DISCOVERY OF A LARGE NUMBER OF CANDIDATE PROTOCLUSTERS TRACED BY ∼15 Mpc-SCALE GALAXY OVERDENSITIES IN COSMOS

Galaxy clusters are extreme products of structure formation. They are ideal laboratories to study galaxy assembly, quenching, and sub/super-halo galaxy environments. It has become clear that to obtain a complete picture of cluster formation, we also need to find and study their progenitors at high redshifts that were still forming. In the past decade, a limited number of observations of "protoclusters" revealed some intriguing properties such as sped-up galaxy evolution (Steidel et al. 2005), abnormal metallicities (Kulas et al. 2013), and the enhancement of star-forming galaxies (Overzier et al. 2008; Hayashi et al. 2012), extreme starbursts (Capak et al. 2011), extended Lyα blobs (Matsuda et al. 2012), and active galactic nuclei (AGNs) (Lehmer et al. 2009; Martini et al. 2013). However, exactly how these clues are related to the formation of clusters as a whole is not yet understood.

Due to the low number density of cluster progenitors and the difficulties in identifying them, only ∼10 protoclusters have been discovered in "random" fields (e.g., Steidel et al. 1998, 2005; Ouchi et al. 2005; Toshikawa et al. 2012). Highly biased tracers like radio galaxies and quasars have been used to narrow down the search volume, generating another ∼10 structures (e.g., Pentericci et al. 2000; Kurk et al. 2000, 2004; Venemans et al. 2002, 2004, 2007; Galametz et al. 2010; Trainor & Steidel 2012). However, the number of cluster progenitors not traced by radio galaxies should far exceed the number that is based on AGN duty cycle arguments (West 1994). A recent compilation of structures observed to date can be found in Chiang et al. (2013).

In Chiang et al. (2013) we presented the physical properties and observational signatures of protoclusters predicted in ΛCDM models using a large set of simulated clusters drawn from the Millennium Run simulations in WMAP1 and WMAP7 cosmologies. The progenitor regions of galaxy clusters can already be identified at very high redshifts given their significant large-scale (few tens of comoving Mpc) density contrasts compared to the field. Systematic searches in future large galaxy redshift surveys are thus very promising.

Although suffering from significant redshift uncertainties, the current generation of deep and wide photometric surveys may already provide the first large and relatively unbiased sample of cluster progenitors at z ≳ 2. In this Letter, we extend our methods from Chiang et al. (2013) to the regime of moderate redshift precision to search for cluster progenitors in the 1.62 deg² COSMOS/UltraVISTA survey using photometric redshifts. The COSMOS field is being targeted by a great number of surveys, many of which are aimed at studying large-scale structure at high redshift (Silverman et al. 2009; Kovač et al. 2010; Diener et al. 2013; Kashino et al. 2013). Focusing on the correlation between galaxy properties and their environments, Scoville et al. (2013) have generated a set of galaxy density maps of this field with dynamically varying scales. Specifically for the purpose of searching for cluster progenitors, we generate an alternative set of large-scale galaxy density maps designed to maximize the contrast between cluster progenitors and the field. By comparing the data with a set of matched simulated fields incorporating galaxy selection effects and redshift uncertainties, we have identified a large sample of candidate high-redshift cluster progenitors. Our technique recovers two previously known "protoclusters" (Spitler et al. 2012; Y.-K. Chiang et al., in preparation), suggesting that the algorithm is robust. We present the positions and redshifts of the candidates, together with estimates of their present day descendant masses. We adopt a cosmology [h, Ω_m, Ω_Λ, n_s, σ₈] = [0.73, 0.25, 0.75, 1, 0.9], but note that our results are relatively insensitive to the assumed values of σ₈ and H₀ (see Chiang et al. 2013).

The Muzzin et al. (2013) galaxy catalog covers 1.62 deg² of the COSMOS/UltraVISTA field with 30 photometric bands from ultraviolet to infrared. The catalog is complete (90%) to K_s, AB = 23.4 mag. Photometric redshifts (z_phot) were computed using the code of Brammer et al. (2008). Ilbert et al. (2013) compiled an alternative COSMOS catalog (not used directly in this Letter). By comparison mainly with the zCOSMOS-bright and faint spectroscopy (Lilly et al. 2007, 2009; S. J. Lilly et al., in preparation), Scoville et al. (2013) present the estimated z_phot uncertainty of the later catalog as a function of redshift and K_s magnitude, where we obtain an estimated average z_phot uncertainty of σ_z = 0.025(1 + z) for the galaxies we will be using (K_s < 23.4; 1.5 ≲ z ≲ 3). In our analysis we will assume that this σ_z is the typical uncertainty in the distribution of the galaxies in redshift space. We will show in Section 3 that this value of σ_z indeed gives consistent overdensity distributions when comparing the observations with our simulation.

Cluster progenitors manifest themselves by having high galaxy overdensities defined as $\delta _{{\rm gal}}(\boldsymbol {x})\equiv (n_{{\rm gal}}(\boldsymbol {x})-\langle n_{{\rm gal}}\rangle)/\langle n_{{\rm gal}}\rangle$, where $n_{{\rm gal}}(\boldsymbol {x})$ is the local galaxy number density in a designated window (specified later) and 〈n_gal〉 is the mean galaxy number density over the whole field. To calculate $\delta _{{\rm gal}}(\boldsymbol {x})$, we use galaxies in the Muzzin et al. (2013) catalog with K_s, AB < 23.4. A small fraction (∼4%) of the galaxies with a broad and/or multi-modal z_phot distribution is excluded, but we note that our final results are nearly the same with or without this quality cut.

With these galaxies, we generate a three-dimensional overdensity map of the COSMOS field on a regularly spaced grid with a spacing of 1 arcmin on the sky and 0.01 in redshift. For each grid point, we calculate δ_gal in a cylindrical window with a radius r = 5 arcmin (∼15 comoving Mpc in diameter at z ∼ 2) and a redshift depth full width of l_z = σ_z = 0.025(1 + z). This window is designed to maximize the contrast between cluster progenitors and field based on the projected size of protoclusters (∼10–30 comoving Mpc at z ∼ 2) while not over-resolving the galaxy distribution in redshift due to the z_phot uncertainties.³

To quantify the relation between δ_gal(z), the overdensity, and the cluster mass at z = 0 M_{z = 0}, we use a set of simulated observations matched to the COSMOS data set. We start with the 24 1.4 × 1.4 deg² lightcones from Henriques et al. (2012) that are based on the Millennium Run simulations (Springel et al. 2005) and the Guo et al. (2011) semi-analytic model with the Bruzual & Charlot (2003) stellar population synthesis models. To match our selection of galaxies in COSMOS, we set the same K_s magnitude limit. Next, we implement the z_phot errors in a set of Monte Carlo realizations (20 realizations for each of the 24 lightcones). We shuffle the redshifts (which include the line-of-sight peculiar velocity component) of the galaxies in the simulation according to a Gaussian distribution with a σ_z similar to that of the real COSMOS sample. Since the simulated catalog contains about twice as many galaxies as the real catalog for K_s < 23.4, we further take out a random subset of the simulated galaxies in these realizations to recreate the same level of Poisson counting errors. Next, we generate δ_gal maps for each realization using the same procedure used for the real data. Because we know the locations of all clusters in the simulations, we can now calibrate the M_{z = 0}  −  δ_gal(z) relation. We extract δ_gal distributions for the whole volume and for clusters in three mass bins ("Fornax-" type: M_{z = 0} = 1–3 × 10¹⁴ M_☉, "Virgo-" type: M_{z = 0} = 3–10 × 10¹⁴ M_☉ and "Coma-" type: M_{z = 0} > 10¹⁵ M_☉), allowing us to characterize regions in the COSMOS field according to their overdensities.

3.1. The Large-scale Density Field in COSMOS/UltraVISTA

Figure 1 shows, with filled histograms (yellow), the probability distributions of δ_gal for COSMOS at three redshifts (z = 1.8, 2.3, and 2.8), with δ_gal defined as in Section 2. Only data in the central 1.2 × 1.0 deg² region of the field are used to avoid the incompleteness at the edges. The shape of the δ_gal distribution is close to Gaussian with a high δ_gal tail. Even with the large smoothing scale of ∼15 comoving Mpc and moderate redshift projections, the high tails of δ_gal (thus, the departure from Gaussian distribution) are clearly seen, suggesting that structure growth at this scale has evolved toward the nonlinear regime expected for forming galaxy clusters.

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To compare the real data with our matched simulated observations, we overplot in Figure 1 the δ_gal distributions of the simulation (whole volume, including fields and clusters). The δ_gal distributions of the observation (yellow) and simulation (black) match very well,⁴ indicating that the overall large-scale galaxy clustering probed by the COSMOS data is consistent with our ΛCDM models. This also suggests that our matched simulation recreates the main observational effects and bias successfully. The δ_gal distribution of cluster progenitors in the simulation are shown as unfilled histograms in Figure 1 for three present day cluster mass bins. The mean δ_gal for each mass bin is ∼0.25, ∼0.5, and ∼0.8–1.0 for "Fornax," "Virgo," and "Coma" protoclusters respectively. The center of the cluster progenitors in the simulation is defined by the K_s band flux weighted average positions of the member galaxies. In general, the progenitors of higher mass clusters show higher δ_gal but there is a certain degree of overlap due mainly to the redshift uncertainties and sub-dominant effects such as the intrinsic scatters of the M_{z = 0}–δ_gal(z) relation and Poisson errors.

To further examine how well our matched simulation fits the data, we show zoom-in regions of the high δ_gal tails in Figure 1. The high δ_gal tails of the simulation and observation match remarkably well, especially for the z ∼ 1.8 and 2.3 bins. This indicates that the simulation is a good approximation of the observation and that our interpretation of the observed overdensities will be nearly unbiased.⁵

We present, in Figure 2, the δ_gal maps for a selection of redshift slices in the COSMOS field. Each slice has a redshift width of 0.025(1 + z) and shows a variety of cosmic structures from voids (blue), filaments (green), to overdense peaks (red). The regions in red have a δ_gal well in the high tail regime of the δ_gal distribution (Figure 1) where we expect to find cluster progenitors. We note that our maps are consistent with Scoville et al. (2013) but differ in the fact that we tend to preserve the large protocluster scale overdensities instead of breaking them up into multiple sub-structures.

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3.2. Progenitors of Galaxy Clusters in COSMOS/UltraVISTA

By utilizing the fact that progenitors of structures with higher present day mass will, on average, have a higher δ_gal (Figure 1), we can select protoclusters in the COSMOS/UltraVISTA field by selecting regions with the highest δ_gal. However, not all regions with a high δ_gal will be cluster progenitors due to the significant overlap of the δ_gal distributions between the field and clusters. Also, lower mass structures are much more abundant, which contaminate the high δ_gal regions. This is difficult to see from Figure 1 where the δ_gal distributions are normalized. We have quantified this effect in Figure 3, where we derive the probabilities for a region with a given δ_gal to be non-protocluster (light purple) or a protocluster in any of the three mass ranges (dark purple). This analysis was performed by calculating δ_gal at a large number of random positions in the simulated volume, which is ∼24 times larger than the COSMOS field. Any region with >15% of the galaxies in the cylindrical window which will evolve to a present day cluster was considered to be a "protocluster region".⁶ Figure 3 quantifies the δ_gal cut required to reach a certain confidence level for cluster progenitor identification. We use P_pc and P_Coma to specify the probabilities for a structure to be the progenitor of at least a genuine cluster (M_{z = 0} > 10¹⁴ M_☉) and of a "Coma-" like protocluster (M_{z = 0} > 10¹⁵ M_☉), respectively.

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We can now select protocluster candidates using the following criteria: (1) δ_gal > 〈δ_gal, Coma〉, where 〈δ_gal, Coma〉 is the mean overdensity of "Coma" protoclusters, (2) P_pc ≳ 0.6, and (3) visual inspections, requiring that the structures have a fairly smooth overdensity profile on the sky and along the redshift axis, and filament-like structures are excluded. The structures shown in Figure 2 are among the most robust candidates. In total, we obtain 36 protocluster candidates in the central 1.2 × 1.0 deg² of the COSMOS/UltraVISTA field at 1.6 < z < 3.1. The candidate list and the derived probabilities are summarized in Table 1. Their estimated positions are based on the local maximums of the smoothed density field, which are accurate to σ_R.A. ∼ σ_Decl. ∼ 1–3 arcmin and σ_z ∼ 0.02–0.07. These structures typically have P_pc ∼ 70% and P_Coma ∼ 10%. These probabilities were evaluated in exactly the same way as for Figure 3, but at the redshift of each individual structure.

Table 1. Protocluster Candidates

ID	z	R.A.	Decl.	δgala	Ppcb	PComac	z2ndd
1	1.62	149.593	1.89	1.83$^{+0.32}_{-0.29}$	0.66	0.05
2	1.73	150.093	2.207	1.23$^{+0.29}_{-0.25}$	0.59	0.08	1.78
3	1.74	150.343	2.407	1.1$^{+0.27}_{-0.24}$	0.54	0.06
4	1.87	149.893	1.907	1.27$^{+0.31}_{-0.27}$	0.66	0.12
5	1.94	150.043	2.174	1.25$^{+0.32}_{-0.28}$	0.66	0.12	1.90
6	2.07	149.709	2.007	1.59$^{+0.40}_{-0.34}$	0.82	0.15
7	2.07	150.126	2.24	1.37$^{+0.39}_{-0.33}$	0.73	0.13		e
8	2.20	149.609	1.774	1.37$^{+0.44}_{-0.37}$	0.74	0.11
9	2.21	149.843	1.807	1.34$^{+0.45}_{-0.38}$	0.72	0.1
10	2.23	150.326	1.89	1.33$^{+0.45}_{-0.38}$	0.71	0.09	2.27
11	2.24	149.676	2.007	1.95$^{+0.50}_{-0.43}$	0.85	0.18
12	2.26	149.859	1.94	1.49$^{+0.47}_{-0.39}$	0.75	0.1
13	2.36	150.693	2.19	1.24$^{+0.47}_{-0.39}$	0.66	0.06
14	2.37	149.643	1.974	1.49$^{+0.50}_{-0.42}$	0.72	0.07	2.41
15	2.38	150.209	1.707	1.17$^{+0.46}_{-0.38}$	0.63	0.05	2.42
16	2.39	150.476	2.657	1.25$^{+0.48}_{-0.39}$	0.65	0.05
17	2.42	149.809	2.124	1.91$^{+0.52}_{-0.44}$	0.79	0.1
18	2.44	149.643	2.674	1.18$^{+0.46}_{-0.38}$	0.63	0.04
19	2.45	150.076	2.274	1.34$^{+0.49}_{-0.40}$	0.67	0.05		f
20	2.48	149.576	1.957	2.08$^{+0.54}_{-0.46}$	0.81	0.11	2.53
21	2.53	150.293	2.324	1.86$^{+0.52}_{-0.44}$	0.78	0.1	$_{2.47}^{2.60}$	g
22	2.61	149.509	1.907	1.56$^{+0.52}_{-0.43}$	0.71	0.08
23	2.62	150.359	2.674	1.66$^{+0.53}_{-0.44}$	0.74	0.09
24	2.64	150.576	2.674	1.36$^{+0.50}_{-0.41}$	0.67	0.06
25	2.68	150.009	2.207	1.2$^{+0.50}_{-0.41}$	0.63	0.05
26	2.69	150.343	2.557	1.6$^{+0.54}_{-0.45}$	0.71	0.08
27	2.72	149.626	2.324	1.53$^{+0.55}_{-0.45}$	0.7	0.07
28	2.74	149.526	1.907	2.22$^{+0.63}_{-0.53}$	0.82	0.14
29	2.74	150.309	2.507	1.82$^{+0.59}_{-0.48}$	0.76	0.1	2.77
30	2.77	150.009	1.974	1.35$^{+0.56}_{-0.45}$	0.66	0.05
31	2.81	150.343	2.64	1.93$^{+0.65}_{-0.53}$	0.77	0.1	2.83
32	3.01	149.943	1.774	2.37$^{+0.99}_{-0.77}$	0.79	0.11
33	3.02	150.276	2.324	2.5$^{+1.03}_{-0.79}$	0.81	0.11
34	3.04	149.709	1.907	2.28$^{+1.04}_{-0.79}$	0.78	0.1
35	3.04	149.909	2.007	2.28$^{+1.04}_{-0.79}$	0.78	0.1
36	3.08	150.293	2.507	3.1$^{+1.25}_{-0.96}$	0.85	0.13

Notes. ^aGalaxy overdensity calculated in a cylindrical window with r = 5' and a redshift depth of 0.025(1 + z). ^bProbability of the structure being a protocluster with M_{z = 0} > 10¹⁴ M_☉ given its δ_gal and redshift. P_pc corresponds to the sum of the probabilities of all three cluster mass bins in Figure 3. ^cProbability of the structure being a "Coma-type" protocluster with M_{z = 0} > 10¹⁵ M_☉ given its δ_gal and redshift. ^dRedshift of its secondary density peak if present. ^eZ-FOURGE protocluster (z = 2.09; Spitler et al. 2012). ^fHPS protocluster (z = 2.44; Y.-K. Chiang et al., in preparation). ^gThe signal might be from a line-of-sight filament or multiple structures.

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As shown in Figure 2, these candidates show strong galaxy clustering at the scales of ∼10–20 arcmin (∼15–30 comoving Mpc). We do not resolve the extension along the line of sight due to the z_phot errors. In general, structures with redshift separated by σ_z ≫ 0.025(1 + z) are expected to be physically uncorrelated, which should be the case for the candidates listed. However, line-of-sight filaments cannot be completely excluded (e.g., see PC21). Given the z_phot uncertainties, a significant fraction of the tracer galaxies of these protocluster candidates are likely to be fore- and background interlopers. By examining the regions selected by similar criteria in our matched simulation, we found that ∼15%–40% of the photometric redshift galaxy candidates are expected to be true protocluster members that will merge into a cluster-scale halo by z = 0.

Although our technique was specifically designed to find cluster progenitors in the presence of appreciable errors in photometric redshift, until we have spectroscopic confirmation we will consider the targets (Table 1) as (strong) candidates of forming clusters. However, two of our candidates have already been independently confirmed by other surveys, suggesting that our finder is robust. The first candidate, PC07 (z ∼ 2.07), coincides with a structure discovered by Spitler et al. (2012) in a deep medium-band photometric survey. They found a large number of galaxies in three adjacent clumps of 5 comoving Mpc (diameter), for which spectroscopic follow-up gave a more precise redshift of 2.09. They identified this structure as the progenitor region of a massive cluster. The second candidate, PC19 (z ∼ 2.45), coincides with a large overdensity of Lyα emitters (LAEs) discovered as part of the HETDEX Pilot Survey (HPS; Adams et al. 2011). This particular structure contains nine bright LAEs in a concentrated peak at z ∼ 2.44, and is also consistent with the properties expected for a forming, massive cluster (Y.-K. Chiang et al., in preparation).

Based on Figure 3, we can estimate the purity of our cluster progenitor finding algorithm by computing the average probability for a structure to be a protocluster. For δ_gal > 〈δ_gal, Coma〉, we get a level of purity ∼70%. This purity can be found in another way from our sample of 36 protocluster candidates listed in Table 1. The sum of all P_pc and P_Coma is ∼26 and ∼3, respectively, which is the number of true cluster progenitors ("Coma-" type progenitors) expected if a follow-up spectroscopic campaign is performed. The estimated purity from the sample is again ∼26/36 = 〈P_pc〉 ∼ 70%.

We can also estimate the completeness from Figure 1 by calculating the probability for a cluster progenitor to have δ_gal above the threshold we set (δ_gal > 〈δ_gal, Coma〉). We then get a level of 9%, 7%, 17%, and 50% completeness for all cluster progenitors, "Fornax-," "Virgo-," and "Coma-" type protoclusters, respectively. These numbers are consistent with our sample of 36 candidates and 26 (three) true protoclusters ("proto-Comas"): the total comoving volume probed is ∼2.2 × 10⁷ Mpc³ for the central 1.2 × 1.0 deg² region of the COSMOS field at 1.6 < z < 3.1. Scaled from the cluster abundance in the Millennium Simulation, we expect a total ∼290 protoclusters in this volume, which can be further broken down to ∼240 "Fornax-," ∼55 "Virgo-," and ∼5 "Coma-" types, respectively. The number of 26 (three) true protoclusters ("proto-Coma") that we found are in good agreement with these numbers when we take into account the completeness. There is a strong trade-off between the purity and completeness. In our case, it is mainly the photometric redshifts that blend the δ_gal distributions.

A closer look at Figure 2 and Table 1 shows that there appear to be multiple structures in the south-west corner of the field at different redshifts. However, they are separated by underdense regions along the line of sight with separations of ≫100 comoving Mpc, suggesting that they are physically uncorrelated. By examining the existing catalog of X-ray structures in this field (Finoguenov et al. 2007), we have excluded the possibility that lensing magnification by nearby clusters is responsible for boosting the high-redshift number counts (i.e., Ford et al. 2013).

We note that our analysis of the ∼15 comoving Mpc-scale clustering is solely designed for identifying cluster progenitor structures as a whole and does not necessarily imply the presence of any specific environmental impacts on such scales. However, future studies of the interplay between galaxy properties and environment will benefit from having a large systematic sample of cluster progenitors such as the one presented here.

This work successfully generates a large sample of strong candidates of cluster progenitors in COSMOS, providing a rich set of targets suitable for spectroscopic follow-up that will allow detailed studies of their galaxy properties. Many of our candidates in the central regions of the field may soon be confirmed by spectroscopic redshifts from the zCOSMOS-faint survey (S. J. Lilly et al., in preparation), or with Very Large Telescope/KMOS observations planned in the COSMOS field. It is also possible that these dense protocluster regions will show up in planned studies that will use background quasars and bright Lyman break galaxies to perform Lyα forest tomographic mapping (Lee et al. 2013). Our methods applied to COSMOS can be tuned to search for cluster progenitors with the upcoming spectroscopic/photometric redshift surveys such as HETDEX, the Dark Energy Survey, and the Subaru Hyper Suprime-Cam and Prime Focus Spectrograph surveys. The much larger volumes and various cosmic epochs probed by these surveys will open up a statistical and multi-dimensional (e.g., mass and redshift) window that will allow a deeper understanding of the (early) formation of galaxies, gas, and dark matter in the most extreme cosmic structures.

We thank Edward Robinson and John Silverman for helpful discussions and Adam Muzzin for compiling the COSMOS/UltraVISTA galaxy catalog, which includes datasets from Martin et al. (2005), Capak et al. (2007), McCracken et al. (2012), and Sanders et al. (2007). The Millennium Simulation databases used were constructed as part of the activities of the German Astrophysical Virtual Observatory (GAVO).