The DESI Survey Validation: Results from Visual Inspection of the Quasar Survey Spectra

To assist in the interpretation of the results presented in this paper, we provide a brief overview of the DESI instrument, the QSO target selection, and the Redrock spectral template–redshift fitting code. We refer the interested reader to the referenced papers for more details.

DESI (DESI Collaboration et al. 2016b; Abareshi et al. 2022) is a multiobject spectrograph on the NOAO 4 m Mayall telescope at Kitt Peak in Arizona. It uses 5000 robotically controlled positioners to place fibers across a 7.5 deg² field of view (Abareshi et al. 2022; T. Miller et al. 2023, in preparation; Silber et al. 2023). The optical signal from the fibers is fed to optical spectrographs with sensitivity over 360–980 nm. Each optical spectrograph provides medium-resolution spectra across three channels: R > 2100 in blue (360–590 nm), R > 3200 in green (566–722 nm), and R > 4100 in red (747–980 nm).

The overall scale of the DESI experiment requires various supporting data products and software pipelines including the DESI Legacy Imaging Surveys (Zou et al. 2017; Dey et al. 2019; D. J. Schlegel et al. 2023, in preparation), extensive spectroscopic and template-fitting pipelines (S. J. Bailey et al. 2023, in preparation; Guy et al. 2022), and pipelines to assign fibers to targets (A. Raichoor et al. 2023, in preparation), optimize the tiling and planning of the survey observations (E. Schlafly et al. 2023, in preparation), and select targets for spectroscopic observations (Myers et al. 2023).

The standard template-fitting code utilized within DESI is called Redrock (S. J. Bailey et al. 2023, in preparation). Redrock uses a set of templates to represent the spectral properties of the broad object classes identified in DESI: QSOs, galaxies, and stars. ⁴⁸ Combinations of these spectral templates were constructed to provide composite solutions. Redrock determines the best-fitting redshift and template solutions to each DESI spectrum across the full range of redshift–template parameter space, selecting the best-fitting solutions on the basis of the lowest reduced χ² values.

In this paper we refer to both a standard Redrock pipeline and a modified pipeline. The standard Redrock pipeline is the same as that adopted for the DESI galaxy survey components. The modified pipeline (also referred to as "QSO maker") also adopts Redrock, as in the standard pipeline, but additionally utilizes two QSO "afterburner" algorithms (QuasarNet and Mg II afterburner; see Section 2.3.2). These "afterburner" algorithms search for significant QSO features missed by Redrock, which can consequently result in either (1) the reclassification of a galaxy to a QSO or (2) a revised redshift estimate for an identified QSO. Any revised redshifts from the modified pipeline are then refined using Redrock but with a tight prior (dz = 0.05 width top-hat function) to prioritize solutions that match the identified features (Chaussidon et al. 2022); see Section 3.3 for a more detailed description and calculation of the performance of the modified pipeline with respect to the standard Redrock pipeline.

The QSO survey targets are selected using a combination of optical (g, r, z) and mid-IR (W1, W2) colors to reduce the contamination from stars, which can have similar optical colors to QSOs. To reduce the contamination from galaxies, an optical morphology cut is also applied, selecting only sources with a "point-spread function" morphology in the DR9 legacy imaging (Dey et al. 2019). To improve the efficiency of the QSO selection, a random-forest machine-learning approach is adopted. The random forest is trained on both QSOs and stars, aiming to optimize across 11 parameters (10 color selections from the optical–mid-IR bands plus r-band magnitude) to preferentially select the former and eliminate the latter. For more details of the QSO target selection and survey strategy, see Chaussidon et al. (2022).

For the visual-inspection data explored in this paper, the targets were selected using the more liberal SV1 selection down to r ≈ 23.5 mag. However, to replicate the expected results in the main DESI survey, we also applied the more conservative main-survey target selection down to r ≈ 23 mag, which we refer to here as the "main target selection" but is occasionally referred to elsewhere as SV3 (Chaussidon et al. 2022).

VI of the optical spectra in DESI is crucial for several key reasons: the development and evaluation of the DESI spectroscopic pipeline processes, a quantitative assessment of the target-selection approaches, and the identification of physically interesting subsets from the selected-target populations. Given the scale of the main DESI survey (>40 million spectroscopically identified targets) and the time-consuming nature of VI, it is prohibitively expensive to visually inspect each spectrum. ⁴⁹ VI by its nature is also prone to human error and therefore requires each spectrum to be inspected by more than one person. Consequently, the VI efforts in DESI are primarily focused on assisting in the development of the pipeline and target-selection approaches to optimize both the effectiveness and quality of the spectroscopic outputs.

The key focus of the VI is to assess the quality of each optical spectrum from the point of view of the measurement of a spectroscopic redshift to construct a "truth table." Overall the same VI approach was adopted across both the QSO and galaxy survey components in DESI. However, due to the large variety of optical spectral types identified within the QSO survey (see Section 3.1), a significant fraction of the VI effort within the QSO survey was also devoted to the spectroscopic classification of the selected targets. Consequently, this paper focuses more on the optical spectroscopic classifications of the targets than the galaxy VI paper (see Lan et al. 2023) and, ultimately, calculates the performance of the QSO survey using only the spectrally classified QSOs rather than all targets.

A summary of the different phases of VI for the QSO survey is provided in Table 1. The initial two rounds were heavily focused on the development of the DESI spectroscopic pipeline and the refinement of the overall VI approach while the latter two rounds were more focused on quantifying the performance of the spectroscopic pipeline. Given the significant developments that occurred between the first two rounds and the later two rounds, the results presented in this paper are focused on the latter; i.e., the deep-field VI and the sparse VI. The optical spectroscopic observations were also shorter in the first two VI rounds, with exposure times comparable to the main DESI survey (≈1000 s) as compared to the ≈3–10 times longer exposures for the deep-field and sparse VI. However, the basic VI approach whereby each target spectrum is assessed by more than one inspector and then merged by the QSO survey VI lead (TMD for the first two rounds and DMA for the last two rounds) is common to both phases. ⁵⁰

Each target spectrum is evaluated using the Prospect visualization tool. ⁵¹ A more extended description of Prospect is provided in Lan et al. (2023); however, the salient details relevant for an understanding of the QSO survey VI are given here. Prospect displays the unsmoothed optical spectrum and associated noise/error spectrum for each target spectrum; see Figure 1 for example spectra. The nine best-fitting redshift and spectral-template solutions calculated by the Redrock spectral fitting code are also listed, along with the Δχ² differences between each subsequent best-fitting solution. The visual inspector can smooth the spectrum and evaluate the spectral quality taking into account the overlapping regions of the three different spectral arms where breaks and discontinuities in the optical spectrum can occur. The visual inspector is then required to record:

• 1.  
  Any problems and issues in the optical spectrum (e.g., poor sky subtraction; significant breaks and discontinuities within a spectral arm).
• 2.  
  An assessment of the optical spectral classification (QSO, galaxy, or star) on the basis of the shape of the continuum emission and the identified emission and absorption lines. Targets are primarily classified as a QSO from the detection of broad permitted emission lines, strong nonstellar continuum, and/or prominent narrow high-excitation emission lines. Galaxies are identified based on the detection of low-excitation narrow emission and absorption features while stars are primarily identified from the detection of a stellar continuum with associated absorption lines at z ≈ 0.
• 3.  
  The identification of physically interesting features or spectral subtypes (e.g., extreme absorption or emission features; identification of active galactic nucleus, AGN, spectral features within a galaxy spectrum; unusual optical continuum shapes; identification of a broad absorption-line quasar (BALQSO), damped Lyα system, blazar, or two objects contributing to the spectrum).
• 4.  
  An assessment of the spectroscopic redshift. The spectroscopic redshift is manually calculated by the visual inspector within Prospect by aligning the spectral features to the observed-frame wavelengths of potential emission and absorption lines, overlaid on the optical spectrum. The spectroscopic redshift can be refined in this way to four decimal places using a zoomed-in view of the spectrum if necessary.
• 5.  
  An assessment of the quality of the optical spectroscopic redshift using a numerical code from 0–4, defined as the VI quality class and described in more detail below.

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The VI quality class indicates the reliability of the optical spectroscopic redshift measurement, as assessed by the visual inspector. The reliability of a spectroscopic redshift is related to more than just the signal-to-noise ratio (S/N) of the spectrum and also depends on the spectral shape, strength of spectral features (i.e., emission and absorption lines), and the redshift of the target (since the redshift will dictate which spectral features are present in the observed wavelength range). Example spectra to illustrate the five different VI quality classes are provided in Figure 1 and associated qualitative descriptions are given below.

VI quality class 4: the secure identification of two or more spectral features (i.e., emission or absorption lines) indicating a confident spectroscopic redshift. Thanks to the high spectral resolution of the DESI data, the [o ii]λ3727,3729 doublet can often be spectrally resolved, yielding a confident spectroscopic redshift even in the absence of no other identified features (see Figure 3 of Lan et al. 2023 for an example).

VI quality class 3: the identification of one secure spectral feature plus additional weak spectral features indicating a probable spectroscopic redshift.

VI quality class 2: the identification of one spectral feature indicating a possible spectroscopic redshift.

VI quality class 1: continuum identified but no clear identified spectral features indicating an unreliable redshift.

VI quality class 0: a weak or absent signal indicating a problem or issue with the optical spectrum.

The VI lead merges the results from all of the visual inspectors to determine the spectroscopic redshift, VI quality class, and spectral type for each target. We calculate the spectroscopic redshift difference between visual inspectors using the following basic formalism:

$$\begin{eqnarray}&&{{dz}}_{{\rm{A}},{\rm{B}}}=\displaystyle \frac{| {z}_{{\rm{A}}}-{z}_{{\rm{B}}}| }{(1+{z}_{{\rm{A}}})},\end{eqnarray} \tag{ 1 }$$

where in this case dz_A,B refers to the difference between the two VI redshifts, z_A and z_B, and which we define as dz_VI.

A mean spectroscopic redshift is calculated when there is good agreement between the visual inspectors (dz_VI < 0.0033), and a mean VI quality class is calculated when the quality class differs by ≤1 between visual inspectors.

For targets where there is a significant difference between the visual inspectors in terms of the spectroscopic redshift (dz_VI ≥ 0.0033), the VI quality class (a difference of more than 1), or the selected spectral type (more than one spectral type selected), the VI lead uses Prospect to reevaluate the optical spectrum and manually determine the target redshift, quality class, and optical spectral type. Overall, for the QSO survey, the VI lead reevaluates ≈20% of the optical spectra.

A spectrum is considered high quality with a robust spectroscopic redshift when the VI quality class is ≥2.5 (referred to hereafter as VI ≥2.5), calculated either from the average quality class of the visual inspectors or by the VI lead, when the spectrum is reevaluated. Otherwise, the spectrum is considered low quality with an unreliable spectroscopic redshift; i.e., VI <2.5.

The data analyzed in this paper is taken from the last two VI phases when the pipeline process was mature and stable: the deep-field and sparse VI (see Table 1). Overall, ≈6000 spectra were visually inspected in these latter VI phases. The exposures for the optical spectra from these data sets are ≈3–10 times deeper than the nominal main DESI depth; see Tables 2 and 3 for the depth of each tile. The higher S/N provided by these deep spectra allows for more reliable VI results and, consequently, more accurate truth tables. Since these deep spectra were obtained not from a single very long exposure but from the combination of many shorter exposures, they also allow for the construction of multiple shallower target spectra to replicate the quality of the spectra at the ≈1000 s depth of the main 5 yr survey, an aspect that we exploit to calculate the overall performance of the main DESI survey; see Section 4.

Table 2. Tiles Used in the Deep-field Visual Inspection

Tile ID	Position	${t}_{\exp }$	Common Name
	(R.A., Decl.) (deg)	(s)
80605	(36.448, −4.601)	7020	XMM-LSS
80607	(106.740, 56.100)	9210	Lynx
80609	(150.120, 2.206)	8300	COSMOS

Note. The columns show the identification number of each DESI tile, the R.A. and decl. of the tile center, the median dark-time exposure time, and the common names typically adopted for these well-studied fields.

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2.3.1. Deep-field VI Data Sets

2.3.2. Sparse VI Data Sets

The three fields inspected in the deep-field VI (described in Section 2.3.1) only comprise ≈10% of the SV tiles in the quasar survey. To complement the deep-field VI we also visually inspected targets in the other 27 SV tiles observed and processed within the Cascades data assembly. However, unlike the deep-field VI, we focused our efforts on visually inspecting key subsets of the selected quasar targets to either improve the source statistics of comparatively rare target subsets identified in the deep-field VI or to test potential issues in the identification pipeline. Consequently, the VI of these fields is referred to as the "sparse VI." The key details of these 27 tiles are provided in Table 3 and a breakdown of the target selections for the sparse VI is given in Table 4 and described below.

Table 3. Tiles Used in the Sparse Visual Inspection

Tile ID	Position	${t}_{\exp }$
	(R.A., Decl.) (deg)	(s)
80620	(144.000, 65.000)	6920
80622	(155.000, 32.325)	5390
80669	(38.000, 0.500)	4550
80673	(85.500, −20.200)	3540
80674	(87.000, −23.200)	2750
80675	(98.500, 44.500)	4120
80676	(97.500, 47.700)	4810
80677	(104.500, 36.000)	3550
80678	(102.500, 39.000)	4880
80679	(111.000, 41.500)	3470
80680	(111.000, 44.800)	6050
80681	(115.000, 32.375)	4800
80682	(115.000, 32.375)	4420
80683	(116.000, 15.500)	3890
80684	(114.500, 18.400)	3890
80685	(120.000, 34.000)	5380
80686	(124.000, 34.300)	3540
80688	(130.700, 22.300)	5560
80690	(135.000, 32.375)	6370
80692	(139.000, 32.375)	5620
80693	(135.000, 83.000)	5250
80694	(162.000, 83.000)	3650
80699	(155.000, 32.375)	4130
80700	(159.000, 32.375)	4800
80707	(192.900, 27.100)	5860
80711	(213.000, 51.450)	5280
80712	(217.000, 53.550)	3060

Note. The columns show the identification number of each DESI tile, the R.A. and decl. of the tile center, and the median dark-time exposure time.

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Table 4. Target Subsets Explored in the Sparse VI

Target Selection	N
QuasarNet	1307
SQUEzE	962
MgII afterburner	765
Unique missed QSOs	1717
MgII absorption systems	138
Nonrepeatable redshifts	731
Unique targets	2391

Note. Each row shows the number of targets visually inspected for each target-selection approach in the sparse VI. The total number of unique targets from the missed QSO selection approaches is highlighted in bold in addition to the total number of unique targets visually inspected across all target-selection approaches; the number of overlapping targets between each selection approach is shown in Figure 2.

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For the quasar survey, the main focus of the sparse VI was to calculate the performance of several independent quasar-identification approaches (QuasarNet, SQUEzE, and Mg ii afterburner); these approaches are referred to generically here as "afterburners" since they are performed on the DESI spectroscopy following the standard Redrock spectroscopic pipeline. As demonstrated from the deep-field VI in Section 3, while the spectral classification of a quasar by the standard Redrock pipeline is highly reliable, it misses a nonnegligible fraction of genuine quasars, the majority of which we can recover through the afterburner approaches; see Section 3.2 and the brief afterburner descriptions below. We generically refer to QSOs missed by Redrock as "missed QSOs."

QuasarNet (QN; Busca & Balland 2018) utilizes a deep convolutional neural network classifier with multiple layers of convolution to identify emission lines and to calculate the most likely target redshift. SQUEzE (SQ; Pérez-Ràfols & Pieri 2020a; Pérez-Ràfols et al. 2020b) also adopts a machine-learning approach but uses a random-forest classifier to assess the identification of emission peaks and to calculate the most likely target redshift. The performance of QN and SQ has been previously evaluated using the visually inspected spectra from the SDSS BOSS quasar survey (Farr et al. 2020) to assess the utility of these approaches in the quasar identification in the DESI quasar survey. By comparison, the Mg ii afterburner searches for significant broad Mg ii emission at the best-fitting Redrock redshift for systems spectrally classified as galaxies (see Section 6.2 of Chaussidon et al. 2022). It therefore differs from QN and SQ in not independently calculating the target redshift but switches the spectroscopic classification from galaxy to quasar when probable broad Mg ii emission is detected.

In selecting targets for the missed QSO component of the sparse VI, we required an optical magnitude of r < 23.2, the nonidentification of a quasar from the best-fitting Redrock template solution from the Cascades data assembly, and a minimum confidence threshold depending on the afterburner approach: QN_C_LINE_BEST > 0.95 for QN, PROB > 0.4 for SQ, or a Δχ² > 16 improvement in the fitted spectra when broad Mg ii emission is included for the Mg ii afterburner. We chose these thresholds based on the results from the afterburner codes performed on the deep-field VI to achieve a balance between selecting genuine missed QSOs and providing a data set for which to further assess the reliability of the afterburner approaches. Although the three afterburners differ in their identification approaches, there is a reassuringly high level of overlap between the selected targets; see the target-selection approach breakdown in Table 4 and the Venn diagram in the lower panel of Figure 2.

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In addition to the missed QSOs, we also visually inspected (1) a sample of r < 23.2 mag candidate Mg ii absorption systems and (2) targets where the best-fitting Redrock spectral template–redshift solutions differed significantly between the coadded spectroscopy and shallower nominal main DESI survey depth data. The latter are referred to as "nonrepeatable redshifts" and selected when

$$\begin{eqnarray}{\rm{\Delta }}{\chi }^{2}(\mathrm{short})\gt 20\ \& \ {\rm{\Delta }}{\chi }^{2}(\mathrm{long})\gt 100\ \& \ {dz}\gt 0.05,\end{eqnarray} \tag{ 2 }$$

where dz refers to the relative redshift difference between the measured redshifts of individual short (>700 s) and coadded long (>3000 s) exposure spectra, and Δχ² refers to the difference in reduced Δχ² between the best-fitting and second-best-fitting Redrock spectral template solutions. See Equation (1) for the basic formalism for calculating dz using the short- and long-exposure redshifts.

The VI of the Mg ii absorption systems was undertaken to assist in the development of an Mg ii absorption-line selection tool and will be presented in L. Napolitano et al. (2023 in preparation). The VI for the nonrepeatable redshifts were taken to analyze the spectroscopic pipeline and are not further investigated in this paper. For completeness, we summarize the number of selected targets from these target-selection approaches in Table 4 and illustrate their modest overlap with respect to the missed QSOs in the top panel of Figure 2.

In Figure 3 (top panels) we show the distribution of VI quality classes and high-quality (VI ≥2.5) VI redshifts from the deep-field VI for both the SV1 and main target selections. The basic results from the deep-field VI are also presented in Table 5. The majority of the optical spectroscopy is of high quality (VI ≥2.5), yielding reliable spectroscopic redshifts and optical spectral classifications; we also note that there are ≈10× more VI = 4 spectra than VI = 3 spectra.

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A larger fraction of targets (≈93%) that meet the conservative main-target selection have higher-quality spectra than is found for the fainter and more liberal SV1 selection (≈86%). The high-quality redshift distributions peak around z ≈ 1 for both the main and SV1 target selections and include all spectroscopic classes (QSOs, galaxies, and stars); indeed, the significant peak at z ≈ 0 is due to a nonnegligible fraction of stars. At z > 1.6 (the redshift threshold uniquely traced by the QSO survey within DESI), there are modest differences between the SV1 and main target selection approaches, demonstrating that the more conservative main target selection provides comparable high-redshift source statistics to the liberal SV1 selection. The excess number of z < 1.6 targets in the SV1 selection are a combination of galaxies, lower-redshift QSOs, and stars.

In Figure 4 the distributions of optical spectral class for both the main and SV1 target selections are shown, which are further quantified in Table 5. The main selection is significantly more efficient than SV1 at selecting QSOs (≈34% for SV1 and ≈71% for main). However, a significant fraction of targets are classified as either galaxies or stars for both selections; indeed, for SV1, galaxies are more dominant than QSOs. Such a large diversity in optical spectral classification is not seen in the DESI galaxy surveys (Lan et al. 2023) and is largely due to the challenge in robustly selecting QSOs from stars and galaxies using only photometric data. At the faint optical magnitudes probed by DESI, distinguishing between galaxies and QSOs becomes more challenging than for shallower optical surveys such as the SDSS since the emission from the host galaxy can become as significant as the QSO for the lower-luminosity (or more dust-reddened) systems identified.

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In Figure 5 (left) the r-band fiber magnitude versus redshift for the SV1 target selection in the deep-field VI is shown, with targets plotted on the basis of optical spectral class. The galaxies and QSOs have different redshift distributions with the galaxies predominantly at low redshift, with few at z > 1.5, while the QSOs extend out to z ≈ 5, peaking at z ≈ 1.0–2.5. Most of the low-quality spectra have faint magnitudes (r > 23 mags), at least partially explaining the significantly higher fraction of low-quality spectra in the fainter SV1 selection than for the main selection (i.e., lower-S/N data); see Table 5. However, the majority of the low-quality identifications occur at distinct redshift peaks and ranges. These redshift peaks are largely due to Redrock erroneously identifying a noise feature (often due to poor sky subtraction) as an emission line; e.g., the most prominent peak around z ≈ 1.5–1.7 is due to Redrock identifying [o ii] at ≈9300–10000 Å where the data can be particularly noisy (see the VI = 1 spectrum in Figure 1 for a good example).

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The results presented so far are based solely on the VI. However, since the vast majority of the optical spectra in the DESI survey will not be visually inspected, it is instructive to compare the VI results to the output from the spectroscopic pipelines. In Table 6 the pipeline results for both the SV1 and main target selections are shown, split as a function of the optical spectral class and subdivided between the standard and modified pipelines. Here we focus on the results from the standard Redrock pipeline and defer comparisons with the modified pipeline to Section 3.3. The standard Redrock pipeline reliably identifies QSOs, with ≈97% (SV1) and ≈99.5% (main) visually confirmed as high-quality QSOs. A slightly lower ≈88% of Redrock-identified stars are visually confirmed as high-quality stars, independent of target-selection approach, while by comparison <69% of the Redrock-identified galaxies are found to be high-quality identifications; indeed, the vast majority of the low-quality identifications reported in Table 5 are classified by Redrock as galaxies. However, despite the high reliability of Redrock-identified QSOs, a nonnegligible fraction of high-quality QSOs identified in the VI are missed by the standard Redrock pipeline (≈14% for SV1 and ≈11% for main). As shown in the following subsection, the majority of the high-quality QSOs missed by Redrock can be recovered with the afterburners.

In Figure 3 (bottom panels) we show the distribution of VI quality classes and high-quality VI redshifts for the missed QSO selection from the sparse VI for both the SV1 and main target selections. The missed QSO VI results are also presented in Table 5. As for the deep-field VI, the majority of the optical spectra are high quality: ≈95% (SV1) and ≈97% (main) have VI ≥2.5. The even larger fraction of high-quality spectra, as compared to the deep-field VI, is likely due to the additional requirement that the targets exceed the confidence threshold required by at least one of the afterburners. Individually, each of the afterburner approaches selects >90% high-quality QSOs, which rises to >96% when focusing on the main target selection, demonstrating the high reliability of the afterburners in identifying high-quality QSOs; see Table 7.

In Figure 5 (right) we show the r-band fiber magnitude versus redshift for the SV1 target selection for the missed QSOs, with targets plotted on the basis of optical spectral class. A significant difference is seen between the QSOs in the sparse VI and the deep-field VI (Figure 5, left) with many of the former QSOs populating a clearly defined curved band across the r-band–redshift plane at z ≈ 0.4–1.7, leading to a narrower overall redshift distribution (see Figure 3). The primary origin of this r-band–redshift curved band is the identification of broad Mg ii emission at the redshift of a Redrock-identified galaxy. This is illustrated in Figure 6: the Mg ii afterburner targets are tightly distributed over z = 0.4–1.7. For these missed QSOs, Redrock has measured the correct redshift but classified the target as a galaxy rather than a QSO.

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However, the QuasarNet and SQUEzE afterburners have also identified a population of missed QSOs across a wider redshift range. For these systems, Redrock failed to identify the QSO and also measured the wrong redshift. To illustrate these points, we plot in Figure 7 (top) the redshift from the standard Redrock pipeline versus the VI redshift: good agreement is found for many systems at z < 1.7, but a significant fraction of targets clearly have catastrophic redshift failures. ⁵³ However, as shown in Figure 7 (bottom), better redshift agreement is achieved when either the QuasarNet or SQUEzE afterburner redshift is adopted in preference to Redrock, providing the foundations for the construction of the modified pipeline for the QSO survey (Chaussidon et al. 2022), as described next.

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On the basis of the VI results presented in Section 3.1, the standard Redrock pipeline reliably distinguishes QSOs from stars and galaxies with just a small fraction of Redrock-identified QSOs with low-quality spectra (≈4% for SV1 and ≈1% for main). A nonnegligible fraction of high-quality QSOs (≈14% for SV1 and ≈11% for main) is missed by the standard Redrock pipeline but, as demonstrated in Section 3.2, we can reliably recover the majority using the afterburners. Consequently, a combination of the QSO identification approaches from both Redrock and the afterburners should lead to a larger selection of high-quality QSOs. This is the key motivation for the development of a modified pipeline to optimize the selection of QSOs (Chaussidon et al. 2022), commonly referred to as "QSO maker." In the following analyses we use the VI results to quantify the performance of the modified pipeline and compare these results to the standard Redrock pipeline.

Below we provide a summary of the key steps in the modified pipeline and refer the reader to the flowchart in Figure 9 of Chaussidon et al. (2022) for an illustration. Essentially, targets are classified as QSOs when identified by either the standard Redrock pipeline, the Mg ii afterburner, or QuasarNet, adopting the same afterburner confidence thresholds used for the sparse VI missed QSO selection (see Section 2.3.2). Redrock is then used to recalculate the spectroscopic redshift when either (1) QuasarNet identifies a QSO unidentified by the Mg ii afterburner or (2) when QuasarNet identifies the target as a QSO and the Redrock redshift disagrees with the QuasarNet redshift (i.e., dz > 0.05; see Equation (1) for the basic formalism of dz). To improve the final redshift measurement, the QuasarNet redshift is used as an input prior to Redrock with a tight top-hat redshift distribution of dz = 0.05, and only QSO template solutions are adopted in the redshift fitting.

To quantify the effectiveness of the modified pipeline for the identification of QSOs, we compare to the standard Redrock pipeline and the VI in the deep fields; see Table 6. The modified pipeline identifies a significantly larger number of QSOs for both the main and SV1 selections, the vast majority of which are high quality (≈93% for SV1 and ≈98% for main). Furthermore, almost all of the QSOs missed by the standard Redrock pipeline are reliably recovered by the modified pipeline (just 1%–2% of the high-quality QSOs are missed), providing a >10% increase in the number of high-quality QSOs. The overall number of QSOs with low-quality spectra is increased by factor ≈3 compared to the standard Redrock pipeline, but they only account for ≈2% of the modified-pipeline QSOs for the main target selection (≈7% for SV1).

The modified pipeline also provides significant improvements in the redshift measurements over the standard Redrock pipeline for the challenging-to-identify missed QSOs. This point is most clearly illustrated by focusing on the redshifts of the missed QSOs in the sparse VI: see Figure 7 (top) where we compare the modified and standard-pipeline redshifts of the high-quality missed QSOs to the VI redshifts. Unlike the standard Redrock pipeline, only a modest fraction of missed QSOs identified by the modified pipeline have catastrophic redshift failures, and QSOs are reliably identified out to z ≈ 4.

The QSO recovery rate effectively quantifies the "completeness" of the QSO identification against the visually inspected QSO sample. We calculate the QSO recovery rate as

$$\begin{eqnarray}&&\mathrm{QSO}\ \mathrm{recovery}\ \mathrm{rate}=\displaystyle \frac{{N}_{\mathrm{RR}:\mathrm{VI},\mathrm{QSO}}(\mathrm{VI}\ \geqslant 2.5)}{{N}_{\mathrm{VI},\mathrm{QSO}}(\mathrm{VI}\ \geqslant 2.5)},\end{eqnarray} \tag{ 3 }$$

where RR:VI refers to Redrock-identified QSOs that are spectrally confirmed as QSOs from the VI. The results are presented in Table 8. The modified pipeline recovers ≈94% of the visually inspected QSOs, a significant improvement over the standard Redrock pipeline (≈86% recovered). As expected, these results are worse than those achieved using the coadded spectra (modified pipeline: ≈99% recovered; standard pipeline: ≈89% recovered); see Table 6.

A key DESI metric is the fraction of QSO spectra with high-quality (VI ≥2.5) redshifts within a given dz threshold (dz_thresh). We refer to this quantity as the "good redshift purity," which we define as

$$\begin{eqnarray}&&\begin{array}{l}\mathrm{Good}\ \mathrm{redshift}\ \mathrm{purity}\\ =\,\displaystyle \frac{{N}_{\mathrm{RR},\mathrm{QSO}}(\mathrm{VI}\ \geqslant 2.5\ \& \ {{dz}}_{\mathrm{VI},\mathrm{RR}}\ \leqslant \ {dz}\_{thresh})}{{N}_{\mathrm{RR},\mathrm{QSO}}}\end{array}\end{eqnarray} \tag{ 4 }$$

where dz_VI,RR is the relative VI–RR redshift offset calculated following Equation (1) and replacing z_A and z_B with z_VI and z_RR, respectively. In our companion galaxy VI paper, a threshold of dz_thresh = 0.0033 (equivalent to dv = 1000 km s⁻¹) was used (Lan et al. 2023). However, given the greater uncertainty in measuring redshifts from broad QSO emission lines, we also consider the more liberal threshold of dz_thresh = 0.010 (equivalent to dv = 3000 km s⁻¹). Our good-redshift purity results are shown in Table 9.

The DESI scientific requirements for this analysis are framed as the "catastrophic redshift failure," which is related to Equation (4) as:

$$\begin{eqnarray}&&\begin{array}{l}\mathrm{Catastrophic}\ \mathrm{redshift}\ \mathrm{failure}\\ =\,1-\mathrm{Good}\ \mathrm{redshift}\ \mathrm{purity}.\end{array}\end{eqnarray} \tag{ 5 }$$

The required catastrophic redshift failure rate for the tracer QSOs is <5% (good redshift purity of >95%) for dz_thresh = 0.0033, which is achieved for both pipelines; see Table 9. The required catastrophic redshift failure rate for the Lyα QSOs is <2% (good redshift purity of >98%), which is also achieved for both pipelines with dz_thresh = 0.010.

These analyses have quantified the overall good-redshift purity but we would also expect these results to vary with data quality. In our companion galaxy paper (Lan et al. 2023), the good-redshift purity was calculated as a function of Δχ², which is defined as the difference in χ² between the best-fitting and second-best-fitting Redrock template–redshift solution for each target: high Δχ² values are more likely to correspond to higher-quality spectra. We do not consider Δχ² in our analyses here partly because Redrock identifies high-quality QSOs down to the Δχ² = 0 limit with just a small fraction of low-quality spectra. However, adopting this approach would also limit our analyses to just the standard Redrock pipeline since the modified pipeline takes a more complex approach in the calculation of redshifts, adopting a tight redshift prior using the QN redshift but only for a fraction of the QSOs. Instead, to provide insight on the dependence of the spectroscopic redshift accuracy with data quality, we use the r-band magnitude as a "proxy" of the data quality.

In Figure 8 we plot the good-redshift purity as a function of r-band magnitude for both the tracer and Lyα QSOs to show how the results depend on both data quality and dz_thresh. The required good-redshift purity of >95% is achieved for the tracer QSOs over the full r-band magnitude range for both dz thresholds with both pipelines. ⁵⁴ A broadly similar trend is also seen for the Lyα QSOs, although the good-redshift purity varies more greatly with dz than for the tracer QSOs, from <90% for dz_thresh = 0.0033 to >96% for dz_thresh = 0.010 regardless of the pipeline. The good-redshift purity of the tracer QSOs decreases with r-band magnitude, as expected if data quality drives the overall redshift uncertainties. A similar behavior is also seen for the Lyα QSOs except for dz_thresh = 0.0033 where the good-redshift purity is comparatively flat at ≈85%–90% over almost the full plotted r-band magnitude range. This shows that Redrock is unable to reliably measure redshifts within dz < 0.0033 for ≈10%–15% of the Lyα QSOs, unrelated to data quality, which is likely due to complexity in the rest-frame UV spectra for a subset of the QSOs (e.g., complex and poorly defined emission peaks due to broad emission and absorption features).

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The redshift precision quantifies the random error in the QSO redshift measurements. The DESI scientific requirement for this parameter is for the random error between individual QSO redshifts to be Δz < 0.0025(1 + z), equivalent to velocity offsets of Δv < 750 km s⁻¹, within a Gaussian core (i.e., 1 σ). In this calculation, we exploit the multiple short-exposure redshift measurements available for each target to calculate the redshift offset (expressed as the velocity offset, dv, in kilometers per second) between each redshift pair (i, j)

$$\begin{eqnarray}&&{{dv}}_{i,j}=\displaystyle \frac{{z}_{\mathrm{RR},i}-{z}_{\mathrm{RR},j}}{(1+{z}_{\mathrm{RR},i})}\times c.\end{eqnarray} \tag{ 6 }$$

The random error is then estimated as the dispersion from the distribution of redshift-pair offsets. Following Lan et al. (2023), we calculate the median absolute deviation (MAD), rather than the standard deviation, to minimize the impact of outlier measurements. We then scale the MAD value by 1.4828 to represent the 1σ error and divide by $\sqrt{2}$ to take account of the fact that the dispersion includes measurement errors from two redshifts:

$$\begin{eqnarray}&&\mathrm{Scaled}\ \mathrm{MAD}\ \mathrm{value}=\displaystyle \frac{\mathrm{MAD}\times 1.4828}{\sqrt{2}}.\end{eqnarray} \tag{ 7 }$$

The results are shown in Table 9, and the variation in the scaled MAD value with r-band magnitude is presented in Figure 9. Overall, the DESI scientific requirements are met for all QSO subsets with scaled MAD values of Δv < 300 km s⁻¹ for even the faintest QSOs; however, clear trends with r-band magnitude are seen for both the tracer and Lyα QSOs, demonstrating the general impact of data quality on the precision of individual redshift measurements. No significant differences are seen between the two pipelines.

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The redshift accuracy quantifies the systematic accuracy of the QSO redshifts. The DESI scientific requirement is for a redshift accuracy of Δz < 0.0004(1 + z), equivalent to velocity offsets of Δv < 120 km s⁻¹, in the redshifts of the tracer QSOs. To provide an assessment of the redshift accuracy, we matched the DESI QSOs to the SDSS DR16 quasar catalog (Lyke et al. 2020) using a 5'' search radius and calculated the median redshift offset. Overall, we found matches to 292 SDSS quasars of which 176 are tracer QSOs (a further 84 are Ly α QSOs). In our analyses we used the ≈1000 s DESI spectra for these matched quasars, which increases the source statistics by a factor ≈5.

The overall measured median velocity offsets for all-matched QSOs are ≈70 km s⁻¹ for both pipelines; see Table 9 and Figure 10. The median velocity offsets for the tracer QSOs are even smaller at ≈30 km s⁻¹, meeting the DESI scientific requirements for both pipelines and consistent with the standard error of the median. As shown in Table 9, the larger velocity offset measurements for the all-matched QSO sample is due to the Lyα QSOs, which have median velocity offsets of ≈340 km s⁻¹. This same effect is remarked upon in the DESI QSO target-selection paper (see Section 7.3 of Chaussidon et al. 2022), and the cause is investigated extensively in the SDSS eBOSS BAO paper (see Appendix B of du Mas des Bourboux et al. 2020). Two factors likely drive the systematic redshift inaccuracy of the Lyα QSOs: (1) Lyα absorption features entering the DESI bandpass and distorting the profile of the Lyα emission line, and (2) Mg ii emission leaving the DESI bandpass and, consequently, causing the pipeline redshift measurements to be more reliant on the less-reliable C iv emission line (e.g., see Tytler & Fan 1992; Hewett & Wild 2010). We note that since the SDSS DR16 quasar catalog is limited to r < 22, the redshift accuracy may be worse for the faintest DESI targets.

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In Figure 11 (left) we plot the r-band magnitude versus redshift for the QSOs identified by Redrock in the deep-field VI and compare them to the afterburner-identified missed QSOs from the sparse VI. The missed QSOs have a more strongly peaked redshift distribution than the Redrock QSOs due to the enhanced "clump" of systems in the r-band–redshift plane, also seen in Figure 5 (right). The missed QSOs also fill out a fainter region in the r-band magnitude–redshift plane in Figure 11 (left) than the Redrock QSOs: at any given redshift out to z ≈ 1.7, the missed QSOs are identified to fainter r-band magnitudes than the Redrock-identified QSOs. Consequently, the inclusion of the afterburners leads to a much more comprehensive QSO census, particularly at z < 1.7 due to the identification of optically fainter systems.

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In Figure 11 (left), we also plot the magnitude–redshift tracks for an M_I = −23 mag QSO to provide a basic discrimination between luminous QSOs and lower-luminosity systems. As can be seen, many of the z < 1.7 missed QSOs lie above the M_I = −23 mag QSO tracks indicating that they are probably relatively low-luminosity QSOs, more analogous to Seyfert galaxies identified in the local universe than classical QSOs. Indeed, for the majority of the z < 1.7 missed QSOs, Redrock identifies the correct redshift but classifies the target as a galaxy, consistent with that expected for a low-luminosity QSO. We visually demonstrate this in Figure 11 (right) where we again plot r-band magnitude versus redshift but now split the missed QSOs on the basis of dz: a clear division in the redshift distribution is seen with the missed QSOs at z < 1 having reliable redshifts (dz < 0.01) while the missed QSOs at z > 1.7 have predominantly large catastrophic redshift failures (dz > 0.1), with a mix of reliable redshifts and redshift failures over z ≈ 1.0–1.7. The missed QSOs with redshift failures have a broadly similar redshift distribution to the Redrock QSOs (see Figure 11) when the correct redshift is identified.

To further shed light on the physical origins of the differences between the Redrock QSOs and the missed QSOs, we constructed median composite spectra for both samples by stacking the rest-frame optical spectra; see Figure 12. ⁵⁵ The Redrock QSO composite has all of the features of a classical QSO: prominent broad emission lines and a strongly rising continuum to rest-frame UV wavelengths. However, by comparison, the missed QSO composite has a much flatter continuum slope with a deficit of emission at shorter wavelengths, enhanced emission at longer wavelengths, and stronger narrow forbidden lines (e.g., [Ne v] and [O ii]). The frequency-dependent drop in the continuum emission to UV wavelengths for the missed QSOs is the characteristic signature of dust extinction along the line of sight. To provide insight on the origin of the enhanced longer-wavelength emission, we produced a zoomed-in image of the spectral region around ≈3800 Å; see Figure 12 (inset). The missed QSOs have stronger Balmer and Ca H + K absorption lines, the expected signatures from a significant host-galaxy contribution, which also explains the enhanced continuum longward of 4000 Å (i.e., the emission from stars in the host galaxy).

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Overall, the reason the missed QSOs were misidentified by the standard Redrock pipeline appears to be due to the significant contribution from the host galaxy and/or the suppression of the rest-frame UV emission from dust extinction. The requirement for Redrock to fit the DESI spectra across all of the galaxy surveys, in addition to the QSO survey, limits the range of QSO templates that can be effectively utilized, and, consequently, it is not possible to account for the full diversity of the QSO spectral class; see also Footnote 53. Redrock can therefore measure the correct redshift of a red QSO when prominent host-galaxy features are present in the optical spectrum, as is the case for low-luminosity QSOs up to z ≈ 1.7 (i.e., distant analogs of Seyfert galaxies), where the majority of the strongest host-galaxy features lie within the DESI spectral bandpass. Therefore, it is unsurprising that the vast majority of the missed QSOs at z < 1, and a significant fraction of missed QSOs out to z ≈ 1.7, have reliable redshifts even though the standard Redrock pipeline identifies them as galaxies instead of QSOs; the often noisy data at >8500 Å (see Figure 1 for examples) is likely responsible for the decrease in the reliable redshift fraction for missed QSOs at z ≈ 1.0–1.7. At higher redshifts, the strongest host-galaxy features move out of the DESI spectral bandpass, and, without a red QSO template solution, Redrock cannot reliably measure the target redshift.

The composite spectra shown in Figure 12 demonstrate the broad diversity between the QSOs identified by the standard Redrock pipeline and the missed QSOs recovered by the afterburners. However, they do not reveal the full range of spectral diversity within the QSO survey. To provide a glimpse of the overall spectral diversity of targets in the QSO survey, in Figure 13 we plot the DESI spectra for individual QSOs, selected to cover a broad range in spectral diversity.

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The first spectrum is an example of an optically faint high-redshift QSO. Many high-redshift QSOs have been identified in previous QSO surveys; however, the fainter optical magnitude limit of DESI allows for the reliable identification of lower luminosity, and therefore more typical, systems. The second spectrum is an example of a QSO with a prominent host galaxy, broadly similar to the missed QSO composite shown in Figure 12: the strong host-galaxy absorption features are highlighted in green and are consistent with a post-starburst. The identification of the host galaxy is due to both the faint optical magnitude limit of DESI and the relatively high spectral resolution, which provide the potential to characterize the host-galaxy properties (e.g., luminosity-weighted stellar age and host-galaxy mass) for a significant fraction of the DESI QSOs. The third spectrum is a spectacular example of an optically faint low-ionization BALQSO, where strong broad absorption troughs are seen blueward of both the low-ionization (Mg ii) and high-ionization (C iv; C iii]) broad emission lines. DESI is able to identify BALQSOs down to fainter optical magnitudes than previous optical QSO surveys. On the basis of the VI, >10% of the high-quality deep-field QSOs showed visual evidence for broad absorption-line features at z > 1.57. The fourth spectrum is an example of an individual dust-reddened QSO missed by the standard Redrock pipeline but identified by the afterburners. The faint optical magnitude of DESI combined with the optical–mid-IR color selection allows for the identification of redder and fainter QSOs than those identified in the SDSS. The fifth spectrum shows a QSO where only narrow lines are detected: the identification of the strong high-excitation [Ne v] emission line provides evidence that this is a QSO as opposed to a galaxy. Due to the requirement for a point-source optical morphology, the QSO survey will only identify a subset of the narrow-line QSO population since the majority are expected to have extended optical morphologies (i.e., due to optical emission being dominated by the host galaxy). The last spectrum shows a QSO with strong associated absorption features: in this example, a significant fraction of the absorption appears to be due to the host-galaxy environment since absorption features are identified at the systemic redshift of the QSO. The relatively high spectral resolution of DESI allows for the comprehensive identification of narrow absorption features. A comprehensive evaluation of Mg ii absorption systems identified in the QSO survey will be provided in L. Napolitano et al. (2023, in preparation).

The combination of the Redrock- and afterburner-identified QSOs provides a comprehensive selection of QSOs. However, what is the nature of the galaxies detected in the QSO survey, and could they host weak QSO or AGN activity? Following the same approach as for the QSO composites (see Footnote 55), we stacked the rest-frame spectra of the high-quality galaxies identified in the deep-field VI of the QSO survey to construct a median galaxy composite; see Figure 14. The galaxy composite shows a strong rise to UV wavelengths, similar to the Redrock QSO composite, but lacks the associated QSO signature of broad emission lines. Furthermore, there is no evidence for [Ne v] in the galaxy composite, a high-excitation emission line typically seen in AGNs and QSOs; see Figure 14 (inset). The galaxy composite is also distinguishable from the Redrock QSO composite in having a strongly rising continuum to long wavelengths; the continuum rise is significantly stronger than that seen in the missed QSO composite. This continuum rise to long wavelengths is due to the stellar emission from the host galaxy, as is apparent from the very strong Balmer and Ca H + K absorption features; see Figure 14 (inset). Many absorption features at the wavelengths expected for metal lines (e.g., Fe ii, Al iii, and S iii) are also seen in the galaxy composite.

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What is the nature of these systems, and what is the origin of the strong UV continuum, which is undoubtedly the primary reason for their selection within the QSO survey? These systems are most likely compact galaxies undergoing significant star formation activity, similar to the z ≈ 0.6 post-starburst galaxies identified in the SDSS survey (Tremonti et al. 2007). The galaxies explored in Tremonti et al. 2007 had strong blueshifted Mg ii absorption systems, indicative of powerful galactic winds with v > 500 km s⁻¹. Our galaxy composite shows Mg ii absorption but it is only slightly blueshifted. However, these DESI galaxies are several magnitudes fainter than those identified in SDSS and, consequently, they likely host less-powerful galactic winds. Furthermore, the galaxy composite only provides an average Mg ii absorption constraint, and some individual systems may show significantly stronger blueshifted Mg ii absorption.

Overall, on the basis of this brief analysis, we do not find any clear evidence for additional significant QSO activity from the galaxy composite, despite the strong UV continuum emission. Weak QSO (or AGN) activity may be present in a small fraction of the systems, which would be missed by our analysis but could be revealed through more detailed inspection and spectral fitting of the individual DESI spectra. On the basis of the VI, AGN features (i.e., [Ne v]; strong [O iii]; C iii]) were noted by visual inspectors for just eight (≈0.5%) of the 1491 high-quality galaxies, although the true number of unidentified AGNs could be much higher. Indeed, cross-matching the 101 high-quality galaxies with sensitive Chandra observations in the COSMOS field (Marchesi et al. 2016) revealed five X-ray detections with X-ray luminosities consistent with moderate-to-high-luminosity AGN activity (≈10⁴²–10⁴⁴ erg s⁻¹; Brandt & Alexander 2015), suggesting an X-ray AGN fraction within the galaxy population selected by the DESI quasar survey of ≈5%.

The vast majority of the optical spectra in DESI are produced by a single object. However, for a small fraction of the spectra, at least two objects contribute to a single optical spectrum. We show some examples in Figure 15 from the deep-field VI. The first spectrum shows a stellar binary system composed of a hot white dwarf and a cool M-type red dwarf; the overall continuum shape is similar to that of a QSO but the strong absorption features identify the two stars. The second spectrum shows a QSO spectrum that is contaminated at long wavelengths by an optically bright M-type red dwarf, which outshines the QSO in the associated finding chart. The other remaining spectra show the clear signatures of a higher-redshift QSO spectrum contaminated by a lower-redshift galaxy. Overall, on the basis of the VI, ≈1% of the optical spectra in the DESI quasar survey appear to be the superposition of at least two contributing targets. The systems where both targets are galaxies and/or QSOs can provide a rich data set with which to probe the dark-matter component of the foreground target via strong lensing.

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