The Infrared Medium-deep Survey. VI. Discovery of Faint Quasars at z ∼ 5 with a Medium-band-based Approach

Here we describe the imaging data from which quasar candidates are selected based on the broadband colors. This selection is the initial step of the high-redshift quasar selection, which will be refined later through medium-band imaging follow-up observations (Section 3). The sample selection was first carried out on the optical data from the CFHTLS Wide Survey (Hudelot et al. 2012) and the NIR data from the IMS (M. Im et al. 2018, in preparation) and the Deep eXtragalactic Survey (DXS; Lawrence et al. 2007). There are four extragalactic fields covered by these surveys: XMM-Large Scale Structure survey region (XMM-LSS), CFHTLS Wide survey second region (CFHTLS-W2), Extended Groth Strip (EGS), and Small Selected Area 22h (SA22). Figure 1 shows the positions and layouts of tiles in CFHTLS (black squares), IMS (blue squares), and DXS (purple squares). Hereafter, for convenience, we refer to the combination of NIR data from IMS and DXS as "IMS."

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For CFHTLS, we used stacked images from the TERAPIX processing pipeline (see Hudelot et al. 2012 and the T0007 documentation file¹³ ), which are given for each CFHTLS tile in each CFHTLS field. Note that "CFHTLS tile" here denotes the 1° × 1° area named from the position of each MegaCam field of view of the Wide survey (e.g., W1+0+0), while "CFHTLS field" indicates the four extragalactic fields of the Wide survey (e.g., W1, W2, W3, and W4). The zero-point (zp) of each tile was reestimated by comparing the point sources in CFHTLS with those in Sloan Digital Sky Survey Data Release 12 (SDSS DR12). Through the SQL service of SDSS, we selected point sources, classified as star-like sources, within the appropriate magnitude range of 17 < r < 18.5, considering the saturation level of CFHTLS and the photometric accuracy (magnitude errors <0.1 mag) of SDSS data in all the bands. For the position-matched sources with reliable photometry (i.e., spatially isolated point sources without saturation), we compared their auto-magnitudes (MAG_AUTO in SExtractor; Bertin & Arnouts 1996) from CFHTLS with their point-spread function (PSF) magnitudes from SDSS and determined a reliable zp for each tile. In this process, we converted the auto-magnitudes in optical bands (u'g'r'i'z') into SDSS photometric systems (ugriz), following the transformations from MegaCam to SDSS.¹⁴ For the tiles, which do not overlap with the SDSS area, we used the overlapped stars in adjacent CFHTLS fields. The average and standard deviation of the zp value offsets in u, g, r, i, and z bands are 0.14 ± 0.04 mag, −0.06 ± 0.02 mag, −0.05 ± 0.02 mag, −0.06 ± 0.02 mag, and −0.09 ± 0.03 mag, respectively.

On the other hand, for IMS, we stacked the images of each detector covering the area of 1365 × 1365 instead of stacking the images of each IMS tile covering the 0.75 × 0.75 deg² area, in order to determine a reliable zp for each image. The zp of each stacked image was scaled to 28.0 in the Vega system by comparing the J-band auto-magnitudes of point sources in IMS and those from the Two Micron All Sky Survey (2MASS) catalog (Skrutskie et al. 2006). The average 5σ point-source detection limits of the optical/NIR images are u = 26.1 mag, g = 26.4 mag, r = 25.9 mag, i = 25.6 mag, z = 24.6 mag, and J = 22.9 mag¹⁵ , enabling us to select z ∼ 5 quasars with i ≲ 23 mag or those as faint as M₁₄₅₀ ≲−23 mag. For photometry, we detected sources in the i'-band images and estimated fluxes in each band within 2 × FWHM_i' diameters, using the dual-image mode of the SExtractor software, with DETECT_THRESH of 1.3 and DETECT_MINAREA of 9, corresponding to a ∼4σ detection limit. By applying aperture correction factors derived from bright stars in each filter image, we converted the aperture magnitudes to total magnitudes. Note that the total magnitudes were also converted to the SDSS photometric system.

Although we adjusted the zp values of the optical/NIR images with point sources in the SDSS/2MASS catalogs, respectively, there are small inconsistencies of stellar loci on the order of ≲0.1 mag on color–color diagrams from tile to tile. Compared to the stellar libraries of Pickles (1998), these offsets were already reported by the TERAPIX team as one can see in their color–color diagrams (see footnote 13). Since the color offset can affect the quasar candidate selection substantially, we calculated the color offsets of stellar loci in each CFHTLS tile to correct the inconsistencies and improve the color selection for quasar candidates (see details in Appendix A). Note that the color offsets are not adjusted for the apparent magnitudes of the quasars in this paper, but are used only for the color selection of quasar candidates in Section 2.2.

For the Galactic extinction correction, we used the extinction map of Schlafly & Finkbeiner (2011) with the Cardelli et al. (1989) law assuming R_V = 3.1. To account for the pixel-to-pixel correlation from the image-combining process, we scaled magnitude errors accordingly, using the noise properties (σ_N) of an effective aperture size N in each image (Gawiser et al. 2006; Jeon et al. 2010; Kim et al. 2015).

The broadband color selection follows the criteria of McGreer et al. (2013), where they defined the color selection by simulating the color tracks using low-redshift SDSS quasar spectra that are redshifted to z ∼ 5. Considering the deeper depths of CFHTLS and IMS, we made a minor change to the i-magnitude limit. The following shows the selection criteria that we used:

• 1.  
  i < 23,
• 2.  
  S/N (u) < 2.5,
• 3.  
  g−r > 1.8 or S/N (g) < 3.0,
• 4.  
  r−i > 1.2,
• 5.  
  i−z < 0.625 ((r−i) − 1.0),
• 6.  
  i−z < 0.55,
• 7.  
  i − J < ((r−i) − 1.0) + 0.56,

where the signal-to-noise ratio (S/N) values are directly estimated from the fluxes and flux errors in the aperture mentioned above. The candidates satisfying the criteria were visually inspected to exclude spurious objects such as cross-talks, diffraction spikes, etc., resulting in 70 z ∼ 5 quasar candidates. The positions of the candidates (orange circles) are plotted on the layouts in Figure 1. Figure 2 shows the color–color diagrams (g − r versus r − i, r − i versus i − z, and r − i versus i − J) of objects in the multiband catalog and the broadband color selection criteria (the black solid lines). The broadband photometries of our candidates are listed in Table 1. In this paper, we only include the candidates that are spectroscopically observed in this work or previous works (e.g., M18) and also observed in medium bands, instead of the full sample of our candidates (see details of the spectroscopic sample in Section 4).

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To further exclude interlopers and better determine redshifts photometrically, we observed our candidates in medium bands with SQUEAN from 2015 December to 2018 April. Since the Lyman-alpha (Lyα; 1216 Å) break of a z ∼ 5 quasar is expected to be located at λ_obs ∼ 7300 Å, the medium-band observations were performed mainly with the m725 and m775 filters. If the two medium-band data were not enough to identify the object as a z > 5.1 quasar (i.e., m725 − m775 < 1; see Section 3.2), additional imaging data in the m675 band were also obtained. For the spectroscopically identified quasars, if needed, observations in the m675 and/or m825 bands were also carried out to check the accuracy of the ${z}_{\mathrm{phot}}$ from medium-band data. For each band, we took 3–70 frames with exposure times of 1–3 minutes, which gives the total integration time of 0.05–1.75 hr per band per filter. Note that brighter candidates (i < 22 mag) were observed as high-priority targets, when the observing condition was unstable with a seeing size of >12. Among the 70 quasar candidates, 58 candidates were observed in the m725 and m775 bands, and 45 of them were further observed in the m675 band.

We reduced the medium-band data, following the procedure in Jeon et al. (2016). After subtracting the bias and dark frames, we divided the science frames by the normalized flat frames, which were produced from the twilight sky. Excluding the images taken under bad weather conditions (e.g., low signals due to heavy clouds), the science images after the reduction were combined. We first detected the sources in the combined images with a detection threshold of ∼2.7σ (DETECT_THRESH of 1.2 and DETECT_MINAREA of 5). The zp of each medium-band image was determined by fitting the stellar templates to the broadband photometry (riz) of stars in each field (see details in Jeon et al. 2016). Note that we regarded auto-magnitudes of the stars in each medium band as total magnitudes for the zp determination. The uncertainty in the zp determination is found to be ∼0.03 mag, by taking the standard deviation of the zp values from the stars in the same field. For each quasar candidate, we estimated the aperture magnitude (size of 2 × FWHM_mb is used, where FWHM_mb is FWHM of point sources in each medium-band image) with forced photometry on the target position determined in the i-band image. We applied the aperture correction factor determined from the stars in each field. Like the broadband photometry, the Galactic extinction was corrected by following the Cardelli et al. (1989) law assuming R_V = 3.1 with the extinction map of Schlafly & Finkbeiner (2011), and we also scaled the SExtractor-derived magnitude errors to account for the correlated noise in the stacked image (σ_N). We gave the upper limit, which is defined as the magnitude limit for the 2.7σ detection, to the objects with no detection or magnitudes less than the upper limit. The observing runs and the medium-band photometry are given in Table 2. As with Table 1, only the spectroscopically examined candidates are listed.

Figure 3 shows the color–color diagrams for the medium bands only (top panel for m675−m725 versus m725−m775) and for the combinations of broad- and medium-band colors (bottom panels for r − i versus m675−m725 and r − i versus m725−m775, respectively). The gray filled circles represent the colors of the 175 star templates covering various spectral types and luminosity classes (Gunn & Stryker 1983) and the 41 L/T dwarf star models (Burrows et al. 2006). The other symbols are identical to those in Figure 2. We followed the color selection criteria with medium bands suggested by Jeon et al. (2016):

• 1.  
  m675 − m725 > 1 and m675 − m725 > m725−m775 + 1.5 (4.7 < z < 5.1),
• 2.  
  m725 − m775 > 1 (5.1 < z < 5.5),

which are plotted as dotted lines in Figure 3. The top panel in the figure shows the above criteria at a glance. Among 45 candidates observed in the m675, m725, and m775 bands, 33 candidates satisfy the above color selection criteria. The medium-band color criteria (m675 − m725 > 1 and m725 − m775 > 1) could be roughly adopted to the combination of broad- and medium-band colors (dashed lines). Note that the former criterion is limited by r − i color: m675−m725 > 0.5 (r−i) − 0.25.

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Spectroscopic observations of 13 candidates were carried out with Gemini Multi-Object Spectrographs (GMOS; Hook et al. 2004) on Gemini-North and Gemini-South 8 m Telescopes at Maunakea, Hawaii, and Cerro Pachon, Chile, respectively, on 2016 September 3–8 (PID: GS-2016B-Q-46), 2018 March 20 and June 18 (PID: GS-2018A-Q-220), and 2018 May 18 (PID: GN-2018A-Q-315). The sky was almost clear, with average seeings of ∼10. To ease the sky subtraction for the faint targets, the Nod & Shuffle (N&S) observing mode was adopted with a 10 width N&S slit. The spectra were obtained by using the R150+_G5326 grating, which has a resolution of R ∼ 315 at 717 nm for a slit width of 10, and the GG455_G0329 or OG515_G0330 filters to avoid the zeroth-order overlap. This setup gives the wavelength range of 4550 or 5150–10300 Å. In order to cover the gaps between the chips on the Hamamatsu CCD, the central wavelengths were set to 7100 and 7250 Å. This setting allows the detection of the redshifted Lyα break, which is expected to be located at ∼7200 Å for z ∼ 5 quasars. For the observing run in the 2018A semester, we set the central wavelengths to 4300 and 4600 Å for the Gemini-South, in order to avoid the bad columns on the CCD, and 6350 and 6650 Å for the Gemini-North. Note that we adopted a 4 × 4 binning in spatial/spectral pixels to maximize the S/N.

For one target, IMS J221046+024313, we obtained its spectrum through the MOS observing mode of GMOS-S (PID: GS-2016B-Q-11), during which we observed other targets of interest for another program. For the MOS observation with the N&S mode, we used the same R150+_G5326 grating with the RG610_G0331 filter, and the central wavelengths were set to 8900 and 9000 Å. To increase the S/N, the spectrum was also binned with 4 × 4.

For data reduction, the spectra were processed by using the Gemini IRAF package. After the bias subtraction and flat-fielding, sky lines were subtracted with the shuffled spectra. The wavelength calibration was done with CuAr arc lines, and the flux calibration was done with standard stars (LTT 7379, CD 329927, and Wolf 1346). For IMS J221036 + 024313 with the MOS observation, the wavelength calibration preceded the sky subtraction owing to the alignments of sky lines in the spatial direction. The aperture size for the spectral extraction was set at 10 in diameter for all cases. Note that the overall flux scale of each spectrum was adjusted using the i-magnitude of each target. In order to increase the S/N, we binned the spectra along the spectral direction by a factor of 2–5 (pixels) by using the inverse-variance weighting method (e.g., Kim et al. 2018). This binning gives the spectral resolution of ∼300.

The optical spectra of the other two candidates were obtained by the Inamori-Magellan Areal Camera and Spectrograph (IMACS; Dressler et al. 2011) on the Magellan Baade 6.5 m Telescope in Las Campanas Observatory, Chile, on 2016 December 3–5. Unlike the Gemini observations, the Magellan spectra were obtained with a standard long-slit mode (not N&S). We used the f/4 camera of IMACS with a grating of 150 lines mm^–1, giving a spectral resolution of ∼600 at 7200 Å for a 09 slit, and used the OG570 filter to avoid the overlap. This setup gives a wavelength coverage of 5700–9740 Å. Note that we used chips 5 and 8 of the f/4 camera, which have the highest sensitivities among the IMACS CCD chips. To maximize the S/N, each spectrum was binned by 2 × 2 during the observation.

For data reduction, we followed general reduction processes: bias subtraction and flat-fielding. After the wavelength calibration with HeNeAr lines, we generated 2D maps of sky lines, by performing a polynomial fitting for pixel values along the spatial direction. We combined the processed 2D spectra from different chips with the astronomical software SWarp (Bertin 2010). Note that there are CCD gaps along the spectral direction, which are located at λ_obs = 6530–6630 Å and >9700 Å. Identical to the Gemini spectra, the fluxes within a 10 diameter aperture were extracted and flux-calibrated using both the spectra of A0V standard stars (HD 18225, HD 85589) and the i-magnitude of each target. The binning was also performed for these spectra in a similar way to that for the Gemini spectra, but the binned spectra have a spectral resolution of ∼600.

For some of the medium-band observed objects, we adopted their spectral parameters such as ${z}_{\mathrm{spec}}$ and M₁₄₅₀ from the literature. They mainly come from the catalog of z ∼ 5 quasar candidates by M18, which also used the optical data from CFHTLS to select quasar candidates. Of the 38 quasars they identified with spectroscopy, we used spectral parameters of 18 quasars; they are located in our survey area (IMS) and satisfy our broadband color criteria with the magnitude limit (i ≲ 23 mag). Two quasars among them, IMS J221520−000908 and IMS J222216−000406, are also identified by Ikeda et al. (2017), but we took their spectral parameters from M18. Note that we revise the ${z}_{\mathrm{spec}}$ of IMS J140150+514310 from 4.20 in M18 to 5.17 since the Lyα and Lyβ lines are located at 7500 and 6320 Å, respectively, along with other possible emission lines at the same redshift (see Figure 9 of M18). The M₁₄₅₀ value of the quasar is also revised with the ${z}_{\mathrm{spec}}$. Additionally, we used the spectral parameters of four quasars, which are not included in the final catalog of M18 but spectroscopically identified by them. Consequently, we used the ${z}_{\mathrm{spec}}$ and M₁₄₅₀ values of 22 quasars from M18, which are listed in Table 4. Note that there are no M₁₄₅₀ values for the four quasars excluded in the final catalog of M18. Including our spectroscopically identified quasars, the total number of spectroscopically identified quasars we used for our study is 35.

Table 4.  Quantities of z ∼ 5 Quasars from the Model Fitting

	Photometry				Spectroscopy
ID	${z}_{\mathrm{phot}}$	M1450	${\alpha }_{\lambda }$	log EW	${z}_{\mathrm{spec}}$	M1450	log EW	References
		(mag)		(Å)		(mag)	(Å)
IMS J021315−043341	${4.70}_{-0.10}^{+0.23}$	$-{23.7}_{-0.2}^{+0.1}$	$-{1.8}_{-0.9}^{+0.5}$	${0.9}_{-0.3}^{+0.8}$	${4.884}_{-0.035}^{+0.003}$	$-{23.65}_{-0.45}^{+0.73}$	${1.9}_{-0.3}^{+0.3}$	(1)
IMS J021523−052946	${5.22}_{-0.07}^{+0.17}$	$-{25.8}_{-0.1}^{+0.1}$	$-{2.6}_{-0.6}^{+0.4}$	≲0.5	5.13	−25.6	⋯	(2)
IMS J021811−064843	${4.71}_{-0.07}^{+0.04}$	$-{24.8}_{-0.1}^{+0.1}$	$-{1.8}_{-0.5}^{+0.5}$	${0.9}_{-0.3}^{+0.7}$	${4.874}_{-0.028}^{+0.033}$	$-{24.66}_{-0.20}^{+0.23}$	${1.6}_{-0.6}^{+0.2}$	(1)
IMS J022112−034232	${4.73}_{-0.03}^{+0.17}$	$-{24.5}_{-0.2}^{+0.1}$	$-{1.8}_{-0.7}^{+0.4}$	${1.9}_{-0.6}^{+0.2}$	${4.976}_{-0.003}^{+0.003}$	$-{24.27}_{-0.14}^{+0.23}$	${2.2}_{-0.2}^{+0.2}$	(1)
IMS J022113−034252	${4.74}_{-0.01}^{+0.03}$	$-{26.4}_{-0.1}^{+0.1}$	$-{1.8}_{-0.2}^{+0.4}$	${1.9}_{-0.2}^{+0.2}$	5.02	−27.0	⋯	(2)
IMS J085024−041850	${4.70}_{-0.14}^{+0.07}$	$-{24.1}_{-0.1}^{+0.1}$	$-{2.8}_{-0.7}^{+1.0}$	${1.3}_{-0.7}^{+0.4}$	${4.799}_{-0.003}^{+0.003}$	$-{24.18}_{-0.08}^{+0.07}$	${2.0}_{-0.2}^{+0.2}$	(1)
IMS J085028−050607	${5.20}_{-0.04}^{+0.17}$	$-{23.9}_{-0.1}^{+0.2}$	$-{2.4}_{-1.1}^{+1.0}$	${1.7}_{-0.2}^{+0.2}$	${5.357}_{-0.008}^{+0.003}$	$-{23.47}_{-0.11}^{+0.22}$	${2.2}_{-0.2}^{+0.2}$	(1)
IMS J085225−051413	${4.77}_{-0.09}^{+0.20}$	$-{23.5}_{-0.1}^{+0.2}$	$-{2.8}_{-0.7}^{+1.0}$	${1.1}_{-0.5}^{+0.6}$	${4.819}_{-0.003}^{+0.003}$	$-{23.67}_{-0.08}^{+0.08}$	${1.7}_{-0.2}^{+0.2}$	(1)
IMS J085324−045626	${4.74}_{-0.10}^{+0.21}$	$-{23.8}_{-0.2}^{+0.1}$	$-{2.2}_{-0.8}^{+0.7}$	${1.1}_{-0.5}^{+0.6}$	${4.832}_{-0.004}^{+0.004}$	$-{23.89}_{-0.05}^{+0.04}$	${1.8}_{-0.2}^{+0.2}$	(1)
IMS J135747+530543	${5.20}_{-0.03}^{+0.10}$	$-{25.5}_{-0.1}^{+0.1}$	$-{2.0}_{-0.5}^{+0.4}$	${1.5}_{-0.2}^{+0.2}$	5.32	−25.5	⋯	(2)
IMS J135856+514317	${4.91}_{-0.04}^{+0.04}$	$-{25.7}_{-0.1}^{+0.1}$	$-{2.4}_{-0.3}^{+0.4}$	${1.3}_{-0.2}^{+0.2}$	4.97	−25.9	⋯	(2)
IMS J140147+564145	${4.76}_{-0.02}^{+0.06}$	$-{24.5}_{-0.1}^{+0.1}$	$-{1.8}_{-0.5}^{+0.2}$	${2.1}_{-0.2}^{+0.2}$	4.98	−24.7	⋯	(2)
IMS J140150+514310	${5.16}_{-0.01}^{+0.15}$	$-{23.4}_{-0.1}^{+0.2}$	$-{2.0}_{-0.9}^{+0.6}$	${1.9}_{-0.2}^{+0.2}$	5.17a	$-{23.4}^{a}$	⋯	(2)
IMS J140440+565651	${4.56}_{-0.03}^{+0.09}$	$-{24.7}_{-0.1}^{+0.1}$	$-{1.6}_{-0.8}^{+0.4}$	$\lesssim 0.5$	4.74	⋯	⋯	(2)
IMS J141432+573234	${5.14}_{-0.07}^{+0.04}$	$-{24.8}_{-0.1}^{+0.1}$	$-{2.4}_{-0.8}^{+0.9}$	${1.3}_{-0.7}^{+0.3}$	5.16	−24.7	⋯	(2)
IMS J142635+543623	${4.75}_{-0.01}^{+0.01}$	$-{26.2}_{-0.1}^{+0.1}$	$-{2.0}_{-0.5}^{+0.2}$	${1.7}_{-0.2}^{+0.2}$	4.76	−26.3	⋯	(2)
IMS J142854+564602	${4.73}_{-0.12}^{+0.27}$	$-{24.0}_{-0.3}^{+0.1}$	$-{1.8}_{-1.1}^{+0.5}$	$\lesssim 0.5$	4.73	−24.0	⋯	(2)
IMS J143156+560201	${4.72}_{-0.04}^{+0.04}$	$-{25.3}_{-0.1}^{+0.1}$	$-{2.2}_{-0.6}^{+0.7}$	$\lesssim 0.5$	4.75	⋯	⋯	(2)
IMS J143705+522801	${4.83}_{-0.11}^{+0.14}$	$-{23.8}_{-0.1}^{+0.2}$	$-{2.4}_{-0.5}^{+0.7}$	${1.5}_{-0.5}^{+0.4}$	4.78	⋯	⋯	(2)
IMS J143757+515115	${5.33}_{-0.24}^{+0.12}$	$-{24.2}_{-0.1}^{+0.3}$	$-{2.0}_{-0.7}^{+1.0}$	${1.5}_{-0.9}^{+0.3}$	5.17	−24.1	⋯	(2)
IMS J143804+573646	${4.83}_{-0.20}^{+0.20}$	$-{23.5}_{-0.2}^{+0.2}$	≲−3.6	${0.7}_{-0.2}^{+1.0}$	4.84	−23.5	⋯	(2)
IMS J143831+563946	${4.74}_{-0.07}^{+0.04}$	$-{24.5}_{-0.1}^{+0.1}$	≲−3.6	${1.1}_{-0.5}^{+0.5}$	4.82	⋯	⋯	(2)
IMS J143945+562627	${4.70}_{-0.06}^{+0.03}$	$-{23.4}_{-0.1}^{+0.1}$	$-{1.4}_{-0.8}^{+0.8}$	${1.9}_{-0.9}^{+0.2}$	4.70	−23.2	⋯	(2)
IMS J220233+013120	${5.31}_{-0.23}^{+0.10}$	$-{24.5}_{-0.1}^{+0.2}$	$-{2.8}_{-0.7}^{+1.0}$	≲0.5	${5.208}_{-0.003}^{+0.022}$	$-{23.85}_{-0.13}^{+0.10}$	${2.0}_{-0.2}^{+0.2}$	(1)
IMS J220522+025730	${4.65}_{-0.07}^{+0.07}$	$-{24.4}_{-0.1}^{+0.1}$	$-{1.8}_{-0.6}^{+0.5}$	${1.3}_{-0.7}^{+0.4}$	${4.743}_{-0.012}^{+0.004}$	$-{24.40}_{-0.12}^{+0.15}$	${1.8}_{-0.2}^{+0.2}$	(1)
IMS J220635+020136	${5.05}_{-0.15}^{+0.07}$	$-{24.2}_{-0.1}^{+0.1}$	$-{1.4}_{-0.5}^{+0.3}$	${1.9}_{-0.3}^{+0.2}$	${5.101}_{-0.003}^{+0.003}$	$-{24.41}_{-0.08}^{+0.11}$	${1.9}_{-0.2}^{+0.2}$	(1)
IMS J221004+025424	${4.55}_{-0.05}^{+0.07}$	$-{23.6}_{-0.1}^{+0.1}$	$-{1.2}_{-0.7}^{+0.4}$	${1.7}_{-0.7}^{+0.4}$	${4.638}_{-0.004}^{+0.003}$	$-{23.80}_{-0.05}^{+0.06}$	${1.8}_{-0.2}^{+0.2}$	(1)
IMS J221037+024314	${5.15}_{-0.06}^{+0.07}$	$-{25.2}_{-0.1}^{+0.1}$	$-{1.8}_{-0.7}^{+0.6}$	${0.9}_{-0.3}^{+0.6}$	${5.204}_{-0.012}^{+0.010}$	$-{25.23}_{-0.03}^{+0.03}$	${1.4}_{-0.2}^{+0.2}$	(1)
IMS J221118+031207	${4.68}_{-0.12}^{+0.06}$	$-{24.7}_{-0.1}^{+0.2}$	$-{1.8}_{-0.5}^{+0.6}$	${0.7}_{-0.2}^{+0.8}$	${4.821}_{-0.003}^{+0.003}$	$-{24.42}_{-0.13}^{+0.12}$	${2.0}_{-0.2}^{+0.2}$	(1)
IMS J221251−004231	${4.76}_{-0.01}^{+0.03}$	$-{26.0}_{-0.1}^{+0.1}$	$-{2.6}_{-0.3}^{+0.2}$	${1.7}_{-0.2}^{+0.2}$	4.95	−26.3	⋯	(3)
IMS J221310−002428	${4.74}_{-0.03}^{+0.20}$	$-{23.4}_{-0.2}^{+0.1}$	$-{1.8}_{-0.8}^{+0.8}$	${1.9}_{-0.5}^{+0.3}$	4.80	−23.5	⋯	(2)
IMS J221520−000908	${5.40}_{-0.20}^{+0.06}$	$-{24.5}_{-0.1}^{+0.1}$	$-{1.2}_{-0.5}^{+0.5}$	${2.1}_{-0.2}^{+0.2}$	5.28	−24.5	⋯	(2)
IMS J221622+013815	${4.87}_{-0.12}^{+0.20}$	$-{23.4}_{-0.2}^{+0.1}$	$-{0.8}_{-0.7}^{+0.3}$	${1.7}_{-0.4}^{+0.2}$	4.93	−23.3	⋯	(2)
IMS J221644+001348	${4.78}_{-0.04}^{+0.09}$	$-{25.8}_{-0.1}^{+0.1}$	$-{1.8}_{-0.4}^{+0.4}$	${1.3}_{-0.7}^{+0.3}$	5.01	−25.8	⋯	(2)
IMS J222216−000406	${4.79}_{-0.10}^{+0.24}$	$-{24.2}_{-0.2}^{+0.2}$	$-{2.2}_{-0.6}^{+0.5}$	${1.5}_{-0.9}^{+0.6}$	4.95	−24.3	⋯	(2)

Note. The systematic uncertainty of the redshift determination with the Lyα fitting (Δz ≲ 0.1; Kim et al. 2015, 2018; M18) is not included in the uncertainties of ${z}_{\mathrm{phot}}$ and ${z}_{\mathrm{spec}}$. The spectral properties are from (1) this work, (2) M18, and (3) McGreer et al. (2013). For spectroscopic data in this work, we fixed ${\alpha }_{\lambda }$ to −1.54 when fitting our quasar SED model (see Section 5.3.3). Note that M₁₄₅₀ from (2) and (3) are determined by the i-band magnitudes and ${z}_{\mathrm{spec}}$, which are matched to model quasar spectra. The difference in cosmological parameters between the literature and this work is also concerned.

^aFor IMS J140150+514310, M18 provides ${z}_{\mathrm{spec}}$ = 4.20. However, we revise it to be ${z}_{\mathrm{spec}}$ = 5.17 from the Lyα break in the spectrum shown in Figure 9 of M18 (see details in Section 4.3). M₁₄₅₀ is the value that assumes ${z}_{\mathrm{spec}}$ = 5.17.

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We present the optical spectra of the 15 broadband-selected quasar candidates in Figure 4. Thirteen of them have clear Lyα breaks at 7000–7500 Å in their spectra, showing that they are high-redshift quasars. Most of the quasars also have strong Lyα emission line (S/N ≥ 5), while IMS J021811−064843 does not. In addition, some spectra show broad emission lines such as C iv (e.g., IMS J085024−041850, IMS J085324−045626, IMS J221037+024314). The quasar spectra we obtained show no significantly unusual feature, except for IMS J221118+031207, which has a seemingly broadened Fe complex at ∼8000 Å. Out of the 15 candidates we observed, 10 quasars (marked with b in Table 1) are newly discovered ones, and 3 were independently identified by M18. On the other hand, the other 2 candidates selected by broadband color criteria are identified as nonquasar objects (bottom panels of Figure 4), considering that they have no significant break or emission-line feature.

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In this section, we examine the effectiveness of using medium-band data obtained by SQUEAN for finding z ∼ 5 quasars. Figure 5 summarizes the numbers of our candidates along the i-band magnitude at various selection or observation stages. There are 70 broadband-selected candidates (gray histogram); 45 of them were observed in three medium bands (m675, m725, and m775; green histogram), and 33 of the 45 candidates satisfy the color criteria (orange histogram) given by Jeon et al. (2016). Among the 33 medium-band-selected candidates, 28 of them have spectroscopic data, and all of them are identified as high-redshift quasars (red histogram). We suggest that the other 5 medium-band-selected candidates are also high-redshift quasars that are bright (i < 22 mag) and have high-S/N medium-band data, and yet their SED shape is very much in agreement with the other confirmed quasars. On the other hand, 27% (12 out of 45) of the broadband-selected candidates were removed by the medium-band color criteria. Out of the 12 excluded candidates, 4 turned out to be quasars. IMS J143945+562627 and IMS J221004+025424 are excluded owing to their redshift (z ≤ 4.7), so their exclusion is under special circumstances. The other two, IMS J220522+025730 and IMS J220635+020136, are not selected since they have shallow depth images in the m675 band, which gives only a lower limit on the m675−m725 color. Excluding these two quasars, we estimate that the contaminants occupy 23% (10 out of 43) of the broadband-selected sample. Note that we assumed that the 10 candidates are all nonquasars or quasars that are out of the explored redshift range. Figure 5 shows the histogram of our candidates for z ∼ 5 quasars along the i-band magnitude. The medium-band selection becomes more important if we concentrate on faint objects. At 22 < i < 23, in comparison to i < 23, the contamination rate increases to 47% (9 out of 19, except IMS J220635+020136) for the broadband selected candidates that are rejected after the medium-band observation. This is due to the increase of faint red stars that can act as interlopers, and without the medium-band approach, the exclusion of such objects becomes more challenging as we go to fainter magnitudes. Consequently, this medium-band approach is an effective way to narrow down the number of plausible candidates for z ∼ 5 quasars.

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However, our method is limited by the broadband selection and photometry. As one can see in Figure 2, there are four quasars at z ∼ 5 reported by M18 that were excluded from our broadband-selected candidates (purple open diamonds). Except for a quasar with a red i − z color of 1.0, not included in the final catalog of M18, the other three quasars were not selected by our selection criteria because there are small differences in broadband magnitudes (∼0.1 mag) between M18 and this work. In other words, we may have missed 10% (4 out of 39) of quasars (or candidates) during our broadband selection. We checked whether the photometric accuracy is the main reason for missing 10% of quasars during the broadband selection by using our SED model described in 5.3. We randomly generated 10⁵ mock quasars at 4.7 ≤ z ≤ 5.4 based on the SED model, controlled by the QLF of M18 with the parameter ranges determined by previous studies (see details in Section 5.3), including photometric uncertainties of 0.1 mag. A total of 11.4% of the mock quasars are rejected by our criteria, corresponding to the fraction of the missed quasars. Thus, to have a highly complete sample, a rather generous broadband selection or a selection from a sample with higher photometry accuracy is desirable before applying the medium-band selection.

The estimation of ${z}_{\mathrm{spec}}$ requires spectra with good S/N, which is usually expensive in observing time. As a good alternative, ${z}_{\mathrm{phot}}$ does not require observing time as extensive as spectroscopy, and it is still useful for deriving properties of high-redshift quasars. While ${z}_{\mathrm{phot}}$ of quasars can be determined by red colors from a sharp break at wavelength shorter than Lyα, their accuracy depends critically on how exactly one can sample the break in multiband photometry. In that regard, medium-band photometry can be useful since its dense wavelength sampling can improve the wavelength estimation of the break. We describe here our derivation of ${z}_{\mathrm{phot}}$ and ${z}_{\mathrm{spec}}$ with a quasar SED model.

5.3.1. Quasar SED Model

5.3.2. Photometric Redshift

Based on the fluxes from the broad- and medium-band observations, ${z}_{\mathrm{phot}}$ was determined by finding the minimum χ² value between the observed fluxes and the model fluxes, where χ² is defined as

$$\begin{eqnarray}&&{\chi }^{2}=\displaystyle \sum _{i}{\chi }_{i}^{2}+\displaystyle \sum _{j}{\chi }_{j}^{2}.\end{eqnarray} \tag{ 1 }$$

${\chi }_{i}^{2}$, the first term, is a standard form of χ² for the filters with detection,

$$\begin{eqnarray}&&{\chi }_{i}^{2}={\left(\displaystyle \frac{{f}_{o,i}-{f}_{m,i}}{{\sigma }_{i}}\right)}^{2},\end{eqnarray} \tag{ 2 }$$

where f_o,i is the observed flux in the ith band, σ_i is the standard deviation (or uncertainty) of the observed flux, and f_m,i is the model flux in the same band, which is calculated by integrating the quasar model fluxes with the weight of the transmission curve of the band. For the case of the filters with the upper limit of fluxes, we refer to the χ² derivation by Sawicki (2012), which gives ${\chi }_{j}^{2}$ of the second term of Equation (1),

$$\begin{eqnarray}\begin{array}{rcl}{\chi }_{j}^{2} & = & -2\mathrm{ln}{\displaystyle \int }_{-\infty }^{{f}_{\mathrm{lim},j}}\exp \left[-\displaystyle \frac{1}{2}{\left(\displaystyle \frac{{f}_{o,j}-{f}_{m,j}}{{\sigma }_{j}}\right)}^{2}\right]{df}\\ & = & \ -2\mathrm{ln}\left\{\sqrt{\displaystyle \frac{\pi }{2}}\,{\sigma }_{j}\left[1+\mathrm{erf}\left(\displaystyle \frac{{f}_{\mathrm{lim},j}-{f}_{m,j}}{\sqrt{2}{\sigma }_{j}}\right)\right]\right\},\end{array}\end{eqnarray} \tag{ 3 }$$

where f_lim,j is the upper limit of the flux in the jth band, f_m,j is the model flux in the same band, σ_j is the sensitivity in the same band, and erf(x) is the error function for the numerical calculation: $\mathrm{erf}(x)=(2/\sqrt{\pi }){\int }_{0}^{x}{e}^{-{t}^{2}}{dt}$. Note that we limited the ${\chi }_{j}^{2}$ value by ${\chi }_{j}^{2}\leqslant 0$ to restrict the χ² value to being negative.

The minimum χ² was searched in the following parameter space of z, M₁₄₅₀, ${\alpha }_{\lambda }$, and EW: 4.5 ≤ z ≤ 5.5 with a step size of 0.01, −27.5 ≤ M₁₄₅₀ (AB mag) ≤ −22.5 with a step size of 0.1 mag, −3.6 ≤ ${\alpha }_{\lambda }$ ≤ 0.4 with a step size of 0.2, and 0.5 ≤ log(EW/Å) ≤ 2.5 with a step size of 0.2. Note that the above ranges of ${\alpha }_{\lambda }$ and EW are chosen to cover the ${\alpha }_{\lambda }$ and EW values within about 2σ of the average values for high-redshift quasars, ${\alpha }_{\lambda }$ = −1.6 ± 1.0 (Mazzucchelli et al. 2017) and log(EW/Å) of =1.542 ± 0.391 in the rest frame (Bañados et al. 2016). For each model, we estimated the model flux in each band by calculating the mean flux in each band, which was weighted by the filter transmission curve.

For each quasar, we calculated the ${\chi }_{\mathrm{red}}^{2}$ value (the reduced χ² value, defined as ${\chi }_{\mathrm{red}}^{2}\equiv {\chi }^{2}/{\nu }_{\mathrm{dof}}$, where ν_dof is the degree of freedom) for each model with broad (grizJ) and existing medium-band (m675–m825) fluxes. For the broadband photometry, we gave additional errors on the broadband magnitudes considering the possible variability of quasars between the observing dates of the broad- and medium-band observations.¹⁶ We found the minimum ${\chi }_{\mathrm{red}}^{2}$ value (${\chi }_{\mathrm{red},\min }^{2}$) as the best-fit result and interpolated ${\chi }_{\mathrm{red}}^{2}$ values in the four parameter spaces to find points of ${\chi }_{\mathrm{red}}^{2}={\chi }_{\mathrm{red},\min }^{2}+1$, which are regarded as the marginal points for the errors of each parameter at the 1σ confidence level. Note that the interpolation may over/underestimate the 1σ errors by the bin size, but we expect that the effect is negligible. The best-fit results for 35 spectroscopically identified quasars are listed in Table 4, and Figure 6 shows the SEDs of the quasars with the best-fit models (blue solid lines).

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5.3.3. Spectroscopic Redshift (${z}_{{spec}}$)

5.3.4. Medium-band Photometric Redshift Accuracy

In Table 4, the best-fit results of our z ∼ 5 quasar sample are listed. The median uncertainty of ${z}_{\mathrm{spec}}$ is only 0.004, while that of ${z}_{\mathrm{phot}}$ is 0.09. The left panel of Figure 7 shows the comparison of ${z}_{\mathrm{spec}}$ and z_phot,BB, the photometric redshift determined with only broadband photometry, for 35 quasars. They show a loose correlation with a linear Pearson correlation coefficient of r_c = 0.58. If we introduce the additional medium-band photometry for the ${z}_{\mathrm{phot}}$ determination, there is a tight correlation between ${z}_{\mathrm{spec}}$ and ${z}_{\mathrm{phot}}$ with the improved r_c of 0.90 (right panel of Figure 7). For the two cases, the scatters of normalized median absolute deviations of $| {\rm{\Delta }}z| /(1+z)$ (σ_NMAD) are 0.029 and 0.016, respectively, where Δz ≡ ${z}_{\mathrm{spec}}$ − ${z}_{\mathrm{phot}}$ and the ${z}_{\mathrm{spec}}$ are used for the reference redshifts.

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Compared to the identical line (the black dashed line), there is a trend of ${z}_{\mathrm{phot}}$ slightly lower than ${z}_{\mathrm{spec}}$, which is described by the linear relation of ${z}_{\mathrm{spec}}$ = 1.087 × ${z}_{\mathrm{phot}}$ − 0.506 (the red solid line in Figure 7). For a simple comparison, we plotted the distribution of Δz/(1 + z) in Figure 8. The median Δz/(1 + z) values for ${z}_{\mathrm{phot}}$ (red histogram) and z_phot,BB (blue histogram) are slightly biased toward lower redshift (−0.010 and −0.023, respectively). The small systematic bias in Δz/(1 + z) could be explained by the limitation in our quasar models and the filter system. A quasar model with a stronger Lyα emission can give a ${z}_{\mathrm{phot}}$ value that is slightly larger than a model with a weaker Lyα emission since both the models give the same amount of flux within a certain passband that samples the light above the sharp break at Lyα. For that reason, the ${z}_{\mathrm{phot}}$ probability distribution has a longer tail toward higher redshift. Since we adopt ${z}_{\mathrm{phot}}$ at the maximum probability (the best-fit value), this can result in a slight underestimation in ${z}_{\mathrm{phot}}$. In addition, the magnitudes at wavelengths longer than Lyα have smaller uncertainties than the wavelength below Lyα, and this can lead to a slight underestimation in ${z}_{\mathrm{phot}}$ by giving more weight to the longer-wavelength magnitudes during the model fitting. Then, the fitting procedure tries to fit the longer-wavelength magnitudes better by adjusting the Lyα strength to preferentially allow a strong Lyα emission model with larger ${z}_{\mathrm{phot}}$ values. We confirm this by increasing the photometry accuracy of a filter below Lyα of a ${z}_{\mathrm{phot}}$ = 4.7 quasar from 0.05 to 0.5 mag. When the photometric error increases, the ${z}_{\mathrm{phot}}$ value drops by 0.1. Previous studies of quasar observations in medium bands also support this explanation. Jeon et al. (2016) used similar models that have a sharp break to measure ${z}_{\mathrm{phot}}$ of the bright quasar sample at 4.7 < z < 6.0 with the SQUEAN medium-band observations, and the Δz/(1 + z) distribution is a Gaussian distribution of −0.010 ± 0.012 (Jeon et al. 2016). On the other hand, Wolf et al. (2003) used the SDSS quasar spectrum (Vanden Berk et al. 2001) without IGM attenuation for the ${z}_{\mathrm{phot}}$ determination of low-redshift quasars at 0.6 < z < 3.5 with medium-band observations from the COMBO-17 survey. Their ${z}_{\mathrm{phot}}$ values are almost identical to ${z}_{\mathrm{spec}}$ with uncertainty of ≲0.05, corresponding to the low IGM attenuation toward the lower-redshift quasars.

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The standard deviation of the ${z}_{\mathrm{phot}}$ case (0.018) is smaller than that of the z_phot,BB case (0.043) by a factor of 2.4, in agreement with the previous suggestion that the ${z}_{\mathrm{phot}}$ determination could be improved with the inclusion of medium-band data. Our ${z}_{\mathrm{phot}}$ estimation method with the medium-band data opens up the possibility of constructing QLFs at redshift bins finer than previous attempts using broadband-based ${z}_{\mathrm{phot}}$ where they constructed QLFs with a coarse bin (e.g., 4.7 < z < 5.4 in M18).

In summary, using the medium-band data, we can estimate the ${z}_{\mathrm{phot}}$ values of quasars accurately, comparable to the low-resolution spectroscopy. As we described above, the ${z}_{\mathrm{phot}}$ values of high-redshift quasars with i < 23 mag determined by the broad- and medium-band data are reasonably matched to ${z}_{\mathrm{spec}}$ by an uncertainty of $\langle | {\rm{\Delta }}z| /(1+z)\rangle =0.016$. Together with the low contamination rate of our medium-band-based approach, a percentage-level ${z}_{\mathrm{phot}}$ accuracy improves the LF and the number density estimation of z ∼ 5 quasars and can even allow us to trace the large-scale distribution of quasars.

The amount of on-source integration we spent on each object (i < 23 mag) was about 2–3 hr. This was for using a 2.1 m telescope under the seeing of 10 to 15. In comparison, for the spectroscopic observations with Gemini or Magellan, we invested about 1–2 hr of time per target, including overheads. Considering that 1–2 m class telescope time is much more readily available, the medium-band-based approach is a very cost-effective way to identify high-redshift quasars and measure their redshifts to 1%–2% accuracy.