Detecting and Characterizing Mg ii Absorption in DESI Survey Validation Quasar Spectra

DESI spectra are observed using three spectrographs, which are commonly referred to as "b," "r," and "z" due to their wavelength coverage, that together span a wavelength region of 3600–9824 Å. The three spectrographs have approximately constant wavelength resolutions of Δλ ≈ 1.7 Å (DESI Collaboration et al. 2016b, 2022). The flux values associated with a DESI observation are extracted using a linear wavelength grid in 0.8 Å wavelength steps (Guy et al. 2023).

In this paper, we will use data from DESI's early data release (EDR). These data are separated into three stages of survey validation, which we refer to as "sv1," "sv2," and "sv3." These surveys are distinct from each other, both in time frame and targeting implementation, and are detailed in Myers et al. (2023) and DESI Collaboration et al. (2023). Each of these stages, as well as the main survey, are further divided into bright-time and dark-time programs.

The typical effective exposure time DESI aims to achieve during dark-time observations is 1000 s. This timing is set by the need to classify and obtain redshifts for the luminous red galaxy sample that is observed concurrently with the quasar sample during dark-time (see Section 4 of Zhou et al. 2023). The relationship between effective exposure time and signal-to-noise is detailed in Section 4.1.4 of Guy et al. (2023). Note that quasars are only intended to be targeted during dark-time, see Myers et al. (2023) for further discussion of the distinction between DESI's bright-time and dark-time programs.

DESI will, over the course of its survey, reobserve targets to improve the quality of its data. During the main survey, Lyα forest quasars are scheduled, at high priority, to be observed with four times the exposure time at which direct tracers quasars are typically observed, although all quasars can ultimately be reobserved at low priority (see Section 5.3.3 of Schlafly et al. 2023, for details). During survey validation, all quasars at redshifts z > 1.6 were observed for four times the typical exposure time (e.g., Chaussidon et al. 2023). This distinction carries implications for our completeness with respect to redshift, we comment on this further in Section 2.4.

To perform our search for absorbers in the most robust fashion, we chose to use spectra that coadd all observations of a given target. We will refer to these spectra as being "healpix coadded" because this is how they are grouped within the DESI spectral reduction file structure (Górski et al. 2005). We will also make use of the spectra that coadd a subset of observations, i.e., all observations from a single night, to determine the completeness of our sample (see Section 2.4).

Observations of the same target made during different survey validation stages are not coadded, and as such it is possible that a target could be present in several of these surveys. In such cases, we will only consider the results of our absorber search for only the healpix coadded spectrum from the survey, which has the highest squared template signal-to-noise (TSNR2; see Section 4.14 of Guy et al. 2023 for a full description of this statistic).

TSNR2 is calculated for different target classes (i.e., emission line galaxies, luminous red galaxies, and quasars) according to their expected spectral properties and redshift distribution. This results in a more informed statistic that better weights relevant spectral features, such as emission lines and the Lyα Forest. Notably, TSNR2 values for different target classes cannot be fairly compared, so when we refer to TSNR2 generically throughout this paper we will be referring to the TSNR2_QSO statistic.

Our analysis relies on parent quasar catalogs generated via three tools: Redrock (RR; S. Bailey et al. 2023, in preparation), ³¹ which is a PCA-based template classifier that is part of the main DESI spectroscopic pipeline (Guy et al. 2023); QuasarNet (QN; Busca & Balland 2018), ³² which is a neural network based quasar classifier (see also Farr et al. 2020); and an Mg ii-emission-based code, which is designed to identify AGN-like spectra that show both strong galactic emission features and broad Mg ii emission. The results from the visual inspection of quasar spectra informed the need for, and use of, these tools (Alexander et al. 2023).

Initial spectral types (QSO or non-QSO for our purposes) as well as initial redshifts are determined by RR. QN and the Mg ii-emission code are then run as afterburners. The outputs of the two afterburners can result either in RR being re-run with adjusted redshift priors, or in the case of the Mg ii-emission code the spectral type being changed to QSO when a broad Mg ii-emission line is detected. Notably, redshifts are always ultimately determined by RR. A more complete overview of the application of these tools to construct quasar catalogs, as well as the verification of the completeness and purity of this approach, can be found in Chaussidon et al. (2023). The resulting catalog has a purity greater than >99% and a median redshift of z = 1.72, with 68% of quasars having redshifts between 1.07 < z < 2.46 (Chaussidon et al. 2023).

We search these spectra for absorption doublets by first applying a Gaussian smoothing kernel with a standard deviation of two, as described in the Astropy documentation (Astropy Collaboration et al. 2022). This smoothing is performed to reduce the effect of noisy regions/pixels on the background quasar continuum that we estimate in the following step. We estimate this continuum from the smoothed flux values of the spectra using a combination of median filters. Specifically, we choose to weight the combination of a 19 and 39 pixel filter such that the contribution of the narrower 19 pixel filter is strongest at low wavelengths and decreases across the wavelength space, whereas the opposite is true for the 39 pixel filter, which contributes to the estimated continuum value most strongly at high wavelengths.

These pixel values were informed by a preliminary set of Mg ii absorptions that were detected using more rudimentary methods. The precise values have been chosen to ensure that the two absorption lines of the Mg ii doublet are cleanly separated into individual absorption lines by the estimated continuum. We find that this combination reliably models the broad emission features that are observed in DESI quasar spectra, but not any narrow absorption features that may be present. The choice to effectively broaden the filter at high wavelengths accounts for the broadening of Mg ii systems due to redshift.

An example of both the smoothing process and the estimated continuum can be seen in the central panel of Figure 1. The bottom panel of Figure 1 demonstrates that emission features are not retained in a residual obtained by subtracting the median-filter-estimated continuum from the Gaussian-smoothed data, but any absorption features remain as positive features in the residual. Also evident is the increased residual noise beyond our search limit in the Lyα forest, which makes it evident why it is difficult to resolve metal lines in this region.

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To detect doublets, we find every group of consecutive positive residuals and calculate a signal-to-noise ratio as:

$$\begin{eqnarray}&&{\rm{S}}/{\rm{N}}=\displaystyle \frac{{\sum }_{p1}^{p2}C-F}{{\left({\sum }_{p1}^{p2}{\sigma }^{2}\right)}^{1/2}}\end{eqnarray} \tag{ 1 }$$

where C and F are the continuum and flux values, respectively, σ² is the variance of the spectrum, and p1 and p2 are the first and last indices of a particular group of consecutive positive residuals. We additionally fit a preliminary Gaussian model to each set of residuals, which allows us to estimate the line center, and the determined values for line amplitude and width are later used to inform the initial state of the Markov Chain Monte Carlo (MCMC) sampler. If two absorption lines are found to have S/N values greater than 2.5 and 1.5, respectively, and a rest-frame wavelength separation of 7.1772 ± 1.5 Å, where 7.1772 Å is the laboratory separation of Mg ii (e.g., Pickering et al. 1998), then this doublet is regarded as being a likely candidate.

A similar detection method was used in Raghunathan et al. (2016); however, we find that our approach improves the detection of relatively low-signal absorption systems in high-signal QSO spectra. Note that our rest-frame line separation uncertainty value, 1.5 Å, has been chosen to consider as many candidate absorbers as possible without encompassing the rest-frame separation of Si iv, which is another absorber doublet that is commonly strong in QSO spectra.

To further verify these systems, we next perform an MCMC analysis using the emcee software (Foreman-Mackey et al. 2013). The decision to use MCMC to fit the relatively simple model of a doublet absorption line was made in the interest of fully understanding the posterior distributions of our parameters, as well as increasing the likelihood of recovering low-signal absorbers.

To ensure that the full signal of the absorber is recovered, we use a different continuum in fitting the systems than the one previously described and used in the initial detection step. The continuum used in detection is designed to ensure that the individual lines of the Mg ii doublet are detected separately, in the case of particularly strong or broad absorbers this can result in some of the absorption signal being lost in the residual. However, when fitting the absorber, we instead construct a continuum to ensure that the the full signal is retained.

We first attempt to calculate an appropriate QSO continuum using the NonnegMFPy tool as implemented in Zhu & Ménard (2013) and Anand et al. (2022). NonnegMFPy utilizes nonnegative matrix factorization (NMF, see Lee & Seung 1999) to determine a basis set of eigen-spectra and through their reconstruction estimate an observed quasar continuum.

In cases where the NMF tool is unable to estimate a continuum due to an inability to converge, or the chi-squared value of the estimated continuum is greater than 4 (approximately 32 % of DESI EDR QSOs) we estimate a secondary continuum using a wide, 85 pixel median filter. In cases where this median-filter continuum provides a spectra fit with a lower chi-squared value, we instead use this continuum. The width of this median filter is informed by the previously referenced preliminary sample of detected Mg ii absorbers and ensures that no signal is lost in estimating the continuum, even for the broadest absorption systems.

For each absorber candidate, we consider a region of 80 pixels, or 64 Å, around the detected doublet. This value allows the sampler to explore a region of redshift space that will ultimately be much larger than the redshift uncertainty for a high quality fit, while simultaneously allowing for the detection of multiple Mg ii systems in a single spectrum. We then fit a five-parameter model of the form:

$$\begin{eqnarray}&&F={A}_{1}\exp \displaystyle \frac{-{\left[\lambda -{C}_{1}\right]}^{2}}{2{\sigma }_{1}^{2}}+{A}_{2}\exp \displaystyle \frac{-{\left[\lambda -{C}_{2}\right]}^{2}}{2{\sigma }_{2}^{2}}\end{eqnarray} \tag{ 2 }$$

where the two Gaussian line profiles are defined by their center C, width σ and amplitude A. Note that C₁ and C₂ are both set by the same underlying redshift parameter, i.e., C₁ = (z + 1) × 2796.3543 Å.

The only prior attached to this model is the redshift range implied by the 80 pixel region around the suspected doublet. Initial values for our parameters are informed by the results of the detection step, with the minimum value in the group of residuals informing the line amplitude and the number of consecutive negative pixels informing the standard deviation.

We use 32 walkers and run the model for 15,000 steps. We then discard the first 1000 steps as a burn-in period and store the remaining 14,000 steps for each candidate MCMC feature. Finally, we select only those models that have high mean acceptance fractions (>0.45) and estimated integrated autocorrelation times ³³ that are less than 1 per cent of the chain length, indicating that the majority of proposed steps were accepted and that the model was well fitted by the MCMC process.

After running this pipeline on our parent sample of 83,207 DESI QSOs, we find a total of 29,797 systems in 18,219 individual healpix coadded spectra that meet our criteria.

In this sample there are a small number of entries with Mg ii absorption redshifts greater than the background quasar redshift, which may initially seem to suggest that the absorber is more distant than the quasar, ³⁴ In analyzing the physical interpretation of this scenario, it is standard to work in velocity rather than redshift space, and to define a velocity offset as:

$$\begin{eqnarray}&&{v}_{\mathrm{off}}=c\displaystyle \frac{{z}_{\mathrm{Mg}\,{\rm\small{II}}}-{z}_{\mathrm{QSO}}}{1+{z}_{\mathrm{QSO}}}.\end{eqnarray} \tag{ 3 }$$

Velocity offset values within approximately ±6000 km s⁻¹ are indicative of an associated absorption system, wherein the QSO emission and metal line absorption arise from the same galaxy or galaxy cluster (Shen & Ménard 2012). However, in systems with larger velocity offset values, it must be true that one of the redshifts is poorly determined—because it is physically impossible for a system that is absorbing the light from a quasar to lie behind that quasar.

From a brief visual inspection of these systems we find a number of true Mg ii systems in quasar spectra with incorrect redshifts. Additionally, we find a number of false Mg ii systems, which are often detected in star or galaxy spectra that have been misidentified as quasars or spectra with unusual error features. We therefore decide to group those systems with velocity offsets greater than 5000 km s⁻¹ into a separate catalog of physically impossible absorbers for the purpose of diagnosing spectra that have been misclassified as quasars or assigned an incorrect redshift. We will comment on this separate catalog further in Section 4.1. Removing the 374 entries with v_off > 5000 km s⁻¹ results in a preliminary sample of 29,423 suspected Mg ii absorbers.

In the interest of both assessing and potentially improving our catalog purity, we next conducted a visual inspection of 1000 randomly selected systems that pass the MCMC process and do not have physically impossible redshifts, as described above. This process involves several steps: confirming that the background spectrum is indeed that of a quasar, verifying that two absorption lines have been well fitted by the MCMC process, and determining if additional metal lines can be fitted at the same redshift. Note that the presence of additional metal lines is considered only in confirming borderline cases where the fit absorption lines are weak.

Visually inspecting 1000 randomly selected Mg ii absorbers, following the steps outlined above, we find 808 that constitute true Mg ii absorption and 192 which do not. This suggests an initial purity of 80.8%. Based upon the statistics of these systems, we have developed a series of quality cuts to improve the purity of our detected sample with minimal effect on completeness.

The first cut that we perform is to remove systems for which one or both of the fit Gaussians have a positive amplitude. This outcome is not disallowed by the MCMC priors to facilitate a full exploration of the parameter space but is clearly not indicative of an absorption feature. Note that in such a case, the initial line amplitude values were given as negative; however, the MCMC process has converged on a positive line solution in the course of fitting. There are 77 such systems in the visual inspection set, all of which were identified as false Mg ii systems and as such we impose a cut that all systems are required to have negative amplitudes for both fit line profiles.

We can next consider another class of possible contaminants, systems in which two Gaussians with negative amplitude can be fitted at the proper separation of Mg ii but whose line amplitudes and/or widths are not characteristic of Mg ii. To determine an appropriate selection, we must consider both the physical nature of Mg ii absorption and the Gaussian line parameter posteriors of our visually inspected sample. To visualize these posteriors, we have plotted the ratio of line amplitudes against the ratio of line widths in Figure 2. In both cases, we consider the statistic of the leading 2796 Å line divided by the statistic of the 2803 Å line.

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From the inset panel of this figure, we observe that the distribution of our visual inspection set in this space is tightly clustered around a value of roughly [1.1, 1.1], which indicates (empirically) that the 2796 Å line of the Mg ii doublet tends to have a slightly larger amplitude and be slightly wider than the second.

The innate flux ratio of the 2796–2803 Å lines is determined by the ratio of their collisional rate coefficients or equivalently by their quantum degeneracy factors. This ratio for Mg ii is F₂₇₉₆/F₂₈₀₃ = 2, and has been experimentally verified (e.g., Mendoza 1981; Sigut & Pradhan 1995). However, because the majority of systems observed here are saturated, the observed ratio of absorption line area approaches 1.

When visually inspecting these systems, we observe some true Mg ii absorbers where the amplitude and/or width of the 2803 Å line is greater than that of the 2796 Å line. This should not be possible theoretically; however, the systematic uncertainties inherent to observation can produce this result. With this in mind, we can draw a selection in this parameter space that includes the region of highest density/physical likelihood and allows for slight variation due to observational uncertainties, while still maximizing the purity of the post-cut selection. The selection takes the form of a circle and is described by:

$$\begin{eqnarray}&&{\left(\displaystyle \frac{{\mathrm{AMP}}_{\lambda 2796}}{{\mathrm{AMP}}_{\lambda 2803}}-1.4\right)}^{2}+{\left(\displaystyle \frac{{\sigma }_{\lambda 2796}}{{\sigma }_{\lambda 2803}}-1.4\right)}^{2}\lt 0.81\end{eqnarray} \tag{ 4 }$$

where AMP is the amplitude of the fit line and σ the width. Note that all points with amplitude and width ratios between 1.0 and 2.0 are included in this selection. After applying a cut to our sample according to the boundaries of this circle, we remove 50 true positives and 108 false positives.

After imposing these cuts, the visual inspection sample contains 758 true positive Mg ii systems and seven false positives for a nominal 99.1% purity. Presuming Gaussian noise on this measurement, we assign a ±3.16% error on this purity. Applying these cuts to our pre-visual inspection sample of 29,423 absorber candidates leaves a population of 23,921 absorbers.

In this section, we will investigate the completeness of our sample. We will first determine its dependence on the quality of input spectra by using nightly data reductions. We then consider its relationship with the rest-frame EW of absorption systems as determined by the creation of simulated absorbers.

2.4.1. Reanalysis of Nightly Reduction

The healpix coadded spectra that we search for absorbers are created by combining multiple individual observations, as described in Section 2.2. These individual observations have lower S/Ns, which makes recovering absorption features more challenging. This allows for a natural test of the completeness of our approach with respect to the TSNR2 of input spectra.

By searching the nightly coadded spectra, generally composed of a few individual observations, for a known Mg ii absorber, we can quantify the performance of our pipeline as a function of absorber redshift and spectral S/N. We chose to use the nightly coadded spectra rather than individual observations because this spans the region of relevant TSNR2 values more fully. Additionally, in rare cases where a target is observed on only a single night, we do not consider the results of its reanalysis because the healpix coadded and nightly coadded spectra are the same.

Figure 3 shows the TSNR2 distribution of healpix coadded quasar spectra. Results are shown for both targets with any number of observations and those targets with at least four observations. Note that we have grouped quasars with a TSNR2 value >140 because above this threshold we find that Mg ii detection is not sensitive to the TSNR2 of the background quasar. Additionally, we note that this final bin happens to contain only entries with at least four observations and accounts for approximately one-third of the full healpix coadded sample.

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Having determined the population of TSNR2 values, we can now determine the performance of our pipeline in recovering known Mg ii absorbers as a function of TSNR2. To do so, we consider all 23,921 detected absorbers and recover the spectra of their nightly coadded observations. We then run the doublet-finder portion of our pipeline on these observations, recording whether the known Mg ii doublet can be recovered in these lower-TSNR2 spectra. The results of this search are displayed in Figure 4—as can be readily seen, our percentage of recovered absorbers decreases with TSNR2, as anticipated. The percentage of recovered absorbers is also noticeably worse in the lowest redshift bin. This happens because the DESI instrument has a lower throughput at the blue end (DESI Collaboration et al. 2022).

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We can next consider the average completeness per TSNR2 bin, averaging across redshift space. By multiplying the number of quasars in each bin of TSNR2, i.e., Figure 3, by this average completeness per bin, we can determine the number of quasars in each bin for which we would expect to be able to recover Mg ii absorbers. We determine the expected completeness by summing these results across TSNR2 bins and normalizing by the total number of quasars. By doing so for the results shown in Figure 4, we recover an expected completeness of 88.0% for QSOs with any number of observations and 92.8% for QSOs with at least four observations.

2.4.2. Injection of Synthetic Absorbers

In addition to determining our completeness with respect to the quality of searched spectra, it is also informative to determine our ability to recover absorbers with different innate absorption strengths, described by the rest-frame EW of the 2796 Å line (${W}_{0}^{\lambda 2796}$). To do so, we follow the approach of Zhu & Ménard (2013)—see their Section 3.3 and Figure 7—and generate synthetic absorber systems at a wide range of values of ${W}_{0}^{\lambda 2796}$.

These mock absorbers are generated by first setting ${W}_{0}^{\lambda 2796}$ equal to a random value between 0 and 4 Å. This upper limit has been chosen as systems with ${W}_{0}^{\lambda 2796}\gt 4$ Å account for less than 3% of our sample. The rest-frame EW of the second line of the doublet, ${W}_{0}^{\lambda 2803}$, is then determined by drawing a value from the posterior of doublet ratio values (${W}_{0}^{\lambda 2796}$/${W}_{0}^{\lambda 2803}$) found in our sample. In the same fashion, we determine a value for the rest-frame Gaussian standard deviation of both lines. This sets the line amplitudes, such that the determined values of W₀ are representative.

We have chosen to inject these systems in real DESI quasar spectra, specifically those quasars from the parent catalog used in this study in which no real Mg ii absorbers were detected. This ensures that these spectra have realistic error properties. For quasars with z < 2.15, synthetic absorbers are injected at every pixel that corresponds to an absorber redshift between z = 0.3 and z = 2.5. For quasars with z > 2.15, to avoid the Lyα forest region, injection starts at the first pixel red-ward of the Lyα emission line.

After constructing the absorber model, as detailed above, the model is resampled into the DESI wavelength coverage. The flux values of pixels that lie within the absorption lines are then replaced by the model values. The model is then scaled by the average flux values in the pixels it is replacing and noise is added, with values being drawn from a normal distribution centered on the error spectrum values of the pixels being replaced. The resulting spectrum is then run through the doublet-finder portion of our pipeline to test whether the injected absorber is recovered.

The results of this test, for a sample of 6000 randomly selected quasars, are shown in Figure 5. The heatmap in the left-hand panel clearly shows that our completeness decreases rapidly for systems below ${W}_{0}^{\lambda 2796}$ = 0.8 Å. Regions of decreased completeness at constant absorber redshift are also visible. These are associated with common skylines, such as the high pressure sodium bump at ∼5900 Å or OH lines at ∼9200 Å (e.g., Zhu & Ménard 2013).

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The marginalized distributions shown at the right-hand side of Figure 5 shows that in addition to decreasing rapidly at low values of ${W}_{0}^{\lambda 2796}$, our completeness also slowly decreases at ${W}_{0}^{\lambda 2796}\gt 2.4$ Å. We suspect this may be a result of the lines of these very strong absorbers blending together, such that they cannot be separately resolved by our code. We will seek to address this issue in future catalog releases.

Considering the completeness with respect to redshift, we can see that it slowly increases with redshift, and is generally lower at the far red and blue ends of the wavelength coverage. Dips in completeness at z ∼ 1.1 and z ∼ 1.7 are likely to be related to the DESI spectrograph crossover regions (DESI Collaboration et al. 2022), where noise values tend to be higher. Completeness increasing with redshift is a notable difference when compared to the results of Zhu & Ménard (2013), and demonstrates that absorber searches performed with DESI will be more complete to absorbers at higher redshift because of its wavelength coverage and the depth of its observations.

It will be necessary to re-evaluate our completeness when considering observations taken during the DESI Main Survey because direct tracer quasars with redshifts 1.6 < z < 2.15 are unlikely to have been observed for four times the typical exposure time, as they were for survey validation observations.

Having outlined how the completeness of our sample is related to the S/N properties of the spectra analyzed, as well as the redshift and absorbing strength of the intervening systems, we will now consider the properties of the systems that were detected.

We describe the data columns that we catalog for each detected absorption system in the Appendix. We will now give a brief overview of these columns and their use.

We first retain sufficient information to uniquely identify each analyzed healpix coadded spectrum, specifically the DESI TARGETID (see Myers et al. 2023), R.A., decl., and phase of the DESI survey. We additionally store the Redrock ZWARN bitmask, which details possible redshift warnings, as well as various TSNR2 values of each spectrum, and the best quasar redshift for each spectrum (derived from the parent quasar catalogs, as discussed in Section 2.2).

We also record the rest-frame EWs of both lines, as well as the central posterior distribution values for all five MCMC fit parameters, as described in Section 2.2. For the EWs, as well as the fit parameters, we also provide lower and upper error bars, as determined from the 16th and 84th percentiles of their posterior distributions.

The created Mg ii absorber catalogs are available online. ³⁵ We have also retained the full 14,000-step MCMC chains for each detected absorber, which will be made available upon request.

As discussed in Section 2.2, we have detected a small number of systems that have an offset velocity that suggests the absorber is behind the quasar, which is physically impossible. In total, there are 374 such systems, which we will refer to as "PI" absorbers. These PI systems comprise roughly 1.3% of our initial pre-quality-cuts sample of 29,797 absorbers. To improve the utility of this PI subset, we first apply the same quality cuts as for the main sample, which reduces the PI absorber sample to 108 systems in 84 unique spectra. Inspecting these spectra, we find 34 entries where the Mg ii absorption is clearly real, and the QSO redshift poorly determined. Nineteen of these systems are Lyα forest quasars and two illustrative spectra are shown in Figure 8. We additionally find two instances of misidentified star spectra, and one instance of a QSO that has been redshifted at a value greater than that which we find in visual inspection; note that in these three cases the Mg ii absorption is not real.

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The relatively low number of true PI absorbers that are found demonstrates the extremely high accuracy of the DESI redshift schema. Extrapolating from these results to the full five-year DESI sample, we would anticipate finding only 1200 true PI absorbers. Given these numbers, it may be worthwhile to occasionally visually inspect these systems and reclassify any Lyα forest quasars with true PI absorbers such that they can be reobserved to improve the signal of the observation. We leave this consideration to future work.

Once an Mg ii absorption system has been identified at a particular redshift, we can search for other common metal lines, such as Fe ii, C iv, and Si iv, knowing precisely where in the spectrum these lines should appear. This enables the detection of these lines at relatively lower S/N.

A pilot analysis that involved the visual inspection of 1000 randomly selected Mg ii absorbers to search for Fe ii, C iv, and Si iv at the same redshift yielded the results in Table 1. The "Id. Rate" column in Table 1 shows the raw percentage of inspected Mg ii absorption systems in which the additional line could be identified, the "Vis. Rate" column shows the percentage of inspected absorption systems in which the non-Mg ii absorption species would be found at a wavelength > 4000 Å such that it would be readily visible to the DESI instrument. ³⁶ Finally, the "Scaled Id. Rate" column scales the Id. Rate by [100/Vis.Rate] to give the percentage of the time the line was identified when expected to be visible. We choose to use 4000 Å because this tends to be the region where the noise in the DESI spectra reaches a consistent level (being noisier at lower wavelengths).

These results imply that (when visible) Fe ii is identifiable in 91.1% of systems and C iv and Si iv are similarly identifiable in 72.8% and 66.4% of systems, respectively. These results are promising and suggest that an algorithmic approach could reliably characterize additional absorption features when seeded with a redshift derived from a certain absorption doublet, such as Mg ii.