Subaru High-z Exploration of Low-luminosity Quasars (SHELLQs). XI. Proximity Zone Analysis for Faint Quasar Spectra at z ∼ 6

Our faint sample consists of 11 quasars at $5.93\leqslant z\leqslant 6.56$ (Table 1). All these quasars were discovered by the Subaru High-z Exploration of Low-Luminosity Quasars project (SHELLQs) using Hyper Suprime-Cam (HSC; Furusawa et al. 2018; Kawanomoto et al. 2018; Komiyama et al. 2018; Miyazaki et al. 2018) on the Subaru Telescope (e.g., Matsuoka et al. 2016, 2018a, 2018b). The spectroscopic identification was carried out with the Faint Object Camera and Spectrograph (FOCAS; Kashikawa et al. 2002) mounted on the Subaru Telescope for J0859+0022, J1153+0055, J1202−0057, J1208−0200, J2216−0116, and J2304+0045, and the Optical System for Imaging and low-intermediate-Resolution Integrated Spectroscopy (OSIRIS; Cepa et al. 2000) mounted on the Gran Telescopio Canarias for J0921+0007, J1406−0116, J1545+4232, J2216−0116, J2228+0152, and J2239+0207. FOCAS provides spectral coverage from ${\lambda }_{\mathrm{obs}}=0.75$ to $1.05\ \mu {\rm{m}}$ with a resolution $R\sim 1200$, and OSIRIS provides spectral coverage from ${\lambda }_{\mathrm{obs}}=0.74$ to 1.0 μm with a resolution $R\sim 1500$. The exposure times are 170 minutes for J1202−0057, and 15 or 30 minutes for the other quasars.

Table 1.  Overview of Our Faint Sample and Proximity Zone Sizes

Name	R.A.	Decl.	z	Redshift Line	References	M1450 (mag)	Rp (pMpc)	${R}_{p,\mathrm{corr}}^{-25}$ (pMpc)
J0859+0022	08h59m0719	+00°22'559	${6.3903}_{-0.0005}^{+0.0005}$	[C ii]	1	−23.10 ± 0.27	1.14 ± 0.03	3.14 ± 0.09
J0921+0007	09h21m2056	+00°07'229	${6.563}_{-0.001}^{+0.002}$	Mg ii	3	−26.16 ± 0.29	3.05 ± 0.45	1.64 ± 0.24
J1152+0055	11h52m2127	+00°55'366	${6.3637}_{-0.0005}^{+0.0005}$	[C ii]	1	−25.08 ± 0.07	2.67 ± 0.03	2.56 ± 0.03
J1202−0057	12h02m4637	−00°57'017	${5.9289}_{-0.0002}^{+0.0002}$	[C ii]	1	−22.83 ± 0.08	0.74 ± 0.01	2.34 ± 0.04
J1208−0200	12h08m5923	−02°00'348	${6.1165}_{-0.0002}^{+0.0002}$	[C ii]	2	−24.36 ± 0.09	0.62 ± 0.01	0.87 ± 0.02
J1406−0116	14h06m2912	−01°16'112	${6.292}_{-0.002}^{+0.002}$	Mg ii	3	−24.76 ± 0.18	0.14 ± 0.05	0.16 ± 0.05
J1545+4232	15h45m0562	+42°32'116	${6.511}_{-0.004}^{+0.003}$	Mg ii	3	−24.76 ± 0.17	2.14 ± 0.18	2.43 ± 0.20
J2216−0016	22h16m4447	−00°16'501	${6.0962}_{-0.0003}^{+0.0003}$	[C ii]	1	−23.65 ± 0.20	0.66 ± 0.02	1.36 ± 0.04
J2228+0152	22h28m2783	+01°28'095	${6.0805}_{-0.0004}^{+0.0004}$	[C ii]	2	−24.00 ± 0.04	2.11 ± 0.02	3.60 ± 0.04
J2239+0207	22h39m4747	+02°07'475	${6.2497}_{-0.0004}^{+0.0004}$	[C ii]	2	−24.60 ± 0.15	1.65 ± 0.02	2.04 ± 0.03
J2304+0045	23h04m2297	+00°45'054	${6.3504}_{-0.0002}^{+0.0002}$	[C ii]	4	−24.28 ± 0.03	1.15 ± 0.01	1.68 ± 0.02

Note. The columns show the object name, coordinates, the redshift and its error, the lines used to measure redshift, absolute magnitude M₁₄₅₀, proximity zone sizes R_p, and luminosity-corrected proximity zone sizes ${R}_{p,\mathrm{corr}}^{-25}$. References for redshifts: (1) Izumi et al. (2018), (2) Izumi et al. (2019), (3) M. Onoue et al. (2020, in preparation), (4) T. Izumi et al. (2020, in preparation).

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Accurate redshift measurements are needed for an accurate prediction of the intrinsic spectra and are important in measuring R_p. The redshifts of eight of these quasars are from Izumi et al. (2018, 2019) and T. Izumi et al. (2020, in preparation) and have been accurately measured by the [C ii] 158 μm emission line. The three quasars, J0921+0007, J1406−0116, and J1545+4232, have Mg ii λ2798 redshifts, as well as a black hole mass (${M}_{\mathrm{BH}}$) and Eddington ratio (${L}_{\mathrm{bol}}/{L}_{\mathrm{Edd}}$) measured from K-band spectra taken by Subaru/MOIRCS (ID: S19A-015, PI: M. Onoue). The Mg ii redshifts were derived from the peaks of the best-fit single Gaussian profiles of the emission lines, for which the power-law continuum and the rest-frame UV iron pseudocontinuum were subtracted beforehand with the empirical iron template of Vestergaard & Wilkes (2001). More details of the observations and the spectral analysis will be described in a forthcoming paper (M. Onoue et al. 2020, in preparation). One broad absorption line (BAL) quasar, J1205−0000, is excluded from our sample because it is difficult to determine its intrinsic spectrum. The absolute magnitude M₁₄₅₀ of each quasar is taken from Matsuoka et al. (2018a, 2018b) and Onoue et al. (2019). They were obtained by converting UV magnitudes, assuming the power-law continuum slope of ${\alpha }_{\lambda }=-1.5$ (${F}_{\lambda }\propto {\lambda }^{{\alpha }_{\lambda }}$) for J1202−0057, J2228+0152, and J2304+0045 (Matsuoka et al. 2018a, 2018b), and by fitting ${\alpha }_{\lambda }$ for the other quasars (Onoue et al. 2019).

In addition to our new quasar spectra, we use the sample of luminous quasars analyzed in Eilers et al. (2017). These spectra are taken from the igmspec¹⁶ database. We exclude those quasars whose redshifts were measured based on the Lyα emission line alone, as this line usually gives a redshift uncertainty as large as ∼1000 km s⁻¹, in order to unify the redshift accuracy with our faint quasar sample. We also update some redshifts which have newly measured [C ii] or Mg ii lines (Willott et al. 2017; Decarli et al. 2018; Shen et al. 2019). We also exclude J0100+2802, because Fujimoto et al. (2020) suggested this extremely bright quasar could be amplified by gravitational lensing, while there is still debate for the interpretation.¹⁷ In the end, we use 26 quasar spectra from Eilers et al. (2017), the systemic redshifts of which are determined with [C ii], Mg ii, or CO emission lines, as summarized in Table 2.

Table 2.  Overview of Our Bright Sample and Proximity Zone Sizes

Name	R.A.	Decl.	z	Redshift Line	References	M1450 (mag)	Rp (pMpc)	${R}_{p,\mathrm{corr}}^{-25}$ (pMpc)
J0002+2550	00h02m3939	+25°50'3496	5.818 ± 0.007a	Mg ii	15	−27.31	8.83 ± 0.46	2.58 ± 0.13
J0005−0006	00h05m5234	−00°06'5580	5.844 ± 0.001	Mg ii	6	−25.73	2.91 ± 0.06	1.97 ± 0.04
J0050+3445	00h55m0291	+34°45'2165	6.253 ± 0.003	Mg ii	5	−26.70	3.96 ± 0.17	1.60 ± 0.07
J0148+0600	01h48m3764	+06°00'2006	5.98 ± 0.01	Mg ii	10	−27.39	6.11 ± 0.64	1.71 ± 0.18
J0210−0456	02h10m1319	−04°56'2090	6.4323 ± 0.0005	[C ii]	8	−24.53	1.38 ± 0.03	1.77 ± 0.04
J0226+0302	02h26m0187	+03°02'5942	6.5412 ± 0.0018	[C ii]	9	−27.33	3.66 ± 0.09	1.06 ± 0.03
J0227−0605	02h27m4329	−06°05'3020	6.212 ± 0.007a	Mg ii	15	−25.28	2.27 ± 0.40	1.95 ± 0.35
J0303−0019	03h03m3140	−00°19'1290	6.078 ± 0.007	Mg ii	3	−25.56	2.28 ± 0.44	1.69 ± 0.33
J0836+0054	08h36m4386	+00°54'5326	5.810 ± 0.003	Mg ii	2	−27.75	5.16 ± 0.20	1.19 ± 0.05
J0842+1218	08h42m2943	+12°18'5058	6.0763 ± 0.0005a	[C ii]	14	−26.91	6.95 ± 0.04	2.52 ± 0.01
J0927+2001	09h27m2182	+20°01'2364	5.7722 ± 0.0006	CO	4	−26.76	4.69 ± 0.05	1.84 ± 0.02
J1030+0524	10h30m2711	+05°24'5506	6.309 ± 0.009	Mg ii	1	−26.99	6.00 ± 0.51	2.08 ± 0.18
J1137+3549	11h37m1773	+35°49'5685	6.009 ± 0.010a	Mg ii	15	−27.36	5.81 ± 0.62	1.66 ± 0.18
J1148+5251	11h48m1665	+52°51'5039	6.4189 ± 0.0006	[C ii]	11	−27.62	4.70 ± 0.03	1.16 ± 0.01
J1250+3130	12h50m5193	+31°30'2190	6.138 ± 0.005a	Mg ii	15	−26.53	4.91 ± 0.29	2.17 ± 0.13
J1306+0356	13h06m0827	+03°56'2636	6.0337 ± 0.0004a	[C ii]	14	−26.81	6.51 ± 0.02	2.48 ± 0.01
J1319+0950	13h19m1130	+09°50'5152	6.1330 ± 0.0007	[C ii]	7	−27.05	4.99 ± 0.04	1.68 ± 0.01
J1335+3533	13h35m5081	+35°33'1582	5.9012 ± 0.0019	CO	4	−26.67	0.70 ± 0.10	0.29 ± 0.04
J1411+1217	14h11m1129	+12°17'3728	5.904 ± 0.002	Mg ii	2	−26.69	4.61 ± 0.13	1.88 ± 0.05
J1602+4228	16h02m5398	+42°28'2494	6.083 ± 0.005a	Mg ii	15	−26.94	6.82 ± 0.29	2.43 ± 0.10
J1623+3112	16h23m3181	+31°12'0053	6.2572 ± 0.0024	[C ii]	12	−26.55	5.05 ± 0.14	2.21 ± 0.06
J1630+4012	16h30m3390	+40°12'0969	6.065 ± 0.007	Mg ii	3	−26.19	5.25 ± 1.03	2.79 ± 0.55
J1641+3755	16h41m2173	+37°55'2015	6.047 ± 0.003	Mg ii	5	−25.67	4.00 ± 0.18	2.80 ± 0.13
J2054−0005	20h54m0649	−00°05'1480	6.0391 ± 0.0001	[C ii]	7	−26.21	3.12 ± 0.01	1.64 ± 0.01
J2229+1457	22h29m0165	+14°57'0900	6.1517 ± 0.0005	[C ii]	11	−24.78	0.48 ± 0.04	0.54 ± 0.04
J2329−0301	23h29m0828	−03°01'5880	6.4164 ± 0.0008a	[C ii]	13	−25.25	2.73 ± 0.04	2.39 ± 0.04

Notes. Same as Table 1, but for the bright sample from Eilers et al. (2017). Absolute magnitudes M₁₄₅₀ are taken from Bañados et al. (2016). References for redshifts: (1) Jiang et al. (2007), (2) Kurk et al. (2007), (3) Carilli et al. (2010), (4) Wang et al. (2010), (5) Willott et al. (2010), (6) De Rosa et al. (2011), (7) Wang et al. (2013), (8) Willott et al. (2013), (9) Bañados et al. (2015), (10) Becker et al. (2015), (11) Willott et al. (2015), (12) Eilers et al. (2017), (13) Willott et al. (2017), (14) Decarli et al. (2018), (15) Shen et al. (2019).

^aThe redshifts updated from Eilers et al. (2017), Willott et al. (2017); Decarli et al. (2018); Shen et al. (2019).

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Figure 1 compares magnitudes and redshifts between our new sample and that of Eilers et al. (2017). Our new sample is 2–3 mag fainter than that of Eilers et al. (2017). The combined sample gives us a dynamic range of 5 mag in luminosity.

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We estimate the quasar intrinsic spectra after normalizing at rest 1280 Å with principal component spectra (PCS) from a principal component analysis (PCA) of low-redshift quasar spectra. This approach is justified by lack of spectral evolution of quasars (e.g., Jiang et al. 2009). In PCA, the quasar spectrum, ${q}_{i}(\lambda )$, is modeled as a mean quasar spectrum, $\mu (\lambda )$, and a linear combination of PCS:

$$\begin{eqnarray}&&{q}_{i}(\lambda )\sim \mu (\lambda )+\displaystyle \sum _{j=1}^{m}{c}_{{ij}}{\xi }_{j}(\lambda ),\end{eqnarray} \tag{ 2 }$$

where i refers to a ith quasar, ${\xi }_{j}(\lambda )$ is the jth PCS, and c_ij is the weight. We use the PCS from Suzuki et al. (2005). First, ${c}_{{ij}}^{{\prime} }$, the weights for the spectrum redward of 1216 Å, are derived by

$$\begin{eqnarray}&&{c}_{{ij}}^{{\prime} }={\int }_{1216\mathring{A}}^{{\lambda }_{\mathrm{upper}}}[{q}_{i}(\lambda )-\mu (\lambda )]{\xi }_{j}(\lambda )d\lambda ,\end{eqnarray} \tag{ 3 }$$

where ${\lambda }_{\mathrm{upper}}$ is the upper limit of available wavelength in each observed quasar spectrum. Suzuki et al. (2005) produced PCS for 1216–1600 Å, while our faint sample usually has coverages up to ∼1350 Å.

Then we use the projection matrix ${\boldsymbol{X}}$ to calculate c_ij, the weights for the whole intrinsic spectrum, covering the entire spectral region between 1020 and 1600 Å, using

$$\begin{eqnarray}&&{c}_{{ij}}={c}_{{ij}}^{{\prime} }\cdot {\boldsymbol{X}}.\end{eqnarray} \tag{ 4 }$$

The projection matrix ${\boldsymbol{X}}$ is also taken from Suzuki et al. (2005). It is the matrix which satisfies the relation ${\boldsymbol{C}}={\boldsymbol{D}}\cdot {\boldsymbol{X}}$, where ${\boldsymbol{C}}$ and ${\boldsymbol{D}}$ are the weights of principal components of the whole and the redward of the quasar spectrum derived in Suzuki et al. (2005), respectively.

Eilers et al. (2017) mainly used PCS from Pâris et al. (2011), but we use PCS and the projection matrix from Suzuki et al. (2005), who constructed the PCS using fainter quasars at $z\lt 1$ than those of Pâris et al. (2011). However, we found no significant difference in the results between the two.We use five PCS for all quasar spectra.

The spectra of our faint sample and the PCA fits are shown in Figure 2.

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We adopt the same definition of proximity zone size as was used in Fan et al. (2006). It is the physical distance between the quasar host galaxy (${z}_{{\rm{Q}}}$) and the point where the transmitted flux ratio first drops below 0.1, using the observed quasar spectrum after smoothing to a resolution of 20 Å in the observed frame (${z}_{\mathrm{GP}}$). We regard the first of three consecutive pixels blueward of Lyα as the end of the proximity zone (Eilers et al. 2017), and calculate proximity zone sizes using

$$\begin{eqnarray}&&{R}_{p}=\displaystyle \frac{{D}_{{\rm{Q}}}-{D}_{\mathrm{GP}}}{1+{z}_{{\rm{Q}}}},\end{eqnarray} \tag{ 5 }$$

where ${D}_{{\rm{Q}}}$ and ${D}_{\mathrm{GP}}$ are the comoving distances implied by ${z}_{{\rm{Q}}}$ and ${z}_{\mathrm{GP}}$, respectively. Figure 3 shows the continuum-normalized spectra around the proximity zone of each quasar in our faint quasar sample, and the measured R_p are listed in Tables 1 and 2.

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In general, the observed wavelength range of the rest-UV spectrum of $z\sim 6$ quasars is limited, which could cause a poor prediction of the intrinsic spectrum using PCA. The near-IR (NIR) spectra are available for five quasars, J0859+0022, J1152+0055, J1208−0200, J2216−0016, and J2239+0207 (Onoue et al. 2019), which extend spectral coverage much further to $\sim 2.5\,\mu {\rm{m}}$. The NIR spectra of the first two, J0859+0022 and J1152+0055, were taken by the Very Large Telescope/X-SHOOTER, and the NIR spectra of the latter three were taken by the Gemini Near-InfraRed Spectrograph. In addition, for the first two, the optical spectra taken by X-SHOOTER are available, which have higher resolutions and deeper integrations than the FOCAS/OSIRIS one (Onoue et al. 2019). We use their optical and NIR spectra to measure R_p of these five quasars. When we use only the optical spectra, the resultant R_p are 1.22 ± 0.06 pMpc, 2.60 ± 0.03 pMpc, 0.62 ± 0.01 pMpc, 0.66 ± 0.02 pMpc, and 1.31 ± 0.02 pMpc. Three of them, J0859+0022, J1208−0200, and J2216−0016, are consistent within the errors with those in Table 1, suggesting that our R_p measurements are not significantly affected by the limited wavelength coverage.

Several quasars show a weak or no Lyα emission line, i.e., J1208−0200 and J1406−0116, as is often seen in $z\sim 6$ quasars (e.g., Bañados et al. 2014). This could give rise to a poor PCA fit around the wavelength of Lyα showing apparent negative Lyα emission. As a test, we remeasured R_p for these two quasars using a simple power-law fit to the continuum (Fan et al. 2006; Carilli et al. 2010) over wavelength intervals devoid of emission lines at 1275–1295 and 1325–1335 Å in the rest frame. The resultant R_p are 0.55 ± 0.01 pMpc and 1.03 ± 0.41 pMpc for J1208−0200 and J1406−0116, respectively. The R_p of J1406−0116 is larger than the PCA measurement, which gives an extremely small R_p, probably due to its relatively noisy spectrum. Although it is hard to determine which measurement is likely to be more accurate for J1406−0116 due to their relatively poor quality spectra, we decide to adopt the PCA measurement to keep consistency with the other sample. The R_p of J1406−0116 might have large uncertainty, but we find this discrepancy does not affect the final result of the luminosity (Section 4.2) and redshift (Section 4.3) dependences.

Figure 4 shows a comparison in R_p for the bright sample between our measurement and Eilers et al. (2017). They are in good agreement with each other except for those quasars whose redshifts have been updated using data from Willott et al. (2017), Decarli et al. (2018), and Shen et al. (2019). Consequently, this moderately changes the PCA fit, supporting our previous statement that accurate redshift measurements are needed for the accurate R_p measurements.

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It should be noted that the spectrum signal-to-noise ratios (S/N) of the faint sample are generally lower than those of the bright sample. We check the R_p uncertainties due to the spectral noise by the following Monte Carlo simulation using the noise spectra. In this process, the flux of each spectral pixel was associated with a random error perturbed within the measured 1σ error. We generated 100 mock spectra and repeated the PCA. The R_p uncertainty of the trials is found to be 0.33 ± 0.32 pMpc, which is comparable to the errors due to the redshift uncertainty, except for the two quasars J0921+0007 (0.71 pMpc) and J1202−0057 (1.06 pMpc). We also found the error is almost negligible for the two quasar spectra, J0859+0022 and J1152+0055, taken by X-SHOOTER. The 16th and 84th percentiles of these uncertainties are 0.07 pMpc and 0.64 pMpc, respectively. We confirm this additional error does not significantly change the result. It is not clear how large the error for the bright sample from Eilers et al. (2017) is. To make a fair comparison with the bright sample, this error is not taken into account.

To illustrate the luminosity dependence, we create mean-stacked spectra of the faint and the bright samples, and measure R_p for both. These spectra were generated by normalizing each spectrum by the flux density at 1280 Å of PCA fit, converting to the rest frame, and then mean stacking. When we measure R_p of these spectra, we assume the mean redshifts of each sample as the stacked quasar redshift. Figure 5 shows the two stacked spectra. The R_p of our faint and bright quasar samples are ${R}_{p}=2.23\pm 0.03$ pMpc and 5.45 ± 0.06 pMpc, respectively. Our faint sample shows significantly smaller R_p than that of the bright sample, as predicted by Equation (1).

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Matsuoka et al. (2019a) suggested the faint sample shows systematically narrower Lyα emission. The composite spectra shown in Figure 5 based on more accurate systemic redshift definitely shows that the faint quasar sample has narrower Lyα emission than the brighter sample. The reason for this is unclear, it may be partly due to contamination from narrow line quasars with exceptionally narrow Lyα emission lines (Kashikawa et al. 2015; Matsuoka et al. 2019a).

Figure 6 shows the relation between quasar proximity zone sizes R_p and quasar absolute magnitude M₁₄₅₀. We define α as a power-law index of luminosity dependence of R_p (${R}_{p}\propto {10}^{-0.4{M}_{1450}/\alpha }$). A power-law fit to our measurements weighted by errors gives $\alpha =1.80\pm 0.29;$

$$\begin{eqnarray}&&{R}_{p}=(1.73\pm 0.21)\times {10}^{-0.4\times ({M}_{1450}+25)/(1.80\pm 0.29)}\ \mathrm{pMpc}.\end{eqnarray} \tag{ 6 }$$

In the fit, we weight the measurement by the errors. The 1σ uncertainty of this fit is calculated by bootstrapping the fit 1000 times. The best fit described in Eilers et al. (2017) is

$$\begin{eqnarray}&&{R}_{p}=4.71\times {10}^{-0.4\times ({M}_{1450}+27)/3.42}\ \mathrm{pMpc}.\end{eqnarray} \tag{ 7 }$$

We normalize the relation at ${M}_{1450}=-25$, which is the midpoint of our data, while Eilers et al. (2017) normalized at ${M}_{1450}=-27$. We obtain a steeper relation than the best fit in Eilers et al. (2017). The luminosity dependence of proximity zone sizes could, in principle, depend on the IGM ionization state. Equation (1) indicates that R_p is proportional to $\alpha =3$ in the case of a neutral IGM, while Bolton & Haehnelt (2007) showed analytically that the proximity zone size scales as $\alpha =2$, in the case of a highly ionized IGM. Our result on the luminosity dependence is close to the prediction for the ionized IGM, suggesting that most of the surrounding IGM is ionized at $z\sim 6$. As described in the Introduction, the observed proximity zone sizes R_p are not strictly identical to the distances to the ionization front, and the actual luminosity dependence could be affected by the detailed ionizing process; therefore, radiative transfer simulations would be required to make a further comparison with our result. The simulation of Eilers et al. (2017), whose fit is over the luminosity range of their sample, predicts a scaling of $\alpha =2.35$ in a highly ionized IGM.

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In order to examine the redshift evolution of R_p, we use the luminosity scaling of our data from Equation (6);¹⁸

$$\begin{eqnarray}&&{R}_{p,{\rm{c}}{\rm{o}}{\rm{r}}{\rm{r}}}^{-25}={R}_{p}\times {10}^{0.4\times ({M}_{1450}+25)/1.80}\end{eqnarray} \tag{ 8 }$$

to rescale the measured R_p, and the derived ${R}_{p,\mathrm{corr}}^{-25}$ are listed in Tables 1 and 2. Figure 7 shows the redshift evolution of proximity zone sizes corrected by absolute magnitude. We define β as a power-law index of a dependence on redshifts of ${R}_{p,\mathrm{corr}}^{-25}$ (${R}_{p,\mathrm{corr}}^{-25}\propto {(1+z)}^{\beta }).$ A power-law fit using both the faint and the bright quasar sample gives $\beta =-3.79\pm 1.72;$

$$\begin{eqnarray}&&{R}_{p,\mathrm{corr}}^{-25}=(1.82\pm 0.18)\times {\left(\displaystyle \frac{1+z}{7}\right)}^{-3.79\pm 1.72}\mathrm{pMpc}.\end{eqnarray} \tag{ 9 }$$

The 1σ uncertainty is calculated by bootstrapping. The redshift dependency is steeper than the best fit by Eilers et al. (2017), $\beta =-1.44$. When we do not weight the measurement by the errors as Eilers et al. (2017) did not, a power-law fit gives $\beta =-1.61$, consistent with Eilers et al. (2017). It is substantially shallower than that found in earlier studies, which presented a linear fit to their corrected measurements for $z\gt 5.7$ quasars (Carilli et al. 2010; Venemans et al. 2015). When we correct R_p using Equation (8) for the measurements by Carilli et al. (2010) and Venemans et al. (2015), the power-law fit gives $\beta =-8.40\pm 0.91,-7.83\pm 0.36$, respectively. Thus we conclude that our R_p shows a mild evolution at $z\sim 6$.

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When using only the bright quasar sample, we obtain

$$\begin{eqnarray}&&{R}_{p,\mathrm{corr}}^{-25}=(1.78\pm 0.19)\times {\left(\displaystyle \frac{1+z}{7}\right)}^{-4.86\pm 1.94}\mathrm{pMpc},\end{eqnarray} \tag{ 10 }$$

as the best fit, which is consistent with Equation (9) for the full sample. We note that Eilers et al. (2017) corrected the luminosity dependence of R_p with a factor $\alpha =2.35$ rather than their best-fit result, $\alpha =3.42$. On the other hand, the best fit using the faint sample only is

$$\begin{eqnarray}&&{R}_{p,\mathrm{corr}}^{-25}=(1.68\pm 0.44)\times {\left(\displaystyle \frac{1+z}{7}\right)}^{-0.00\pm 2.00}\mathrm{pMpc}.\end{eqnarray} \tag{ 11 }$$

No redshift dependence is detected, and the ${R}_{p,\mathrm{corr}}^{-25}$ is slightly smaller than that of the bright sample only. All these three fits show a shallow to no redshift evolution. A Kolmogorov–Smirnov test to access the statistical significance of the difference between the faint sample and the bright sample yielded p = 0.93, suggesting that the difference between the two is statistically insignificant; the two samples have almost the same distribution of corrected proximity zone sizes, albeit the faint sample has large errors. The size of our faint sample is still small, and we will be able to make firmer conclusions as the sample of faint quasars with accurate redshifts grows.

Davies et al. (2019) presented a radiative transfer simulation to investigate the behavior of R_p. They found that the only quasars with ${R}_{p,\mathrm{corr}}\lesssim 2.5$ pMpc are young (${t}_{Q}\lesssim {10}^{4}$ yr), where R_p is normalized to an absolute magnitude of ${M}_{1450}=-27$. This corresponds to ${R}_{p,\mathrm{corr}}^{-25}\lesssim 0.90$ pMpc with our normalization at ${M}_{1450}=-25$ using Equation (8). There are two quasars that meet this criterion in the faint sample, J1208−0200 and J1406−0116, and two in the bright sample, J1335+3533 and J2229+1457, which Eilers et al. (2017) also suggested have an exceptionally small proximity zone size. We should note that the R_p measurement of J1406−0116 might be inaccurate due to a poor PCA fit (see Section 3.2). These four quasars may be young, but it is also possible that neutral gas lying along the quasar sightline truncates the proximity zones. One piece of evidence for such a clump of high column density neutral gas, such as damped Lyα systems (DLAs) and Lyman limit systems, would be the presence of associated metal-line absorbers (Eilers et al. 2017). Eilers et al. (2018b) conducted spectroscopic observations of J1335+3533 and ruled out the possibility that its small R_p is due to an associated absorption system. J1208−0200 shows significant absorption redward of the Lyα emission line, implying the presence of a strong foreground absorption feature such as a proximate DLA, which could exhibit low-ionization metal absorption lines. We search corresponding low-ionization metal absorption lines in the spectrum of J1208−0200, Si ii (1260.42 Å and 1304.37 Å), O i (1302.16 Å), and [C ii] (1334.53 Å), and find no clear absorption features. However, the spectra of our faint quasar sample, in general, have insufficient S/N to identify very weak metal absorption features.

Eight objects in our faint sample have Mg ii-based measurements of black hole mass ${M}_{\mathrm{BH}}$ and Eddington ratio (Onoue et al. 2019) and M. Onoue (2020, in preparation), as do 21 objects in the bright sample (Shen et al. 2019). We examine the correlation between black hole mass, Eddington ratio, and proximity zone size in Figure 8. Young quasar candidates suggested by extremely small R_p tend to have smaller ${M}_{\mathrm{BH}}$ and lower Eddington ratio, though there is no clear correlation.

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Meyer et al. (2019) found that the average blueshift of the C iv emission line with respect to low-ionization lines in quasar spectra increases significantly at $z\gt 6$. The authors interpreted this trend as due to strong outflows, likely related to the relative youth of high-z quasars. Five objects in our faint sample, J0859+0022, J1152+0055, J1208−0200, J2216−0016, and J2239+0207, were found to have significant C iv blueshift with respect to Mg ii lines (Onoue et al. 2019, Table 3). Interestingly, the quasar with the most extreme blueshifted C iv is J1208−0200 (1830 km s⁻¹), and J2216−0016 (1170 km s⁻¹) is the second most extreme among these five quasars. J1208−0200 is suggested as young quasar candidate because of its extreme small proximity zone, and J2216−0016 also exhibits a relatively small proximity zone, ${R}_{p,\mathrm{corr}}^{-25}=1.36$ pMpc. Both observational quantities consistently indicate the young age of quasars. Farina et al. (2019) recently conducted a sensitive search for extended Lyα halos around $z\sim 6$ quasars with the Multi Unit Spectroscopic Explorer. While they detected significant extended Lyα emissions around 12 quasars, one of the young quasar candidates, J2229+1457, does not show an extended Lyα halo. Another young quasar candidate from our faint sample, J2216−0016, is also observed by Farina et al. (2019) and it also does not have an extended Lyα halo. As discussed in Farina et al. (2019), a young quasar with ${t}_{Q}\lt {10}^{4}\,\mathrm{yr}$ does not have enough time to light up an extended Lyα halo with more than a 10 pkpc radius, large enough to be observed by their survey. Along with the proximity zone size and the C iv blueshift, the Lyα halo extension could be another promising observational diagnostic of young quasars; however, a larger sample is obviously required to make a clear conclusion.

Eilers et al. (2020) additionally found four young quasar candidates with extremely small proximity zone sizes. They constrained the fraction of young quasars within the luminous (${M}_{\mathrm{UV}}\lesssim -25$) quasars as $5 \% \lt {f}_{\mathrm{young}}\lt 9 \%$, while it is interesting to note that our faint sample exhibits a high fraction as $\sim 2/11\sim 18 \%$. Future observations of such first quasars will reveal the nature of quasar activity, such as their lifetime and duty cycle.