EVIDENCE THAT MOST TYPE-1 AGNs ARE REDDENED BY DUST IN THE HOST ISM

The seventh data release (DR7) of the SDSS contains about a million extragalactic spectra covering the wavelength range of 3800–9200 Å with 2.5 Å resolution. This includes the spectra of 105,783 AGNs brighter than ${M}_{i}=-22.0\,\mathrm{mag}$ (Schneider et al. 2010), which have an average signal-to-noise ratio (S/N) of 10 pixel⁻¹. Shen et al. (2011) present a compilation of the properties for these AGNs, including continuum and emission line measurements around the ${\rm{H}}\alpha$, ${\rm{H}}\beta$, and Mg ii wavelength regions which we use in this paper. The SDSS pipeline measures redshift, z, using the broad emission lines in AGNs with errors of ${\rm{\Delta }}z=0.002$ (Hewett & Wild 2010) compared to the host galaxy. We choose to use the redshifts measured by Hewett & Wild (2010) based on the narrow emission lines, which are likely more accurate. We limit our sample to AGNs with $0.35\lt z\lt 0.5$ in order to include the NaID absorption doublet (5889.95 Å, 5895.92 Å) and the 3000 Å continuum in our wavelength window. The spectra are corrected for MW foreground dust, using the maps of Schlegel et al. (1998) and the extinction law derived by Cardelli et al. (1989).

Our final sample consists of 4946 QSOs. We present in Figure 1 their distribution in z, FWHM of the broad ${\rm{H}}\beta$ line, and bolometric luminosity ${L}_{\mathrm{bol}}$. The value of ${L}_{\mathrm{bol}}$ is derived from the ${L}_{3000\mathring{\rm{A}} }$ measurements of Shen et al. (2011) using the bolometric correction factor of Richards et al. (2006). Figure 1 also shows the distribution of the optical continuum slope ${\alpha }_{\mathrm{opt}}$, which is calculated as follows:

$$\begin{eqnarray}&&{\alpha }_{\mathrm{opt}}=\displaystyle \frac{\mathrm{log}[{L}_{\nu }(3000\,\mathring{\rm{A}} )/{L}_{\nu }(5100\,\mathring{\rm{A}} )]}{\mathrm{log}(5100/3000)}-0.25\end{eqnarray} \tag{ 1 }$$

where ${L}_{\nu }(\lambda )$ is the monochromatic luminosity at rest frame wavelength λ measured by Shen et al. (2011). The offset of −0.25 is introduced since on average 13% of the emission at 3000 Å is due to line and bound-free emission (Trakhtenbrot & Netzer 2012).

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The relation between ${\alpha }_{\mathrm{opt}}$ and the intrinsic AD slope depends on both the amount of extinction along the line of sight and the host contribution to the continuum emission ${f}_{\mathrm{host}}(\lambda )$. We note that since we use a relatively small baseline to measure the slope ($\mathrm{log}(5100/3000)=0.23$), the relation between intrinsic emission and ${\alpha }_{\mathrm{opt}}$ is quite sensitive to ${f}_{\mathrm{host}}$ at $5100\,\mathring{\rm{A}}$ and $3000\,\mathring{\rm{A}}$, e.g., a value of ${f}_{\mathrm{host}}=0.1$ at either wavelength will change the implied intrinsic slope by ±0.2. We discuss the effect of ${f}_{\mathrm{host}}$ further below.

We interpolate each spectrum to an identical grid of 0.5 Å in rest frame wavelength, in the range 5700–6100 Å, which contains the NaID absorption doublet. We use the Savitzky–Golay (SG) smoothing algorithm (Savitzky & Golay 1964)⁴ with a third order polynomial fit and a moving window size of 35 Å to fit and divide out the continuum, thus obtaining normalized fluxes. We exclude from the fitting range the wavelengths 5875–5920 Å, in order to avoid the He i emission line (5875.6 Å) and NaID absorption lines (5889.95 Å, 5895.92 Å). The NaID absorption line is not detected in almost all individual spectra due to the limited S/N of the SDSS spectra.

We divide the spectra into two-dimensional bins based on their optical slope and the FWHM of their broad ${\rm{H}}\beta$ line. The latter binning is done since the NaID absorption doublet lies on the red wing of the broad He i feature, which has a width that correlates tightly with the broad Hβ width. Therefore, stacking in bins of FWHM avoids spurious features that are created when stacking objects with very different FWHMs. We find that in order to reach a sufficient S/N to measure the depth of the NaID line, we must stack at least 200 spectra. In order to have a similar number of spectra in every bin, we choose the following FWHM bins: 1000–3000, 3000–4000, 4000–6000, and 6000–10,000 $\,\mathrm{km}\,{{\rm{s}}}^{-1}$. Each of the FWHM bins contains roughly 1200 spectra, and we divide them into six ${\alpha }_{\mathrm{opt}}$ bins, which we stack using the median at each wavelength. Our final sample contains 24 stacked spectra with S/N in the range 27–39.

Figure 2 shows the six stacked spectra with different optical slopes for each FWHM bin. These are the independent spectra with which we perform the fitting throughout the paper. One can see that the NaID absorption profile lies on the red wing of the He i emission line at 5876 Å. Although there is some variation in the He i profile between different ${\alpha }_{\mathrm{opt}}$ bins, the EW of the NaID absorption grows markedly as ${\alpha }_{\mathrm{opt}}$ decreases.

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One can see additional absorption features in the stacked spectra. The absorption line at 5780 Å shows little change as a function of the optical slope and its EW is approximately 2 Å throughout the different bins. We speculate that this line is due to Fe i absorption (5780 Å). However, a certain identification requires a detailed comparison with the strengths of other known Fe absorption lines (in the 4000–5600 Å wavelength range) and is beyond the scope of our paper. Figure 2 shows an additional absorption feature at 5855 Å on the blue side of the He i emission line, which we call the blue absorption feature (BAF). The origin of the BAF is likely not NaID, since it is usually a resolved trough and is offset from the rest wavelength of NaID by about $1800\,\mathrm{km}\,{{\rm{s}}}^{-1}$. The BAF strength is not correlated with the strength of other photospheric features' strength (such as Fe i 5780 Å). However, we account for this absorption when modelling the He i and NaID lines.

In most bins the NaID doublet appears as a single blended profile, suggesting the width of the individual lines are typically larger than their wavelength separation of 6 Å ($300\,\mathrm{km}\,{{\rm{s}}}^{-1}$). Only in the reddest spectra of the FWHM $=\,2200\,\mathrm{km}\,{{\rm{s}}}^{-1}$ bin is the doublet clearly resolved. The combined profile of the NaID doublet has an FWHM in the range of 7–9 Å ($350\mbox{--}450\,\mathrm{km}\,{{\rm{s}}}^{-1}$).

In Figure 3, we compare the velocity profile of the stacked NaID absorption feature with the velocity distribution of narrow Mg ii absorbers found by Shen & Ménard (2012, hereafter SM12). SM12 found that 2% of SDSS AGNs at $0.4\lt z\lt 2$ exhibit a narrow Mg ii absorption feature in single spectra. The top-left panel in Figure 3 shows the velocity distribution of the SM12 absorbers. As in this study, the systemic velocity of the host in the Mg ii-absorber sample is derived from the velocity of the narrow emission lines. SM12 argue that Mg ii absorbers with velocities $v\lt -1500\,\mathrm{km}\,{{\rm{s}}}^{-1}$ are consistent with cosmologically intervening absorbers along the line of sight toward the AGN (see also Wild et al. 2008) since the velocity distribution profile flattens out at $v\lt -1500\,\mathrm{km}\,{{\rm{s}}}^{-1}$. Therefore, to assess the velocity distribution of the associated (non-intervening) absorbers, we fit the positive velocity part of the distribution with a Gaussian. In the bottom-left panel we compare this Mg ii velocity distribution with the NaID absorption profile of the ${\alpha }_{\mathrm{opt}}=-0.74,\,\mathrm{FWHM}=3400\,\mathrm{km}\,{{\rm{s}}}^{-1}$ bin. This bin is chosen since it shows strong NaID absorption which facilitates the comparison. The black line is the stacked AGN spectrum after subtracting out the He i line, where we use the Hβ profile as a template for He i. The profiles of He i and Hβ are compared in the right panel. The red dashed line in the bottom-left panel is the expected profile for a NaID doublet convolved with the Gaussian shown in the top-left panel. Figure 3 shows that the velocity profile of the stacked NaID absorption feature is consistent with the velocity distribution of associated Mg ii absorbers found by SM12.

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In order to measure the EW of the NaID line in the stacked spectra, we perform a joined fit. The He i line is modeled with the Hβ profile of the same stacked spectrum. The NaID doublet profile is modeled as a single unresolved line with the width suggested by the Mg ii absorption distribution shown in Figure 3. The BAF strength correlates with ${\alpha }_{\mathrm{opt}}$, and therefore changes from one stacked spectrum to the next. We fit a Gaussian function to account for it. To solve for the various parameters of interest, we minimize the ${\chi }^{2}$ of the following function:

$$\begin{eqnarray}&&f(\lambda )={a}_{{\rm{H}}}\cdot {\rm{H}}\beta (\lambda )+b+{a}_{N}\cdot N(\lambda )+G({a}_{G},\sigma ,{\lambda }_{0},\lambda )\end{eqnarray} \tag{ 2 }$$

where ${\rm{H}}\beta (\lambda )$ is the shifted and rescaled ${\rm{H}}\beta$ profile (with a fixed width), N is the NaID profile, and G is the Gaussian function that accounts for the BAF. We allow the continuum parameter, b; the scaling parameters a_H, a_N, and a_G; and the width of the BAF, σ, to change from one stacked spectrum to the next. The central wavelengths for all the features are fixed. The NaID EW is then extracted from the best fit. Different fitting procedures, e.g., using a Voigt profile for the BAF and Gaussians for the NaID doublet, give essentially the same EWs. Figure 4 shows the quality of the fit we obtain for different FWHM and ${\alpha }_{\mathrm{opt}}$ bins. The stacked spectra are shown in black, the He i fits in blue, and the NaID and BAF features are shaded in gray and cyan, respectively.

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For a given FWHM bin, in addition to dividing the spectra into six bins of different ${\alpha }_{\mathrm{opt}}$, we sort the spectra in ${\alpha }_{\mathrm{opt}}$ and use a running median filter with a precision of 0.01 in ${\alpha }_{\mathrm{opt}}$. Using the running median, we essentially incorporate the information of every low S/N spectrum into many high S/N spectra. The stacked spectra of the running median are therefore not statistically independent. We measure the EW of these spectra and present them as small crosses (with no uncertainties) in Figure 5. This is done in order to trace the behavior qualitatively and examine the scatter around each of the 24 independent stacked spectra.

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Additionally, we measure the EW of NaID and the median ${\alpha }_{\mathrm{opt}}$ for 24 independent spectra. The uncertainties in ${\alpha }_{\mathrm{opt}}$ are dominated by the uncertainty of 0.08 in the correction for emission lines discussed in Section 2.1. The uncertainties in EW(NaID) are calculated during the line fitting.

Figure 5 shows the EW(NaID) versus ${\alpha }_{\mathrm{opt}}$ relation for the four FWHM bins. The measured EW(NaID) is linearly proportional to ${\alpha }_{\mathrm{opt}}$, with similar slopes in the different FWHM bins. We fit a linear function of the form

$$\begin{eqnarray}&&\mathrm{EW}(\mathrm{NaID})=a(\alpha -{\alpha }_{0})+b\end{eqnarray} \tag{ 3 }$$

to the six independent measurements of EW versus ${\alpha }_{\mathrm{opt}}$ in each FWHM bin, where ${\alpha }_{0}$ is the bluest ${\alpha }_{\mathrm{opt}}$ at each FWHM. We use an orthogonal least square minimization, which takes into account the uncertainties in both variables. The best linear fits are shown in Figure 5 and listed in Table 1.

Table 1.  EW (NaID) and ${\alpha }_{\mathrm{opt}}$ Relations

FWHM $(\mathrm{km}\,{{\rm{s}}}^{-1})$	${\alpha }_{0}$	EW at ${\alpha }_{0}$ (Å)	EW Versus ${\alpha }_{\mathrm{opt}}$ Slope
2200	−0.11	0.05 ± 0.10	−1.92 ± 0.09
3400	−0.12	0.58 ± 0.14	−1.96 ± 0.08
4900	−0.43	1.67 ± 0.16	−2.10 ± 0.10
7300	−0.33	2.08 ± 0.19	−2.00 ± 0.11

Note. Fit parameters for the linear relations between EW(NaID) and ${\alpha }_{\mathrm{opt}}$ shown in Figure 5.

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In Figure 6 we compare the NaID absorption feature with the Mg b absorption complex. Mg b absorption likely originates in stellar photospheres since it requires a significant population of excited ions, while in the ISM most ions are at the ground state. Hence, we can use Mg b to estimate the stellar photosphere contribution to the trends of EW(NaID) versus ${\alpha }_{\mathrm{opt}}$ and EW(NaID) versus FWHM seen in Figure 5. The right panels in Figure 6 show the Mg b absorption features in the normalized spectra from Figure 2, where different rows plot different FWHM bins and different colors denote different ${\alpha }_{\mathrm{opt}}$ bins. These features can be compared to the NaID features shown in the left panels.

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Measuring EW(Mg b) accurately is complicated by the fact that its wavelengths coincide with the wavelengths spanned by the optical BLR Fe ii forest. However, it is evident from Figure 6 that in a given FWHM bin, the Mg b feature does not significantly change with ${\alpha }_{\mathrm{opt}}$, in contrast to the significant trend apparent in NaID. The lack of trend in Mg b with ${\alpha }_{\mathrm{opt}}$ suggests that the trend of NaID with ${\alpha }_{\mathrm{opt}}$ is not due to an increasing contribution from stellar photospheres. In contrast, the strength of the Mg b features increases with increasing FWHM. Therefore, it seems plausible that the trend of EW(NaID) with FWHM is associated with an increasing contribution from stellar photospheres. The trend of EW with FWHM is further addressed in the discussion.

A stellar photosphere origin is also unlikely to explain the largest EW(NaID) = 4.8 Å we observe (Figure 5) since the maximum EW(NaID) seen in the spectrum of individual stars is 5.6 Å (Burstein et al. 1984; Faber et al. 1985). Therefore, in order to explain an EW of 5 Å with stellar photospheres, one has to populate the entire AGN host with stars that have the maximum EW(NaID), and assume the contribution of the AGN continuum at 6000 Å is entirely negligible, which is unlikely.

Various studies suggest that the BLR resides within the dust sublimation radius (Netzer & Laor 1993; Kaspi et al. 2000; Suganuma et al. 2006; Bentz et al. 2009; Koshida et al. 2014), and hence any dust surrounding the AGN will reside on larger scales. The BLR is therefore likely to also be extincted by the dust which reddens the AGN continuum. In this section we test this prediction by comparing the observed BLR Balmer ratio ${\rm{H}}\alpha$/${\rm{H}}\beta$ with ${\alpha }_{\mathrm{opt}}$. This is somewhat similar to Dong et al. (2008) where the aim was to find the line ratio in the bluest (largest ${\alpha }_{\mathrm{opt}}$) AGNs. As shown below, our analysis is more general and applied to the entire sample rather than the sub-group with the smallest ${\rm{H}}\alpha$/${\rm{H}}\beta$.

To calculate the expected ${\rm{H}}\alpha$/${\rm{H}}\beta$ as a function of ${\alpha }_{\mathrm{opt}}$ in our scenario, we quantify the dust extinction in magnitude at wavelength λ as ${R}_{\lambda }{E}_{{\rm{B}}-{\rm{V}}}$, where ${E}_{{\rm{B}}-{\rm{V}}}$ is the color excess which is proportional to the dust column, and R_λ is the assumed extinction law. Since in our suggested picture ${\alpha }_{\mathrm{opt}}$ is determined by the dust column along the line of sight, ${\alpha }_{\mathrm{opt}}$ is related to ${E}_{{\rm{B}}-{\rm{V}}}$ via

$$\begin{eqnarray}&&{\alpha }_{0}-{\alpha }_{\mathrm{opt}}=\displaystyle \frac{{R}_{3000}-{R}_{5100}}{2.5\mathrm{log}(5100/3000)}\,{E}_{{\rm{B}}-{\rm{V}}}\,.\end{eqnarray} \tag{ 4 }$$

Assuming the reddening dust completely covers the BLR, then

$$\begin{eqnarray}&&\mathrm{log}\left(\displaystyle \frac{{({\rm{H}}\alpha /{\rm{H}}\beta )}_{\mathrm{int}}}{{({\rm{H}}\alpha /{\rm{H}}\beta )}_{\mathrm{obs}}}\right)=\displaystyle \frac{{R}_{4861}-{R}_{6563}}{2.5}{E}_{{\rm{B}}-{\rm{V}}},\end{eqnarray} \tag{ 5 }$$

where ${({\rm{H}}\alpha /{\rm{H}}\beta )}_{\mathrm{int}}$ and ${({\rm{H}}\alpha /{\rm{H}}\beta )}_{\mathrm{obs}}$ are the intrinsic and observed Hα/Hβ ratios, respectively. Combining Equations (4) and (5) we therefore expect

$$\begin{eqnarray}\mathrm{log}(\displaystyle \frac{{({\rm{H}}\alpha /{\rm{H}}\beta )}_{\mathrm{obs}}}{{({\rm{H}}\alpha /{\rm{H}}\beta )}_{\mathrm{int}}} & = & 0.23({\alpha }_{0}-{\alpha }_{\mathrm{opt}})\displaystyle \frac{{R}_{4861}-{R}_{6563}}{{R}_{3000}-{R}_{5100}}\\ & \approx & 0.1({\alpha }_{0}-{\alpha }_{\mathrm{opt}}).\end{eqnarray} \tag{ 6 }$$

The approximation in Equation (6) is based on the Pei (1992) formulation for the MW-, LMC-, and SMC-type extinction curves, in which $0.23({R}_{4861}-{R}_{6563})/({R}_{3000}-{R}_{5100})$ is equal to 0.099, 0.100, and 0.096, respectively. The similarity of these values is the result of the narrow wavelength range considered here. It suggests that the exact nature of the extinction law is a minor source of uncertainty. In low-density gas ${({\rm{H}}\alpha /{\rm{H}}\beta )}_{\mathrm{int}}$ is equal to $2.74\mbox{--}2.86$, assuming "Case B" recombination (Osterbrock & Ferland 2006). However, in the dense BLR gas ($\gt {10}^{9}\,{\mathrm{cm}}^{-3}$), the value of ${({\rm{H}}\alpha /{\rm{H}}\beta )}_{\mathrm{int}}$ may be different due to line optical depths and collisional effects (Netzer 2013).

To derive the median ${({\rm{H}}\alpha /{\rm{H}}\beta )}_{\mathrm{obs}}$ as a function of ${\alpha }_{\mathrm{opt}}$, we use the catalog of Shen et al. (2011) who measured the broad components of the ${\rm{H}}\alpha$ and ${\rm{H}}\beta$ emission lines. As the ${\rm{H}}\alpha$ emission line is observable only for redshifts $z\lt 0.4$, we use only the 1296 AGN in the redshift range $0.35\lt z\lt 0.4$. We group the AGN into bins with width ${\rm{\Delta }}{\alpha }_{\mathrm{opt}}=0.1$, and plot the median ${({\rm{H}}\alpha /{\rm{H}}\beta )}_{\mathrm{obs}}$ in each bin in the left panel of Figure 7. The uncertainty on ${\alpha }_{\mathrm{opt}}$ is calculated in Section 2.4 and the uncertainty of the median ${({\rm{H}}\alpha /{\rm{H}}\beta )}_{\mathrm{obs}}$ is the weighted median of the uncertainties in every ${\alpha }_{\mathrm{opt}}$-bin, where the uncertainties in each bin are measured using the line measurement uncertainties given by Shen et al. (2011). We also show the median ${({\rm{H}}\alpha /{\rm{H}}\beta )}_{\mathrm{obs}}$ in different FWHM bins, where each ${\alpha }_{\mathrm{opt}}$ bin contains the same number of objects.

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The dashed lines in the left panel of Figure 7 are the expected relations between ${({\rm{H}}\alpha /{\rm{H}}\beta )}_{\mathrm{obs}}$ and ${\alpha }_{\mathrm{opt}}$ (Equation (6)), for ${\alpha }_{0}=-0.1$ and ${({\rm{H}}\alpha /{\rm{H}}\beta )}_{\mathrm{int}}=3$. We find a best-fit ${({\rm{H}}\alpha /{\rm{H}}\beta )}_{\mathrm{int}}=3.02\pm 0.21$, close to the value expected from Case B recombination. This best-fit value is consistent with the Balmer ratio of blue AGNs previously measured by Dong et al. (2008). The uncertainty of 0.21 on the mean Hα/Hβ ratio is due to the uncertainties of the mean ratios and the best fit.

It is important to note that the distribution of Hα/Hβ ratios for the bluest objects is quite broad (3.02 ± 1.19), and there are many objects with Hα/Hβ significantly larger and significantly smaller than 3 with individual uncertainties that clearly distinguish them from the mean. Thus, we see no evidence for a "single-value Hα/Hβ," which is also supported by Schnorr-Müller et al. (2016), who studied the BLR of nine Seyfert 1 galaxies using up to six broad H i lines in each spectrum. Figure 7 demonstrates that the slope of the relation between ${({\rm{H}}\alpha /{\rm{H}}\beta )}_{\mathrm{obs}}$ and ${\alpha }_{\mathrm{opt}}$ is consistent with the expected slope. The best-fit slope of the entire sample is:

$$\begin{eqnarray}&&\mathrm{log}\,\displaystyle \frac{{({\rm{H}}\alpha /{\rm{H}}\beta )}_{\mathrm{obs}}}{3.02\pm 0.21}=(0.0950\pm 0.053)({\alpha }_{0}-{\alpha }_{\mathrm{opt}}),\end{eqnarray} \tag{ 7 }$$

while the best fit for each of the FWHM 2200, 3400, 4900, and 7300 $\mathrm{km}\,{{\rm{s}}}^{-1}$ bins is

$$\begin{eqnarray}\mathrm{log}\,\displaystyle \frac{{({\rm{H}}\alpha /{\rm{H}}\beta )}_{\mathrm{obs}}}{3.01\pm 0.42} & = & (0.103\pm 0.0091)({\alpha }_{0}-{\alpha }_{\mathrm{opt}})\\ \mathrm{log}\,\displaystyle \frac{{({\rm{H}}\alpha /{\rm{H}}\beta )}_{\mathrm{obs}}}{3.36\pm 0.51} & = & \,\,(0.064\pm 0.016)({\alpha }_{0}-{\alpha }_{\mathrm{opt}})\\ \mathrm{log}\,\displaystyle \frac{{({\rm{H}}\alpha /{\rm{H}}\beta )}_{\mathrm{obs}}}{3.37\pm 0.47} & = & (0.0876\pm 0.0094)({\alpha }_{0}-{\alpha }_{\mathrm{opt}})\\ \mathrm{log}\,\displaystyle \frac{{({\rm{H}}\alpha /{\rm{H}}\beta )}_{\mathrm{obs}}}{3.50\pm 0.53} & = & (0.0728\pm 0.0079)({\alpha }_{0}-{\alpha }_{\mathrm{opt}})\end{eqnarray} \tag{ 8 }$$

respectively. Therefore, the dependence of ${({\rm{H}}\alpha /{\rm{H}}\beta )}_{\mathrm{obs}}$ on ${\alpha }_{\mathrm{opt}}$ supports our interpretation that ${\alpha }_{\mathrm{opt}}$ is determined by the dust column along the line of sight, such that ${E}_{{\rm{B}}-{\rm{V}}}$ can be derived from ${\alpha }_{\mathrm{opt}}$ via Equation (4).

Given the typical ${E}_{{\rm{B}}-{\rm{V}}}$, we can also study the effect of reddening on additional broad lines at shorter wavelengths, in particular the ${\rm{L}}\alpha$/${\rm{H}}\beta$ ratio. For galactic-type reddening, and ${E}_{{\rm{B}}-{\rm{V}}}=0.08\,\mathrm{mag}$, we would predict the observed ratio to be 3.8 times smaller than the intrinsic one. This issue has been discussed extensively in numerous papers since the late 1970s (see Netzer & Davidson 1979). Moreover, Netzer et al. (1995) and Bechtold et al. (1997) showed that the ${\rm{L}}\alpha$/${\rm{H}}\beta$ ratio is strongly correlated with the continuum luminosity ratio L(1215 Å)/L(4866 Å), exactly in the same manner as we find here for ${\rm{H}}\alpha$/${\rm{H}}\beta$. These studies, and several others that followed, are all based on very small samples and will not be discussed further in this paper.

We also calculate the median ${({\rm{H}}\alpha /{\rm{H}}\beta )}_{\mathrm{obs}}$ of the NLR as a function of ${\alpha }_{\mathrm{opt}}$, using the narrow components of Hα and Hβ measured by Shen et al. (2011). These NLR measurements might be subjected to significant uncertainties since the NLR is weak compared to the BLR in luminous AGNs and separating the two profile components is challenging and occasionally highly uncertain. The relation between ${({\rm{H}}\alpha /{\rm{H}}\beta )}_{\mathrm{obs}}$ in the NLR and ${\alpha }_{\mathrm{opt}}$ is shown in the right panel of Figure 7. The value of ${({\rm{H}}\alpha /{\rm{H}}\beta )}_{\mathrm{obs}}$ at ${\alpha }_{\mathrm{opt}}={\alpha }_{0}$ is 4.07 ± 0.48, larger than the Case B value of $2.74\mbox{--}2.86$. This is not unexpected, since the Balmer photons are likely extincted by dust within the NLR clouds, thus increasing ${({\rm{H}}\alpha /{\rm{H}}\beta )}_{\mathrm{int}}$ above the Case B value (see Figure 6 in Stern et al. 2014 and also Dopita et al. 2002). The observed slope of the relation between ${({\rm{H}}\alpha /{\rm{H}}\beta )}_{\mathrm{obs}}$ and ${\alpha }_{\mathrm{opt}}$ in the NLR is shallower than the expected slope derived in Equation (6) and observed in the BLR. The weaker reddening of the NLR may be because the NLR emission line region is extended, and hence only part of the sightlines to the NLR traverse the extincting dust. This is in contrast with the BLR, which is compact and lies behind all the dust.

In our suggested scenario, ${\alpha }_{\mathrm{opt}}$ is related to ${E}_{{\rm{B}}-{\rm{V}}}$ via Equation (4). The coefficient in Equation (4) can be calculated for an assumed extinction law, which gives

$$\begin{eqnarray}{E}_{{\rm{B}}-{\rm{V}};\mathrm{MW}} & = & 0.188({\alpha }_{0}-{\alpha }_{\mathrm{opt}})\\ {E}_{{\rm{B}}-{\rm{V}};\mathrm{SMC}} & = & 0.209({\alpha }_{0}-{\alpha }_{\mathrm{opt}})\\ {E}_{{\rm{B}}-{\rm{V}};\mathrm{LMC}} & = & 0.194({\alpha }_{0}-{\alpha }_{\mathrm{opt}})\\ {E}_{{\rm{B}}-{\rm{V}};\mathrm{GB}}\, & = & 0.239({\alpha }_{0}-{\alpha }_{\mathrm{opt}})\end{eqnarray} \tag{ 9 }$$

where we used the prescriptions for the MW, SMC, and LMC extinction laws from Pei (1992), and also the "gray dust" formulation from Gaskell & Benker (2007). For simplicity, we henceforth assume an MW extinction law, though the results remain the same when applying SMC, LMC, or GB extinction laws instead. Equation (9) implies that for ${\alpha }_{0}=-0.1$, a typical AGN with ${\alpha }_{\mathrm{opt}}=-0.5$ has ${E}_{{\rm{B}}-{\rm{V}}}=0.08\,\mathrm{mag}$.

Applying Equation (9) to the EW(NaID) versus ${\alpha }_{\mathrm{opt}}$ relation found for the FWHM $=\,2200\,\mathrm{km}\,{{\rm{s}}}^{-1}$ bin (Table 1) we get

$$\begin{eqnarray}&&\displaystyle \frac{\mathrm{EW}{(\mathrm{NaID})}_{\mathrm{QSO}}}{\mathring{\rm{A}} }=(10.08\pm 0.55){E}_{{\rm{B}}-{\rm{V}}}\end{eqnarray} \tag{ 10 }$$

This relation is seen in Figure 5 (black dashed line).

In the left panel of Figure 8, we compare Equation (10) to the EW(NaID) versus ${E}_{{\rm{B}}-{\rm{V}}}$ relations observed in the ISM of local galaxies. We show the measurements of Poznanski et al. (2012, hereafter P12), who used over a million extragalactic SDSS spectra stacked in the observer frame to study the mean relation between sodium absorption and dust extinction in the MW. Figure 8 shows that in the MW, EW(NaID) saturates after reaching EW ∼ 1 Å, while in the AGN studied here a linear dependence between EW(NaID) and ${E}_{{\rm{B}}-{\rm{V}}}$ persists to higher values of EW(NaID). The difference in the EW where the absorption feature saturates may be due to the difference between the integrated velocity fields along stacked MW sightlines, compared to the integrated velocity fields along stacked sightlines to the centers of AGN hosts.

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In order to compare the P12 relation to the relation found here, we fit a linear relation to the measurements of P12 in the optically thin regime (blue line), which is:

$$\begin{eqnarray}&&\displaystyle \frac{\mathrm{EW}{(\mathrm{NaID})}_{\mathrm{MW}}}{\mathring{\rm{A}} }=(12.54\pm 0.35){E}_{{\rm{B}}-{\rm{V}}}.\end{eqnarray} \tag{ 11 }$$

One can see that this relation is close to that we find for AGNs in Equation (10).

Additional NaID measurements for the MW and Magellanic Clouds (SMC, LMC) have been compiled by Welty et al. (2012, hereafter W12)⁵ and contain measurements by Welty et al. (2006) and Cox et al. (2006). Since the W12 measurements are given toward individual lines of sight rather than in stacked spectra, the relation exhibits a large scatter. This scatter implies an uncertainty in the ${E}_{{\rm{B}}-{\rm{V}}}$ limit in which the optically thin regime ends. We therefore can obtain only lower and upper limits on the linear relation of EW(NaID) and ${E}_{{\rm{B}}-{\rm{V}}}$:

$$\begin{eqnarray}{\displaystyle \frac{\mathrm{EW}{(\mathrm{NaID})}_{\mathrm{SMC}}}{\mathring{\rm{A}} }}_{\min } & = & (9.92\pm 0.72){E}_{{\rm{B}}-{\rm{V}}}\\ {\displaystyle \frac{\mathrm{EW}{(\mathrm{NaID})}_{\mathrm{SMC}}}{\mathring{\rm{A}} }}_{\max } & = & (15.05\pm 0.61){E}_{{\rm{B}}-{\rm{V}}}.\end{eqnarray} \tag{ 12 }$$

The upper and lower limit for the SMC measurements is also shown in Figure 8. This relation is consistent with the AGN relation.

In the right panel of Figure 8 we show the relation between ${E}_{{\rm{B}}-{\rm{V}}}$ and ${N}_{\mathrm{Na}{\rm{I}}}$. We perform the comparison also in ${N}_{\mathrm{Na}{\rm{I}}}$ due to the difference in velocity dispersion between the different environments. Since there is no evidence of saturation in the AGN sample, we use the optically thin limit to calculate ${N}_{\mathrm{Na}{\rm{I}}}$ (e.g., Draine 2011):

$$\begin{eqnarray}&&{N}_{\mathrm{Na}{\rm{I}}}=3.4\cdot {10}^{12}\left(\displaystyle \frac{\mathrm{EW}(\mathrm{NaID})}{\mathring{\rm{A}} }\right)\,{\mathrm{cm}}^{-2}\,,\end{eqnarray} \tag{ 13 }$$

which together with Equation (10) yields

$$\begin{eqnarray}&&{N}_{\mathrm{Na}{\rm{I}}}=(3.4\pm 0.2)\cdot {10}^{13}\,\displaystyle \frac{{E}_{{\rm{B}}-{\rm{V}}}}{\,\mathrm{mag}}\,{\mathrm{cm}}^{-2}\,.\end{eqnarray} \tag{ 14 }$$

For the other samples we use the ${N}_{\mathrm{Na}{\rm{I}}}$ published in the respective papers. Note that while the QSO and P12 measurements are mean relations, the Welty measurements are individual measurements that give a sense of the scatter around this mean. As implied by the left panel, the relation between ${N}_{\mathrm{Na}{\rm{I}}}$, EW(NaID) and ${E}_{{\rm{B}}-{\rm{V}}}$ is similar in all environments shown in Figure 8.

Gas associated with dust along the line of sight to the central BH will be photoionized by the AGN radiation. We can therefore compare the observed relation between EW(NaID) and ${E}_{{\rm{B}}-{\rm{V}}}$ to the relation expected in gas in photoionization equilibrium in the vicinity of the AGNs.

4.1.1. The Expected EW(NaID)

The ratio of the neutral sodium column ${N}_{\mathrm{Na}{\rm{I}}}$ to ${E}_{{\rm{B}}-{\rm{V}}}$ is

$$\begin{eqnarray}&&\displaystyle \frac{{N}_{\mathrm{Na}{\rm{I}}}}{{E}_{{\rm{B}}-{\rm{V}}}}={f}_{\mathrm{Na}{\rm{I}}}\cdot \tfrac{{N}_{\mathrm{Na}}}{{N}_{{\rm{H}}}}\cdot \tfrac{X}{{m}_{{\rm{p}}}}\cdot \tfrac{{{\rm{\Sigma }}}_{{\rm{g}}}}{{{\rm{\Sigma }}}_{{\rm{d}}}}\cdot \tfrac{{{\rm{\Sigma }}}_{{\rm{d}}}}{{E}_{{\rm{B}}-{\rm{V}}}}=1.2\cdot {10}^{16}{f}_{\mathrm{Na}{\rm{I}}}\cdot \\ &&\quad \left(\tfrac{{N}_{\mathrm{Na}}/{N}_{{\rm{H}}}}{2.1\cdot {10}^{-6}}\right)\left(\tfrac{{{\rm{\Sigma }}}_{{\rm{g}}}/{{\rm{\Sigma }}}_{{\rm{d}}}}{100}\right)\left(\tfrac{{{\rm{\Sigma }}}_{{\rm{d}}}/{E}_{{\rm{B}}-{\rm{V}}}}{1.3\cdot {10}^{-4}}\right)\,\,{\mathrm{cm}}^{-2}\,{\mathrm{mag}}^{-1}\end{eqnarray} \tag{ 15 }$$

where ${f}_{\mathrm{Na}{\rm{I}}}$ is the fraction of sodium which is neutral, ${N}_{\mathrm{Na}}$ is the sodium column, ${N}_{\mathrm{Na}}/{N}_{{\rm{H}}}$ is the sodium abundance relative to hydrogen, X is the hydrogen mass fraction, ${{\rm{\Sigma }}}_{{\rm{g}}}={N}_{{\rm{H}}}{m}_{{\rm{p}}}/X\,[{\rm{g}}\,\,{\mathrm{cm}}^{-2}]$ is the gas surface density, and ${{\rm{\Sigma }}}_{{\rm{d}}}$ is the dust surface density (${{\rm{\Sigma }}}_{{\rm{d}}}/{{\rm{\Sigma }}}_{{\rm{g}}}$ is the dust-to-gas ratio). The numerical values are for Galactic dust, while the sodium abundance is normalized by its solar value.⁶ Comparison of Equation (15) with (14) suggests ${f}_{\mathrm{Na}{\rm{I}}}\approx 0.003$.

The value of ${f}_{\mathrm{Na}{\rm{I}}}$ depends mainly on the ionization parameter U:

$$\begin{eqnarray}&&U\equiv \displaystyle \frac{{\int }_{{\nu }_{0}}^{\infty }{L}_{\nu }/(h\nu )d\nu }{4\pi {r}_{{\rm{d}}}^{2}{n}_{e}c}\,,\end{eqnarray} \tag{ 16 }$$

where ${\nu }_{0}$ is the Lyman-edge frequency, ${r}_{{\rm{d}}}$ is the distance of the dusty gas from the central radiation source, and c is the speed of light. The dependence of ${f}_{\mathrm{Na}{\rm{I}}}$ directly on n_e or ${r}_{{\rm{d}}}$ (beyond the dependence on U) is weak. To constrain U based on the observed relation, we run version 13.03 of cloudy (Ferland et al. 2013) with an MW grain mixture and the following SED shape. The intrinsic optical–UV slope is assumed to equal the ${\alpha }_{0}=-0.1$ found above, in the range 1100 Å < λ < 1 μm. The X-ray luminosity at $2\,\mathrm{keV}$ is set such that the (observed) optical to X-ray ratio is equal to typical values seen in $L={10}^{45}\,\mathrm{erg}\,{{\rm{s}}}^{-1}$ AGNs (Just et al. 2007). For simplicity, we interpolate with a single power law between 1100 Å and $2\,\mathrm{keV}$. At λ > 1 μm, $2\,\mathrm{keV}\lt h\nu \lt 100\,\mathrm{keV}$, and $h\nu \gt 100\,\mathrm{keV}$ we assume spectral slopes of 2, −1, and −2, respectively. We run models with U in the range ${10}^{-4}\mbox{--}10$, corresponding to ${n}_{e}={10}^{4}\mbox{--}0.1\,{({r}_{{\rm{d}}}/\mathrm{kpc})}^{-2}\,{\mathrm{cm}}^{-3}$ for a ${L}_{\mathrm{bol}}={10}^{45}\,\mathrm{erg}\,{{\rm{s}}}^{-1}$ AGN with the above SED. We include in the calculation the effect of radiation pressure on the dust grains, which is significant at $U\gtrsim 0.01$ (Dopita et al. 2002; Groves et al. 2004). We use the depleted ISM abundance set implemented in cloudy, except for the sodium abundance which we assume has solar abundance. The total gas column is set to equal ${N}_{{\rm{H}}}=4.4\times {10}^{20}\,{\mathrm{cm}}^{-2}$ which reproduces the typical ${E}_{{\rm{B}}-{\rm{V}}}=0.08\,\mathrm{mag}$ found above.

Figure 9 shows the EW(NaID) calculated by cloudy for different U, compared to the observed $\mathrm{EW}(\mathrm{NaID})\approx 0.8\,\mathring{\rm{A}}$. The observed EW(NaID) is reproduced for $U\approx {10}^{-2.5}$. Note that only in low-ionized gas ($U\lesssim 0.01$) is any Na i absorption expected. In gas with a higher ionization level ${f}_{\mathrm{Na}{\rm{I}}}$ is practically zero. This conclusion is robust to reasonable changes in the assumed SED shape, the assumed gas metallicity, or the exact amount of sodium depletion.

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4.1.2. Line Emission from the Dusty Gas

In Figure 7, we showed that the dust that reddens the continuum also extincts the BLR, which suggests that the dust resides along the line of sight to the central source. However, Figure 9 suggests that gas along these sightlines is highly ionized, and is not expected to create a Na i absorption feature. Why then are ${\alpha }_{\mathrm{opt}}$ and EW(NaID) correlated?

One possibility is that the dusty gas is the ISM of the host galaxy, as depicted in the schematic cartoon in Figure 10. At host galaxy scales ($\gtrsim \,\mathrm{kpc}$), some of the gas will be ionized by the AGN, but some of the gas will be shielded from the AGN radiation via obscuration on smaller scales (e.g., by the torus). In this picture, dust extinction occurs on all sightlines, both the sightline to the AD and BLR and the sightlines to the stars. Neutral sodium, however, exists only in shielded regions, and hence the Na i absorption feature is imprinted only on the stellar continuum. A correlation between ${\alpha }_{\mathrm{opt}}$ and EW(NaID) is then expected if ISM columns along shielded and non-shielded sightlines are correlated. Such a correlation seems plausible, for example, if the range of ISM columns is driven by the inclination of our line of sight relative to the host galaxy disk. In this case, both non-shielded and shielded sightlines are expected to have larger columns in edge-on hosts compared with face-on hosts. Another possibility is that the range of ISM columns is driven by the total ISM mass. In this scenario as well, ISM-rich hosts are expected to exhibit larger columns than ISM-poor hosts along all sightlines, which would produce the observed correlation.

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Is the relative stellar contribution to the continuum ${f}_{\mathrm{host}}$ at 6000 Å large enough that the NaID absorption feature is expected to be observable? SL12 found that in low-z SDSS AGNs with ${L}_{\mathrm{bol}}={10}^{45.2}\,\mathrm{erg}\,{{\rm{s}}}^{-1}$, which is the mean ${L}_{\mathrm{bol}}$ of the objects analyzed here (Figure 1), the average host emission through the SDSS 3'' fiber is half of the AGN continuum emission at 6000 Å, i.e., ${f}_{\mathrm{host}}(6000\,\mathring{\rm{A}} )=0.33$ (see their Figure 13). This comparable AGN and host contributions to the continuum is further supported by the median EW(broad Hα) of 300 Å in our sample (measured by Shen et al. 2011 on objects in which Hα is observed), compared to the mean EW(broad Ha) of $570\,\mathring{\rm{A}}$ relative to the AGN continuum found by SL12. For comparison, Figure 2 shows that the deepest NaID absorption feature in our stacked spectra is only 10% of the continuum emission. Therefore, it is possible that the NaID absorption feature is imprinted only on the stellar emission.

This suggested scenario naturally explains the similarity of the ${N}_{\mathrm{Na}{\rm{I}}}$ versus ${E}_{{\rm{B}}-{\rm{V}}}$ relation in QSOs and in local galaxies shown in Figure 8 since the conditions in the shielded ISM of AGN hosts are plausibly not very different from those in an inactive galaxy. Also, this large-scale dust scenario is supported by the analysis above of the NLR Balmer ratio (Figure 7) and the analysis of the NLR BPT ratios versus ${L}_{\mathrm{UV}}/{L}_{\mathrm{broad}{\rm{H}}\alpha }$ in type-1 AGNs (Stern & Laor 2013), both of which suggest that the scale of the reddening dust is at least as large as the NLR, i.e., on scales much larger than $100\,\mathrm{pc}$ for the luminous objects in our sample.

The non-negligible host contribution also suggests the intrinsic AD slope is bluer than the value of ${\alpha }_{0}$ found here. Assuming ${f}_{\mathrm{host}}(3000\,\mathring{\rm{A}} )=0.1$ and ${f}_{\mathrm{host}}(5100\,\mathring{\rm{A}} )=0.25$, as suggested by Shen et al. (2011) and SL12 for ${L}_{\mathrm{bol}}={10}^{45.2}\,\mathrm{erg}\,{{\rm{s}}}^{-1}$ AGN⁷ , implies an intrinsic AD slope which is larger by 0.35 than found above, i.e., an intrinsic AGN slope of ${\alpha }_{0}+0.35=0.25$. This value is consistent with the slope of ∼0.2 expected for the average ${M}_{\mathrm{BH}}=0.7\cdot {10}^{8}\,{M}_{\odot }$ and $L/{L}_{\mathrm{Edd}}=0.25$ found by Shen et al. (2011) in objects with $\mathrm{FWHM}=2000\,\mathrm{km}\,{{\rm{s}}}^{-1}$. We note though that a more careful decomposition between the host continuum, the AGN continuum, and the line emission as a function of FWHM and ${\alpha }_{\mathrm{opt}}$ is required to derive accurately the true intrinsic AD slope.

In the scenario suggested in the previous section, EW(NaID) is expected to increase with ${f}_{\mathrm{host}}$. Since host galaxies have redder optical slopes than AGNs, then a large ${f}_{\mathrm{host}}$ would also imply a relatively red ${\alpha }_{\mathrm{opt}}$. One may therefore wonder whether the ${\alpha }_{\mathrm{opt}}$ versus EW(NaID) relation is actually driven by the range in ${f}_{\mathrm{host}}$ in the sample rather than by the distribution in the dusty gas column as suggested above. We find this possibility unlikely for a few reasons. First, in this varying host contribution scenario one would expect the Mg b feature to become stronger with decreasing ${\alpha }_{\mathrm{opt}}$. Figure 6 suggests that there might be a weak increase in EW(Mg b) with ${\alpha }_{\mathrm{opt}}$ in the largest FWHM bins, but this trend is significantly weaker than the trend of EW(NaID) with ${\alpha }_{\mathrm{opt}}$, and hence the change in the host contribution with ${\alpha }_{\mathrm{opt}}$ implied by Mg b is insufficient to explain the relation of EW(NaID) with ${\alpha }_{\mathrm{opt}}$. Second, a change in host contribution fails to explain why the broad Hα/Hβ ratio changes with ${\alpha }_{\mathrm{opt}}$ (Figure 7). And third, the required change in ${f}_{\mathrm{host}}$ should be evident as a change in EW(broad Hα) with ${\alpha }_{\mathrm{opt}}$, in contrast to the reddening scenario where EW(broad Hα) is expected to remain constant. In our sample, objects with ${\alpha }_{\mathrm{opt}}=-0.4$ have a median EW(broad Hα)$\,=\,340\,\mathring{\rm{A}}$ which suggests ${f}_{\mathrm{host}}(6560\,\mathring{\rm{A}} )\approx 1-340/570\,=\,0.4$, while objects with ${\alpha }_{\mathrm{opt}}=-1.5$ have a median EW(broad Hα) $=\,270\,\mathring{\rm{A}}$ which suggests ${f}_{\mathrm{host}}(6560\,\mathring{\rm{A}} )\approx 1-270/570=\,0.52$. Therefore, ${f}_{\mathrm{host}}$ likely increases by a mild factor of ∼1.3 from objects with ${\alpha }_{\mathrm{opt}}=-0.4$ to objects with ${\alpha }_{\mathrm{opt}}=-1.5$. This increase in ${f}_{\mathrm{host}}$ falls short of the increase in the median EW(NaID) by a factor of 3.6, from $1.1\,\mathring{\rm{A}}$ at ${\alpha }_{\mathrm{opt}}=-0.4$ to $4.0\,\mathring{\rm{A}}$ at ${\alpha }_{\mathrm{opt}}=-1.5.$ ⁸ Therefore, the change in ${f}_{\mathrm{host}}$ implied by the change in EW(broad Hα) is too weak to explain the EW(NaID) versus ${\alpha }_{\mathrm{opt}}$ relation.

We note that a correlation between ${\alpha }_{\mathrm{opt}}$ and ${f}_{\mathrm{host}}$ is also expected if the physical size spanned by the SDSS fiber changes with ${\alpha }_{\mathrm{opt}}$. However, no such trend exists in our sample. Objects with ${\alpha }_{\mathrm{opt}}=-2$ have a mean z of 0.41, similar to the mean z = 0.435 of objects with ${\alpha }_{\mathrm{opt}}=0$.

What is the origin of the offset between the EW(NaID) versus ${E}_{{\rm{B}}-{\rm{V}}}$ relations in different FWHM bins (Figure 5)? Assuming the BLR is in virial motion, then ${M}_{\mathrm{BH}}\propto {\mathrm{FWHM}}^{2}{R}_{\mathrm{BLR}}$, where ${R}_{\mathrm{BLR}}$ is the size of the BLR. Reverberation mapping studies have shown that ${R}_{\mathrm{BLR}}\propto {L}^{0.6\pm 0.1}$ (Kaspi et al. 2005; Bentz et al. 2009). Therefore, in our sample where the dynamical range in L is small (Figure 1), we expect ${M}_{\mathrm{BH}}$ to increase with FWHM. The different implied ${M}_{\mathrm{BH}}$ in the different FWHM bins may suggest a different intrinsic AGN SED, which can change ${\alpha }_{0}$.

Another possible difference between the different FWHM bins arises from the the well-known relations between ${M}_{\mathrm{BH}}$ and the bulge properties (Magorrian et al. 1998; Ferrarese & Merritt 2000), which have been shown to apply also to the host galaxies of AGNs (Laor 1998; Peterson et al. 2004). The typical ${f}_{\mathrm{host}}$ and/or stellar age may therefore change with FWHM. This conclusion is supported by Figure 6, which shows that absorption features that arise in stellar photospheres become more prominent at large FWHM (see also Figure 18 in SL12).

The measured ${\alpha }_{\mathrm{opt}}$ in our sample can be converted to ${E}_{{\rm{B}}-{\rm{V}}}$ using Equation (9). The top-left panel in Figure 11 shows the ${E}_{{\rm{B}}-{\rm{V}}}$ distribution of AGNs with FWHM = 2200 km s⁻¹, assuming an MW extinction law (values are larger by 10% for an SMC law). The mean ${E}_{{\rm{B}}-{\rm{V}}}$ is 0.12 mag, while the median ${E}_{{\rm{B}}-{\rm{V}}}$ is 0.1 mag. Note that some QSOs have negative ${E}_{{\rm{B}}-{\rm{V}}}$ due to slopes bluer than the derived ${\alpha }_{0}$. The standard absolute deviation of these negative ${E}_{{\rm{B}}-{\rm{V}}}$ values is 0.039 mag. These negative values provide an estimate of the various systematic errors in our derivation of ${E}_{{\rm{B}}-{\rm{V}}}$, probably due to variance in the host and BLR contribution to ${\alpha }_{\mathrm{opt}}$, and due to the dispersion in the intrinsic AD slope. If this scatter is solely due to the distribution in intrinsic slopes, it suggests a standard deviation of 0.2 in the intrinsic slope distribution.

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The similarity of the slopes of the EW(NaID) versus ${\alpha }_{\mathrm{opt}}$ relations in all FWHM bins (see Table 1 and Figure 5) suggests that we can use the same relation to derive ${E}_{{\rm{B}}-{\rm{V}}}$ also in the bins with FWHM = 3500, 4900, and $7500\,\mathrm{km}\,{{\rm{s}}}^{-1}$. However, the determination of ${\alpha }_{0}$ in these large FWHM bins is not straightforward since in these bins there are no stacks with $\mathrm{EW}(\mathrm{NaID})=0$, possibly due to the contribution of stellar photospheres to the NaID absorption feature.

Assuming that ${\alpha }_{0}$ is equal to the lowest ${\alpha }_{\mathrm{opt}}$ seen for each FWHM (listed in Table 1) implies a mean ${E}_{{\rm{B}}-{\rm{V}}}=0.1\,\mathrm{mag}$ for the entire sample and a median ${E}_{{\rm{B}}-{\rm{V}}}=0.08\,\mathrm{mag}$. The implied ${E}_{{\rm{B}}-{\rm{V}}}$ distributions under this assumption are shown in Figure 11. Alternatively, assuming that ${\alpha }_{0}$ at all FWHM bins is equal to the ${\alpha }_{0}=-0.1$ found for FWHM $=\,2200\,\mathrm{km}\,{{\rm{s}}}^{-1}$ implies a somewhat larger mean ${E}_{{\rm{B}}-{\rm{V}}}=0.13\,\mathrm{mag}$ and median ${E}_{{\rm{B}}-{\rm{V}}}=0.1\,\mathrm{mag}$. In the extreme case where ${\alpha }_{0}$ is equal to the extrapolation of the EW(NaID) versus ${\alpha }_{\mathrm{opt}}$ relation to $\mathrm{EW}(\mathrm{NaID})=0$ (${\alpha }_{0}=0.18,0.37,0.71$ for FWHM $=\,3500$, 4900, and $7500\,\mathrm{km}\,{{\rm{s}}}^{-1}$, respectively), the implied mean ${E}_{{\rm{B}}-{\rm{V}}}$ is $0.19\,\mathrm{mag}$ and the median ${E}_{{\rm{B}}-{\rm{V}}}$ is $0.17\,\mathrm{mag}$.

To summarize, at least half of the AGNs in our sample have ${E}_{{\rm{B}}-{\rm{V}}}\gt 0.08\,\mathrm{mag}$, and at least a quarter have ${E}_{{\rm{B}}-{\rm{V}}}\gt 0.18\,\mathrm{mag}$. For comparison, Lusso et al. (2013) found that only 24% of type 1s in the XMM-COSMOS survey have ${E}_{{\rm{B}}-{\rm{V}}}\gt 0.1\,\mathrm{mag}$. Krawczyk et al. (2015) found that 2.5% (13%) of the non-BALs (BALs) in their SDSS-based sample have ${E}_{{\rm{B}}-{\rm{V}}}\gt 0.1\,\mathrm{mag}$, and 0.1% (1.3%) have ${E}_{{\rm{B}}-{\rm{V}}}\gt 0.2\,\mathrm{mag}$. Capellupo et al. (2015) found that 70% of their sample have negligible dust columns. The lower dust columns found by previous studies compared to this work (except for Capellupo et al. 2015) are a direct result of their assumption that the typical AGN is not reddened by dust.

Using the cloudy models described above, we obtain the fraction of incident radiation absorbed by the dusty gas for the typical ${E}_{{\rm{B}}-{\rm{V}}}=0.08\,\mathrm{mag}$ AGN (${\alpha }_{\mathrm{opt}}=-0.5$). We find that given the assumed SED and grain properties, about a third of the incident, radiation, integrated over all wavelengths, is absorbed by the dust along a typical line of sight. This result suggests that the bolometric luminosity ${L}_{\mathrm{bol}}$ of type-1 AGNs, as derived from the optical, are typically underestimated by a factor of ${(2/3)}^{-1}=1.5$.

Given the very high level of ionization of the newly suggested line of sight gas, the corresponding column of dust, and the large covering factor, we need to consider other types of emission and absorption by this component.

The cloudy model described above can be used to estimate the fraction of the radiation absorbed by the dusty line of sight component for every value of ${E}_{{\rm{B}}-{\rm{V}}}$ and covering factor. As before, we do not consider a component which is less than about $100\,\mathrm{pc}$ from the center since our model assumes similar column densities on galactic scales. As already noted, for the typical ${E}_{{\rm{B}}-{\rm{V}}}=0.08\,\mathrm{mag}$ case, approximately a third of the incident radiation is absorbed by the dust. Given the assumed distance, this energy must be re-radiated at FIR energies with peak wavelength that depend on the dust location. For ISM-type densities (∼1 cm⁻³) and a typical bolometric luminosity of ${10}^{45}\,\mathrm{erg}\,{{\rm{s}}}^{-1}$, the required U of $\sim 1\mbox{--}10$ (Figure 9) is achieved at $1\mbox{--}10\,\mathrm{kpc}$. The corresponding dust temperatures, assuming optically thin dust and graybody emission with a spectral emissivity index $\beta =1.5\mbox{--}2\,$is in the range $10\mbox{--}40\,{\rm{K}}$. Given the fraction absorbed and a typical covering factor of ∼0.5, the total luminosity emitted in the FIR is hence of order $0.15\,{L}_{\mathrm{bol}}$. The FIR emission in individual objects may vary significantly around this average value depending on the ${E}_{{\rm{B}}-{\rm{V}}}$ distribution along different directions in single sources which could be different than the ${E}_{{\rm{B}}-{\rm{V}}}$ distribution seen in a sample. However, the ensemble average FIR emission is very large and such emission cannot escape detection. We note that there are also other claims in the literature for cold dust in AGNs (e.g., Symeonidis et al. 2016), but these results are still open to interpretation.

It is not our intention to investigate the issue of FIR emission by the obscuring dusty gas in this paper. Such a study requires more detailed considerations, comparison with other FIR sources of emission (mostly star formation in the host galaxy), and more. We will return to this topic in a forthcoming publication.

The consideration detailed above, which is summarized in Figure 9, suggests $U\sim 1\mbox{--}10$. Such a large ionization parameter is typical of X-ray gas in AGNs (Netzer 2013) and may have observational consequences that have not been studied so far. For example, if $U\sim 10$ and the UV—X-ray SED is typical of AGNs with ${L}_{\mathrm{bol}}={10}^{45}\,\mathrm{erg}\,{{\rm{s}}}^{-1}$, elements like O, Ne, Mg, and Si will be very highly ionized. In this case, the strongest X-ray features are absorption and emission lines of O viii, Ne x, Mg xii, etc. Emission line intensities, absorption line EWs, and other properties depend, again, on the gas distribution, velocity field, and level of ionization at different locations. This topic is beyond the scope of the present paper and is differed to our future paper.