Target Selection and Sample Characterization for the DESI LOW-Z Secondary Target Program

The LOW-Z sample was designed specifically to complement the main DESI BGS sample. The DESI BGS consists of two samples: the BGS Bright sample, which targets all objects with r < 19.5, and the BGS Faint Sample, which targets objects between 19.5 < r < 20.175 with an additional set of color-dependent cuts (Table 2). The BGS program is significantly larger than the LOW-Z sample: 864 objects per square degree in the Bright sample and 533 objects per square degree in the Faint sample. It is expected to achieve >80% fiber allocation for BGS Bright targets and >95% redshift success rates for both samples.

However, DESI BGS is a bright-time program, meaning that targets are observed during bright conditions (determined based on observing conditions such as seeing, transparency, airmass, and sky brightness). This means that BGS is limited in its ability to obtain redshifts for the faintest and lowest surface brightness objects. In contrast, LOW-Z is a dark-time program. This allows the LOW-Z survey to complement the BGS in two key ways: (1) LOW-Z goes over half a magnitude fainter than the BGS Faint sample and a full magnitude and a half fainter than the BGS Bright sample, helping to fill in objects at the faint end of the galaxy luminosity function; and (2) LOW-Z objects are observed in dark rather than bright time, which allows us to target objects fainter than the BGS fiber magnitude cut at r_fib = 22.9 without drastically increasing our redshift failure rate (see discussion in Section 4.6), meaning that the LOW-Z sample will be more complete than BGS for very low surface brightness objects.

Due to the DESI fiber assignment strategy, most objects that overlap between the two samples will be allocated fibers in bright time as part of the main BGS survey. ³⁶ However, for BGS objects in the LOW-Z sample that do not receive fiber allocation in bright time, LOW-Z provides a second opportunity for fiber assignment with a higher likelihood of redshift success for objects with 22 < r_fib < 22.9 (Section 4.6). Since BGS observations supersede LOW-Z observations in terms of priority, objects that overlap between the two samples and receive fiber allocation in bright time are removed from dark-time target lists.

We select objects using the catalog from the Data Release 9 (DR9) of the DESI Legacy Imaging Surveys (Zou et al. 2017; Dey et al. 2019; D. Schlegel et al. 2023, in preparation). ³⁷ The DR9 catalog consists of data from three imaging projects: the Beijing-Arizona Sky Survey, the DECam Legacy Survey, and the Mayall z-band Legacy Survey.

We use the TYPE flag to identify galaxies as all objects whose TYPE ≠ PSF and remove duplicated Gaia entries using TYPE ≠ DUP. We use FLUX and MW_TRANSMISSION to calculate dereddened magnitudes. We use SHAPE_R as our effective photometric radius, R_r,eff. For bands in grz we additionally define SIGMA_GOOD for the purpose of implementing quality cuts. Unless explicitly defined below, these quantities come directly from the DR9 catalog ³⁸ and the definitions can be found in the relevant citations above.

$$\begin{eqnarray*}&&{\mathtt{SIGMA}}\_{\mathtt{GOOD}}=\left\{\begin{array}{l}{\mathtt{FLUX}}\times \sqrt{{\mathtt{FLUX}}\_{\mathtt{IVAR}}},\mathrm{if}\ {\mathtt{RCHISQ}}\lt 100;\\ 0,\mathrm{otherwise}.\end{array}\right.\end{eqnarray*}$$

While the DR9 photometric catalog is generally very clean, it still contains some spurious objects, including shredded sources, false-positive detections, and sources with highly overestimated magnitudes. We apply a set of quality cuts to remove the majority of these spurious objects from our targets. Specifically, we only include objects that satisfy all of the following criteria:

$$\begin{eqnarray*}\begin{array}{rcl} & & {\mathtt{SIGMA}}\_{\mathtt{GOOD}}\geqslant 5.0\ (\mathrm{any}\ \mathrm{two}\ \mathrm{bands});\\ & & {\mathtt{FRACFLUX}}\leqslant 0.35\ (\mathrm{any}\ \mathrm{two}\ \mathrm{bands});\\ & & {\mathtt{RCHISQ}}\leqslant 2.0\ (\mathrm{any}\ \mathrm{two}\ \mathrm{bands});\\ & & {\mathtt{SIGMA}}\_{\mathtt{GOOD}}\geqslant 30\ \mathrm{or}\ {\mathtt{RCHISQ}}\leqslant 0.85\ (\mathrm{any}\ \mathrm{two}\ \mathrm{bands});\\ & & {\mathtt{g}}-{\mathtt{r}}\gt -0.1.\end{array}\end{eqnarray*}$$

These criteria were first developed for the SAGA Survey (Mao et al. 2021), and later adopted for cleaning the LOW-Z sample. The criteria on SIGMA_GOOD aim to remove false-positive detections, those on FRACFLUX aim to remove shredded sources from a brighter companion, those on RCHISQ aim to remove sources with very inaccurate model fits, and finally, those on g − r aim to remove sources with very different fits in g and r bands. We visually inspect the resulting targets to set the thresholds in these criteria so that they remove the majority of these spurious objects without impacting our target selection completeness.

We exclude objects that are within 1.5 times the radius of an object in the Siena Galaxy Atlas (SGA) catalog (Moustakas et al. 2023) or within 4 times the half-light radius of any non-SGA objects in DR9 catalogs brighter than r = 16. Galactic radii in SGA are defined as the radius at the 25 mag arcsec⁻² surface brightness isophote. This was done as a further cleaning step to avoid targeting misidentified remnants of bright galaxies and was designed to remove only those objects that significantly overlap with the light of a brighter galaxy. This should not strongly impact the sample satellite galaxies in the LOW-Z survey. However, for a detailed comparison of the differential impact of environment on isolated and satellite dwarf galaxies, the LOW-Z sample is well suited for comparison with satellites from the SAGA Survey, as the two were selected using nearly identical color and surface brightness criteria and span a similar range in magnitudes and distances.

Accurately identifying low-redshift galaxies using only photometric data is difficult, even when spectroscopic training sets are available. Most current photometric redshift algorithms have been trained on data that has been explicitly color selected for high-redshift galaxies. In addition, low-redshift objects are vastly outnumbered by higher-redshift objects in almost every available training set. There are a few thousand objects per square degree between 19 < r < 21, all but tens of which we expect to be bright galaxies at a higher redshift (z > 0.03). Thus, efficiently selecting low-redshift objects in this regime requires careful study.

Here, we present a set of catalog-level photometric cuts designed specifically for the target selection of low-redshift (z < 0.03) objects to high completeness (hereafter referred to as the z < 0.03–complete photometric cuts). These cuts are developed based on the photometric cuts first introduced by the SAGA Survey (Mao et al. 2021). The SAGA Survey Stage II targeting cuts were tested extensively by the SAGA Survey team, including tests with a complete spectroscopic survey of objects around two SAGA systems. These cuts were found to be complete out to z < 0.01 at a target density of ∼200 objects per square degree; hence, we will refer to the SAGA Survey Stage II targeting cuts as the z < 0.01–complete photometric cuts hereafter. The z < 0.03–complete cuts presented here are identical to the z < 0.01–complete photometric cuts but with an increase in the surface brightness and color thresholds used:

$$\begin{eqnarray}{\mu }_{{r}_{o},\mathrm{eff}}+{\sigma }_{\mu }-0.7\,({r}_{o}-14)\gt \left\{\begin{array}{ll}16.8 & (z\lt 0.03-\mathrm{complete})\\ 18.5 & (z\lt 0.01-\mathrm{complete})\end{array}\right.,\end{eqnarray} \tag{ 1 }$$

$$\begin{eqnarray}{(g-r)}_{o}-{\sigma }_{\mathrm{gr}}+0.06({r}_{o}-14)\lt \left\{\begin{array}{ll}0.99 & (z\lt 0.03-\mathrm{complete})\\ 0.9 & (z\lt 0.01-\mathrm{complete})\end{array}\right.,\end{eqnarray} \tag{ 2 }$$

where r_o , g_o are the extinction-corrected r- and g-band apparent magnitudes respectively, ${\mu }_{{r}_{o},\mathrm{eff}}$ is effective surface brightness, σ_μ is the error on ${\mu }_{{r}_{o},\mathrm{eff}}$, and ${\sigma }_{{gr}}\equiv \sqrt{{\sigma }_{g}^{2}+{\sigma }_{r}^{2}}$ is the error on the (g − r)_o color. We calculate ${\mu }_{{r}_{o},\mathrm{eff}}$ and σ_μ analogously to Mao et al. (2021). We present the validation of the completeness z < 0.03–complete photometric cuts in Section 4.5.

The full LOW-Z target sample consists of all objects at 19 < r < 21 passing the z < 0.03–complete photometric cuts (Equations (1) and (2)). However, in order to maximize our observed sample of low-redshift objects, we split the target sample into three tiers, which roughly correspond to our expectation of a given object being legitimately low-redshift. A CNN algorithm selects the first tier, while the second and third tiers correspond to different regions in color–surface brightness parameter space. The LOW-Z tiers are hierarchical, such that objects in Tier 1 are excluded from Tier 2, and objects from Tiers 1 and 2 are excluded from Tier 3.

3.3.1. Tier 1: CNN Selection from Imaging

3.3.2. Tier 2 and Tier 3: Catalog-level Photometric Selection

3.3.3. Summary of LOW-Z Tiers

Between the beginning of the DESI One-Percent Survey through the end of the scheduled summer shutdown in July, redshifts were obtained for 143,486 unique LOW-Z targets. Of the full sample, 6633 are from Tier 1 (4.6%), 9479 are from Tier 2 (6.6%), and the remaining 127,374 are from Tier 3 (88.8%) (Table 3). The Tier 3 objects dominate the sample due to the overlap with BGS. BGS targets have higher priority than LOW-Z and therefore have a higher fiber allocation fraction. Of the total number of objects that were allocated fibers in Tier 3, 120,002 (94.2%) received fibers as part of the BGS sample (along with 5478 (82.6%) objects in Tier 1 and 724 (7.6%) objects in Tier 2). ³⁹ The redshift distribution of all three tiers can be seen in the left panel of Figure 2. This figure represents 96% of the LOW-Z sample, with only 4% of objects having redshifts z > 0.3 (the high-z tail is not plotted for visual clarity). The median redshift of all objects in Tier 1 is 0.05, for Tier 2, it is 0.12, and for Tier 3, it is 0.15. While this demonstrates the effectiveness of the whole LOW-Z program at selecting low-redshift galaxies, it especially exemplifies the efficacy of the CNN at selecting a sample of the lowest redshift objects (z < 0.03).

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Focusing on the lowest redshift objects (z < 0.03) in the LOW-Z sample, we are left with a sample of 2019 objects: 1257 are from Tier 1 (62.3%), 122 are from Tier 2 (6.0%), and 640 are from Tier 3 (31.7%) (Table 3). Approximately 20% of the CNN-selected sample consists of objects at z < 0.03, consistent with the expected purity based on CNN cross-validation results. Of the z < 0.03 sample, 356 are faint (r > 19.5) non-BGS targets: 201 from Tier 1, 114 from Tier 2, and 41 from Tier 3.

We can also examine the sample of objects that received fibers specifically as part of the LOW-Z program (rather than BGS targets in the LOW-Z sample). These targets are interesting because they were observed in dark time, making it possible to get successful redshifts for fainter and lower surface brightness objects. Out of the 143,486 LOW-Z objects, 17,437 were observed during dark time. While 155 of these represent dark-time observations of BGS objects (due to overlap with the luminous red galaxies (LRG) or emission line galaxies (ELG) samples), the rest are objects outside the BGS main sample (Table 2). Out of the 17,437 objects, 1160 (6.6%) are from Tier 1, 8757 (50.2%) are from Tier 2, and 7520 (43.1%) are from Tier 3. On average, the dark-time sample has slightly higher redshifts than the full sample. However, the median redshifts in Tier 1 and Tier 2 are the same as for the full sample, indicating this is mainly driven by the objects in Tier 3, which have a median redshift of 0.20. This result is likely due to the targeting error referenced in Section 3.3.3, meaning that the majority of Tier 3 objects in this regime are being sampled from the z < 0.03–complete photometric cuts outside of both the z < 0.01–complete color and surface brightness cuts. Since these objects are the reddest and most compact objects we target, we expect this sample to contain the lowest density of low-redshift objects. The full redshift distribution can be seen in the right panel of Figure 2. As shown in Figure 10, we are significantly more likely to obtain successful redshifts for low r_fib objects if they were observed in dark time.

In Figure 3, we also plot the apparent magnitude–redshift distribution for both the LOW-Z, BGS, and overlapping samples at z < 0.03 for the One-Percent and Early Main Survey data. About 80% of the z < 0.03 objects are in the overlapping sample. A further 17% of objects are exclusively LOW-Z galaxies; these galaxies tend to be fainter than the overlapping sample, as expected given the apparent magnitude range of the two surveys. The final 3% of objects are exclusively BGS objects. These objects tend to be higher redshift and are discussed further in Section 4.5.

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The absolute r-band magnitude and stellar mass of the full LOW-Z sample at z < 0.03 is shown in the left and center panels of Figure 4. K-corrected r-band absolute magnitudes are derived using the program FastSpecFit. ⁴⁰ Stellar masses are derived using g − r color and absolute r-band magnitude following Mao et al. (2021). While the distributions of Tier 2 and Tier 3 distributions look similar, the CNN-selected objects tend to be fainter in M_r and at lower stellar masses. The LOW-Z sample contains a considerable number of galaxies with M_* < 10⁹ M_⊙, making it an interesting data set for studying dwarf galaxies. Out of the full LOW-Z sample, 22,679 objects have M_* < 10⁹ M_⊙, 2011 objects have M_* < 10⁸ M_⊙, and 98 objects have M_* < 10⁷ M_⊙. The right panel of Figure 4 shows the distribution of stellar mass as a function of redshift colored by tier. On average, both redshift and stellar mass increases as a function of tier, with Tier 1 objects making up the tail end of the stellar mass and redshift distribution (as can also be seen in the center panel of Figure 4). The median stellar mass for Tier 1 is 10^8.4 M_⊙ compared with 10^9.0 and 10^9.7 M_⊙ for Tiers 2 and 3, respectively. Example objects at z < 0.03 can be seen in Figure 5, sorted by decreasing surface brightness and increasing stellar mass. Since stellar mass depends on color and surface brightness, higher stellar mass objects can be seen to be redder and have larger absolute magnitudes.

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The effective surface brightness versus physical radius for the LOW-Z galaxies at M_* < 10⁹ M_⊙ is shown in Figure 6. Of the LOW-Z dwarf galaxies, 469 are in the ultra-diffuse regime as defined by van Dokkum et al. (2015).

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As the LOW-Z program is a secondary target program, not all targets will be observed during the DESI survey. To understand the observed density of targets, we examine completed tiles taken as part of the One-Percent Survey. Out of the full sample, 36,481 objects received fibers during the One-Percent Survey, corresponding to an observed target density of ∼200 objects per square degree ([11, 41, 150] per square degree in Tier [1–3]; Table 1) or approximately a 67% fiber allocation fraction for the LOW-Z program. These numbers are consistent with close to 100% fiber allocation for objects that overlap with the BGS survey and approximately 30% fiber allocation for objects observed in dark time as part of the LOW-Z survey (Table 1). Since we are a spare fiber program, the observed target density will vary over the sky depending on the density of the primary targets. However, because we are a dark-time survey, our targets are primarily being displaced by ELG, LRG, and quasar targets. All of these surveys are focused on much higher-redshift targets (z > 0.4), so our observed target density should not depend on the local density of objects at low redshift but rather should vary approximately independently of the low-redshift environment across the sky.

Since the One-Percent Survey had a different survey strategy than the main survey, which may have led to more LOW-Z targets receiving fibers than in the main survey, we verify these numbers using the DESI fiber assignment code (A. Raichoor et al. 2023, in preparation) run on a small patch of the sky. After seven passes, we find that ∼30% of our dark-time targets are assigned fibers, while for BGS, after four passes in bright time, we find that ∼75% of targets are assigned fibers. This is lower than our estimate from the One-Percent Survey, which is most likely due to the extra passes per tile completed during the One-Percent Survey. Combining the fiber allocation between bright and dark times gives a total fiber allocation for the LOW-Z survey of ∼50%.

Using data from the One-Percent Survey, we can also estimate the number of low-redshift (z < 0.03) targets per square degree we can expect to be observed as part of the LOW-Z Survey. During the One-Percent Survey, the LOW-Z sample selection returned 661 objects with z < 0.03. Since the One-Percent Survey covered 180 deg², this corresponds to approximately 3.7 observed objects per square degree (Table 1). This number may be a slight overestimation for the full survey as the One-Percent Survey had longer exposures and more passes per tile than the main survey.

We further validate our sample selection methods by using all redshifts from DESI Y1 data, including redshifts that are not from the LOW-Z program. As these objects are not part of the LOW-Z photometric sample, it allows us to examine if any low-redshift objects are missed from our sample selection. Due to the overall design of the DESI survey, at low redshifts (z < 0.1), this sample is dominated by galaxies from the BGS galaxy sample. While the BGS sample is only complete out to r = 19.5, it is not subject to the same color and surface brightness cuts as the LOW-Z sample, allowing us to validate the completeness of the current set of catalog-level photometric cuts for a sample of objects outside of the LOW-Z selection. However, this calculation is limited by the dominance of the LOW-Z sample at low redshifts in the DESI data as well as underlying incompleteness in the Legacy Imaging DR9 photometric catalogs used to select all DESI targets. We discuss these limitations further at the end of this section.

Figure 7 shows the low-redshift galaxies in DESI as a function of r, g − r, μ_r,eff, and redshift. The gray line is constrained to have the same slope as the z < 0.01–complete and z < 0.03–complete photometric cuts, and the intercept is varied to capture 95% of the sample. We see a steady redshift-dependent evolution for both the g − r and μ_r,eff fits. We recover that the z < 0.01–complete photometric cuts are complete to the SAGA goal of z < 0.01. Furthermore, the difference between the fit and the z < 0.03–complete photometric cuts is negligible for both g − r and surface brightness. This indicates that the z < 0.03–complete photometric cuts are indeed quite complete out to the LOW-Z sample goal of z < 0.03 relative to the broader cuts used to select BGS galaxies.

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Focusing on the z < 0.03 objects that are not in the LOW-Z sample, we can divide the objects into three categories: (1) objects that are outside the LOW-Z color–surface brightness cuts, (2) objects that are within the LOW-Z color–surface brightness cuts but that were excluded from the LOW-Z sample due to our catalog cleaning cuts (Section 3.1), and (3) junk objects. The third category mainly consists of misclassified pieces of brighter galaxies. Examples of objects from each of the three categories can be seen in Figure 8.

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The objects in the first and second categories tend to be compact, high-surface brightness objects, while the objects in category three tend to be miscentered large, bright nearby galaxies. Out of the 994 objects with DESI spectra at z < 0.03 that are not part of the LOW-Z survey, only 97 are outside of the z < 0.03–complete photometric cuts. This aligns with what we see in Figure 7 that ∼95% of the sample at z < 0.03 is within the z < 0.03–complete photometric cuts. These 97 objects represent less than 5% of the sample at z < 0.03. A further 397 are within the z < 0.03–complete photometric cuts but are removed from the sample due to the photometric cleaning cuts imposed in Section 3.1. The majority of these objects are removed by the cut on SIGMA_GOOD ≥30 and RCHISQ ≤0.85. As a result, we modify our target selection in Y2 so that they do not include these requirements (see Section 6 for details). The remaining are junk objects.

In order to better understand the objects that were being missed outside of the z < 0.03–complete photometric cuts, we visually inspected the spectra of the 97 objects. Twenty of these objects were found to be either quasars or stars misidentified as galaxies. Another six were objects at z ∼ 0.1 misclassified as z < 0.03. Removing these objects left us with 71 objects that were actually galaxies at z < 0.03 outside of the z < 0.03–complete photometric cuts, all of which come from the BGS sample. Out of the 71 objects, 20 are outside of the z < 0.03–complete color cuts, 41 are outside of the z < 0.03–complete surface brightness cuts, and a further 10 are outside of both the color and surface brightness cuts. The color–surface brightness distribution of objects can be seen in Figure 9. The vast majority of these objects are at z > 0.02 (66 out of 71).

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We further investigate the 30 objects that fall outside of our z < 0.03–complete color cuts. These objects are of particular interest as we want a complete sample of quenched objects in order to further understand dwarf galaxy formation as a function of environment with the LOW-Z sample. Of these objects, 28/30 are at z > 0.02, and all of them are at z > 0.01. Four of these objects are blended objects with incorrect photometry. Most of the remaining are in extremely high-density environments (13/30 are members of the Coma Cluster), where we expect to find the reddest and most compact low-mass objects.

Removing all objects in Coma and with obvious photometric errors, we are left with only 13 objects. While these objects represent an interesting sample for further follow-up, they do not indicate a significant population of isolated quenched objects outside of our z < 0.03–complete color cuts.

As stated above, this analysis is limited by the sample of redshifts available in DESI, which is dominated by objects selected by the LOW-Z program. Since LOW-Z is pushing the forefront for faint low-redshift surveys, accurate characterization of its completeness is difficult given the lack of available data with which to compare; externally validating our redshift completeness will remain an active area of research for the program going forward. We are also limited by catalog-level incompleteness in the Legacy Imaging Survey DR9 catalogs used to select DESI targets, especially for the lowest surface brightness objects. We anticipate that these biases will be better characterized by current (e.g., Aihara et al. 2018; Danieli et al. 2020; Carlsten et al. 2022) and future low surface brightness galaxy surveys (e.g., Spergel et al. 2015; Ivezić et al. 2019; Borlaff et al. 2022), and partially ameliorated by more advanced techniques for constructing and cleaning photometric catalogs (e.g., Walmsley et al. 2019; Greco et al. 2021; Tanoglidis et al. 2021; Di Teodoro et al. 2023).

In addition to incompleteness in our target selection, an additional source of incompleteness comes from observed sources for which we are unable to accurately determine a redshift. We discuss redshift failure rates further in the following section. However, since we do not see evidence for a population of galaxies we are missing with our current z < 0.03–complete photometric cuts, we do not propose an update to the photometric selection for DESI Y2 (Section 6.2).

Since our sample extends to fainter r-band apparent magnitudes than the BGS sample, we are interested in the redshift success rates for these objects. This has important implications both for understanding the power of the DESI instrument as well as understanding the completeness of the observed LOW-Z sample. We define a successful redshift as a redshift with ZWARN = 0 and Δχ² > 30, indicating no warning flags raised and a high level of redshift confidence (Δχ² is the difference in χ² for the two best-fitting models). Redshift failure as a function of r, g − r, μ_r,eff, and r_fib is shown in Figure 10. We separate out bright and dark-time observations to show the dependence of the failure rate on observing conditions. However, we do not separate between observations taken in Y1 and the One-Percent Survey. Despite the differences in survey strategy and longer exposure times for the One-Percent data, we do not find a significant difference in the redshift failure rates as a function of any of the variables we consider between DESI One-Percent and Y1, leading to our choice to show results from the combined sample.

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Redshift failure rates show negligible evolution as a function of r and g − r for both bright and dark-time targets, indicating that DESI is able to capture redshifts out to our apparent magnitude limit of r = 21 in dark-time and out to the BGS limit of r = 20.2 in bright time across the full range of g − r colors included in the z < 0.03–complete color cuts. The increase in redshift failures in dark time at r < 19.5 is due to the fact that the only objects in this regime observed in dark time are objects outside of the BGS r_fib cut and thus correspond to a sample of objects with r_fib > 22.9. Therefore, the increasing failure rate can be attributed to their high r_fib rather than a magnitude dependence. We do see a significant increase in redshift failures for the lowest surface brightness and r_fib objects. The failure rate increases to almost 40% at μ_r = 27 mag arcsec⁻² for both dark- and bright-time targets. The trend with r_fib is even more dramatic, with failures increasing to around 70% at the bright-time limit of r_fib = 22.9 for objects observed in bright time and to a similar rate at r_fib = 24 for objects observed in dark time. This indicates that object surface brightness and, by extension, fiber magnitude rather than apparent magnitude is the biggest limitation for getting successful LOW-Z redshifts with DESI. In addition, it can be seen in Figure 11 that redshift failure is correlated with p_CNN at fixed r_fib, which is statistically driven by bright-time observations (the dark-time spectroscopic failure rates do not show a significant trend). This is concerning because it indicates that redshift failure rates may be correlated with the likelihood of an object being low redshift. Observational effects may be able to explain this trend: the spectra of lower redshift galaxies feature the [O ii] doublet emission line at bluer observed wavelengths, where the DESI spectrograph is less sensitive (see, e.g., Abareshi et al. 2022). ⁴¹ Thus, it becomes more difficult to confirm the redshift for bona fide lower redshift galaxies via the distinguishing [O ii] spectral feature. If p_CNN truly selects lower redshift galaxies, then we may expect targets with higher values of p_CNN to result in a higher rate of redshift failures. We expect to be able to characterize this potential effect significantly better using the full Y1 and Y2 data sets.

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Our resulting LOW-Z sample provides a more comprehensive data set for retraining and validating the CNN. During the same time period, the SAGA Survey has obtained more redshifts for objects within the projected virial radius of z ∼ 0.01 host galaxies (Y.-Y. Mao, in preparation). Our updated training set consists of 29,537 SAGA redshifts and 139,245 DESI LOW-Z objects within the expanded color–surface brightness selection that includes 95% of z < 0.03 galaxies (Equations (3) and 4). We retrain our CNN using the same architecture and framework described in Appendix A using the updated redshift catalog. ⁴³ Because our aim is to form a complete survey of z < 0.03 galaxies and BGS has already demonstrated a high level of completeness for low-redshift objects, we evaluate the retrained CNN performance on targets outside of the BGS cuts.

We perform k = 5 fold cross validation and save each CNN model trained on an 80% subset of the data; our results are based on the averaged predictions over the ensemble of five CNNs. From the cross-validation results, we are able to assess the completeness as a function of p_CNN, or equivalently, target density. A given p_CNN threshold corresponds to different number densities in the northern and southern skies due to differences in telescope instrumentation and BGS selection criteria. We propose a CNN-selected target density of 95 deg⁻² for objects outside of the BGS cuts and in the magnitude regime 19 ≤ r < 21.15, which corresponds to p_CNN > 0.0894 in the northern sky and p_CNN > 0.1198 in the southern sky. For 19 ≤ r < 21 objects outside BGS cuts, we expect that the retrained CNN can achieve 85%–90% completeness for z < 0.03 objects. This target list comprises ∼10⁵ objects at r < 21 that would otherwise not be targeted by BGS. We also note that the p_CNN thresholds correspond to >95% completeness for objects in our entire redshift catalog (including BGS objects). Our CNN forecasts for Y2 are shown in Table 4. We compare the performance of the Y1 and Y2 CNNs in Appendix B.

Our Y2 sample, which began getting data in Fall 2022, consists of all objects between 19 ≤ r < 21.15 and r_fib < 23.5 within the z < 0.03–complete photometric cuts (Section 3.2) and excluding objects in the BGS Bright and Faint samples for objects with r_fib < 22. The full sample of LOW-Z targets for Y2 is then divided into two tiers of priority (Table 1):

Y2 Tier 1 (∼97 objects per square degree) consists of objects selected by the retrained CNN from the z < 0.03–complete photometric cuts sample. Our selection includes the top-ranked 95 objects per square degree outside BGS cuts in the 19 < r < 21.15 range, in addition to the top ∼1.7 CNN-selected objects per square degree with r_fib > 22. This latter set of objects represents BGS targets that may encounter high-redshift failure rates in bright observing time.

Y2 Tier 2 (∼325 objects per square degree) consists of all objects from the z < 0.03–complete photometric cuts sample that are outside of the main BGS color cuts (Ruiz-Macias et al. 2020) or at r_fib > 22.0 (and are not in Tier 1).

We plan to continue to characterize the Y2 sample as new data comes in, although at present we do not plan to make further significant updates to our targeting strategy during the DESI main survey.

We parameterize the fit in Section 4.5 as a function of redshift and find that the redshift evolution of the intercept is well described by a linear fit. For the color cuts, the redshift evolution is described by the equation

$$\begin{eqnarray}&&{(g-r)}_{o}-{\sigma }_{{gr}}+0.06({r}_{o}-14)\gt 2.62\times z+0.90,\end{eqnarray} \tag{ 3 }$$

while the surface brightness cuts evolve as

$$\begin{eqnarray}&&{\mu }_{{r}_{o},\mathrm{eff}}+{\sigma }_{\mu }-0.7\,({r}_{o}-14)\lt -14.35\times z+17.33.\end{eqnarray} \tag{ 4 }$$

This parameterization gives us a way to estimate target density as a function of redshift and magnitude for a complete LOW-Z survey using only catalog-level photometric information from DR9.

An example of projected target density as a function of redshift for a range of cuts in apparent r-band magnitude is shown in Figure 13. As expected, there is a trade-off between maximum apparent magnitude and redshift. We estimate that for z < 0.03, we could be complete out to r < 21 at 350 targets per square degree and r < 22 at 800 targets per square degree. We can use the GAMA luminosity and stellar mass functions to translate our completeness to a function of stellar mass (Loveday et al. 2015; Wright et al. 2017). For a survey of z < 0.03 galaxies out to r < 22 we expect to be complete for galaxies with M_* > 10⁷ M_⊙. These results can help inform future planning for DESI II and beyond on how to design an optimally targeted low-redshift survey.

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