1]Cosmic Dawn Center (DAWN), Denmark 2]Niels Bohr Institute, University of
Copenhagen, Jagtvej 128, DK-2200 Copenhagen N, Denmark 3]Department of
Astronomy, University of Geneva, Chemin Pegasi 51, 1290 Versoix, Switzerland
4]Center for Astrophysics, Harvard University, 60 Garden Street, Cambridge, MA
02138, USA 5]Institute of Astronomy, University of Cambridge, Madingley Road,
Cambridge CB3 0HA, UK 6]Kavli Institute for Cosmology Cambridge, University of
Cambridge, Madingley Road, Cambridge CB3 0HA, UK 7]Center for Computational
Astrophysics, Flatiron Institute, 162 Fifth Ave, New York, NY 10010, USA
8]Cavendish Laboratory, University of Cambridge, 19 JJ Thomson Avenue,
Cambridge CB3 0HE, UK 9]Astrophysics Research Institute, Liverpool John Moores
University, 146 Brownlow Hill, Liverpool L3 5RF, UK 10]California Institute of
Technology, Pasadena, CA 91125, USA 11]New Mexico State University, Las
Cruces, 88003 NM, USA 12]Stockholm University, Department of Astronomy and
Oskar Klein Centre for Cosmoparticle Physics, AlbaNova University Centre,
SE-10691, Stockholm, Sweden 13]MIT Kavli Institute for Astrophysics and Space
Research, Cambridge, MA 02139, USA 14]Institute of Science and Technology
Austria (ISTA), Am Campus 1, 3400 Klosterneuburg, Austria 15]European Southern
Observatory, Karl-Schwarzschild-Str. 2, 85748 Garching, Germany 16]Department
of Physics & Astronomy and Leicester Institute of Space & Earth Observation,
University of Leicester, University Road, Leicester LE1 7RH, UK 17]Centre for
Astrophysics and Cosmology, Science Institute, University of Iceland, Dunhagi
5, 107 Reykjavik, Iceland 18]Institute for Astronomy, Royal Observatory,
University of Edinburgh, Edinburgh EH9 3HJ, UK

# A massive, neutral gas reservoir permeating a galaxy proto-cluster after the
reionization era

Kasper E. Heintz  Jake S. Bennett  Pascal A. Oesch  Albert Sneppen  Douglas
Rennehan  Joris Witstok  Renske Smit  Simone Vejlgaard  Chamilla Terp  Umran
S. Koca  Gabriel B. Brammer  Kristian Finlator  Matthew J. Hayes  Debora
Sijacki  Rohan P. Naidu  Jorryt Matthee  Francesco Valentino  Nial R. Tanvir
Páll Jakobsson  Peter Laursen  Darach J. Watson  Romeel Davé  Laura C. Keating
Alba Covelo-Paz  [  [  [  [  [  [  [  [  [  [  [  [  [  [  [  [  [  [

###### Abstract

Galaxy clusters are the most massive, gravitationally-bound structures in the
Universe, emerging through hierarchical structure formation of large-scale
dark matter and baryon overdensities. Early galaxy “proto-clusters” are
believed to be important physical drivers of the overall cosmic star-formation
rate density and serve as “hotspots” for the reionization of the intergalactic
medium [1]. Our understanding of the formation of these structures at the
earliest cosmic epochs is, however, limited to sparse observations of their
galaxy members [2, 3, 4, 5, 6], or based on phenomenological models and
cosmological simulations [7, 8]. Here we report the detection of a massive
neutral, atomic hydrogen (H i) gas reservoir permeating a galaxy proto-cluster
at redshift $z=5.4$, observed one billion years after the Big Bang. The
presence of this cold gas is revealed by strong damped Lyman-$\alpha$
absorption features observed in several background galaxy spectra taken with
JWST/NIRSpec in close on-sky projection. While overall the sightlines probe a
large range in H i column densities, $N_{\rm HI}=10^{21.7}-10^{23.5}$ cm-2,
they are similar across nearby sightlines, demonstrating that they probe the
same dense, neutral gas. This observation of a massive, large-scale
overdensity of cold neutral gas challenges current large-scale cosmological
simulations and has strong implications for the reionization topology of the
Universe.

## Main Text

The neutral, atomic hydrogen (H i) gas content in the early Universe has
historically been probed via absorption-spectroscopy of the ground-state
Lyman-$\alpha$ (Ly$\alpha$) transition in bright quasar or gamma-ray burst
sightlines at redshifts $z=2-6$ [9, 10, 11, 12, 13, 14]. More recently with
the advent and exquisite near-infrared sensitivity and capabilities of the
James Webb Space Telescope (JWST), extremely strong damped Ly$\alpha$
absorption (DLA) features have been detected in spectra of entire galaxies at
redshifts $z>8$ [15], corresponding to $600$ Myr after the Big Bang. From a
search for and characterization of these DLA galaxies based on spectroscopic
observations with the _JWST_ Near-Infrared Spectrograph (NIRSpec) Prism-mode
[16] we identified ten galaxies at $z=5.4-6.0$, all showing extreme DLA
features. One particular source was identified to have the majority of the
absorbing gas in its distant foreground [17], with an absorption-redshift
consistent with an overdense region of foreground galaxies at $z\approx 5.4$
reported in the same field [5] and in close projected distance to the
background galaxy. We thus sought to investigate the DLA features observed in
the ten background galaxies in more detail and characterize the baryonic
components of this rare, massive galaxy proto-cluster. Charting the abundance
and distribution of the cold, dense gas around these early galaxy
overdensities provides key insight into their formation, star-formation
history and their impact on the ionizing photon output believed to drive the
large-scale reionization of the Universe.

To characterize the galaxy members of the proto-cluster first detected in the
field by Helton et al. [5] we use JWST NIRCam slitless grism observations
obtained through the “First Reionization Epoch Spectroscopically Complete
Observations” (FRESCO) survey (GO-1895, PI: Oesch; [18]). This survey is
designed to cover two extragalactic legacy fields with unprecedented near-
infrared spectroscopic depth at $4-5\mu$m in the F444W filter. We identify the
same overdensity, including $\gtrsim 25$ galaxies at $z=5.35-5.40$ within a
projected physical distance of $1\,$pMpc (Methods), centred approximately at
the celestial coordinates R.A. = $3^{\rm h}32^{\rm m}20^{\rm s}$, Decl. =
$-27^{\circ}49^{\prime}50^{\prime\prime}$. The redshift of the proto-cluster
members are accurately measured by first imposing a photometric prior and then
requiring at least $5\sigma$ detections of H$\alpha$, with occasional
simultaneous detections of [N ii], which is covered throughout redshifts
$z=4.9-6.6$ by design. The identified proto-cluster galaxy members span a
large range in brightness and mass, with absolute UV magnitudes from $M_{\rm
UV}=-18.0$ up to $-21.5$ mag (Methods). The total estimated halo mass of the
galaxy proto-cluster system is $\log(M_{\rm halo}/M_{\odot})=12.6-12.8$,
obtained through stellar-to-halo mass abundance matching [5].

The ten galaxies in the background to this galaxy proto-cluster with strong
DLA features have all been observed with the JWST/NIRSpec Prism configuration,
mainly as part of the JWST Advanced Deep Extragalactic Survey (JADES, see
Table 1 and Methods). The reduced and processed 1D spectra used in this study
were obtained from the DAWN JWST Archive (DJA)111https://dawn-
cph.github.io/dja/ [16] and are all photometrically-calibrated to the
available JWST/NIRCam photometry and corrected from slitloss according to the
exact source position in the shutter (Methods). The final reduced 1D spectra
for each of the ten sources with strong DLAs in the field are shown in Fig. 1.
For each galaxy, we determine their redshifts based on the multitude of
nebular emission lines detected in the spectra. Since we can pin-point the
exact background-galaxy redshifts, we are able to accurately model the
Ly$\alpha$ transmission of each individual source. We model the intrinsic
galaxy continuum at rest-frame UV wavelengths ($1200-2600\,\AA$) covered by
the JWST/NIRSpec Prism spectra using three approaches: assuming either a
standard spectral power-law, $F_{\lambda}\propto\lambda^{-\beta}$, a
representative galaxy template model, or via direct spectro-photometric
modelling of the spectral energy distribution, all convolved with the spectral
resolution of the NIRSpec Prism configuration (Methods). We find that the
results are insensitive within 0.1 dex to the exact choice of the three model
versions of the intrinsic spectra. This is likely because the broad Ly$\alpha$
absorption trough and strong damping feature dominates over small potential
variations in the intrinsic spectra. Throughout the work, we report the
results using the high-redshift galaxy spectral templates [19] as the
intrinsic continuum model.

We model the optical depth of Ly$\alpha$ and quantify the H i column density,
$N_{\rm HI}$, with a Voigt profile, following the approximation of [20]. For
large H i column densities, the Lorentzian wings dominate the shape of the
observed Ly$\alpha$ absorption line profile such that the optical depth,
$\tau$, is only sensitive to the column density of neutral atomic hydrogen. We
further assume that there is a negligible damping effect from the neutral
hydrogen fraction of the intergalactic medium (IGM) at these redshifts, since
the large-scale reionization of the Universe is expected to be fully complete
by then [21]. Even in the unlikely scenario where these galaxies probe a fully
neutral IGM, the observed Ly$\alpha$ damping features are not consistent with
any IGM transmission models since the derived column densities produce
stronger damping wings than expected for a fully neutral IGM (Methods). We
first model the DLA features assuming that the majority of the absorption
originates in the interstellar or circumgalactic medium of the background
galaxies, $z_{\rm abs}=z_{\rm gal}$. However, as demonstrated in Fig. 1, none
of the target background galaxies have DLA profiles consistent with the
majority of the neutral, atomic hydrogen gas being located at the source
location. Generally, the spectra show DLA features with very shallow roll-
overs, inconsistent with a DLA line profile with any given H i column density
at the source redshift.

The model posteriors on $z_{\rm abs}$ seem to independently converge on a
foreground, lower-redshift, solution and for the majority of cases exclude the
galaxy redshifts at $>3\sigma$ confidence (Methods). To quantify whether the
cluster redshift provides a better solution to the models, we integrate over
the likelihood levels from the Nested Sampling analysis to determine the Bayes
factor based on the fit evidence for both models, assuming either $z_{\rm
abs}=z_{\rm gal}$ or $z_{\rm abs}=5.387$, the median of the galaxy proto-
cluster redshift. For seven out of the total ten galaxies with strong DLA
features, we determine Bayes factors of $>100$ as summarized in Table 1, thus
with very strong evidence in favor of the galaxy proto-cluster redshift over
the galaxy redshifts. For two out of ten, we determine Bayes factors $77$ and
$99$, still showing very strong evidence for the cluster redshift. For one
case, the galaxy at $z_{\rm gal}=5.6166$ with ID 13877, we do not find
evidence for preferring one model over the other, though the close association
and on-sky proximity to another sightline probing similar foreground neutral
gas abundances favors the cluster-redshift solution. At the proto-cluster
redshift, we measure substantial integrated H i column densities in the range
$N_{\rm HI}=10^{21.7}-10^{23.5}\,$cm-2, revealing the presence of an extended
neutral, dense region permeating and surrounding the galaxy proto-cluster
extending out to $\sim 2$ pMpc as illustrated in Fig. 2.

An independent observational test of the hypothesis of a foreground neutral
gas reservoir relies on the spatial distribution of sightlines and their
corresponding H i column densities. The patchy and filamentary structure found
in simulations would suggests little-to-no correlation for random sightlines
drawn on Mpc or even hundreds of kpc scales, while scales below 100 kpc should
trace similar parts of the foreground absorber (see Fig. 3 and Methods).
Indeed, this is the pattern displayed by the spatial distribution of the
observed column-densities with: i) no overall radial structure, but instead
patchy regions with variations of $N_{\rm HI}$ up to 1.8 orders in magnitude,
and ii) large degree of coherence between galaxies with small projected
distance (see Methods and Extended Figs. 4 and 5). Specifically, the two
galaxy-pairs with smallest angular separation (ID; 13577 and 13877, 13618 and
13620) while separated by several Mpc in radial distance are within
respectively $20$ and $70$ kpc in their projected angular diameter distance at
$z=5.387$. These galaxies display similar column densities (i.e. consistent
within a factor of 2.6 and 1.3), which is more homogeneous than the two order-
of-magnitude variations seen across sightlines – and up to ten-fold smaller
fractional variation than the median variation between sightlines with
projected distance above $100$ kpc. This strongly disfavors the interpretation
of multiple DLAs along similar line-of-sights as these systems are distinct
(in absolute distance) but must be hidden behind a similar gas-reservoir. The
similarity in inferred column density is, however, naturally explained by the
small projected distance at the proto-cluster redshift. An alternative
scenario, given that the median absorption redshift is $z_{\rm
abs}=5.53^{+0.19}_{-0.23}$, where the uncertainties denote the 16th to 84th
percentiles of the distribution (Methods), could be that the galaxy sightlines
are probing a separate, physically disassociated proto-cluster at $z\approx
5.5$. This would, however, require that all the galaxy members are below the
line-detection limit of FRESCO, in contrast to the cluster at $z=5.4$, since
no overdensity of galaxies are observed in that region and redshift interval,
or that we are observing it in a young, nascent stage.

To determine an approximate upper bound on the mass of the cold, neutral gas
connected to this proto-cluster we assume that it can be physically modelled
as a simple circular disk in the source plane, with $M_{\rm HI,tot}=\langle
N_{\rm HI}\rangle\pi R^{2}_{\rm HI,max}f_{\rm cov,HI}$. For the derived mean
$\langle N_{\rm HI}\rangle=10^{22.5}$ cm-2 and maximum observed radial size of
the H i gas, $R^{2}_{\rm HI,max}=2$ pMpc, and assuming a 10% covering fraction
$f_{\rm cov,HI}=0.1$, this yields $M_{\rm HI,tot}=3\times 10^{14}\,M_{\odot}$.
This corresponds to an overdensity of $\delta=10^{4}$ from the cosmic baryonic
average at $z\approx 5$ [22], three orders of magnitude in excess of the
predicted galaxy overdensity [5]. Due to the limited set of galaxy sightlines,
likely only covering one part of the predicted filament structure or cold gas
stream, and the expected large density variations of the gas it is impossible
to observationally constrain the full covering fraction, $f_{\rm cov,HI}$,
both in the line-of-sight and projected on the sky.

To understand the covering fraction, infall and the physical state of the cold
gas surrounding these early galaxy proto-clusters, we employ a range of
simulations (Methods) that allow us to probe the neutral gas permeating such
massive galaxy overdensities [23, 24]. Such high-column density systems are
not captured in reionization simulations designed to model the IGM, as they
use simplified galaxy formation models which turns all dense gas into stars
and thereby only predict the large-scale ionization fields around these
massive halos [25]. Other cosmological radiation hydrodynamic simulations [26,
27] do not sample large enough simulation boxes and therefore cannot probe the
correct sample of halo assembly histories that would produce those baryonic
mass overdensities [24].

Fig. 3 shows H i column densities of the neutral gas permeating a simulated
galaxy proto-cluster at $z=5.5$ from a specific set of simulation designed to
probe these overdensities, with a halo mass $M_{\rm h,200}=5.5\times
10^{12}\,M_{\odot}$ [23]. This was selected to match the estimated halo mass
of the observed proto-cluster [5]. Projected over the entire depth of the zoom
region of the simulation ($\sim 2$ pMpc), similar to the observed scales
probed by the galaxy absorption sightlines, we extract a total H i gas mass of
$M_{\rm HI}=1.4\times 10^{13}\,M_{\odot}$ or $M_{\rm HI,R_{200}}=4.6\times
10^{11}\,M_{\odot}$ within the radius at which the spherically averaged mass
density reached 200 times the critical mass density ($R_{200}$). For this
particular zoom-in simulation, only a small fraction $\approx 2\%$ of
sightlines are expected to probe column densities $N_{\rm HI}>10^{21}\,$cm-2,
with less than a permille at $N_{\rm HI}>10^{22}\,$cm-2. However, if we modify
the simulation to the extreme and assume that all the gas cells are fully
neutral, we find that nearly every sightline probes gas with column densities
$N_{\rm HI}>10^{21}$ cm-2 though still rarely with $N_{\rm HI}>10^{22}$ cm-2
(0.1% of the pixels). This shows that while there is sufficient gas around
such a halo to agree with the observational inference, matching the number of
high H i columns found would require a significantly higher neutral fraction
than is seen in the fiducial simulation.

Considering other simulations that specifically targets rare, massive galaxy
proto-clusters ($M_{\rm vir}\sim 10^{14}\,M_{\odot}$ at $z=2$) [24], we find
that the covering fraction of the cold, neutral gas can be up to $15\%$ at
$z=5.4$ with several sightlines that probe similarly dense gas ($N_{\rm
HI}>10^{21.7}\,$cm-2) in multiple filaments as observed here (Methods).
Compared to the default simulation, these $100$ proto-clusters have almost an
order-of-magnitude higher halo mass at the target redshift $z=5.4$.
Importantly, we show that the viewing angle and exact column density cut
impacts the covering fraction significantly. If we consider the sightlines
with column densities above $N_{\rm HI}>10^{21}\,\mathrm{cm}^{-2}$, the mean
covering fraction increases dramatically (with wide scatter) across all of the
simulated proto-clusters – but still depends heavily on viewing angle.
Therefore, correctly sampling the assembly history distribution and capturing
“extremely rare” objects is paramount in interpreting the observations. By
comparing our results with these rare overdensities recovered in simulations
suggest that we are observing the formation and assembly of the primary
baryonic component into one of the most massive structures in the present-day
Universe.

This study provides the first direct observational evidence for dense, neutral
hydrogen gas environment connected to a massive galaxy proto-cluster at
$z=5.4$ shortly after the end of the reionization era, just one billion years
after the Big Bang. There has been growing evidence for an increasing cold gas
component in the overall baryon budget of galaxy proto-clusters with redshifts
[28], and past simulations showed that early galaxy-cluster structures should
be dominated by cold-gas accretion [29]. Observations of galaxies and quasars
in overdensities at lower redshifts, $z\sim 2-3$, have also hinted at dense,
extended neutral gas environments but at substantially lower column densities
than observed here. Extending this type of study to the reionization epoch
have further previously been limited by the small volume population of bright
quasars and the lack of sensitive near-infrared spectroscopy to cover the
redshifted rest-frame continuum around the Ly$\alpha$ transition at redshifts
$z\gtrsim 5$. With the advent of JWST, we are now able to identify large
numbers of galaxy proto-clusters at rest-frame optical wavelengths and map
their Ly$\alpha$ properties. As demonstrated here, this provides the required
sensitivity to chart the large-scale cold, neutral gas directly in absorption
using the more numerous population of background galaxies as cosmic
backlights. This is particularly important given that even extremely deep
observations targeting the Ly$\alpha$ emission from the neutral gas on large
scales around early galaxy or quasar overdensities are not sensitive enough to
detect this gas in emission [30]. Our results highlight the often overlooked
fact that regions of high ionization fraction is a necessary, but not
sufficient condition for the escape of ionizing photons from galaxies or
galaxy clusters [31]; for such massive cold gas reservoirs as seen here, the
total amount of neutral gas may still be high enough to impede escape. If such
massive neutral gas reservoirs are common in and around early galaxy
overdensities, this has strong implications for the cosmological evolution and
topology of reionization. This would greatly change how the tomography of
reionization is reconstructed in large cosmological simulations, largely
driven by galaxy overdensities, and our understanding of this last major phase
transition of the Universe.

Data availability

The JWST imaging and spectroscopic data are publicly available on the JWST
MAST archive at https://mast.stsci.edu. The data has been processed using
public software codes; grizli v. 1.9.11 [32] and MsaExp v. 0.6.17 [33]. The
reduced spectroscopic data are all available on the DAWN JWST Archive
(DJA)222https://dawn-cph.github.io/dja/.

Acknowledgments This work has received funding from the Swiss State
Secretariat for Education, Research and Innovation (SERI) under contract
number MB22.00072. The Cosmic Dawn Center (DAWN) is funded by the Danish
National Research Foundation under grant DNRF140. The data products presented
herein were retrieved from the DAWN JWST Archive (DJA). DJA is an initiative
of the Cosmic Dawn Center, which is funded by the Danish National Research
Foundation under grant DNRF140. This work is based on observations made with
the NASA/ESA/CSA James Webb Space Telescope. The data were obtained from the
Mikulski Archive for Space Telescopes at the Space Telescope Science
Institute, which is operated by the Association of Universities for Research
in Astronomy, Inc., under NASA contract NAS 5-03127 for JWST. J.S.B.
acknowledges support from the Simons Collaboration on ‘Learning the Universe’.
J.S.B.’s simulations used resources from the Cambridge Service for Data Driven
Discovery (CSD3) operated by the University of Cambridge Research Computing
Service (www.csd3.cam.ac.uk), provided by Dell EMC and Intel using Tier-2
funding from the Engineering and Physical Sciences Research Council (capital
grant EP/P020259/1). K.F.’s simulation utilized resources from the New Mexico
State University High Performance Computing Group, which is directly supported
by the National Science Foundation (OAC-2019000), the Student Technology
Advisory Committee, and New Mexico State University and benefits from
inclusion in various grants (DoD ARO-W911NF1810454; NSF EPSCoR OIA-1757207;
Partnership for the Advancement of Cancer Research, supported in part by NCI
grants U54 CA132383 (NMSU)). K.F. also gratefully acknowledges support from
the National Science Foundation (NSF) under Award Number 2006550. M.J.H. is
fellow of the Knut & Alice Wallenberg Foundation. D.S. acknowledges support
from the Science and Technology Facilities Council (STFC). U.S.K. was
partially funded by the Summer Undergraduate Research Fellowships program at
Caltech.

Author contributions

K.E.H. wrote the manuscript and led the analysis. G.B. reduced and extracted
the photometric and spectroscopic data. R.S. and J.W. identified the first
evidence for strong damped Lyman-$\alpha$ absorption in the target galaxies.
P.A.O. led the FRESCO observations and analysis of the galaxy proto-cluster
members. S.V., C.T., and U.K. performed the Lyman-$\alpha$ modelling of the
spectra. J.B. and D.R. performed the simulations and extracted the relevant
data. A.S. did the statistical clustering analysis. All authors contributed to
the text and interpretations of the results.

Competing interests

The authors declare no competing interests.

Figure 1: JWST/NIRSpec Prism Spectra of the ten galaxies with apparent strong
DLAs, in close on-sky proximity to the massive galaxy proto-cluster at
redshift $z=5.387$. The best-fit models for each spectrum are shown by the
solid black lines, using the high-redshift galaxy template spectra as the
intrinsic continuum models, and the models with fixed $z_{\rm abs}=z_{\rm
gal}$ are shown by the dashed black lines.

Figure 2: Spatial and redshift distribution of the galaxy proto-cluster
members and the background galaxies with strong DLAs. The cluster members
identified from the FRESCO survey at $z=5.35-5.40$ are shown by open blue
circles, and the background galaxies with grey star symbols. Their impact
parameters are shown in the left JWST/NIRCam image, color-coded according to
the H i column densities derived at the cluster redshift.

Table 1: Positions, source IDs, and line-of-sight absorption of the ten
background galaxies.

R.A. (J2000) | Decl. (J2000) | Prog. ID | Source ID | $z_{\rm gal}$ | $z_{\rm abs}$ | $\log(N_{\rm HI}/{\rm cm^{-2}})$ | Bayes factor
---|---|---|---|---|---|---|---
|  |  |  |  |  |  | ($z_{\rm abs}=5.387$ /
|  |  |  |  |  |  |  $z_{\rm abs}=z_{\rm gal}$)
53.167303 | $-27.802870$ | 1210 | 5113 | 5.8215 | $5.24\pm 0.16$ | $23.55\pm 0.20$ | 76
53.154087 | $-27.766062$ | 1210 | 9842 | 5.8051 | $5.60\pm 0.10$ | $22.45\pm 0.05$ | 168
53.121759 | $-27.797633$ | 1210 | 13176 | 5.9440 | $5.4\pm 0.10$ | $23.26\pm 0.02$ | 629
53.1297219 | $-27.808177$ | 1210 | 13577 | 5.5711 | $5.46\pm 0.10$ | $22.11\pm 0.03$ | 347
53.119112 | $-27.760802$ | 1210 | 13618 | 5.9482 | $5.77\pm 0.10$ | $22.38\pm 0.03$ | 368
53.130574 | $-27.807725$ | 1210 | 13877 | 5.6166 | $5.55\pm 0.15$ | $21.70\pm 0.25$ | 0.1
53.11537 | $-27.814767$ | 1210 | 15099 | 5.7725 | $5.61\pm 0.10$ | $22.55\pm 0.05$ | 99
53.126535 | $-27.818092$ | 1210 | 13704 | 5.9315 | $5.65\pm 0.10$ | $22.44\pm 0.05$ | 220
53.12259 | $-27.760569$ | 1210 | 13620 | 5.9204 | $5.74\pm 0.10$ | $22.25\pm 0.03$ | 613
53.104756 | $-27.832291$ | 2198 | 7807 | 5.3960 | $5.30\pm 0.10$ | $23.40\pm 0.10$ | –
|  |  |  |  |  |  |

22footnotetext: Notes. The spectroscopic redshift, $z_{\rm gal}$, is derived
from the nebular emission lines. $z_{\rm abs}$ lists the best-fit Ly$\alpha$
absorption redshift, where the column density, $N_{\rm HI}$, assumes the mean
of the proto-cluster redshift $z_{\rm abs}=5.387$. The Bayes factor for this
model over the intrinsic galaxy model is provided in the last column. ${\rm
BF}>100$ is highly significant, $70-100$ is very significant.

Figure 3: Simulated density maps of H i column density, $N_{\rm HI}$, for a
proto-cluster with halo mass, $M_{\rm h,200}=5.5\times 10^{12}\,M_{\odot}$ at
$z=5.53$ [23]. The width of the image on the left is $20\times R_{200}$ ($\sim
1.6$ pMpc), representing approximately the scales of the probed galaxy
absorption sightlines. The dashed circle represents the radius at which the
spherically averaged mass density reached 200 times the critical mass density
($R_{200}$).

## Methods

Cosmology

Throughout this work, we assume a standard flat $\Lambda$CDM cosmological
model based on the most recent Planck measurements [34], with a Hubble
constant $H_{0}=67.4\,{\rm km\,s^{-1}\,Mpc^{-1}}$, matter density,
$\Omega_{\rm m}=0.315$, and dark energy density, $\Omega_{\rm\Lambda}=0.685$.
Cosmological measurements such as the co-moving and proper distances,
luminosity distances, and age of the Universe are based on the measured
redshifts $z$ and computed using Astropy [35].

Observations and data reduction

Nine out of the ten identified background galaxies were observed as part of
the deep JWST Deep Extragalactic Survey (JADES, prog. ID: 1210) survey [36],
and the additional one source observed as part of Prog. ID 2198 [37], as
summarized in Table 1. All galaxies were observed with the JWST/NIRSpec low-
resolution ($\mathcal{R}\approx 100$) Prism configuration [38], covering
wavelengths from $0.6-5.3\,\mu$m.

The ten galaxies were reduced and post-processed using MsaExp v. 0.6.17 [33]
and obtained from the DAWN JWST Archive (DJA)333https://dawn-
cph.github.io/dja/. The details on the spectroscopic pipeline for the
reductions and post-processing are outlined in Heintz et al. [16]. Briefly,
DJA utilizes the Stage 2 output from the Mikulski Archive for Space Telescopes
(MAST) JWST archive and performs standard wave-length, flat-field and
photometric calibrations on the individual NIRSpec exposure files. MsaExp
corrects the inverse-noise and the bias levels in individual exposures and
perform a slit-loss correction based on the morphology and position with the
shutter of the source. This correction greatly improves the overall flux
calibration of the spectra, both in terms of colors and absolute flux
densities, to within $\approx 15\%$ [15, 39]. The final 1D spectra were
generated by optimally extracting the trace from the 2D spectra using an
inverse-weighted sum of the 2D spectra in the dispersion direction [40]. The
final 1D spectra are shown in Fig. 1.

The ten background sources were identified based on their broad apparent
damped Lyman-$\alpha$ absorption (DLA) profile and their close on-sky
proximity as part of the JWST/NIRSpec PRImordial gas Mass AssembLy (PRIMAL)
archival survey [16]. The galaxies in this sample are all selected to have
robust emission-line redshift measurements and sufficient signal-to-noise
(${\rm S/N}>3$) of the continuum around the redshifted rest-frame ultraviolet
and Ly$\alpha$ wavelength region to ensure robust measurements of the damping
wings. This is essential to disentangle the contributions from the
intergalactic medium (IGM), ionized UV bubbles, or local dense neutral atomic
hydrogen in the interstellar or circumgalactic medium of the galaxies.

The observations of the cluster-member galaxies were obtained from the First
Reionization Epoch Spectroscopically Complete Observations (FRESCO) survey,
prog. ID: 1895 [18]. FRESCO covered the two GOODS/CANDELS fields with deep
($\sim 2\,$hr) pointings using the NIRCam/grism F444W filter slitless
spectroscopic configuration. This yields a spectral coverage over
$3.8-5.0\,\mu$m with resolving power $\mathcal{R}=1600$. The redshifts of the
cluster members were derived based on their rest-frame optical emission lines,
primarily H$\alpha$ and occasionally [N ii] when detected. Complementary
photometry in the target fields was used to derive the spectral energy
distribution of each source, the photometric redshifts were used as priors for
the line identifications and emission-line redshift measurements [18].

Characteristics of the galaxy proto-cluster members

The foreground galaxy proto-cluster were first identified by Helton et al. [5]
based on slitless JWST/NIRCam grism observations of the field from the FRESCO
survey. Using the extracted H$\alpha$ catalog from this survey, we identify
the same overdensity here, including $\gtrsim 25$ galaxies at $z=5.35-5.40$.
The redshift distribution of the full set of sources from the FRESCO survey
with significant, ${\rm S/N}>5$, detections of H$\alpha$ at $z=4.9-6.6$ is
shown in Extended Fig. 1 with the galaxy overdensity highlighted. The average
spectroscopic redshift of the large-scale structure is $z=5.387$. The galaxy
cluster is centred at celestial coordinates R.A. = $3^{\rm h}32^{\rm m}20^{\rm
s}$, Decl. = $-27^{\circ}49^{\prime}50^{\prime\prime}$. The spatial and
brightness distribution of the cluster members are shown in Extended Fig. 2.
The majority of the sources are located within 1 pMpc from the estimated
center of the cluster. We observe no strong dependence of the spatial location
of the sources on the absolute UV brightness, but note that the brightest
members ($M_{\rm UV}<-20$ mag) are all located within $\sim 1$ pMpc whereas
the faintest proto-cluster galaxies ($M_{\rm UV}>-19$ mag) are found in the
outskirts. This would be consistent with the predicted “inside-out” growth
early galaxy proto-clusters [1].

Modelling the damped Lyman-$\alpha$ absorption feature

To model the broad DLA features observed in each of the background galaxy
spectra, we first considered the effects of a partly neutral intergalactic
medium (IGM). The optical depth from the Gunn-Peterson effect due to
absorption from H i in the IGM can be described via a single redshift-
dependent parameter, the average neutral hydrogen fraction $x_{\rm HI}=n_{\rm
HI}/n_{\rm H,tot}$ [41, 42]. Since the large-scale reionization of the IGM on
average is determined to be complete, $x_{\rm HI}\rightarrow 0$, by redshift
$z\approx 5.5-6$ [43, 21, 44] this likely does not contribute to the observed
Ly$\alpha$ damping wings in the ten background galaxy spectra. To be
conservative, we include a prescription for the IGM component following [41]
but using the approximation by [45] setting the maximum redshift to $z_{\rm
gal}$ and integrate down to $z=5.4$. For all cases, however, the observed DLA
broadening are much greater than expected for even a fully neutral IGM with
$x_{\rm HI}=1$, corresponding to an equivalent H i column density of $N_{\rm
HI}=10^{21.2}\,$cm-2 [15]. To reach the observed column densities of $N_{\rm
HI}\gtrsim 10^{22}-10^{23}\,$cm-2 requires overdensities $\sim 3-10\times$ the
global average, equivalent to $x_{\rm HI}=3-10$. This latter estimate of the
neutral gas mass overdensity is consistent with the predicted galaxy
overdensity [5].

We modelled the DLA profiles with a Voigt profile, assuming a single-redshift
origin, approximated as:

$\tau_{\rm DLA}=CaH(a,x)N_{\rm HI}$ (1)

Here $C$ is the photon absorption constant, $a$ is the damping parameter, and
$H(a,x)$ is the Voigt-Hjerting function [20], with $x$ representing the
difference in rest-frame wavelength with respect to the resonant wavelength of
Ly$\alpha$ expressed in Doppler units. For strong DLA features where the
Lorentzian wings dominate the shape of the absorption-line profile the optical
depth is only sensitive to the column density of neutral atomic hydrogen,
$N_{\rm HI}$ and does not depend on the Doppler broadening. This approximation
is typically assumed in the study of foreground absorbers associated with
galaxies in bright quasar or gamma-ray burst sightlines [9, 10, 11, 12, 13,
14], and have more recently been applied to single high-redshift galaxies as
well [15, 46, 47, 48, 49]. It assumes that a dominating fraction of the
absorbing gas is located at the approximate same redshift when integrating
over the line-of-sight column density, in contrast to typical IGM
approximations that integrate over longer redshift intervals. The former
approximation best represents the scenario of a massive foreground neutral gas
reservoir connected to a single galaxy overdensity, but the small variations
in the spectra could be due to a radial distribution along the line of sight
($z_{\rm abs}\pm 0.1$) of the foreground gas.

We model the intrinsic continuum spectral energy distribution (SED) underlying
the DLA component using three different prescriptions: i) A rest-frame UV
spectral shape following a simple power-law of the form
$F_{\lambda}\propto\lambda^{-\beta}$, ii) A set of galaxy template spectra
designed to match the blue rest-frame UV colors of high-redshift galaxies
[19], and iii) Direct modelling of the SED using Eazy [50], but excluding
photometric filter bandpasses that include the redshifted Lyman-$\alpha$ edge.
We find that the results on the derived $N_{\rm HI}$ are generally insensitive
to the exact choice of the underlying intrinsic continuum SEDs and dust
attenuation ($\Delta\log N({\rm HI/cm^{-2}})\lesssim 0.1$) since the small
variations in the intrinsic spectral shape is negligible compared to the
observed broad damping wings which mainly drive the column density
estimations. For the following analysis we use the high-redshift galaxy
template spectra, specifically the recommended binc100z001age6.cloudy model
with weak intrinsic Lyman-$\alpha$ emission and young stellar population. The
exact choice of the galaxy template does not have a larger impact on the
results either. Following Heintz et al. [15] we sampled the posterior
probability distributions of the DLA H i column densities using the MultiNest
algorithm [51] implemented in the PyMultiNest-package [52]. This approach
determines the marginal likelihood (evidence of the fit) via a transformation
of the likelihood space into a one-dimensional probability distribution. The
output results are derived by sampling this posterior distribution, weighted
by the assumed prior probability distribution. By integrating the likelihood
levels we calculate the evidence of the fit used for model comparison.

For each background galaxy, we modelled the spectrum using the galaxy
templates as the intrinsic SEDs with the added visual extinction, $A_{V}$, the
average IGM neutral fraction, $x_{\rm HI}$, and the H i column density,
$N_{\rm HI}$ as free parameters. We used flat, conservative priors on $N_{\rm
HI}$ in the range $\log(N_{\rm HI}/{\rm cm}^{-2})=18-24$. Motivated by the
single-case study of Terp et al. [17], we first leave the absorption redshift,
$z_{\rm abs}$, as a free parameter in the fit. The resulting posterior
distribution functions (PDFs) are shown in Extended Fig. 3. In the majority of
cases, excluding the galaxy with source ID 13877 at $z_{\rm gal}=5.6166$, the
PDFs all prefer a lower-redshift solution, excluding the background-galaxy
redshift solution at $>3\sigma$ confidence. We note also that the galaxy with
source ID 7807 at $z_{\rm gal}=5.3960$ is likely embedded within the galaxy
proto-cluster and therefore by selection probe slightly foreground gas to the
mean cluster-redshift, though the PDF is still consistent at $1\sigma$
confidence with the mean. From the joint PDFs of the individual redshift
solutions we find combined, median absorption redshift of $z_{\rm
abs}=5.53^{+0.19}_{-0.23}$ where the uncertainties denote the 16th to 84th
percentiles of the distribution. The galaxy proto-cluster redshift is thus
consistent within $1\sigma$ confidence to the derived absorption redshift.
Further, when performing the modelling using a prior on $z_{\rm abs}=5.387$ we
find that the Bayes factor of the two models suggest no significant
difference. We therefore set $z_{\rm abs}=5.387$ in the following analysis,
and report the Bayes factor over the galaxy redshift in Table 1. For all cases
but the galaxy with source ID 13877 at $z_{\rm gal}=5.6166$, the foreground
galaxy-cluster redshift solution is preferred at high significance. With this
assumption, we derive H i column densities in the range $N_{\rm
HI}=10^{21.7}-10^{23.5}$ cm-2. In Extended Fig. 4 we show the impact
parameters of the background galaxy sightlines from the estimated proto-
cluster center, size-coded according to the foreground H i column density and
color-coded according to galaxy redshift. We find no dependence on the
inferred $N_{\rm HI}$ with background galaxy redshift and no apparent radial
dependence on the derived $N_{\rm HI}$, though note a strong coherence between
close on-sky galaxy-sightlines. The lack of radial dependence is in any case
not expected given the large density variations of the filamentary structures
permeating these massive galaxy overdensities predicted from simulations [23,
24], as also highlighted in the section below.

To statistically investigate the internal coherence between sightlines, we
show in Extended Fig. 5 the ratio of inferred H i column densities and the
projected distance between pairs of objects. The two pair of objects with the
smallest projected distance (20 and 70 kpc apart at $z\approx 5.4$) display
equivalent column densities suggesting they probe similarly dense foreground
regions. In physical space, these pairs are clearly distinct with each galaxy
being separated by tens of co-moving Mpc. Comparing to the observed
distribution of $N_{\mathrm{H\,I}}$-ratios for all objects at projected
distances, $250\,\mathrm{kpc}<d<1\,\mathrm{Mpc}$, these nearest pairs are
outliers given their observed degree of coherence. The KS-test statistic gives
a 9% probability of randomly getting two column-densities as similar as that
contained by the two nearest pairs (i.e. all objects within 100 kpc). Further,
given the 5 pairs within 250 kpc projected distance, the probability of
randomly getting the observed similar column-densities is less than 2.5%.

There is now mounting evidence in the literature that a higher prevalence of
DLAs in galaxy spectra are associated with overdensities. Observations from
the ground of galaxy or quasar overdensities at redshifts $z\sim 2-3$ have
revealed large, neutral gas reservoirs connected to the cluster members [53,
54, 55, 56, 57]. At higher redshifts towards the reionization era, the first
evidence came from the serendipitous detection of a massive foreground
absorber in close on-sky proximity to one of the most massive proto-clusters
at $z>5$ discovered to date [17]. This scenario was required to explain the
simultaneous detection of strong Lyman-$\alpha$ emission and DLA absorption
(source ID 13176 with $z_{\rm gal}=5.944$ also studied here), though it have
also been reported as a potential galaxy dominated by nebular-continuum
emission at rest-frame UV and optical wavelengths [58]. The second such object
with potential nebular-continuum emission at $z=7.8$ from the latter study
was, however, also later associated with a galaxy overdensity [59]. There is
also recent evidence for an excess fraction of DLAs identified from
photometry-only in independent galaxy fields associated with galaxy
overdensities [60], lending strong credibility to this scenario. The results
presented here is the first conclusive, large-scale detection of the cold,
neutral medium connected to a high-redshift galaxy proto-cluster.

Predictions from simulations

In order to illustrate how the large, spatially-coherent neutral regions in
the post-reionization Universe such as those suggested by Extended Fig. 5
challenge models, we compare the coherent length scale with its associated
column density in Extended Fig. 6. For a uniform medium with overdensity
$\delta$, co-moving size $L$, and neutral fraction $f_{\rm HI}$, the neutral
gas column density is

$N_{\rm HI}=f_{\rm HI}\langle n_{\rm H}\rangle L(1+\delta)~{},$ (2)

where $\langle n_{\rm H}\rangle$ is the mean hydrogen number density. This
relationship is shown for several trial values of $f_{\rm HI}(1+\delta)$.
Adopting our measured range of H i columns and projected separations yields
the blue error bar and limit. Overdensities in the range $f_{\rm
HI}(1+\delta)=10^{3}-10^{4}$ are required to match the column density
distribution, consistent with that derived from the simple geometric
assumption about the spatial distribution of the gas.

Orange points with error bars indicate the expected trend at $z=5.5$ from the
cosmological radiation hydrodynamic Technicolor Dawn simulations, which
simultaneously track galaxy evolution and H i reionization [26]. The measured
combination of H i column density and coherent length scale do not arise in
the simulation. However, as the simulation spans only 24.35 cMpc, it does not
include the large, more rare density fluctuations required to reach the halo
masses estimated for this galaxy overdensity. We note additionally that the
inferred length scale of coherent H i absorption may be inaccurate because our
galaxies were _selected_ to show strong H i absorption. A more complete
characterization of the distribution of H i columns within this region would
be needed to test whether the inferred overdensities are indeed overestimated
by 2–3 orders of magnitude.

To provide a more direct theoretical comparison to the observations, we employ
a modified version of the fable suite of simulations, tailored to follow the
evolution of galaxy groups and clusters [61]. We run a zoom simulation of a
halo with mass $M_{200}=5.5\times 10^{12}\,\mathrm{M}_{\odot}$ at $z=5.5$.
This object grows into a large cluster at $z=0$, with a mass
$M_{200}=1.30\times 10^{15}\,\mathrm{M}_{\odot}$ consistent with the Coma
cluster, and was taken from a parent dark matter only simulation, the (4.1
Gpc)3 Millennium XXL [62]. The Lagrangian region of this zoom – the region
within which all dark matter particles will end up within $5\times R_{500}$ of
the $z=0$ cluster – is aspherical but has a diameter of at least $7.5\,$pMpc
at $z=5.5$. All H i maps are then made projecting along the $z$-axis through
the entire depth of this Lagrangian region.

In this simulation we also use the shock refinement scheme introduced in [23].
This significantly increases gas mass resolution by a factor of 512 within
$\approx 500$ pkpc around the centre of the halo, with cells having a mass of
$3.2\times 10^{4}\,\mathrm{M}_{\odot}$. Outside of this region the gas remains
at the base resolution of the simulation, with cell masses of $1.64\times
10^{7}\,\mathrm{M}_{\odot}$. For full details of this scheme, see [23]. A full
treatment of the neutral fraction of gas within the simulation would require
radiative transfer. In this simulation we instead use the prescription of [63]
to estimate the H i content of each gas cell, which is then summed to provide
the column density maps in Fig. 3.

To make predictions for the assembly and later evolution of this galaxy proto-
cluster, we extract the halo mass and baryonic mass components at a range of
redshifts, $z=10,8,5.5,2,0$ corresponding to $0.47$, $0.64$, $1.0$, $3.3$, and
$13.8$ Gyrs after the Big Bang as shown in Extended Fig. 7. We plot the mass
of the total gas and the H i gas component within the entire zoom region (1.6
pMpc) and within $R<R_{200}$ and compare it to the halo mass and the stellar
mass contained within $R<R_{200}$. At all redshifts, the neutral gas mass
appear to only comprise $\approx 1-5\%$ of the total gas within the box.
However, focusing on the central region within $R<R_{200}$, the gas is largely
neutral until $z\approx 5.5$ at which point the gas becomes more ionized and
eventually (by $z\approx 2$) processed into stars. Intriguingly, these
simulations further show that the halo and stellar mass surpass the total and
local neutral gas budget, respectively, at redshifts $z\sim 2-3$. This is
coincident with the peak of the average cosmic star-formation rate density
[64]. This is further evidence that the availability of pristine, neutral gas,
or the lack thereof, is likely a key physical driver of the overall cosmic
star formation history causing the eventual turnover and decline observed at
the present day.

Similarly, we also consider the Manhattan Suite, a set of $100$ zoom-in
simulations focused on galaxy clusters with
$M_{\mathrm{200,c}}>10^{14}\,\mathrm{M}_{\mathrm{\odot}}$ at $z=2$, and
baryonic particle resolution $2\times 10^{7}\,\mathrm{M}_{\odot}$ [24]. The
suite is intentionally biased towards the most rapidly assembling, massive
halos in the early Universe in order to mimic the observational selection bias
towards highly star forming and over-dense structures at high redshift. By
analyzing the $100$ most massive progenitor chains in the simulations at
$z=5.4$, we determined the covering fractions of neutral hydrogen column
densities above $10^{21}\,\mathrm{cm}^{-2}$, $10^{21.3}\,\mathrm{cm}^{-2}$,
$10^{21.5}\,\mathrm{cm}^{-2}$, and $10^{21.7}\,\mathrm{cm}^{-2}$ within
$R_{\mathrm{200,c}}$, along the $3$ principal axes, and produced probability
density functions of the covering fractions (see the bottom plot in Extended
Fig. 8). While the proto-clusters in the Manhattan Suite are rare, not all of
the viewing angles or progenitor histories produce significant sightlines
above $10^{21.7}\,\mathrm{cm}^{-2}$. However, there is an extended tail in the
distributions where the proto-cluster has up to $15\%$ covering fraction of
neutral hydrogen, especially if we allow slightly lower column densities.
Compared to the focused zoom, we stress the importance of a statistical sample
of proto-clusters that are focused on the most massively assembling halos in
order to capture the extreme gas densities that we present in this work. The
proto-clusters in the Manhattan Suite will go on to form galaxy clusters with
masses $M_{\mathrm{200,c}}\sim 10^{15}\,\mathrm{M}_{\mathrm{\odot}}$ at $z=0$,
which are the most massive structures today.

Our results presented are in stark contrast to previous cosmological
reionization simulations that do not capture the large neutral gas
overdensities observed here, which require more detailed galaxy formation
simulations. These large overdensities are, however, crucial to model in order
to obtain a complete census of galaxy assembly and star-formation rates in
galaxy proto-clusters and the effect of the more dense, massive neutral gas
surrounding these overdensities on the expected reionization topology.

Extended Fig. 1. Redshift distribution of the sources in FRESCO with
significant, ${\rm S/N}>5$, detections of H$\alpha$ at $z=4.9-6.6$. The galaxy
overdensity identified in the survey at $z=5.35-5.40$ is highlighted.

Extended Fig. 2. Spatial distribution of the identified galaxy proto-cluster
members at $z=5.35-5.40$. The sources are color-coded by their rest-frame UV
absolute magnitude, $M_{\rm UV}$. The centroid of the cluster is marked by the
cross, and the ellipse show the region within 1 pMpc. The FRESCO survey
footprint is marked by the blue line.

Extended Fig. 3. Posterior distributions of the DLA modelling leaving the
absorption redshift, $z_{\rm abs}$, as a free parameter. The vertical bars
indicate the background galaxy redshifts. Most galaxy sightlines prefer a
foreground absorber and exclude a host-galaxy origin at $>3\sigma$ confidence.

Extended Fig. 4. The spatial distribution of the galaxy sightlines as a
function of impact parameter from the center of the proto-cluster, color-coded
by the derived foreground H i column densities.

Extended Fig. 5. Relative line-of-sight H i column densities as a function of
projected distance at $z=5.4$. The right hand panel indicates the CDF of
$N_{\mathrm{H\,I}}$-ratios. The dashed line indicates the median of the
observed distribution of $N_{\textit{H}\,I}$ ratio. The galaxies associated
with the smallest on-sky projected distance display similar column-densities.
Objects with projected distance $d<100$,$100<d<250$, $d>250$ kpc are indicated
in black, dark-blue and blue respectively.

Extended Fig. 6. Relationship between neutral gas overdensity $f_{\rm
HI}(1+\delta)$, column density, and co-moving coherent length scale. The blue
error bar indicates our measurement; lines indicate the expected relationship
for assuming a unity fill factor, and orange points indicate the trend
obtained by subsampling the Technicolor Dawn (TD) simulation at $z=5.5$. The
observations would imply overdensities $f_{\rm HI}(1+\delta)\approx
10^{3}-10^{4}$ if the probed sightlines represent the entire region. Such
large, spatially-coherent, neutral regions do not arise in the simulation at
$z=5.5$, confirming that they are quite rare.

Extended Fig. 7. The simulated redshift evolution of the halo and baryonic
mass in the proto-cluster at $z=5.4$. Solid lines show the total mass within
the full simulation zoom region and the dashed lines the mass within
$R<R_{200}$.

Extended Fig. 8. (top) An example projection of the neutral hydrogen density
from the Manhattan Suite at $z=5.4$, centered on the most massive structure in
the simulation suite. The panels are three views along the three principal
axes, and the coordinates are in co-moving Mpc. There is spatially-extensive
high column density ($>10^{21}\,\mathrm{cm}^{-2}$) gas through the halo.
(bottom) The squares show the probability density function of covering
fractions at a minimum column density threshold (given in the legend). The
curves are gamma function fits to the simulation data. The histograms of
columns are produced from all $100$ unique proto-clusters in the Manhattan
Suite at $z=5.4$, with $3$ viewing angles each (along the principal axes). The
transition region between $10^{21}\,\mathrm{cm}^{-2}$ and
$10^{21.7}\,\mathrm{cm}^{-2}$ shows a wide variety of possible covering
fractions depending on the proto-cluster and viewing angle.

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