THE SDSS-IV EXTENDED BARYON OSCILLATION SPECTROSCOPIC SURVEY: QUASAR TARGET SELECTION

The goal of the eBOSS quasar survey is to study the scale of the BAO in two distinct redshift regimes: z ∼ 1.5 using the clustering of quasars, and z ∼ 2.5 using high-redshift quasars as backlights to illuminate the Lyα Forest. Broadly, this approach requires a sample of statistically selected quasars in the redshift range 0.9 < z < 2.2 (which we will refer to as "CORE quasars") and quasars selected at z > 2.1 (which we will refer to as "Lyα quasars").

A major difference between the two samples is the homogeneity of the target selection technique. The selection of CORE quasars must be statistically uniform. Lyα quasars, however, can be selected heterogeneously, because a clustering measurement using the Lyα Forest does not require the background quasars to have a uniform (or even a reproducible) selection. In fact, the full redshift range of the CORE sample will extend well beyond 0.9 < z < 2.2, and many CORE quasars can thus be utilized as Lyα quasars. The terminology "CORE quasars" therefore refers to how the quasars were targeted, whereas the terminology "Lyα quasars" refers to the redshift of the quasar.

Full details of the techniques used to forecast requirements for the eBOSS quasars are provided in our companion overview paper (Dawson et al. 2015). Those forecasts imply the following broad requirements for quasar target selection, driven by instrument capabilities and a 2% measurement of the BAO distance scale (G. Zhao et al. 2016, in preparation). For the CORE quasars:

• 1.  
  survey area > 7500 deg²;
• 2.  
  total number of 0.9 < z < 2.2 quasars > 435,000 (this corresponds to 58 deg⁻² over exactly 7500 deg²);
• 3.  
  a total density of assigned fibers of <90 deg⁻² (effectively a target density of ≲115 deg⁻² for reasons noted at the end of this section);
• 4.  
  redshift precision³⁷ <300 km s⁻¹ rms for z < 1.5 and $(300+400(z-1.5))$ km s⁻¹ for z > 1.5;
• 5.  
  catastrophic redshift errors (exceeding 3000 km s⁻¹) < 1%, where the redshifts are not known to be in error;
• 6.  
  maximum absolute variation in expected target density as a function of imaging survey sensitivity, stellar density, and Galactic extinction of <15% within the survey footprint;
• 7.  
  maximum fluctuations in target density due to imaging zero-point errors of <15% in each individual band used for targeting.

Once these CORE requirements are met, the remaining fibers not allocated to other eBOSS target classes are assigned to the Lyα target class. These Lyα quasars have the following additional constraints and requirements.

• 1.  
  BOSS quasars within the eBOSS area with S/N³⁸ pixel⁻¹ = 0, or 0.75 < S/N pixel⁻¹ < 3 must be reobserved.
• 2.  
  Flux calibration at least as accurate as BOSS.
• 3.  
  Recalibration of the BOSS high-z quasar sample using a spectroscopic pipeline that is consistent with that of eBOSS.

A subtlety arises for item (3) of the CORE requirements; targets with existing good spectroscopy from earlier iterations of the SDSS are not assigned fibers as part of eBOSS (see Section 4.4.10). On average, this saves 25 fibers deg⁻². Therefore, this paper will typically quote a total target density of 115 deg⁻², but this corresponds to a density of assigned fibers of only 90 deg⁻² for CORE quasars.

All eBOSS quasar targets are ultimately tied to the SDSS-I/II/III images collected in the ugriz system (Fukugita et al. 1996) using the wide-field imager (Gunn et al. 1998) on the SDSS telescope (Gunn et al. 2006). SDSS-I/II mostly derived imaging over the ∼8400 deg² "Legacy" area, ∼90% of which was in the north Galactic Cap (NGC). This imaging was released as part of SDSS Data Release 7 (DR7; Abazajian et al. 2009). The legacy imaging area of the SDSS was expanded by ∼2500 deg² in the south Galactic Cap (SGC) as part of DR8 (Aihara et al. 2011). The SDSS-III/BOSS survey used DR8 imaging for target selection over ∼7600 deg² in the NGC and ∼3200 deg² in the SGC (Dawson et al. 2013). Quasar targets are being selected for eBOSS over the same areas as BOSS, and ultimately eBOSS will observe quasars over a subset of at least 7500 deg² of this area.

Although adopting the same area as BOSS, eBOSS target selection takes advantage of the updated calibrations of the SDSS imaging. Schlafly et al. (2012) applied the "uber-calibration" technique of Padmanabhan et al. (2008) to Pan-STARRS imaging (Kaiser et al. 2010), achieving an improved global calibration compared with SDSSDR8. Targeting for eBOSS is conducted using SDSS imaging that is calibrated to the Schlafly et al. (2012)  Pan-STARRS solution, as fully detailed in D. Finkbeiner et al. (2016, in preparation). We will refer to this set of observations as the "updated" imaging.

The specific version of the updated SDSS imaging used in eBOSS target selection is stored in the calib_obj or "data sweep" files (Blanton et al. 2005). These data correspond to the native files used in the SDSS-III data model³⁹ and the updated Pan-STARRS-calibrated data sweeps will be made available in a future SDSS Data Release. The magnitudes derived from these data sweeps are AB magnitudes (not, e.g., asinh "Luptitudes"; Lupton et al. 1999). Note that the XDQSOz targeting technique (Bovy et al. 2012) adopted by eBOSS is designed to handle noisy data, so it can rigorously incorporate small (and even negative) fluxes when classifying quasars.

The WISE (Wright et al. 2010) surveyed the full sky in four mid-infrared bands centered on 3.4, 4.6, 12, and 22 μm, known as W1, W2, W3, and W4. For eBOSS we only use the W1 and W2 bands, which are substantially deeper than W3 and W4. Over the course of its primary mission and "NEOWISE post-cryo" continuation, WISE completed two full scans of the sky in W1 and W2. More than 99% of the sky has 23 or more exposures in W1 and W2; the median coverage is 33 exposures. We investigate whether the non-uniform spatial distribution of WISE exposure depth presents a problem for modeling CORE quasar clustering in Section 6.

We use the "unWISE" coadded photometry from Lang (2014) applied to SDSS imaging sources (as detailed in Lang et al. 2014). This approach produces forced photometry of custom coadds of the WISE imaging at the positions of all SDSS primary sources. Using forced photometry rather than catalog-matching avoids issues such as blended sources and non-detections. Because the WISE scale is 275 pixel⁻¹ (roughly seven times as large as SDSS), and many of our targets have WISE fluxes below the "official" WISE catalog detection limits, using forced photometry is of significant benefit.

The PTF⁴⁰ is a wide-field photometric survey aimed at a systematic exploration of the optical transient sky via repeated imaging over 20,000 deg² in the northern Hemisphere (Law et al. 2009; Rau et al. 2009). The PTF image processing is presented in Laher et al. (2014), while the photometric calibration, system, and filters are discussed in Ofek et al. (2012). In 2013 February, the next phase of the program, iPTF (intermediate PTF) began. Both surveys use the CFHT12K mosaic camera, mounted on the 1.2 m Samuel Oschin Telescope at Palomar Observatory. The camera has an 8.1 deg² field of view and 1'' sampling. Because one detector (CCD03) is non-functional, the usable field of view is reduced to 7.26 deg². Observations are mostly performed in the Mould-R broadband filter, with some in the SDSS g-filter. Under median seeing conditions, the images are obtained with 20 FWHM, and reach 5σ limiting AB magnitudes of m_R ≃ 20.6 and ${m}_{{g}^{\prime }}\simeq 21.3$ in 60 s exposures. The cadence varies between fields, and can produce one measurement every five nights in regions of the sky dedicated to supernova searches. Four years of PTF survey operations have yielded a coverage of ∼90% of the eBOSS footprint.

Two automated data processing pipelines are used in parallel in the search for transients: a near-real-time image subtraction pipeline at Lawrence Berkeley National Laboratory, and a database populated on timescales of a few days at the Infrared Processing and Analysis Center (IPAC). The eBOSS analysis uses the individual calibrated frames available from IPAC (Laher et al. 2014).

We developed a customized pipeline based on the SWarp (Bertin et al. 2002) and SCAMP (Bertin 2006) public packages to build coadded PTF images on a timescale adapted to quasar targeting (i.e., typically 1–4 epochs per year, depending on the cadence and total exposure time within each field). Using the same algorithms, a full stack is also constructed by coadding all available images. This full stack is complete at 3σ to g ∼ 22.0, and has more than 50% completeness to quasars at g ∼ 22.5. The full stack is used to extract a catalog of PTF sources from each of the coadded PTF images. The light curves (flux as a function of time) for all of these PTF sources are measured.

The eBOSS CORE sample is designed to provide a statistically selected sample of 115 deg⁻² targets that—after eBOSS spectroscopy of the 90 deg⁻² targets that do not have existing good SDSS spectra—comprises >58 deg⁻² total quasars with accurate redshifts in the range 0.9 < z < 2.2 (see Section 2). This >58 deg⁻² quasars will consist of both new quasars from eBOSS spectroscopy and previously known quasars from the sample of 25 deg⁻² targets that have existing SDSS spectroscopy. To achieve this goal eBOSS uses two complementary methods: an optical selection using the XDQSOz method of Bovy et al. (2012), and a mid-IR-optical color cut using WISE imaging. The specifics of these two methods are detailed in the next few sections.

The starting sample for CORE targeting is all point sources in SDSS imaging that are PRIMARY, have (de-extincted) PSF magnitudes of g < 22 or  r < 22 and a FIBER2MAG ⁴¹ of i > 17, and have good IMAGE_STATUS.⁴² These basic initial cuts are discussed further in Section 4.3.

Point sources in the SDSS are denoted by the flag objc_type == 6, corresponding to a magnitude cut based on star-like or galaxy-like profile fits of ${\mathtt{psfMag}}-{\mathtt{modelMag}}\leqslant 0.145$ (Stoughton et al. 2002). A concern might be that a selection to r ∼ 22 might suffer incompleteness to quasars at r ≳ 21, where star-galaxy separation in SDSS imaging was initially argued to break down due to errors on profile fits (e.g., Stoughton et al. 2002; Scranton et al. 2002). In general, however, at the limit of the SDSS imaging the trend is to classify faint, ambiguous sources as point-like. The expectation is then that a selection approaching r ∼ 22 will become increasingly contaminated by galaxies that are classified as unresolved, rather than miss quasars that are classified as resolved (see also the discussion in Section 4.5.1 of Richards et al. 2009b). Further, requiring objc_type == 6 and applying XDQSOz reduces galaxy contamination to ≲10%, even at i ∼ 22 (see Figure 11 of Bovy et al. 2012), so we expect our selection to remain robust even to r ∼ 22 (which, on average, corresponds to i ∼ 21.85 for 0.9 < z < 2.2 quasars).

From the initial sample of magnitude-limited PRIMARY point sources, objects are targeted if they have an XDQSOz probability of being a quasar at z > 0.9 of more than 20% (i.e., PQSO(z > 0.9) > 0.2). It is important to note the subtle distinction between the specific goal of the CORE sample and the sample it produces. The goal of CORE is to uniformly target >58 deg⁻² quasars in the redshift range 0.9 < z < 2.2, but no attempt is made to restrict the upper redshift range of the CORE quasar sample. The CORE is left free to recover quasars at z > 2.2 because, although such quasars are outside the preferred CORE redshift range, they remain useful as tracers of the Lyα Forest. To this moderate-probability XDQSOz sample, a WISE-optical color cut is applied to further reduce the target density by filtering out obvious stars based on optical-mid-IR colors. Finally, objects are not targeted if they have existing good spectroscopy from earlier iterations of the SDSS unless a visual inspection as part of BOSS produced an ambiguous classification. The resulting set of objects comprises the eBOSS CORE quasar sample.

4.1.1. XDQSOz

XDQSO (Bovy et al. 2011a) is a method of classifying quasars in flux-space using extreme deconvolution (XD; Bovy et al. 2011b) to estimate the density distribution of quasars as compared to non-quasars. Effectively, XDQSO takes any test point in flux-space, together with its flux errors, and convolves that error envelope with deconvolved distributions of the quasar and of the non-quasar loci. By weighting this convolution with a prior representing the expected numbers of quasars and non-quasars, the test point is assigned a probability of being a quasar. XDQSO inherits many desiderata from XD, including the rigorous incorporation of (and extrapolation from) errors on fluxes, and the ability to distinguish the effect on quasar probabilities of data that are completely missing from data that are merely of low significance. This feature is a boon for quasar classification near the limits of imaging data where flux errors are large. For eBOSS targeting, we adopt the XDQSOz method (Bovy et al. 2012), which extends the XDQSO schema to provide probabilistic classifications for quasars in any specified range of redshift.

In pursuit of the eBOSS CORE goal of >58 deg⁻² 0.9 < z < 2.2 quasars, a test spectroscopic survey in the W3 field of the CFHT Legacy Survey was conducted.⁴³ This CFHTLS-W3 test survey was deemed necessary because no iteration of the SDSS-I/II/III specifically targeted quasars as faint as r ∼ 22 over the redshift range 0.9 < z < 2.2. Although the CFHTLS-W3 test survey informed the initial quasar target selection for eBOSS, and so will be used to describe the broad ideas behind that target selection, it only contained ∼1600 quasars and was easily supplanted by the SEQUELS survey described in Section 5, which comprised ∼21,700 quasars. Readers interested in an up-to-date description and depiction of the properties of eBOSS quasars as compared to SDSS-I/II/III, should therefore consult Section 5.3 and, in particular, Figures 17 and 18.

The CFHTLS-W3 test survey is detailed in the appendix of Alam et al. (2015). Broadly, an optical selection was applied to SDSSDR8 imaging, restricting to PRIMARY point sources in the (PSF, unextincted) magnitude range 17 < r < 22. From this initial sample, objects were targeted for follow-up spectroscopy if they had an XDQSOz probability of greater than 0.2 of being a quasar at any redshift (i.e., PQSO(z > 0.0) > 0.2).

Because the CFHT W3 test survey targeted objects regardless of their redshift probability density (all objects with PQSO(z > 0.0) > 0.2), the results of the survey could be optimized to better recover quasars in the eBOSS CORE redshift range of 0.9 < z < 2.2. One initial outcome of the CFHT W3 test survey, then, was that objects with PQSO(z > 0.0) > 0.2 but PQSO(z > 0.9) < 0.2 were rarely quasars in the eBOSS redshift range of interest, as demonstrated in Table 1. Further, restricting the redshift range of eBOSS quasar targets to z > 0.9 is desirable to mitigate losses of (e.g., eBOSS Luminous Red Galaxies targeted at z < 0.9; c.f. Prakash et al. 2015b) due to fiber collisions between neighboring targets. Therefore, it was decided to focus only on targets with PQSO(z > 0.9) > 0.2 for eBOSS targeting; we will subsequently restrict our discussion to such targets.

Table 1.  Efficiency of Quasar Target Selection in the CFHTLS-W3 Test Survey as a Function of XDQSOz Probability Cut

ID	PQSO
(Rows 1–4)					(z > 0.0) > 0.2
zspec range	(z > 0.0)		(z > 0.9)		and
For quasars	>0.2		>0.2		(z > 0.9) < 0.2
(Rows 5–7)	N	%	N	%	N	%
Stars	27.0	18.2%	23.3	16.8%	3.6	39.6%
Galaxies	13.9	9.4%	12.3	8.8%	1.6	17.8%
Unidentified	2.4	1.6%	2.2	1.6%	0.2	2.0%
Quasars	105.0	70.8%	101.3	72.8%	3.7	40.6%
z < 0.9	13.2	8.9%	10.9	7.9%	2.3	24.8%
0.9 < z < 2.2	70.9	47.8%	69.7	50.1%	1.2	12.9%
z > 2.2	20.9	14.1%	20.7	14.9%	0.3	3.0%
Total	148.3	100%	139.1	100%	9.2	100%

Note. The total survey area was 11.0 deg² and N, the number of spectroscopically confirmed targets, is always expressed in deg⁻² over this area.

Download table as:  ASCIITypeset image

Figure 2 shows the typical positions of XDQSOz PQSO(z > 0.9) > 0.2 quasars in SDSS colors. To demonstrate the position of XDQSOz-selected quasars in optical color space, we use the large spectroscopically confirmed quasar sample from the DR10 quasar catalog of Pâris et al. (2014). In general, XDQSOz selects similar regions of color space to SDSS targets from earlier surveys (e.g., Richards et al. 2001), with the majority of the quasar-star separation occuring in the ugr filters.

Zoom In Zoom Out Reset image size

Whether an XDQSOz PQSO(z > 0.9) selection alone is sufficient to meet the eBOSS targeting goal of 58 deg⁻² quasars is investigated in Figure 3, where the sky density of XDQSOz-selected targets as a function of probability threshold is compared to that of confirmed quasars in the requisite CORE redshift range (0.9 < z < 2.2; see Section 2.2). Figure 3 displays three curves that correspond to source densities in the CFHTLS-W3 test program, which can be used to estimate the "true" densities of quasars and targets expected in eBOSS. The lowest (magenta) curve represents all sources in SDSS imaging in the CFHTLS-W3 field that meet the basic CORE cuts (i.e., PRIMARY point sources within the CORE magnitude limits), as a fraction of the total density of ∼3330 deg⁻² such sources. The central (red) curve represents all quasars that were spectroscopically confirmed as part of the CFHTLS-W3 program, as a fraction of the total density of ∼135 deg⁻² such sources. The upper (blue) curve represents all quasars in the specific CORE redshift range of 0.9 < z < 2.2 that were spectroscopically confirmed as part of the CFHTLS-W3 program as a fraction of the total density of ∼85 deg⁻² such sources. Because the CFHTLS-W3 program was limited to PQSO(z > 0.0) > 0.2, the test sample is partially incomplete to quasars that have PQSO(z > 0.9) < 0.2; such quasars only appear in the CFHTLS-W3 test data due to targeting approaches that did not use XDQSOz selection. Figure 3 therefore provides best estimates only for PQSO(z > 0.9) > 0.2.

Zoom In Zoom Out Reset image size

Figure 3 can be used to estimate the total density of quasars and targets that might be expected in eBOSS for different PQSO(z > 0.9) constraints. For example, to estimate the sky density of all quasars at PQSO(z > 0.9) > 0.6, one would find the corresponding fraction of total (∼0.57) and multiply by the total for all quasars (134.3 deg⁻²) to obtain ∼77 deg⁻². The vertical lines in Figure 3 depict the necessary constraints to achieve the requisite eBOSS CORE density of 58 deg⁻² 0.9 < z < 2.2 quasars and the requisite eBOSS target density of 115 deg⁻² (see Section 2.2). The maximum target density of 115 deg⁻² is achieved at PQSO(z > 0.9) > 0.45, which would result in 64.9 deg⁻² CORE quasars. In actuality, a more relaxed constraint of PQSO(z > 0.9) > 0.2 is adopted for eBOSS,⁴⁴ which further improves quasar targeting. This relaxed constraint, which is labeled "Adopted cut with IR constraint (see Section 4.1.3)" in Figure 3, was achieved through an additional constraint on mid-IR-optical color (see also Section 4.1.2).

Figure 4 depicts how relaxing constraints on PQSO(z > 0.9) to thresholds as low as our adopted PQSO(z > 0.9) > 0.2 affects the redshift distribution of targeted quasars. The resulting N(z) distributions are broadly similar, but the PQSO(z > 0.9) > 0.2 selection has a tail to z < 0.9 and contains a smaller fraction of quasars in the CORE target range of 0.9 < z < 2.2. This drop is more than offset by the PQSO(z > 0.9) > 0.2 selection containing more total quasars (c.f., Figure 3). The peak near z ∼ 1.3 is likely an artifact of the small sample size in the CFHTLS-W3 test program (c.f., Figure 17). Figure 4 demonstrates that the majority of quasars selected at PQSO(z > 0.9) > 0.2 remain useful for eBOSS by being in the CORE redshift range of 0.9 < z < 2.2. In fact, there is an additional advantage to relaxing the XDQSOz probability; doing so tends to introduce new quasars at z > 2.1, while retaining the quasars in the CORE redshift range. Quasars at z > 2.1 remain useful for the purposes of eBOSS as part of the Lyα sample (see Section 4.2).

Zoom In Zoom Out Reset image size

4.1.2. Mid-IR-optical Color Cuts

Starlight tends to greatly diminish at wavelengths redwards of 1–2 μm, making galaxies, and in particular stars, dim in the mid-IR, whereas Active Galactic Nuclei (AGN) have considerable IR emission. Photometric selection techniques based on WISE data can therefore be used to target active galaxies, and such techniques uncover both unobscured and obscured quasars over a range of luminosities (e.g., Stern et al. 2012; Assef et al. 2013; Yan et al. 2013).

Significantly more than half of the objects targeted using mid-IR selection are low-luminosity unobscured AGN at z < 1 or obscured quasars (e.g., Lacy et al. 2013; Hainline et al. 2014). This makes a pure WISE selection approach imperfect for eBOSS targeting, because objects without an optical spectrum and/or AGN at z < 0.9 will not typically have utility for the eBOSS CORE goal of targeting >58 deg⁻² 0.9 < z < 2.2 quasars. WISE remains ideal, however, for removing contaminating stars from eBOSS quasar selection. Figure 5 demonstrates the utility of a WISE-optical color cut in selecting against stars. This color cut is based on stacking optical and WISE fluxes to attain as great a depth as possible. A stack is created from SDSS PSF fluxes according to

$$\begin{eqnarray}&&\text{Optical Stack}\;=\;{f}_{{\rm{opt}}}=({f}_{g}+0.8{f}_{r}+0.6{f}_{i})/2.4,\end{eqnarray} \tag{ 1 }$$

and from fluxes in the bluest (and also deepest) WISE bands according to

$$\begin{eqnarray}&&{WISE}\;\mathrm{Stack}={f}_{{WISE}}=({f}_{W1}+0.5{f}_{W2})/1.5,\end{eqnarray} \tag{ 2 }$$

where the weights are chosen to roughly yield the highest combined S/N for a typical z < 2 quasar. The sample depicted by black points in Figure 5 represents objects with any eBOSS quasar targeting bit set (see Section 4.4). This sample has been limited to r > 21 and g < 22 to illustrate the scatter at the faint end of eBOSS, demonstrating the power of the WISE data in filtering stars that other methods target due to these stars' resemblance to quasars in optical colors.

Zoom In Zoom Out Reset image size

As part of the the CFHTLS-W3 test survey introduced in Section 4.1.1  WISE was photometered at the positions of SDSS PRIMARY sources (see Section 3.2) in the CFHT Legacy survey W3 field. A WISE-SDSS selected sample was created by applying the cut depicted in Figure 5 to these W3-test-field sources;

$$\begin{eqnarray}&&{m}_{{\rm{opt}}}-{m}_{{WISE}}\geqslant (g-i)+3,\end{eqnarray} \tag{ 3 }$$

where m_opt and m_WISE are defined in Equations (1) and (2) after converting the stacked fluxes to magnitudes.⁴⁵ An inclusive star-galaxy separation of objc_type == 6 or ${m}_{{\rm{opt}}}-{m}_{{\rm{model}}}\lt 0.1,$ where m_model is the equivalent of Equation (1) but for SDSS model magnitudes, was adopted. This is inclusive in the sense that objc_type == 6 corresponds to a star-galaxy separation of ${\mathtt{psfMag}}-{\mathtt{modelMag}}\leqslant 0.145$ (as also discussed further in Section 4), but based on SDSS fluxes in all bands, not just the bands stacked in m_opt. In addition, magnitude limits of 17 < m_opt < 22 were enforced. Finally, an optical color cut of $g-i\lt 1.5$ was applied in an attempt to excise the highest redshift quasars (this cut is not obvious in Figure 5 because other programs in the CFHTLS-W3 test program repopulated this parameter space). The squares with error bars in Figure 5 depict the typical range of colors of spectroscopically confirmed quasars in different redshift bins. The separation of these points from the green line suggests that WISE is robust for quasar selection across the CORE redshift range of 0.9 < z < 2.2.

Figure 6 demonstrates whether a WISE-optical cut of ${m}_{{\rm{opt}}}-{m}_{{WISE}}\geqslant (g-i)+x$ is sufficient, in isolation, to meet the eBOSS targeting goal of 58 deg⁻² 0.9 < z < 2.2 quasars (contingent on our additional restrictive cuts to the W3-test-field targets, such as $g-i\lt 1.5$). Figure 6 is an exact analog of Figure 3, and a detailed description of how these figures can be interpreted is provided in Section 4.1.1. Figure 6 implies that a cut of about ${m}_{{\rm{opt}}}-{m}_{{WISE}}\geqslant (g-i)+4.25$ is necessary to meet the requisite eBOSS target density of 115 deg⁻² and that, therefore, only 34.1 deg⁻² CORE quasars could be obtained with a WISE-optical selection alone. As discussed further in Section 4.1.3, by combining XDQSOz selection with WISE eBOSS we could use the "Adopted cut..." plotted in Figure 6. This relaxed cut does achieve eBOSS targeting goals.

Zoom In Zoom Out Reset image size

Figure 7 demonstrates that relaxing cuts on x in the function ${m}_{{\rm{opt}}}-{m}_{{WISE}}\geqslant (g-i)+x$ does not strongly affect the redshift distribution of targeted quasars. This figure shows that 65%–70% of quasars selected by this WISE-SDSS cut are in the CORE redshift range, regardless of the value of x. Overall, there is less variation in the eBOSS CORE 0.9 < z < 2.2 redshift distribution with x as compared to the variation in Figure 4, because the WISE-optical cut has less power to discriminate redshift as compared to ugriz over most of the CORE range (c.f. Figure 5). Instead of augmenting the CORE quasar range, relaxing x tends to expand the fraction of quasars at about z > 2. This outcome is desirable, given that z > 2.1 quasars can be used as part of the eBOSS Lyα sample (see Section 4.2).

Zoom In Zoom Out Reset image size

By redshifts of z ∼ 6, about half of quasars are not detected in the WISE W1 and W2 bands (Blain et al. 2013). In addition, a 10σ detection in WISE W2 is equivalent to i ∼ 19.8 (Stern et al. 2012), which may not detect all quasars to the effective eBOSS limits of r ∼ 22. Thus it is worth investigating whether the WISE data photometered for eBOSS targeting (see Section 3.2) are sufficiently deep for our purposes. Figure 8 addresses this issue by plotting known DR10 quasars as a function of S/N in our WISE stack (m_WISE). The stack depth is sufficient to identify 90% of 0.9 < z < 2.2 BOSS quasars at a S/N of 2 in the stack to r < 21.9. Although the depth of WISE becomes limiting near r ∼ 22 for eBOSS CORE quasars, about 93% of 0.9 < z < 2.2 BOSS quasars would be selected by our WISE-optical cut; this is because of the combined effect that few quasars are both blue in g − i and faint in WISE.

Zoom In Zoom Out Reset image size

4.1.3. Combined Mid-IR and Optical Selection

After analyzing our CFHTLS-W3 test data (as outlined in Sections 4.1.1 and 4.1.2) it became clear that the overall number of CORE quasars targeted at the eBOSS fiber density could be increased by combining an XDQSOz probability limit with a WISE-optical cut. It was possible to only partially study the XDQSOz probability and WISE-optical cut beyond the limits to which they had been tested in the CFHTLS-W3 program—using those XDQSOz-selected quasars that failed the WISE-optical cut and vice versa. Because the combination of the two original test cuts exceeded eBOSS goals, however, it was decided to proceed with an eBOSS CORE quasar target selection corresponding to both

$$\begin{eqnarray}&&{\rm{PQSO}}(z\gt 0.9)\gt 0.2\;\;\;\;\;\;\;\;\;\;\;\;\mathrm{and}\\ &&\quad {m}_{{\rm{opt}}}-{m}_{{WISE}}\geqslant (g-i)+3.\end{eqnarray} \tag{ 4 }$$

The "Adopted cut..." lines in Figures 3 and 6 demonstrate that in combination these constraints easily achieve the eBOSS CORE goal of 58 deg⁻² 0.9 < z < 2.2 quasars. It turns out that the combined XDQSOz-and-WISE-optical constraints that correspond to these adopted cuts require close to the maximum eBOSS quasar target density of 115 deg⁻² (see Section 2.2) and achieve an overall density of ∼70 deg⁻² 0.9 < z < 2.2 quasars. The expected eBOSS CORE quasar density arising from these constraints is explored in more detail in Section 5.1.

The goal of eBOSS Lyα quasar targeting is to compile as large a sample of new z > 2.1 quasars as possible using the remaining available fibers that were not allocated to other eBOSS targets. The eBOSS Lyα sample is not required to be homogeneously selected; it is therefore targeted using several different selection algorithms and sources of imaging—even imaging that only partially covers the eBOSS footprint.

The majority of new eBOSS Lyα quasars are targeted using two techniques. First, the CORE sample described in Section 4.1 is a source of new Lyα quasars, because its selection contains no requirement to intentionally remove z > 2.1 quasars. Second, a variability selection is used to target additional Lyα quasars. The CORE and variability-selected samples each select ∼5 deg⁻² new Lyα quasars, with only ∼1.5 deg⁻² in common (see also Table 4 in Section 5.2). The variability-selected targets undergo a different set of initial flag and flux cuts as compared to other target classes (see Section 4.2.1).

eBOSS uses two additional techniques to target more Lyα quasars and acquire more signal in the Lyα Forest. First, all previously unidentified sources within 1'' of a radio detection in the FIRST survey (Becker et al. 1995; Helfand et al. 2015) are targeted. Then, quasars that had low S/N spectra in BOSS are retargeted. The target categories specific to Lyα selection are detailed in the following and are summarized in Section 4.4.

4.2.1. Variability Selection

Time-domain photometric measurements can exploit quasars' intrinsic variability in order to distinguish them from stars of similar colors (e.g., van den Bergh et al. 1973; Hawkins 1983; Cimatti et al. 1993; Rengstorf et al. 2004a, 2004b; Claeskens et al. 2006; Sesar et al. 2007; Kozłowski et al. 2010; MacLeod et al. 2010; Schmidt et al. 2010; Palanque-Delabrouille et al. 2011, 2013a, 2015). The time-variability of astronomical sources can be described using the "structure function," a measure of the amplitude of the observed variability as a function of the time delay between two observations (e.g., Cristiani et al. 1996; Giveon et al. 1999; Vanden Berk et al. 2004; Rengstorf et al. 2006). This function can be modeled as a power law parameterized in terms of A, the mean amplitude of the variation on a one-year timescale (in the observer's reference frame), and γ, the logarithmic slope of the variation amplitude with respect to time (Schmidt et al. 2010). With Δm_ij defined as the difference between the magnitudes of the source at time t_i and t_j, and assuming an underlying Gaussian distribution of Δm values, the model predicts an evolution of the variance σ²(Δm) with time according to

$$\begin{eqnarray}&&{\sigma }^{2}({\rm{\Delta }}m)={\left[A{({\rm{\Delta }}{t}_{{ij}})}^{\gamma }\right]}^{2}+({\sigma }_{i}^{2}+{\sigma }_{j}^{2}),\end{eqnarray} \tag{ 5 }$$

where ${\sigma }_{i}$ and σ_j are the imaging errors at time t_i and t_j. Quasars should lie at high A and γ; non-variable stars near A = γ = 0 and variable stars should have γ near 0 even if A is large. In addition, variable sources (whether stars or quasars) are expected to deviate greatly from a model with constant flux. This deviation is quantified by computing the χ² of the fit of the light curve compared to a constant-flux model.

Using customized PTF R-band stacks (see section Section 3.3), light curves are built for all PTF sources. The PTF sources are matched to SDSS imaging catalogs, and the selection is restricted to SDSS PRIMARY point sources. With the PTF light curves in hand, all additional cuts are then applied using SDSS imaging information. SDSS cuts of g < 22.5 and r > 19 are then applied. When SDSS r-band data are available, the R-band PTF light curve, adjusted to SDSS r, is extended to include the SDSS fluxes. These PTF+SDSS light curves typically contain three to four PTF "coadded epochs," where each PTF coadded epoch is obtained by coadding the exposures within a given PTF observational season. The number of exposures in each season varies from ∼10 to a few dozen for typical fields.

Because the density of PTF images varies across the sky, so does the efficiency of the variability-based selection. To account for this, the thresholds of the variability cuts are adapted as a function of position in order to reach an average target density of ∼20 deg² across the eBOSS footprint. Constraints of 5.0 < χ² < 200.0 for combined PTF+SDSS measurements are typically necessary; smaller χ² values are obtained for non-variable sources, while larger values often signify artifacts. The parameters of the variability structure function are forced to lie in the parameter space bounded by γ > 0 and $\gamma \gt -30A+1.5,$ as illustrated by the green lines in Figure 9. Tighter χ² cuts are applied to light curves for which the variability parameters A and γ cannot be computed reliably, such as light curves with fewer than three PTF epochs.

Zoom In Zoom Out Reset image size

To maximize the efficiency of quasar selection, the variability selection is complemented by loose color cuts designed to reject stars. Cuts of c₃ < 1.4–0.55 × c₁ and c₃ < 0.3–0.1 × c₁ are imposed, where

$$\begin{eqnarray}{c}_{1} & = & 0.95(u-g)+0.31(g-r)+0.11(r-i)\\ {c}_{3} & = & -0.39(u-g)+0.79(g-r)+0.47(r-i),\end{eqnarray} \tag{ 6 }$$

as defined in Fan (1999). In these equations, ugri are PSF magnitudes measured in the SDSS imaging. This color cut is illustrated in Figure 10, where the regions above the red and green lines are rejected.

Zoom In Zoom Out Reset image size

Finally, a region in color space mostly populated by bright variable stars, that passes both the color and the variability cuts, is removed. These stars are apparent in the top panel of Figure 11—but are clearly absent in the lower panel, which depicts known quasars. These contaminating variable stars are removed by rejecting sources that lie in the color box 0.85 < c₁ < 1.35 and c₃ > −0.2 if they are brighter than r = 20.5. This cut is not applied to fainter sources.

Zoom In Zoom Out Reset image size

4.2.2. Reobservation of BOSS Quasars

4.2.3. Radio Selection

SDSS imaging includes a great deal of metadata⁴⁷ , and, notably, contains flags (in the form of bitmasks) that can be used to characterize photometric quality.⁴⁸ Initially, eBOSS adopts a set of obvious and necessary cuts on SDSS imaging parameters. The target selection is restricted to PRIMARY sources in the SDSS to avoid duplicate sources. Targets are cut on (de-extincted) PSFMAG to near the limits of SDSS imaging, in part driven by the necessary exposure times to obtain spectra of reasonable S/N. These limits are g < 22 or r < 22 for CORE quasars and g < 22.5 for the Lyα quasar sample, which can be more speculative and inhomogeneous in its selection. A bright limit of FIBER2MAGi > 17 is adopted for all eBOSS targets to prevent light leaking between adjacent fibers (see Dawson et al. 2015). Quasars selected by variability and intended purely for Lyα studies have a more restrictive bright-end cut of r > 19, because there are few high-redshift quasars brighter than r = 19. Finally, the restriction that quasar targets must be unresolved in imaging (objc_type == 6) is imposed. This is necessary because at fainter magnitudes extended sources begin to dominate SDSS imaging, and at r > 21.2 there are three times as many objc_type == 3 (extended) sources as objc_type == 6 (point-like) sources. Targeting extended sources would greatly increase the eBOSS fiber budget, while recovering few z > 0.9 quasars.

Our CFHTLS-W3 test program (outlined in Section 4.1.1) had relaxed limits on star-galaxy separation and magnitude, meaning that it is possible to show that our basic flag cuts for eBOSS quasar targeting represent sensible choices. Adopting the selection outlined in Section 4.1.3, a cut on objc_type == 6 discards only 4.6% of quasars but requires 3.5× fewer fibers. Enforcing faint limits of g < 22 or r < 22 discards 5.8% of quasars but requires 11.5× fewer fibers.

Typically, previous SDSS quasar targeting algorithms (Richards et al. 2002; Ross et al. 2012) have employed additional constraints on image quality to reduce spurious targets. Given that the CFHTLS-W3 test program did not adopt strict flag cuts, it could be used to assess which flag cuts might be worthwhile for eBOSS targeting (see Figure 12). A range of individual SDSS flag cuts are plotted in Figure 12, which demonstrates that there are essentially no SDSS flags that discard targets without also discarding useful z > 0.9 quasars. The one exception is the DEBLENDED_AS_MOVING flag (number 32), which does not obviously discard quasars, but which only saves 0.3 deg⁻² targets. In addition to the results in Figure 12, we also tested numerous standard combinations of flags used by other SDSS quasar targeting algorithms, such as the INTERP_PROBLEMS and DEBLEND_PROBLEMS combinations outlined in the appendices of Bovy et al. (2011a) and Ross et al. (2012). In no case did we find a flag combination that removed significant numbers of targets without also discarding useful quasars. We do not study why the SDSS image quality flags have limited utility for eBOSS targeting—speculatively the flags may become less meaningful near the faint limits of SDSS imaging and/or our incorporation of WISE data may ameliorate SDSS artifacts. In any case, based on this analysis and the fact that the basic eBOSS selection already achieves the requisite target density, we make no additional SDSS flag cuts.

Zoom In Zoom Out Reset image size

It is likely that certain regions of the SDSS imaging will have to be masked further for quasar clustering analyses, due to areas around bright stars (both in WISE and SDSS imaging) or bad imaging fields, for example (see Ross et al. 2011, and Section 6). For instance, due to how the SDSS geometry was initially defined for "uber-calibration," small overlap regions (∼1 deg²) in SDSS run 752 are misaligned between SDSS and our WISE photometering. Such regions do not have a major impact on target homogeneity, however, and may differ for different eBOSS target classes, so such geographic areas will be masked post-facto, depending on a specific science purpose. One set of regions that was masked a priori for BOSS quasar targeting corresponded to bad u-columns (e.g., see Figure 1 of White et al. 2012). Specifically testing target density in areas with bad SDSS u-columns did not suggest they have greatly different eBOSS CORE target densities (∼116–118 deg⁻² versus the average of ∼115 deg⁻² for the typical survey area), however, so bad u-columns are not specifically masked a priori for eBOSS targeting.

In general, the only large geographic areas that should certainly not be photometric in SDSS imaging are regions with catastrophic values of IMAGE_STATUS.⁴⁹ For eBOSS CORE quasar targeting, we avoid all areas with IMAGE_STATUS set to BAD_ROTATOR, BAD_ASTROM, BAD_FOCUS, SHUTTERS, FF_PETALS, DEAD_CCD, or NOISY_CCD in any filter. Quasars targeted on the basis of their variability in PTF for Lyα studies do not undergo cuts on IMAGE_STATUS because there is no requirement for Lyα quasars to be selected homogeneously. The full set of flag cuts eventually adopted is outlined succinctly in Figure 1.

The tests summarized in Sections 4–4.3 provide sufficient information to justify the choices made to target quasars in eBOSS. This section provides an outline of how the eBOSS targeting bits directly correspond to the specified choices. A visual representation of the overall targeting algorithm is also provided in Figure 1. Unless otherwise specified, each target class is derived from the imaging outlined in Section 3 and undergoes the basic flag cuts outlined in Section 4.3 (PRIMARY, objc_type == 6, magnitude cuts, and good IMAGE_STATUS). The numerical value of each eBOSS quasar targeting bit is listed in Table 2. The density and success rate of each class of target is described further in Section 5.

4.4.1.  QSO_EBOSS_CORE

4.4.2.  QSO_PTF

4.4.3.  QSO_REOBS

4.4.4.  QSO_EBOSS_KDE

4.4.5.  QSO_EBOSS_FIRST

4.4.6.  QSO_BAD_BOSS

4.4.7.  QSO_BOSS_TARGET

4.4.8.  QSO_SDSS_TARGET

4.4.9.  QSO_KNOWN

4.4.10.  DO_NOT_OBSERVE: Which Previously known Quasars are Targeted?

The parameter space for eBOSS quasar targeting overlaps that of earlier iterations of the SDSS. The bits QSO_BAD_BOSS, QSO_BOSS_TARGET, QSO_SDSS_TARGET, and QSO_KNOWN work together to determine a sample of objects for which eBOSS does not need to obtain an additional spectrum because a good classification and redshift should already exist (if the object is a quasar). Targets are not observed if QSO_BOSS_TARGET, QSO_SDSS_TARGET, or QSO_KNOWN are set, unless  QSO_BAD_BOSS is set. In addition, QSO_REOBS always forces a reobservation of an earlier BOSS quasar. In Boolean notation, DO_NOT_OBSERVE is then set according to quasar target bits if:

$$\begin{eqnarray}&&\left({\mathtt{QSO}}\_{\mathtt{KNOWN}}\;\parallel \;{\mathtt{QSO}}\_{\mathtt{BOSS}}\_{\mathtt{TARGET}}\;\parallel \right.\\ &&\left.{\mathtt{QSO}}\_{\mathtt{SDSS}}\_{\mathtt{TARGET}}\right)\\ &&\qquad \qquad \mathrm{and}\;!({\mathtt{QSO}}\_{\mathtt{BAD}}\_{\mathtt{BOSS}}\;\parallel \;{\mathtt{QSO}}\_{\mathtt{REOBS}}).\end{eqnarray} \tag{ 7 }$$

The reduction in target density from implementing this schema is significant. Broadly, the total density of eBOSS CORE quasar targets that have to be allocated a fiber drops from ∼115 deg⁻² to close to ∼90 deg⁻² with effectively no loss of useful quasars (see Section 5). This filtering allows eBOSS to target a larger number of Lyα quasars using the QSO_PTF method, and may ultimately result in a larger total area for eBOSS.

4.4.11.  DR9_CALIB_TARGET: Which Version of the SDSS Imaging was Used?

SEQUELS comprises two chunks of BOSS covering ∼810 deg² in total area.⁵² SEQUELS approximates the region bounded by the SDSS Legacy imaging footprint and 120° ≤ α_J2000 < 210° and +45° ≤ δ_J2000 < +60°. Targets are selected as described thus far for eBOSS with five slight differences.

• 1.  
  The bright-end cut enforced on all target classes in SEQUELS was i > 17 on FIBERMAG  rather than on FIBER2MAG. This choice makes a tiny difference to the selected targets, of the order of 0.2%.
• 2.  
  IMAGE_STATUS flags were not applied in SEQUELS. More than 97% of the SEQUELS area has good IMAGE_STATUS according to our definition from Section 4.3. The remaining ∼3% of area, however, would not have been observed in eBOSS proper.
• 3.  
  The QSO_EBOSS_KDE target class (see Section 4.4) was observed in SEQUELS, but was discontinued for eBOSS.
• 4.  
  CORE quasar targets in eBOSS are all selected from the updated imaging described in Section 3.1. In SEQUELS the superset arising from both the updated and DR9 imaging was targeted, because the updated imaging calibrations were considered to be preliminary. As we outline in this section, the updated imaging is sufficient to meet eBOSS goals, so targeting using DR9 imaging was discontinued after SEQUELS. In this section, we only discuss the results arising from the use of the updated imaging.
• 5.  
  For SEQUELS the QSO_PTF target density was set at ∼35 deg⁻², which is higher than the typical eBOSS density of this target class of ∼20 deg⁻².

Spectroscopic observations for SEQUELS were conducted in the same fashion as general BOSS plates (see Dawson et al. 2013), with average exposure times of 75 minutes. The SEQUELS observations contained in DR12 consist of 66 plates over an effective area of 236.3 deg². The coverage is depicted in Figure 13. The targeting completeness, defined as the fraction of all targets that have received a fiber in each overlapping sector of the survey, is plotted.⁵³ Sectors are derived using the MANGLE software package (e.g., Swanson et al. 2008).

Zoom In Zoom Out Reset image size

Every object targeted as a quasar or identified as a likely quasar by the automated pipeline (Bolton et al. 2012) was visually inspected following the procedures presented in Pâris et al. (2014). The final classifications are described in DR12Q. A summary of the results is reported in Table 3. Figures 14–16 display typical SEQUELS spectra as a function of g-band magnitude. It is apparent that even the faintest quasars observed in SEQUELS (Figure 16) can be identified and assigned a redshift on visual inspection, even with no smoothing or other enhancements to the spectrum. A caveat is that SEQUELS was conducted during particularly good observing conditions, and there is therefore no guarantee that the quality of SEQUELS spectra will be representative of the full eBOSS survey.

Zoom In Zoom Out Reset image size

Zoom In Zoom Out Reset image size

Zoom In Zoom Out Reset image size

Based on Table 3, we expect that of the order of 96% of all quasar targets in eBOSS will be confidently classified to r < 22, and ≃99% of CORE quasars should be confidently identified. There are a number of reasons to believe that SEQUELS may slightly overestimate our ability to classify quasars in every area of the eBOSS survey. First, the SEQUELS area contains relatively good imaging when compared to several eBOSS areas in the SDSS SGC region (see Section 6). Second, as SEQUELS occurred concurrently with BOSS observations, some z > 2 BOSS quasars that would not be reobserved in eBOSS were tagged as SEQUELS targets—and, in general, z > 2 quasars are easier to classify as the strong Lyα line and the Lyα Forest are redshifted into the BOSS spectrograph bandpass at about z > 2. More comprehensive details of the eBOSS pipeline and spectral classification procedures—and, in particular, whether the pipeline meets the requirements discussed in Section 2.2—are provided in our companion overview paper (Dawson et al. 2015).

Perhaps the most critical aspect of eBOSS quasar targeting is that a sufficiently high density of quasars is obtained to make meaningful and/or improved measurements of the BAO distance scale. Contingent on the effective area of SEQUELS (as depicted in Figure 13), we can estimate the quasar density expected for eBOSS. Making this estimate is relatively straightforward: it is obtained by dividing the total number of spectroscopically confirmed quasars in SEQUELS by the completeness-weighted area of the survey as a function of targeting approach and redshift. For this purpose, "completeness" means targeting completeness to the statistically selected quasar sample, which here is defined as the fraction of CORE quasar targets that received a fiber for spectroscopic observation. Targeting incompleteness occurs in SEQUELS for two main reasons: First, due to collisions, a fiber cannot always be placed on neighboring targets, causing general incompleteness on a plate; and, second, certain plates in SEQUELS are yet to be observed, causing significant incompleteness in areas where yet-to-be-observed plates overlap completed plates. Table 4 presents estimates of the eBOSS quasar density. In addition to weighting the CORE quasar counts by completeness on a sector-by-sector basis, Table 4 details results as a function of completeness. Ultimately, eBOSS is expected to have a targeting completeness of 0.95 (due to collisions, fibers will only be placed on 95% of quasar targets), so it is worth noting that the statistics in Table 4 are somewhat dependent on completeness.

The results in Table 4 have been produced in a manner that should reflect the eventual targeting schema for eBOSS. One subtlety is that most, but not all, BOSS observations had been completed in the depicted area in Figure 13 by the time of SEQUELS observations. To better mimic eBOSS, estimates in Table 4 are produced by substituting non-SEQUELS (BOSS) identifications from DR12Q over SEQUELS targets, where they exist, and such objects are treated as previously observed, known quasars (i.e., when such objects have a good spectrum from DR12Q, they are treated as if they had a known redshift from BOSS and as if the DO_NOT_OBSERVE bit had been set; see Section 4.4.10). At the outset of SEQUELS, 8921 potential SEQUELS targets had the DO_NOT_OBSERVE bit set due to a prior good spectrum in SDSS-I, II, or III. Based on our substitution process, only an additional 267 (∼3%) quasars would have had the DO_NOT_OBSERVE bit set due to yet-to-be-completed BOSS observations, and only 92 (∼1%) of these additional quasars would have been in the redshift range 0.9 < z < 2.2.

It is critical for users of eBOSS data to be able to accurately track previously known quasars from earlier versions of the SDSS. Table 4 implies that of the order of ∼13 deg⁻² 0.9 < z < 2.2 quasars will be included in eBOSS as a prior confirmation. This number of ∼13 deg⁻² previously identified CORE quasars is as might be expected. The SDSSI/II quasar catalog of Schneider et al. (2010) contains ∼75,000 0.9 < z < 2.2 quasars spread over 9400 deg² (∼8 deg⁻²). The BOSS quasar catalog of DR12Q contains ∼65,000 0.9 < z < 2.2 quasars spread over 10,700 deg² (∼6 deg⁻²). These catalogs also contain ∼1 deg⁻² mutual 0.9 < z < 2.2 quasars. Depending on SEQUELS sector, the number of known quasars in the CORE redshift range can vary widely, from as few as 5 deg⁻² to as many as 25 deg⁻² due to the complex set of ancillary programs that were conducted as part of BOSS (see, e.g., Dawson et al. 2013).

The main purpose of this section is to investigate whether the eBOSS target selection as applied to SEQUELS meets the requirements discussed in Section 2.2, which amounts to a success rate of >58 deg⁻² 0.9 < z < 2.2 quasars over 7500 deg². Whether the area requirements of Section 2.2 will be met are discussed in Dawson et al. (2015). The results from the SEQUELS area suggest that eBOSS will meet its quasar targeting requirements in terms of number densities. For a targeting completeness reflective of eBOSS (∼95%), a completeness-weighted density of 72.0 deg⁻² 0.9 < z < 2.2 quasars were identified in SEQUELS. This suggests that the eBOSS CORE quasar selection will identify (0.95 × 72.0 =) 68.4 deg⁻² 0.9 < z < 2.2 quasars.

The SDSS imaging in the SEQUELS area may be of above-average quality, which could inflate these expectations (see Section 6). There are also reasons to believe, however, that the eBOSS quasar density may be higher than SEQUELS expectations. For instance, SEQUELS data were reduced using the SDSS-III spectroscopic pipeline, which, with augmentations, might improve on the ∼1% loss due to unidentifiable quasars listed in Table 3. Also, there are 1.5–2 deg⁻² additional objects in the CORE redshift range in SEQUELS that are not included in Table 4 because they are classified as "unknown" or as galaxies upon visual inspection. In theory, these objects can also be used for eBOSS clustering analyses (although such objects have a median redshift of ∼1.1).

Fibers not allocated to other eBOSS target classes are assigned to finding new Lyα quasars (z > 2.1). In Table 4 we show that SEQUELS contains (7.0 × 0.95) = ∼6.7 deg⁻² new Lyα quasars acquired by the CORE selection and (4.1 × 0.95) = ∼3.9 deg⁻² new Lyα quasars acquired by other selections (mainly objects with the QSO_PTF bit set). These results are likely robust for CORE targets (given the caveats discussed in the previous paragraph). Lyα quasar target density may fluctuate across the survey with the availability of PTF imaging (see Section 4.2.1), so SEQUELS is a reasonable but imperfect estimate of the success rate for new QSO_PTF Lyα quasars in eBOSS. In particular, the target density of QSO_PTF sources was 35 deg⁻² in SEQUELS, but is expected to be close to 20 deg⁻² across the entire eBOSS footprint (see Section 5.1). Thus expected density of new z > 2.1 quasars from the eBOSSQSO_PTF program is quoted as 3–4 deg⁻² in the abstract of this paper. There are also reasons to believe, however, that results from SEQUELS may underestimate the success of eBOSS. Most notably, our companion surveys such as TDSS (Morganson et al. 2015) target some Lyα quasars in addition to those targeted by the QSO_EBOSS_CORE and QSO_PTF approaches (see, e.g., J. Ruan et al. 2016, in preparation).

Beyond the cosmological goals of eBOSS, the quasar sample produced by SDSS-IV should be unparalleled, exceeding the depth and numbers of any previous quasar sample. As there is likely to be significant interest in the nature of eBOSS for quasar science, quasars observed as part of SEQUELS are broadly characterized in this section. Because SEQUELS observations were conducted in tandem with BOSS, some quasars that would not normally receive a fiber in eBOSS because of existing BOSS spectroscopy did receive a SEQUELS fiber. Throughout this section, we treat such objects as if they had the DO_NOT_OBSERVE bit set by correctly incorporating (non-SEQUELS) redshifts and classifications from the DR12 quasar catalog (I. Pâris et al. 2016, in preparation), as also described in the discussion of Table 4 in Section 5.2.

The redshift distribution of quasars in SEQUELS is plotted in Figure 17 and is similar to the expectation from Figure 4. The measurements of the SEQUELS N(z) are listed in Table 5. When combined with the expected total eBOSS quasar target density over all redshifts of ∼99 deg⁻² (see Table 4) and the expected 7500 deg² area of eBOSS, the SEQUELS N(z) should be sufficient to project science results using an eBOSS-like sample. The redshift-absolute-magnitude distribution of SEQUELS is provided in Figure 18. This figure illustrates why eBOSS will be the next-generation quasar survey, complementing the (largely) i < 19 space of SDSS-I/II and the (largely) z < 0.9 and z > 2.2 space of BOSS, by filling in the i > 19 and 0.9 < z < 2.2 quasar space in an unprecedented fashion.

Zoom In Zoom Out Reset image size

Zoom In Zoom Out Reset image size

The overall expected quasar numbers for eBOSS can be estimated from the SEQUELS N(z) and number densities. Projecting from Table 4 and assuming a minimum eBOSS area of 7500 deg² (Section 2.2), eBOSS should, conservatively, comprise at least 500,000 spectroscopically confirmed 0.9 < z < 2.2 quasars selected in a uniform manner with which to pursue quasar clustering studies such as the BAO scale, and at least 500,000 total new quasars (at any redshift) that have never been spectroscopically identified and characterized. Overall, at the completion of eBOSS, the SDSS surveys will have provided unique spectra of more than 800,000 total quasars, including SDSS areas outside the eBOSS footprint and new quasars observed by the TDSS and SPIDERS surveys.

Previous studies of large-scale galaxy clustering over the SDSS footprint (e.g., Ross et al. 2011) have demonstrated that systematics that produce target density variations at a level of ∼15% or less can be controlled for by weighting the random catalog by a model of the effect of that systematic. Beyond the 15% level, systematics become more difficult to "weight" for, perhaps because some major systematics are covariant. When the effect of systematics exceeds the 15% level, that area of the survey may have to be excised from clustering analyses.

As part of eBOSS target selection, a set of regression tests were devised to study how possible systematics in SDSS and WISE imaging may affect target density—and whether such effects are below the ∼15% level that could be modeled with a suitable weighting scheme. The slate of systematics, which represents a reasonable (but not necessarily exhaustive) list of quantities that could bias eBOSS target density, is further detailed in a companion paper (Prakash et al. 2015b). Relevant to the WISE imaging; the systematics include the median numbers of exposures per pixel, the fraction of exposures contaminated by the moon, and the total flux per pixel, all in the W1 band (W1covmedian, moon_lev, W1median). Relevant to the SDSS imaging, the systematics include the FWHM and background sky-level in SDSS z-band, which are used to track the quality of the seeing and the sky brightness. Additional systematics include Galactic latitude (to map the density of possible contaminating stars) and Galactic dust (extinction in the r-band is used to represent this systematic).

The adopted regression technique is also detailed in Prakash et al. (2015b). Briefly, the potential eBOSS imaging footprint is deconstructed into equal-area pixels of 0.36 deg². The eBOSS CORE quasar target density and the mean value of each systematic is determined for each of these pixels. The observed surface density (SD_obs) of eBOSS CORE quasar targets in each pixel can be expressed as a linear model of systematics

$$\begin{eqnarray}&&{{\rm{SD}}}_{{\rm{obs}}}={S}_{0}+\displaystyle \sum _{i=1}^{7}{S}_{i}{x}_{i}+\epsilon ,\end{eqnarray} \tag{ 8 }$$

where S₀ is the mean target density across the pixels, S_i is the weight accorded to fluctuations in target density (x_i) due to systematic i, and is the combined effect of noise and variance, which is approximated as a Gaussian. Multilinear regression is used to determine S₀ and S_i by minimizing the value of reduced χ² across the pixels. This regression is conducted separately in each Galactic hemisphere, such that different coefficients are derived for the NGC and SGC regions of the SDSS imaging.

Once the coefficients of the linear regression model for systematics have been established, a statistic designated the Predicted Surface Density, PSD, is computed. The PSD is obtained by using S₀ and S_i to calculate what the eBOSS CORE quasar density should be in a given pixel if the linear regression model is an adequate description

$$\begin{eqnarray}&&{\rm{PSD}}={S}_{0}+\displaystyle \sum _{i=1}^{7}{S}_{i}{x}_{i}.\end{eqnarray} \tag{ 9 }$$

Figure 19 presents a histogram of the CORE quasar PSD as predicted from the derived linear regression model coefficients across all of the systematics. A total of 96.7% of the SDSS imaging footprint in the NGC fluctuates in CORE quasar PSD at less than 15%.⁵⁴ The corresponding fraction is 76.7% in the SGC footprint.

Zoom In Zoom Out Reset image size

Figure 20 illustrates these deviations on the sky using a map of the PSD statistic, which serves to illustrate the most problematic areas of the SDSS footprint for eBOSS. The right-hand panel of Figure 20 approximates the "mask" that will be necessary to ameliorate the effects of systematics on clustering measurements that use eBOSS CORE quasars. The effective area or random catalog in each region of the eBOSS footprint can be re-weighted by the values displayed in the right-hand panel of Figure 20, although regions that deviate by more than 15% from expectation may need to be excised from the survey in order to reach the target density variation requirement of Section 2.2. The central panel of Figure 20 is a particularly clear illustration of why the PSD is regressed separately in the NGC and SGC regions—the NGC appears to be more robust to systematics than the SGC.

Zoom In Zoom Out Reset image size

To determine whether a linear regression adequately models the effect of systematics on the target density of eBOSS CORE quasars, calculate the statistics designated the ${\mathrm{Reduced}\_\mathrm{PSD}}_{j}$ and the ${\mathrm{Residual}\_\mathrm{PSD}}_{j}$ in Prakash et al. (2015b). The ${\mathrm{Reduced}\_\mathrm{PSD}}_{j}$ is derived from the PSD by omitting the j'th systematic term when calculating the PSD, in order to represent the deviation from the PSD caused by each systematic. The difference between the PSD and the observed sky density of targets, called the Residual Surface Density, Residual_SD, is then calculated. If a linear model is an appropriate representation of the regression of a given systematic, then the $\mathrm{Residual}\_\mathrm{PSD}$ should be well-represented by a model with a slope of S_j. Formally,

$$\begin{eqnarray}{\mathrm{Reduced}\_\mathrm{PSD}}_{j} & = & {\rm{PSD}}-{S}_{j}\times {x}_{j},\\ {\mathrm{Residual}\_\mathrm{SD}}_{j} & = & {{SD}}_{{\rm{obs}}}-{\mathrm{Reduced}\_\mathrm{PSD}}_{j}.\end{eqnarray} \tag{ 10 }$$

Figure 21 shows how the CORE quasar Residual_SD varies as a function of each of the individual systematics, together with the underlying distributions of those systematics. In general, a linear regression seems to be adequate for modeling variations in CORE quasar target density. Figure 21 suggests that sky brightness, and, in particular, Galactic extinction, are the main culprits in causing variations in eBOSS CORE quasar target density. The SGC has a 68% range of r-band extinction of 0.075 to 0.19 with a median of 0.12, whereas the NGC has a 68% range of r-band extinction of 0.032 to 0.10, with a median of only 0.057. The corresponding numbers for z-band sky flux are 4.1–6.8 with a median of 5.1 in the SGC and 3.3–4.6 with a median of 3.8 in the NGC. The higher median and wider range of values of these systematics in the SGC are likely responsible for both the suppressed density of SGC targets and the larger rms in predicted surface density that can be seen in Figure 20. These systematics will act to reduce the effective depth of an exposure and hence increase the error on the fluxes of a test object being assigned a quasar probability by the XDQSOz method. In effect, as the flux errors for a test object increase, the formal probability that the object is a quasar is reduced, and fewer objects are then assigned PQSO(z > 0.9) > 0.2 by XDQSOz.

Zoom In Zoom Out Reset image size

Overall, the eBOSS quasar targeting algorithm outlined in this paper is expected to produce quasar samples for clustering measurements that are robust against systematics across essentially the entire NGC and across about three-quarters of the SGC. This statement may be pessimistic, as eBOSS does not attempt to restrict the CORE quasar redshift range to 0.9 < z < 2.2 in advance of spectroscopic confirmation. Quasars at z > 2.2 are closer to the stellar locus in optical color space, so the target density of quasars at z > 2.2 may fluctuate more due to systematics than at z < 2.2. Weighting for systematics as a function of quasar redshift is a possible avenue for further improving eBOSS clustering measurements once target redshifts have been confirmed by spectroscopy. The final eBOSS footprint is yet to be derived, but in a worst-case scenario if the entire SGC has to be observed, only ∼86.7% of eBOSS will meet the requirements of Section 2.2. This fraction of useful area is almost exactly offset by the expected excess of eBOSS CORE quasars. Table 4 implies that eBOSS will confirm (0.95 × 72.0 =) 68.4 deg⁻² 0.9 < z < 2.2 quasars. Serendipitously, 68.4 deg⁻² × 0.867 = 59.3 deg⁻², exceeding the requirement of 58 deg⁻² 0.9 < z < 2.2 quasars noted in Section 2.2.

A further requirement of eBOSS is that fluctuations in target density due to shifting zero-point calibrations across the SDSS imaging footprint are well controlled. Similar to Section 6.1, such fluctuations need to be kept below the 15% level (see also Section 2.2).⁵⁵ To study how changes in zero-point affect the density of eBOSS CORE quasar targets, each band used in the eBOSS CORE quasar selection is offset by ±0.01 mag (i.e., scaled by 1% in flux) and the resulting fractional changes in target density are determined after re-running the target selection pipeline. Each SDSS band is tested individually. Because the WISE bands are only incorporated into eBOSS CORE quasar target selection in a stack (see Equation (2)), both W1 and W2 are simultaneously shifted by ±0.01 mag and the result is reported as a single band (henceforth denoted W).

The resulting fractional fluctuations in target density from these offsets (N⁻¹[ΔN/Δm]) can then be multiplied by the zero-point rms error expected for the imaging calibrations used by eBOSS (see Section 3) to determine the expected rms variation in number density due to zero-point calibrations shifting across the eBOSS footprint. We adopt the zero-point errors in [u, g, r, i, z] of [13, 9, 7, 7, 8] mmag rms from D. Finkbeiner et al. (2016, in preparation) and conservatively estimate a zero-point error of 20 mmag rms for the W stack (see Jarrett et al. 2011). Assuming that the zero-point errors can be modeled using a Gaussian distribution, 95% of CORE quasar targets in eBOSS will be within ±2σ of the expected rms variation. In other words, 95% fractional variance in target density can be interpreted as meaning that 95% of the area of the sky is expected to be described by fluctuations of ±2σ. Thus, the overall 95% fractional variance in target density due to zero-point errors can be expressed (as a percentage) as 100% × 4 × [zero-point error] × [N⁻¹(ΔN/Δm)]. Table 6 displays the results of this analysis, which indicate that the g-band is the least robust to zero-point variations when selecting eBOSS CORE quasars. Even the g-band, however, causes a (2σ) variation of only 3%, which is far less than the 15% limit outlined in Section 2.2. eBOSS CORE quasar target selection is thus completely robust to zero-point errors.