A SURVEY OF z ∼ 6 QUASARS IN THE SLOAN DIGITAL SKY SURVEY DEEP STRIPE. II. DISCOVERY OF SIX QUASARS AT z_AB>21

High-redshift quasars serve as cosmological probes for studying the early universe. In recent years, about 40 quasars at z ∼ 6 have been discovered; the most distant ones are at z ∼ 6.4 (Fan et al. 2006; Willott et al. 2007). They harbor billion-solar-mass black holes, and thus are essential in understanding black hole accretion and galaxy formation in the first billion years of cosmic time. Most of the known quasars at z ∼ 6 were discovered from ∼8000 deg² of imaging data of the Sloan Digital Sky Survey (SDSS; York et al. 2000). These luminous quasars (z_AB ⩽ 20, M₁₄₅₀ ∼ −27) were selected as i-dropout objects using optical colors; follow-up near-infrared (NIR) photometry and optical spectroscopy were used to distinguish against late-type dwarfs (e.g., Fan et al. 2001a). Several other high-redshift quasars have also been discovered based on their infrared or radio emission (e.g., Cool et al. 2006; McGreer et al. 2006).

Currently, ongoing surveys of z ∼ 6 quasars include the UKIRT Infrared Deep Sky Survey (UKIDSS; Warren et al. 2007) and the Canada–France High-redshift Quasar Survey (CFHQS; Willott et al. 2005). The UKIDSS survey is being carried out in the YJHK bands using the Wide-Field Camera (Casali et al. 2007) on the 3.8 m UKIRT telescope. It will survey 7500 deg² of the northern sky. The resulting NIR data together with the SDSS multicolor optical data can be used to select high-redshift quasar candidates. The UKIDSS team has found two quasars at z ∼ 6 (Venemans et al. 2007; Mortlock et al. 2008). These quasars are fainter than z_AB = 20, the magnitude selection limit that the SDSS team used (Fan et al. 2006). The CFHQS survey is an optical imaging survey of ∼550 deg² in the griz bands on the Canada–France–Hawaii Telescope (Willott et al. 2009). The survey is about 2 mag deeper than the SDSS wide survey. The CFHQS team has found 10 quasars at z ∼ 6 to date, including the most distant quasar known at z = 6.43 (Willott et al. 2007, 2009).

This paper is the second in a series presenting z ∼ 6 quasars selected from the SDSS southern survey, a deep imaging survey obtained by repeatedly scanning a 300 deg² stripe along the celestial equator. In Jiang et al. (2008, hereafter Paper I), we reported the discovery of five quasars at 5.85 ⩽ z ⩽ 6.12 in 260 deg² of the deep stripe. Together with another quasar known in this region (Fan et al. 2004), they constructed a complete flux-limited quasar sample at 20 < z_AB < 21. Based on the combination of this sample, the luminous quasar sample from ∼8000 deg² of SDSS, and the Cool et al. (2006) sample, we found a steep slope at the bright end of the quasar luminosity function (QLF) at z ∼ 6. In this paper, we present the discovery of six new quasars in the SDSS deep stripe. All six quasars are about 1 mag fainter than those reported in Paper I, or 2 mag fainter than the luminous SDSS quasars. With these new quasars, we can measure the QLF over 3 mag. The basic procedures of candidate selection, follow-up observations, and data reduction are similar to the procedures used in Paper I.

The structure of the paper is as follows. Section 2 briefly introduces the construction of the SDSS co-added imaging data. Section 3 describes our selection criteria and follow-up observations of quasar candidates. We present the six new quasars in Section 4 and discuss the QLF at z ∼ 6 in Section 5. We summarize the paper in Section 6. Throughout the paper, we use a Λ-dominated flat cosmology with H₀ = 70 km s⁻¹ Mpc⁻¹, Ω_m = 0.3, and Ω_Λ = 0.7 (Spergel et al. 2007).

2.1. SDSS Deep Imaging Data

The SDSS was an imaging and spectroscopic survey of the sky (York et al. 2000) using a dedicated wide-field 2.5 m telescope (Gunn et al. 2006) at Apache Point Observatory. Imaging was carried out in drift-scan mode using a 142 megapixel camera (Gunn et al. 1998) which gathered data in five broad bands, ugriz, spanning the range from 3000 to 10000 Å (Fukugita et al. 1996), on moonless photometric (Hogg et al. 2001) nights of good seeing. The effective exposure time was 54 s. The images were processed using specialized software (Lupton et al. 2001), and were photometrically (Tucker et al. 2006; Ivezić et al. 2004) and astrometrically (Pier et al. 2003) calibrated using observations of a set of primary standard stars (Smith et al. 2002) on a neighboring 20 inch telescope. All magnitudes are roughly on an AB system (Oke & Gunn 1983), and use the asinh scale described by Lupton et al. (1999).

The primary goal of the SDSS imaging survey was to scan 8500 deg² of the northern Galactic cap (hereafter referred to as the SDSS main survey). In addition to the main survey, SDSS also conducted a deep survey by repeatedly imaging a 300 deg² area on the celestial equator in the southern Galactic cap in the fall (hereafter referred to as the SDSS deep survey; Abazajian et al. 2009). This deep stripe (also called Stripe 82; see Stoughton et al. 2002) spans 20^h < R.A. < 4^h and −125 < decl. < 125. The multi-epoch images, when co-added, allow the selection of much fainter quasars than the SDSS main survey. We used the 10-run co-added data (constructed in 2005) in Paper I and found five z ∼ 6 quasars with 20 < z_AB < 21 in this area.

The construction of the co-added images is close, but not identical, to that of J. Annis et al. (2009, in preparation), Paper 1, and Abazajian et al. (2009). We used 50–60 scans from the SDSS deep southern stripe, restricting ourselves to fields with r band seeing less than 2'' and r-band sky fainter than 19.5 mag arcsec⁻². Because our selection algorithm uses only r-, i-, and z-band photometry, we did not co-add the u- and g-band data. The input images are the SDSS-corrected frames (or fpC images). Each input image was calibrated to a standard SDSS zero point and weighted on a field-by-field basis with

$$\begin{equation} w=\frac{T}{\rm FWHM^2\,\sigma ^2}, \end{equation} \tag{ 1 }$$

where T is the transparency as measured by the relative zero point of the image, FWHM is the full width at half-maximum of the point-spread function (PSF), and σ² is the variance of the sky. We did not use mask files in the weight map. After sky background was estimated and subtracted, the images were mapped onto a uniform rectangular output astrometric grid using a modified version of the registration software SWARP (Bertin et al. 2002). The weight maps were subjected to the same mapping. The final co-added images are about 2 mag deeper than the SDSS single-run data. The median seeing of the co-adds as measured in the z band is ∼12.

2.2. Photometry

3.1. Quasar Selection Procedure

3.2. NIR Photometry and Optical Spectroscopic Observations

From the spectroscopic observations of 32 candidates on the MMT we discovered six new quasars at z ∼ 6 in the SDSS deep stripe. The other candidates are all late M or L/T dwarfs. Figure 1 shows the z-band finding charts of the quasars, and Table 1 gives their optical and NIR properties. The i_AB and z_AB magnitudes are taken from the SDSS deep imaging data, and the Y and J magnitudes are obtained from our SQIID and PANIC observations. Four of the six quasars were discovered in our main quasar search and comprise a flux-limited sample at z_AB < 21.8. The other two quasars were found among our z_AB>22 candidates (although they are not a complete sample); their discovery implies that we can reach deeper than z_AB = 22 in the future. Figure 2 shows the optical spectra of the six quasars. The total exposure time on each quasar was 90–120 minutes on the MMT. Each spectrum has been scaled to the corresponding z_AB magnitude given in Table 1, and thereby is on an absolute flux scale with an uncertainty of ∼10%.

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In Paper I redshifts were measured from either the Lyα, N v λ1240 (hereafter N v), or the O i λ1304 (hereafter O i) emission line, but the quasars in this paper are 1 mag fainter, and the spectra do not have the signal-to-noise ratio (S/N) to detect weak lines. We thus estimate the redshifts from Lyα. Four quasars, SDSS J023930.24–004505.4¹¹ (hereafter SDSS J0239–0045), SDSS J214755.41+010755.3 (hereafter SDSS J2147+0107), SDSS J230735.35+003149.4 (here- after SDSS J2307+0031), and SDSS J235651.58+002333.3 (hereafter SDSS J2356+0023), have prominent Lyα emission lines. For each of them, we measure the Lyα line center using a Gaussian profile to fit the upper ∼50% of the line. Redshifts derived from the Lyα line center are usually biased because the blue side of Lyα is affected by Lyα forest absorption. The mean shift with respect to the systemic redshift at z>3 is about 600 km s⁻¹ (Shen et al. 2007), corresponding to δz ∼ 0.015 at z ∼ 6. We correct for this bias for the redshifts of the four quasars. The other two quasars, SDSS J012958.51–003539.7 (hereafter SDSS J0129–0035) and SDSS J205321.77+004706.8 (hereafter SDSS J2053+0047), show very weak Lyα emission. Their redshifts are simply estimated from the position of the onset of sharp Lyα absorption. The results are listed in Column 2 of Table 1. The redshift error of 0.03 quoted in the table is the scatter in the relation between Lyα redshifts and systemic redshifts measured from other lines (Shen et al. 2007), which is much larger than the statistical uncertainty of our fitting process.

We measure the rest-frame equivalent width (EW) and FWHM of the Lyα emission line for each quasar, after fitting and subtracting the continuum. The wavelength coverage of each spectrum is too short to fit the continuum slope, so we assume that it is a power law with a slope α_ν = −0.5 ($f_{\nu }\sim \nu ^{\alpha _{\nu }}$), and normalize it to the spectrum at rest frame 1275–1295 Å, a continuum window with little contribution from line emission. For the four quasars with prominent Lyα emission, we use double Gaussian profiles to fit the broad and narrow components of Lyα. In SDSS J2356+0023, N v is clearly detected and blended with Lyα, so we add an additional Gaussian profile for that line. Since the blue side of the Lyα emission line is strongly absorbed by the Lyα forest, we only fit the red side of the line and assume that the unabsorbed line is symmetric. We ignore the weak Si ii λ1262 emission line on the red side of N v. For the two quasars whose Lyα emission is very weak, we calculate the Lyα+N v EW by integrating the continuum-subtracted spectra over the wavelength range 1216 Å <λ₀< 1250 Å. The measured EW and FWHM are shown in Table 2. We also give the FWHM of Lyα in units of km s⁻¹. The EW and FWHM of Lyα for SDSS J0239–0045, SDSS J2147+0107, SDSS J2307+0031, and SDSS J2356+0023 have taken into account the effect of Lyα forest absorption; while for SDSS J0129–0035 and SDSS J2053+0047, the listed EW values include the N v line, and were not corrected for Lyα forest absorption. The best-fitting power-law continuum is also used to calculate m₁₄₅₀ and M₁₄₅₀, the apparent and absolute AB magnitudes of the continuum at rest frame 1450 Å. The results are given in the last two columns of Table 2.

The quasars in this paper have average Lyα EW and FWHM of 31 Å and 10 Å (with large scatters of 23 Å and 5 Å), significantly smaller than those in typical low-redshift quasars or more luminous quasars at z ∼ 6 (Paper I). This is not caused by a selection effect, since quasars with stronger Lyα emission have larger i–z colors and thus are easier to find by our selection criteria. The narrowness of the Lyα emission lines may imply small central black hole masses in these high-redshift objects. Black hole masses in quasars can be estimated from the widths of broad emission lines; strong UV lines such as C iv λ1549 (hereafter C iv) and Mg ii λ2800 (hereafter Mg ii) are frequently used (e.g., McLure & Dunlop 2004; Vestergaard & Peterson 2006; Shen et al. 2008). In luminous z ∼ 6 quasars black hole masses measured in this way are usually several billion solar masses (e.g., Jiang et al. 2007; Kurk et al. 2007). Although there is no established relation between the width of Lyα and those of C iv and Mg ii, the two narrow Lyα line quasars in Paper I (SDSS J000552.34–000655.8 and SDSS J030331.40–001912.9) also have narrow C iv and Mg ii lines. Their estimated black hole masses are only (2–3) × 10⁸ M_☉, and the corresponding Eddington luminosity ratios are close to 2 (Kurk et al. 2007, 2009). Therefore, the narrowness of the Lyα emission lines in this paper could also indicate small black hole masses and high Eddington luminosity ratios, suggesting that the black holes in low-luminosity quasars at early epochs grow on an Eddington timescale.

4.1. Notes on Individual Objects

We derive the spatial density of the four quasars with z_AB < 21.8 using the traditional 1/V_a method (Avni & Bahcall 1980). The available volume for a quasar with absolute magnitude M₁₄₅₀ and redshift z in a magnitude bin ΔM and a redshift bin Δz is

$$\begin{equation} V_{a} = \int _{\Delta M}\int _{\Delta z}p(M_{1450},z) \frac{dV}{dz} dz\,dM, \end{equation} \tag{ 4 }$$

where p(M₁₄₅₀, z) is the selection function, the probability that a quasar of a given M₁₄₅₀ and z would enter our sample given our selection criteria. The calculation of the selection function is described in detail in Paper I. We use one M₁₄₅₀–z bin for our small sample. The redshift integral is over the redshift range 5.7 < z < 6.6 and the magnitude integral is over the range covered by the sample. The spatial density and its statistical uncertainty can be written as

$$\begin{equation} \rho = \sum _i \frac{1}{V_{a}^{i}}, \ \ \sigma (\rho) = \left[\sum _i \left(\frac{1}{V_{a}^{i}}\right)^2 \right]^{1/2}, \end{equation} \tag{ 5 }$$

where the sum is over all quasars in the sample. We find that the spatial density at 〈M₁₄₅₀〉 = −25.1 is ρ = (7.5 ± 3.8) × 10⁻⁹ Mpc⁻³ mag⁻¹.

In the SDSS main survey, 17 quasars at z>5.7 were selected using similar criteria and comprise a flux-limited sample with z_AB < 20 over ∼8000 deg² (hereafter Sample I). The six quasars of Paper I form a flux-limited sample with z_AB < 21 (hereafter Sample II). The QLF at z ∼ 6 based on these two SDSS samples and the Cool et al. (2006) sample with one quasar is well fit to a single power law Φ(L₁₄₅₀) ∝ L^β₁₄₅₀, or,

$$\begin{equation} \Phi (M_{1450})=\Phi ^{\ast }10^{-0.4(\beta +1)(M_{1450}+26)}, \end{equation} \tag{ 6 }$$

with β = −3.1 ± 0.4. In this paper, four quasars make a flux-limited sample with 21.0 < z_AB < 21.8 over ∼195 deg² (hereafter Sample III). We combine the three SDSS samples to derive the QLF at z ∼ 6. The quasars in Sample I are divided into three luminosity bins as shown in Figure 3. As described in Paper I, we assume that the bright-end QLF is a power law, and we use Equation (5) to fit (1) Samples I and II (the four luminous data points in Figure 3) and (2) Samples I–III (all the data points in Figure 3). We only consider luminosity dependence and neglect redshift evolution over our narrow redshift range. We find that β = −2.9 ± 0.4 and −2.6 ± 0.3, respectively, and the goodness of fit in both cases is acceptable (χ²_ν = 0.7 and 0.9) due to large statistical errors. At low redshift, QLFs can be described by a double power law characterized by a break luminosity, and bright-end and faint-end slopes. The current sample is not deep enough to reach the break luminosity at z ∼ 6. The derived slope at z ∼ 6 is slightly flatter than the bright-end slope at z ∼ 2 but steeper than that at z ∼ 4 (Richards et al. 2006; Hopkins et al. 2007).

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Sample III does not include any quasars at z>6.1. The fraction of z>6.1 quasars among the known SDSS quasars at z>5.7 is ∼25%, so the probability of having no z>6.1 quasars among a sample of six is (0.75)⁶ = 0.18, if they obey the same redshift distribution. This is not a small probability, but to test our sensitivity to an as yet undiagnosed selection bias against z>6.1 quasars, we recalculated the spatial density of Sample III over the redshift range 5.7 < z < 6.1. The power-law slope of the QLF changes from −2.6 to −2.8, i.e., by less than 1σ.

We have discovered six quasars in the redshift range 5.8 ⩽ z ⩽ 6.0 in the SDSS deep stripe. The objects are about 2 mag fainter than the luminous z ∼ 6 quasars found in the SDSS main survey (Fan et al. 2006) and 1 mag fainter than the quasars reported in Paper I. The Lyα emission lines in these quasars are significantly weaker and narrower than those in low-redshift quasars or more luminous quasars at z ∼ 6. The narrowness of the emission lines may indicate small black hole masses and high Eddington luminosity ratios, and therefore short black hole growth timescales.

Four of the quasars make a flux-limited sample at z_AB < 21.8 over an effective area of 195 deg². The other two quasars were found in a search for quasars with z_AB>22, and do not comprise a complete sample. The comoving quasar spatial density at 〈M₁₄₅₀〉 = −25.1 is (7.5 ± 3.8) × 10⁻⁹ Mpc⁻³ mag⁻¹. We model the QLF at z ∼ 6 based on the combination of this sample, the luminous SDSS quasar sample, and the Paper I sample. The QLF is well described as a single power law Φ(L₁₄₅₀) ∝ L^β₁₄₅₀ with a slope β = −2.6 ± 0.3 down to M₁₄₅₀ ∼ −25. The slope changes to −2.9 ± 0.4 if the new sample is excluded.

The discovery of the two faintest quasars in this paper indicates that we can probe 0.5 mag deeper than the complete z_AB < 21.8 sample. We are constructing new co-added images by including more available data and by improving our co-addition procedure. The new co-added images will be run through PHOTO for accurate PSF photometry. We hope to obtain a complete sample with z_AB ⩽ 22.5 over the full SDSS southern stripe in the next few years.

We acknowledge supports from NSF grants AST-0307384 and AST-0806861 and a Packard Fellowship for Science and Engineering (L.J., X.F., and F.B.). X.F. also acknowledges support from Max Planck Society. M.A.S. acknowledges the support of NSF grant AST-0707266. We thank the MMT staff, Magellan staff, and KPNO staff for their expert help in preparing and carrying out the observations.

Funding for the SDSS and SDSS-II has been provided by the Alfred P. Sloan Foundation, the Participating Institutions, the National Science Foundation, the U.S. Department of Energy, the National Aeronautics and Space Administration, the Japanese Monbukagakusho, the Max Planck Society, and the Higher Education Funding Council for England. The SDSS Web site is http://www.sdss.org/. The SDSS is managed by the Astrophysical Research Consortium for the Participating Institutions. The Participating Institutions are the American Museum of Natural History, Astrophysical Institute Potsdam, University of Basel, University of Cambridge, Case Western Reserve University, University of Chicago, Drexel University, Fermilab, the Institute for Advanced Study, the Japan Participation Group, Johns Hopkins University, the Joint Institute for Nuclear Astrophysics, the Kavli Institute for Particle Astrophysics and Cosmology, the Korean Scientist Group, the Chinese Academy of Sciences (LAMOST), Los Alamos National Laboratory, the Max-Planck-Institute for Astronomy (MPIA), the Max-Planck-Institute for Astrophysics (MPA), New Mexico State University, Ohio State University, University of Pittsburgh, University of Portsmouth, Princeton University, the United States Naval Observatory, and the University of Washington.

Facilities: Sloan, Mayall (SQIID), Magellan:Baade (PANIC), MMT (Red Channel Spectrograph)