Ultraviolet and Optical Emission Line Outflows in the Heavily Obscured Quasar SDSS J000610.67+121501.2: At the Scale of the Dusty Torus and Beyond

After correcting for the Galactic reddening of $E(B-V)=0.078$ mag (Schlegel et al. 1998), we transformed the photometric data and the optical and NIR spectroscopic flux into the rest-frame values with an emission redshift of $z=2.3174\pm 0.0003$, which is carefully determined by fitting a Gaussian to the Lyα narrow line. The photometric and spectroscopic data are shown by red squares and black and blue curves in Figure 1. Note that the absolute flux calibration is operated based on the SDSS and UKIDSS photometry for both optical and NIR spectra. With the multiwavelength spectroscopic and photometric data, we construct the broadband spectral energy distribution (SED) of SDSS J0006+1215 spanning from 1100 Å to 6.65 μm in the rest frame. For comparison, the quasar composite is composed of the SDSS DR7 quasar composite ($\lambda \leqslant 3000\,\mathring{\rm A} ;$ Jiang et al. 2011) and the NIR template ($\lambda \gt 3000\,\mathring{\rm A} ;$ Glikman et al. 2006). It is obvious that the observed SED of SDSS J0006+1215 shows a very different shape from the quasar composite. There is a striking "V"-shape turning at i band in the SED of SDSS J0006+1215, which is likely to be caused by a type of excess broadband absorption or the spectral combination of two different continuum slopes.

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For the first case, the unusual shape is quite similar to the excess broadband absorption near 2250 Å (EBBA) in BAL quasars reported by Zhang et al. (2015a). Therefore, the spectrum. of SDSS J0006+1215 is fit to search the quasar-associated 2175 Å absorber using the quasar composite reddened by a parameterized extinction curve (Fitzpatrick & Massa 1990) in the quasar rest frame, where a Drude component represents the potential 2175 Å bump (more details can be found in Section 2 of Zhang et al. 2015a). For SDSS J0006+1215, the parameters of the Drude component are $c3=92.07\pm 3.83$, ${x}_{0}=4.71\pm 0.02$ μm⁻¹, and $\gamma \ =5.32\pm 0.26$ μm⁻¹. The bump strength is ${A}_{\mathrm{bump}}\ =\pi c3/(2\gamma )=27.16\pm 1.76$ μm. Apparently, the width (γ) and strength (${A}_{\mathrm{bump}}$) of the bump deviate heavily from those of the bumps for the Milky Way (Fitzpatrick & Massa 1990), LMC (Gordon et al. 2003) curves, and the quasar-associated 2175 Å extinction curves (Jiang et al. 2011; Zhang et al. 2015a) (see Figure 2 of Zhang et al. 2015a). Therefore, the broadband absorption model is not preferred.

For the second case, the fibers feeding the SDSS-III BOSS spectrograph subtend a diameter of 2'' on the sky, and light from quasar pairs with small angular separations can be included through such a fixed aperture. The physical size, to which the diameter corresponds, indicates that the spectrum of SDSS J0006+1215 would also be polluted by its host galaxy. However, the Lyα and Hα emission lines simultaneously presented in the blue and red ends of the optical–NIR spectrum suggest that both spectral components of SDSS J0006+1215 could be quasar-type spectra. Thus, we try the combination of a red quasar spectrum and a blue one, which are the dominant components of the spectrum of SDSS J0006+1215 with $3000\,\mathring{\rm A} \lesssim \lambda \lesssim 7000$ Å and $\lambda \lesssim 2000\,\mathring{\rm A}$, respectively. Here, we use (1) a quasar composite scaled and multiplied by the SMC extinction law with a free parameter $E(B-V)$ to refer to the red component, and (2) a quasar composite scaled by a power-law form ($\propto {\lambda }^{-{\alpha }_{\lambda }}$) to match the warped blueward. In addition, a hot dust emission component is used to add the emission lacking in the infrared composite ($\lambda \gtrsim 9000$ Å). Finally, we can decompose the broadband SED in rest-frame wavelength with the following model:

$$\begin{eqnarray}{F}_{\lambda } & = & {C}_{1}{\lambda }^{-{\alpha }_{\lambda }}{F}_{\mathrm{composite},\lambda }+{C}_{2}A\\ & & \times (E(B-V),\lambda ){F}_{\mathrm{composite},\lambda }+{C}_{3}{B}_{\lambda }({T}_{\mathrm{dust}}),\end{eqnarray} \tag{ 1 }$$

where C₁, C₂, and C₃ are the factors for the respective components, $A(E(B-V),\lambda )$ is the dust extinction to the quasar emission, ${F}_{\mathrm{composite},\lambda }$ is the quasar composite, and ${B}_{\lambda }({T}_{\mathrm{dust}})$ is the Planck function. We perform least-squares minimization using the IDL procedure MPFIT developed by C. Markwardt.⁵ The values of $E(B-V)$ and ${\alpha }_{\lambda }$ are 0.7512 ± 0.0049 and 1.1388 ± 0.0061, respectively. The typical temperature of hot dust is T ∼ 1600 K. In Figure 1, the sum and three components of the best-fit model are shown by green and pink curves.

The fitting results suggest that the continuum of SDSS J0006+1215 is heavily suppressed by dust reddening (see also, Ross et al. 2015; Hamann et al. 2017); however, the warped blueward spectrum is even bluer than the average slope of quasars. We notice that the broadband SED of SDSS J0006+1215 is similar to those of three high polarized quasars, i.e., PKS 2355-535 (Scarpa & Falomo 1997), O i 287 (Li et al. 2015), and SDSS J091501.71+241812.1.⁶ This provides a guess that the warped blueward spectrum of SDSS J0006+1215 is the scattered component arising from an extensive region. In such a situation, the warped blueward spectrum would present high polarized fluxes; unfortunately, the faint magnitudes of SDSS J0006+1215 are unfit for the current spectropolarimetry observation.

The spectrum of SDSS J0006+1215 shows strong Lyα+N v, Si iv+[O iv], C iv, Hβ+$[{\rm{O}}\,{\rm{III}}]$, and Hα emission lines; however, ambiguous [C iii]+[Si iii]+Al iii and Mg ii emission lines are submerged in large noises. To further study the emission lines, we first subtract the underlying pseudocontinuum from the observed spectra. In this work, linear functions (${f}_{\lambda }={c}_{1}\ast \lambda +{c}_{2}$) estimated from two continuum windows are used as the local continua of the emission lines. In Hβ+$[{\rm{O}}\,{\rm{III}}]$ and Hα regimes, we also adopt the I Zw 1 Fe ii template provided by Véron-Cetty et al. (2004) and convolve it with a Gaussian kernel in velocity space to match the width of Fe ii multiplets in the observed spectra. The continuum windows are [1160, 1180] Å and [1270, 1290] Å for Lyα+N v, [1320, 1350] Å and [1430, 1450] Å for Si iv+[O iv], [1480, 1500] Å and [1600, 1620] Å for C iv, [4320, 4720] Å and [5080, 5300] Å for Hβ+$[{\rm{O}}\,{\rm{III}}]$, and [6150, 6250] Å and [6850, 6950] Å for Hα. In the right panels of Figure 2, the local continua and Fe ii multiplets are marked by gray dashed and pink lines. After subtracting the continuum model, we show the profiles of emission lines in their common velocity space in the left panels of Figure 2.

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It is also clearly shown that the peaks of broad lines in SDSS J0006+1215 tend to be blueshifted with respect to the Lyα narrow line, which indicates that the profiles of these broad lines contain an emission-line outflow component. In particular, the line profiles of C iv and Lyα+N v of SDSS J0006+1215 are almost the same as those of IRAS 13224-3809 and 1H 0707-495 reported by Leighly & Moore (2004). The profile of the C iv line is even entirely blueshifted (top left panel); the unusual C iv/Hα width ratio, ∼0.71, is larger than the value in the quasar composite spectrum (see Table 2). Those suggest that the normal UV BELs of SDSS J0006+1215 might also be obscured, as is the continuum. If this is true, the C iv profile we observed is dominated by the emission-line outflows and the gravitationally bound component, i.e., the normal BEL, of C iv is possibly absent. Here, we start the line profile fittings with the C iv line by one Gaussian. The peak velocity of the C iv BBEL is blueshifted 2119 km s⁻¹, and the FWHM is 4821 km s⁻¹. Later, we use the modeled profile of the C iv line to recover the BBEL outflows of other emission lines.

Table 2.  Emission-line Parameters of SDSS J0006+1215

		SDSS J0006+1215				Vanden Berk et al. Composite
Ions	${\lambda }_{\mathrm{lab}}$	Velocity	FWHM	Flux	Note	Rel. Flux
	Å	(km s−1)	(km s−1)	(10−17 erg s−1 cm−2)		(100 $\times \,F/{F}_{\mathrm{Ly}\alpha }$)
Lyα	1215.67	0	429 ± 30	20.81 ± 1.91	narrow	⋯
Lyα	1215.67	−2119	4821	105.55 ± 12.20	outflow	100.00
N v	1240.14	−2119	4821	96.94 ± 11.40	outflow	2.46
Si iv+O iv]	1396.76	−2119	4821	13.00 ± 4.32	outflow	8.13
C iv	1549.06	−2119 ± 179	4821 ± 486	54.07 ± 6.31	outflow	25.29
C iii]	1908.73	−2119	4821	9.71	outflow, upper limit	21.19
Hβ	4862.68	⋯	⋯	89.50	total	8.65
⋯	⋯	0	6927	69.07 ± 15.04	broad	⋯
⋯	⋯	−2119	4821	20.43 ± 4.15	outflow	⋯
[O iii]	4960.30	−2119	4821	15.01	outflow	0.69
[O iii]	5008.24	−2119	4821	45.04 ± 9.03	outflow	2.49
Hα	6564.61	⋯	⋯	557.45	total	30.83
⋯	⋯	0	6927 ± 231	494.06 ± 114.76	broad	⋯
⋯	⋯	−2119	4821	63.39 ± 16.34	outflow	⋯

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First, the emission line of Si iv is depicted by the scaled C iv profile. Actually, the strength of the Si iv line is polluted by the emission of [O iv] λλ1397, 1399, 1401, 1404, 1407 (see Figure 7 of Vanden Berk et al. 2001). A similar approach is taken in the fitting of the Lyα and N v lines, where the normal BEL components are absent. Then we use one narrow Gaussian component to model the Lyα narrow line and two broad Gaussian components to model the Lyα and N v BBEL components. The shifts and widths of broad Gaussian components are tied to those of the C iv line. In the top right panel, the sum of the local continuum (gray dotted line) and the Lyα narrow Gaussian (green line) plus the Lyα and N v BBEL outflows (blue lines) can well recover the observed spectrum.

Compared with UV emission lines, hydrogen Balmer lines in the optical waveband are still dominated by the gravitationally bound BELRs, and their profiles might only contain weak BBEL outflows. To separate the hydrogen Balmer emission line outflows, we use three Gaussian profiles to model the entire profile of the Hα line: one, with the shift and width settings of the C iv line, represents the BBEL outflows, and the other two, with the center wavelengths set to 6564.41 Å, represent the normal Hα BEL. They are shown by blue and green lines in the middle right panel, respectively. In the Hβ+$[{\rm{O}}\,{\rm{III}}]$ regime, we use the unshifted two-Gaussian profile of the Hα line to model the normal Hβ BEL (green line) and three Gaussians (blue lines) with the same shifts and widths as the C iv line to model the BBEL outflows of the Hβ and $[{\rm{O}}\,{\rm{III}}]$ doublets in sequence. The details of these components are shown in the bottom right panel of Figure 2.

For all of the emission lines, we list the best-fit parameters in Table 2. Here, let us revert to the left panels of Figure 2. We show the total fitted profile of each emission line by red lines and the sum of the unblueshifted components of the corresponding line (and other lines only in the Lyα+N v or Hβ+$[{\rm{O}}\,{\rm{III}}]$ regimes) by pink lines. The differences between the two above items are the BBEL outflows of each line (blue line). The fit between the observed spectra with the continuum-subtracted and the total fitted profiles indicates the rationality of the existence of the BBEL outflows in all emission lines. Although the shifts of the peaks of the Hα line and the profile fitting of the Hβ+$[{\rm{O}}\,{\rm{III}}]$ regime strongly suggest the existence of hydrogen Balmer line outflows, it must be said that the BBEL strengths of hydrogen Balmer lines have large measurement uncertainties because of the multicomponent decomposition.

The errors of line fluxes provided by MPFIT do not account for the uncertainty introduced by the pseudocontinuum subtraction. To take this and other possible effects into account, we adopt a bootstrap approach to estimate the typical errors for our emission-line measurement. We generate 500 spectra by randomly combining the scaled model outflow emission lines (denoted as "A") and the scaled model unblueshifted emission lines (denoted as "B") with the scaled model pseudocontinuum (denoted as "C"). Then, we fit the simulated spectra following the same procedure as described in the above paragraphs. For each parameter, we consider the typical error to be the standard deviation of the relative difference between the input (x_i) and the recovered (x_o), $({x}_{o}-{x}_{i})/{x}_{i}$. These relative differences turn out to be normally distributed for every parameter. Thus, the estimated typical 1σ errors are $\gtrsim 10 \%$ for C iv, Lyα, and N v and $\gtrsim 20 \%$ for Hα, Hβ, and $[{\rm{O}}\,{\rm{III}}]$; the derived flux errors are listed in Table 2.

Various interesting facts are summarized as follows: (1) The Lyα narrow line is the only narrow emission line in the spectrum of SDSS J0006+1215. The FWHM of the Lyα narrow line is 429 ± 30 km s⁻¹, and the flux is $(20.81\pm 0.89)\times {10}^{-17}$ erg s⁻¹. (2) The extreme C iv line with ${\mathrm{EW}}_{{\rm{C}}{\rm{IV}}}=117.79\pm 8.10\,\mathring{\rm A}$ far exceeds that of typical quasars (${\mathrm{EW}}_{{\rm{C}}{\rm{IV}}}\approx 20\mbox{--}50\,\mathring{\rm A}$). SDSS J0006+1215 and 12 other extremely red objects with ${\mathrm{EW}}_{{\rm{C}}{\rm{IV}}}\geqslant 100\,\mathring{\rm A}$ are actually classified as Extreme EW objects, which were considered to possibly be caused by suppressed continuum emission analogous to type II quasars in the unified model in Ross et al. (2015). However, flux emitted from the abnormal BELR is the other important reason, and it is interpreted as the BBEL outflows in this work. (3) The Hα/Hβ flux ratio of their unblueshifted components is 7.15 ± 2.27; however, the intrinsic value of Hα/Hβ of the BELR is 3.06, with a standard deviation of 0.03 dex (Dong et al. 2008). The extremely high flux ratio suggests that the extinction of the BELR is $E(B-V)={0.92}_{-0.34}^{+0.26}$, which does not contradict the extinction we measured from the continuum of SDSS J0006+1215. (4) However, the Hα/Hβ flux ratio of the outflowing components is 3.10 ± 1.01, which suggests that the outflow emission region is not obscured and reddened.

From the emission-line fittings, we can derive the central black hole mass using the commonly used virial mass estimators. We use the broad Hα line-based mass formalism given by Greene & Ho (2005):

$$\begin{eqnarray}{M}_{\mathrm{BH}} & = & ({2.0}_{-0.3}^{+0.4})\times {10}^{6}{\left(\displaystyle \frac{{L}_{{\rm{H}}\alpha }}{{10}^{42}\mathrm{erg}{{\rm{s}}}^{-1}}\right)}^{0.55\pm 0.02}\\ & & \times {\left(\displaystyle \frac{{\mathrm{FWHM}}_{{\rm{H}}\alpha }}{{10}^{3}\mathrm{km}{{\rm{s}}}^{-1}}\right)}^{2.06\pm 0.06}{M}_{\odot },\end{eqnarray} \tag{ 2 }$$

where ${L}_{{\rm{H}}\alpha }$ and ${\mathrm{FWHM}}_{{\rm{H}}\alpha }$ are the luminosity and width of the Hα line, respectively. Here, we only use the unblueshifted component emitted from the gravitationally bound BELR. Supposing that the BELs also follow the continuum extinction, the corrected luminosity of the normal Hα BEL is ${L}_{{\rm{H}}\alpha }=4.74\times {10}^{45}\,\mathrm{erg}\,{{\rm{s}}}^{-1}$. Together with ${\mathrm{FWHM}}_{{\rm{H}}\alpha }\ =6927\,\mathrm{km}\,{{\rm{s}}}^{-1}$, the central black hole mass is estimated to be ${M}_{\mathrm{BH}}=1.13\times {10}^{10}\,{M}_{\odot }$, with an uncertainty of a factor of ∼2.6 (from the intrinsic scatter of ∼0.41 dex for this single-epoch method compared with the results of reverberation mapping; Ho & Kim 2015). The monochromatic continuum luminosity ${L}_{5100}=\lambda {L}_{\lambda }$ at 5100 Å is directly calculated from the local continuum of the Hβ regime, and the extinction-corrected luminosity ${L}_{5100}=6.46\times {10}^{46}$ erg s⁻¹. The bolometric luminosity, ${L}_{\mathrm{bol}}=2.30\times {10}^{47}$ erg s⁻¹, is estimated from the monochromatic luminosity, ${L}_{5100}$, using the conversion given by Runnoe et al. (2012). Our bootstrap approach showed that the typical 1σ error of the continuum under Hβ+$[{\rm{O}}\,{\rm{III}}]$ emission lines is $\sim 10 \%$, and thus the uncertainty of ${L}_{\mathrm{bol}}$ is also on the order of 10%. The derived Eddington ratio is thus ${l}_{{\rm{E}}}={L}_{\mathrm{bol}}/{L}_{\mathrm{Edd}}=0.17$. Based on the bolometric luminosity, the amount of mass being accreted is estimated as ${\dot{M}}_{\mathrm{acc}}={L}_{\mathrm{bol}}/\eta {c}^{2}=41\,{M}_{\odot }\,{\mathrm{yr}}^{-1}$, where we assumed an accretion efficiency η of 0.1, and c is the speed of light.

From the point of view of UV-band photometric and spectroscopic observations, SDSS J0006+1215 is a fairly blue but faint quasar. The relative color and absolute magnitude at i band are ${\rm{\Delta }}(g-i)=-0.22$ and ${M}_{i}=-24.17$, bluer and fainter than most quasars in the SDSS-III/BOSS. If our inference regarding the unusual SED of SDSS J0006+1215 is true, it is heavily obscured with $E(B-V)=0.75$. And the above-mentioned characters of color and luminosity are measured based on the scattering component. The luminosity of SDSS J0006+1215 is heavily underestimated; when we compare the UV magnitudes and spectrum of SDSS J0006+1215 with the quasar composite, it is easy to see that the observed magnitudes of SDSS J0006+1215 are fainter than the representation by approximately 4.5 mag. Following the quasar luminosity functions measured in the SDSS-III/BOSS and SDSS-IV/eBOSS (e.g., Ross et al. 2013; Palanque-Delabrouille et al. 2016), we can derive the quasar number density with similar redshift and luminosity as follows: $\varnothing (z\sim 2.2-2.6,{M}_{i}\sim -28)\sim {10}^{-8}\,{\mathrm{Mpc}}^{-3}\,{\mathrm{mag}}^{-1}$. The total spectroscopic footprint of the BOSS DR12 is approximately 10,400 deg², and the value without masked regions due to bright stars and data that do not meet the survey requirement is 9376 deg². If there are quite a number (∼100) of quasars that have an SED and redshift similar to those of SDSS J0006+1215, that will redouble the bright end of the quasar luminosity function and lead to the statistical aberrations regarding the type I and type II ratio of the luminous AGNs at an intermediate redshift. A statistical sample study in the future would be very useful to sort out this question.

As described in Section 3.2, the decomposition of the emission-line profiles indicates the presence of outflows in emission as revealed by the blueshifted components of C iv, Lyα, N v, $[{\rm{O}}\,{\rm{III}}]\,\lambda \lambda$4959, 5007, and hydrogen Balmer lines, with a similar symmetric profile with a blueshifted velocity of 2119 km s⁻¹ and an FWHM of 4821 km s⁻¹. In this subsection, we analyze and determine the physical properties of the emission-line outflows using the photoionization synthesis code Cloudy (the latest version, last described by Ferland et al. 1998).

To investigate the physical properties for the emission-line outflows, we use the Cloudy simulations and confront these models with the measured line ratios to determine the density (n_H), column density (N_H), and ionization parameter (U). We know that the BBEL manifests itself well in C iv, Si iv+[O iv], Lyα, and N v, with the entire emission-line profile being blueshifted since the normal BELs are heavily suppressed, and the BBEL also dominates the emission of $[{\rm{O}}\,{\rm{III}}]$. However, the Si iv+[O iv] BBEL is weak, with a large uncertainty. Moreover, the resonant scattering can contribute a significant part of the N v line, and it may give rise to an anomalous strong N v line (Hamann et al. 1993; Wang et al. 2007). Even in some objects, e.g., 0105-265, almost half of the Lyα fluxes are scattered (Ogle et al. 1999). Thus, Lyα, C iv, and $[{\rm{O}}\,{\rm{III}}]$ are chosen to confront the models, and Si iv+[O iv] and the absent [C iii] are just used to examine the reasonability of the constrained parameter space. We consider that the BBEL emission region is not obscured, and adjacent lines are not urged. It is better for us to use the line ratios with large differences in ionization potential, i.e., $[{\rm{O}}\,{\rm{III}}]$λ5007/Lyα and C iv/Lyα, in order to probe different zones in a gas cloud. Furthermore, the critical density (${n}_{\mathrm{crit}}$) of $[{\rm{O}}\,{\rm{III}}]\,\lambda \lambda$4959, 5007 is $7.0\times {10}^{5}\,{\mathrm{cm}}^{-3}$, and we thus infer that the BBEL outflows should originate from the less dense part of the outflows, with a density lower than ${n}_{\mathrm{crit}}$.

We consider a gas slab illuminated by a continuum source in the extensive parameter space. The outflowing gases are assumed to have uniform density and a homogeneous chemical composition of solar values and be free of dust. The incident SED applied is a typical AGN multicomponent continuum described as a combination of a blackbody "Big Bump" and power laws.⁷ The "Big Bump" component peaks at ≈1 Ryd and is parameterized by T = 1.5 × 10⁵ K. The slope of the X-ray component, the X-ray-to-UV ratio, and the low-energy slope are set to be ${\alpha }_{{\rm{x}}}=-1$, ${\alpha }_{\mathrm{ox}}=-1.4$, and ${\alpha }_{\mathrm{UV}}=-0.5$, respectively. This UV-soft SED is regarded as more realistic for radio-quiet quasars than the other available SEDs provided by Cloudy (see the detailed discussion in Section 4.2 of Dunn et al. 2010). We calculated a series of photoionization models with different ionization parameters, electron densities, and hydrogen column densities. The ranges of parameters are $-3\leqslant {\mathrm{log}}_{10}\,U\leqslant 1$, $1\leqslant {\mathrm{log}}_{10}\,{n}_{{\rm{H}}}\,({\mathrm{cm}}^{-3})\leqslant 6$, and $18\leqslant {\mathrm{log}}_{10}\,{N}_{{\rm{H}}}\,({\mathrm{cm}}^{-2})\leqslant 24$, with a step of 0.2 dex.

We extract the simulated $[{\rm{O}}\,{\rm{III}}]$λ5007, C iv, and Lyα fluxes from the Cloudy simulations and show the line ratios $[{\rm{O}}\,{\rm{III}}]$λ5007/Lyα and C iv/Lyα by the red and green lines in Figure 3. The red and green areas show the observed 1σ uncertainty ranges of $[{\rm{O}}\,{\rm{III}}]$λ5007/Lyα and C iv/Lyα, so the overlapping region is the possible parameter space for the BBEL outflows of this object. Model calculations suggest that the gas clouds in two irregular regions with ${\mathrm{log}}_{10}\,{N}_{{\rm{H}}}\,({\mathrm{cm}}^{-2})\sim 21.0$ and ${\mathrm{log}}_{10}\,{N}_{{\rm{H}}}\,({\mathrm{cm}}^{-2})\sim 22.0$ can generate the observed line ratios of SDSS J0006+1215 (Figure 3). Fortunately, the absence of [C iii] gives the upper limit of $9.71\times {10}^{-17}\,\mathrm{erg}\,{{\rm{s}}}^{-1}\,{\mathrm{cm}}^{-2}$, and the flux ratio of [C iii]/Lyα (cyan area in Figure 4) just covers the high column density region as the reliable parameter space. It is regrettable that the density cannot be more firmly confined. The Cloudy simulation gives a density range of ${\mathrm{log}}_{10}\,{n}_{{\rm{H}}}\,({\mathrm{cm}}^{-3})\leqslant 5.8$, which is an upper limit, as $[{\rm{O}}\,{\rm{III}}]\,\lambda \lambda$4959, 5007 also suggested. In Figure 5, the modeled and observed line ratios of Si iv+[O iv] and Lyα are shown in blue. It is clear that observed Si iv+[O iv]/Lyα is overlapped with the $[{\rm{O}}\,{\rm{III}}]$λ5007/Lyα and C iv/Lyα areas, but Si iv+[O iv]/Lyα makes the possible parameter space of the outflowing gases narrower. In summary, the outflowing gases can survive in the parameter space with ${\mathrm{log}}_{10}\,{n}_{{\rm{H}}}\,({\mathrm{cm}}^{-3})\leqslant 5.8$, ${\mathrm{log}}_{10}\,U\sim -0.5$, and ${\mathrm{log}}_{10}\,{N}_{{\rm{H}}}\,({\mathrm{cm}}^{-2})\sim 22.0$. Actually, the reliable parameter-space region is essentially dynamic with the gas density.

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Based on the physical properties determined by Cloudy, we estimate the distance R of the outflows away from the central source. The ionization parameter U depends on R and the rate of hydrogen-ionizing photons emitted by the central source Q and is given by

$$\begin{eqnarray}&&U={\int }_{{\nu }_{0}}^{\inf }\displaystyle \frac{{L}_{\nu }}{4\pi {R}^{2}h\nu {n}_{{\rm{H}}}c}\,d\nu =\displaystyle \frac{Q}{4\pi {R}^{2}{n}_{{\rm{H}}}c},\end{eqnarray} \tag{ 3 }$$

in which ${\nu }_{0}$ is the frequency corresponding to the hydrogen edge, ${n}_{{\rm{H}}}$ is is the density of the outflows, and c is the speed of light. To determine the hydrogen-ionizing rate Q, we scale the UV-soft SED to the extinction-corrected flux of SDSS J0006+1215 at 5100 Å (rest frame) and then integrate over the energy range $h\mu \geqslant 13.6\,\mathrm{eV}$ of this scaled SED. This yields $Q=1.17\times {10}^{57}\,\mathrm{photons}\,{{\rm{s}}}^{-1}$. ${n}_{{\rm{H}}}$ has been estimated as ${n}_{{\rm{H}}}\leqslant {10}^{5.8}\,{\mathrm{cm}}^{-3}$. Using this Q value, together with the derived ${n}_{{\rm{H}}}$ and U, the lower limit of R can be derived to be 41 pc. The radius of broad emission line regions, ${R}_{\mathrm{BLR}}$, can be estimated using the formula based on the luminosity at 5100 Å,

$$\begin{eqnarray}&&{R}_{\mathrm{BELR}}=\alpha {\left(\displaystyle \frac{{L}_{5100}}{{10}^{44}\mathrm{erg}{{\rm{s}}}^{-1}}\right)}^{\beta }\,\mathrm{lt}-\mathrm{days},\end{eqnarray} \tag{ 4 }$$

where the parameters α and β are 30.2 ± 1.4 and 0.64 ± 0.02, respectively, given in Greene & Ho (2005). Thus, the luminosity yields ${R}_{\mathrm{BLR}}\approx 1.3$ pc. Meanwhile, the radius of the inner side of the dust torus, ${R}_{\mathrm{Torus}}$, can also be estimated based on the thermal equilibrium of the inner side of the torus as

$$\begin{eqnarray}&&{R}_{\mathrm{Torus}}=\sqrt{\displaystyle \frac{{L}_{\mathrm{bol}}}{4\pi \sigma {T}^{4}}},\end{eqnarray} \tag{ 5 }$$

where σ is the Stefan–Boltzmann constant, and $T(\sim 1500\,{\rm{K}})$ is the temperature of the inner side of the tours. Then, we get ${R}_{\mathrm{Torus}}\approx 16$ pc. Formulae in Burtscher et al. (2013) and Kishimoto et al. (2011) gave the dust sublimation radii as 5.4 and 2.0 pc, respectively, smaller than the above estimation. In any case, the outflows are located externally of the torus. This result is consistent with the supposition of our spectral qualitative analysis, i.e., the dusty torus only obscures the continuum and the normal BELR rather than the BBEL outflows.

Assuming that the outflow materials can be described as a thin partially filled shell, the average mass-flow rate ($\dot{M}$) and kinetic luminosity (${\dot{E}}_{k}$) can be derived as follows (Borguet et al. 2012):

$$\begin{eqnarray}&&\dot{M}=4\pi R{\rm{\Omega }}\mu {m}_{p}{N}_{{\rm{H}}}v,\end{eqnarray} \tag{ 6 }$$

$$\begin{eqnarray}&&{\dot{E}}_{k}=2\pi R{\rm{\Omega }}\mu {m}_{p}{N}_{{\rm{H}}}{v}^{3},\end{eqnarray} \tag{ 7 }$$

where R is the distance of the outflows from the central source, Ω is the global covering fraction of the outflows, $\mu =1.4$ is the mean atomic mass per proton, m_p is the mass of protons, N_H is the total hydrogen column density directly derived from the photoionization modeling of the outflow gases, and v is the flux-weight-averaged velocity of the outflow gases. Here, v is replaced by the blueshifted velocity of the BBEL peaks. We note that the BBELs originate from the gases outflowing along different directions with respect to the observer, and thus the observed outflow velocity of the BBEL is a sum of the projected velocities of the outflowing gases along different directions and should be a lower limit of the velocity of the outflow materials. Furthermore, we can estimate the global covering fraction for SDSS J0006+1215 by comparing the measured ${L}_{[{\rm{O}}{\rm{III}}]\lambda 5007}$ with the predicted one by the Cloudy model. In Cloudy modeling, the emergent values of ${L}_{[{\rm{O}}{\rm{III}}]\lambda 5007}$ are output with the covering fraction being assumed to be 0.05 to 1 and are shown as a function of n_H (U) and Ω in Figure 6. Meanwhile, we show the measured ${L}_{[{\rm{O}}{\rm{III}}]\lambda 5007}$ with errors in gray. The comparison gives a global covering fraction for SDSS J0006+1215 of ∼6%–15%. In the studies of BAL quasars, the fraction of BAL quasars is generally used as the global covering fraction of BAL outflow gases. The fraction is generally 10%–20% in optical-selected quasars (e.g., Trump et al. 2006; Gibson et al. 2010; Zhang et al. 2014) and $\sim 30 \%$ (e.g., Maddox et al. 2008) or even 44% (Dai et al. 2008) in NIR-selected quasars. We consider that BAL and BEL outflows may be different appearances viewed from different inclination angles but representing the same physical component, which is suggested by many works (e.g., Richards et al. 2011; Wang et al. 2011; Liu et al. 2016); the global covering fraction of BEL outflows will follow these values. The value we obtained in SDSS J0006+1215 is slightly smaller than those estimated from optical-selected BAL quasars. Thus, for the upper limit of the density ${n}_{{\rm{H}}}={10}^{5.8}\,({\mathrm{cm}}^{-3})$ and the global covering fraction $\sim 10 \%$, the kinetic luminosity and mass-loss rate are calculated as $\dot{{E}_{k}}=1.74\times {10}^{43}\,\mathrm{erg}\,{{\rm{s}}}^{-1}$ and $\dot{M}=12.23\,{M}_{\odot }\,{\mathrm{yr}}^{-1}$, respectively, for $U={10}^{-0.5}\,,\,{N}_{{\rm{H}}}\ ={10}^{22.0}\,{\mathrm{cm}}^{-3}$.

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In general, the high-velocity outflows require kinetic luminosities to be of the order of a few percent of the Eddington luminosity (e.g., Scannapieco & Oh 2004; Di Matteo et al. 2005; Hopkins & Elvis 2010); however, in the case of SDSS J0006+1215, the reported lower limit on the kinetic luminosity ($\dot{{E}_{k}}\sim {10}^{-5}\,{L}_{\mathrm{Edd}}$) is not of a sufficient value to efficiently drive AGN feedback. Note that this comparison is probably only a lower limit for the following reasons: (1) The weight-averaged velocity v we use in Equation (5) is a sum of the projected velocities of the outflowing gases along different directions, the value of which is underestimated and should be a lower limit of the outflow velocity. (2) The distance of the outflows, R, is also a lower limit, and the outflow gases perhaps survive at greater distances from the central source.

As the only narrow emission line in SDSS J0006+1215, the Lyα narrow line presents strong emission. In theory Lyα photons scatter in neutral hydrogen until they either escape or are absorbed by dust grains. For SDSS J0006+1215, possible explanations are the NELR emission, the star formation in host galaxy, or the scattering of the obscured Lyα emission by the outflows. Before proceeding further, we first discuss whether the NELR and star-forming contribution are preferred in SDSS J0006+1215 through other relevant narrow lines. If Lyα of SDSS J0006+1215 is the narrow emission line from the NELR, this situation can be confirmed through the presence of high-ionization lines, e.g., C iv in the rest-frame UV, or other lines such as He ii that may also indicate AGN activity. The typical relative intensities of Lyα and C iv narrow emission lines in Seyfert 2 spectra are 55 and 12, respectively (from Ferland & Osterbrock 1986). Under this condition, the derived flux of the C iv narrow line is $\sim 4.54\times {10}^{-17}\,\mathrm{erg}\,{{\rm{s}}}^{-1}\,{\mathrm{cm}}^{-2}$. Like the Lyα narrow line, we use one Gaussian with a width of 429 km s⁻¹ to model the theoretical C iv narrow line, which is shown via the green line in the top panel of Figure 7. Apparently, the theoretical C iv narrow line would not appear in the spectrum of SDSS J0006+1215; otherwise, it should be detected at $\gtrsim 7\sigma$.

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With the assumption that the Lyα emission is produced by photoionization by stars and the absence of extinction, one can estimate the Hα flux while assuming a case B recombination theory (Osterbrock 1989), ${f}_{\mathrm{esc}}(\mathrm{Ly}\alpha )\,$ $=f(\mathrm{Ly}\alpha )/(8.7\times f({\rm{H}}\alpha ))$, where ${f}_{\mathrm{esc}}(\mathrm{Ly}\alpha )$ is the Lyα escape fraction, $f(\mathrm{Ly}\alpha )$ is the observed Lyα flux, and $f({\rm{H}}\alpha )$ is the Hα flux. When Lyα photons are 100% escaped, we obtain the flux and luminosity of Hα for the H ii region, $f({\rm{H}}\alpha )=(2.39\pm 0.10)\ \times {10}^{-17}$ erg s⁻¹ cm⁻² and ${L}_{{\rm{H}}\alpha }=(3.20\pm 0.13)\times {10}^{42}\,\mathrm{erg}\,{{\rm{s}}}^{-1}$. Following the related star formation rate $\mathrm{SFR}({M}_{\odot }\,{\mathrm{yr}}^{-1})\ =7.9\,\times \,{10}^{-42}\,{L}_{{\rm{H}}\alpha }\,(\mathrm{erg}\,{{\rm{s}}}^{-1})$ (Kennicutt 1998), SFR is estimated to be $\mathrm{SFR}=25.28\pm 1.03\,{M}_{\odot }\,{\mathrm{yr}}^{-1}$. When we use the profile of the Lyα narrow line to model the theoretical Hα (pink line in the bottom panel of Figure 7), the height of this Gaussian profile is 0.26 erg s⁻¹ cm⁻² Å⁻¹, which is commensurate with the fluctuations of the NIR spectrum. Previous studies find that ${f}_{\mathrm{esc}}(\mathrm{Ly}\alpha )$ is not constant and spans a wide range of values. At a similar redshift to SDSS J0006+1215, the average escape fraction from various methods is 5.3% ± 3.8% by performing a blind narrowband survey in Lyα and Hα (Hayes et al. 2010), 29% at $1.9\leqslant z\leqslant 3.5$ with the comparison between Lyα flux and dust-corrected UV continuum (Blanc et al. 2011), $\gt 7$% at z = 2.1 and 3.1 with the comparison between Lyα flux and X-ray flux (Zheng et al. 2012), and ∼12%–30% at z = 2.2 with the comparison between Lyα and Hα luminosity (Nakajima et al. 2012). In the bottom panel of Figure 7, we also show the theoretical Hα profiles with ${f}_{\mathrm{esc}}(\mathrm{Ly}\alpha )=90 \%$, 80%, 70%, 50%, 30%, and 10% in sequence. It becomes apparent that there is a threshold of almost no possibility of the existence of the Hα narrow line superposed on the Hα narrow line; however, it also cannot be ruled out by the low spectrum quality of the Hα regime of SDSS J0006+1215. Thus, the scattering of the obscured Lyα emission by the outflows is the most promising option.

Alternately, the NELR in AGNs is the largest spatial scale for the ionizing radiation from the central source. In the case of the NELR, the Lyα emission comes from a spatially extended region, so at least to some extent physical and kinematic distributions can be mapped out directly. In comparison to the NELR, the star-forming region in galaxies is generally of compact morphology and typically characterized by a small but resolved "core" with kiloparsec scales rather than the axisymmetric bi-conic ionized region. The high-resolution Lyα imaging will also clearly demonstrate the presence or location of the extent structures. For the possible participation of scattering, spectropolarimetric observations of the Lyα line will seek final clarification.