SHADOW OF A COLOSSUS: A z = 2.44 GALAXY PROTOCLUSTER DETECTED IN 3D Lyα FOREST TOMOGRAPHIC MAPPING OF THE COSMOS FIELD

The study of high-redshift (z > 2) galaxy protoclusters is a topic of increasing interest, providing a route to studying galaxy evolution, AGNs, plasma physics, and our models of gravity. They are also critical laboratories for understanding the growth of massive galaxy clusters at z ∼ 0. While many studies have successfully found protoclusters around active supermassive black holes such as radio galaxies or luminous quasars (see Hennawi et al. 2015 and Cooke et al. 2014 for recent examples, or Chiang et al. 2013 for a compilation), it is difficult to tell whether these "signpost" protoclusters are representative of the overall population—which, at least in simulations, shows a wide range of properties.

More uniform, "blind," search techniques are therefore required for unbiased samples of protoclusters. Several such objects have been found serendipitously in photometric or galaxy redshift surveys (e.g., Steidel et al. 2005; Gobat et al. 2011; Cucciati et al. 2014; Yuan et al. 2014; Casey et al. 2015). Searching photometric redshift catalogs (Chiang et al. 2014) is another promising new technique, but is limited to fields with extensive multi-wavelength photometry that enable accurate photometric redshfits. Unfortunately we expect protoclusters to be rare, and surveying large volumes of space with these techniques is expensive.

Recently, Stark et al. (2015b) (hereafter S15) argued that 3D tomographic reconstructions of the intergalactic medium (IGM) Lyα (Lyα) forest absorption (Pichon et al. 2001; Caucci et al. 2008; Lee et al. 2014b) can be used to efficiently search for protoclusters. A protocluster's Lyα absorption signature extends over a large region ($r\gtrsim 5\;{h}^{-1}\text{}\;\mathrm{Mpc}$) allowing it to be mapped by background galaxies separated by several transverse Mpc, corresponding to relatively bright limiting magnitudes (≲24.5 mag) and therefore accessible to existing 8–10 m class telescopes. In fact several studies have already found Lyα absorption associated with protoclusters either in single sightlines (Hennawi et al. 2015) or by stacking multiple background spectra (Cucciati et al. 2014; T. Hayashino et al. 2016, in preparation). Moderate-resolution spectra with careful sightline selection should enable 3D mapping even with modest signal-to-noise ratios (S/N).

In Lee et al. (2014a; hereafter L14b), we made the first attempt at Lyα forest tomography using a set of 24 background Lyman-break galaxy (LBG) spectra within a 5' ×  12' area in the COSMOS field. This marked the first-ever use of LBGs, instead of quasars, for Lyα forest analysis, and the resulting reconstruction at 2.20 < z < 2.45 was the first 3D map of the z > 2 universe probing Mpc-scale structures. In this paper, as part of the pilot observations for the COSMOS Lyman-Alpha Mapping And Tomography Observations (CLAMATO) survey to map the high-redshift IGM, we extend the L14b map volume by a factor of ∼2.5×. This volume starts to approach that where we expect to see protocluster candidates in a blind survey: in N-body simulations at z ∼ 2.5 the comoving number density of halo progenitors which by z = 0 have masses above ${10}^{14}\;{h}^{-1}{M}_{\odot }$ is $\sim {10}^{-5}\;{h}^{3}\;{\rm{Mpc}}{}^{-3}$, or to ${10}^{-6}\;{h}^{3}\;{\rm{Mpc}}{}^{-3}$ for the progenitors of $3\times {10}^{14}\;{h}^{-1}{M}_{\odot }$ halos (e.g., Stark et al. 2015b). In the simulations of S15, mock observations with similar sightline density and noise as CLAMATO found more than ∼75% of the protoclusters which would eventually grow to form clusters more massive than $3\times {10}^{14}\;{h}^{-1}{M}_{\odot }$ at z = 0 but only ∼20% of the protoclusters which would form ${10}^{14}\;{h}^{-1}{M}_{\odot }$ halos by z = 0. Our observations probe a volume of V = 5.8 × 10⁴ h⁻¹Mpc³ at 2.2 < z < 2.5. To the extent that these simulations are accurate, there is a ∼O(10%) chance we should find a $M\gt {10}^{14}\;{h}^{-1}\text{}{M}_{\odot }$ protocluster in the surveyed volume (see also Section 5).

Two other developments in the past year lend additional synergy: (i) the first data release of the MOSDEF survey (Kriek et al. 2015, hereafter K15), whose near-infrared (NIR) nebular line redshifts reduce systemic redshift uncertainties hence allowing a cleaner comparison with our tomographic map; and (ii) the discovery of a z = 2.45 galaxy protocluster within our target field (Diener et al. 2015; hereafter D15; Chiang et al. 2015; hereafter C15).

As we shall see, our tomographic map suggests a complex 3D multi-pronged structure for this protocluster, while also revealing other intriguing structures. We also find that galaxies co-eval with our map preferentially inhabit higher absorption regions of the IGM, suggesting that Lyα tomography does indeed probe the underlying large scale structure.

This paper is organized as follows: we describe the data in Section 2 and tomographic reconstruction of the foreground IGM in Section 3, and then describe simulations used for the subsequent analysis (Section 4). Section 5 then describes the protoclusters and overdensities found within our map volume.

In this paper, we assume a concordance flat ΛCDM cosmology, with Ω_M = 0.27, Ω_Λ = 0.73 and ${H}_{0}=70\;\text{km s}{}^{-1}\;{\mathrm{Mpc}}^{-1}$. The exact choice of cosmology does not significantly affect our resulting tomographic reconstruction, since it primarily affects the conversion of redshift and angular separation into comoving distances.

We targeted 2.3 < z < 3 galaxies and AGNs within the COSMOS field (Capak et al. 2007; Scoville et al. 2007) in order to probe the foreground IGM Lyα forest absorption at z ∼ 2.3. Top priority was given to objects with confirmed redshifts from the zCOSMOS-Deep (Lilly et al. 2007) and VUDS (Le Fèvre and Tasca 2015) spectroscopic surveys, while we also, where available, added grism redshift information kindly provided by the 3D-HST team (e.g., Brammer et al. 2012). We also selected targets based on photometric redshifts from Ilbert et al. (2009) as well as Salvato et al. (2011) for X-ray detected sources, which have ${\sigma }_{z}/(1+z)\approx 0.03$ and <10% catastrophic failure rate. This target selection process was carried out in 2014 February, prior to the publications by Diener et al. (2015) and Chiang et al. (2015) reporting galaxy overdensities in the field.

We observed these targets with the LRIS Double-Spectrograph (Oke et al. 1995; Steidel et al. 2004) on the Keck I telescope at Maunakea, Hawai'i, during 2014 March 26–27/29–30 and 2015 April 18–20, using multi-object slitmasks. We used the B600/4000 grism on the blue arm and R400/6000 grating on the red with the d560 dichroic¹¹ , although we work only with the blue spectra in this study. With our 1'' slits, this yields $R\equiv \lambda /{\rm{\Delta }}\lambda \approx 1000$, which corresponds to a line of sight FWHM of $\approx 3.2\;{h}^{-1}\text{}\;\mathrm{Mpc}$ at z ∼ 2.3. Despite inclement weather, we managed ∼15 hrs on-target, observing 7 overlapping masks with 7200–9000 s exposure times. The observations were mostly carried out in 05–1'' seeing, although one mask was observed in ≈14 seeing and consequently had a low yield of useable spectra. The data was reduced with the LowRedux package in the XIDL suite of data reduction software¹² , and objects targeted in more than one mask had their spectra co-added. We extracted 162 unique spectra, of which 58 objects had secure visual identifications at redshifts 2.3 ≲ z ≲ 3.0 and therefore Lyα forest absorption covering our desired 2.2 < z < 2.5 range, as well as adequate S/N (${\rm{S}}/{\rm{N}}\geqslant 1.3$ per $1.2\;\mathring{\rm A}$ pixel) within the Lyα forest. The majority of these sources are LBGs identified through Lyα emission or intrinsic absorption, although our sample also includes 4 QSOs, one of which is our brightest object (g = 20.12). The faintest object satisfying our S/N criterion was a g = 25.18 LBG, although this was observed in two masks; the faintest object from a single mask has g = 24.85. Table 1 summarizes the sources with useable Lyα forest for our subsequent reconstruction—"failed" sources with inadequate ${\rm{S}}/{\rm{N}}$ or unsuitable redshift will be tabulated in a future data release.

Table 1.  Background Sources for Lyα Forest Reconstruction

ID#	α (J2000)a	δ (J2000)a	g-maga	zphotob	zspec	Confidencec	Object Type	texp (s)	${\rm{S}}/{{\rm{N}}}_{\mathrm{Ly}\alpha }$ d
00852	10 00 14.773	+02 16 59.38	24.50	2.40	2.377	4	GAL	7200	2.2
00856	10 00 38.639	+02 16 33.24	24.75	2.21	2.504	3	GAL	7200	2.8
00857	10 00 22.423	+02 16 25.36	24.69	2.66	2.650	3	GAL	7200	2.1
00858	10 00 33.882	+02 16 20.42	24.28	0.22	2.747	3	GAL	7200	1.5
00863	10 00 29.392	+02 16 11.32	24.07	2.87	2.917	4	GAL	7200	1.7
00871	10 00 21.218	+02 14 54.56	24.43	2.13	2.299	3	GAL	7200	2.4
00877	10 00 29.055	+02 14 07.55	24.43	2.50	2.432	3	GAL	7200	3.4
00889	10 00 34.662	+02 13 11.17	24.35	−99.90	2.702	3	GAL	7200	1.3
00892	10 00 25.137	+02 12 56.66	23.84	2.37	2.324	4	GAL	7200	5.4
00903	10 00 28.920	+02 11 32.28	24.71	2.65	2.688	4	GAL	7200	2.1
00922	10 00 28.180	+02 09 31.43	24.00	2.85	2.828	4	GAL	7200	2.6
00941	10 00 08.566	+02 17 22.56	24.35	2.34	2.448	4	GAL	14400	2.4
00951	10 00 04.369	+02 15 33.98	23.55	2.64	2.673	4	GAL	7200	5.7
00954	10 00 07.006	+02 15 11.63	24.32	2.68	2.657	4	GAL	21600	3.6
00958	10 00 07.317	+02 14 54.71	24.20	2.89	2.894	4	GAL	7200	3.3
00959	10 00 08.925	+02 14 40.63	20.12	2.66	2.670	3	QSO	7200	45.3
00962	10 00 00.710	+02 14 29.22	24.36	2.23	2.267	4	GAL	7200	2.1
00965	09 59 58.810	+02 14 23.28	24.40	2.53	2.442	3	GAL	7200	1.7
00974	09 59 49.449	+02 13 48.47	24.25	−99.90	2.421	4	GAL	7200	1.7
00982	10 00 05.057	+02 12 45.22	24.68	2.70	2.658	3	GAL	7200	1.4
00986	09 59 58.755	+02 12 44.42	24.57	2.70	2.556	4	GAL	7200	1.5
00990	09 59 57.202	+02 12 25.38	24.35	2.65	2.458	3	GAL	7200	1.3
00994	10 00 11.034	+02 12 04.10	23.43	2.71	2.709	4	QSO	7200	9.8
01009	10 00 03.263	+02 10 07.57	24.43	2.62	2.623	4	GAL	7200	2.0
01016	10 00 05.464	+02 08 45.42	24.65	2.74	2.623	4	GAL	14400	2.6
01252	10 00 38.405	+02 21 17.17	24.73	2.55	2.556	4	GAL	7200	2.2
01260	10 00 19.050	+02 20 26.16	24.55	2.62	2.679	3	GAL	7200	1.3
01262	10 00 28.491	+02 20 15.43	24.52	2.62	2.552	4	GAL	7200	2.6
01265	10 00 15.491	+02 19 44.58	23.20	2.55	2.450	4	QSO	14400	11.9
01276	10 00 19.153	+02 18 24.66	24.77	2.71	2.679	3	GAL	7200	1.7
01324	10 00 08.708	+02 22 24.82	24.82	−99.90	2.730	3	GAL	7200	1.4
01349	10 00 05.544	+02 19 04.48	25.18	2.69	2.678	4	GAL	14400	1.9
01753	10 00 38.350	+02 22 16.43	24.39	2.52	2.458	4	GAL	7200	2.5
01754	10 00 35.431	+02 22 01.88	23.98	−99.90	2.452	4	GAL	7200	3.6
01865	10 00 24.265	+02 14 30.23	24.69	2.63	2.646	4	GAL	14400	2.9
01886	10 00 31.073	+02 12 25.92	24.26	2.32	2.305	4	GAL	7200	1.6
12505	10 00 34.449	+02 16 54.37	24.25	2.56	2.408	4	GAL	7200	2.9
12541	10 00 24.796	+02 15 30.60	24.53	2.55	2.495	4	GAL	28800	3.6
12568	10 00 40.598	+02 14 18.13	24.33	2.21	2.451	3	GAL	7200	2.5
12604	10 00 39.620	+02 13 38.82	24.17	2.51	2.437	3	GAL	7200	2.9
12619	10 00 19.420	+02 13 12.04	23.73	2.91	3.032	3	GAL	7200	4.0
12826	10 00 01.853	+02 14 47.90	24.33	2.48	2.525	3	GAL	7200	1.7
12836	10 00 11.213	+02 15 03.56	23.95	2.30	2.280	3	GAL	7200	1.8
12960	10 00 09.419	+02 10 43.10	24.38	2.38	2.434	3	GAL	7200	1.7
14925	10 00 55.638	+02 20 13.81	24.01	2.44	2.455	4	GAL	5400	1.9
15140	10 00 26.880	+02 22 21.58	24.39	2.39	2.466	4	GAL	7200	3.0
15159	10 00 22.694	+02 21 29.84	23.79	2.32	2.466	4	GAL	7200	2.1
15171	10 00 22.603	+02 20 54.64	23.64	2.26	2.274	4	GAL	14400	5.6
15175	10 00 42.836	+02 21 12.89	24.76	2.75	2.858	3	GAL	5400	1.3
15182	10 00 29.817	+02 20 55.97	24.74	2.48	2.513	3	GAL	7200	1.5
15214	10 00 27.590	+02 19 39.25	24.28	2.58	2.551	3	GAL	7200	2.7
15218	10 00 41.547	+02 19 31.40	24.26	2.64	2.614	4	GAL	12600	3.0
15230	10 00 32.128	+02 19 11.24	24.60	2.82	2.862	4	GAL	7200	1.5
15268	10 00 37.654	+02 18 02.99	24.63	2.50	2.505	3	GAL	7200	2.0
15363	09 59 56.748	+02 22 43.82	24.85	2.51	2.565	3	GAL	7200	1.3
15399	10 00 04.823	+02 21 13.07	22.24	2.66	2.689	4	QSO	14400	13.5
15473	10 00 10.334	+02 19 00.98	24.72	2.43	2.443	3	GAL	14400	1.9
15492	09 59 50.237	+02 18 27.29	23.82	2.44	2.556	4	GAL	7200	1.3

Notes.

^aSource positions and magnitudes from Capak et al. (2007). ^bPhotometric redshift estimate from Ilbert et al. (2009). ^cRedshift confidence grade, similar to that described in Lilly et al. (2007) but without fractional grades. ^dMedian per-pixel spectral ${\rm{S}}/{\rm{N}}$ within Lyα forest.

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Several example spectra are shown in Figure 1, while the source positions are shown in Figure 2. The latter also indicates the 118 × 135 footprint of our tomographic map. Within the map footprint, we have 52 background sources which translates to a projected area density of $\sim 1200\;{\mathrm{deg}}^{-2}$. An additional six sources lie just outside the footprint but will be included in the reconstruction input. The mean transverse separation between the Lyα forest sightlines probing the foreground IGM is $\langle {d}_{\perp }\rangle \approx 2.4\;{h}^{-1}\text{}\;\mathrm{Mpc}$.

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We next estimate the intrinsic continua, C, of the sources. For the quasars, we apply PCA-based mean-flux regulation (MF-PCA; e.g., Lee et al. 2012; Lee et al. 2013a). Each spectrum is fitted with a continuum template to obtain the correct shape for the intrinsic emission lines, which is further fitted with a linear function within the Lyα forest region such that it yields a mean absorption consistent with Becker et al. (2013). Since the integrated forest variance over each $\sim 400\;{h}^{-1}\text{}\;\mathrm{Mpc}$ sightline is equivalent to only ∼2% rms (e.g., Tytler et al. 2004) this technique allows automated continuum-fitting with <10% rms errors even with noisy spectra.

This technique was applied to the restframe $1041\;\mathring{\rm A} \lt \lambda \lt 1185\;\mathring{\rm A}$ Lyα forest region of the quasar spectra using templates from Pâris et al. (2011), masking intrinsic broad absorption where necessary. A similar process is applied on the galaxies, albeit assuming a fixed continuum template from Berry et al. (2012) and adopting a more generous Lyα forest range ($1040\;\mathring{\rm A} \lt \lambda \lt 1195\;\mathring{\rm A}$). We also mask $\pm 5\;\mathring{\rm A}$ around possible intrinsic absorption at N ii λ1084.0, N i λ1134.4, and C iii λ1175.7. We estimate that the continuum errors are approximately ∼10% rms for the noisiest spectra (${\rm{S}}/{\rm{N}}\sim 2$ per pixel) and improving to ∼4% rms for ${\rm{S}}/{\rm{N}}\sim 10$ spectra.

We then compute the Lyα forest fluctuations, ${\delta }_{F}$, from the observed spectral flux density, f:

$$\begin{eqnarray}&&{\delta }_{F}=\displaystyle \frac{f}{C\langle F(z)\rangle }-1,\end{eqnarray} \tag{ 1 }$$

where $\langle F(z)\rangle$ is the mean Lyα transmission from Faucher-Giguère et al. (2008) evaluated at redshift z. The δ_F values from our background sources, along with the associated pixel noise errors ${\sigma }_{N}$ estimated by the reduction pipeline, constitute a sparse sampling of the IGM Lyα forest absorption, which we will reconstruct in the next section.

For the tomographic reconstruction, we define a 3D output grid with cells of comoving size $0.5{h}^{-1}\text{}\;\mathrm{Mpc}$, spanning a transverse comoving length at z = 2.35 of $14\;{h}^{-1}\text{}\;\mathrm{Mpc}$ in the R.A. direction and $16\;{h}^{-1}\text{}\;\mathrm{Mpc}$ in decl. (Figure 2). The output grid spans $2.2\lt {z}_{\alpha }\lt 2.5$ along the line of sight, corresponding to $260\;{h}^{-1}\text{}\;\mathrm{Mpc}$ with our simplification that the comoving distance-redshift relationship is evaluated at fixed z = 2.35. The overall comoving volume is $V=14\;{h}^{-1}\text{}\;\mathrm{Mpc}\times 16\;{h}^{-1}\text{}\;\mathrm{Mpc}\times 260\;{h}^{-1}\text{}\;\mathrm{Mpc}$ $=\;58240\;{h}^{-3}\;{\mathrm{Mpc}}^{3}$ $\approx \;{(38.8{h}^{-1}\text{}\mathrm{Mpc})}^{3}$, i.e., nearly 2.5× greater volume than the L14b map, which corresponds approximately to Slices #5–7 in Figure 2.

As in L14b, we use a Wiener filtering implementation developed by S15. The reconstructed flux field on the output grid is given by

$$\begin{eqnarray}&&{\delta }_{F}^{{\rm{rec}}}={{\boldsymbol{C}}}_{\mathrm{MD}}\cdot {({{\boldsymbol{C}}}_{\mathrm{DD}}+{\boldsymbol{N}})}^{-1}\cdot {\delta }_{F},\end{eqnarray} \tag{ 2 }$$

where ${{\boldsymbol{C}}}_{\mathrm{DD}}+{\boldsymbol{N}}$ and ${{\boldsymbol{C}}}_{\mathrm{MD}}$ are the data–data and map–data covariances, respectively. We assumed a diagonal form for the noise covariance matrix ${\boldsymbol{N}}\equiv {N}_{{ii}}={\sigma }_{N,i}^{2}$, and assumed a Gaussian covariance between any two points r₁ and r₂, such that ${{\boldsymbol{C}}}_{\mathrm{DD}}={{\boldsymbol{C}}}_{\mathrm{MD}}={\boldsymbol{C}}({{\boldsymbol{r}}}_{1},{{\boldsymbol{r}}}_{2})$ and

$$\begin{eqnarray}&&{\boldsymbol{C}}({{\boldsymbol{r}}}_{1},{{\boldsymbol{r}}}_{2})={\sigma }_{F}^{2}\mathrm{exp}\left[-\displaystyle \frac{{({\rm{\Delta }}{r}_{\parallel })}^{2}}{2{L}_{\parallel }^{2}}\right]\mathrm{exp}\left[-\displaystyle \frac{{({\rm{\Delta }}{r}_{\perp })}^{2}}{2{L}_{\perp }^{2}}\right],\end{eqnarray} \tag{ 3 }$$

where ${\rm{\Delta }}{r}_{\parallel }$ and ${\rm{\Delta }}{r}_{\perp }$ are the distance between ${{\boldsymbol{r}}}_{1}$ and ${{\boldsymbol{r}}}_{2}$ along, and transverse to the line of sight, respectively. We adopt a transverse and line of sight correlation lengths of ${L}_{\perp }=\langle {d}_{\perp }\rangle \approx 2.5\;{h}^{-1}\text{}\;\mathrm{Mpc}$ and ${L}_{\parallel }=2.0\;{h}^{-1}\text{}\;\mathrm{Mpc}$, respectively, as well as a normalization of ${\sigma }_{F}^{2}=0.05$. These values are different from that adopted in L14b, but were determined by S15 to be roughly optimal for our sightline separation and were applied to their simulated maps.

The resulting tomographic reconstruction of the foreground IGM is presented in Figure 3 as a 3D visualization, while Figure 4 shows the same map as a series of 2D projections across ${\rm{\Delta }}\chi =2\;{h}^{-1}\text{}\;\mathrm{Mpc}$ along the R.A. direction; a movie of the 3D visualization can be viewed online.¹³ As in L14b, we see large overdensities and underdensities spanning $\gtrsim 10\;{h}^{-1}\text{}\;\mathrm{Mpc}$. The enlarged map volume also allows us to repeat the comparison of the map with coeval galaxies within the same volume. Using an internal compilation of spectroscopic redshifts within the COSMOS field (albeit updated from the one used in L14b), we find 61 coeval galaxies, primarily from the zCOSMOS-Deep (Lilly et al. 2007), VUDS (Le Fèvre and Tasca 2015), and MOSDEF (K15) surveys. We overplot these galaxy positions on Figure 4. These aforementioned surveys are known to be uniformly flux-limited; we momentarily leave out galaxies targeted specifically as protocluster members, which will be discussed in Section 5.

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We compare the distribution of map values at the galaxy positions with the overall map PDF in Figure 5. There is a clear skew in the absorption at the galaxies' positions toward negative ${\delta }_{F}^{{\rm{rec}}}$ values, confirming that both the tomographic map and galaxy positions sample high-density regions. A two-sample Kolgomorov–Smirnov test finds $P=1.2\times {10}^{-6}$ that the galaxy values are drawn from the overall distribution; this is a considerable improvement from the analogous comparison with 18 coeval galaxies in L14b, which had P = 0.24.

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There are several effects, however, that can introduce scatter into this comparison between galaxy positions and the large-scale IGM. Even in the absence of map reconstruction errors and with perfect redshift determinations, one expects a slight mismatch from the slightly different velocity fields traced by galaxies and the Lyα forest, which is in turn due to the different halo biases of both tracers. However, in our case we expect the primary sources of scatter to be reconstruction errors in the tomographic map, as well as line of sight positional uncertainties (${\sigma }_{v}\sim 300\;\text{km s}{}^{-1}$ or ${\sigma }_{\mathrm{los}}\sim 3.5\;{h}^{-1}\text{}\;\mathrm{Mpc}$) on the galaxies comparable to our map resolution. The latter arises from redshift errors induced by low spectral resolution (R < 200) (Lilly et al. 2007; Le Fèvre et al. 2013) as well as intrinsic scatter between the true systemic redshift compared with redshift estimates from Lyα emission or UV absorption lines (e.g., Adelberger et al. 2005; Steidel et al. 2010; Rakic et al. 2011). L14b showed using simulated reconstructions that this redshift error, along with reconstruction noise in the tomographic maps, would scatter some galaxies from overdensities into adjacent underdensities in the tomographic map.

However, galaxy redshifts measured in the NIR have much smaller redshift errors (${\sigma }_{v}\sim 60\;\text{km s}{}^{-1}$, Steidel et al. 2010) due both to the higher resolution (R ∼ 3500, Kriek et al. 2015) and the fact that rest-frame optical nebular lines are much better tracers of the systemic frame, so when we restrict the PDF comparison only to the 31 galaxies observed in the NIR by MOSDEF, we find an even stronger skew toward higher map overdensities: the MOSDEF galaxies sample a median map value of ${\delta }_{F}^{{\rm{rec}}}\approx -0.16$, whereas the other galaxies have a median of ${\delta }_{F}^{{\rm{rec}}}\approx -0.09$. This comparison is encouraging and indicates that with expanded map volumes, we will be able to study correspondingly larger samples of coeval galaxies as a function of large-scale environment, with cuts in various galaxy properties such as star formation rates, metallicities, AGN activity etc.

It is worth briefly mentioning the large regions in our tomographic map with positive ${\delta }_{F}^{{\rm{rec}}}$ (blue regions in Figure 4) that are completely empty of galaxies. These likely correspond to the high-redshift voids recently discussed in Stark et al. (2015a), but we defer a more detailed investigation to a subsequent paper.

Before we proceed to search for overdensities in the COSMOS tomographic map, we first describe the N-body simulations that we will use to facillitate our subsequent analysis, which are the same simulations as S15. These are 2560³-particle TreePM (White 2002) simulations with $8.6\times {10}^{7}\;{h}^{-1}{M}_{\odot }$ equal-mass particles within a ${(256{h}^{-1}\text{}\mathrm{Mpc})}^{3}$ comoving volume. The assumed cosmology was consistent with Planck Collaboration et al (2013): ${{\rm{\Omega }}}_{{\rm{m}}}\approx 0.31$, ${{\rm{\Omega }}}_{{\rm{b}}}{h}^{2}\approx 0.022$, h = 0.6777, n_s = 0.9611, and ${\sigma }_{8}=0.83$.

Using a friends-of-friends algorithm to identify halos, S15 found 425 halos at z = 0 with $M\geqslant {10}^{14}\;{h}^{-1}\text{}\;\mathrm{Mpc}$ that were defined as galaxy clusters. The progenitor halos for each cluster were traced backwards to z = 2.5, and their center-of-mass at that epoch defined as the corresponding z = 2.5 protocluster positions.

The velocities and particles at z = 2.5 were used to generate Lyα forest spectra with the fluctuating Gunn–Peterson approximation (Croft et al. 1998; Rorai et al. 2013). From these skewers, S15 also generated tomographic maps from realistic mock data sets with various sightline sampling and noise properties. These reconstructions used the same Wiener-filtering code described in Section 3. In this paper, we will work primarily with their simulated reconstructions with average sightline separation $\langle {d}_{\perp }\rangle =2.5\;{h}^{-1}\text{}\;\mathrm{Mpc}$ binned on to a ${(1{h}^{-1}\text{}\mathrm{Mpc})}^{3}$ grid, which were designed specifically to match the L14b data set, including the spectral resolution and ${\rm{S}}/{\rm{N}}$ distribution in the mock spectra.

Since progenitors of massive z ∼ 0 clusters occupy overdensities on ∼5–10 ${h}^{-1}\text{}\;\mathrm{Mpc}$ scales at $z\gt 2$ (Chiang et al. 2013), S15 argued that an efficient way to identify z ∼ 2.5 protoclusters in Lyα forest tomographic maps is to first smooth the map with a $\sigma =4\;{h}^{-1}\text{}\;\mathrm{Mpc}$ Gaussian kernel to obtain the smoothed flux ${\delta }_{F}^{{\rm{sm}}}$, and then identify regions with ${\delta }_{F}^{{\rm{sm}}}\lt -3.5\;{\sigma }_{{\rm{sm}}}$, where ${\sigma }_{{\rm{sm}}}^{2}$ is the map variance in the map after smoothing¹⁴ . In this paper, we opt for a more relaxed criterion of ${\delta }_{F}^{{\rm{sm}}}\lt -3\;{\sigma }_{{\rm{sm}}}$ in order to more easily identify interesting structures within our small map volume.

In Figure 6 we show the distribution of smoothed ${\delta }_{F}^{{\rm{sm}}}/{\sigma }_{{\rm{sm}}}$ values from the overall ${(256{h}^{-1}\text{}\mathrm{Mpc})}^{3}$ simulation volume (dotted-blue histogram), while the red histogram shows the minimum ${\delta }_{F}^{{\rm{sm}}}/{\sigma }_{{\rm{sm}}}$ within $4\;{h}^{-1}\text{}\;\mathrm{Mpc}$ of each of the 425 protoclusters within the simulation; the shaded histogram shows the subset of 51 protoclusters that will grow into $M\gt 3\times {10}^{14}\;{h}^{-1}\text{}\;\mathrm{Mpc}$ clusters by z = 0. This clearly shows that protoclusters occupy extreme ${\delta }_{F}^{{\rm{sm}}}/{\sigma }_{{\rm{sm}}}$ regions that are well-separated from the overall distribution.¹⁵

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S15 have shown that using a flux threshold to select protoclusters yields good purity: applying a ${\delta }_{F}^{{\rm{sm}}}\lt -3\;{\sigma }_{{\rm{sm}}}$ threshold on the simulated tomographic map with $\langle {d}_{\perp }\rangle =2.5\;{h}^{-1}\text{}\;\mathrm{Mpc}$, we found 172 candidate protoclusters of which 130 will eventually collapse into a $M\geqslant {10}^{14}\;{h}^{-1}\;{h}^{-1}\text{}{M}_{\odot }$ halo by z = 0 ($\sim 75\%$ purity); another 31 candidates ($\sim 19\%$) have group-sized descendants of $3\times {10}^{13}\;{h}^{-1}\text{}{M}_{\odot }\ \lt M(z=0)\lt {10}^{14}\;{h}^{-1}\text{}{M}_{\odot }$, while only 11 candidates ($\sim 6\%$) will evolve into a low-mass halo ($M(z=0)\ \lt 3\quad \times \quad {10}^{13}\;{h}^{-1}\text{}{M}_{\odot }$). These results are slightly lower in purity than those described in S15 due to our looser threshold.

Figure 7 shows several of the simulated protoclusters, in each case comparing three tomographic reconstructions matched to the L14b data, but with different random realizations of the sightline positions and pixel noise. The progenitors of massive clusters occupy such extended overdensities that they can be robustly detected with our sightline sampling, although at lower masses ($M(z=0)\sim {10}^{14}\;{h}^{-1}\text{}{M}_{\odot }$) the absorption signature can be less pronounced and is less likely to be selected by our criterion (e.g., bottom panel of Figure 7).

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The overall completeness of this selection criterion is ∼30% for all $M(z=0)\gt {10}^{14}\;{h}^{-1}\text{}{M}_{\odot }$ cluster progenitors (130/425), but this improves dramatically for higher-mass progenitors: we detect 48/51 protoclusters with $M(z=0)\ \gt 3\quad \times \quad {10}^{14}\;{h}^{-1}\text{}{M}_{\odot }$ (>90% completeness). The comoving space density of $M(z=0)\gt {10}^{14}\;{h}^{-1}\text{}{M}_{\odot }$ clusters is $n\approx 2.5\times {10}^{-5}\;{h}^{3}\;{\mathrm{Mpc}}^{-3}$ within our simulation, which translates to an expectation of ∼1.5 protoclusters within our present observed map volume ($V\approx 5.8\times {10}^{4}\;{h}^{-3}\;{\mathrm{Mpc}}^{3}$) with a $\sim 50\%$ detection probability through IGM tomography.

Figure 6 also shows the smoothed ${\delta }_{F}^{{\rm{sm}}}/{\sigma }_{{\rm{sm}}}$ distribution from our COSMOS tomographic map (black histogram), with both the ${\sigma }_{{\rm{sm}}}$ values derived individually for the data and simulated maps. There is some disagreement in the distributions from the data and the simulations, but the Lyα forest absorption PDF is known to be a notoriously difficult quantity to model: our simulation used a DM-only N-body code that models only gravitational clustering, but not the hydrodynamics of the IGM (White et al. 2010), nor have we attempted to accurately model systematics such as the continuum-errors, spectral noise, optically thick absorbers (e.g., Lee et al. 2015), temperature-density relationship, or Jeans smoothing (Rorai et al. 2013). For the present analysis, it is of some concern that our map PDF is somewhat larger at ${\delta }_{F}^{{\rm{sm}}}\lt -3\;{\sigma }_{{\rm{sm}}}$ than the simulated PDF, but this is likely to be due to damped Lyα absorbers (DLAs) and Lyman-limit systems (LLSs) with column densities of ${N}_{{\rm{H}}{\rm{I}}}\gtrsim {10}^{17}\;{\mathrm{cm}}^{-2}$ contaminating individual sightlines. By adding individual fake DLAs to our simulated reconstructions, we found that these could cause small regions with limited transverse extent ($\lesssim 1\;{h}^{-1}\text{}\;\mathrm{Mpc}$) to cross our protocluster threshold, but they cannot cause extended transverse IGM signatures characteristic of massive protoclusters (Figure 7), since this requires strong correlated absorption across multiple adjacent sightlines. Over the total Δ z ∼ 12 redshift path-length of our Lyα forest spectra we expect only ∼2 DLAs with ${N}_{{\rm{H}}{\rm{I}}}\gt {10}^{20.3}\;{\mathrm{cm}}^{-2}$ (Prochaska et al. 2005), which makes it very unlikely that chance alignments of DLAs could cause a spurious protocluster candidate. Careful forward-modeling of such systematics would be desirable to characterize marginal protocluster candidates in future data sets, but as we shall see we have only one protocluster candidate in our data, which is highly extended ($\gtrsim 10\;{h}^{-1}\text{}\;\mathrm{Mpc}$) in both the transverse and line of sight dimensions.

Another effect which could affect our analysis are the continuum errors in the input spectra, which unfortunately was not incorporated into the simulated recontructions. However, while continuum errors are known to strongly affect the inferred properties of the low-density Lyα forest (Lee 2012), they affect the transmission in highly absorbed regions only logarithmically. To verify this, we ran a set of mock reconstructions on a sub-volume of the simulation box with different realizations of random continuum errors (at the same level expected in our data, see Section 2), but with the same set of sightlines and pixel noise seeds held constant. We find that the random continuum errors have little effect on the detectability of protoclusters and the strength of the absorption minimum even at lower-masses ($M(z=0)\sim {10}^{14}\;{h}^{-1}\text{}{M}_{\odot }$), in contrast to the effects of random sightline sampling and pixel noise which cause much greater variations. We therefore feel it is reasonable to neglect the effect of continuum errors in our current mocks, although future efforts to characterize statistical samples of protoclusters should take this into account. Similarly, since the IGM temperature-density relationship affects primarily the low-absorption/high-transmission end of the forest (Bolton et al. 2008; Lee 2012), uncertainties should have a negligible effect on the detectability of overdensities.

S15 showed that various quantities related to the Lyα forest absorption signature of simulated z = 2.5 protoclusters can be related to their z = 0 descendant masses, although they showed this mostly as a function of the "true" Lyα absorption field in the simulation. We now carry out a similar analysis, but incorporating forward modeling by using the 130 protoclusters identified through the tomographic maps of the same simulated absorption field, which incorporate realistic random sparse sampling of the intervening sightlines as well as noise and spectral resolution matched to our data. This can then be directly compared with overdensities identified in our data (Section 5.1). In the following discussion, "protocluster candidates" refer to ${\delta }_{F}^{{\rm{sm}}}\lt -3\;{\sigma }_{{\rm{sm}}}$ regions in the $\sigma =4\;{h}^{-1}\text{}\;\mathrm{Mpc}$ Gaussian-smoothed tomographic maps. Individual protocluster candidates are defined through a $4\;{h}^{-1}\text{}\;\mathrm{Mpc}$ linking length regardless of physical continuity, so it is possible for a single candidate to be comprised of multiple disconnected structures, so long as their voxels can be linked to within $4\;{h}^{-1}\text{}\;\mathrm{Mpc}$.

Since the Lyα forest absorption is a tracer of the underlying dark matter (DM) density, it should be possible to estimate the total z ∼ 2.5 mass encompassed by IGM protocluster candidates. While a full inversion of the underlying matter density field from IGM tomographic maps is a challenging problem beyond the scope of this work (although see Nusser & Haehnelt 1999; Pichon et al. 2001; Kitaura et al. 2012), we can use our simulations for the more limited goal of estimating the z = 2.5 mass enclosed within the protocluster regions. This exploits the tight relationship found by Lee et al. (2014b) between the map flux after smoothing by $\sigma =4\;{h}^{-1}\text{}\;\mathrm{Mpc}$ Gaussian, ${\delta }_{F}^{{\rm{sm}}}$, and ${\delta }_{\mathrm{dm}4}$, the underlying DM overdensity smoothed to the same scale. Figure 8 shows this relationship from our simulation (binned in ${(1{h}^{-1}\text{}\mathrm{Mpc})}^{3}$ voxels), which can be fitted with a second-order polynomial:

$$\begin{eqnarray}&&{\delta }_{\mathrm{dm}4}\approx 5.502{({\delta }_{F}^{{\rm{sm}}})}^{2}\;{\rm{\mbox{--}}}3.681\;{\delta }_{F}^{{\rm{sm}}}+0.947.\end{eqnarray} \tag{ 4 }$$

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We then apply this mapping to the ${\delta }_{F}^{{\rm{sm}}}$ values within z = 2.5 tomographic map voxels encompassed by the ${\delta }_{F}^{{\rm{sm}}}/{\sigma }_{{\rm{sm}}}\lt -3$ protocluster contour, and then sum these DM overdensities over the protocluster candidate ("pc") region to define a raw "tomographic mass":

$$\begin{eqnarray}&&{M}_{{\rm{tomo,raw}}}=\left(\displaystyle \sum ^{{\rm{pc}}}{\delta }_{\mathrm{dm}4}\right)\times \ 8.1\times {10}^{10}{h}^{-1}\text{}{M}_{\odot },\end{eqnarray} \tag{ 5 }$$

where $M=8.1\times {10}^{10}{h}^{-1}\text{}{M}_{\odot }$ is the cosmic mean density of DM and baryons multiplied by the ${(1{h}^{-1}\text{}\mathrm{Mpc})}^{3}$ comoving volume of our map voxels. Figure 9 shows the estimated z = 2.5 raw tomographic masses for the protocluster candidates in our simulation against the "true" unsmoothed DM mass within each protocluster region. There is a reasonably tight relationship between ${M}_{{\rm{dm}}}$ and M_tomo,raw, but the latter systematically underestimates by ∼20% the true DM mass over the $\sim {10}^{13{\rm{\mbox{--}}}14}\;{h}^{-1}\text{}{M}_{\odot }$ range typical of our protocluster regions, because it was calibrated to the smoothed DM field and not the true DM field (binned in $1\;\;{h}^{-3}\;{\mathrm{Mpc}}^{3}$ cells in our simulation). Since the protocluster boundaries (defined by ${\delta }_{F}^{{\rm{sm}}}/{\sigma }_{{\rm{sm}}}\lt -3$) are still significantly overdense, the smoothing smears DM out of the protocluster regions hence causing an underestimate of protocluster mass. To get an accurate estimate of the z = 2.5 DM mass enclosed within any protocluster candidates identified in a tomographic map, we would therefore need to correct the raw tomographic masses by the power law found to fit Figure 9:

$$\begin{eqnarray}&&{M}_{{\rm{tomo}}}\approx {10}^{14.21}{\left(\displaystyle \frac{{M}_{{\rm{tomo,raw}}}}{{10}^{14}{h}^{-1}\text{}{M}_{\odot }}\right)}^{1.079}\;{h}^{-1}\text{}{M}_{\odot }.\end{eqnarray} \tag{ 6 }$$

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This is the formula we use when we henceforth refer to "tomographic masses." Since this calibration is based on the tomographic signal of an ensemble of protoclusters with realistic sightline sampling and noise, the scatter in Figure 9 provides a measure of the uncertainty in the protocluster mass estimate.

As suggested by S15, we also checked if the z = 2.5 tomographic protocluster mass could be used to predict the z = 0 descendant mass. This is shown for our simulated protocluster candidates in Figure 10, where we see a trend for increasing $M(z=0)$ with M_tomo, which can be fitted with the following power law:

$$\begin{eqnarray}&&M(z=0)\approx {10}^{14.5}{\left(\displaystyle \frac{{M}_{{\rm{tomo}}}}{{10}^{14}{h}^{-1}\text{}{M}_{\odot }}\right)}^{0.27}\;{h}^{-1}\text{}{M}_{\odot }.\end{eqnarray} \tag{ 7 }$$

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Part of the ∼0.2 dex scatter in this relationship is due to the reconstruction error in our simulated tomographic maps (since we have realistic pixel noise and sightline sampling), but S15 have also shown that the dominant contributor to this scatter is in fact intrinsic, i.e., due to diversity in the morphologies of cluster progenitors at fixed M(z = 0).

Another quantity shown by S15 to correlate with z = 0 cluster mass is the IGM absorption peak associated with the protocluster candidates in the smoothed tomographic maps. Figure 11 shows this for our simulated protocluster candidates. Again, we see a relationship between the absorption depth ${({\delta }_{F}^{{\rm{sm}}}/{\sigma }_{{\rm{sm}}})}_{{\rm{min}}}$ and the final z = 0 cluster mass, although there is more scatter than the analogous plot in S15 (Figure 5 in their paper) since we are working with realistic reconstructed tomographic maps rather than the "true" absorption field in the simulation. We fit the following function to the distribution:

$$\begin{eqnarray}&&M(z=0)\approx {10}^{13.5{\rm{\mbox{--}}}0.24{({\delta }_{F}^{{\rm{sm}}}/{\sigma }_{{\rm{sm}}})}_{\mathrm{min}}}\;{h}^{-1}\text{}{M}_{\odot }.\end{eqnarray} \tag{ 8 }$$

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This absorption depth provides an alternative to M_tomo as an estimator for $M(z=0)$, although both quantities are not completely independent.

In this section, we analyze our reconstructed Lyα forest map (Section 3) and look for IGM overdensities, aided by what we learned from the analysis of simulations in the previous section. We will then also discuss two overdensities within our volume identified from external galaxy data sets.

5.1. IGM Overdensities

5.1.1. z = 2.45 Protocluster

We now apply the protocluster-finding criterion on our COSMOS tomographic map. After smoothing by a $\sigma =4\;{h}^{-1}\text{}\;\mathrm{Mpc}$ Gaussian kernel, we find one large IGM overdensity within our map that clearly satisfies the ${\delta }_{F}^{{\rm{sm}}}\lt -3\;{\sigma }_{{\rm{sm}}}$ protocluster threshold (Figure 4). The absorption peak is at a redshift of z = 2.442 and approximately centered on [R.A., decl.] ≈ [15006, 221]. This overdensity is extended in both the line of sight and transverse dimensions: it can be seen in Figure 4 to continuously extend from $z\approx 2.435{\rm{\mbox{--}}}2.450$ (Slices #3–5), or an extent of ${\rm{\Delta }}v\approx 1300\;\text{km s}{}^{-1}$ along the line of sight, while Figure 12 shows line of sight map projections centered on the low- and high-redshift ends of this overdensity (z = 2.435 and z = 2.450), showing that it spans up to $\sim 10\;{h}^{-1}\text{}\;\mathrm{Mpc}$ ($\sim 4\;$ pMpc) in the transverse direction—the overall morphology of the protocluster in the unsmoothed map can be seen in Figure 13.

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Interestingly, the absorption minima associated with these overdensities in Figure 12 appear in between sightline positions. This appears to be a common occurence for most strong overdensities in the map, implying that most of these features are caused by strong correlated absorption across multiple adjacent sightlines within roughly one smoothing kernel, rather than absorption in individual sightlines as might be caused by a DLA. This lends additional confidence that the overdensities are not spurious features.

The total comoving volume of this protocluster candidate (defined as that within the ${\delta }_{F}^{{\rm{sm}}}\lt -3\;{\sigma }_{{\rm{sm}}}$ contour) is $V\approx 540\;{h}^{-3}\;{\mathrm{Mpc}}^{3}\approx {(8{h}^{-1}\text{}\mathrm{Mpc})}^{3}$. Assuming pure Hubble flow, we evaluate the pairwise separations between all voxels within the overdensity to find a maximum linear extent of ${L}_{{\rm{max}}}\approx 19\;{h}^{-1}\text{}\;\mathrm{Mpc}$, which subtends over thrice our effective spatial resolution element (defined as 2.35×our effective reconstruction length of $2.5\;{h}^{-1}\text{}\;\mathrm{Mpc}$). Due to line of sight velocity dispersions of ${\sigma }_{v}\quad \sim$ 200–300 $\text{km s}{}^{-1}$ in such protoclusters, ${L}_{{\rm{max}}}$ is likely overestimated by ∼10%–20%. However, it would require detailed modeling beyond the scope of this paper to estimate the true real-space size. Nevertheless, recall that our mock IGM maps (Section 4) are all in redshift-space, so our subsequent comparisons with simulated protoclusters below should be unbiased.

Applying the "tomographic mass" estimation calibrated with our simulations (Equations (4)–(6)), the total z = 2.45 DM mass enclosed within the ${\delta }_{F}^{{\rm{sm}}}/{\sigma }_{{\rm{sm}}}\lt -3$ contour is ${M}_{{\rm{dm}}}\equiv {M}_{{\rm{tomo}}}=(1.1\pm 0.6)\times {10}^{14}\;{h}^{-1}\text{}{M}_{\odot }$, where the uncertainty is estimated from the scatter seen in the ensemble of simulated protoclusters (error bars in Figure 9).

This IGM overdensity corresponds to a known object: Castignani et al. (2014) and Chiang et al. (2014) reported a protocluster candidate at z ∼ 2.4 in this region based on the presence of a radio galaxy and excess of photometric-redshift objects, which were subsequently spectroscopically confirmed by D15 who reported an overdensity of 11 LBGs at z ≈ 2.45, several of which we plot as filled squares in Figure 12. This was corroborated by a more recent spectroscopic study of Lyα emitters (LAEs) by C15, which are plotted as filled triangles in Figure 12. The position of these LBGs and LAEs at $z\approx 2.435{\rm{\mbox{--}}}2.450$ appear spatially well-correlated with our Lyα overdensity at the same redshifts.

The tomography also shows that the elongated transverse configuration of the z = 2.450 protocluster galaxies is due to two sub-structures at that redshift (Figure 12(a)) connected by a lower-density "bridge" well-sampled by our sightlines. Note that due to edge effects, it is possible that the protocluster might extend beyond our map boundary.

We now make an estimate of the descendant (z = 0) mass of this protocluster based on its IGM tomography signature at z ≈ 2.45. The tomographic mass enclosed within its ${\delta }_{F}^{{\rm{sm}}}/{\sigma }_{{\rm{sm}}}\lt -3$ boundaries implies, through Equation (7), that it will eventually collapse into a $M(z=0)=(3.0\pm 1.5)\ \times {10}^{14}\;{h}^{-1}\text{}{M}_{\odot }$ object, i.e., an intermediate-mass Virgo-like cluster. The uncertainty is, again, based on the scatter of in the simulated protoclusters (Figure 10), with which we calibrated Equation (7). The maximum smoothed absorption associated with the protocluster also provides an alternative estimate of the $z\sim 0$ masses via Equation (8). Applied to the absorption peak of ${({\delta }_{F}^{{\rm{sm}}}/{\sigma }_{{\rm{sm}}})}_{\mathrm{min}}\approx -4.0$ seen at z = 2.450, this implies $z\sim 0$ masses of $M\approx (3.0\pm 1.7)\times {10}^{14}\;{h}^{-1}\text{}{M}_{\odot }$. While these two estimates are not fully independent since ${M}_{{\rm{tomo}}}$ is calibrated through the map pixel values, it is reassuring that they give consistent results.

5.1.2. One or Two z = 0 Clusters?

From the unsmoothed tomographic map (Figures 4 or 13), the z = 2.45 IGM overdensity is comprised of several lobes along its $z\approx 2.435{\rm{\mbox{--}}}2.450$ extent, although the morphology is somewhat more continuous after applying the $4\;{h}^{-1}\text{}\;\mathrm{Mpc}$ Gaussian smoothing. From the sample of simulated protoclusters, we noticed that elongated protocluster candidates identified through the mock tomographic maps were sometimes associated with progenitors from two separate z = 0 clusters.¹⁶

Out of the 130 protoclusters identified through the tomographic reconstruction of our ${(256{h}^{-1}\text{}\mathrm{Mpc})}^{3}$ simulation volume, we find that 34 (∼25%) could in fact be associated with a secondary z = 0 cluster. Many of these "binary" protoclusters appeared elongated (e.g., middle panel in Figure 7), so we compute ${L}_{{\rm{max}}}/{V}^{1/3}$ on their ${\delta }_{F}^{{\rm{sm}}}/{\sigma }_{{\rm{sm}}}\lt -3$ boundaries as a rough measure of their elongation. This is shown in Figure 14, which compares ${L}_{{\rm{max}}}/{V}^{1/3}$ with $M(z=0)$ for both unitary and binary protocluster candidates. In the lower panels of Figure 14, we see that the binary fraction of the IGM protocluster candidates is low ($\lt 10\%$) for roughly spherical (${L}_{{\rm{max}}}/{V}^{1/3}\sim 1$) overdensities but increases with ${L}_{{\rm{max}}}/{V}^{1/3}$ and approaches $\sim 90\%$ at ${L}_{{\rm{max}}}/{V}^{1/3}\sim 2.5$, although this is somewhat affected by the small sample sizes ($\lt 10$) for such elongated protocluster candidates. Nevertheless, it is clear that protocluster candidates with highly elongated IGM morphologies are likely to evolve into two separate clusters by $z\sim 0$.

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Our z = 2.44 IGM overdensity has a maximum extent of ${L}_{{\rm{max}}}\approx 19\;{h}^{-1}\text{}\;\mathrm{Mpc}$ and an enclosed volume of $V\approx 540\;{h}^{-3}\;{\mathrm{Mpc}}^{3}$, which leads to ${L}_{{\rm{max}}}/{V}^{1/3}\sim 2.3$. From Figure 14, we see that $\sim 70\%$ of simulated protoclusters with $L/{V}^{1/3}\gt 2$ collapsed into two separate z = 0 clusters. This indicates a high probability that the IGM overdensity in our map will eventually collapse into two separate z = 0 clusters with $M(z=0)\sim {10}^{14}\;{h}^{-1}\text{}{M}_{\odot }$, possibly centered on the two lobes of the protocluster at z = 2.435 and z = 2.450.

5.1.3. Less Significant IGM Overdensities

Apart from the significant z = 2.44 IGM overdensity in our map that fulfils the protocluster criterion defined by S15, there are also several smaller "hot-spots" that can be seen in the unsmoothed map (Figures 3 and 4), none of which fulfill the ${\delta }_{F}^{{\rm{sm}}}\lt -3\;{\sigma }_{{\rm{sm}}}$ threshold due to their limited size. In Slices #4–6, there is a smaller overdensity at z ≈ 2.23 with transverse extent of $\lesssim 5\;{h}^{-1}\text{}\;\mathrm{Mpc}$ in the lower part of the map (${y}_{\mathrm{perp}}\approx 5\;{h}^{-1}\text{}\;\mathrm{Mpc}$), which appears to have several associated galaxies from zCOSMOS. This overdensity has an absorption minimum corresponding to values of ${\delta }_{F}^{{\rm{sm}}}\approx -2.4\;{\sigma }_{{\rm{sm}}}$ after smoothing and thus does not satisfy our protocluster criterion. However, as seen in Figure 6, such relatively strong overdensities could represent one of the $\sim 70\%$ of $M(z=0)\sim {10}^{14}\;{h}^{-1}\text{}{M}_{\odot }$ protoclusters that are missed by our selection criterion. Follow-up observations, especially in conjunction with a detailed analysis of the associated galaxies, could reveal more about this structure.

There are another two apparent overdensities in Slice #1 at $z\approx 2.27$ and $z\approx 2.48$ at ${y}_{\mathrm{perp}}\approx 3\;{h}^{-1}\text{}\;\mathrm{Mpc}$ and ${y}_{\mathrm{perp}}\approx 9\;{h}^{-1}\text{}\;\mathrm{Mpc}$, respectively. Neither of these overdensities (${\delta }_{F}^{{\rm{sm}}}\sim [-1.5,-1.0]\;{\sigma }_{{\rm{sm}}}$) satisfy our protocluster criterion, although this part of the map likely suffers from edge effects. A better characterization of these possible overdensities would require an extention of the map area beyond its current boundaries.

5.2. Galaxy Overdensities

Apart from the overdensity in the Lyα absorption map, we now discuss two galaxy overdensities from external data sets that fall within our map volume.

5.2.1. z = 2.30

During our comparison of the map overdensities and coeval galaxies, we noticed a compact overdensity of MOSDEF galaxies at z ≈ 2.30 centered on [R.A., decl.] = [150°06, 2°20] (pink circles in Slices #3–4 of Figure 4); the line of sight projection centered on this redshift is also shown in Figure 15(a)). This is comprised of 6 galaxies within $\approx 2\;{h}^{-1}\text{}\;\mathrm{Mpc}$ (or $\approx 1\;$ pMpc) on the sky, and a line of sight extent of ${\rm{\Delta }}z\approx 0.006$ or ${\rm{\Delta }}v\approx 560\;\text{km s}{}^{-1}$. If these galaxies fairly trace the underlying population, then within the subtended comoving volume the number density is ${\rho }_{\mathrm{gal}}\sim 0.3\;{h}^{3}\;{\mathrm{Mpc}}^{-3}$, which translates to an overdensity of ${\rho }_{\mathrm{gal}}/\langle {\rho }_{\mathrm{gal}}\rangle \sim 40$ relative to a mean number density of $\langle {\rho }_{\mathrm{gal}}\rangle \sim 7\times {10}^{-3}\;{h}^{3}\;{\mathrm{Mpc}}^{-3}$, estimated from $2\lt z\lt 3$ sources with $H\leqslant 24.5$ in the Santini et al. (2015) CANDELS/GOOD-S catalog (see Lee et al. 2013b for a similarly compact $z\sim 3.7$ overdensity). Within this structure, the quartet of galaxies at [R.A., decl.] $\approx \quad [150\buildrel{\circ}\over{.} 058,2\buildrel{\circ}\over{.} 200]$ is even more compact: with a sky footprint of $\sim 0.17\;{\mathrm{arcmin}}^{2}$ and ${\rm{\Delta }}z\approx 0.003$, this implies ${\rho }_{\mathrm{gal}}/\langle {\rho }_{\mathrm{gal}}\rangle \gtrsim 100$.

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In Figures 4 and 15(a), we do not see any large absorption decrement associated with these galaxies, although the sightline sampling could be better. These galaxies occupy map values of ${\delta }_{F}^{{\rm{rec}}}\sim -0.1$ or ${\delta }_{F}^{{\rm{sm}}}\sim -0.002$ after smoothing, therefore based on the calibration between smoothed flux and DM overdensity (Equation (4)), this suggests, at face value, that the MOSDEF galaxies occupy a region with $\rho /\bar{\rho }\sim 1$, i.e., roughly the mean density of the universe. This is consistent with the ZFOURGE distribution of $K\lt 24.8$ galaxies with photometric redshifts $2.1\lt z\lt 2.3$ (Spitler et al. 2012) in the same field, which appears to show roughly mean density at the position of these MOSDEF galaxies, although z = 2.300 is at the edge of the redshift range in the ZFOURGE map. Note that since their map is smoothed over a much larger radial window (Δz = 0.2) than the Δz ≈ 0.006 line of sight extent of the MOSDEF overdensity, the ZFOURGE map is not in conflict with the presence of the MOSDEF overdensity.

In Figure 6, we indicate the ${\delta }_{F}^{{\rm{sm}}}/{\sigma }_{{\rm{sm}}}$ value associated with this overdensity after smoothing with a $\sigma =4\;{h}^{-1}\text{}\;\mathrm{Mpc}$ Gaussian, i.e., the quantity we used to search for protoclusters. This corresponds to ${\delta }_{F}^{{\rm{sm}}}/{\sigma }_{{\rm{sm}}}\approx -0.05$, which is far from our ${\delta }_{F}^{{\rm{sm}}}/{\sigma }_{{\rm{sm}}}\lt -3.5$ protocluster threshold and at a value characteristic of typical regions of the map. In comparison with the simulations we see that none of the 425 protoclusters within the volume have such a weak absorption despite very diverse samplings of sightline and spectral ${\rm{S}}/{\rm{N}}$ across these protoclusters. In other words, even the worst-sampled protoclusters within our simulated tomographic reconstructions have stronger large-scale IGM absorption than this overdensity of galaxies. Furthermore, as can be seen in the bottom panel of Figure 7, even protoclusters that do not satisfy our ${\delta }_{F}^{{\rm{sm}}}\lt -3\;{\sigma }_{{\rm{sm}}}$ IGM detection threshold still exhibit moderate absorption over large ($\sim 10\;{h}^{-1}\text{}\;\mathrm{Mpc}$) scales which we do not see in the vicinity of these MOSDEF galaxies.

One possibility is that galaxy formation feedback has suppressed IGM opacity in the immediate vicinity of these galaxies on scales of our $\sim 2.5\;{h}^{-1}\text{}\;\mathrm{Mpc}$ effective smoothing of our tomographic reconstruction. This could a similar effect observed by Adelberger et al. (2005), who claimed a detection of elevated Lyα transmission within $\sim 0.5\;{h}^{-1}\text{}\;\mathrm{Mpc}$ of $z\sim 3$ LBGs due to galactic winds, although this effect was not seen in hydrodynamical simulations (Kollmeier et al. 2006; Viel et al. 2013), nor did subsequent observations (Steidel et al. 2010; Crighton et al. 2011) manage to reproduce this result. However, due to the compactness (mean 3D comoving separation $\sim 0.6\;{h}^{-1}\text{}\;\mathrm{Mpc}$) of this z = 2.30 galaxy overdensity it is possible that the effect of feedback has been enhanced beyond that observable in individual LBGs. Another possibility is that a hot ($T\gt {10}^{6}\;{\rm{K}}$) intra-cluster medium (ICM) has already formed from the virialization of such a compact overdensity, similar to that observed in X-rays for a z = 2.07 cluster (Gobat et al. 2011). The presence of a hot ICM would also suppress the Lyα forest absorption on scales of $\sim 1\;{h}^{-1}\text{}\;\mathrm{Mpc}$ (assuming a virial mass of $M\sim {10}^{13.5}\;{h}^{-1}\text{}{M}_{\odot }$).

It is possible that a better sampling could reveal a stronger overdensity in the immediate vicinity (within $\lesssim 1{\rm{\mbox{--}}}2$ Mpc) of this galaxy overdensity, but there is little strong absorption in the neighboring sightlines we do have, which constrains the transverse extent of the associated IGM absorption to $\lt 4\;{h}^{-1}\text{}\;\mathrm{Mpc}$ comoving, or $\lt 2\;$ Mpc physical. The lack of large-scale overdensity suggests that this association of galaxies is unlikely to grow into a massive galaxy cluster by z ∼ 0 (Chiang et al. 2013) due to the lack of available material to accrete from its large-scale environment. We demonstrate this by applying a very conservative toy galactic feedback model on our simulated tomographic maps: for all map voxels within $1.5\;{h}^{-1}\text{}\;\mathrm{Mpc}$ (approximately the virial radius of $\sim 2\times {10}^{14}\;{h}^{-1}\text{}{M}_{\odot }$ halo) of the absorption peak associated with each protocluster, we set F = 1 or δ_F = 0.25 (since we adopted $\langle F\rangle =0.8$), i.e., zero Lyα absorption, and then smooth and evaluate the absorption minimum associated with each protocluster as before. The resulting distribution is shown as the red dot-dashed histogram in Figure 6. This is shifted toward higher ${\delta }_{F}^{{\rm{sm}}}/{\sigma }_{{\rm{sm}}}$ compared to the original protocluster distribution as expected, but only by a small amount insufficient to match the low map absorption associated with the z = 2.300 MOSDEF overdensity.

While it is possible that we have been unlucky with our sightline sampling and there is in fact an extended IGM overdensity that just happened to avoid our sightlines, the current data implies that regardless of any possible effects from galactic feedback or a hot ICM on scales of $\lesssim 1\;{h}^{-1}\text{}\;\mathrm{Mpc}$, this z = 2.300 overdensity of galaxies appears unlikely to evolve into a $M\gtrsim {10}^{14}\;{h}^{-1}\text{}{M}_{\odot }$ galaxy cluster by z ∼ 0, and could instead be a precursor of a compact galaxy group (Hickson 1997). This contrasts with the similarly compact z = 3.8 LBG overdensity found by Lee et al. (2013b), in which follow-up observations revealed a large-scale LAE overdensity (Lee et al. 2014c).

5.2.2. z = 2.47

Recently, Casey et al. (2015) reported a protocluster that was initially identified as a close association of dusty star-forming galaxies (DSFGs), but was also shown to correspond to an LBG overdensity. While the reported center of this overdensity lies outside our map volume, several of the protocluster members fall just within the edge of our map boundary. Their projected transverse positions are juxtaposed with our map in Figure 15(b). Encouragingly, there is an IGM overdensity associated with these galaxies right at the edge of our map, which is sampled by two sightlines: one in the top-left corner of our map area (Figure 15(b)) and another just outside the map boundary (sightline 15175 in Figure 2). Clearly, more data would be required to carry out a detailed investigation of this structure.

In this paper, we describe Lyα forest tomographic reconstructions of the 2.2 < z < 2.5 Lyα forest from 58 background LBG and QSO spectra within a ∼12' ×  14' area of the COSMOS field, which maps the IGM large-scale structure with an effective smoothing scale of $\sim 2.5\;{h}^{-1}\text{}\;\mathrm{Mpc}$ over a comoving volume of $V\approx 5.8\times {10}^{4}\;{h}^{-3}{\mathrm{Mpc}}^{3}$.

Our main findings can be summarized as follows:

• 1.  
  We compared our map with 61 coeval galaxies with known spectroscopic redshifts from other surveys. These galaxies preferentially occupy highly absorbed regions of the map at high statistical significance; this skew is even stronger with the subsample of 31 galaxy redshifts measured with NIR nebular lines from MOSDEF (K15), which suffer less line of sight positional error that could scatter galaxies into underdense map regions. Future tomographic maps encompassing hundreds of coeval galaxies will allow an investigation of $z\sim 2{\rm{\mbox{--}}}3$ galaxies as a function of their large-scale IGM environment.
• 2.  
  After applying the smoothed flux threshold advocated by S15 for finding galaxy protoclusters on Lyα forest tomographic maps, we find one significant and extended (${L}_{{\rm{max}}}\approx 19\;{h}^{-1}\text{}\;\mathrm{Mpc}$) IGM overdensity at $z\approx 2.44$ that is associated with a galaxy protocluster reported by Diener et al. (2015) and Chiang et al. (2015). Within the $\sim 540\;{h}^{-3}\;{\mathrm{Mpc}}^{3}$ volume of this overdensity, we estimate an enclosed mass of ${M}_{{\rm{dm}}}(z=2.5)\ =(1\pm 0.6)\times {10}^{14}\;{h}^{-1}\text{}{M}_{\odot }$. In comparison with the distributions of size and IGM absorption depth of simulated protoclusters, we argue that this object will likely collapse into a $M(z=0)\approx 3\quad \times \quad {10}^{14}\;{h}^{-1}\text{}{M}_{\odot }$ cluster, although from its elongated morphology (${L}_{{\rm{max}}}/{V}^{1/3}\sim 2.3$) there is a likelihood that it will fragment into two separate clusters by $z\sim 0$. Deeper IGM tomographic observations to fully characterize the morphology of this overdensity, along with detailed modeling incorporating the associated member galaxies, could allow us better distinguish between these scenarios.
• 3.  
  Within our map volume, we note a compact overdensity of six MOSDEF galaxies at z = 2.300 within a $\sim 1\;{h}^{-1}\text{}\;\mathrm{Mpc}$ transverse radius and ${\rm{\Delta }}v\approx 600\;\text{km s}{}^{-1}$ along the line of sight. There is no large IGM overdensity associated with these galaxies; rather, they occupy a region of approximately mean absorption on scales of several Mpc. While it is possible that galaxy feedback or a hot ICM has suppressed the Lyα absorption in the immediate vicinity ($\lesssim 1\;{h}^{-1}\text{}\;\mathrm{Mpc}$) of this overdensity, the lack of an extended $r\gtrsim 5\;{h}^{-1}\text{}\;\mathrm{Mpc}$ overdensity implies that they are unlikely to grow into a massive cluster by $z\sim 0$. However, the current sightline configuration does not sample this region well, and more observations will be needed to better characterize the environment of this overdensity.

These observations were from the pilot phase of the upcoming CLAMATO survey, which is aimed at mapping the $z\sim 2{\rm{\mbox{--}}}3$ IGM across a $\sim 1\;{\mathrm{deg}}^{2}$ area of the COSMOS field. This pilot study validates the ability of Lyα forest tomographic reconstructions to study large-scale structure at these unprecedentedly high redshifts, particularly protocluster overdensities that will eventually collapse into massive galaxy clusters by $z\sim 0$. A $1\;{\mathrm{deg}}^{2}$ survey over $2.2\lt z\lt 2.5$ spanning a comoving volume of $V\sim {10}^{6}\;{h}^{-1}\text{}\;\mathrm{Mpc}$ would yield ∼8 protocluster detections with $M(z=0)\gt {10}^{14}\;{h}^{-1}\text{}{M}_{\odot }$ of which ∼3 would be progenitors of Virgo-like clusters ($M(z=0)\gtrsim 3\quad \times \quad {10}^{14}\;{h}^{-1}\text{}{M}_{\odot }$ or larger; see also S15).

Apart from identifying protoclusters with blind tomographic surveys such as CLAMATO, the insights from this paper suggest that it would also be profitable to carry out similar observations targeted at known or suspected protoclusters at $z\sim 2{\rm{\mbox{--}}}3$. Indeed, over such limited fields it could be worthwhile to pursue higher-${\rm{S}}/{\rm{N}}$ integrations on higher area-densities of background sources than we have achieved here, which would allow reconstructions on smaller scales with reduced map noise (see Lee et al. 2014b for a detailed discussion). In synergy with spectroscopic confirmation of coeval member galaxies and boosted by detailed modeling using simulations like those used here, such observations could reveal the likely assembly mechanism of individual protoclusters, which would allow workers to build up a global picture of massive cluster formation from high-redshifts to $z\sim 0$.

We are grateful to the entire COSMOS collaboration for their assistance and helpful discussions. J.F.H. acknowledges generous support from the Alexander von Humboldt foundation in the context of the Sofja Kovalevskaja Award. The Humboldt foundation is funded by the German Federal Ministry for Education and Research. The data presented herein were obtained at the W. M. Keck Observatory, which is operated as a scientific partnership among the California Institute of Technology, the University of California and the National Aeronautics and Space Administration. The Observatory was made possible by the generous financial support of the W. M. Keck Foundation. The authors also wish to recognize and acknowledge the very significant cultural role and reverence that the summit of Maunakea has always had within the indigenous Hawai'ian community. We are most fortunate to have the opportunity to conduct observations from this mountain.