The Fraction and Kinematics of Broad Absorption Line Quasars across Cosmic Time

The observed fraction of BAL quasars with respect to non-BAL quasars is the convolution of the intrinsic BAL quasar occurrence and a quasar selection function. Standard quasar selection algorithms in optical surveys rely on multicolor imaging data which probe the rest-frame UV quasar spectrum at z > 2 (e.g., Richards et al. 2002). These UV colors can be affected by BAL troughs associated with high-ionization species such as C iv. In addition, BAL quasars typically show redder UV continua than non-BAL quasars (e.g., Reichard et al. 2003; Gibson et al. 2009). Depending on redshift, BAL quasars may thus show UV colors resembling those of stars, and may be more easily missed by spectroscopic samples than non-BAL quasars.

Aiming to measure the intrinsic fraction of BAL quasars across cosmic time, two main approaches can be followed. One possibility is to translate the observed BAL fraction (f_obs) into an intrinsic fraction (f_int) by correcting for selection effects. Previous attempts to correct for these effects, however, resulted in very different f_int (by a factor of 3), and different f_obs to f_int corrections (by a factor of 5), even considering the same set of selection effects and similar redshift intervals. When considering quasars from SDSS and from the Large Bright Quasar Survey, f_int (f_obs) values in the range 13.4 (8.0)% to 40.7 (23%) have been reported, as summarized in Table 1. In all these cases, the derived f_int mostly depends on the adopted assumptions with regard to the input BAL properties, such as the distributions of the velocity, width, and depth of the absorption, and on the relation between the above quantities and reddening. The spread of plausible assumptions naturally leads to large uncertainties. The true f_int could in principle be derived by quantifying the selection effects on a set of synthetic spectra based on a physical model of BAL quasar outflows. Such an approach would nonetheless suffer from large uncertainties, due to the lack of a self-consistent physical model able to widely reproduce the properties of the BAL quasar population (e.g., Elvis 2000; Xu et al. 2020).

In this work, we follow a different approach that allows us to bypass the above issues. As we are mainly interested in the redshift evolution of the BAL fraction and kinematic properties, we apply a similar selection function at all redshifts. In particular, we consider rest-frame optically bright quasars to measure the BAL fraction in the redshift interval z ≃ 2–6.5. At z ≃ 2–4, the rest-frame optical band is probed by near-IR surveys such as the Two Micron All Sky Survey (2MASS; Skrutskie et al. 2006) and the UKIRT Infrared Deep Sky Survey (UKIDSS; Warren et al. 2007) in the H and K bands. For higher-redshift quasars (z ∼ 6), a similar spectral coverage is provided by the Wide-field Infrared Survey Explorer (WISE; Wright et al. 2010) in the W1 and W2 bands (see Bischetti et al. 2022 for details). The rest-frame optical selection allows us to minimize selection effects by avoiding those biases generated by UV absorption troughs in the color selection. The f_obs-to-f_int correction in rest-frame optical-selected quasars is indeed expected to be modest (10%–20%): Dai et al. (2008) found a f_int = 23% ± 3% in the SDSS and 2MASS K-band bright quasars at z ≃ 2–4 (f_obs ∼ 20%). This fraction is similar to that found by Ganguly et al. (2007) and Ganguly & Brotherton (2008) when combining SDSS and 2MASS catalogs (23%). Again, Maddox et al. (2008) reported a f_int = 18.5% in SDSS and UKIDSS bright quasars, considering the fraction of quasars missed by the UKIDSS survey (f_obs = 17.5%). As a general trend, the observed BAL fraction calculated in rest-frame optical-selected quasars is roughly 50% higher than the BAL fraction observed in quasars selected only in the rest-frame UV: ${f}_{\mathrm{obs}}^{\mathrm{optical}}\simeq 1.5\times {f}_{\mathrm{obs}}^{\mathrm{UV}}$. In addition, the observed and intrinsic BAL fractions calculated in rest-frame optical-selected quasars are similar. They are also similar to the intrinsic BAL fraction calculated in quasars selected only in the rest-frame UV: ${f}_{\mathrm{obs}}^{\mathrm{optical}}\simeq {f}_{\mathrm{int}}^{\mathrm{optical}}\sim {f}_{\mathrm{int}}^{\mathrm{UV}}$.

The f_obs of quasar samples selected from X-ray to radio surveys, affected by a variety of different selection effects, is typically lower or similar to 20% (e.g., Becker et al. 2000; Giustini et al. 2008), supporting the fact that an optical rest-frame selection limits selection biases against BAL quasars. In general, BAL fractions higher than 20% have been reported only (i) when considering the absorption index (AI; Hall et al. 2002) criterion to identify BAL quasars, instead of the so-called "balnicity index" criterion considered in this work (Weymann et al. 1991; see Section 3.2). The AI criterion identifies as BAL troughs the absorption features that are wider than 1000 km s⁻¹, and typically results in a 2 times higher BAL fraction than when using BI > 0 (Dai et al. 2008). Although the AI criterion can be used to identify the shallowest absorption features, it results in a large fraction of false BAL identifications when applied to spectroscopic data with modest spectral resolution (Knigge et al. 2008). In addition, (ii) BAL fractions higher than 20% have been reported in the reddest quasars (Urrutia et al. 2008; Glikman et al. 2012), which however constitute a minority (∼10%) of the rest-frame optical-selected quasars.

Given the above evidence, the BAL fractions presented in this work and their redshift evolution are robust against selection effects.

The low-redshift sample consists of 1578 quasars at 2.13 < z < 3.20 from the catalog of SDSS Data Release 7 (DR7) quasars by Shen et al. (2011), selected to be detected by 2MASS in the H (1.7 μm) and K (2.2 μm) bands, which cover rest-frame optical regions of the quasar spectrum, similar to those probed by W1 and W2 in the high-redshift sample. We also include 327 SDSS DR7 quasars at 3.6 < z < 5.0 from the Shen et al. (2011) catalog, requiring them to be detected in the 2MASS K band (which correspond to W1 at z ∼ 6). These quasars are about a factor of 10 more luminous than the average SDSS quasar at z > 2.13, with a median magnitude of M_1450Å = −26.6 (−26.5 at z < 3.2, −26.9 at 3.6 < z < 5; see Figure 1). Their spectra have a typical S/N ∼ 18 per 70 km s⁻¹ pixel in the 1500–1600 Å range. We derive L_Bol by applying a bolometric correction to the monochromatic luminosity of the rest-frame UV continuum (see Figure 1, with a typical scatter of ∼0.2 dex; Richards et al. 2006; Runnoe et al. 2012). This sample benefits from measured BH masses (Shen et al. 2011), which are based on the Mg ii line for z ≲ 2.3 quasars (349 quasars) and on the C iv emission line (1160 quasars) at z > 2.3, including the empirical correction for nonvirial motions by Coatman et al. (2017). We verified that the Mg ii and C iv BH masses are consistent, for the 340 quasars in which both tracers are available, within the respective ∼0.3–0.5 dex uncertainties (e.g., Vestergaard & Osmer 2009), in agreement with the results of Shen et al. (2011). For the subsample of quasars already discovered by SDSS Data Release 5 (DR5), the occurrence and properties of BAL outflows were investigated by Gibson et al. (2009), providing us with a reference analysis to test our BAL-identification method. For the remaining quasars, BAL identification in the catalog was based on visual inspection (Shen et al. 2011). In this work and in Bischetti et al. (2022), we have reanalyzed all SDSS quasars in the 2.1 < z < 5.0 sample, following the approach described in Section 3.

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The high-redshift sample used in this work consists of 30 luminous quasars (median AB magnitude M_1450Å = −26.9) at 5.8 ≲ z ≲ 6.6 from the XQR-30 survey. Their magnitude and redshift distributions are shown in Figure 1 (Bañados et al. 2016; Mazzucchelli et al. 2017; Reed et al. 2017; Decarli et al. 2018; Wang et al. 2019; Eilers et al. 2020). These quasars are selected to be bright in both the rest-frame UV (AB magnitude J ≤ 19.8 for z < 6.0 sources and J ≤ 20.0 for quasars at z ≥ 6.0) and in the rest-frame optical, being all detected by WISE in the W1 (3.4 μm) and W2 (4.6 μm) bands (Bañados et al. 2016; Ross & Cross 2020). Further details about the selection of XQR-30 quasars, data reduction of the X-Shooter spectra, and the target list are given in Bischetti et al. (2022). This sample benefits from deep X-Shooter observations (S/N ≳ 25 per 50 km s⁻¹ pixel in the rest-frame spectral range 1600–1700 Å), and robust, Mg ii-based BH masses (Lai et al. 2022). As for the low-redshift sample, we verified the consistency between Mg ii- and C iv-based BH masses. Bolometric luminosities are computed via rest-frame UV bolometric correction using the same method applied to the low-redshift sample (Runnoe et al. 2012).

A systematic search and characterization of C iv BAL outflows in XQR-30 was performed in Bischetti et al. (2022), based on the same approach used in this work (Section 3). Although X-Shooter spectra of similar quality (S/N ≳ 10) exist to date for several luminous quasars at 5.0 < z < 5.4, we do not consider them in this work as they have been mostly selected for studies of intervening absorbers and are therefore biased against the presence of BAL features (Becker et al. 2019).

To search for BAL absorption troughs, the first step is to model the intrinsic continuum emission in the rest-frame UV. A possible approach is to fit the spectra with a quasar emission model accounting for continuum and line emission, and extrapolating this model to the spectral region affected by the BAL (Figure 2). Models typically include a power-law component to reproduce the quasar continuum emission, and Voigt or Gaussian profiles to account for emission lines (Gibson et al. 2009; Shen et al. 2011, 2019). Alternatively, more complex, nonphysically motivated functions such as splines are sometimes used, as they can be more flexible in reproducing a variety of quasar spectra (e.g., Bruni et al. 2019). Both approaches require that a sufficiently large portion of the quasar spectrum is free from both absorption and emission lines, allowing one to anchor the fit. However, this condition is often unsatisfied in the spectral region between Lyα and C iv, resulting in large uncertainties (Figure 2). In addition, both methods are largely dependent on the regions of the spectrum that are masked prior to fitting, especially in those cases where BAL features cover a wide spectral range or affect emission-line profiles.

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These uncertainties can be minimized using composite templates built from observed quasar spectra. Quasar spectra can be combined via different techniques such as principal component analysis (Trump et al. 2006; Pâris et al. 2018; Guo & Martini 2019) or nonnegative matrix factorization (Allen et al. 2011). Here we build, for each quasar of the sample, a composite template based on a large number of SDSS quasar spectra classified as non-BAL in Gibson et al. (2009), each matching within ±20% its color and the equivalent width (EW) of the C iv line (Shen et al. 2011). Given the anticorrelation between the EW of C iv and its blueshift with respect to the quasar redshift due to outflowing gas motions (Coatman et al. 2017; Vietri et al. 2018), the latter criterion allows us to reproduce all levels of asymmetry in the C iv line profile. A similar approach was recently adopted by Wang et al. (2018, 2021b), who created composite templates based on matching the C iv blueshift of two z > 7 BAL quasars. The C iv EW or the blueshift criteria should in principle produce similar composite templates. However, SDSS quasar redshifts rely on automatic fitting procedures based on a limited spectral coverage, and are therefore affected by uncertainties on the C iv blueshift that can reach thousands of kilometers per second, leading to an inaccurate selection of the quasar spectra contributing to the template. We find that a better spectrum–template agreement can be achieved by using the C iv EW during the selection of the quasar spectra.

Concerning the quasar colors, we consider the F (1700 Å)/F (2100 Å) flux ratio to reproduce the continuum slope redwards of C iv, and the F (1290 Å)/F (1700 Å) flux ratio to account for a change in the continuum slope as observed in red quasar spectra (e.g., Trump et al. 2006; Shen et al. 2019). We calculate F (1700 Å) and F (2100 Å) as median flux values over 100 Å and F (1290 Å) over 30 Å in the rest frame. The underlying assumption is that the observed and intrinsic continuum emission do not differ around 1290 Å, that is, the bluest spectral region, redward of Lyα, free from strong emission lines. In fact, Lyα forest absorption complicates our measure of the λ < 1216 Å quasar continuum, owing to the absorption becoming stronger with increasing redshift. In the case that BAL absorption troughs affect the spectral region close to 1290 Å, our approach would provide a lower limit on the intrinsic quasar continuum emission and on the absorption BI (Section 2).

Starting from the total Shen et al. (2011) catalog of 11,800 SDSS quasars in the redshift range 2.13 < z < 3.20, for which SDSS spectroscopy probes the 1216–2100 Å wavelength range, the composite template spectrum is built as the median of a hundred randomly selected, non-BAL (Gibson et al. 2009; Shen et al. 2011) quasar spectra. The above number is a trade-off between using stringent selection criteria and ensuring that the composite template is not affected by individual quasar spectra. The composite template is normalized to the median flux value of the quasar spectrum in the rest-frame 1650–1750 Å spectral interval, avoiding prominent emission lines and strong telluric absorption for the redshift interval covered by our sample (Smette et al. 2015). Figure 2 shows that the above approach provides us with (i) a solid reconstruction of the C iv profile even when affected by strong absorption features, (ii) a reasonable estimate of the quasar emission blueward of C iv also in the most absorbed spectra, and (iii) a conservative estimate of the continuum emission, typically lower or similar to the continuum reproduced by the Gibson et al. (2009) and Bruni et al. (2019) models. Figure 3 shows examples of the SDSS and X-Shooter spectra for the quasars belonging to the 2.1 < z < 5.0 and 5.8 < z < 6.6 samples, respectively. The X-Shooter spectra and composite templates for the remaining 5.8 < z < 6.6 quasars are shown in the Appendix in Figure 11. Normalized spectra are obtained by dividing each spectrum by its matched composite template (Figure 4).

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The standard indicator used to identify absorption features in quasar spectra due to BAL outflows is the balnicity index (BI), first introduced by Weymann et al. (1991), which is a modified EW of the BAL absorption and is less affected by false BAL identification than the AI criterion (Knigge et al. 2008). Here we adopt the BI definition by Gibson et al. (2009):

$$\begin{eqnarray}&&\mathrm{BI}={\int }_{0}^{{v}_{\mathrm{lim}}}\left(1-\displaystyle \frac{f(v)}{0.9}\right){Cdv},\end{eqnarray} \tag{ 1 }$$

where f(v) is the normalized spectrum, C = 1 if f(v) < 0.9 for contiguous troughs of >2000 km s⁻¹, and C = 0 otherwise. The f(v) < 0.9 threshold identifies as BAL features only the spectral regions dipping by 10% or more below the quasar continuum level, and represents a trade-off between taking into account typical uncertainties on the level of the modeled quasar continuum and including shallow absorption features (Weymann et al. 1991).

We search the normalized spectra for BAL features in the region between Lyα and C iv, that is, corresponding to ${v}_{\mathrm{lim}}$∼ 64,000 km s⁻¹ for C iv BAL outflows, ∼35,000 km s⁻¹ for Si iv, and ∼6000 km s⁻¹ for N v, respectively. We do not extend the search to smaller wavelengths due to the stronger intergalactic medium absorption blueward of Lyα with increasing redshift, preventing us from a homogeneous BAL identification at different epochs. We identify the minimum (${v}_{\min }$) and maximum (${v}_{\max }$) BAL velocity for a given transition, as the lowest and highest velocity for which C = 1 in Equation (1), respectively. Previous studies have been typically limited to ${v}_{\mathrm{lim}}={\rm{25,000}}$ km s⁻¹ (Trump et al. 2006; Gibson et al. 2009; Guo & Martini 2019), to avoid discriminating between BAL outflows associated with C iv and Si iv ions. Here we exploit the fact that the C iv optical depth is usually similar to or larger than the Si iv depth in BAL quasars (Dunn et al. 2012). This allows us to use the velocity range of the C iv BAL troughs to identify absorption associated with Si iv (Figure 4; see also Wang et al. 2018; Bruni et al. 2019). This implies that absorption features blueward of Si iv are due to a low-velocity Si iv BAL if a C iv BAL with similar velocity is observed. Otherwise, these features are considered to be produced by a high-velocity (${v}_{\max }\gtrsim {\rm{30,000}}$ km s⁻¹) C iv BAL (see also Rodríguez Hidalgo et al. 2020). We similarly assume that the C iv optical depth is larger than those of Mg ii and N v and apply the methodology above to identify Mg ii and BAL features. We measure the BAL width, defined as ${w}_{\max }$ = ${v}_{\max }$− ${v}_{\min }$. The distributions of BI, ${v}_{\min }$, and ${v}_{\max }$ for the C iv BAL quasars identified in our sample are shown in Figure 2 of Bischetti et al. (2022), and values for individual quasars at 5.8 < z < 6.6 are listed in their Table E1. Uncertainties on the BAL parameters have been computed taking into account the uncertainty on both slope and normalization of the best-fit composite template, following the method in Bischetti et al. (2022). Briefly, we created for each quasar a bluer and a redder template as the median of the 33% bluest and the 33% reddest spectra contributing to the best-fit template, and we used them to create new normalized spectra, from which the range of variation of the BAL parameters is calculated. The median uncertainties (68% confidence level) on BI, ${v}_{\min }$, ${v}_{\max }$, and ${w}_{\max }$ are 310, 200, 380, and 340 km s⁻¹, respectively, while uncertainties for individual quasars in the 5.8 < z < 6.6 sample are given in Table 2. We note that adopting a lower threshold of ∼0.8 in Equation (1) would identify as a BAL only the deepest absorption features (corresponding to a BI ≳ 1000 km s⁻¹), and would typically imply lower ${v}_{\max }$(higher ${v}_{\min }$) by ∼1000–2000 km s⁻¹.

Table 2. Si iv and N v BAL Parameters

Name	Species	BI	${v}_{\min }$	${v}_{\max }$
(1)	(2)	(3)	(4)	(5)
PSOJ009−10	Si iv	2880${}_{-160}^{+750}$	33,040${}_{-110}^{+220(* )}$	38,360${}_{-1360}^{+150(* )}$
PSOJ065+01	Si iv	${660}_{-150}^{+430}$	17,240${}_{-210}^{+130}$	27,190${}_{-510}^{+1030}$
PSOJ089−15	Si iv	8150${}_{-620}^{+710}$	2280${}_{-120}^{+150}$	28,040${}_{-220}^{+160}$
	N v	2280${}_{-280}^{+190}$	2270${}_{-110}^{+150}$	5,870${}_{-170}^{(* * )}$
J0923+0402	Si iv	7970${}_{-150}^{+230}$	6110${}_{-150}^{+150}$	24,330${}_{-200}^{+350}$
PSOJ217−07	Si iv	${440}_{-150}^{+170}$	30,460${}_{-120}^{+270}$	35,000${}_{-100}^{+430}$
PSOJ231−20	N v	${630}_{-190}^{+230}$	${140}_{-210}^{+130}$	2350${}_{-140}^{+160}$
PSOJ239−07	Si iv	${230}_{-120}^{+310}$	${830}_{-120}^{+160}$	3360${}_{-120}^{+1010}$
	N v	1,810${}_{-100}^{+130}$	${820}_{-120}^{+100}$	5720${}_{-100}^{+110}$
J2211−3206	Si iv	3420${}_{-110}^{+130}$	9550${}_{-470}^{+290}$	19,120${}_{-140}^{+350}$
J2250−5015	Si iv	1320${}_{-110}^{+170}$	29,460${}_{-810}^{+150}$	37,540${}_{-130}^{+170}$

Notes. (1) Quasar ID, (2) ionic species of the BAL, (3–5) balnicity index, minimum and maximum velocity of the Si iv BAL outflows, in units of kilometers per second. Positive ${v}_{\min }$ and ${v}_{\max }$ values indicate blueshifted absorption. (*) We assume the same range of ${v}_{\min }$ and ${v}_{\max }$ of the C iv BAL (Bischetti et al. 2022). (**) ${v}_{\max }$ corresponds to rest-frame 1216 Å, below which the spectrum is dominated by Lyα forest absorption (Section 3).

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Although the identification of BAL features in high-redshift quasars is mostly based on C iv, due to its high optical depth, the combined study of several other ionic species can be used to investigate the ionization level, kinematic structure, and column density of the outflow (e.g., Filiz et al. 2014; Baskin et al. 2015). However, only a few cases of non-C iv BAL outflows at z ≳ 6 have been reported so far (Wang et al. 2018, 2021b).

Here we find that, of the 14 C iv BAL quasars identified in Bischetti et al. (2022), eight also show a BAL system associated with the Si iv ion (namely, PSOJ009-10, PSOJ065+01, PSOJ089-15, J0923+0402, PSOJ217-07, PSOJ239-07, J2211-3206, and J2250-5015), three show a N v BAL (namely, PSOJ089-15, PSOJ231-20, and PSOJ239-07), and one (J0923+0402) shows a Mg ii BAL. Figure 4 shows as an example the normalized spectrum of quasar J0923+0402 at z ∼ 6.6, for which we identify strong BAL systems associated with C iv, Si iv, and Mg ii ions. The C iv BAL is characterized by a BI (C iv) = 15,370 km s⁻¹ and extends between ${v}_{\min }$(C iv) =6090 km s⁻¹ and ${v}_{\max }$(C iv) =29,500 km s⁻¹ (Bischetti et al. 2022). We identify a Si iv BAL spanning a similar velocity range, with BI (Si iv) = 7390 km s⁻¹, and a less prominent Mg ii BAL with BI (Mg ii) = 2340 km s⁻¹. We cannot assess the presence of a N v BAL in this quasar, because of almost no transmitted flux blueward of Lyα.

We thus classify 12 quasars as HiBALs, and quasar J0923+0402 (z ≃ 6.63) as a LoBAL. In the case of PSOJ189-15 (z ≃ 5.97), strong telluric contamination affecting the spectral region blueward of Mg ii does not allow us to validate/rule out the presence of a Mg ii BAL. Our results increases by a factor of about 4 the number of Si iv BAL quasars identified at z ≳ 6 (Wang et al. 2021b). The presence of a Si iv BAL in J2211-3206 (z = 6.33) was previously suggested by Chehade et al. (2018). A few hints of Mg ii absorption in z ≳ 6 quasars have been reported so far (e.g., Maiolino et al. 2004; Wang et al. 2021b).

The BAL parameters measured for the Si iv and N v BAL outflows are listed in Table 2, and their residual spectra are shown in the Appendix in Figure 12. The Si iv BAL features are characterized by a BI ∼ 200–8100 km s⁻¹, which are typically smaller (10%–60%) than those measured in C iv, consistently with what has been found for SDSS quasars (Gibson et al. 2009). The only exception is PSOJ009-10, for which BI (C iv) = 1110 km s⁻¹ (Bischetti et al. 2022) and BI (Si iv) = 2880 km s⁻¹. However, this quasar shows a very red spectrum with almost no Lyα and N v emission, overfitted by the composite template at λ < 1270 Å (Figure 11 in the Appendix). This suggests strong absorption, consistent with the presence of a Si iv BAL outflow, whose properties are nevertheless highly uncertain. For the N v BALs, we measure BI ∼600–2300 km s⁻¹.

Given that the 2.1 < z < 5.0 quasars in our sample did not benefit from a homogeneous identification and characterization of BAL outflows from the literature (Section 2.2), we have reanalyzed their spectra following the approach described in Section 3. In Figure 5, we compare our results with those by Gibson et al. (2009), who provided BI, ${v}_{\min }$, and ${v}_{\max }$ for the 1317 SDSS DR5 quasars in our sample (Schneider et al. 2007). We identify as BALs 162 out of the 207 BAL quasars found by Gibson et al. (2009). The remaining quasars, classified as non-BAL quasars in our analysis, have only very weak BAL absorption in Gibson et al. (2009; all but five have BI < 500 km s⁻¹), likely owing to the flat continuum emission in the C iv–Si iv spectral region not being well reproduced by the reddened power-law continuum model used by Gibson et al. (2009), introducing a small systematic on the true continuum level. One example is shown in Figure 6 (top panel) for quasar SDSSJ1215+0906 (z = 2.72), previously classified as a BAL quasar with a BI ≃ 120 km s⁻¹ by Gibson et al. (2009), which we instead identify as a non-BAL. In addition, small differences between the DR5 and DR7 spectra can easily produce BI variations of a few hundred kilometers per second (e.g., Byun et al. 2022; Vietri et al. 2022). On the other hand, we identify 39 new BAL quasars that were classified as non-BALs by Gibson et al. (2009). One example is SDSS quasar J1432+1139 (z = 2.99; see Figure 6, middle panel), showing high-velocity C iv BAL features with ${v}_{\min }$ ∼ 29,000 km s⁻¹, that is, outside the spectral range investigated by Gibson et al. (2009). When comparing the properties of the BAL quasars identified in both our work and Gibson et al. (2009), we find on average no systematic difference in BI, with a significant scatter at BI ≲ 1000 km s⁻¹ (Figure 5(a)). We measure higher BI for those quasars in which the BAL absorption reaches ${v}_{\max }$> 25,000 km s⁻¹, as Gibson et al. (2009) did not account for absorption troughs beyond this threshold. We typically measure larger BI in those cases in which the absorption has ${v}_{\min }$< 3000 km s⁻¹ and thus affects the blue side of the C iv line, as it can be seen for SDSS J2238-0808 (z = 3.17) in Figure 6 (bottom panel). This is due to the fact that our composite templates better reproduce the asymmetric C iv profiles, typically showing a more prominent blue wing due to ionized outflows, than the Voigt profiles in Gibson et al. (2009).

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The majority of the C iv BAL outflows show ${v}_{\max }$ and ${v}_{\min }$ velocities similar to those measured by Gibson et al. (2009). In a few cases, we measure lower ${v}_{\max }$ because of the different continuum treatments, and we identify a subsample of BAL quasars with extremely fast BAL outflows (${v}_{\max }$∼ 25,000–40,000 km s⁻¹), missed by Gibson et al. (2009). These high-velocity BAL outflows are visible as a cutoff around ${v}_{\max }^{{\rm{G}}09}\sim {\rm{25,000}}$ km s⁻¹ in Figure 5(b). Our findings are consistent with the results of Bruni et al. (2019) and Rodríguez Hidalgo et al. (2020), who reported the presence of BAL outflows reaching velocities of 10%–15% of the light speed in a small fraction of SDSS quasars at z ∼ 2–4. In the case of absorption with ${v}_{\min }$< 3000 km s⁻¹ (Figure 5(c)), we typically measure ${v}_{\min }$ lower by a factor of about 2 with respect to Gibson et al.'s (2009) estimates, likely because the Voigt profiles employed in their modeling underestimate the intrinsic emission of the C iv blue wing (Figure 6, bottom).

Our results indicate an evolution with redshift of the properties of BAL outflows in luminous quasars at 2.1 < z < 6.8. We find that the BAL fraction below z ∼ 4.5 is almost constant and close to 20%–25% (Figure 7), while it significantly increases up to almost 50% at z ∼ 6. The trend at 2.1 < z < 4.5 is consistent with the results of previous studies focusing on rest-frame optical luminous quasar samples (Dai et al. 2008; Maddox et al. 2008), which reported a modest evolution of the BAL fraction with redshift. However, heavily reddened broad-line quasars are expected to represent a high fraction of the bright quasar population at z > 2 (Banerji et al. 2015; Glikman et al. 2018), and may be missed by SDSS, from which our 2.1 < z < 4.5 sample is drawn. Several recent surveys (e.g., Schindler et al. 2019; Boutsia et al. 2021; Grazian et al. 2022) have indeed shown that the SDSS selection of bright quasars at high redshift could possibly suffer from incompleteness by up to 30%–40% at z ∼ 4, and up to a factor of a few at z ∼ 5 (Wolf et al. 2020; Onken et al. 2022), plausibly affecting also z ∼ 6 quasars. Our 5.8 < z < 6.6 quasar sample is limited to J ≤ 19.8–20.0 magnitudes and probes similar depths in the J and WISE bands (see Table ED1 in Bischetti et al. 2022). Accordingly, we may miss red BAL quasars at z ∼ 6, detected by WISE but too faint in the rest-frame UV to match our selection (e.g., Kato et al. 2020). Due to the above limitations and to the limited number of z ≳ 5 quasars in our sample, we cannot accurately probe the BAL fraction evolution in the highest-redshift bins. Nevertheless, we can safely assess that the increase in the BAL fraction between z < 4.5 and z ∼ 6 is a robust evolutionary trend, and that selection effects (e.g., including dust-reddened quasars) would increase this difference even further.

By investigating the dependence of the BAL fraction on the quasar nuclear properties, we can safely exclude that the large difference between the BAL fraction at z ≲ 4.5 and z ∼ 6 is due to differences in quasar luminosity and accretion rate. Instead, the higher BAL fraction at z ∼ 6 can be explained either with wider-angle outflows or as a result of longer blow-out phases of BH-driven outflows compared with z ≲ 4.5 (Bischetti et al. 2022). A redshift evolution of the BAL geometry is indeed suggested by the increase with redshift of the velocity range spanned by the BAL troughs, as traced by ${w}_{\max }$ (Murray & Chiang 1998; Elvis 2000; Hall et al. 2002). Although the link of ${w}_{\max }$ to the velocity dispersion of the outflowing gas is not straightforward, as we mostly observe blends of outflowing components (e.g., Borguet et al. 2013), the increase of ${w}_{\max }$ may be interpreted as stronger turbulence in the higher-redshift BAL outflows. In a scenario of chaotic cold accretion (CCA), gas turbulence on scales similar to those of BALs (∼100 pc; Arav et al. 2018) is linked to the condensation and funnelling of the cold gas phase toward the BH, higher turbulence implying stronger inflows and, in turn, triggering more efficient phases of BH feedback (Gaspari et al. 2020).

We find that the BAL velocity (either ${v}_{\max }$ and ${v}_{\min }$) typically increases with redshift, suggesting that BAL outflows in the high-z universe might be more easily accelerated to very high velocity than at later cosmic epochs. A viable explanation might be the presence of dust mixed with the ionized gas in the BAL clouds, which would significantly increase the radiation boost efficiency (Ishibashi et al. 2017; Costa et al. 2018) and accelerate the BAL outflows to the observed extreme ${v}_{\max }$ ∼ 20,000–50,000 km s⁻¹ (Bischetti et al. 2022). At later cosmic epochs, although BAL quasars are known to show relatively redder UV colors (Reichard et al. 2003; Trump et al. 2006; Gibson et al. 2009), no strong difference in the optical colors of BAL and non-BAL quasars is typically observed, at least in optically bright sources (e.g., Dai et al. 2008).

Alternative scenarios that could explain the higher BAL velocities at early epochs might be related to different properties of BH accretion at different redshift. CCA toward the BH is expected to be favored at higher redshift, because of a larger fraction of a clumpy cold gas phase in the quasar hosts, boosting BH-driven outflows to higher velocities (Gaspari & Sadowski 2017). Also, BALs could be launched with higher velocities if BHs are spinning more rapidly at high redshift (King et al. 2008; Zubovas & King 2021). High BAL velocities have been more commonly found in sources with softer spectral energy distributions, that is, lower X-ray to optical luminosity ratios, either from direct X-ray observations of low-z quasars (Laor & Brandt 2002) or using indirect tracers such as the EW of the He ii λ1640 Å emission line in SDSS quasars (Richards et al. 2011; Baskin et al. 2015; Rodríguez Hidalgo et al. 2020). For the highest-redshift bins in which we observe the largest values of ${v}_{\max }$ and ${v}_{\min }$ (see Figure 8), there is very limited information on the X-ray properties. Only a few tens of quasars have been targeted with sensitive observations at z > 5, including only a few BAL quasars, some of which do exhibit the softest optical to X-ray slopes (Nanni et al. 2017; Vito et al. 2019; Wang et al. 2021a). The weakness of the He ii emission line makes its detection very challenging at these redshifts (e.g., Shen et al. 2019). The characterization of the He ii emission in the 5.8 < z < 6.6 sample, enabled by the high S/N of the X-Shooter spectra from the XQR-30 survey, will be presented in a forthcoming paper.

The broad and often saturated BAL profiles associated with C iv prevent us from an accurate measurement of the outflowing gas mass and hence of the energy injected by the outflow into the galaxy medium (Dunn et al. 2012; Borguet et al. 2013). Nevertheless, assuming that BAL outflow masses at z ∼ 6 are similar to those measured using unsaturated absorption lines in z ∼ 2 quasars (Moe et al. 2009; Dunn et al. 2010), we can estimate that BAL quasars at z ∼ 6 globally inject about 20 times more energy with respect to z ∼ 2–4 quasars (Bischetti et al. 2022). Indeed, the outflow kinetic power linearly scales with the BAL fraction and with the third power of ${v}_{\max }$(Equations (5) and (6) in Bischetti et al. 2017). This result strongly points toward a phase of efficient BH feedback occurring at z ∼ 6, as the energy injected by these BAL outflows will likely suppress gas accretion and slow down BH growth (e.g., Torrey et al. 2020). This likely represents the first observational evidence of what has been so far only predicted by cosmological simulations of the early assembly of bright quasars. BHs at the center of bright quasars are indeed expected to grow exponentially at very high redshift (z ≫ 6), with accretion rates close to the Eddington limit or beyond (Inayoshi et al. 2016; Pezzulli et al. 2016), while around z = 6 BH growth is expected to significantly slow down because BH feedback has become strong enough to remove gas from the central galaxy regions and to prevent further accretion onto the BH (Costa et al. 2014; van der Vlugt & Costa 2019). BHs powering bright quasars at z ∼ 6, with typical masses of ∼10⁹ M_⊙ (Mazzucchelli et al. 2017; Shen et al. 2019; Farina et al. 2022), have been found to be typically overmassive by a factor of ∼10 with respect to the mass of their host galaxies, when compared to the BH mass versus galaxy dynamical mass relation observed in the low-redshift universe (Gaspari et al. 2019; Pensabene et al. 2020; Neeleman et al. 2021). State-of-the-art measurements of the BH mass (based on the Mg ii line), and of the dynamical mass (based on spatially resolved C ii λ158 μm observations) for the quasars in our 5.8 < z < 6.6 sample confirm this result, indicating that BH growth must have dominated over the host-galaxy growth at z > > 6 and that a transition epoch during which BH growth decelerates must occur at z ≲ 6, leading toward the symbiotic BH and galaxy growth (e.g., Lamastra et al. 2010; Zubovas & King 2021; Inayoshi et al. 2022). An early BH mass assembly in bright quasars occurring at z > 6 is also supported by the fact that the largest BH masses measured at z ∼ 6 and at z ∼ 2 only differ by a factor of a few (Trakhtenbrot 2021) and by the increase of the median BH accretion rate with redshift for a given quasar luminosity (Yang et al. 2021; Farina et al. 2022).

The above scenario points toward BH feedback as a likely driver of BH growth suppression, but other physical processes might be in place. The cosmic evolution of the BAL fraction is key to identify the dominant mechanism responsible for slowing down BH growth. A sharp decrease of the BAL fraction occurring between z ∼ 6 and z ∼ 5 would strongly point toward a phase of efficient BH feedback occurting on a short timescale (few tens of millions of years; Negri & Volonteri 2017) and quickly removing gas from the central regions of the galaxy (Zubovas & King 2013). Conversely, a smooth decrease of the BAL fraction from z ∼ 6 to z ∼ 4, would rather indicate that several processes may be at play in the transition, including a (less efficient) BH feedback and secular processes, such as a change in the merger rate or in the gas condensation rate, reducing the active phase duty cycle on a timescale of several hundreds of millions of years (Gaspari et al. 2019; O'Leary et al. 2021). To discriminate between these competing scenarios, a crucial step is to obtain a reliable measure of the evolution of the BAL fraction with redshift in representative samples, with a cosmic time sampling <100–200 Myr. Currently, the sample presented in this work and, particularly, the lack of sources at 5 < z < 5.8 do not allow us to accurately probe the high-redshift evolution of the BAL fraction between z ∼ 4.5 and z ∼ 6. New high-quality spectroscopic observations of an absorption-unbiased sample of rest-frame optical bright quasars are necessary to fill this gap and test whether efficient BH feedback is the dominant mechanism leading to the symbiotic BH–galaxy growth phase.

On the other hand, it is unclear whether and on what timescales BAL outflows can affect the evolution of the host galaxies of z ∼ 6 quasars. Observations of BAL quasars at intermediate redshift report mass outflow rates up to several hundreds of solar masses per year (e.g., Fiore et al. 2017; Bruni et al. 2019), consistent with theoretical expectations from models of BH-driven outflows for an efficient feedback mechanism (Faucher-Giguère & Quataert 2012; Zubovas & King 2012) and outflow sizes based on photoionization analysis that can reach kiloparsec scales (Arav et al. 2018; Byun et al. 2022), suggesting that BAL outflows may also affect the physical properties of the galaxy medium and, in turn, the galaxy growth.

If the effect of BAL feedback extends to kiloparsec scales, host-galaxy properties such as the star formation rate (SFR) would be expected to be different in BAL and non-BAL quasars. If conflicting results have been reported at z ∼ 2 (e.g., Zhang et al. 2014; Wethers et al. 2020) and at z ∼ 6, large uncertainties affect SFR measurements (Wang et al. 2019; Tripodi et al. 2022; Di Mascia et al. 2023) and do not allow us to investigate differences within our 5.8 < z < 6.6 sample. A correlation is also expected between the strength of BH feedback and the cooling rate of the hot and warm gas phases in the quasar host galaxies, due to heating and turbulence injection into the ISM (e.g., Gaspari 2015).