Observational Evidence for Large-scale Gas Heating in a Galaxy Protocluster at z = 2.30

The possible presence of a protocluster at z = 2.30 in the COSMOS field was first noted as a compact overdensity of galaxies by Lee et al. (2016), along with the unusually high Lyα transmission given the overdensity. However, no detailed analysis was carried out.

The protocluster was subsequently confirmed by Ata et al. (2022). In this study, they applied the techniques of density reconstructions and constrained simulations to existing large-scale spectroscopic surveys that have targeted galaxies at the z ∼ 2–3 epoch in the COSMOS field (e.g., zCOSMOS, VUDS, MOSFIRE; Lilly et al. 2007; Kriek et al. 2015; Le Fèvre et al. 2015). First, in Ata et al. (2021), the COSMIC-BIRTH hybrid Monte Carlo density reconstruction algorithm (Kitaura et al. 2021) was applied to estimate the underlying density field and corresponding initial density fluctuations (at z = 100) that would eventually evolve to provide the best match for the 2.0 < z < 2.5 spectroscopic galaxy distribution over the central ∼1 deg² of COSMOS. This technique computes the Bayesian posterior probability of the possible initial conditions, thus sampling the uncertainties inherent in the observational data. A subset of the initial condition realizations was used to seed numerical N-body "constrained" simulations (dubbed the "COSTCO" suite; Ata et al. 2022) that were run to z = 0 to track the gravitational evolution of the density field traced by the observed galaxies. They then identified galaxy clusters with M > 2 × 10¹⁴ h⁻¹ M_⊙ in the z = 0 simulation snapshot, which were then matched to observed structures at 2.0 <z < 2.5. This study confirmed several previously known protoclusters in COSMOS, such the ZFIRE protocluster at z = 2.095 (Nanayakkara et al. 2016) and the "Hyperion" proto-supercluster at z ≈ 2.45–2.50 (Cucciati et al. 2018). In addition to these, a number of new protoclusters were also discovered.

COSTCO J100026.4+020940 (hereafter COSTCO-I), located at R.A. = 150110 ± 0042, decl. = 2161 ± 0040 and z =2.298 ± 0.007, was one of the strongest detections (at 8.7σ significance) among these newly discovered protoclusters. The final mass was estimated to be M(z = 0) = (4.6 ± 2.2) ×10¹⁴ h⁻¹ M_⊙. While Ata et al. (2022) did not further examine COSTCO-I in detail, we searched the spectroscopic redshift catalog compiled by Momose et al. (2022) and identified member galaxies of COSTCO-I. Since the position of COSTCO-I varies among the realizations, we adopted the following approach to obtain a robust choice of core members. First, we used the position of COSTCO-I reported by Ata et al. (2022) as an initial guess for the protocluster center and selected galaxies within a 6 h⁻¹ Mpc transverse radius and line-of-sight (LOS) velocity window of ∣Δv∣ < 600 km s⁻¹. Then, we iteratively recalculated the protocluster center as the median position of the member galaxies and repeated the member selection until convergence. With this method, we found seven galaxies in the vicinity of COSTCO-I. Note that these galaxies are merely the putative collapsed core; the full Lagrangian extent that would eventually collapse into the z = 0 cluster occupies a larger extent than this. Of these core galaxies, the most massive galaxy has a stellar mass of M_* = 5.6 × 10¹⁰ M_⊙. These galaxies are shown in Figure 1, which is an interactive figure that can be viewed online and has also been uploaded to Zenodo.

After identifying the protocluster core, we estimated the group mass, M_V , in order to set the upper limit to the extent of the intragroup or intracluster medium (ICM) that could already be present at z = 2.30. We used the virial theorem approach outlined by Girardi et al. (1998),

$$\begin{eqnarray}&&{M}_{V}=\displaystyle \frac{3\pi }{2}\displaystyle \frac{{\sigma }_{p}^{2}{R}_{p}}{G},\end{eqnarray} \tag{ 3 }$$

where G is the gravitational constant, and R_p = 0.577 pMpc and σ_p = 361 km s⁻¹ are the projected radius and LOS velocity dispersion, respectively, as defined in Girardi et al. (1998). This yielded a core virial mass of M_V = 8.2 × 10¹³ M_⊙. This estimate assumed that the protocluster core is already virialized, which would set an upper limit on the amount of hot intragroup gas that might be present; if these galaxies did not form a virialized halo, the amount of extended hot gas would be significantly less. We also cannot discount the possibility of the velocity spread being caused by the galaxies being lined up in a filament along the LOS over several megaparsecs. However, since the COSMOS-BIRTH density reconstruction technique takes peculiar velocities into account, both possibilities (lack of virialization or an LOS filament) are in principle included in the posterior results. In other words, we are confident that COSTCO-I will collapse into a cluster regardless of whether our estimate of the core properties is accurate.

For this analysis, we also had in hand the z = 2.30 matter overdensity field, ${\delta }_{m}=\rho /\bar{\rho }-1$, where ρ is the matter density, from 57 constrained realizations of the COSTCO N-body simulation suite that was designed to match the observed COSMOS galaxy distribution. These simulation outputs have a box size of L_box = 512 h⁻¹ Mpc and are binned in 256³ grid cells, covering the COSMOS volume in the redshift range 2.00 < z < 2.52. The second panel of Figure 2 shows the matter density contrast from one realization of COSTCO in the vicinity of the COSTCO-I protocluster. Note that the barycenter of COSTCO-I in this particular COSTCO realization shown in Figure 2 is slightly offset from the reported position by Ata et al. (2022), which comes from averaging over all of the realizations in the COSTCO suite. This illustrates the fact that the ensemble of COSTCO realizations represents a posterior sample encapsulating our uncertainties regarding the protocluster masses and positions.

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We now briefly describe the Lyα forest absorption maps that we used to study the large-scale gas in the COSTCO-I protocluster, which is from the CLAMATO survey (Lee et al. 2014, 2018; Horowitz et al. 2022).

The CLAMATO survey was a spectroscopic survey that targeted z ∼ 2–3 UV-bright background sources that probe the Lyα forest in the COSMOS field using the LRIS spectrograph on the Keck I telescope. For the first time, star-forming galaxies were also systematically targeted as background sources in addition to the traditional quasars. This enabled a high density of Lyα forest sight lines on the sky (857 deg⁻²), which yielded a mean transverse separation of 2.35 h⁻¹ Mpc over a footprint of ∼0.2 deg² in the center of the COSMOS field.

The raw spectra were reduced, and then the unabsorbed continuum C was estimated using the mean flux regulation technique (Lee 2012). After selecting spectra with a continuum-to-noise ratio (C/N) criterion 〈C/N〉 ≥ 1.2, the final sample for 3D reconstruction comprised 320 galaxies and quasars in total. For each spectral pixel in the rest frame 1041 Å < λ < 1185 Å, the Lyα transmitted flux is defined as

$$\begin{eqnarray}&&{\delta }_{F}=\displaystyle \frac{f}{C\langle F\rangle (z)}-1,\end{eqnarray} \tag{ 4 }$$

where 〈F〉(z) is the average transmission at a given redshift z. The processed pixel data were mapped to a comoving volume covering 34 h⁻¹ Mpc × 28 h⁻¹ Mpc × 438 h⁻¹ Mpc along the R.A., decl., and LOS dimensions, respectively.

The Wiener filtering algorithm dachshund (Stark et al. 2015a) was then applied on the pixel data to create a reconstructed map of the 3D Lyα absorption ${\delta }_{F}^{{\rm{w}}}$ in the redshift range 2.05 < z < 2.55. The correlation lengths adopted for this reconstruction are L_⊥ = 2.5 and L_∥ = 2.0 h⁻¹ Mpc in the transverse and LOS dimensions, respectively.

Note that as part of their CLAMATO data release, Horowitz et al. (2022) also reconstructed the underlying 3D matter density field using a different constrained realization method (Horowitz et al. 2021) from COSTCO. However, this used a combination of coeval galaxy positions in addition to the Lyα absorption as its input, assuming an FGPA-type relationship. Since we would like to use only the Lyα forest transmission for this analysis, we will use the Wiener-filtered Lyα map instead of the matter density map. The 3D contours in Figure 1 indicate the Lyα absorption in the vicinity of COSTCO-I. It is clear that the region in the vicinity of COSTCO-I exhibits only average absorption (${\delta }_{F}^{{\rm{w}}}\sim 0$) instead of the strong absorption expected of a protocluster (Stark et al. 2015a; Qezlou et al. 2022).

We use 57 COSTCO realizations at the z = 2.3 snapshot to generate the mock IGM tomography data that are matched to CLAMATO observational properties. To convert the real-space matter density of COSTCO into redshift-space transmission F_sim, we make use of the FGPA relation (Equation (2)). In our calculation, we adopt the widely used value β = 1.6 (e.g., Kooistra et al. 2022a). Note that the τ value here is extracted from real space; to be consistent with the observations, we shift the τ to the redshift-space value τ_red and then compute the Lyα transmission in redshift space from

$$\begin{eqnarray}&&{F}_{\mathrm{sim}}=\exp (-{\tau }_{\mathrm{red}}).\end{eqnarray} \tag{ 5 }$$

As the proportional coefficient of the FGPA relation (Equation (2)) is yet to be determined, we keep it as an unknown and solve its value by setting a mean transmission value (Becker et al. 2013),

$$\begin{eqnarray}&&\langle {F}_{\mathrm{sim}}\rangle =\langle F{\rangle }_{z=2.30}=0.8447.\end{eqnarray} \tag{ 6 }$$

Note that the resolution of the simulations is relatively coarse, with a grid of 2 h⁻¹ Mpc. Therefore, the resulting FGPA transmission sight lines cannot be expected to accurately reproduce the small-scale statistics of the Lyα forest. However, the Appendix of Horowitz et al. (2021) shows that even such a coarse grid resolution should suffice to recover the structures of the cosmic web on scales of ∼2 h⁻¹ Mpc. We therefore do not expect the low resolution of the COSTCO suite to significantly affect our analysis.

With the simulated FGPA transmission field F_sim from the COSTCO suite in hand, we proceeded to generate mock skewers that reproduce the observational properties of CLAMATO as closely as possible through the following steps.

• 1.  
  We extract noiseless 1D F_sim sight lines at the [x, y, z] positions probed by the CLAMATO sight lines. This process incorporates the positions of the CLAMATO sight lines in the plane of the sky, as well the finite lengths of the segments along each LOS based on the redshift of the background sources. We also applied the pixel masks that were used to mask metal-line absorption in the CLAMATO spectra.
• 2.  
  Continuum errors were introduced using the process described by Krolewski et al. (2017). This assumed that the continuum estimation process results in 10% fluctuations in the observed transmission, i.e.,

  $$\begin{eqnarray}&&{F}_{\mathrm{obs}}=\displaystyle \frac{{F}_{\mathrm{sim}}}{1+{\delta }_{\mathrm{cont}}},\end{eqnarray} \tag{ 7 }$$

  where δ_cont is a Gaussian random deviate with a mean value of zero and standard deviation of 0.1.
• 3.  
  Random pixel noise was added based on the signal-to-noise ratio (S/N) estimated for each individual CLAMATO sight line. This resulted in a final transmitted flux of

  $$\begin{eqnarray}&&F={F}_{\mathrm{obs}}+{N}_{\mathrm{obs}},\end{eqnarray} \tag{ 8 }$$

  where the Gaussian random deviate N_obs (with standard deviation σ = F/S/N) is the noise term. Finally, we obtained δ_F = F/〈F〉 − 1 and computed the noise σ_F from the S/N value of each sight line.

For each COSTCO realization, we repeated the final noise-addition step 20 times with different noise seeds to enhance the size of our mock sample. As a result, we have 57 × 20 = 1140 sets of mock skewers with identical spatial sampling and S/N properties as CLAMATO that were all designed to be consistent with the galaxy density field observed in the COSMOS field. We dub this the COSTCO-FGPA sample. We compiled the pixel positions, δ_F and σ_F , and fed them into dachshund, as was done with the real CLAMATO data. In the Wiener reconstruction, we kept the correlation lengths, L_∥ = 2 and L_⊥ = 2.5 h⁻¹ Mpc, the same as that of CLAMATO. In the Appendix, we compare the overall properties of COSTCO-FGPA with the real CLAMATO data.

The output of these mock reconstructions, ${\delta }_{F}^{{\rm{w}}}$, thus constitutes our null hypothesis; based on our knowledge of the COSTCO-I protocluster from the observed galaxy distribution, the COSTCO-FGPA mock data represent what we expect to see if the associated Lyα forest follows the FGPA. Moreover, the ensemble of 1140 mock realizations represents all of our uncertainties regarding the protocluster properties estimated by COSTCO (mass distribution and position), as well as those stemming from CLAMATO (sight-line sampling and pixel noise).

In the third and fourth panels of Figure 2, we show the COSTCO-FGPA maps for one realization and the ensemble mean, respectively. One can immediately see the difference of ${\delta }_{F}^{{\rm{w}}}$ between the CLAMATO and COSTCO-FGPA. The CLAMATO IGM transmission value at the position of COSTCO-I is close to the mean (${\delta }_{F}^{{\rm{w}}}\sim 0$), while from the COSTCO-FGPA realization, one sees strong absorption (${\delta }_{F}^{{\rm{w}}}\lt -0.2$) at the same position. The presence of an absorption feature in the averaged δ_F map for COSTCO-FGPA further confirms the mock absorption feature.

As the COSTCO-FGPA ${\delta }_{F}^{{\rm{w}}}$ shares the same shape and coordinate system with CLAMATO ${\delta }_{F}^{{\rm{w}}}$, we can perform a direct, quantitative comparison between CLAMATO and any COSTCO-FGPA realization at the position of the protocluster. First, we smooth the ${\delta }_{F}^{{\rm{w}}}$ maps with an R = 4 h⁻¹ Mpc top-hat kernel (Stark et al. 2015b), and then we compute the mean ${\delta }_{F}^{{\rm{w}}}$ value enclosed by an R = 15 h⁻¹ Mpc sphere centered at the reported COSTCO-I position; we refer to this quantity as ${\delta }_{F}^{\mathrm{pc}}$. The radius is inspired by Ata et al. (2022), who defined a protocluster as a structure that consistently formed a z = 0 cluster within an R = 15 h⁻¹ Mpc radius of each other across the different realizations.

We computed ${\delta }_{F}^{\mathrm{pc}}$ centered on the protocluster for all 1140 COSTCO-FGPA realizations and compared them with the value computed from CLAMATO. This distribution is shown in the central panel of Figure 3. The CLAMATO Lyα transmission associated with COSTCO-I is clearly more transparent (less absorbed) than seen in the COSTCO-FGPA mocks; we find that only three out of a total of 1140 COSTCO-FGPA realizations exhibit a ${\delta }_{F}^{\mathrm{pc}}$ value greater than that seen in CLAMATO. The COSTCO-FGPA mocks represent the null hypothesis that the gas in COSTCO-I is following the FGPA, for which we find a probability of p = 1–3/1140 = 0.00263 (corresponding to 2.79σ assuming a Gaussian distribution) after incorporating all known uncertainties. This is well below the standard hypothesis testing threshold of p = 0.05, indicating a clear rejection of the null hypothesis; the protocluster gas in COSTCO-I does not follow the FGPA. Based on Equation (2), the reduced Lyα optical depth (i.e., increased transmission) in COSTCO-I might be due to an increase in the large-scale gas temperature or enhanced local UV background.

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COSTCO-I is not the only COSTCO-detected protocluster that falls within the CLAMATO volume. We therefore also computed ${\delta }_{F}^{\mathrm{pc}}$ for these other protoclusters, which include well-known structures such as the ZFIRE protocluster at z = 2.11 (Nanayakkara et al. 2016) and the various peaks of Hyperion at z ≈ 2.45–2.52 (Cucciati et al. 2018). These are shown in the noncentral panels of Figure 3, where the CLAMATO Lyα transmission is generally consistent with the COSTCO–CLAMATO mocks. This suggests that a transparent Lyα forest in the protocluster gas is not a ubiquitous process at this epoch, although we cannot rule out more subtle deviations from the FGPA with the current data. Indeed, there are hints that the ZFIRE protocluster might not obey the FGPA (bottom middle panel of Figure 3), but more detailed studies would be needed to confirm this.

The transparent Lyα forest of COSTCO-I extends across physical scales of >4 pMpc. We have identified a compact overdensity of galaxies that forms the putative protocluster core, which would have a characteristic radius of r₂₀₀ = 400 pkpc = 0.92 h⁻¹ Mpc based on our estimated virial mass of M_V = 5.78 × 10¹³ h⁻¹ M_⊙. This is considerably smaller than the extent of the transparent gas we see in the protocluster and therefore unlikely to be due to early formation of an ICM. Indeed, previous studies of hot gas possibly associated with ICM formation at z ∼ 2 (e.g., Wang et al. 2016; Champagne et al. 2021) were on much smaller scales of ∼100 kpc. In any case, Lee et al. (2016) tested a toy model in which the Lyα transmission was set to 100% transmission ($F\equiv \exp (-\tau )\,=1$) within a 1.5 h⁻¹ Mpc radius of a simulated protocluster but with the gas outside following the FGPA. This had a negligible effect on the averaged ${\delta }_{F}^{\mathrm{pc}}$ computed over several megaparsecs, so a virialized ICM with r₂₀₀ = 0.92 h⁻¹ Mpc cannot be responsible for the spatially extended deviation from the FGPA.

We believe there are three possibilities for this large-scale (>4 pMpc) protocluster heating. The first scenario is that the protocluster gas is being collisionally shock-heated due to gravitational collapse of the accreting material on large scales. However, this seems to be disfavored by prior theoretical analysis of the large-scale Lyα forest signal in z ∼ 2 protoclusters. Miller et al. (2021) studied z ∼ 2.4 protoclusters within the IllustrisTNG100 hydrodynamical simulation (Weinberger et al. 2017; Pillepich et al. 2018). They found that for a uniform UV background, the effect of collisional ionization is negligible on the smoothed 3D Lyα forest signal associated with protoclusters. Kooistra et al. (2022b), on the other hand, performed zoom-in hydrodynamical simulations on a set of galaxy protoclusters with various phenomenological preheating prescriptions of the protocluster gas. They did, however, perform fiducial runs where gas hydrodynamics was in effect, but no feedback or preheating was applied. Even in the z = 2 protoclusters associated with the most massive z = 0 clusters (M(z = 0) ∼ 10¹⁵ h⁻¹ M_⊙), simple gravitational shock heating appears to be generally insufficient to make the ∼megaparsec-scale Lyα absorption significantly more transparent than the canonical FGPA. These two studies, however, analyzed only a small number of simulated protoclusters: ∼20 by Miller et al. (2021) and five by Kooistra et al. (2022a). Therefore, while they did not find large-scale gravitational shock heating at z ∼ 2.3, we cannot rule out the possibility that this is in progress in a small fraction of protoclusters. A more comprehensive study involving large numbers of simulated protoclusters would help clarify this.

The second possibility for the large-scale heating is that feedback processes from protocluster galaxies or active galactic nuclei (AGN) are responsible for the reduced absorption in COSTCO-I. Kooistra et al. (2022b) applied a simple phenomenological preheating model to the protocluster gas, which imposed an entropy floor, K_floor, such that the protocluster gas cells at z = 3 have internal gas entropy values of $T\ {n}_{e}^{-2/3}\gt {K}_{\mathrm{floor}}$, where T is the gas temperature and n_e is the electron density (see also Borgani & Viel 2009). Their results showed that a significant entropy floor of K_floor ≳50 keV cm⁻³ would be required to cause increased Lyα transmission to δ_F ∼ 0 in z ∼ 2 protoclusters. Kooistra et al. (2022b) were agnostic on the possible mechanisms that could cause such preheating. Over the years, however, there has been a growing consensus that feedback from AGN is necessary to reproduce various properties related to galaxy clusters and groups (e.g., Puchwein et al. 2008; McCarthy et al. 2010). The AGN feedback is included in the IllustrisTNG100 simulation analyzed by Miller et al. (2021), who showed that it does not appear to cause strong deviations from an FGPA-like relationship between the Lyα transmission and matter density in z = 2.44 protoclusters. However, the AGN feedback energy in the TNG model is deposited isotropically in the immediate vicinity of each supermassive black hole. The AGN feedback in the Simba simulations (Dave et al. 2019), on the other hand, implements a collimated-jet feedback scheme for low Eddington ratio AGN. This allows feedback energy to reach much larger scales compared with TNG (Tillman et al. 2022). The AGN jet feedback also appears to be driving large-scale heating at z ∼ 2 in the HorizonAGN suite (Chabanier et al. 2020) with significant effects on global Lyα forest statistics, although they did not focus on protoclusters. At low z, radio lobes from giant radio galaxies have been shown to extend up to ∼4–5 Mpc (Delhaize et al. 2021; Oei et al. 2022), so similar mechanisms operating in high-redshift protoclusters could be heating up the proto-ICM over similar scales.

Finally, an enhanced local UV radiation field, Γ_uv, from AGN within the protocluster could be an alternative cause of deviations from the FGPA. However, Miller et al. (2021) also considered a radiative model with a realistic quasar luminosity function in their analysis of IllustrisTNG100 protoclusters and showed that this is unlikely to denude the Lyα forest absorption of protoclusters to the extent that we see in COSTCO-I. Rare hyperluminous quasars (with absolute magnitudes of M₁₄₅₀ ≳ −27) would have a more significant effect on the Lyα absorption (Visbal & Croft 2008; Schmidt et al. 2018) than the simulated AGN considered by Miller et al. (2021), but we see no type I quasars within this protocluster. On the other hand, obscured type II quasars emitting anisotropically away from our LOS might indeed cause deviations from the FGPA. Hyperluminous quasars are, however, rare in the universe, and we therefore deem it a less likely cause of the Lyα transparency in COSTCO-I than collisional heating or jet feedback. It would, however, be an exciting discovery if an obscured hyperluminous quasar were responsible for the transparency of COSTCO-I. We will investigate this possibility in a follow-up study of the protocluster members.