Spectroscopy of Broad Absorption Line Quasars at 3 ≲ Z ≲ 5. I. Evidence for Quasar Winds Shaping Broad/Narrow Emission Line Regions

We began by searching for luminous BAL QSOs from the DR12 quasar catalog (Pâris et al. 2017) with absorption index (AI; see Pâris et al. 2017) (C iv) ≳ $8000$ km s⁻¹ at $z\gt 4.3$. To reliably measure the trough width and depth, quasars with apparent overlapping troughs and heavy reddening imprinted on the blueward of the C iv emission line were excluded. Four BAL QSOs remained after this selection. We also include two more newly discovered BAL QSOs at $z\gt 4$ that were reported by recent studies (Yi et al. 2015; Wang et al. 2016).

Due to the rarity of high-AI (C iv) BAL QSOs at $z\gt 4$, we added six BAL QSOs showing relatively strong BAL troughs (2000 km s⁻¹ < AI < 8000 km s⁻¹) and five comparison BAL QSOs with weak BAL troughs (AI < 2000 km s⁻¹) at $2.5\lt z\lt 4$ to our sample. Considering strong telluric absorption windows in the near-IR wavelengths (i.e., 1.35–1.45 and 1.8–1.9 μm), a proper redshift cut was made to keep the Mg ii and/or Hβ emission lines away from these windows. In total, this includes 11 BAL QSOs at $2.5\lt z\lt 4$. Together with the six BAL QSOs at $4.3\lt z\lt 5$ from the first stage and another five BAL QSOs at $3\lt z\lt 4$ from Zuo et al. (2015), our final sample consists of 22 BAL QSOs with newly and previously obtained near-IR spectra.

The basic descriptions of these BAL QSOs are tabulated in Table 2, where most of these measurements are retrieved from Pâris et al. (2017). The systemic redshift values are determined by the [O iii], Hβ, or Mg ii lines from near-IR spectra, depending on their appearance. We visually inspected all spectra before performing quantitative measurements. We identified 12 LoBAL QSOs in this sample. Another three cannot be identified due to low signal-to-noise ratio (S/N) spectra and/or an incapability of identifying LoBALs in strong telluric absorption windows. The LoBAL fraction, therefore, is 54.5% (12/22) or potentially higher due to unidentifiable LoBALs. We do note that this high fraction is likely caused by our preference in selecting strong BAL QSOs to construct the sample.

Table 2.  C iv BAL Properties of 22 BAL QSOs in the Sample

Name	R.A.	Decl.	AI (C iv)	vmin	vmax	vcen	EW	${d}_{\mathrm{BAL}}$	z	Type
	(J2000)	(J2000)	($\mathrm{km}\,{{\rm{s}}}^{-1}$)	($\mathrm{km}\,{{\rm{s}}}^{-1}$)	($\mathrm{km}\,{{\rm{s}}}^{-1}$)	($\mathrm{km}\,{{\rm{s}}}^{-1}$)	(Å)
014049.18−083942.5	25.20492	−8.66181	1760 ± 12	23134	28496	25857	11.9 ± 0.3	0.42	3.717	Hi
015048.83+004126.2	27.70346	0.69061	538 ± 4	2913	4005	3470	3.4 ± 0.2	0.57	3.701	Hi
021646.94−092107.3	34.19561	−9.35204	2697 ± 15	11695	23009	13740	19.4 ± 0.6	0.58	3.732	Hi
074628.70+301419.0 $\unicode{x029EB}$	116.61961	30.23863	11060 ± 45	7016	30120	9600	68.1 ± 0.7	0.81	3.173	Lo
APM08279	127.92375	52.75486	1276 ± 97	4125	10607	7587	10.0 ± 0.9	0.29	3.911	Hi
083718.63+482806.5	129.32764	48.46848	8068 ± 48	2645	15299	8141	48.3 ± 0.4	0.73	3.64	Lo
084401.95+050357.9 $\unicode{x029EB}$	131.00813	5.06608	9173 ± 60	4656	28197	13935	59.2 ± 0.5	0.48	3.36	Lo
091935.36+193834.7	139.89737	19.64297	13189 ± 80	1077	22360	10304	79.2 ± 0.6	0.71	3.541	Lo
103256.70+514014.5	158.23628	51.6707	11018 ± 66	1231	27751	9989	69.6 ± 0.7	0.62	3.925	Lo?
115023.57+281907.4	177.59825	28.31875	788 ± 5	1109	2549	1832	4.92 ± 0.3	0.63	3.12	Hi
120447.15+330938.7 $\unicode{x029EB}$	181.19647	33.16077	12430 ± 76	6048	29166	16577	76.3 ± 0.5	0.63	3.652	Lo
121027.62+174108.9 $\unicode{x029EB}$	182.61508	17.68581	6484 ± 87	14122	29000	20965	41.8 ± 0.7	0.5	3.831	Lo
123754.82+084106.7	189.47844	8.68522	2938 ± 18	1612	6109	3710	17.5 ± 0.3	0.74	2.897	Hi
125958.72+610122.9	194.99469	61.02303	478 ± 3	3375	4941	4238	3.76 ± 0.2	0.39	3.572	Hi
141546.24+112943.4	213.94267	11.49540	4896 ± 32	3209	13804	7533	31.3 ± 0.3	0.56	2.556	Lo
150332.17+364118.0	225.88404	36.68833	4387 ± 20	3924	28213	5232	32.3 ± 0.6	0.76	3.261	Lo
012247.34+121624.0 $\unicode{x029EB}$	20.69730	12.27330	14360 ± 1900	5886	30479	14438	76.1 ± 8.9	0.68	4.82	Lo
092819.28+534024.1 $\unicode{x029EB}$	142.08037	53.67337	9711 ± 49	8035	27634	9445	59.7 ± 0.8	0.85	4.47	Lo
104846.63+440710.7 $\unicode{x029EB}$	162.19431	44.11966	12258 ± 74	4820	25899	13520	74.3 ± 0.6	0.67	4.39	Lo
133529.45+410125.9	203.87271	41.02388	5143 ± 32	16436	26873	20803	32.0 ± 0.4	0.59	4.3	Lo
151035.29+514841.0	227.64705	51.81141	6790 ± 28	5160	21578	5749	43.0 ± 2	0.77	5.096	Lo?
163810.38+150058.2	249.54325	15.01617	5030 ± 29	21700	32700	26850	31.7 ± 3	0.55	4.84	Lo?

Note. Here v_cen is a flux-weighted centroid velocity in the C iv BAL trough; v_min and v_max are the corresponding minimum and maximum velocities, respectively; EW is the equivalent width; and ${d}_{\mathrm{BAL}}$ is the average depth across the entire C iv BAL trough. Hi/Lo represent high-/low-ionization BALs, respectively. The filled diamonds indicate the seven QSOs with relatively high S/N and ${v}_{\min }\gt$ 3000 km s⁻¹ that are used to produce the composite spectra of strong BAL QSOs (see Section 3.5). The Lo? symbol represents an unidentifiable LoBAL due to the lack of wavelength coverage or strong contamination from telluric absorption.

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Our optical spectra in the sample are primarily obtained from the DR14 SAS website⁹ by matching the coordinates of the selected BAL QSOs to source positions within a 3'' tolerance. These spectra are corrected for calibration errors that result from atmospheric differential refraction and fiber offsets during observations (see Margala et al. 2016 for details).

Additional optical spectroscopic observations were carried out during several runs from 2015 to 2018 using the Yunnan Faint Object Spectrograph and Camera mounted on the Lijiang 2.4 m telescope (LJT/YFOSC; Fan et al. 2015). The FWHM of the YFOSC imaging data varies mostly in the range from 10 to 25; we thus chose a slit of 18 for the spectroscopic observations. Each night the neon/helium arc lamps were taken for wavelength calibration and a spectrophotometric standard star was observed, followed by the target at similar airmass and position. All of the calibration data, including bias, sky flat fields, and internal lamp flats, were obtained at the beginning/end of each observing night. The data reduction was performed by IRAF packages following standard reduction steps for bias/sky subtractions, flat-fielding correction, and flux calibration.

The near-IR spectroscopic observations of all objects tabulated in Table 2 were carried out with the TripleSpec spectrograph (Wilson et al. 2004) at the Palomar Hale 200 inch telescope (P200/TripleSpec; Wilson et al. 2004). TripleSpec provides a wide wavelength coverage from 0.95 to 2.46 μm at an average spectral resolution of $R\sim 2700$, allowing simultaneous observations in the JHK bands. A high Fowler depth ($6\sim 10$) is set for faint objects to optimize the readout noise after each single exposure. A slit width of 1'' and the ABBA dither pattern along the slit were chosen to improve the sky subtraction for all targets throughout these observational runs. Total exposure times varied between 24 and 60 minutes, depending on the apparent magnitudes and weather conditions. During each night, several telluric A0V standard stars were observed at a similar airmass compared to that of the target.

The data reduction for the spectroscopic data from TripleSpec is performed using the modified IDL-based Spextool3 package (Cushing et al. 2004), as described in detail from Zuo et al. (2015). The standard process includes sky background subtraction, flat-field correction, wavelength identification, and telluric correction. Based on the reduced near-IR spectra, we determine systemic redshift using the [O iii], Hβ, or Mg ii emission lines, ordered by descending priority when available.

The object J0122+1216 was discovered as a quasar using the Lijiang 2.4 m telescope (Yi et al. 2015) in optical spectroscopy; later, it was further identified as a LoBAL QSO at z = 4.82 using near-IR spectroscopy (Yi et al. 2017). Recently, this LoBAL QSO was investigated by Jeon et al. (2017), where their measurements of the luminosity and BH mass are consistent with those from Yi et al. (2017). As the quality of near-IR spectra obtained by the Magellan telescope (see Jeon et al. 2017) is much higher than that from Yi et al. (2017), we use their near-IR spectra (in private communication) for J0122+1216 in this work.

One of the brightest quasars is APM 08279; its brightness is due to gravitational lensing (Irwin et al. 1998). Another lensed quasar showing a "cloverleaf" structure (Magain et al. 1988) is J1415+1129. Since previous studies reported a wide range of possible magnification factors (4–100) for this quasar, for simplicity, we choose to use the bolometric luminosity, assuming that it is equal to the Eddington luminosity limit.

Similar to previous studies (e.g., Grier et al. 2016; Yi et al. 2019a), we adopt a reddened power-law model to fit the continuum with a nonlinear least-squares fitting algorithm. We modeled the continuum in each spectrum using an SMC-like reddened power-law function from Pei (1992) with three free parameters, including the amplitude, power-law index, and extinction coefficient. The initial continuum fit windows are composed of relatively line-free (RLF) regions. However, these default windows do not always reasonably sample the continuum for all quasars in the sample, so they are adjusted where necessary to reach an acceptable fit. In particular, apparent emission/absorption lines present in the default windows among all spectra have been excluded.

We mask pixels flagged by "and-mask" from the SDSS pipeline before the continuum fit. All spectra are then converted to the rest frame using the redshifts determined by the [O iii], Hβ, or Mg ii lines from the near-IR spectra. Some emission and/or absorption features appear to be frequently present in the same fitting regions. Therefore, we adopt a sigma-clipping algorithm that consists of fitting the reddened power-law function to the RLF windows for each spectrum and then rejecting data points that deviate by more than 3σ from the continuum fit for each pixel in each window. The final continuum fit is obtained by refitting the remaining data points. We do not attach physical meaning to the values of $E(B-V)$ derived from our fits, since there is a degeneracy between the UV spectral slope and intrinsic reddening. The uncertainty of the continuum fit is obtained via a Monte Carlo approach through randomizations of spectral errors in the RLF windows. Then, quantities such as AI (C iv), minimum/maximum trough velocities, and equivalent width (EW) are measured based on the reddened power-law fits (see Table 2).

The near-IR spectroscopic observations were carried out under nonphotometric conditions. In addition, the cross-dispersion mode of spectroscopy may lead to a large uncertainty for near-IR spectral flux calibration, so an absolute flux calibration is required for reliable measurements of QSO properties. Since quasars usually show less variability at redder wavelengths, we use the converted photometric flux at SDSS i/z; 2MASS J/H/K, if it existed; and WISE 1/2 to scale the spectral flux. Although the photometric and spectroscopic data were not simultaneously observed, for simplicity, we assume no significant continuum variability between the photometric and spectroscopic epochs for all QSOs in the sample. For the BAL QSOs without J/H/K magnitudes in our sample, we select reference BAL QSOs with J/H/K magnitudes and similar optical spectral shapes to our targets from DR14. We then use the models that are best fitted for the continua of the reference QSOs to fit our targets with SDSS-i/z and WISE-1/2 magnitudes.

As an example demonstrated in Figures 1 and 2, two BAL QSOs were finally chosen as a reference to guide the local spectral energy distribution (SED) fit for the target (J120447.15+330938.7) without near-IR photometric observations. The SEDs in the two matched BAL QSOs appear to be redder than non-BAL QSOs, most likely due to intrinsic reddening and Lyα-forest absorption at high redshift. We only account for the local SED fit between 1600 and 10000 Å in the rest frame, where a power-law or reddened power-law continuum shape is expected. A long-wavelength cut is necessary, since the hot-dust reprocessing starts to dominate the QSO SED at $\lambda \gt 10000\,\mathring{\rm A}$. The local SEDs of the two reference QSOs can be well fitted by the power-law and reddened power-law models, respectively (see Figure 2). Finally, we fit the local SED of our target using the above two models that are applied to the SED fitting process of the two reference QSOs in the same wavelength range (see Figure 3). Their differences are taken as propagated uncertainties for the placement of the continuum. As the uncertainty is dominated by the above procedures, we did not account for additional uncertainties, such as the uncertainty generated from Monte Carlo simulations.

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In general, we found that the 5100 Å flux density derived from a power-law fit is quite close to that from a reddened power-law fit, while a larger deviation may appear at 3000 Å for these quasars without near-IR photometric observations in the sample. Thus, the continuum placement at 5100 Å is our preferential choice for the conversion to the bolometric luminosity using the nominal factors (5.18 for 3000 Å and 9.26 for 5100 Å, respectively; see Shen et al. 2011). Finally, the absolute flux calibration is corrected by the Galactic extinction using the Rv = 3.1 Milky Way extinction model (Cardelli et al. 1989) and a corresponding Av value (Schlafly & Finkbeiner 2011).

Emission line properties are measured by fitting the local regions around the Hβ and/or Mg ii emission lines with a pseudocontinuum+line model (see inset panels in Figure 3). Strong telluric absorption windows are masked out in the near-IR spectra before fitting. For consistency, we adopt a similar method of continuum fitting and emission line modeling from Schulze et al. (2017), which is illustrated as follows.

• 1.  
  The continua around the Mg ii and Hβ emission lines are fitted by the model including a power-law function+optical/UV Fe ii template (Boroson & Green 1992; Salviander et al. 2007). We do not consider the Balmer continuum in this work.
• 2.  
  The BEL fitting is then based on the pseudocontinuum-subtracted spectrum. No more than one narrow and three broad Gaussians are adopted to fit the BELs. We mask out absorption troughs during the fitting around the Mg ii emission line if its profile is affected by these troughs.
• 3.  
  Due to the weakness of the [O iii] emission line in the sample and spectral quality, the [O iii] emission line is fitted by one Gaussian for most quasars in the sample. The upper limits on [O iii] blueshift and [O iii] FWHM are set by 1000 and 2000 $\mathrm{km}\,{{\rm{s}}}^{-1}$, respectively, to account for possible broad [O iii] components that may be associated with quasar outflows.
• 4.  
  Since the widely used Boroson & Green (1992) template may fail to provide a satisfactory Fe ii fit for all spectra, following Bischetti et al. (2017), we add an additional two Gaussians during the fit for those objects with strong Fe ii emission at ∼4940 and ∼5040 Å, respectively.

The upper limit on the velocity width (2000 km s⁻¹) used for the [O iii] line fit is obviously larger than the typical velocity width ($\lt 900$ km s⁻¹) of narrow emission lines (NELs). However, this upper limit is reasonable, since the signatures of NEL outflows appear to be common in the luminous quasar population, particularly at high redshifts (e.g., Netzer et al. 2004; Harrison et al. 2014; Bischetti et al. 2017). The wavelength separation between the [O iii] λ5007 and [O iii] λ4960 components has been constrained to the range from 45  to 50 Å in the rest frame, with the ratio of their amplitudes constrained between 2.5:1 and 3:1. Limited by the quality of these near-IR spectra, we use only one Gaussian to fit the [O iii] λ5007 emission line for the majority in the sample, except for three QSOs with apparent broad [O iii] profiles and high S/Ns (J0844+0503, J1259+6101, and J1415+1129; see Figure 4). In particular, we applied two methods to decompose the plateau-like profile around the Hβ + [O iii] region in J0844+0503. One is followed by the above procedures; the other is based on the introduction of extremely blueshifted (>1700 km s⁻¹) and broad [O iii] components (e.g., Coatman et al. 2019; Perrotta et al. 2019). The two methods yield a similar [O iii] EW including both narrow and broad Gaussians, but we favor the latter, since this quasar has subrelativistic BAL outflows that may affect its NEL region (e.g., Faucher-Giguère et al. 2012). For the measurement of the FWHM of the Hβ emission line, we consider all broad Gaussians (up to three components) during the fitting process.

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Spectral fits around the Mg ii emission line, however, are more challenging for various reasons. First, there is no available Mg ii-based size–luminosity relation such as that derived from the Hβ line from reverberation mapping campaigns (e.g., Kaspi et al. 2000; Bentz et al. 2013), indicating that BH mass estimates using the Mg ii line may be less reliable than those using the Hβ line. Second, the Mg ii line profile is potentially affected by absorption in our sample, especially for these objects showing deep and wide C iv BAL troughs. Although the Mg ii BAL troughs are generally weaker and narrower than those found in C iv, they are often attached on the Mg ii emission line profile, making their identifications more difficult than those of C iv BAL troughs. Third, Popovic et al. (2019) reported that the Mg ii BEL appears to originate from two subregions: one contributes to the line core that is probably virialized, and the other is associated with an emitting region characterized by outflows and inflows nearly orthogonal to the disk, which mostly contributes to the emission of the Mg ii broad line wings. Fourth, whether or not one considers the narrow component during the Mg ii line decomposition may significantly affect the FWHM measurement of the broad Mg ii line. Other challenges arise from different recipes of the single-epoch relation used in previous studies, the possibility of Mg ii emission line blueshift (cannot be determined without the aid of Hβ), and the correction for the Mg ii-based BH mass (e.g., Woo et al. 2018), and these issues need to be considered as well. Therefore, some caveats must be kept in mind when using the Mg ii broad line for the BH mass estimation, especially in these quasars with extremely broad Mg ii emission lines (FWHM > 6000 $\mathrm{km}\,{{\rm{s}}}^{-1}$; e.g., Yi et al. 2019b) and/or strong blue asymmetric profiles in the Mg ii emission line (e.g., Plotkin et al. 2015).

To mitigate the contamination of absorption and reconstruct the Mg ii emission line in a reasonable sense, we mask out these absorption regions through visual inspection. The peak position of the Mg ii emission line is constrained to the wavelength range between 2796  and 2803 Å. No more than one narrow and three broad Gaussian components are taken into account during the Mg ii emission line fit. Since the spectral quality does not allow us to decompose the Mg ii line in a reliable way, we did not exclude the narrow component for the FWHM Mg ii measurement, even if it exists in some cases. Therefore, the FWHM of the Mg ii emission line is determined by combining both the broad and narrow (if it exists) Gaussian components after the spectral fitting. This would not bias our statistical results, since it causes a systematic underestimation of the FWHM Mg ii for each quasar in the sample.

The whole spectral fitting process for an individual object is demonstrated in Figure 3, in which we scaled the optical/near-IR spectra by a ratio between the spectral flux and the continuum fit based on the converted photometric flux. The local SED fits derived from both the power-law and reddened power-law functions are demonstrated by the cyan and red dashed lines, respectively. All of the spectral fitting results around the Mg ii and/or Hβ emission lines in the sample are shown in Figure 4.

At high redshift, the single-epoch scaling relation is the primary method adopted to estimate BH mass in quasars. A general equation of the relation can be expressed as follows:

$$\begin{eqnarray}&&\mathrm{log}\left(\displaystyle \frac{{M}_{\mathrm{BH}}}{{M}_{\odot }}\right)=a+b\times \mathrm{log}\left(\displaystyle \frac{\lambda {L}_{\lambda }}{{10}^{44}{\mathrm{ergs}}^{-1}}\right)+2\mathrm{log}\left(\displaystyle \frac{\mathrm{FWHM}}{{\mathrm{kms}}^{-1}}\right).\end{eqnarray} \tag{ 1 }$$

There are several parameter configurations ($a,b$) in terms of the scaling relation from the literature (for details, see Section 3.7 in Shen et al. 2011). As a sample study, it is mandatory to adopt the same method to avoid introducing additional uncertainties for the measurements of each object. Throughout this work, for Hβ, we use the configuration of $a=0.91,b=0.5$ following Vestergaard & Peterson (2006); for Mg ii, we use the configuration of $a=0.86,b=0.5$ following Vestergaard & Osmer (2009).

To quantify the measurement errors, we randomize spectral errors in the line fitting window via 100 Monte Carlo simulations and consider the standard deviation as the measurement error for each quasar. The typical measurement errors are small, only ∼0.1 dex (see Table 3). However, we do note that the main uncertainties are dominated by systematic errors, which amount to ∼0.4 dex or even higher according to previous studies (e.g., Shen et al. 2011).

There are seven QSOs (∼32%) in our sample having strong C iv BAL features (C iv BAL EW > 60 Å) with an average S/N > 7 at 3000  or 5100 Å. All of them are LoBALs and exhibit large C iv BEL blueshifts measured by the apparent C iv BEL peak. This method yields only a lower limit on the C iv BEL blueshift due to the blueshifted BAL effect. In addition, all seven QSOs have trough velocity widths of ${\rm{\Delta }}v\gt 10,000$ km s⁻¹ and BAL velocities of ${v}_{\max }\gt 20,000$ km s⁻¹ along our line of sight, indicating powerful nuclear outflows that may be capable of affecting their host galaxies via an energy-conserving expansion process (e.g., Faucher-Giguère et al. 2012). We thus construct a composite spectrum from these QSOs to investigate similarities and differences in the continuum and emission line properties compared with the non-BAL composite from Zuo et al. (2015) matched in luminosity and the non-BAL composite from Vanden Berk et al. (2001).

These optical/near-IR spectra used to construct the composite spectrum cover a wide wavelength range from 900  to 5500 Å in the quasar rest frame. All selected spectra are normalized at 1600 Å for the optical spectra and 3600 Å for the near-IR spectra. We use the geometric mean among these normalized spectra to produce stacked spectra as shown in Figure 5, where the composite spectra at $900\,\mathring{\rm A} \lt \lambda \lt 1700$ Å (top panel) and $1800\,\mathring{\rm A} \lt \lambda \lt 5500$ Å (bottom panel) are generated by the optical and near-IR spectra, respectively. Since the near-IR spectra of the seven BAL QSOs have different redshifts ranging from 3.179 to 4.82, the composite spectra have some breaks due to the cut of the telluric absorption windows.

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The BAL composite spectrum shows significant intrinsic reddening at $\lambda \lt 2000\,\mathring{\rm A}$, though it appears to be largely free of reddening at $\lambda \gt 4000\,\mathring{\rm A}$. The conspicuous differences between the BAL and non-BAL composites at ${\lambda }_{\mathrm{rest}}\lt 1600$ Å could be due primarily to strong BAL absorption in C iv, Si iv, N v+Lyα, and O vi+Lyβ at a similar velocity, plus stronger intergalactic medium absorption at higher redshift. After scaling the two non-BAL composites to the BAL composite, we found that all of them have a similar Fe ii emission line profile at $4500\mathring{\rm A} \lt {\lambda }_{\mathrm{rest}}\,\lt$ 4700 Å, suggesting that optical Fe ii emission may not depend on redshift, luminosity, and the presence of outflows. After performing a spectral fit to the Hβ+[O iii] region (see Figure 5), we found a narrow unshifted (cyan) and broad blueshifted [O iii] doublets (magenta). In addition, the entire Hβ emission line profile can be well fitted by a single, almost unshifted Gaussian and a very broad redshifted Gaussian, supporting the idea that the Hβ emission line in BAL QSOs can serve as an equally reliable BH estimator as in non-BAL QSOs. The BAL composite shows an apparently wider Hβ emission line profile than the two non-BAL composites, probably signaling an intrinsic difference between the two quasar populations (see the separation between Populations A and B using FWHM Hβ from Sulentic et al. 2000). However, when taking a close-up look at the inset panel of Figure 5, the broadening effect of the Hβ emission line in the BAL composite appears to be caused by the lack of peaky profiles in both Hβ and [O iii] compared to the two non-BAL composites. This implies that the presence of outflow may predominantly affect the NELs that originated from large-scale regions. We discuss this issue in Section 5.

In good agreement with the finding from Yi et al. (2017), our composite spectrum of strong BAL QSOs reveals a striking blueshift among all of the high-ionization BELs (∼3100 $\mathrm{km}\,{{\rm{s}}}^{-1}$, possibly higher due to the blueshifted BAL effect) and nearly black absorption troughs, which in turn provides evidence in support of outflows affecting the high-ionization BEL regions. Moreover, the composite spectrum shows significant reddening at $\lambda \lt 3000$ Å and weak [O iii] emission. As a comparison, less than 25% of the non-BAL QSOs from Zuo et al. (2015) matched in redshift and luminosity show comparable weakness of the [O iii] emission. In addition, the average C iv BEL blueshift is ∼600 km s⁻¹  from Zuo et al. (2015), within which only one quasar has a C iv BEL blueshift larger than 2000 km s⁻¹ (in private communication). It is worth noting at this point that all of the above studies do not have simultaneous optical/near-IR spectroscopic data, which may potentially lead to larger uncertainties in the C iv BEL blueshift than the values given above. However, the C iv BEL blueshift could remain unchanged even if the C iv BEL flux varies dramatically from epoch to epoch (e.g., Ross et al. 2019).

Previous studies based on non-BAL QSO samples found that the FWHM distribution of the Mg ii BEL is (linearly) correlated with that of the Hβ BEL at a high significance level (e.g., Trakhtenbrot & Netzer 2012; Zuo et al. 2015); thus, the Mg ii BEL is usually considered as an alternative BH mass estimator in good agreement with the Hβ line in the non-BAL population.

There are 13 objects in our sample with simultaneous observations of the Mg ii and Hβ emission lines that provide an opportunity to test whether this correlation holds in the luminous BAL QSOs at high redshift. Four quasars (marked by open red squares in the top panel of Figure 6) in our sample have relatively low-S/N spectra and/or broad absorption attached on the Mg ii line, which may bias the statistical results. We checked the correlation after excluding them and found that the results are consistent with the subsample of 13 objects via the Spearman test. Therefore, we use the entire subsample of 13 BAL QSOs in our analyses below.

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We choose three non-BAL comparison samples (Zuo et al. 2015; Coatman et al. 2017; and Vietri et al. 2018; hereafter Zuo15, C17, and V18, respectively) within a similar range of luminosity and redshift to our sample. The sample of Zuo15 includes 24 non-BAL QSOs at a similar redshift and luminosity to our sample, among which 22 have the coverage of both the Hβ and Mg ii emission lines. The near-IR spectra from Zuo15 and our sample were obtained by the same instrument (P200/TripleSpec), largely alleviating uncertainties caused by different instruments for the comparisons. The comparison sample of C17 consists of 230 non-BAL QSOs at $1.5\lt z\lt 4$, from which we select 19 within the same redshift and luminosity ranges to our sample ($z\gt 2.56$ and 46.5 < log${L}_{5100}\lt 47.3$). Additionally, we select 13 non-BAL QSOs at $z\sim 3.3$ and log${L}_{5100}\sim 47$ from Vietri et al. (2018) to construct the V18 comparison sample.

According to the single-epoch scaling relation, the BH mass measurement is proportional to the square of FWHM and root square of monochromatic luminosity (the former is an indirect measurement depending on sophisticated analyses, as roughly mentioned in Section 3.3), and it is essential to investigate the distributions of the two quantities in our sample and compare them with other studies. As shown in the top panel of Figure 6, the distribution of FWHM Mg ii versus FWHM Hβ in this work is broadly consistent with that from Zuo et al. (2015) via orthogonal distance regression fits¹⁰ (the red and green dashed lines are the two fits for the two samples, respectively). Although there is no significant difference in the distribution of FWHM Mg ii from the two samples, as determined via a two-sample Kolmogorov–Smirnov (K-S) test (${p}_{\mathrm{KS}}=0.23$), a difference may exist in the distribution of FWHM Hβ (${p}_{\mathrm{KS}}=0.1$). In addition, both FWHM distributions of the two samples deviate from the one-to-one line (black), with more objects showing FWHM Hβ larger than FWHM Mg ii. However, the FWHM distribution between the two different BELs from our sample is less correlated compared with Zuo15, which is confirmed via the Spearman test ($r=-0.09,p=0.775$ and $r=0.67,p=0.0006$ for our sample and Zuo15, respectively). The lack of correlations in our sample is likely due to strong nuclear outflows traced by BALs and/or BEL blueshifts when noticing that both samples have a similar luminosity and redshift range.

Conversely, the two samples follow a similar linear relation in the distribution of 5100 versus 3000 Å monochromatic luminosity (see red/green dashed lines in the bottom panel of Figure 6). Specifically, we found strong correlations for both samples via the Spearman tests ($r=0.92,p={10}^{-5}$ and $r=0.75,p=5\times {10}^{-5}$ for this work and Zuo15, respectively), which are consistent with previous studies based on non-BAL QSOs. The similarity in the luminosity relation and difference in the FWHM relation between the BAL and non-BAL samples, to some extent, support the scenario where strong BAL outflows are affecting the (Mg ii) BEL regions.

Unlike the investigation and comparison of direct measurements in the above subsection, here we have to use derived measurements to explore the effect of outflows, due to the lack of simultaneous observations or reported Mg ii and Hβ lines from the C17 and V18 studies. We use the 16 BAL QSOs at $z\lt 4$ from our sample and compare them with the above three non-BAL QSO samples based on near-IR spectroscopy in a similar luminosity and redshift range to our sample (see Figure 7). Based on the two-sample K-S test, there is no statistically significant difference in the distributions of Eddington ratios between the BAL and non-BAL samples; but potential differences may exist in the distribution of BH masses (${p}_{\mathrm{KS}}=0.14$) between this work and Zuo15, tentatively hinting that the growth of SMBHs in our sample is regulated by BAL outflows. Since the K-S test is incapable of finding differences in the correlation strength between different parameters, and our sample, at first glance, appears to have no correlation in the distribution compared to apparent correlations in the other three matched comparison samples, we perform the Spearman test to quantify this difference. We found strong correlations in all three non-BAL comparison samples at a highly significant level but only a tentative correlation in our sample (see Figure 7 and Table 4).

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Table 4.  Near-IR Spectroscopic Studies of BAL QSOs at $z\gtrsim 3$

	L5100a	L5100b	FWHM Hβa	FWHM Hβb	${\lambda }_{\mathrm{Edd}}$
L3000	($0.92,{10}^{-5}$)	($0.75,5\times {10}^{-5}$)	⋯	⋯	⋯
FWHM Mg ii	⋯	⋯	($-0.09,0.775$)	($0.67,0.0006$)	⋯
${M}_{\mathrm{BH}}^{a}$	⋯	⋯	⋯	-	(0.552, 0.026)
${M}_{\mathrm{BH}}^{b}$	⋯	⋯	⋯	⋯	($0.831,2\times {10}^{-6}$)
${M}_{\mathrm{BH}}^{c}$	⋯	⋯	⋯	⋯	($-0.637,0.003$)
${M}_{\mathrm{BH}}^{d}$	⋯	⋯	⋯	⋯	($-0.802,9\times {10}^{-4}$)

Note. Spearman test results ($r,p$) of direct (L₅₁₀₀ and FWHM) and derived (${M}_{\mathrm{BH}}$ and ${\lambda }_{\mathrm{Edd}}$) measurements from different samples, in which $a,b,c,d$ represent this work, Zuo15, C17, and V18, respectively.

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The distributions of BH mass versus Eddington ratio above are unlikely to be biased because all of them are derived from the same BH mass estimator (Hβ), which is largely free of the effects of intrinsic reddening and absorption. Despite a small number of quasars in the four samples, the difference in the correlation strength between the non-BAL and BAL QSO samples is unlikely to be caused by the difference in sample size, as the V18 (blue) sample consisting of fewer QSOs shows an even stronger correlation than those from C17 and our sample (the number of quasars with Hβ-based BH masses in Z15, C17, V18, and this work are 22, 19, 13, and 16, respectively). Therefore, we attribute such a difference to the effects of substantial outflows traced by strong BALs and large C IV BEL blueshifts ubiquitously seen in our sample.

There are another two non-BAL QSO samples with available estimated BH masses and Eddington ratios at $z\sim 4.8$and $z\sim 2.4$ and 3.3 (Netzer et al. 2007; Trakhtenbrot et al. 2011). Although the two samples have a lower luminosity range, they can provide additional diagnostics for systematic comparisons between the BAL and non-BAL populations, particularly in the context of normalized accretion rate, namely Eddington ratio (${\lambda }_{\mathrm{Edd}}$).

In this subsection, we use our entire sample consisting of 22 BAL QSOs at $z\gt 2.5$. The BH masses from all three samples were estimated using the Hβ and Mg ii emission lines at $z\lt 4$ and $z\gt 4$, respectively. Because the bolometric correction factor adopted in this work is about 1.5 times higher than that from the two non-BAL samples (see Section 5.1 from Trakhtenbrot et al. 2011), we correct the distribution of bolometric luminosities by applying the same factor to the two comparison samples. As shown in Figure 8, there is a distinct separation between different quasar samples, with a larger average BH mass in this work (this is quantitatively confirmed by a two-sample K-S test with ${p}_{\mathrm{KS}}=2\times {10}^{-8}$). The vast majority of BAL QSOs in our sample are bounded by log${\lambda }_{\mathrm{Edd}}=-0.5$ and log${\lambda }_{\mathrm{Edd}}=0.5$, with a median Eddington ratio of log${\lambda }_{\mathrm{Edd}}=-0.04$, a value that is approximately equal to that from T11. However, our sample contains BAL QSOs with significantly higher luminosities and BH masses than T11 (see Figure 8).

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There are six LoBAL QSOs at $z\gt 4.3$ in our sample (filled red circles in Figure 8) with BH masses estimated by the Mg ii emission line. We compare the distributions of Eddington ratios between these six LoBAL QSOs and those from T11 sample, as they are also measured using the Mg ii BH mass estimator. Based on the two-sample K-S test, we found that the two samples are likely drawn from the same distribution of Eddington ratio (${p}_{\mathrm{KS}}=0.9$). Therefore, our observational results together indicate that BAL QSOs, on average, do not have higher Eddington ratios than non-BAL QSOs at similar luminosity and/or redshift, supporting the argument that a high Eddington ratio is not sufficient for producing strong outflows (Stern & Laor 2005).

Figure 9 presents the distribution of redshift versus bolometric luminosity from our BAL sample and the aforementioned non-BAL comparison samples. The non-BAL QSOs with bolometric luminosities less than 47.6 erg s⁻¹ in the logarithmic scale are from N07 and T11, as discussed in the above section. Note that at $z\lt 4$, all of the bolometric luminosities and BH masses are derived by the 5100 Å continuum flux and the scaling relation for Hβ, respectively, which, in general, could provide more reliable measurements than those at $z\gt 4$. At fixed luminosity, we do not see any clear trends with respect to the growth of SMBHs either from our BAL sample or the augmented non-BAL samples from Zuo15, C17, V18, N07, and T11. However, limited by the sample size, we cannot draw any conclusions regarding the BH growth and redshift evolution.

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