17. Observed radio flux density at rest-frame 6 cm f_6 cm and optical flux density at rest-frame 2500 Å f₂₅₀₀. Both are in the observed frame.

18. Radio loudness R ≡ f_6 cm/f₂₅₀₀.

19–24. L₅₁₀₀, L₃₀₀₀, L₁₃₅₀ and their errors: continuum luminosity at 5100 Å, 3000 Å and 1350 Å, measured from the spectral fits. No correction for host contamination is made (see discussion in Section 3.6).

25–30. Line luminosity, FWHM, rest-frame equivalent width, and their errors for the broad Hα component.

31–36. Line luminosity, FWHM, rest-frame equivalent width, and their errors for the narrow Hα component.

37–40. Line luminosity, rest-frame equivalent width, and their errors for narrow [N ii] λ6584.

41–44. Line luminosity, rest-frame equivalent width, and their errors for narrow [S ii] λ6717.

45–48. Line luminosity, rest-frame equivalent width, and their errors for narrow [S ii] λ6731.

49–50. 6000–6500 Å iron rest-frame equivalent width and its error.

51–52. Power-law slope α_λ and its error for the continuum fit for Hα.

53–54. Number of good pixels and median S/N per pixel for the Hα region (6400–6765 Å).

55. Reduced χ² for the Hα line fit; −1 if not fitted.

56–61. Line luminosity, FWHM, rest-frame equivalent width, and their errors for the broad Hβ component.

62–67. Line luminosity, FWHM, rest-frame equivalent width, and their errors for the narrow Hβ component.

68. FWHM of broad Hβ using a single Gaussian fit (Shen et al. 2008a).

69–72. Line luminosity, rest-frame equivalent width, and their errors for [O iii] λ4959.

73–76. Line luminosity, rest-frame equivalent width, and their errors for [O iii] λ5007.

77–78. 4435–4685 Å iron rest-frame equivalent width and its error.

79–80. Power-law slope α_λ and its error for the continuum fit for Hβ.

81–82. Number of good pixels and median S/N per pixel for the Hβ region (4750–4950 Å).

83. Reduced χ² for the Hβ line fit; −1 if not fitted.

84–89. Line luminosity, FWHM, rest-frame equivalent width, and their errors for the whole Mg ii profile.

90–95. Line luminosity, FWHM, rest-frame equivalent width, and their errors for the broad Mg ii profile.

96. FWHM of broad Mg ii using a single Gaussian fit (Shen et al. 2008a).

97–98. 2200–3090 Å iron rest-frame equivalent width and its error.

99–100. Power-law slope α_λ and its error for the continuum fit for Mg ii.

101–102. Number of good pixels and median S/N per pixel for the Mg ii region (2700–2900 Å).

103. Reduced χ² for the Mg ii line fit; −1 if not fitted.

104–109. Line luminosity, FWHM, rest-frame equivalent width, and their errors for the whole C iv profile.

110–111. Power-law slope α_λ and its error for the continuum fit for C iv.

112–113. Number of good pixels and median S/N per pixel for the C iv region (1500–1600 Å).

114. Reduced χ² for the C iv line fit; −1 if not fitted.

115–126. Velocity shifts (and their errors) relative to the systemic redshift (cataloged in Schneider et al. 2010) for broad Hα, narrow Hα, broad Hβ, narrow Hβ, broad Mg ii, and C iv. The velocity shifts for the broad lines are measured from the peak of the multiple-Gaussian model fit to the broad component.²⁰ Recall that the velocity shifts of narrow lines were tied together during spectral fits. These velocity shifts can be used to compute the relative velocity offsets between two lines for the same object, such as the C iv–Mg ii blueshift, but should not be interpreted as the velocity shifts from the rest frame of the host galaxy due to uncertainties in the systemic redshift. Positive values indicate blueshift and negative values indicate redshift; value of 3 × 10⁵ indicates an unmeasurable quantity.

127–138. Virial BH masses using calibrations of Hβ (MD04), Hβ (VP06), Mg ii (MD04), Mg ii (VO09), Mg ii (S10), and C iv (VP06). The definitions of the acronym names of each calibration can be found in Section 3.7. Zero value indicates an unmeasurable quantity. We use FWHMs from a single Gaussian fit to the broad component for Hβ (MD04) and Mg ii (MD04); FWHMs from the multiple-Gaussian fit to the broad Hβ for Hβ (VP06); FWHMs from the multiple-Gaussian fit to the entire Mg ii and C iv lines for Mg ii (VO09) and C iv (VP06), respectively; FWHMs from the multiple-Gaussian fit to the broad Mg ii line for Mg ii (S10). See Section 3 for details.

139. The adopted fiducial virial BH mass if more than one estimate is available. See detailed discussion in Section 3.7.

140. The measurement uncertainty of the adopted fiducial virial BH mass, propagated from the measurement uncertainties of continuum luminosity and FWHM. Note that this uncertainty includes neither the statistical uncertainty (≳ 0.3–0.4 dex) from virial mass calibrations, nor the systematic uncertainties with these virial BH masses.

141. Eddington ratio computed using the fiducial virial BH mass.

142. Special interest flag. This is a binary flag: bit#0 set = disk emitters with high confidence (the vast majority are selected based on the Balmer lines); bit#1 set = disk emitter candidates; bit#2 set = double-peaked [O iii] λλ4959,5007 lines. These flags were set upon visual inspection of all z < 0.89 quasars in the catalog. In particular, disk emitter candidates (bit#1 = 1) are those with asymmetric broad Balmer line profile or systematic velocity shifts from the narrow lines; while those with high confidence (bit#0 = 1) show unambiguous double-peaked (or highly asymmetric) broad line profile or large velocity offsets between the broad and narrow lines. Figure 11 shows two examples of disk emitters with high confidence. We call these objects "disk emitters" even though some of them may be explained by alternative scenarios, such as a close SMBH binary (e.g., see discussion in Shen & Loeb 2010).

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One great virtue of the SDSS DR7 quasar sample is that it provides unprecedented statistics for broad-line quasar properties. To demonstrate this, Figures 12–14 show some statistical properties of quasars using our spectral measurements for Hβ, Mg ii, and C iv, respectively. These figures show the typical values of these properties for SDSS quasars as a quick reference. We do not show a similar figure for Hα because quasars with Hα coverage represent only a tiny fraction of the whole sample, and because host contamination is more severe for these low-redshift quasars.

There are correlations among the properties shown in Figures 12–14. Some of these correlations are not due to selection effects. For instance, the well-known Baldwin effect (Baldwin 1977), i.e., the anti-correlation between line EW and continuum luminosity, is clearly seen for C iv and Mg ii. There are also strong correlations between EW and FWHM for Mg ii (e.g., Dong et al. 2009b) and C iv, which are not due to any apparent selection effects. The statistics of our catalog now allows in-depth investigations of these correlations when binning in different quantities such as redshift or luminosity, and to probe the origins of these correlations. However, there are some apparent correlations which are likely due to selection effects inherent in a flux-limited sample, or host contamination. For instance, the apparent anti-correlation between α_λ and log L₅₁₀₀, and the mild negative Baldwin effect below log L₅₁₀₀ ≲ 45 for Hβ seen in Figure 12, are most likely caused by increasing host contamination toward fainter luminosities (see Section 3.6). Moreover, the spectral quality (mainly S/N) has important effects on the measured quantities and may bias the measurements at the low S/N end. Thus one must take these issues into account when using the catalog to study correlations among various properties. The detailed investigations of various correlations will be presented elsewhere.

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Figure 15 shows the so-called 4DE1 projection in the Hβ FWHM versus $R_{\rm Fe\,\mathsc{ii}}={\rm EW_{\rm Fe\,\mathsc{ii}4434-4684}/EW_{H\beta }}$ space (e.g., Sulentic et al. 2000, 2002; Zamfir et al. 2010), which is an extension of the eigenvector space for quasar properties suggested by Boroson & Green (1992). Objects with Hβ FWHM >4000 km s⁻¹ (i.e., population "B" in the terminology of the 4DE1 parameter space of Sulentic and collaborators) have a tendency to have weaker relative iron emission strength for larger FWHMs. The black contours show the distribution of all quasars while the red contours show the distribution of radio-loud (R > 10) quasars. It appears that the radio-loud contours are more vertically elongated, broadly consistent with the phenomenological classification scheme based on the 4DE1 parameter space (e.g., Sulentic et al. 2000, 2002; Zamfir et al. 2010). The physics driving these characteristics in the parameter space is currently not clear and deserves further study.

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Figure 16 shows the correlation between the [O iii] λ5007 luminosity and the continuum luminosity at 5100 Å. This correlation is usually used to estimate the bolometric luminosity using the [O iii] λ5007 luminosity as a surrogate for type-2 quasars (e.g., Kauffmann et al. 2003; Zakamska et al. 2003; Heckman et al. 2004; Reyes et al. 2008). While the correlation is apparent, it has a large scatter, as noted in earlier studies (e.g., Heckman et al. 2004; Reyes et al. 2008). The mean linear relation is

$$\begin{equation} \log L_{\rm [\rm O\,\mathsc{iii}]\lambda 5007}\approx \log L_{5100} -2.5\, \end{equation} \tag{ 15 }$$

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with a scatter ∼0.35 dex. Using the bolometric correction from Richards et al. (2006a), a crude conversion between $L_{\rm [\rm O\,\mathsc{iii}]\lambda 5007}$ and the quasar bolometric luminosity is: $L_{\rm bol}\approx 3200L_{\rm [\rm O\,\mathsc{iii}]\lambda 5007}$.

Figure 17 shows the distributions of velocity shifts between various emission lines. Recall that the velocity of the broad lines is measured from the peak of the multiple-Gaussian fit. The left panel of Figure 17 shows the distributions of velocity shifts between the broad Balmer lines and the narrow lines. The means of these distributions are consistent with zero, hence there is no offset in the mean between the broad and narrow Balmer lines (cf. Bonning et al. 2007). We note that if we did not account for the blue wings of the narrow [O iii] λλ4959,5007 lines during spectral fitting, there would be a net redshift of the order of ∼100 km s⁻¹ between the broad Hβ line and [O iii], which is inconsistent with the results for Hα versus [S ii]. The right panel of Figure 17 shows the velocity offsets between Mg ii and [O iii]  and between C iv and Mg ii. The Mg ii line shows no mean offset from [O iii], while the C iv line shows a systematic blueshift of ∼600 km s⁻¹ with respect to Mg ii (e.g., Gaskell 1982; Tytler & Fan 1992; Richards et al. 2002a); see Richards et al. (2011) for further discussion.

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It is interesting to note that many of the objects in the wings of the velocity offset distributions of the broad Balmer lines versus the narrow lines are either strong disk-emitters (e.g., Chen et al. 1989; Eracleous & Halpern 1994; Strateva et al. 2003), or have the broad component systematically offset from the narrow line center; in other cases the apparent large shifts were caused by poor fits to noisy spectra.