The Complete Calibration of the Color–Redshift Relation (C3R2) Survey: Survey Overview and Data Release 1

In M15 we used COSMOS (Capak et al. 2007; Scoville et al. 2007; Laigle et al. 2016) ugrizYJH photometry of ∼130k galaxies, closely resembling what will be obtained by the Euclid survey, to map the color distribution of galaxies to the Euclid depth ($i\sim 24.5$ AB). We used the SOM algorithm (a manifold learning technique for nonlinear dimensionality reduction) to generate a topologically ordered 2D representation of the high-dimensional color distribution.⁸ Galaxies from COSMOS were then matched back to the self-organized map according to their best-matching color cell in the SOM. This sorting of galaxies enables a variety of analyses, including the density of galaxies in different parts of color space, the median 30-band photometric redshifts from COSMOS as a function of position in color space, and the distribution of spectroscopic redshifts on the map (Figure 1). Importantly, by placing all existing spectroscopy from the COSMOS field on the map, we reveal regions of color space for which no galaxies have existing high-confidence redshifts. Of greatest importance for the C3R2 survey are: (1) the current spectroscopic sampling across color space, and (2) the source density as a function of position in color space, as more common galaxies will contribute more to the cosmic shear signal.

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For C3R2 we need to identify the regions of galaxy color space for which spectroscopic redshifts already exist and where they are systematically missing. We collected existing spectroscopy in COSMOS to do this, as described in M15. These redshifts include (but are not limited to) those from VLT-VIMOS (Lilly et al. 2007; Le Fèvre et al. 2015), Keck-MOSFIRE (Kriek et al. 2015), Keck-DEIMOS (Kartaltepe et al. 2010), and Magellan-IMACS (Trump et al. 2007). For the 2016A run we used only the spectroscopy taken in the COSMOS survey to identify undersampled regions of color space. The reason we could not incorporate spectroscopy from other fields for these observations is that the photometry between fields has to be highly consistent in multiple bands to reliably place galaxies on the same color map; at the time this problem had not been solved. Significant subsequent work has been done to solve this problem for upcoming runs, to be described in a forthcoming paper. The fields that have subsequently been put on a highly consistent color frame in ugrizYJH to the Euclid depth are VVDS, SXDS, and EGS (in addition to COSMOS).

For the 2016A observations we used the SOM derived in M15 to prioritize regions of galaxy multicolor space that are currently undersampled by existing spectroscopic surveys. For observed fields in 2016A other than COSMOS (SXDS and EGS), we attempted to bring the photometry onto the COSMOS color system in order to select the targets in a consistent way. We used the CANDELS (Grogin et al. 2011) photometry in a subset of the COSMOS field, together with the CANDELS photometry in SXDS and EGS, to derive a rough color conversion between the fields.

Target prioritization for C3R2 is based on two main factors: (1) the usefulness of a galaxy for calibrating the P($z| C$) relation, and (2) the likelihood of obtaining a secure redshift given the instrument, exposure time, and expected galaxy properties. The usefulness of a particular galaxy to the redshift calibration effort depends both on how common its colors are in the data and whether high-confidence redshifts for galaxies with similar colors already exist.

Based on these considerations, we developed a prioritization scheme for galaxies that weights sources in unsampled cells of the SOM more heavily, and also gives preference to more common galaxy colors. The priorities for C3R2 are adaptive as new data is obtained and more of the color space is filled in. For the 2016A run our priority scheme was as follows:

• 1.  
  We assign a initial priority value of 10 to objects occupying cells with no spectroscopic redshifts of even moderate quality (the gray regions of the SOM in the middle panel of Figure 1), a starting priority of 3 to objects in cells with a spectroscopic redshift(s) of only moderate confidence, and a starting priority of 1 to galaxies in color cells that already have one or more high-confidence spectroscopic redshifts. Galaxies with existing redshifts of at least moderate confidence were not targeted.
• 2.  
  We multiply each galaxy's priority by the number of objects in its color cell, effectively upweighting sources with common SEDs.⁹
• 3.  
  We penalize objects that are color outliers within their color cell in order to avoid using them for calibration. A small fraction of objects in the sample are not represented well in the SOM, either because they have abnormal colors from photometric errors or the superposition of two or more sources, or are truly rare objects (e.g., X-ray sources). We want to avoid calibrating with these.

As will be described in future data releases, this prioritization scheme has been refined for the 2016B and later observations to more efficiently map the color–redshift relation. In M15 we pointed out that spectroscopic effort could also be intentionally directed at regions of color space with intrinsically higher redshift uncertainty (e.g., with double-peaked redshift PDFs). For now we have not prioritized based on redshift uncertainty; however, as the survey progresses and the color map is filled in we may incorporate this quantity.

A crucial element of the C3R2 survey is the use of best-fit spectral templates to the galaxies to predict the exposure times with different instruments needed to obtain a secure redshift. If we then fail to obtain a redshift under nominal observing conditions we can prioritize the target further for follow-up. This potential re-targeting is important to avoid systematic biases in the redshifts obtained in different parts of color space.

We use a technique developed for the proposed SPHEREx mission (Doré et al. 2014; Stickley et al. 2016) to predict the spectrum of galaxies based on their broadband photometry. In brief, this method fits a set of templates based on the libraries of Brown et al. (2014; for galaxies) and Salvato et al. (2009; for AGNs) to deep multiband photometry. Based on the analysis in Stickley et al. (2016), we can estimate the continuum to within 20% and the emission line strengths to within a factor of two. We then use the instrumental response curves for each telescope and instrument to estimate the required integration time to obtain a redshift to that galaxy, given its estimated photometric redshift. Primary objects for a mask are those expected to yield a redshift within a factor of two of the intended mask integration time. The time estimates were compared with previous observations to verify their accuracy. As described in Section 4.2, we use a flagging scheme to keep track of objects for which a redshift was expected but not obtained. These sources can then be prioritized for additional observations.

DEIMOS observations were conducted using the 600 groove mm⁻¹ grating blazed at 7200 Å and the GG400 blocking filter, with dithering performed to improve sky subtraction. In the initial observing run, we experimented with minimum slit lengths of both 6'' and 10'', with no significant difference in the redshift success rate. In the subsequent DEIMOS observations we settled on a minimum slit width of 8'' as a balance between getting the most targets possible on the mask and getting good sky measurements. Data were reduced using a modified version of the DEEP2 pipeline designed to deal with dithered data.

We used the 400 groove mm⁻¹ blue grism blazed at 3400 Å and the 400 groove mm⁻¹ red grating blazed at 8500 Å, with the D560 dichroic. Our choice of blue grism gives high sensitivity at bluer wavelengths where identifying features are likely to be found for objects with photometric redshifts of $z\sim 1.5\mbox{--}3$, while the red coverage allows for the detection of [O ii] for some sources out to $z\sim 1.6$. The LRIS spectra were reduced using the IRAF-based BOGUS software developed by D. Stern, S. A. Stanford, and A. Bunker, and flux-calibrated using observations of standard stars from Massey & Gronwall (1990) observed on the same night using the same instrument configuration.

MOSFIRE was used in its default configuration. For instrumental details we refer the reader to Steidel et al. (2014). We observed four masks in the Y-band and two in the K-band, using integration times of 180 s with ABAB dithering to improve sky subtraction. Reductions were performed with the MOSFIRE Data Reduction Pipeline (DRP) made available by the instrument team.¹⁰

The redshift flagging scheme we use is similar to that adopted by the zCOSMOS (Lilly et al. 2007), DEEP2 (Newman et al. 2013), and VUDS surveys (Le Fèvre et al. 2015). The quality flags range from 0 to 4, with 4 indicating the highest confidence redshift and 0 indicating that no redshift could be found. The interpretation of the flags is roughly as follows.

• 1.  
  Q = 4: a quality flag of 4 indicates an unambiguous redshift identified with multiple features or the presence of the split [O ii]$\lambda \lambda 3726$, 3729 doublet.
• 2.  
  Q = 3.5: a quality flag of 3.5 indicates a high-confidence redshift based on a single line, with a very remote possibility of an incorrect identification. An example might be a strong, isolated emission line identified as Hα, where other identifications of the line are highly improbable due to the lack of associated lines or continuum breaks. This flag is typically only adopted for LRIS and MOSFIRE spectra.
• 3.  
  Q = 3: a quality flag of 3 indicates a high-confidence redshift with a low probability of an incorrect identification. An example might be the low signal-to-noise ratio detection of an emission line, possibly corrupted by telluric emission or absorption, identified as [O ii]$\lambda \lambda 3726$, 3729, but where the data quality is insufficient to clearly resolve the doublet.
• 4.  
  Q = 2/1: a quality flag of 2 indicates a reasonable guess, while a quality flag of 1 indicates a highly uncertain guess. Sources with these low-confidence redshifts are not included in the data release.
• 5.  
  Q = 0: a quality flag of 0 indicates that no redshift could be identified. As described next, a code indicating the cause of the redshift failure is assigned in place of the redshift.

Figure 2 shows six C3R2 spectra from 2016A as examples of Q = 4, Q = 3.5, and Q = 3 redshift assignments.

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It is important for C3R2 to track redshift failures, as well as the reasons for the failures, in order to avoid systematic biases in the sources selected for calibration. Failed targets that were expected to yield a redshift given the instrument and exposure time can be prioritized for additional follow-up. On the other hand, if no spectroscopic redshift was obtained because of a problem with the observing conditions or data (i.e., bad rows, or the target ended up in a region between two detector arrays), no additional prioritization of that source may be needed.

With these considerations in mind, we developed a system to flag different "failure modes" for objects not yielding a redshift. Four categories of failures are used, with the corresponding code assigned in place of a redshift in our catalog. The failure modes we identify are:

• 1.  
  Code = −91: the object is too faint to identify the redshift. This indicates that a deeper exposure and/or different instrument and/or different wavelength coverage are required to obtain a secure redshift. An example of such a source might be a galaxy expected to have a strong [O ii] emission line at 9800 Å, but where the slit placement caused the wavelength coverage to end at 9500 Å, yielding a continuum detection without any strong spectroscopic features. These sources will be further prioritized in future observations.
• 2.  
  Code = −92: the object is well-detected, but no redshift could be determined. This may require a different instrument for secure redshift determination, due to an incorrect photometric redshift or the wavelength coverage obtained for a given observation. We emphasize that the dividing line between −91 and −92 failure codes is imprecise, and no strong effort was made to homogenize the classification. Fundamentally, both codes can be considered two aspects of the same issue. Again, these sources will increase in priority going forward.
• 3.  
  Code = −93: this flag indicates a corrupted slit, typically due to bad rows/columns in the data or the source falling on or near detector chip gaps. This does not affect the object priority in future observations.
• 4.  
  Code = −94: this flag indicates a missing slit, as an extreme case of code −93. This does not affect the object priority in future observations.

Failure codes −91 and −92 essentially correspond to spectral quality issues (i.e., signal-to-noise ratio, wavelength range), while codes −93 and −94 correspond to data quality issues (i.e., slitmask design issues, detector issues). While in DR1 we distinguished between these four failure modes, considering just the two general categories will be sufficient for the purposes of most analyses.

Failure code −91, the most common failure code, generally indicates that the signal-to-noise ratio of the data was insufficient for redshift determination. Indeed, considering the 131 DEIMOS-observed sources in COSMOS with this failure code, 122 (93%) were anticipated to fail based on our estimated exposure time needed to get a redshift. As with low-confidence redshifts, sources for which we failed to find a redshift are not included in this data release.

We measured the redshifts of 134 serendipitously detected sources that happened to fall in slits with primary C3R2 targets. The coordinates of these sources were identified and they were matched back to the survey catalogs. The redshifts for these sources are included in our published catalog.

Some (unintentional) overlap with literature redshifts allows a check on our results. In COSMOS and EGS we observed 38 sources that have previously existing high-quality redshifts. Most (24) were serendipitous detections. We find an rms discrepancy between our redshifts and the literature values of 4 × 10⁻⁴. C3R2 redshifts are often higher precision than the literature values, which likely explains this small difference. There is no systematic difference between the C3R2 and literature redshifts.

The SOM colored by the median photo-z of sources per cell (the left panel of Figure 1) effectively defines a photometric redshift estimate for each galaxy based on its position in the ugrizYJH color space of Euclid/WFIRST. Figure 4 compares our Q = 4 spectroscopic redshifts with the redshift that would be inferred based on the SOM, with encouraging results. The normalized median absolute deviation (a dispersion measure that is not sensitive to catastrophic outliers Ilbert et al. 2009; Dahlen et al. 2013) defined as,

$$\begin{eqnarray}&&{\sigma }_{\mathrm{NMAD}}=1.48\times \mathrm{median}\left(\displaystyle \frac{| {z}_{p}-{z}_{s}| }{1+{z}_{s}}\right),\end{eqnarray} \tag{ 1 }$$

is 0.027 (2.7%) for the sample, which is quite low.

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Using the standard definition of catastrophic photo-z outliers as those with $| {z}_{p}-{z}_{s}| /(1+{z}_{s})\geqslant 0.15$, we measure a low outlier fraction of 3.8%. The measured bias, defined as

$$\begin{eqnarray}&&\mathrm{mean}\left(\displaystyle \frac{{z}_{p}-{z}_{s}}{1+{z}_{s}}\right),\end{eqnarray} \tag{ 2 }$$

is ≲0.1% after removing the catastrophic outliers. Further improvements to these results will result from folding in all spectroscopic information from C3R2 and other surveys to the P($z| C$) relation encoded by the SOM. Notably, these results are already competitive with or better than the photo-z results of codes tested in Dahlen et al. (2013), where the photometry used comprised 14 bands including full depth CANDELS and Spitzer data.

While the performance we find is quite good, and may be representative of what can be achieved with a survey such as Euclid or WFIRST, the results depend on the depth and stability of the photometry. The photometry used to place objects on the SOM in order to estimate a photo-z in the above analysis is quite deep (i-band depth ∼25.4 AB). The results will degrade as the photometry gets shallower or bands are lost in a manner that can be directly characterized via the SOM. A detailed study of the expected performance from the SOM-based photo-z approach will be the subject of a future paper.

Out of 1079 sources with Q = 4 redshifts and reliable SOM-based photo-z estimates, only 41 (3.8%) are outliers according to the standard definition, $| {z}_{p}-{z}_{s}| /(1+{z}_{s})\geqslant 0.15$. If, instead of the SOM-based photo-z, we use the photo-z for each object based on deep multiband data (e.g., the 30-band COSMOS data), we find an outlier fraction for the same sources of ∼3.1%. Thus the SOM photo-z (effectively based only on the seven color Euclid-like SEDs) performs nearly as well in terms of outlier fraction.

We have analyzed all of the outliers on a case-by-case basis. The majority (24/41; 59%) have individual (rather than SOM-based) photo-z estimates more in line with the measured redshift, indicating that the color cells they belong to have real redshift scatter. For nearly all of these sources, the measured dispersion in the 30-band photo-z's within the relevant color cell is significantly larger than the median redshift dispersion per cell; in other words, these are sources that fall in more degenerate regions of the color space. The SOM can be used to identify these regions in a consistent way in order to either reject them in weak lensing analysis or direct extra spectroscopy at them to characterize the redshift distribution in those cells.

In addition, there are several other examples easily understood as Galactic stars (3) or obvious quasars/active galaxies (2), which are known not to have typical galaxy colors (total = 5/41; 12%). This process caught one mistaken line identification where our initial assessment of a MOSFIRE spectrum identified an isolated, narrow, strong line as [O iii] $\lambda 5007$ with corroborating [O iii] $\lambda 4959$ emission. Subsequent analysis reveals the latter emission line to be due to poorly subtracted telluric emission, and we now identify the strong emission line as Hα (Q = 3.5). The remaining cases seem to be genuine mismatches between the spectroscopic redshift and the photometric redshifts, for both the individual photometric redshift of the galaxy and the SOM-based photometric redshift. Consideration of Hubble imaging reveals at least some of these as likely being due to two close-separation galaxies where the ground-based imaging used for the photometry was unable to separate the sources.

The five nights of observing in 2016A filled in ∼6% of the map, in addition to existing spectroscopy that already filled ∼50% (see Figure 5). Thus, we completed ≳10% of the required calibration. However, some of the remaining observations may prove more challenging. Given the recent progress toward bringing multiple deep fields (and their spectroscopy) onto a consistent color system, the requirements may also change to some extent, in the sense that somewhat fewer spectra are required due to the inclusion of other spectroscopic surveys.

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It should also be noted that a certain fraction of the remaining cells represent faint, red sources for which spectroscopic redshifts are prohibitively difficult to obtain with current instruments. These constitute a small (∼3%) fraction of the unsampled cells. If needed, the SOM provides a consistent method for identifying such objects and removing them from the weak lensing sample.