Spectrophotometric Redshifts in the Faint Infrared Grism Survey: Finding Overdensities of Faint Galaxies

2.1.1. Survey Description

2.1.2. 1D and 2D Spectral Extraction

2.1.3. PA Combination

The sample of FIGS spectra used are described in detail in the following section, the results of which are summarized in Table 2.

Table 2.  A Description of the Spectra Samples of the Four FIGS Fields

Field	Initiala	Not Matchedb	Too Faintc	Low ${ \mathcal N }$ d	Bad Synthetic Fluxe	Aperture Ratiof	Finalg
GN1	1913	263	812	241	21	25	551
GN2	1003	84	161	222	20	50	466
GS1	3106	390	1917	241	11	32	515
GS2	2623	819h	1223	194	13	27	347
Total	8645	1556	4113	898	65	134	1879

Notes.

^aThe number of combined 1D spectra in each field before any quality cuts have been made. ^bThe number of objects with spectra without additional matched photometric data (See Section 2.2.1). ^cThe number of objects with spectra and matching photometry, but with F105 > 26.5 mag. ^dThe number of objects with spectra and matching photometry, but with a net spectral significance of less than 10 (see Section 2.2.2). ^eThe number of objects meeting previous criteria for which we were unable to calculate a synthetic F105W magnitude. ^fThe number of objects meeting previous criteria but rejected for having a large aperture correction or less than 90% full coverage. (see Section 2.2.3). ^gThe number of objects in each field that pass all quality criteria and are used in the final SPZ sample. ^hGS2 lacks deep WFC3 imaging at some roll angles. See Section 2.2.1.

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2.2.1. Broadband Photometric Data

2.2.2. Net Significance

As described in the instrument calibration report (Kuntschner et al. 2011), the WFC3 G102 grism achieves a maximum throughput of 41% at 11000 Å and provides ≥10% system throughput in the wavelength range 8035–11538 Å (see Figure 1). At longer wavelengths, the throughput declines rapidly, making this the effective useful range of the spectra. We assess the content of the individual spectra by computing the net significance (Pirzkal et al. 2004), which is determined by reordering the resolution elements in order of descending S/N, and then iteratively computing a cumulative S/N from the current element and all lower elements. This continues until a maximum S/N is computed. After the cumulative S/N turns over, adding additional data will not increase the S/N. The maximum is then the net significance of the spectrum, ${ \mathcal N }$. As described in Pirzkal et al. (2017), a simulated FIGS spectrum with a continuum level of 3σ per bin is expected to have ${ \mathcal N }\approx 4.5$. It is possible to obtain an artificially high value of ${ \mathcal N }$ for an object if there is unaccounted contamination or errors in the level of background subtraction. To avoid such objects, and to ensure we used only objects with high signal, we imposed a netsig cutoff of ${ \mathcal N }\gt 10$. This eliminates 7%–20% of the initial number of objects in each field. Though it is still possible for contaminated or otherwise low-signal objects to bypass this cutoff, such objects are likely to be caught by further quality cuts.

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2.2.3. Aperture Correction

Because the spectra will need to be combined with photometry to cover the wavelength range needed for a redshift fit, the flux values in the spectra need to be scaled to match those of photometric images. To do this, we define an aperture correction, which is the flux ratio between a photometric flux and a synthetic flux calculated from the spectrum in the same band, as described in Ryan et al. (2007). Figure 1 shows the grism throughput curve plotted against the two nearest HST broadband filters: F850LP and F105W. Both filters extend past the usable wavelength range of the grism, but the F105W band has the closest filter profile correspondence to the grism throughput, since the F850LP sensitivity anticorrelates with that of the grism, resulting in a much broader distribution of aperture corrections. Consequently, we defined the aperture correction ${ \mathcal A }$ in terms of a synthetic F105W band, calculated by integrating over the product of grism spectra with the F105W filter curve:

$$\begin{eqnarray}&&{ \mathcal A }={\mathrm{log}}_{10}\left(\displaystyle \frac{{\rm{F}}105{\rm{W}}(\mathrm{obs})}{{\rm{F}}105{\rm{W}}(\mathrm{synth})}\right).\end{eqnarray} \tag{ 1 }$$

If, for some reason, a synthetic F105W flux cannot be calculated from the spectrum (usually if oversubtraction of contamination left most of the fluxes negative), that spectrum is rejected for SPZ use.

The distribution of the aperture corrections in each field is displayed in Figure 2. The widths of the aperture correction distributions are a function of the spectral extraction method, the broadband apertures, and spectral contamination from nearby objects. However, as noted above, the F105W filter profile goes significantly redder than the G102 wavelength coverage. If an object spectrum in that region is not flat, then the aperture correction produced is likely to be quite large.

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In all of the fields, the distribution peaks sharply near 0, and the distributions feature a negative tail, indicating a tendency of the synthetic F105W measurements to exceed that of the HST photometry. The shape of this distribution becomes clearer when looking at Figure 3, which displays the aperture correction as a function of F105W magnitude (a proxy for the brightness of the spectrum). The aperture corrections only begin to strongly diverge from 0 for fluxes fainter than ∼25.5 mag, with the most deviant objects typically found at the very faintest magnitudes. This is likely a function of contamination, which will make up a larger fraction of the total measured flux in an object with a faint true brightness. Consequently, accurately estimating the contamination in such objects is more difficult, increasing the likelihood that a faint object will retain some contaminating flux. Faint contaminated objects are therefore more likely to have synthetic F105W measurements that are significantly larger than the broadband measurement, hence the negative tail in the distribution. To avoid the influence of such objects, we imposed a cutoff in aperture correction where any object with a ratio off from unity by a factor of 10 or more is rejected. Across all four fields, an average of 6% of the initial sample was rejected for this reason. This correction does not account for any objects whose continuum slope has been altered by the presence of unaccounted background or contamination, which may pass through the aperture correction if the overall integrated flux does not change much. Such objects were later weeded out via visual inspection.

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Some objects do not have a measurement in all 5 PAs, and some PAs do not measure the flux across the total G102 wavelength range. This usually does not cause any issues with the combination of the different PAs, but it may if the only PAs with data do not have overlapping coverage. This can result in combined spectra with gaps in the flux, and such spectra tend to produce very confused results in the redshift fit. These and any other spectra with missed contamination were rejected by visual inspection. These final removals typically amounted to ∼1% of the initial sample.

To estimate the redshifts, we used EAZY (Brammer et al. 2008), a public photometric redshift code. A systematic comparison of nine different photometric redshift codes (including EAZY) across 11 different photometric redshift catalogs (Dahlen et al. 2013) found that no particular code obtained significantly more accurate photometric redshifts compared to the others. Given this, we use EAZY for its modifiability that allows the simple inclusion of grism data alongside photometry.

Given a set of photometric points and corresponding errors, EAZY can iterate over a grid of redshifted spectral templates, calculating synthetic fluxes to compare with the measured photometry. The differences between the synthetic templates fluxes and the observed fluxes are used to define a χ² statistic. This χ² is minimized across the range of template spectra and redshifts to find the best-fit template and redshift. EAZY's template spectra are derived from a library of ∼3000 PÉGASE spectra (Fioc & Rocca-Volmerange 1997), including spectra with variable-strength emission lines. Using the method of non-negative matrix factorization (Blanton & Roweis 2007), Brammer et al. (2008) were able to reduce the large template set to a set of 5 basis templates that, in linear combination, can represent the full range of colors of the initial set. These basis templates, along with a dusty starburst template (a Calzetti extinction law is applied), make up the template set EAZY uses for fitting.

Despite the breadth of this template set, there remains uncertainty in the spectral properties (e.g., variations in dust extinction) that go into constructing template galaxies, which may result in mismatches between the templates and an observed galaxy. To account for this, EAZY provides a template error function to account for this uncertainty when fitting observations to the templates. The template error function provides a per-wavelength error in the template flux derived from the residuals of a large set of redshift fits. This allows the template set to accommodate observational spectral variations that are not accounted for in the physics from which the templates are derived.

Furthermore, to avoid degeneracies in the redshift fitting wherein the redshift probability distribution produces more than one peak, EAZY also provides a grid of magnitude priors in R- and K-bands, which assigns probabilities to measuring a band at a certain brightness at a given redshift, a technique first applied in Benítez (2000). This typically reduces the incidence of catastrophic failures, where the difference between the grism redshift and spectroscopic redshift is more than 10% of (1 + z_spec), by providing a mechanism for avoiding wrong-peak selection in the case of a bimodal probability distribution. In our sample, we use the R-band magnitude prior, calculated from the observer-frame R-band flux.

To include the FIGS spectra in a photometric fitting code, we followed the procedure in Ryan et al. (2007) and reformatted the spectra into a series of narrow photometric bands that could be supplied to EAZY alongside broadband photometry. After passing the net significance and aperture correction procedures without rejection, an individual spectrum is divided into subsamples along its operating wavelength range. The number (and therefore width) of these subsamples can influence the results of the redshift fit. We experimented with a number of bins ranging from a few (width ∼750 Å) to treating each grism element as its own bin (a width of 24.5 Å), in order to obtain the best results. Typically, grism points derived from fewer, broader wavelength bins are better at avoiding errors introduced by problems in the combined spectra (e.g., oversubtraction of contamination), as each bin will include a larger number of pixels, reducing the influence of one or two bad pixels. However, the redshift quality of the whole sample is best with a larger number of narrower bins, as this allows for the more precise location of breaks and emission lines. The cases where oversubtraction or other errors produce inaccurate results are few enough in number that they can be flagged individually, so we attempted the redshift fits with the narrowest grism bands. Bands narrower than a few grism pixels caused the fitting routine to stall and fail to produce a redshift fit. Consequently, we chose to proceed with grism bands ∼140 Å wide (which corresponds to ≤22 spectral "pixels" per spectrum), which was the narrowest range to fit successfully. This may not result in any loss of improvement, as the typical spatial scale of objects in FIGS is a few pixels, so the spectra are smoothed to this extent anyway.

The flux in each of these subsamples is integrated to produce a new "narrowband" flux in each sample. These narrowband fluxes are written into an EAZY input catalog alongside FIGS and 3D-HST broadband photometry. EAZY is also given a "filter profile" for each narrowband in the form of a tophat function bound by the wavelength range of the grism band. EAZY provides the option to smooth the filter profiles R(λ) by applying a Gaussian such that ${{ \mathcal R }}_{i}\,=(1/{b}_{i}){{\rm{\Sigma }}}_{j}R(\lambda )\cdot G({\lambda }_{i},{\lambda }_{j},\sigma )$ where G is a Gaussian function and b_i = Σ_j G. After testing several cases, we obtain the best results with smoothing enabled with σ = 100 Å. We run EAZY on a redshift grid of z = 0.01–6.0, which is the redshift range tested in EAZY's design, with Δz = 0.01 · (1 + z_prev).

Figure 4 shows an example of EAZY input and output for one of the FIGS objects exhibiting a particularly noticeable 4000 Å break. The location of the break is more obvious at the higher resolution of the grism data, which confine it to a ∼100 Å wavelength range, as opposed to the ∼1000 Å coverage provided by the broadband photometry alone.

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To gauge the accuracy of the SPZs compared to photometric redshifts without spectral data (photo-zs), it is helpful to compare the redshifts from both methods with known spectroscopic redshifts (i.e., the conventional standard for accurate redshifts). We created a matching set of photometric redshifts for the SPZ objects by simply running the same catalogs through EAZY stripped of their grism measurements, leaving only the broadband photometry as input for the fit.

The SPZ and photo-z catalogs could each be compared with spectroscopic redshifts for the same objects. To find as many matches with confirmed spectroscopic redshifts as possible, we consulted a compilation of public spectroscopic surveys in GOODS-N and CDFS (N. Hathi 2018, private communication). The spectroscopic redshifts in these compilations were assigned quality flags based on the redshift quality indicated in the parent survey. To ensure the best possible comparison sample, only the spectroscopic redshifts from the two highest-quality bins were used.

Because the limiting magnitude of the FIGS data set goes beyond the limits of ground-based spectra, one should expect objects with spectroscopic redshifts in the FIGS fields to be readily detected. Consequently, these objects can be found using simple (R.A., decl.) matching. This was done with a separation tolerance of 1 arcsecond to account for offsets in different surveys, though for the vast majority of matches the separation is much smaller. This matched set of spectroscopic redshifts was then assured to provide a high-accuracy comparison for the matched SPZs. The number and magnitudes of the SPZ-spectroscopic comparison sample are given in Table 5, and a comparison of magnitudes between the spectroscopic redshifts and the total sample of SPZ objects are given in Figure 5.

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Table 5.  A Summary of the SPZ and Photo-z Quality Results for the Four FIGS Fields

Field	N. Spec-z	F105Wa	Med(ΔzSPZ)b	Med(ΔzPZ)c	SPZ Outliersd	PZ Outliersd
GN1	200	23.3	0.019	0.026	0.07	0.08
GN2	147	23.2	0.024	0.028	0.09	0.10
GS1	131	23.5	0.023	0.029	0.09	0.10
GS2	101	23.2	0.027	0.031	0.15	0.16

Notes.

^aThe median F105W magnitude of the SPZ-spectroscopic comparison sample. ^bThe quantity described is the median value of (z_SPZ − z_spec)/(1 + z_spec) for the field. ^cThe quantity described is the median value of (z_PZ − z_spec)/(1 + z_spec) for the field. ^dThis refers to the fraction of objects for which the fits are catastrophic failures, meaning $| ({z}_{\mathrm{SPZ}}-{z}_{\mathrm{spec}})/(1+{z}_{\mathrm{spec}})| \gt 0.1$.

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For FIGS objects with existing spectroscopic redshifts of the highest accuracy, we calculate the term

$$\begin{eqnarray}&&{\rm{\Delta }}{{\boldsymbol{z}}}_{\mathrm{SPZ}}=\displaystyle \frac{{z}_{\mathrm{SPZ}}-{z}_{\mathrm{spec}}}{1+{z}_{\mathrm{spec}}}.\end{eqnarray} \tag{ 2 }$$

This measures the closeness of each SPZ redshift to the true value given by the spectroscopic redshift. For comparison, we also calculate Δz_PZ for the purely photometric redshifts. The median Δz_SPZ and Δz_PZ for each field is given in Table 5, as well as the outlier rates, defined as the fraction of objects for which $| (z-{z}_{\mathrm{spec}})/(1+{z}_{\mathrm{spec}})| \gt 0.1$. We observe an improvement in Δz_SPZ over Δz_PZ from 0.03 to 0.02 in three of the four fields (see Table 5), and an improvement in the outlier rate in all four.

The distribution of redshift accuracy for the entire sample is illustrated in Figures 6 and 7, where the accuracy of a given object's redshift is measured by

$$\begin{eqnarray}&&\mathrm{log}({\rm{\Delta }}{z}_{\mathrm{SPZ}})=\mathrm{log}\left(\displaystyle \frac{| {z}_{\mathrm{SPZ}}-{z}_{\mathrm{spec}}| }{1+{z}_{\mathrm{spec}}}\right),\end{eqnarray} \tag{ 3 }$$

such that more negative results represent redshift fits closer to the spectroscopic redshift. We calculated these for the spectroscopically matched SPZ and photo-z sets, and plotted a histogram of the results in Figure 6. Values of log $\mathrm{log}({\rm{\Delta }}{{\boldsymbol{z}}}_{\mathrm{SPZ}})\leqslant -2.4$ (which implies $| {z}_{\mathrm{SPZ}}-{z}_{\mathrm{spec}}| \leqslant 0.004\,\cdot (1+{z}_{\mathrm{spec}})$) were binned together, leading to the larger number of objects seen in the highest-accuracy bin. For the whole sample, the SPZs increase the population of this most accurate bin by 52% over photometric redshifts. For F105W < 24 mag, SPZs increase it by 69%. Figure 7, which plots Δz_SPZ versus Δz_PZ, provides an alternative comparison of the results, which calls attention to the number of objects that SPZs rescue from catastrophic failure.

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The median redshift difference for SPZs is 0.023, and 0.029 for photo-zs. Use of the SPZ method increases the number of objects in the most accurate bin by ∼67%. Furthermore, one can see that the SPZ method reduces the incidence of catastrophic failure by reducing the total number of objects for which log(Δz_SPZ) > −1 from 8% to 7% across all four fields. For the subset of objects where F105W < 24 mag, the median redshift difference for SPZs is 0.021, and is 0.027 for photo-zs.

Figure 8 shows Δz_SPZ versus the spectroscopic redshift. The blue shaded region in each plot corresponds to the redshift range in which the 4000 Å break falls within the grism coverage (z = 1.025–1.875). The improvement in accuracy of SPZs over photometric redshifts in this range is comparable to that of the overall sample, and is larger only in GN2. This could indicate that the addition of grism data can be useful in constraining the SED fit even without the 4000 Å break falling in its range, either by identifying features at other redshifts (e.g., emission lines) or by conclusively ruling out the presence of a 4000 Å break where broadband data could not. This may also be explained by the blue region objects being fainter: Figure 9 shows that the majority of catastrophic failures occur beyond F105W > 24 mag. There are also considerably fewer objects in this range with high-accuracy spectroscopic redshifts compared to lower redshifts. These figures also seem to show a slight systematic offset in (z − z_spec)/(1 + z_spec): the median (z − z_spec)/(1 + z_spec) ∼ −0.01 in both SPZs and photo-zs, suggesting a tendency to slightly underestimate the redshift.This could perhaps be explained by the misidentification of the Balmer break (3646 Å) as the 4000 Å break, or the application of the magnitude prior to the redshift calculation could be causing a slight preference for lower redshifts. The results given in Table 5 reflect the median error without correcting for this bias.

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To see if there was a matching angular overdensity, we plotted the J2000.0 (R.A., decl.) positions of the objects in this peak redshift bin in a 2D histogram (Figure 11, left). This shows several points with a high concentration of objects, the peak of which has a number of sources ∼4 times the mean in GN1.

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The same process was repeated with the spectroscopic redshift data set, which shows an overdensity in the same region. To assess this overdensity, we applied a method used for the identification of a candidate cluster in Z-FOURGE (Spitler et al. 2012). We used SPZs to construct a 7th-nearest-neighbor density distribution for the z = 0.8–0.9 redshift slice in GN1 (Figure 12). This was accomplished by constructing a 500 × 500 grid of points across the whole GN1 field. For each point, the number density of nearby objects was determined by

$$\begin{eqnarray}&&n=\displaystyle \frac{N}{\pi {r}_{7}^{2}},\end{eqnarray} \tag{ 4 }$$

where r₇ is the distance from the point to its seventh-nearest neighbor and N = 7 is the number of objects in the redshift slice within the distance r₇. Once this density is calculated for each point in the field, the mean nearest-neighbor density for the slice is determined and used to scale the densities. Spitler and others have tested nearest-neighbor results for values of N ranging from 5–9, and find little change in the significance of cluster detection (Papovich et al. 2010). We performed this analysis for varying values of N as well, and find the same result (see Section 5.2).

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The coordinates and redshift of this overdensity correspond to a z = 0.85 galaxy cluster serendipitously identified with spectroscopic redshifts by Dawson et al. (2001). However, the nearest-neighbor density plot shown in Figure 12 indicates some possible substructures within the overall cluster, which is difficult to identify with the smaller spectroscopic sample alone.

Having verified the viability of the method by recovering the z = 0.85 cluster, we applied the same nearest-neighbor calculation to the rest of the FIGS data set in slices of Δz = 0.1. First, we checked the appropriateness of using N = 7 for a nearest-neighbor radius r_N by recalculating the density map for the same slice with the value of N varying from 5 to 10. For values N > 7, the overdensity is still present, though the significance is diminished with respect to the field background, peaking at 6–7 times the mean density rather than 14.3. For N < 7, the significance of the z = 0.85 cluster remains at a level comparable to N = 7, but other regions in GN1 where there is no spectroscopically confirmed overdensity increased to a significance unsupported by the spectroscopic coverage. Thus, we settled on N = 7, as it demonstrated the best confirmation of the existing overdensity.

We applied the n₇ calculation to each field in slices of Δz = 0.1 from z = 0 to z = 6 (the maximum redshift we allowed in the EAZY calculation). If a slice contained too few objects to perform the calculation, it was skipped (as was the case for many of the high-z slices). To avoid boundary misses, where an overdensity would be missed if its mean redshift were at the boundary between two Δz steps, we iterated in steps of 0.5 · Δz.

For these slices, we applied two different measures of overdensity significance. First, we normalized each point in the density grid by the median nearest-neighbor density for that redshift slice. This is superior to normalizing by the mean, since the value of the mean will be biased toward a high-density peak if one exists. For each slice, we recorded the peak median-normalized density (called ${ \mathcal M }$). This checks the significance of an overdense region relative to the density of the entire field at a given redshift range, but may underestimate significance if the angular size of the structure is large relative to the size of the whole field. For the second method, which is based on the method used by Spitler, we calculated the standard deviation in the nearest-neighbor density grids of adjacent slices (e.g., for the Δz = 0.3–0.4 slice, we take the average standard deviation of the densities in Δz = 0.2–0.3 and Δz = 0.4–0.5), and normalized the density grid by this. The peak value was recorded as ${ \mathcal S }$. For this method, ${ \mathcal S }$ was determined from the nearest redshift slices that did not overlap the Δz of the current slice.

After this broad search, we also conducted a narrower search with Δz = 0.03 · (1 + z_prev) from z = 0 to z = 4 (at higher redshift, there were too few objects per slice). This Δz was selected to match the expected redshift error as determined from our accuracy tests, while also encapsulating the velocity range of a rich cluster, so each redshift slice should contain only objects with the potential to be closely associated.

The overdensity candidates derived from both searches are summarized in Table 6, where we record any redshift slice for which ${ \mathcal M }\gt 10$ and ${ \mathcal S }\gt 10$ via either method, using as a cutoff the lowest-significance detection recorded by Spitler et al. (2012). We consulted the NASA/IPAC Extragalactic Database's list of known clusters to see if the search missed any known clusters. There were not any listed clusters in the FIGS fields that were missed.

Table 6.  Potential Overdensities Identified Through the Nearest-neighbor Method

ID	R.A.	Decl.	z1	${ \mathcal M }$ a	${ \mathcal S }$ b	z2	${{ \mathcal M }}_{2}$	${{ \mathcal S }}_{2}$	N. Galaxies
GN1-0.2	189.211302	+62.303195	0.2–0.3	11.90	47.10	⋯	⋯	⋯	43
GN1-0.3	189.148053	+62.292436	0.25–0.35	16.46	21.28	0.315–0.354	10.05	10.18	10
GN1-0.4	189.202382	+62.276415	0.4–0.5	10.54	13.68	0.435–0.478	5.89	10.30	26
GN1-0.6	189.141025	+62.290214	⋯	⋯	⋯	0.645–0.694	20.43	16.15	24
GN1-0.7	189.177515	+62.272790	⋯	⋯	⋯	0.735–0.787	17.01	18.10	29
GN1-0.8c	189.162108	+62.281327	0.8–0.9	25.16	25.09	0.825–0.880	28.23	24.41	28
GN1-1.2	189.191840	+62.281093	1.25–1.35	15.87	10.28	1.290–1.359	13.31	21.49	7
GN1-1.6	189.149675	+62.287408	1.6–1.7	10.66	21.250	1.680–1.760	7.40	12.86	13
GN1-1.9	189.203733	+62.277585	1.95–2.05	12.97	50.35	1.965–2.054	17.51	15.60	24
GN1-3.2	189.185353	+62.280742	⋯	⋯	⋯	3.21–3.336	27.43	18.41	13
GN2-0.2	189.358060	+62.290507	0.2–0.3	13.80	41.35	0.255–0.293	8.29	64.43	31
GN2-0.5	189.357597	+62.310505	0.5–0.6	10.02	11.59	0.540–0.586	5.81	12.79	16
GN2-0.9	189.376327	+62.290928	⋯	⋯	⋯	0.915–0.972	11.05	15.04	18
GS1-0.1	53.185189	−27.791704	0.1–0.2	10.76	12.91	0.105–0.138	10.67	26.33	15
GS1-0.2	53.166696	−27.787796	0.25–0.35	10.85	27.49	0.270–0.308	12.72	26.22	29
GS1-0.5	53.170932	−27.794401	0.5–0.6	12.32	10.74	⋯	⋯	⋯	23
GS1-0.7	53.161736	−27.789378	⋯	⋯	⋯	0.765–0.818	10.07	15.83	29
GS1-0.9	53.158430	−27.787889	0.9–1.0	11.52	47.80	0.900–0.957	6.04	16.14	48
GS1-1.8	53.153574	−27.777564	1.8–1.9	18.20	41.65	1.815–1.899	20.41	12.83	22
GS2-0.0	53.276137	−27.856452	0.05–0.15	48.87	160.61	0.075–0.107	100.00	378.80	17
GS2-0.1	53.275942	−27.861384	0.1–0.2	15.03	11.41	⋯	⋯	⋯	23
GS2-0.7	53.282187	−27.861471	0.7–0.8	12.11	23.68	0.780–0.833	15.59	32.57	28
GS2-1.6	53.288724	−27.859740	⋯	⋯	⋯	1.665–1.745	16.10	17.19	20
GS2-1.7	53.286967	−27.859913	1.7–1.8	11.85	14.58	1.710–1.807	13.78	13.60	19

Notes. The first set of (z, ${ \mathcal M }$, ${ \mathcal S }$) was derived from the nearest-neighbor search with Δz = 0.1. The second set was derived with Δz = 0.03 · (1 + z_prev). ${ \mathcal M }$ and ${ \mathcal S }$ are significance measures detailed in Section 5.2.

^aThis number is given by the ratio of the peak nearest-neighbor density in the redshift slice to the median density for the slice. ^bThis number is given by the ratio of the peak nearest-neighbor density in the redshift slice to the standard deviation in the densities of the adjacent redshift slices. ^cCluster confirmed in Dawson et al. (2001).

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For comparison, we also ran the systematic search using photometric redshifts with Δz = 0.03 · (1 + z_prev) from z = 0 to z = 4. The results of this comparison are summarized in Table 7. Generally, the photo-z search produced results of lower significance than the SPZ search. The photo-z search misses the ${ \mathcal M },{ \mathcal S }\gt 10$ cutoff for detection for several overdensities found by the SPZ method, and finds only two that the SPZ method does not detect (and one of these is marginal). Furthermore, the photo-z method finds the peak density for GN1-0.8 to be in the 0.870–0.926 redshift bin instead of 0.825–0.880, which we know from spectroscopic redshifts to be correct. This suggests that SPZs are better suited for accurately identifying known overdensities.

Table 7.  Overdensity Search Comparison

ID	zSPZ	${{ \mathcal M }}_{\mathrm{SPZ}}$	${{ \mathcal S }}_{\mathrm{SPZ}}$	zPZ	${{ \mathcal M }}_{\mathrm{PZ}}$	${{ \mathcal S }}_{\mathrm{PZ}}$
GN1-0.3	0.315–0.354	10.05	10.18	⋯	⋯	⋯
GN1-0.4	0.435–0.478	5.89	10.30	⋯	⋯	⋯
GN1-0.5	⋯	⋯	⋯	0.510–0.555	10.79	10.56
GN1-0.6	0.645–0.694	20.43	16.15	0.630–0.679	21.75	19.80
GN1-0.7	0.735–0.787	17.01	18.10	0.750–0.803	24.95	12.88
GN1-0.8	0.825–0.880	28.23	24.41	0.870–0.926	15.11	13.18
GN1-1.2	1.290–1.359	13.31	21.49	1.290–1.359	10.56	13.46
GN1-1.6	1.680–1.760	7.40	12.86	⋯	⋯	⋯
GN1-1.9	1.965–2.054	17.51	15.60	⋯	⋯	⋯
GN1-3.2	3.210–3.336	27.43	18.41	⋯	⋯	⋯
GN2-0.2	0.255–0.293	8.29	64.43	0.255–0.293	7.32	27.85
GN2-0.5	0.540–0.586	5.81	12.79	⋯	⋯	⋯
GN2-0.9	0.915–0.972	11.05	15.04	0.930–0.988	7.04	10.81
GS1-0.1	0.105–0.293	10.67	26.33	⋯	⋯	⋯
GS1-0.2	0.270–0.308	12.72	26.22	0.255–0.293	4.71	16.67
GS1-0.5	⋯	⋯	⋯	0.495–0.54	18.65	34.87
GS1-0.7	0.765–0.818	10.07	15.83	0.765–0.818	4.78	10.60
GS1-0.9	0.900–0.957	6.04	16.14	⋯	⋯	⋯
GS1-1.8	1.815–1.899	20.41	12.83	1.83–1.915	5.77	14.05
GS2-0.0	0.075–0.107	100.00	378.80	0.06–0.092	10.49	25.48
GS2-0.7	0.780–0.833	15.59	32.57	0.795–0.849	13.25	11.82
GS2-1.6	1.665–1.745	16.10	17.19	1.68–1.76	21.01	13.81
GS2-1.7	1.710–1.807	13.78	13.60	1.725–1.807	19.90	14.75

Note. ${ \mathcal M }$ and ${ \mathcal S }$ are significance measures detailed in Section 5.2.

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The known z = 0.85 cluster in GN1 produced peaks of ${ \mathcal M }=25.16$ and ${ \mathcal S }=25.09$ with the broad search method. We find four other slices with a more significant detection in ${ \mathcal S }$. Of these, the GS1/HUDF Δz = 1.8–1.9 slice is most significant in ${ \mathcal M }$ with ${ \mathcal M }=18.20$. The density map for this slice is shown in Figure 13.

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The location of this overdensity matches that of a z = 1.84 overdensity identified in Mei et al. (2015) through the visual inspection of G141 spectra and redshifts, and in Kochiashvili et al. (2015) by a search of NIR narrowband-selected, emission-line galaxies. Mei et al. identifies 13 candidate members of a z = 1.84 protocluster at (53.15565, −27.77930, J2000.0) at a limiting magnitude of F160W < 26 mag, as well as a number of nearby possibly associated galaxy groups at z = 1.87–1.95. This is very near to the point of peak SPZ density (53.15357, −27.77756, J2000.0) identified via the nearest-neighbor method.

This redshift slice contains 22 objects with SPZs, for three of which we have matching spectroscopic redshifts. The characteristics of these objects are summarized in Table 8, where they are grouped by FIGS redshift. Two of the three are consistent with Δz = 1.8–1.9, and the third is z = 2.067. Furthermore, in the CDFS seven Ms X-ray source catalogs (Luo et al. 2017), we were able to visually identify a number of close X-ray active sources at this redshift, most of which are spectroscopically confirmed. The SPZ overdensity, when combined with the Mei et al. overdensity detection and possible presence of X-ray sources, suggests further corroboration of the use of SPZs to identify LSS via this method. Furthermore, it opens up the possibility of using SPZ searches to identify fainter candidate cluster members in already-identified overdensities at comparable redshift (e.g., a GOODS-S but non-HUDF cluster identified in Kurk et al. 2009).

With the narrower search method, the z = 0.85 cluster achieves similar significance, with ${ \mathcal M }=28.23$ and ${ \mathcal S }=24.41$. The z = 1.84 overdensity in GS1 measures a lower but still significant detection via the ${ \mathcal S }$ method, but measures a slightly higher significance via the ${ \mathcal M }$ method. There are four other detections with a greater significance in at least one metric, including a hugely significant detection in GS2 at Δz = 0.075–0.107 (described in Table 9), and a similar number of detections at comparable significance. The GS2 detection does not appear to match any known overdensity, though it could potentially be associated with nearby diffuse X-rays at z = 0.126–0.128 (Finoguenov et al. 2015). This is also consistent with the two objects with known spectroscopic redshifts.