11institutetext:  INAF - Osservatorio Astronomico di Trieste, Via G. Tiepolo
11, 34143, Trieste, Italy 22institutetext: Scuola Normale Superiore, Piazza
dei Cavalieri 7, 56126, Pisa, Italy 33institutetext: IFPU - Institute for
Fundamental Physics of the Universe, via Beirut 2, I-34151 Trieste, Italy
44institutetext: Dipartimento di Fisica e Astronomia, Università degli Studi
di Firenze, Via G. Sansone 1, Italy 55institutetext: INAF - Osservatorio
Astrofisico di Arcetri, Largo E. Fermi 5, I-50125 Firenze, Italy
66institutetext: Dipartimento di Fisica, Sezione di Astronomia, Universitá di
Trieste, via Tiepolo 11, 34143 Trieste, Italy 77institutetext: Centre for
Astrophysics and Supercomputing, Swinburne University of Technology, Hawthorn,
Victoria 3122, Australia 88institutetext: ARC Centre of Excellence for All-Sky
Astrophysics in 3 Dimensions (ASTRO 3D), Australia 99institutetext: Department
of Physics & Astronomy, University of California, Riverside, CA 92521, USA
1010institutetext: Max Planck Institut für Astronomie, Königstuhl 17, D-69117,
Heidelberg, Germany 1111institutetext: Institute for Theoretical Physics,
University of Heidelberg, Philosophenweg 16, 69120 Heidelberg, Germany
1212institutetext: Gemini Observatory, NSF’s NOIRLab, 670 N A’ohoku Place,
Hilo, Hawai’i 96720, USA 1313institutetext: Institute for Astronomy,
University of Edinburgh, Blackford Hill, Edinburgh, EH9 3HJ, UK
1414institutetext: Tata Institute of Fundamental Research, Homi Bhabha Road,
Mumbai 400005, India 1515institutetext: Research School of Astronomy and
Astrophysics, Australian National University, Canberra, ACT 2611, Australia

# Evidence of Pop III stars’ chemical signature in neutral gas at $z\sim 6$

A study based on the E-XQR-30 spectroscopic sample

Alessio Sodini 11 Valentina D’Odorico, E-mail:
<EMAIL_ADDRESS>Stefania Salvadori 4455 Irene Vanni 4455
Manuela Bischetti 1166 Guido Cupani 1133 Rebecca Davies 7788 George D. Becker
99 Eduardo Bañados 1010 Sarah Bosman 10101111 Frederick Davies 1010 Emanuele
Paolo Farina 1212 Andrea Ferrara 22 Laura Keating 1313 Girish Kulkarni 1414
Samuel Lai 1515 Emma Ryan-Weber 7788 Alma Maria Sebastian 7788 Fabian Walter
1010

(Received ; accepted )

###### Abstract

Aims. This study explores the metal enrichment signatures attributed to the
first generation of stars (Pop III) in the Universe, focusing on the E-XQR-30
sample – a collection of 42 high signal-to-noise ratio spectra of quasi-
stellar objects (QSOs) with emission redshifts ranging from 5.8 to 6.6. We aim
to identify traces of Pop III metal enrichment by analyzing neutral gas in the
interstellar medium of primordial galaxies and their satellite clumps,
detected in absorption.

Methods. To chase the chemical signature of Pop III stars, we studied metal
absorption systems in the E-XQR-30 sample, selected through the detection of
the neutral oxygen absorption line at 1302 Å. The O i line is a reliable
tracer of neutral hydrogen and allowed us to overcome the challenges posed by
the Lyman-$\alpha$ forest’s increasing saturation at redshifts above $\sim 5$
to identify Damped Lyman-$\alpha$ systems (DLA). We detected and analyzed 29 O
i systems at $z\geq 5.4$, differentiating between proximate DLAs (PDLA) and
intervening DLAs. Voigt function fits were applied to obtain ionic column
densities, and relative chemical abundances were determined for 28 systems.
These were then compared with the predictions of theoretical models.

Results. Our findings expand the study of O i systems at $z\geq 5.4$ fourfold.
No systematic differences were observed in the average chemical abundances
between PDLAs and intervening DLAs. The chemical abundances in our sample
align with literature systems at $z>4.5$, suggesting a similar enrichment
pattern for this class of absorption systems. A comparison between these DLA-
analogues at $4.5<z<6.5$ with a sample of very metal-poor DLAs at $2<z<4.5$
shows in general similar average values for the relative abundances, with the
exception of [C/O], [Si/Fe] and [Si/O] which are significantly larger for the
high-$z$ sample. Furthermore, the dispersion of the measurements significantly
increases in the high-redshift bin. This increase is predicted by the
theoretical models and indicates a potential retention of Pop III signatures
in the probed gas.

Conclusions. This work represents a significant advancement in the study of
the chemical properties of highly neutral gas at $z\geq 5.4$, shedding light
on its potential association with the metal enrichment from Pop III stars.
Future advancements in observational capabilities, specifically high-
resolution spectrographs, are crucial for refining measurements and addressing
current limitations in the study of these distant absorption systems.

###### Key Words.:

galaxies: high-redshift – QSOs: absorption lines – Stars: Population III –
dark ages, reionization, first stars

##  1 Introduction

Measuring the abundances of chemical elements in galactic and intergalactic
gas provides some of the most useful observables for investigating stellar
formation and evolution in the Universe. In fact, the comparison between the
observed stellar chemical abundances and those predicted by theoretical models
can be used to place constraints on stellar evolution models. In turn, these
models are a key ingredient in constraining the history of galaxy formation
and evolution. (e.g. Maiolino & Mannucci, 2019).

Of particular interest is the first generation of stars in the Universe, the
so-called Population III (Pop III) stars (for a review, see Klessen & Glover,
2023, and references therein). These stars formed from gas produced by the Big
Bang nucleosynthesis, rich in hydrogen and helium but almost metal free.
Models predict that they produced abundant quantities of UV photons which
started the process of H i reionization in the Universe; when they exploded as
supernovae (SNe) they enriched the interstellar medium (ISM) and the
intergalactic medium (IGM) with the first heavy elements. On the other hand,
if, at the end of their life, they turned into black holes (BHs) they could
provide the seeds of the super-massive BH observed at $z\sim 6-7$.

In the conventional framework in which Pop III stars are predominantly
massive, i.e. $\approx 10-1000\,M_{\sun}$ (e.g. Hirano et al., 2014), those
with $140M_{\sun}\leq M_{\rm PopIII}\leq 260M_{\sun}$ will explode as pair
instability supernovae (PISN, Heger & Woosley 2002; Takahashi et al. 2018),
that leave no remnant and distribute the first metals in the gas in and out of
galaxies (e.g. Bromm & Larson, 2004). At intermediate masses, $10M_{\sun}\leq
M_{\rm PopIII}\leq 100M_{\sun}$, first stars can also evolve as SNe but they
can have a variety of explosion energies, thus yielding very different
chemical elements ratios depending upon the mass of the progenitor star and
the SN explosion energy (e.g. Heger & Woosley, 2010; Nomoto et al., 2013;
Limongi & Chieffi, 2018). The nucleosynthetic signature of Pop III stars may
therefore be very different from that of subsequent generations of more metal-
rich stars, i.e. Pop II/I stars (e.g. Salvadori et al., 2019; Vanni et al.,
2023b).

A technique commonly used for testing the predicted existence of Pop III stars
is to identify their chemical traces by analyzing the abundance pattern of
their direct descendants, which can be identified among ancient, metal-poor
stars in the Local Group. Indeed, if massive Pop III stars quickly ended their
lives as energetic SNe, their nucleosynthetic products were efficiently
dispersed into the surrounding gas where subsequent generations of stars were
able to form.

Local observations have reported the existence of many Carbon Enhanced Metal-
Poor stars (CEMP stars, [C/Fe]$>0.7$ Beers & Christlieb 2005), both in the
galactic halo (e.g. Bonifacio et al., 2015; Yoon et al., 2019) and in ultra-
faint dwarf galaxies (e.g. Spite et al., 2018; Simon, 2019). These stars
appear predominantly at [Fe/H]$<-3$ and the most iron-poor among them have
chemical abundance patterns in agreement with those produced by Pop III stars
which exploded as low-energy SNe (e.g. Iwamoto et al., 2005; Marassi et al.,
2015). Stars imprinted by more energetic hypernovae or PISN are more difficult
to be identified since they have normal [C/Fe]$\leq 0.0$ (e.g. Koutsouridou et
al., 2023; Pagnini et al., 2023). However, thanks to other peculiar chemical
abundances, two of them have been recently discovered (Skúladóttir et al.,
2021; Placco et al., 2021). Furthermore, a rare halo star imprinted by a
massive and energetic PISN has been found among alpha-poor stars in the LAMOST
survey (Xing et al., 2023), with strong implications for the initial mass
function of Pop III stars (Koutsouridou et al., 2024).

Another method to find the traces of Pop III stars is to measure the abundance
of elements present in primordial galaxies. This can be done by studying the
metal absorption lines observed in high-redshift QSO spectra (e.g. Welsh et
al., 2021; Saccardi et al., 2023). The main advantage of this observational
technique is that the conversion from the properties of the observed ionic
absorption lines to the total abundance of elements is often simple. This is
especially true for systems with a high neutral hydrogen (H i) column density,
known as Damped Lyman-$\alpha$ systems (DLAs; $\log({N(\mathrm{\mbox{H\,{\sc
i}}})/{\rm cm}^{-2}})\gtrsim 20.3$), which trace galactic environments along
QSO lines of sight (see Wolfe et al., 2005, for a review).

In DLAs, the large amount of neutral hydrogen shields the innermost gas from
the ionizing radiation. Consequently, oxygen, which has a first ionization
potential similar to that of hydrogen111In fact, oxygen is in charge-exchange
equilibrium with H i because the two ionization potentials are almost
identical., will be present in the gas predominantly in the neutral state.
While other elements such as carbon, silicon, magnesium and iron, which have a
first ionization potential significantly lower than $13.6\,\rm eV$, will be
mainly singly ionized. As a result, in the simplest case, the abundance for a
given element can be calculated directly from the measured column density of
ions in a single electronic state (e.g. Rafelski et al., 2012). Complications
arise at lower H i column densities, whereby the ionization effects start to
become significant or in the case of metal depletion onto dust grains (e.g.
Péroux & Howk, 2020).

Thanks to the discovery of metal-enriched absorbers up to $z\sim 6$ (Becker et
al., 2006; Ryan-Weber et al., 2006; Simcoe, 2006; D’Odorico et al., 2013,
2022; Davies et al., 2023a), it is now possible to investigate chemical
abundances in the gas when the Universe was about one billion years old. At
that time, the observed metals could only have been produced by massive stars,
which have a sufficiently short lifespan and which explode as SNe in their
final phase.

At redshifts $z\geq 5$, however, the large density of absorption lines in the
H i Lyman-$\alpha$ (Ly$\alpha$) forest makes it very difficult to measure the
H i column density of single absorption systems. Luckily, many chemical
elements (in particular: C, N, O, Mg, Al, Si, S, Cr, Mn, Fe, Zn) have ionic
transitions that fall outside the Ly$\alpha$ forest, in the region of the
spectrum redward of the Ly$\alpha$ emission of the QSO. As a consequence,
although it is rarely possible to estimate absolute chemical abundances (e.g.
relative to hydrogen) many relative abundances can be determined, which
provide unique constraints on nucleosynthesis in massive (and presumably
metal-poor) stars.

Becker et al. (2012) analyzed the relative abundances of C, O, Si and Fe in
nine low ionization QSO absorption systems at $4.7<z<6.3$, considered to be
DLAs or sub-DLAs (the latter are defined to have $19.0\lesssim\log{N_{\rm
HI}}\lesssim 20.3$) thanks to the presence of the neutral oxygen absorption
line at $1302$ Å. The authors compared the relative abundances of the $z>4.7$
systems with those measured in very metal-poor222Cooke et al. (2011) defines
VMP-DLAs as systems with [Fe/H] $<-2$ following the definition used for stars.
DLA systems (VMP-DLA) at lower redshifts ($2<z<4.5$) observed by Cooke et al.
(2011). The two samples show minimal dispersion in the ratio between the
column densities of any two ions (C ii, O i, Si ii and Fe ii) and no apparent
evolution with redshift. The lack of dispersion suggests that the relative
abundances of the elements are correctly estimated from the ratios of the
corresponding ions, with minimal ionization or depletion effects due to dust
formation (in particular, for the high-$z$ systems). It also suggests that
heavy element enrichment in very metal-poor DLAs at $2<z<6$ are dominated by
the integrated returns of SNe of type II and I. This is confirmed also in
later studies (e.g. Poudel et al., 2018, 2020), in which the lack of exotic
abundances at $z\sim 5-6$ suggests that ordinary Pop II stars (rather than
massive Pop III stars) likely enriched the interstellar gas with metals even
approaching the epoch of hydrogen reionization.

In this work, we exploit the new XQR-30 sample of high-quality spectra of QSOs
at $z\sim 6$ (D’Odorico et al., 2023) to significantly increase the number of
O i absorption systems at $z\gtrsim 5.4$. Our aim is to study the relative
abundance of elements present in primordial galaxies and to obtain information
on the nature of the stars that contributed to the enrichment of the gas.

The paper structure is the following. In Section 2, the spectroscopic sample
used in this work and the data reduction are briefly described. Section 3
reports how we performed the analysis of the spectra, the search and
identification of absorption lines, the fit of the velocity profiles and the
estimate of the H i column densities. In Section 4, we present the relative
abundances of the observed systems and discuss the results obtained by
comparing them with those of similar systems present in the literature at low
and high redshift. Section 6 is dedicated to the discussion of our results and
the comparison with the predictions of theoretical models of enrichment.
Finally in Section 7, we conclude summarizing the obtained results.

##  2 Sample and data reduction

Table 1: List of the E-XQR-30 QSOs.

QSO | $z_{\rm em}$ | Ref. | $\rm R_{VIS}$ | $\rm R_{NIR}$ | SNR | Ref.
---|---|---|---|---|---|---
SDSS J092721.82+200123.7 | 5.7722 | CO,1 | 12900 | 9400 | 36.6 | 2
PSO J308.4829-27.6485 | 5.799 |  Mg ii,2,3 | 11800 | 10600 | 31.2 | 1
SDSS J083643.85+005453.3 | 5.810 | Ly$\alpha$,4 | 13100 | 10200 | 37.5 | 3
PSO J065.9589+01.7235 | 5.8348 | [C ii],5 | 10700 | 9700 | 27.4 | 1
PSO J025.2376-11.6831 | 5.8414 | [C ii],5 | 10500 | 9700 | 27.5 | 1
PSO J242.4397-12.9816 | 5.8468 | [C ii],5 | 10700 | 9700 | 15.0 | 1
PSO J023.0071-02.2675 | 5.850 | Ly$\alpha$,6 | 10900 | 9700 | 18.6 | 1
PSO J183.2991-12.7676 | 5.893 |  Mg ii,2,3 | 11900 | 10000 | 34.1 | 1
PSO J108.4429+08.9257 | 5.955 |  Mg ii,2,3 | 12200 | 9800 | 36.8 | 1
PSO J089.9394-15.5833 | 5.972 |  Mg ii,2,3 | 12000 | 9700 | 28.9 | 1
ULAS J014837.63+060020.0 | 5.977 |  Mg ii,3 | 13300 | 10000 | 60.7 | 4
PSO J029.5172-29.0886 | 5.981 | Ly$\alpha$,4 | 10800 | 9900 | 26.5 | 1
VDES J2250-5015 | 5.985 |  Mg ii,2,3 | 10800 | 9600 | 20.9 | 1
SDSS J081827.40+172251.8 | 5.997 | Ly$\alpha$,4 | 11000 | 7600 | 52.8 | 3
PSO J007.0273+04.9571 | 6.0015 | [C ii],7 | 11500 | 9700 | 28.4 | 1
SDSS J231038.88+185519.7 | 6.0031 | [C ii],8 | 12700 | 9800 | 40.7 | 1
PSO J009.7355-10.4316 | 6.0040 | [C ii],7 | 11500 | 10500 | 24.1 | 1
VST-ATLAS J029.9915-36.5658 | 6.013 |  Mg ii,2,3 | 10100 | 9200 | 25.4 | 1
SDSS J130608.26+035626.3 | 6.0330 | [C ii],7 | 12000 | 9600 | 34.0 | 3
VDES J0408-5632 | 6.033 |  Mg ii,2,3 | 11300 | 9700 | 38.9 | 1
PSO J158.6937-14.4210 | 6.0685 | [C ii],9 | 10800 | 9100 | 29.6 | 1
SDSS J084229.43+121850.4 | 6.0754 | [C ii],7 | 11400 | 10000 | 37.7 | 1
PSO J239.7124-07.4026 | 6.1102 | [C ii],9 | 11300 | 11000 | 34.7 | 1
CFHQS J150941-174926 | 6.1225 | [C ii],10 | 11800 | 8000 | 27.4 | 3
ULAS J131911.29+095051.4 | 6.1347 | [C ii],7 | 13700 | 9800 | 41.1 | 3
PSO J217.0891-16.0453 | 6.1498 | [C ii],10 | 11500 | 10200 | 36.2 | 1
PSO J217.9185-07.4120 | 6.166 |  Mg ii,2,3 | 11200 | 9900 | 24.1 | 1
PSO J060.5529+24.8567 | 6.170 |  Mg ii,2,3 | 11500 | 10300 | 29.0 | 1
PSO J359.1352-06.3831 | 6.1722 | [C ii],9 | 11300 | 10000 | 35.8 | 1
PSO J065.4085-26.9543 | 6.1871 | [C ii],7 | 11700 | 10500 | 41.2 | 1
SDSS J103027.09+052455.0 | 6.304 |  Mg ii,3 | 12300 | 8400 | 16.8 | 3
SDSS J010013.02+280225.8 | 6.3268 | [C ii],7 | 11400 | 10300 | 103.2 | 7
VST-ATLAS J025.6821-33.4627 | 6.3373 | [C ii],7 | 11200 | 9300 | 29.6 | 5,6
VDES J2211-3206 | 6.3394 | [C ii],10 | 10600 | 9100 | 12.5 | 1
DELS J153532.87+194320.1 | 6.381 | Ly$\alpha$,4 | 11600 | 9700 | 15.9 | 1
PSO J183.1124+05.0926 | 6.4386 | [C ii],7 | 11900 | 10200 | 21.8 | 1
WISEA J043947.09+163415.8 | 6.5188 | [C ii],11 | 9500 | 8200 | 114.4 | 8
VDES J0224-4711 | 6.525 |  Mg ii,2,3 | 11200 | 9400 | 15.1 | 1
PSO J036.5078+03.0498 | 6.5405 | [C ii],7 | 10700 | 9200 | 18.4 | 5,6
PSO J231.6576-20.8335 | 6.5869 | [C ii],7 | 10800 | 9800 | 18.0 | 1
PSO J323.1382+12.2986 | 6.5872 | [C ii],7 | 10900 | 9800 | 15.9 | 1
DELS J092347.12+040254.4 | 6.6330 | [C ii],11 | 11600 | 10200 | 10.8 | 1
333The various columns show: the QSO name, the emission redshift, the emission
line used to measure it and its reference, the measured resolution of the
optical and infrared regions of the spectrum, the SNR calculated at $1285$ Å
in the rest frame, and the reference for the X-SHOOTER spectrum.

Redshift: 1 - Carilli et al. (2007), 2 - Bischetti et al. (2022), 3 -
D’Odorico et al. (2023), 4 - Zhu et al. (2021), 5 - Bosman et al. (in prep.),
6 - This work, 7 - Venemans et al. (2020), 8 - Wang et al. (2013), 9 - Eilers
et al. (2021), 10 - Decarli et al. (2018), 11 - Yang et al. (2021). X-SHOOTER
spectrum: 1 - D’Odorico et al. (2023), 2 - Codorenau et al. (2017), 3 -
D’Odorico et al. (2013), 4 - Becker et al. (2015), 5 - Becker et al. (2019), 6
- D’Odorico et al. (2022), 7 - Bosman et al. (2018), 8 - Fan et al. (2019).

The data used for this work (summarized in Table 1) include optical and NIR
spectra of 42 QSOs in the redshift range $5.8\lesssim z\lesssim 6.6$. Thirty
of these QSOs are part of the XQR-30 survey, an ESO Large Programme (ID.
1103.A-0817, P.I. V. D’Odorico) which obtained 248 hours of observation with
the X-SHOOTER spectrograph (Vernet et al., 2011) at the Very Large Telescope
(VLT). For these QSOs, optical spectra (VIS, $\lambda=5500-10,250$ Å) were
obtained using a slit width of $0.9^{\prime\prime}$ corresponding to a nominal
resolving power $R_{\rm VIS}\simeq 8900$, and near-infrared spectra (NIR,
$\lambda=9800-24,800$ Å) using a slit width of $0.6^{\prime\prime}$
corresponding to $R_{\rm NIR}\simeq 8100$. The ultraviolet spectrum of the UVB
arm was not used, since the spectrum of high-redshift QSOs is completely
absorbed in this spectral region.

The other 12 QSOs which are part of the analysed sample, have been retrieved
from the X-SHOOTER archive and have similar characteristics to those of XQR-30
(see Table 1). The total sample, dubbed the enlarged XQR-30 sample (E-XQR-30),
is thoroughly described in D’Odorico et al. (2023).

Here, we briefly review the steps of the spectroscopic data reduction
procedure. The reduction was performed with a proprietary software (see Becker
et al., 2019), which has demonstrated to perform better than the default ESO
pipeline, in particular for what concerns the sky subtraction (see Lopez et
al., 2016). First, the individual frames were corrected for the bias and the
dark current and then divided by the flat field frames. A subtraction of the
sky spectrum on each frame was then performed following Kelson (2003). The
frames were calibrated in wavelength and flux calibrated444Note that this is a
relative flux calibration and not an absolute calibration. based on a standard
star. Corrections for telluric absorptions were performed using a model based
on the ESO SKYCALC Cerro Paranal Advanced Sky Model (Noll et al., 2012; Jones
et al., 2013). Finally, the frames of the individual exposures thus obtained
were added together and a one-dimensional final spectrum was extracted.

As previously mentioned, the nominal resolving power of the VIS and NIR arm of
X-SHOOTER depend on the choice of the slit width. However, if the seeing disk
at the time of observation is smaller than the slit, the resolving power of
the observed spectrum will be larger than the nominal one. The determination
of the correct resolving power of the spectrum is particularly relevant when
fitting absorption lines. The ”true” resolution of the E-XQR-30 spectra was
estimated using an empirical relation between the FWHM of the order spatial
profile and the FWHM of the model fitting the telluric lines in the single
frames (see D’Odorico et al., 2023, for further details). In summary, we find
that the resolving power of the final spectra is always larger than the
nominal one (see the values reported in Table 1) with medians of $R_{\rm
VIS}\simeq 11,400$ and $R_{\rm NIR}\simeq 9800$.

Finally, the systemic redshifts of the QSOs, listed in Table 1, are based on
CO or [C ii] emission, when available, otherwise we considered the
maximum555We adopt the maximum value because the Mg ii line is generally
blueshifted by $\sim 500$ km s-1 with respect to systemic redshift (e.g.
Venemans et al., 2016; Mazzucchelli et al., 2017; Schindler et al., 2020).
between the redshift measured from the Mg ii emission line (Bischetti et al.,
2022; D’Odorico et al., 2023) and that determined from the first Ly$\alpha$
absorption line observed on the peak of the Ly$\alpha$ emission (following Zhu
et al., 2021; Becker et al., 2019). All the spectra of the E-XQR-30 sample are
shown in D’Odorico et al. (2023).

##  3 Data analysis

The analysis of the spectra of the QSO sample was performed with the Astrocook
software (Cupani et al., 2020). Astrocook is a Python 3 (Van Rossum & Drake,
2009) package for analyzing QSO spectra, featuring a graphical user interface
with numerous analysis methods. Below is a description of the analysis
procedure that was used for the E-XQR-30 spectra.

We note that the procedure of detection and identification of all the metal
absorption lines in the 42 spectra of the E-XQR-30 QSO sample is reported in
the general catalogue paper (Davies et al., 2023a), which is the official
reference for the metal lines of the survey. However, we decided to report
here the procedure adopted for the search of the low ionization systems which
was carried out before and independently from the work of Davies et al.
(2023a) for the master thesis of A. Sodini. The results of the Voigt fitting
adopted in this work are in agreement with those in Davies et al. (2023a)
within $1\sigma$.

###  3.1 Detection of the absorption lines and estimate of the intrinsic
emission spectrum

In order to prepare the spectra for our analysis, first we have extracted from
the VIS spectrum the wavelength region that goes from the Ly$\alpha$ emission
of the QSO to $10,100$ Å, to exclude the Ly$\alpha$ forest. We then detected
the absorption lines present in this part of the spectrum. The procedure in
Astrocook looks for the local minima of flux density in the spectrum, after
smoothing with a Gaussian profile to reduce the noise. Different values of the
Gaussian variance are used in descending order to detect lines of different
widths. We used values of the Gaussian variance from $100$ km s-1 to $15$ km
s-1, while we set a threshold to define the prominence of the minima,
expressed as a multiple of the variance of the local flux density, of about
$2-3\,\sigma$. The regions between the local maxima adjacent to each line are
then masked.

At this point, the intrinsic emission spectrum is fitted with Astrocook by
interpolating nodes in the unmasked spectrum with a spline function of chosen
degree. The nodes are placed at fixed velocity intervals (we used $500-750$ km
s-1) considering the median flux density of the surrounding region, from which
outliers are excluded.

We then analyzed the NIR region of the spectrum, selecting the wavelength
range from $10,100$ to $22,000$ Å. The VIS and NIR regions of the spectrum
were equalized, rescaling the flux density in the NIR part; for this operation
we have selected a wavelength range that goes from $10,000$ to $10,200$ Å
common to both regions, in which Astrocook calculates the rescaling factors
from the ratios of the median flux densities. Subsequently, with the same
procedure used for the VIS part of the spectrum, we detected the absorption
lines and we fitted the emission spectrum also for the NIR part, setting the
nodes for the interpolation at intervals of $1000-1500$ km s-1. Finally, the
two parts were stitched together at 10,150 to obtain a single spectrum, and we
revised the fit of the emission spectrum by manually eliminating some nodes
and adding new ones directly on the main spectrum.

###  3.2 Identification and fit of the metal absorption lines

The absorption systems were first automatically identified with Astrocook,
which divides the wavelengths of the detected lines by the laboratory
wavelengths of a list of transitions commonly observed in QSO spectra, and
finds coincidences between the possible redshift values resulting from the
cross-comparison. Identified lines were then fitted with Voigt profiles using
Astrocook, which provides for each line the central redshift, the column
density and the Doppler width.

In the spectra of the QSOs analyzed in this work, we first identified the
lines due to the most common ionic doublets, such as C iv $\lambda\lambda\
1548,\,1550$ Å, Si iv $\lambda\lambda\ 1393,\,1402$ Å and Mg ii
$\lambda\lambda\ 2796,\,2803$ Å. Identifications proposed by Astrocook were
visually inspected to check the correspondence of the line velocity profiles
and then fitted.

Then, we proceeded with the identification of the systems showing absorption
due to O i (dubbed _DLA-analogues_), which are the focus of this work. The
transition due to O i $\lambda\ 1302$ Å was identified by requiring the
simultaneous identification of the transition due to C ii $\lambda\ 1334$ Å
and, possibly, also that due to Si ii $\lambda\ 1304$ Å at the same redshift.
Subsequently, other lines at low ionization associated with the identified
systems were searched for. In particular, we considered: Si ii $\lambda\
1260$, $1526$ Å, Al ii $\lambda\ 1670$ Å and the transitions of the Fe ii
multiplet with rest frame wavelengths $\lambda\ 1608$, $2344$, $2374$, $2382$,
$2586$ and $2600$ Å.

We found in most cases a redshift correspondence also with the Mg ii lines
previously found in the NIR part of the spectrum. However, for systems in the
redshift range $5.5<z_{\rm abs}<5.9$, the doublet of the Mg ii falls in the
spectral region strongly affected by telluric absorptions between the
photometric $H$ and $K$ bands and it is not always detectable (see details in
Appendix B).

Finally, we verified if these low ionization systems were also associated with
previously identified high ionization lines such as those of C iv and Si iv.

When at the redshift of a given system, we did not detect significant
absorption due to some of the previously mentioned ions, or the absorption was
below the 3$\sigma$ detection threshold, we estimated a $3\sigma$ upper limit
to their column density. This limit was estimated starting from the average
signal-to-noise ratio (SNR) per pixel of the spectrum in a wavelength interval
around the expected occurrence of the absorption. This ratio is linked to the
equivalent width of the line, possibly present at that point, by the relation
(Herbert-Fort et al., 2006):

${\rm SNR}\simeq\frac{3\,\lambda_{0,\rm X}}{c\,w_{0,\rm
X}}\sqrt{4.24264\,b\,\Delta v}$ (1)

where $\lambda_{0,\rm X}$ and $w_{0,\rm X}$ are respectively the wavelength
and the equivalent width in the rest frame of the transition X, $b$ is the
Doppler parameter, and $\Delta v$ is the size of the pixels which, for the
analyzed spectra, is equal to 10 km s-1. The $b$ parameter for weak low
ionization lines is assumed to be equal to that of the other ions detected in
the system, while for the upper limits on Si iv and C iv we assumed $b=26$ km
s-1, which is the average value of the Doppler parameter for the detected
systems. The corresponding upper limit on the column density is estimated from
the relation666This relation assumes that the line is on the linear part of
the curve of growth, i.e. that the relation between column density and
equivalent width does not depend on the Doppler parameter.:

$N_{\rm X}=1.13\cdot 10^{20}\frac{w_{0,\rm X}}{f_{\rm X}\,\lambda_{0,\rm
X}^{2}}\ [\rm cm^{-2}]$ (2)

where $f_{\rm X}$ is the oscillator strength of transition X.

To conclude the identification process, we associated, when possible, the
other lines present in the spectrum with the C iv, Si iv and Mg ii systems
found initially and which did not match with the low ionization systems. In
some systems containing C iv, the Si iv doublet and the Mg ii doublet are also
present; in some of these systems we have also detected lines of Si ii, C ii,
Fe ii and Al ii. Some of these low ionization systems could also be DLA-
analogues but they are at $z_{\rm abs}<\lambda_{\rm Ly\alpha}(1+z_{\rm
em})/\lambda_{\rm OI}-1$, and the O i line falls into the Ly$\alpha$ forest.
For this reason they were not taken into consideration for the subsequent
analysis.

The Doppler $b$ parameter is given by the quadrature sum of the thermal and
turbulent components. In the analysis of low ionization systems, we adopted
the following procedure: when the fit of a velocity component returned
comparable $b$ values for the different ionic transitions, we re-performed the
fit of the component by linking their $b$ parameters, assuming that the
turbulent motions are dominant over thermal agitation. Furthermore, to take
into account the instrumental resolution, when the fit of a line returned a
value lower than $b_{\rm ins}/3$777Where $b_{\rm ins}=(c/R)/(2\sqrt{\ln 2})$
is the Doppler parameter corresponding to the instrumental broadening., we re-
performed the fit with the column density and the redshift as free parameters,
but fixing $b$ to this minimum value.

Figure 1: Comparison between two absorption lines fitted with Voigt profiles
in XQR-30 (upper panels; black line: observed spectrum; red line: observed
error; blue line: continuum level; green line: Voigt profile fit) and their
theoretical profiles without the convolution with the instrumental broadening
(lower panels). The theoretical profile of the line on the left is saturated,
while the theoretical profile of the line on the right is not.

Some of the detected lines could also be affected by saturation, which however
at this resolution can be masked by the instrumental broadening of observed
feature. To determine which lines were saturated, we therefore simulated the
theoretical Voigt profile of the lines using the parameters obtained from the
Voigt fitting, without the enlargement due to the resolution of the
instrument, as shown in Figure 1. When the theoretical profile was saturated,
we considered the value of the column density obtained from the fit as a lower
limit.

The velocity plots and the parameters obtained from the fit of the studied
DLA-analogues are reported in Appendix B.

###  3.3 Analysis of the DLA-analogues

In the spectra of the 42 analyzed QSOs of the E-XQR-30 sample, we detected 29
DLA-analogues (i.e., low ionization systems traced by the presence of O i),
along the line of sight to 19 QSOs. We note that in our sample we have two
more O i absorbers with respect the official catalog by Davies et al. (2023a).
This is due to the fact that the O i $\lambda\,1302$ lines of the systems at
$z=5.6993$ in PSO J060+24 and at $z=5.7974$ in SDSS J0100+2802 are falling at
the beginning of the Ly$\alpha$ forest and thus they were excluded from the
official E-XQR-30 sample of metal absorption lines, while we decided to
consider them because the O i column density can be reliably determined. On
the other hand, the proximate system at $z=5.8441$ along the line of sight to
PSO J023-02 shows absorption lines due to fine-structure transitions of C ii
and Si ii, high-ionization transitions due to N v and also a possible
signature of partial coverage in the H i Ly$\alpha$ profile implying that it
could be very close to the ionizing source, possibly arising in a gas outflow
powered by the AGN. For these peculiar characteristics, we decided to exclude
it from the subsequent chemical analysis.

For those systems that have more than one velocity component, the total column
density for each ion was computed as the sum of the column densities of the
single components and the error was obtained propagating the individual
errors.

The total column densities of each ion detected in each O i system are
reported in Table 2. This table also shows the redshift of the system, for
which we have considered the absorption redshift of the O i. For systems with
multiple velocity components, the average redshift of the system was
calculated as the column-density weighted average of the O i redshifts of the
various components:

$z_{\rm abs}=\frac{\sum_{i}{z_{i}N_{i}}}{\sum_{i}{N_{i}}}.$ (3)

Finally, for a system for which the O i absorption could not be fitted
($z=5.8990$ in DELS J1535+1943, see Appendix B), we considered the redshift of
C ii.

Depending on the velocity separation of the systems from the QSO emission
redshift, we distinguish two types of absorption systems: the proximate DLAs
(or PDLAs), with $v_{\rm abs}\leq 5000$ km s-1, and the intervening DLAs at
larger velocity separations. PDLAs are systems which are thought to be
“associated” with the QSO itself, since they are close enough to be affected
by the ionizing flux of the QSO or even to be part of high velocity outflows
powered by the AGN. Intervening DLAs, on the other hand, are generally
independent structures such as galaxies or neutral gas condensations close to
galaxies along the QSO line of sight (e.g. Perrotta et al., 2016).

The velocity separation of absorption systems from the QSO emission redshift
is determined with the relation (Peterson, 1997):

$v_{\rm abs}=\frac{(1+z_{\rm em})^{2}-(1+z_{\rm abs})^{2}}{(1+z_{\rm
em})^{2}+(1+z_{\rm abs})^{2}}c.$ (4)

In our sample of DLA-analogues, 10 are PDLAs, while the other 19 are
intervening systems (see Table 2).

Table 2: Logarithm of the total column densities (in cm-2) of ions detected in
the observed O i systems.

QSO | $z_{\rm abs}$ | ${\log N_{\rm HI}}^{a}$ | ${\log N_{\rm HI}}^{b}$ | $\log N_{\rm OI}$ | $\log N_{\rm CII}$ | $\log N_{\rm SiII}$ | $\log N_{\rm AlII}$ | $\log N_{\rm FeII}$ | $\log N_{\rm MgII}$ | $\log N_{\rm SiIV}$ | $\log N_{\rm CIV}$
---|---|---|---|---|---|---|---|---|---|---|---
PSO J308-27 | $5.4400$ | $>19.10$ | $\cdots$ | $14.09\pm 0.02$ | $13.68\pm 0.03$ | $13.14\pm 0.07$ | $<11.86$ | $12.57\pm 0.06$ | $13.06\pm 0.06$ | $12.67\pm 0.05$ | $13.41\pm 0.07$
PSO J308-27 | $5.6268$ | $>19.79$ | $\cdots$ | $14.78\pm 0.03$ | $14.47\pm 0.03$ | $13.67\pm 0.02$ | $12.45\pm 0.13$ | $13.33\pm 0.03$ | $13.74\pm 0.05$ | $13.12\pm 0.05$ | $13.60\pm 0.12$
PSO J023-02 | $5.4869$ | $>19.33$ | $\cdots$ | $14.32\pm 0.03$ | $14.27\pm 0.15$ | $<13.43$ | $<12.33$ | $12.64\pm 0.10$ | $13.18\pm 0.11$ | $<12.65$ | $<13.51$
PSO J023-02∗∗ | $5.8441$ | $\cdots$ | $\cdots$ | $14.35\pm 0.04$ | $14.32\pm 0.04$ | $13.14\pm 0.04$ | $12.84\pm 0.10$ | $12.95\pm 0.07$ | $\cdots$ | $>14.90$ | $>16.39$
PSO J025-11∗ | $5.7763$ | $>19.23$ | $20.35\pm 0.10$ | $14.22\pm 0.04$ | $14.49\pm 0.03$ | $13.71\pm 0.04$ | $12.58\pm 0.16$ | $13.10\pm 0.05$ | $13.70\pm 0.11$ | $13.80\pm 0.07$ | $14.40\pm 0.05$
PSO J025-11∗ | $5.8385$ | $>20.73$ | $21.25\pm 0.10$ | $>15.72$ | $>15.46$ | $14.79\pm 0.09$ | $13.43\pm 0.20$ | $14.50\pm 0.04$ | $>14.58$ | $13.51\pm 0.03$ | $14.15\pm 0.05$
PSO J108+08 | $5.5624$ | $>18.85$ | $\cdots$ | $13.84\pm 0.03$ | $13.12\pm 0.06$ | $<12.42$ | $<11.56$ | $<11.91$ | $\cdots$ | $<12.39$ | $<13.31$
SDSS J0818+1722 | $5.7912$ | $>19.51$ | $\cdots$ | $14.50\pm 0.02$ | $14.14\pm 0.01$ | $13.33\pm 0.01$ | $\cdots$ | $12.96\pm 0.05$ | $\cdots$ | $<12.58$ | $13.38\pm 0.07$
SDSS J0818+1722 | $5.8767$ | $>19.13$ | $20.20\pm 0.10$ | $14.12\pm 0.02$ | $13.77\pm 0.03$ | $12.96\pm 0.02$ | $<11.90$ | $12.49\pm 0.08$ | $12.96\pm 0.09$ | $12.51\pm 0.07$ | $13.28\pm 0.05$
PSO J007+04∗ | $5.9917$ | $>18.98$ | $20.40\pm 0.10$ | $13.97\pm 0.08$ | $13.45\pm 0.07$ | $12.69\pm 0.04$ | $<12.10$ | $12.57\pm 0.20$ | $<12.84$ | $12.78\pm 0.10$ | $13.42\pm 0.14$
SDSS J2310+1855∗ | $5.9388$ | $>20.28$ | $21.00\pm 0.10$ | $>15.27$ | $>14.33$ | $13.72\pm 0.07$ | $12.17\pm 0.38$ | $13.32\pm 0.07$ | $>13.49$ | $<12.31$ | $<12.95$
PSO J158-14 | $5.8986$ | $>19.61$ | $\cdots$ | $14.60\pm 0.07$ | $14.31\pm 0.03$ | $13.65\pm 0.04$ | $12.26\pm 0.21$ | $13.14\pm 0.03$ | $\cdots$ | $12.83\pm 0.06$ | $13.13\pm 0.09$
PSO J239-07∗ | $5.9918$ | $>18.83$ | $\cdots$ | $13.82\pm 0.06$ | $13.18\pm 0.11$ | $12.60\pm 0.03$ | $<11.75$ | $<12.14$ | $12,47\pm 0.11$ | $<12.33$ | $\cdots$
ULAS J1319+0950∗ | $6.0172$ | $>18.94$ | $\cdots$ | $13.93\pm 0.06$ | $13.17\pm 0.11$ | $12.50\pm 0.04$ | $11.84\pm 0.23$ | $12.45\pm 0.15$ | $12.61\pm 0.16$ | $<12.34$ | $<12.89$
PSO J060+24 | $5.6993$ | $>19.51$ | $\cdots$ | $14.50\pm 0.09$ | $14.22\pm 0.18$ | $13.64\pm 0.03$ | $12.30\pm 0.23$ | $12.96\pm 0.07$ | $\cdots$ | $12.72\pm 0.08$ | $13.29\pm 0.09$
PSO J065-26 | $5.8677$ | $>20.02$ | $\cdots$ | $15.01\pm 0.02$ | $14.53\pm 0.02$ | $13.87\pm 0.03$ | $12.47\pm 0.15$ | $13.42\pm 0.03$ | $13.64\pm 0.05$ | $<12.48$ | $<12.83$
PSO J065-26∗ | $6.1208$ | $>20.42$ | $\cdots$ | $>15.41$ | $>15.24$ | $14.54\pm 0.02$ | $13.21\pm 0.04$ | $13.97\pm 0.03$ | $>14.43$ | $<12.73$ | $<12.99$
PSO J065-26∗ | $6.1263$ | $>19.52$ | $\cdots$ | $14.51\pm 0.03$ | $>14.91$ | $14.04\pm 0.03$ | $13.11\pm 0.05$ | $13.38\pm 0.03$ | $>14.35$ | $13.33\pm 0.03$ | $13.50\pm 0.03$
SDSS J0100+2802 | $5.7974$ | $>19.64$ | $\cdots$ | $14.63\pm 0.03$ | $14.09\pm 0.02$ | $13.56\pm 0.03$ | $12.06\pm 0.08$ | $13.12\pm 0.02$ | $\cdots$ | $12.65\pm 0.12$ | $13.00\pm 0.10$
SDSS J0100+2802 | $5.9450$ | $>18.45$ | $\cdots$ | $13.44\pm 0.04$ | $13.57\pm 0.02$ | $12.77\pm 0.07$ | $11.45\pm 0.14$ | $12.25\pm 0.05$ | $12.64\pm 0.03$ | $12.59\pm 0.08$ | $12.89\pm 0.09$
SDSS J0100+2802 | $6.1114$ | $>19.70$ | $\cdots$ | $14.69\pm 0.14$ | $13.91\pm 0.07$ | $13.01\pm 0.03$ | $11.56\pm 0.10$ | $12.65\pm 0.03$ | $13.10\pm 0.04$ | $<12.01$ | $<12.32$
SDSS J0100+2802 | $6.1434$ | $>19.67$ | $20.20\pm 0.10$ | $14.66\pm 0.02$ | $14.11\pm 0.02$ | $13.27\pm 0.02$ | $11.74\pm 0.11$ | $12.92\pm 0.02$ | $13.26\pm 0.03$ | $<12.07$ | $<12.27$
DELS J1535+1943 | $5.8990$ | $\cdots$ | $\cdots$ | $\cdots$ | $14.64\pm 0.16$ | $13.69\pm 0.07$ | $\cdots$ | $13.17\pm 0.04$ | $13.66\pm 0.19$ | $13.47\pm 0.04$ | $14.14\pm 0.05$
PSO J183+05 | $6.0642$ | $>19.53$ | $\cdots$ | $14.52\pm 0.03$ | $14.31\pm 0.06$ | $13.70\pm 0.04$ | $12.55\pm 0.07$ | $13.15\pm 0.04$ | $13.83\pm 0.19$ | $13.88\pm 0.03$ | $14.47\pm 0.03$
PSO J183+05∗ | $6.4041$ | $>19.79$ | $20.60\pm 0.10$ | $14.78\pm 0.04$ | $14.52\pm 0.07$ | $13.96\pm 0.03$ | $12.39\pm 0.07$ | $13.36\pm 0.03$ | $>14.07$ | $<12.83$ | $<13.06$
WISEA J0439+1634 | $6.2743$ | $>18.18$ | $\cdots$ | $13.17\pm 0.17$ | $13.03\pm 0.12$ | $12.19\pm 0.04$ | $<11.05$ | $<11.60$ | $<11.78$ | $<12.16$ | $<12.50$
VDES J0224-4711 | $6.1228$ | $>19.47$ | $\cdots$ | $14.46\pm 0.02$ | $14.00\pm 0.13$ | $13.37\pm 0.06$ | $<11.94$ | $12.86\pm 0.06$ | $13.14\pm 0.04$ | $<12.76$ | $<12.76$
PSO J036+03 | $6.0611$ | $>19.89$ | $\cdots$ | $13.88\pm 0.04$ | $13.47\pm 0.09$ | $13.09\pm 0.12$ | $11.81\pm 0.23$ | $<12.13$ | $12.89\pm 0.13$ | $12.57\pm 0.11$ | $12.93\pm 0.15$
DELS J0923+0402 | $6.3784$ | $>19.57$ | $\cdots$ | $14.56\pm 0.09$ | $13.84\pm 0.25$ | $13.11\pm 0.05$ | $<12.23$ | $<12.53$ | $12.86\pm 0.14$ | $\cdots$ | $\cdots$

888Errors on measurements and lower limits are $1\sigma$ while upper limits
are $3\sigma$.
$a$$a$footnotetext: Estimate of the H i column density obtained from eq. 5
assuming a metallicity [Fe/H]$\leq-2$.
$b$$b$footnotetext: Estimate of the H i column density derived from the fit of
the Ly$\alpha$ line.
$*$$*$footnotetext: These systems are PDLA.
$**$$**$footnotetext: This system was excluded from the analysis, see its
description in Appendix B.

###  3.4 Estimate of the H i column density

Figure 2: Log $N({\rm\mbox{O\,{\sc i}}})$ as a function of $\log
N({\rm\mbox{H\,{\sc i}}})$ for the VMP DLA systems of Cooke et al. (2011,
triangles). The colour of the symbols refers to their metallicity measured as
[Fe/H] and reported in the side band. The solid black lines are approximately
marking metallicities of [Fe/H] $\simeq-2$, $-3$ and $-4$ (from top to
bottom). The dotted black line indicates the column density threshold defining
DLAs. The red lower limits on $\log N({\rm\mbox{H\,{\sc i}}})$ are the O i
absorbers in our sample, red circles indicate PDLA systems. Dark-red crosses
mark estimated $\log N({\rm\mbox{H\,{\sc i}}})$ for the latter systems,
obtained from the fit of the red damping wing of the absorption.  Figure 3:
Region of the spectrum of the QSO SDSS J2310+1855 corresponding to the
Ly$\alpha$ emission. The black line is the observed spectrum and the red one
is the observed error. The blue line is the intrinsic emission spectrum
modeled with a template (see text), while the green line is the fit of the H i
Ly$\alpha$ absorption line for the PDLA at $z=5.9388$.

The measurement of the H i column density in the observed systems is
complicated by the increasing saturation of the Ly$\alpha$ forest observed at
such high redshifts. Nonetheless, we have tried to estimate these column
densities to understand whether the systems we analysed are predominantly
neutral (as we assume) or partially ionized.

To this aim, we considered the relation between O i and H i column densities
in the sample of VMP-DLAs at $2<z<4.5$ by Cooke et al. (2011). As shown in
Figure 2, we found that there is a clear relation that links these column
densities, which depends upon the metallicity of the system, measured as
[Fe/H]. We verified that VMP-DLA systems with similar [Fe/H] are approximately
aligned on straight lines defined by the relation:

$\log N(\mathrm{\mbox{O\,{\sc i}}})=\log N(\mathrm{\mbox{H\,{\sc
i}}})+\log(n_{\rm O}/n_{\rm H})_{\sun}+0.3+[{\rm Fe}/{\rm H}],$ (5)

implying that the column density ratio of O i to H i for these systems is
consistent with the solar oxygen abundance rescaled at their metallicity and
increased by the $\alpha$ over iron excess, [O/Fe] $\approx 0.3$, produced by
Type II SNe (see e.g. Rafelski et al., 2012). Solving eq. 5 for $\log
N({\rm\mbox{H\,{\sc i}}})$ and assuming that the O i absorbers in our sample
have a metallicity [Fe/H] $\leq-2$, we derived lower limits on their H i
column densities from the measured O i ones. We note that the majority of our
DLA-analogues have [O/Fe] in the range $\sim 0.0-0.5$ consistent with stars
and DLAs at [Fe/H] $\leq-2$, and there are also 5 cases with [O/Fe] $>0.55$
which hint at metallicities [Fe/H] $<-3$ (Cooke et al., 2011; Welsh et al.,
2022). The obtained column density limits are reported in Table 2: 3 systems
have $\log N({\rm\mbox{H\,{\sc i}}})\geq 20.3$, while 21 have $\log
N({\rm\mbox{H\,{\sc i}}})\geq 19$.

For the PDLAs, we estimated the H i column density from the direct fit of the
red damping wing of the typical Lorentzian profile of DLAs which appears in
the region of the Ly$\alpha$ emission of the QSO (see e.g. D’Odorico et al.,
2018, and also Figure 3). In order to carry out the fit, it is necessary to
model the QSO intrinsic emission spectrum in the region of the Ly$\alpha$
emission line. To this aim, we have used the template spectra built as in
Bischetti et al. (2023) to determine the presence of BAL systems. Briefly,
starting from the total catalogue of 11 800 SDSS QSOs in the redshift range
$2.13<z_{\rm em}<3.20$ (Shen et al., 2011), the composite template spectrum is
built as the median of a hundred randomly selected, non-BAL (Gibson et al.,
2009; Shen et al., 2011) QSO spectra matching within $\pm$ 20% the slope of
the rest-frame UV continuum and the equivalent width of the C iv emission line
of the considered E-XQR-30 QSO. The composite template is normalised to the
median flux value of the QSO spectrum in the rest-frame 1650-1750 Å spectral
interval, avoiding prominent emission lines and strong telluric absorption for
the redshift interval covered by our sample. Further details can be found in
Bischetti et al. (2022, 2023).

The composite spectra created in the rest frame were redshifted to the
emission redshift of the considered QSO, rescaled to make the C iv peak
emissions coincide and then used as the continuum level in the context of
Astrocook. In particular, to perform the fit of the Ly$\alpha$ line, we fixed
the absorption redshift at the value determined by the low ionization metal
lines of the system, and the Doppler parameter considering a value of $20$ km
s-1 for each O i component present in the velocity profile999Note that the
shape of the Lorentzian profile does not significantly depend on the chosen
Doppler parameter value. In this way, we determined the column density of H i
that best fit the damping wing observed in the spectrum, with an estimated
error of approximately $\pm 0.1$ dex. This error does not take into account
the uncertainty on the true shape of the spectrum in the Ly$\alpha$ emission
region, which is very difficult to estimate. For some cases, it was possible
to use also the Ly$\beta$ absorption to constrain, in particular, the width of
the H i line (see Figures in Appendix B).

Figure 2 shows that in all the cases in which it was possible to measure
directly $\log N({\rm\mbox{H\,{\sc i}}})$, the obtained value was consistent
with the system being a DLA, even if the value obtained from eq. 5 was much
lower than $\log N({\rm\mbox{H\,{\sc i}}})=20.3$. Based on this result, we
proceeded with the calculation of the relative chemical abundances for the
considered systems assuming they are VMP-DLAs.

##  4 Observational results

###  4.1 Determination of chemical abundances

Table 3: Chemical abundances relative to iron of the elements detected in the
observed O i systems.

QSO | $z_{\rm abs}$ | $\rm[C/Fe]$ | $\rm[O/Fe]$ | $\rm[Mg/Fe]$ | $\rm[Al/Fe]$ | $\rm[Si/Fe]$
---|---|---|---|---|---|---
PSO J308-27 | $5.4400$ | $0.18\pm 0.07$ | $0.33\pm 0.06$ | $0.39\pm 0.08$ | $<0.34$ | $0.56\pm 0.09$
PSO J308-27 | $5.6268$ | $0.21\pm 0.04$ | $0.26\pm 0.04$ | $0.31\pm 0.06$ | $0.17\pm 0.13$ | $0.33\pm 0.03$
PSO J023-02 | $5.4869$ | $0.70\pm 0.18$ | $0.49\pm 0.10$ | $0.44\pm 0.15$ | $<0.74$ | $<0.78$
PSO J025-11∗ | $5.7763$ | $0.46\pm 0.06$ | $-0.07\pm 0.06$ | $0.50\pm 0.12$ | $0.53\pm 0.17$ | $0.59\pm 0.06$
PSO J025-11∗ | $5.8385$ | $>0.03$ | $>0.03$ | $>-0.02$ | $-0.02\pm 0.20$ | $0.28\pm 0.10$
PSO J108+08 | $5.5624$ | $>0.28$ | $>0.74$ | $\cdots$ | $\cdots$ | $\cdots$
SDSS J0818+1722 | $5.7912$ | $0.25\pm 0.05$ | $0.36\pm 0.05$ | $\cdots$ | $\cdots$ | $0.37\pm 0.05$
SDSS J0818+1722 | $5.8767$ | $0.35\pm 0.09$ | $0.44\pm 0.08$ | $0.37\pm 0.12$ | $<0.46$ | $0.46\pm 0.08$
PSO J007+04∗ | $5.9917$ | $-0.05\pm 0.21$ | $0.21\pm 0.22$ | $<0.17$ | $<0.58$ | $0.11\pm 0.20$
SDSS J2310+1855∗ | $5.9388$ | $>0.08$ | $>0.76$ | $>0.07$ | $-0.10\pm 0.39$ | $0.39\pm 0.10$
PSO J158-14 | $5.8986$ | $0.24\pm 0.04$ | $0.27\pm 0.08$ | $\cdots$ | $0.17\pm 0.21$ | $0.50\pm 0.05$
PSO J239-07∗ | $5.9918$ | $>0.11$ | $>0.49$ | $>0.23$ | $\cdots$ | $>0.45$
ULAS J1319+0950∗ | $6.0172$ | $-0.21\pm 0.19$ | $0.29\pm 0.16$ | $0.06\pm 0.22$ | $0.44\pm 0.27$ | $0.04\pm 0.16$
PSO J060+24 | $5.6993$ | $0.33\pm 0.19$ | $0.35\pm 0.11$ | $\cdots$ | $0.39\pm 0.24$ | $0.67\pm 0.08$
PSO J065-26 | $5.8677$ | $0.18\pm 0.04$ | $0.40\pm 0.03$ | $0.12\pm 0.06$ | $0.10\pm 0.16$ | $0.44\pm 0.04$
PSO J065-26∗ | $6.1208$ | $>0.34$ | $>0.25$ | $>0.35$ | $0.29\pm 0.04$ | $0.56\pm 0.03$
PSO J065-26∗ | $6.1263$ | $>0.60$ | $-0.06\pm 0.04$ | $>0.87$ | $0.78\pm 0.06$ | $0.65\pm 0.04$
SDSS J0100+2802 | $5.7974$ | $0.04\pm 0.03$ | $0.32\pm 0.04$ | $\cdots$ | $-0.01\pm 0.08$ | $0.43\pm 0.04$
SDSS J0100+2802 | $5.9450$ | $0.39\pm 0.05$ | $0.00\pm 0.06$ | $0.29\pm 0.06$ | $0.25\pm 0.15$ | $0.51\pm 0.09$
SDSS J0100+2802 | $6.1114$ | $0.33\pm 0.07$ | $0.85\pm 0.14$ | $0.35\pm 0.05$ | $-0.04\pm 0.10$ | $0.35\pm 0.04$
SDSS J0100+2802 | $6.1434$ | $0.26\pm 0.03$ | $0.55\pm 0.03$ | $0.24\pm 0.04$ | $-0.13\pm 0.11$ | $0.34\pm 0.03$
DELS J1535+1943 | $5.8990$ | $0.54\pm 0.16$ | $\cdots$ | $0.40\pm 0.20$ | $\cdots$ | $0.52\pm 0.08$
PSO J183+05 | $6.0642$ | $0.23\pm 0.08$ | $0.18\pm 0.05$ | $0.59\pm 0.20$ | $0.45\pm 0.08$ | $0.54\pm 0.05$
PSO J183+05∗ | $6.4041$ | $0.22\pm 0.07$ | $0.22\pm 0.05$ | $>0.60$ | $0.07\pm 0.08$ | $0.58\pm 0.04$
WISEA J0439+1634 | $6.2743$ | $>0.50$ | $>0.38$ | $\cdots$ | $\cdots$ | $>0.58$
VDES J0224-4711 | $6.1228$ | $0.21\pm 0.14$ | $0.41\pm 0.06$ | $0.18\pm 0.07$ | $<0.13$ | $0.50\pm 0.08$
PSO J036+03 | $6.0611$ | $>0.41$ | $>0.56$ | $>0.66$ | $>0.73$ | $>0.95$
DELS J0923+0402 | $6.3784$ | $>0.38$ | $>0.84$ | $>0.23$ | $\cdots$ | $>0.57$

101010 $*$$*$footnotetext: These systems are PDLA.

We convert directly ionic column densities into total abundances of a given
element in the hypothesis that our systems are predominantly neutral - thus
ionic corrections are not needed - and very metal poor - implying a
negligible, if present, dust depletion (see e.g. Becker et al., 2012).

The relative abundance between two elements X and Y was then calculated using
the relationship:

$\bigg{[}\frac{\rm X}{\rm Y}\bigg{]}=\log\frac{N_{\rm X}}{N_{\rm
Y}}-\log\frac{n_{\rm X_{\sun}}}{n_{\rm Y_{\sun}}}$ (6)

where $N_{\rm X}$ and $N_{\rm Y}$ are the column densities of the ions of
element X and Y detected in the systems, and $n_{\rm X_{\sun}}$ and $n_{\rm
Y_{\sun}}$ are the solar abundances of X and Y in number. All quantities are
calculated with respect to the solar photospheric values presented in Asplund
et al. (2009). The error on relative abundances has been propagated neglecting
the error on solar abundances as the uncertainties on the measured column
densities are dominant. Lower and upper limits on column densities are
reflected in the calculated relative abundances. When both ionic column
densities of X and Y were limits, the relative abundance was not computed.
Note that the chemical abundances of carbon and silicon are determined from
the column densities of C ii and Si ii, implying that C iv and Si iv, if
present, arise in a different gas phase from the low ionization lines.

Table 7 reports the chemical abundances for the DLA-analogues for which it was
possible to estimate the column density of H i, while Tables 3 and 8 show the
relative abundances, with respect to iron and oxygen, of all analysed systems.

Figure 4: Plot of the abundances relative to iron of the elements detected in
our O i systems. In the figures, PDLAs (red filled circles) are distinguished
from intervening DLAs (orange empty circles). The red box represents the
weighted average value of the PDLA abundances with the relative dispersion,
calculated as the standard deviation of the sample mean. The orange box is the
analogue for intervening DLAs.

Figure 4 shows the abundances of O, Mg, Al and Si relative to iron as a
function of $[{\rm C/Fe}]$ for all the systems in our sample. In these plots,
we distinguish between PDLAs (red squares) and intervening DLAs (orange
circles) to check if there are systematic differences between these two
classes of absorbers (although the definition is based empirically only on the
velocity separation from the QSO emission redshift). The colored boxes
represent the weighted average values of the two categories of absorbers, with
their dispersion calculated as the standard deviation of the sample mean. The
weighted averages are computed treating lower and upper limits as measurements
with an error of 0.1 dex.

The plots show that, in general, the average relative abundances of these two
types of absorbers are in agreement within errors. This suggests that the
ionizing flux of the QSO does not have a clear influence on the nature of the
associated systems.

We note that PDLAs present a larger spread in the abundance values with
respect to the intervening ones, this is probably due to the smaller size of
the sample and to the large uncertainties characterising, in particular, the
systems along the sightline to PSO J007+04 and to J1319+0950. These two
systems also present a subsolar abundance of C/Fe (see Figure 4). However, as
we will see in Section 4.2, these abundances are not peculiar, there are other
intervening DLAs at $z>4.5$, detected by Becker et al. (2012) and Poudel et
al. (2020), which present $[{\rm C/Fe}]<0$ as shown in Figure 5.

In the following analysis we will consider the full sample comprising PDLAs
and intervening DLAs.

###  4.2 Comparison with the literature

Figure 5: Comparison of some of the relative abundances of the O i
systems/DLAs at high redshift ($z>4.5$) found in this work (red dots), in
Becker et al. (2012) (blue squares), and Poudel et al. (2018, 2020) (green
diamonds). Dotted lines mark the solar abundance values. We report also the
predictions of the simulations by Kulkarni et al. (2013) at $z=6$, the three
models are described in greater detail the text. Model 1 assigns a 1–100 M⊙
Salpeter IMF to Pop III stars. This is 35–100 M⊙ Salpeter in case of model 2
and 100–260 M⊙ Salpeter for model 3. The prediction of model 1 is the light
blue dot at the junction of the lines of model 2 and 3.

We compared the relative abundances of the elements in the DLA-analogues
identified in this work with those of low ionization systems at similar
redshifts and selected in the same way presented in Becker et al. (2012). For
the systems detected in SDSS J0818+1722, which are in common between the two
samples, we adopted our chemical abundances. We considered also the systems in
the redshift range $4.5\lesssim z\lesssim 5.5$ studied by Poudel et al. (2018,
2020) selecting only those with $\log N_{\rm HI}\geq 20.10$ and metallicity
[Fe/H] $\leq-2.0$ (or [O/H] $\leq-2.0$ when iron is not measured), for a total
of 5 systems. Figure 5 reports 4 combinations of relative abundances computed
with the available chemical elements, it shows that our measurements are in
general agreement with previous ones. It is important to note that due to the
simultaneous saturation of the carbon and oxygen lines in 2 systems of Becker
et al. (2012) and 3 of our systems, the sample for which the [C/O] abundance
could be calculated is limited.

Table 4: Weighted average of the chemical abundances of the VMP-DLAs at $2\leq
z\leq 4.5$ and DLA-analogues at $4.5<z\leq 6.5$.

$z$ | N | Mean | $\sigma_{\rm sample}$ | $\sigma_{\rm mean}$
---|---|---|---|---
$[{\rm C/Si}]$
$2\leq z\leq 4.5$ | 11 | $-0.21$ | 0.08 | 0.02
$4.5<z\leq 6.5$ | 40 | $-0.19$ | 0.12 | 0.02
$[{\rm C/O}]$
$2\leq z\leq 4.5$ | 11 | $-0.38$ | 0.12 | 0.04
$4.5<z\leq 6.5$ | 34 | $-0.11$ | 0.24 | 0.04
$[{\rm C/Fe}]$
$2\leq z\leq 4.5$ | 9 | 0.14 | 0.08 | 0.03
$4.5<z\leq 6.5$ | 37 | 0.22 | 0.14 | 0.02
$[{\rm O/Fe}]$
$2\leq z\leq 4.5$ | 20 | 0.42 | 0.05 | 0.01
$4.5<z\leq 6.5$ | 36 | 0.32 | 0.21 | 0.04
$[{\rm Si/Fe}]$
$2\leq z\leq 4.5$ | 20 | 0.32 | 0.04 | 0.01
$4.5<z\leq 6.5$ | 36 | 0.46 | 0.13 | 0.02
$[{\rm Si/O}]$
$2\leq z\leq 4.5$ | 22 | $-0.11$ | 0.08 | 0.02
$4.5<z\leq 6.5$ | 39 | $0.11$ | 0.25 | 0.04
111111The columns report: the redshift interval, the number of systems, the
weighted average, the standard deviation of the sample and the standard
deviation of the mean.

Figure 6: Relative abundances of DLA systems at $z>2$, as a function of
redshift. The figure shows the DLA analogues studied in this work (solid red
dots), in Becker et al. (2012, solid blue squares) and in Poudel et al. (2018,
2020, solid green diamonds), and the VMP-DLAs analysed in Cooke et al. (2011,
solid black triangles) with the exception of the systems identified in the
QSOs J0035-0918 and J1558-0031, and those in Dutta et al. (2014, solid plum
inverted triangles) in the QSOs J0035-0918 and J0953-0504. The shaded regions
are centred on the weighted average values and represent the standard
deviation of the sample (light gray band) and of the sample mean (dark gray
band) for the systems in the two redshift bins: $2\leq z\leq 4.5$ and
$4.5<z\leq 6.5$.

Following the analysis in Becker et al. (2012), we compared the relative
abundances of the identified high redshift systems ($z>4.5$), with the
abundances of the VMP-DLAs at lower redshift ($2<z<4.5$) presented in Cooke et
al. (2011) and Dutta et al. (2014), to evaluate the evolution of the chemical
composition of the gas with redshift. In the VMP-DLA sample of Cooke et al.
(2011), we omitted the system at $z=2.34010$ found in QSO J0035-0918 and the
system at $z=2.70262$ in J1558-0031 due to possible large uncertainties in
column densities. In the sample of Dutta et al. (2014), we have instead
considered only the system at $z=2.340$ in J0035-0918 (in which the values of
Cooke et al. 2011 are corrected) and the one at $z=4.202$ in J0953-0504.

Figure 6 shows several relative chemical abundances computed for the low and
high-redshift samples as a function of the redshift of the absorbers. The
total number of systems at $z>4.5$ presented in this study has increased by a
factor of $\sim 4$ the sample studied in previous works, allowing us to carry
out the comparison in a more quantitative way. In order to establish if the
distributions of values in the low and high-redshift samples are significantly
different, we determined the weighted averages of the two groups of
measurements (considering lower and upper limits as measurements). The results
are reported in Table 4 and in Figure 6, where the standard deviation of each
sample, $\sigma_{\rm sample}$, is represented by the light grey shaded
regions, while the standard deviation of the mean, $\sigma_{\rm
mean}=\sigma_{\rm sample}/\sqrt{N}$, is represented by the dark grey regions,
both centred on the mean values.

Becker et al. (2012) and Poudel et al. (2018, 2020) had found very good
agreement between the mean values and the dispersions of the VMP-DLAs at
$z<4.5$ and their $z>4.5$ samples. This result suggested that the sources
enriching the high redshift systems had the same nature as those that enriched
the low redshift ones, which most likely were type II SNe from Pop II stars.
Differently, the mean values of the measured relative chemical abundances in
our sample are not all in agreement with those of the lower $z$ sample of VMP-
DLAs, in particular if we consider the error of the mean, the [C/O] and
[Si/Fe] differ by $\sim 7\,\sigma_{\rm mean}$, while [Si/O] differs by $\sim
5.5\,\sigma_{\rm mean}$. Furthermore, we observe an increase in the dispersion
of the measurements of the high-$z$ sample.

We have also carried out the Epps-Singleton test, which is useful to compare
two samples and understand if they are extracted from the same distribution,
for the cases in which both the low and high-redshift samples have a
relatively large number of measurements ([Si/Fe], [Si/O] and [O/Fe]). In all
three cases, we obtain a significance level lower than the generally adopted
threshold $p=0.05$, implying that the null hypothesis (samples are drawn from
the same distribution) is rejected.

The implications of these results are discussed in Sec. 5-6.

##  5 Are we observing the imprint of the first stars?

In order to understand if our high-redshift absorbers have been imprinted by
the first stellar generations, we compare the measured chemical abundance
ratios with the results of two chemical evolution models: the semi-analytic
code by Kulkarni et al. (2013) and the general parametric study by Vanni et
al. (2024).

###  5.1 Comparison with Kulkarni et al. 2013

In Figure 5, we plot, together with our observational results, the predictions
of the semi-analytic chemical evolution model by Kulkarni et al. (2013). This
model incorporates global effects like reionization and photoionization
feedback along with a range of possible Pop III initial mass functions (IMFs).
The model is consistent with a variety of observational constraints on galaxy
and IGM evolution. Kulkarni et al. (2013) calculate the minimum mass of star-
forming galaxies self-consistently and produce galaxies that lie on
observational curves such as the stellar-to-halo mass relation at low redshift
and the mass–metallicity relation. They then explore the influence of Pop III
stars on the predictions of this model, by varying the Pop III stellar IMF.
They consider haloes of different masses that grow according to growth rates
calibrated on the Millennium simulation (Fakhouri et al., 2010). A semi-
analytic model of galaxy formation and chemical evolution is implemented on
these haloes.

Pop I/II stars are formed following a Salpeter IMF with masses in the range
$m_{*}=0.1-100\,M_{\odot}$, while Pop III stars can have three different IMFs:
model 3 covers the PISN range ($m_{*}=100-260\,M_{\odot}$ Salpeter), whereas
models 1 and 2 choose Salpeter IMFs with $m_{*}=1-100\,M_{\odot}$ and
$m_{*}=35-100\,M_{\odot}$, to explore the role of asymptotic giant branch
(AGB) stars and core collapse SNe, respectively. Chemical yields of Pop III
stars are taken from the calculations of Heger & Woosley (2002). The
transition from Pop III to Pop II star formation in any halo is implemented
via a critical metallicity threshold, $Z_{\rm crit}=10^{-4}\,Z_{\odot}$ (Bromm
et al., 2001; Schneider et al., 2003).

In Figure 5, we show the simulated abundances at $z=6$; moving to lower
redshift, the spread of the values decreases, and relative abundances tend to
converge to the average abundance of the PopII stars, represented by the
predictions for model 1 (see Fig. 8 of Kulkarni et al., 2013). Given the four
combinations of relative abundances that we have considered for this
comparison, Figure 5 suggests that the spread of the observed data is not in
agreement with either of the three models considered by Kulkarni et al.
(2013). There does appear to be a weak preference for model 3, in which the
Pop III IMF is 100–260 M⊙ Salpeter, however this does not appear conclusive.

The poor agreement between models and data is perhaps not surprising, as the
three Pop III IMFs considered by Kulkarni et al. (2013) were chosen by these
authors for illustrative purposes only, and recent studies based on stellar
archaeology showed that the Pop III IMF have different mass ranges and shapes
Rossi et al. (2021); Pagnini et al. (2023); Koutsouridou et al. (2024). A
future study could investigate whether there is a Pop III IMF that fits the
data shown in Figure 5 far better. Nonetheless, the general conclusion by
Kulkarni et al. (2013) was that the distribution of metal absorbers in the
relative abundance plane at high redshifts is sensitive to the Pop III IMF,
and a generic signature of Pop III enrichment would be a correlation between
relative abundances along a particular direction. While, with enrichment only
from a universal IMF, one would generally expect the relative abundances to be
clustered around a point in the relative abundance plane. This behaviour is
clearly borne out by the measurements shown in Figure 5.

###  5.2 Comparison with Vanni et al. 2024

In Figures 7 and 8, we compare the observed results with the simple and
general parametric study first developed by Salvadori et al. (2019) and
recently refined by Vanni et al. (2023b, a, 2024).

In a few words, the model investigates the chemical abundance pattern of an
ISM polluted by a Pop III SN by exploring the full parameter space for
explosion energies, ${\rm E=(0.3-100)\times 10^{51}}$ erg, and progenitor
masses, $m_{*}=10-1000\,\rm M_{\odot}$ using the yields by Heger & Woosley
(2002) and Heger & Woosley (2010). The choice of a single Pop III SN explosion
is motivated by the results of hydro-dynamical cosmological simulations (e.g.
Hirano et al., 2014, 2015) and further corroborated by the identification of
present-day stars mono-enriched by Pop III SNe (e.g. Skúladóttir et al., 2021,
Rossi et al. submitted).

The model is very simple, it incorporates the main unknowns of early cosmic
star formation into three free parameters: the star-formation efficiency, the
metal dilution factor, and the mass fraction of metals provided by Pop III
stars with respect to the total one in the ISM, ${\rm f_{PopIII}}$. The
chemical enrichment of the ISM is evaluated after the injection of heavy
elements by Pop III SNe only (${\rm f_{PopIII}=100\%}$) and after the
subsequent contribution of Pop II stars (${\rm f_{PopIII}<100\%}$), which can
promptly form after the Pop III SN explosions when $Z_{\rm
crit}>10^{-4.5}Z_{\odot}$ (Vanni et al., 2023b). Pop II stars are assumed to
form according to a standard Larson IMF, i.e., with masses $m_{*}=\rm
0.1-100\,M_{\odot}$, a peak at $\rm 0.35\,M_{\odot}$, and a Salpeter-like
slope at higher masses.

Two different sets of yields for Pop II SNe are adopted, Woosley & Weaver
(1995) and Limongi & Chieffi (2018, set R, non-rotating), to alleviate the
model from uncertainties arising in yields’ calculation (see Vanni et al.,
2023a, Fig. A1). In order to get consistent results for the two sets of
yields, we assume also for Woosley & Weaver (1995) that all Pop II stars with
$m_{*}\rm\geq 25M_{\odot}$ evolve into black holes, as assumed by Limongi &
Chieffi (2018). To take into account the enrichment due to SNe exploding at
different timescales, we compute the IMF-integrated contribution of Pop II
stars above $23,21,18,15,13\rm M_{\odot}$ (see Salvadori et al., 2019; Vanni
et al., 2024, for details). In Figures 7 and 8, we distinguish between the
abundances determined from the set of yields by Limongi & Chieffi (2018)
(darker grey) and those based on the yields by Woosley & Weaver (1995)
(lighter grey) only in the case with $f_{\rm PopIII}=0.01$ (Pop II only),
while for all the other $f_{\rm PopIII}$ values they are plotted together.

Table 5: Properties of the three systems in our sample presenting the largest [C/O] and [Si/O] abundance ratios.  QSO | $z_{\rm abs}$ |  $v_{\rm abs}$ (km s-1) | $\log N(\mathrm{\mbox{H\,{\sc i}}})$ | [C/O] | [Si/O] | $\log(N_{\rm CII}/N_{\rm CIV})$ | $\log(N_{\rm SiII}/N_{\rm SiIV})$
---|---|---|---|---|---|---|---
PSO J025-11∗ | 5.7763 | 2866 | $20.35\pm 0.1$ | $0.53\pm 0.05$ | $0.67\pm 0.05$ | $0.09\pm 0.05$ | $-0.10\pm 0.08$
SDSSJ0100+2802 | 5.9450 | 16029 | $>18.45$ | $0.39\pm 0.04$ | $0.51\pm 0.08$ | $0.68\pm 0.09$ | $0.18\pm 0.11$
PSO J065-26∗ | 6.1263 | 2543 | $>19.45$ | $>0.66$ | $>0.71$ | $>1.41$ | $0.71\pm 0.04$

One of the key predictions of the model by Vanni et al. (2023b, see their
Figure 12) is that the scatter in the abundance ratios of different chemical
species, such as [C/Fe] and [Mg/Fe], is maximum if we consider the pollution
from Pop III SNe only, and then it progressively decreases as the contribution
of Pop II SNe increases. In other words, gaseous absorbers predominantly
polluted by first stars (${\rm f_{PopIII}\geq 60\%}$), or long-lived first
stars’ descendants formed in these gas clouds, are expected to show a larger
absorber-to-absorber scatter in their chemical abundance ratios with respect
to those predominantly imprinted by normal Pop II stars (${\rm f_{PopIII}\leq
30\%}$). This is in agreement with e.g. the small star-to-star scatter
observed in C-normal halo stars by Cayrel et al. (2004) (see Sec. 4.4 in Vanni
et al. 2023b).

In Figure 7, we compare the [C/O] and [Si/O] values measured in DLAs at
various redshifts (corresponding to the sample shown in Figure 6) with the
maximum extent predicted for these abundance ratios by models accounting for
different contribution of Pop III SNe to the gas enrichment. In order to
ensure consistent metallicities between predictions and observations, we
select only models with [O/H]$\geq-4$. Indeed, both in our sample (see Tab. 7)
and in the literature (see Welsh et al., 2023) the most metal-poor DLAs have
[O/H] $\sim-3$.

We see that $z\lesssim 4.5$ DLAs exhibit a small [C/O] and [Si/O] scatter
among each other, which is consistent with an enrichment only due to Pop II
SNe (${\rm f_{PopIII}=0.01}$). Conversely, for $z\gtrsim 4.5$ we see that the
scatter among different systems increases for both [C/O] and [Si/O]: several
absorbers now require a ${\geq 30\%}$ imprint from Pop III stars to explain
the observed abundances. In particular, we notice three systems with
[C/O]$>0.35$, [Si/O]$>0.50$ and very small error bars, that can only be
explained if Pop III SNe provide $\geq 60\%$ of their metals. The
characteristics of these systems are summarized in Table 5.

We can further investigate the nature of these systems and in general of all
$z>4.5$ absorbers by comparing some of their relative abundances (Figure 5)
with theoretical model predictions. This comparison is reported in Figure 8,
where the shaded areas illustrate the expectations for an ISM imprinted by:
Pop III stars only (larger yellow contours), and by Pop III stars but with an
increasing contribution from normal Pop II SNe (gradually darker and smaller
contours). The solid lines include the abundance ratios for which we have more
than one model.

It is clear from these maps that the $z>4.5$ DLA-analogues are not all
consistent with an enrichment solely driven by Pop II stars (gray contours)
but they require a $\geq 30\%$ contribution from Pop III stars. Furthermore,
we see that the three systems with highest [C/O] values in Table 5 are at the
edge of the $60\%$ Pop III enrichment areas, and consistent with higher Pop
III contribution, in the [O/Fe] vs [C/Fe], [Si/Fe] vs [O/Fe] and [Si/O] vs
[C/O] planes.

Ultimately, the large scatter in the chemical abundance ratios of $z>4.5$ DLA-
analogues is a strong indication of an heterogeneous chemical enrichment
driven by different stellar populations and most likely including Pop III SNe,
which might account for $\geq 60\%$ of the ISM metals.

Figure 7: Comparison between the maximum extent of [C/O] (left panel) and
[Si/O] (right panel) ISM ratios predicted in the model by Vanni et al. (2024,
shaded area) and the measured abundance ratios in absorbers at different
redshifts (points with errorbars as in Figure 6). In each panel the coloured
areas show the contribution of Pop III stars to the chemical enrichment:
$100\%$ (yellow), $90\%$ (orange), $60\%$ (pink), $30\%$ (purple) and $\leq
0.01\%$ (dark grey: Limongi & Chieffi 2018; light grey: Woosley & Weaver
1995). Only the environments with [O/H]$>-4$ are considered. The three
remarkable systems with [C/O]$>0.35$ and [Si/O]$>0.50$ are highlighted using
different symbols and black contours: PSO J025-11 at z=5.7763 (square), SDSS
J0100+2802 at z=5.9450 (star) and PSO J065-26 at z=6.1263 (diamond). Figure 8:
Comparison between different chemical abundance ratios measured in the
considered sample of $z>4.5$ DLA-analogues (points with errorbars as in Figure
5) and predicted in the model by Vanni et al. (2024, shaded area). Shaded
areas are coloured depending upon the contribution level of Pop III stars to
the chemical enrichment: $100\%$ (yellow), $90\%$ (orange), $60\%$ (pink),
$30\%$ (purple) and $\leq 0.01\%$ (dark grey: Limongi & Chieffi 2018; light
grey: Woosley & Weaver 1995). Only the environments with [O/H]$>-4$ are
considered. The three remarkable systems with [C/O]$>0.35$ and [Si/O]$>0.50$
are highlighted using different symbols and black contours: PSO J025-11 at
z=5.7763 (square), SDSS J0100+2802 at z=5.9450 (star) and PSO J065-26 at
z=6.1263 (diamond).

##  6 Discussion

The comparison between our observational findings and model results for the
early metal enrichment, shows that the larger scatter in the abundance ratios
at $z>4.5$ is most likely due to an enrichment by Pop III SNe which, are
predicted to have a broader range of progenitor masses and explosion energies.
However, from a theoretical perspective we can ask ourselves if a larger
abundance scatter can be also driven by other more metal-rich stellar sources.
From an observational point of view, furthermore, we might wonder if we are
really sure about the nature of our absorbers and thus of the robustness of
our measurements.

###  6.1 Are there other possible enrichment sources?

To exclude the possibility of a larger [C/O] and [Si/O] scatter driven by
“exotic” but more metal-rich Pop II SNe exploding as energetic hypernovae or
PISNe (e.g., see Langer et al. 2007), we can use the following arguments.
Firstly, because of their high masses, $140-260\rm M_{\odot}$, PISNe are not
expected to form in environments enriched above the critical metallicity
value, $Z_{\rm crit}$. Indeed, the more efficient gas cooling due to metals
and dust causes the formation of sub-solar proto-stellar gas clouds and the
decrease of the gas accretion rate onto the proto-star (e.g. Klessen & Glover,
2023, for a review). Conversely, we cannot exclude that a fraction of normal
Pop II stars with intermediate masses ($20-40\rm M_{\odot}$) might explode as
more energetic hypernovae (e.g. see Kobayashi et al., 2006). However, if we
account for the contribution of metal-rich Pop II hypernovae using the yields
of Kobayashi et al. (2006), we find that the scatter of Pop II-dominated
environments increases only in the sub-solar regimes of [C/O] and [Si/O],
while our observations show super-solar values. Furthermore, we note that the
scatter predicted for environments enriched by Pop III core-collapse SNe and
hypernovae is still larger than for the ones enriched by Pop II SNe of the
same kinds.

Higher values for the [C/O] abundances can be obtained by accounting for the
contribution of AGB stars (see e.g. Salvadori & Ferrara, 2012) or dust
depletion (Konstantopoulou et al., 2023). On the other hand, the spread in
relative abundance of [Si/O] could be due to the enrichment by SNe type Ia
(SNIa). Thus, it could be argued that the increase in both [C/O] and [Si/O]
abundance ratios is a consequence of the joint enrichment by AGB stars and
SNIa. However, both these sources act on longer timescales (from 30 Myr up to
1 Gyr) than Pop III/II SNe ($<30$ Myr). Therefore, it is at the lower
redshifts, i.e., at z ¡ 4.5, that we should see the chemical imprint of both
these sources in many absorption systems, which instead show an astonishing
small abundance scatter.

Ultimately, the larger scatter of both [C/O] and [Si/O] abundance ratios
towards high-$z$ is a strong indication that these outliers were most likely
imprinted by pristine Pop III SNe, which were more common in the first billion
year of cosmic evolution (e.g. see Pallottini et al., 2014; Jaacks et al.,
2018).

###  6.2 What is the nature of the studied systems?

The direct conversion from the ionic abundance derived from the measured
column density to the total abundance of an element, generally requires the
application of ionization corrections and the correction for the depletion of
the element onto dust grains. A part of the metals can in fact be enclosed in
solid phase dust grains (e.g. Péroux & Howk, 2020).

The formation of dust grains tends to increase with metallicity, but is
considered negligible in DLAs with $\rm[Fe/H]\lesssim-2$ (Vladilo, 2004;
Konstantopoulou et al., 2023). The decreasing metallicity trend of DLAs with
redshift (Rafelski et al., 2014; De Cia et al., 2018) suggests that the
systems studied here may be in this metal-poor regime. However, the
differential contribution of the various elements to dust formation could be a
potential source of error in determining relative abundances.

As for ionization corrections, these are negligible in heavily self-shielded
systems, such as DLAs, in which almost all hydrogen is in the neutral state,
and all metals are predominantly in their neutral or prime excited states. For
sub-DLAs, which have a lower H i column density, the shielding offered by the
neutral gas is significantly reduced and ionization corrections begin to
become important (Péroux et al., 2007). However, when calculating relative
abundances, it is the difference in ionization correction between the two that
matters. Although different elements are ionized differently, the effects will
almost always act in the same direction, which is to reduce the population of
the lowest ionization state present in the gas (O i, C ii, Si ii, etc.). Even
for a partially ionized system, therefore, the ratio between two ions can be
expected to be reasonably close to the ratio between the total elements
(Becker et al., 2012).

Table 6: Column density ratios of C ii to C iv, and Si ii to Si iv, in the
detected O i systems.

QSO | $z_{\rm abs}$ |  $v_{\rm abs}$ (km s-1) | $\log(N_{\rm CII}/N_{\rm CIV})$ | $\log(N_{\rm SiII}/N_{\rm SiIV})$
---|---|---|---|---
PSO J308-27 | $5.4400$ | $16245$ | $0.27\pm 0.08$ | $0.47\pm 0.09$
PSO J308-27 | $5.6268$ | $7686$ | $0.87\pm 0.12$ | $0.55\pm 0.05$
PSO J023-02 | $5.4869$ | $16308$ | $>0.76$ | $\cdots$
PSO J025-11∗ | $5.7763$ | $2866$ | $0.09\pm 0.05$ | $-0.10\pm 0.08$
PSO J025-11∗ | $5.8385$ | $127$ | $>1.31$ | $1.28\pm 0.09$
PSO J108+08 | $5.5624$ | $17396$ | $>-0.19$ | $\cdots$
SDSS J0818+1722 | $5.7912$ | $8945$ | $0.76\pm 0.07$ | $>0.75$
SDSS J0818+1722 | $5.8767$ | $5198$ | $0.49\pm 0.06$ | $0.45\pm 0.07$
PSO J007+04∗ | $5.9917$ | $418$ | $0.03\pm 0.16$ | $-0.09\pm 0.11$
SDSS J2310+1855∗ | $5.9388$ | $2763$ | $>1.38$ | $>1.41$
PSO J158-14 | $5.8986$ | $7290$ | $1.18\pm 0.09$ | $0.82\pm 0.07$
PSO J239-07∗ | $5.9918$ | $5033$ | $\cdots$ | $>0.27$
ULAS J1319+0950∗ | $6.0172$ | $4977$ | $>0.28$ | $>0.16$
PSO J060+24 | $5.6993$ | $20324$ | $0.93\pm 0.2$ | $0.92\pm 0.09$
PSO J065-26 | $5.8677$ | $13615$ | $>1.71$ | $>1.39$
PSO J065-26∗ | $6.1208$ | $2775$ | $>2.25$ | $>1.81$
PSO J065-26∗ | $6.1263$ | $2543$ | $>1.41$ | $0.71\pm 0.04$
SDSS J0100+2802 | $5.7974$ | $22441$ | $1.09\pm 0.10$ | $0.91\pm 0.12$
SDSS J0100+2802 | $5.9450$ | $16029$ | $0.68\pm 0.09$ | $0.18\pm 0.11$
SDSS J0100+2802 | $6.1114$ | $8939$ | $>1.59$ | $>1.00$
SDSS J0100+2802 | $6.1434$ | $7595$ | $>1.84$ | $>1.20$
DELS J1535+1943 | $5.8990$ | $20211$ | $0.50\pm 0.16$ | $0.23\pm 0.08$
PSO J183+05 | $6.0642$ | $15466$ | $-0.16\pm 0.07$ | $-0.18\pm 0.05$
PSO J183+05∗ | $6.4041$ | $1394$ | $>1.46$ | $>1.13$
WISEA J0439+1634 | $6.2743$ | $9906$ | $>0.53$ | $>0.03$
VDES J0224-4711 | $6.1228$ | $16450$ | $>1.24$ | $>0.61$
PSO J036+03 | $6.0611$ | $19664$ | $0.54\pm 0.17$ | $0.52\pm 0.16$
DELS J0923+0402 | $6.3784$ | $10165$ | $\cdots$ | $\cdots$
121212Column $v_{\rm abs}$ reports the velocity separation of the system from
the QSO systemic redshift.
$*$$*$footnotetext: These systems are PDLA.

Figure 9: Ratio of C ii/C iv (left panels) and Si ii/Si iv (right panels)
column densities as a function of redshift (upper panels) and velocity
separation from the systemic redshift of the QSO (lower panels) for our sample
of O i systems. The dotted vertical lines in the upper panels are drawn at
$z=5.7$, the limit beyond which the low ionization phase is expected to
dominate in the gas (Cooper et al., 2019). The vertical dotted lines in the
lower panels mark a velocity separation of $5000$ km s-1, which separates
PDLAs from intervening DLAs. In each panel, the three systems with black
contours (diamond, square and star) are the same highlighted in Figure 8 and
7.

The almost complete absence of transmitted flux in the Lyman forests of the
E-XQR-30 QSOs does not allow us to directly and accurately estimate the H i
column density of the low ionization systems studied in this work and, as a
consequence, their metallicity. As described in Section 3.4, we could estimate
lower limits to $\log N($H i$)$ from the O i column densities measured for our
systems assuming they have a metallicity [Fe/H] $\leq-2$ (see Figure 2) and
for 7 systems we could measure $\log N($H i$)$ from the spectrum. While the
lower limits are in the vast majority of cases below $\log N($H i$)\sim 20$,
in all cases in which we could perform a direct Voigt profile fitting we
derived $\log N($H i$)\geq 20$ confirming the predominantly neutral nature of
the inspected gas.

The ionization state of the considered systems has also been tested evaluating
the ratio between the column densities of two ions of the same element in
different ionization states. This comparison was only possible for carbon and
silicon, which can be detected in singly (C ii and Si ii) and triply (C iv and
Si iv) ionized state. All values are reported in Table 6. In Figure 9, the
values of $\log(N({\rm\mbox{C\,{\sc ii}}})/N({\rm\mbox{C\,{\sc iv}}}))$ and
$\log(N({\rm\mbox{Si\,{\sc ii}}})/N({\rm SiIV}))$ are plotted as a function of
the absorption redshift (upper panels), and of the velocity separation from
the emission redshift of the QSO (lower panels).

At face value, we observe an increasing (decreasing) trend of the upper
envelope of the data distribution with redshift (velocity separation).
Previous works (e.g. D’Odorico et al., 2013; Cooper et al., 2019) showed an
increase of $\log(N({\rm\mbox{C\,{\sc ii}}})/N({\rm\mbox{C\,{\sc iv}}}))$ for
$z\gtrsim 5.7$. This is suggested also by our data both for C and Si, although
we have only a handful of systems at $z<5.7$, and was also observed when
considering the total sample of C iv absorption systems detected in E-XQR-30
and the computation of the cosmic mass density of C iv and C ii (Davies et
al., 2023b). A thorough analysis of the trends of $\log(N({\rm\mbox{C\,{\sc
ii}}})/N({\rm\mbox{C\,{\sc iv}}}))$ and $\log(N({\rm\mbox{Si\,{\sc
ii}}})/N({\rm\mbox{Si\,{\sc iv}}}))$ will be present in a future paper
(Rowlands et al. in prep.).

Considering a conservative threshold of 0.5, the systems for which both
$\log(N({\rm\mbox{C\,{\sc ii}}})/N({\rm\mbox{C\,{\sc iv}}}))$ and
$\log(N({\rm\mbox{Si\,{\sc ii}}})/N({\rm\mbox{Si\,{\sc iv}}}))$ are below this
threshold, that could be those with higher ionization state, are 6: 3 do have
clearly detected high-ionization lines (PSO J308-27 $z=5.44$, PSO J025-11
$z=5.7763$ and PSO J183+05 $z=6.0642$) and the other 3 are instead very weak
systems for which C iv and Si iv are either not detected or very weak (PSO
J108+08 $z=5.5624$, PSO J007+04 $z=5.9917$ and ULAS J1319+0950 $z=6.0172$).

In summary, we have reasons to believe that the majority of the O i systems
that form our sample are VMP-DLAs for which the corrections to chemical
abundances due to ionization or dust depletion are negligible.

##  7 Conclusions

In this work, we looked for the traces of metal enrichment due to the first
generation of stars that formed in the Universe (Pop III), which exploded as
SNe and polluted the gas in their surroundings. To this aim, we analyzed the
E-XQR-30 sample (D’Odorico et al., 2023): a homogeneous sample of high SNR,
intermediate resolution, optical and infrared spectra of 42 QSOs with emission
redshift in the interval $5.8<z_{\rm em}<6.6$.

The chemical signature of Pop III stars was looked for in neutral gas, likely
tracing the ISM of primordial galaxies or satellite clumps in their vicinity.
At lower redshift, this gas is identified through the strong H i absorption of
Damped Ly$\alpha$ systems (DLAs), while at $z>5$ the increasing saturation of
the Ly$\alpha$ forest makes the measurement of the H i column density and,
consequently, the recognition of these systems more and more complicated. We
overcome this problem through the detection of the neutral oxygen absorption
line at $1302$ Å, which is a very good tracer of neutral gas and of DLAs.

In our sample of QSO spectra, we detected 29 O i systems (or DLA-analogues) at
$z\geq 5.4$, along the line of sight to 19 QSOs; 10 of these were classified
as proximate DLA (PDLA, i.e. within $\sim 5000$ km s-1 from the QSO emission
redshift), while the other 19 as intervening DLAs. In each of these O i
systems, we looked for associated low ionization lines due to e.g. C ii, Si
ii, Al ii, Fe ii and Mg ii, and to high ionization ones mainly due to C iv and
Si iv, and performed fits of the velocity profiles with Voigt functions to
derive ionic column densities. A lower limit on the H i column density was
derived from an empirical relation with O i column density, in the hypothesis
that the studied absorbers are very metal poor systems, i.e. with [Fe/H]
$\leq-2$. In the case of PDLAs, we performed also a Voigt profile fitting of
the red damping wing of the H i absorptions and derived direct estimates of
the H i column densities.

Relative chemical abundances were obtained for 28 systems131313One problematic
PDLA was excluded from the analysis. from the ratios of measured column
densities, assuming that ionization and dust depletion had negligible effects.
Our sample increases by a factor of 4 the number of studied O i systems at
$z\geq 5.4$. All abundances with respect to iron and oxygen are reported in
Tables 3 and 8, respectively.

Finally, to understand whether the observed high-redshift absorption systems
were enriched by the first generation of stars, we compared the measured
chemical abundance ratios with those predicted by two theoretical models: the
semi-analytical model coupled with N-body simulations of Kulkarni et al.
(2013) and the general parametric study by Vanni et al. (2024).

The main results of this work are the following.

  * $\bullet$

We found no systematic differences in the average chemical abundances of PDLAs
and intervening DLAs in our sample (see Figure 4). Five PDLA systems have
$\log(N({\rm\mbox{C\,{\sc ii}}})/N({\rm\mbox{C\,{\sc iv}}}))$ and
$\log(N({\rm\mbox{Si\,{\sc ii}}})/N({\rm\mbox{Si\,{\sc iv}}}))$ ratios larger
than 0.5 which should imply a low ionization state, while the other 4 have
moderately low values but all $\gtrsim 0.0$ (see Figure 9). In summary, the
presence of the QSO does not seem to have a strong impact on this class of
systems, possibly due to their very large H i column density.

  * $\bullet$

The chemical abundances measured in our sample are consistent with those of
the literature systems at $z>4.5$ selected with similar criteria (Becker et
al., 2012; Poudel et al., 2018, 2020, see Figure 5). Although, the high
quality of our spectra allows to extend the sample toward lower column density
values. This suggests that the gas was similarly enriched in every DLA at that
time.

  * $\bullet$

We compared the relative abundances of the sample of O i systems at
$4.5<z<6.5$ (E-XQR-30 $+$ literature), with those of the Very Metal-Poor DLAs
at $2<z<4.5$ identified by Cooke et al. (2011) and Dutta et al. (2014) to
highlight any possible evolution with redshift. The average abundances
computed in the two redshift bins are in general agreement within
uncertainties (see Figure 6). However, the dispersion of the measurements in
the higher redshift bin is always larger, and the Epps-Singleton test carried
out for [Si/Fe], [Si/O] and [O/Fe] indicates that the low and high-redshift
measurements are not drawn from the same distribution.

  * $\bullet$

The comparison of the observational results with theoretical predictions
suggests that the increase in the scatter of the relative chemical abundances
at $z>4.5$ could be indicative of gas that partially retains the signature of
Pop III enrichment. In particular, the comparison with the model by Vanni et
al. (2024) singles out three of our systems that could trace gas enriched for
more than 60 % by Pop III stars (see Figure 7 and 8). On the other hand,
absorbers at $z<4.5$ are all compatible with an enrichment predominantly by
Pop II stars.

This work presents the largest sample of low ionization absorption systems at
$z\geq 5.4$, tracing highly neutral gas in the ISM of primordial galaxies or
in their vicinity and possibly probing gas which still shows the imprint of
Pop III metal enrichment.

The main, insurmountable limitation of these kinds of studies is the
impossibility of measuring the H i column density of the studied systems.
However, all the tests we have carried out seem to indicate that they are
indeed DLA or subDLA systems with metallicities of [Fe/H] $\lesssim-2$.

There are other weaknesses affecting this work which however could be solved
in the relatively near future. The resolving power of the E-XQR-30 survey is
still not sufficient to optimally resolve QSO metal absorption lines; this can
introduce systematic uncertainties in the column density measurement due to
the “hidden” saturation of absorption lines. We have faced this problem as
much as we could, but we will have to wait for the ANDES high-resolution
spectrograph for the ELT (Marconi et al., 2022) to carry out extremely
accurate measurements of column densities and detect fundamental elements
(like Zn) that are beyond reach in the present spectra.

Another weak point is the paucity of systems studied in the redshift range
$4.0<z\leq 5.5$ and the heterogeneous and generally poor quality of the
available data at those redshifts (due to low resolution, low SNR and limited
wavelength range). This is the highest redshift range at which the H i lines
can still be detected: a large sample of DLA systems with high-quality,
homogeneous spectroscopic observations would be key to clarify the evolution
of the average chemical abundances and of their dispersion.

###### Acknowledgements.

S.S. and I.V. acknowledge support from the European Research Council (ERC)
under the European Union’s Horizon 2020 research and innovation programme
(grant agreement No 804240). V.D., A.F., S.S., and I.V. acknowledge support
from the PRIN-MIUR17, The quest for the first stars, prot. n. 2017T4ARJ5. This
research was supported by the Australian Research Council Centre of Excellence
for All Sky Astrophysics in 3 Dimensions (ASTRO 3D), through project number
CE170100013. E.P.F. is supported by the international Gemini Observatory, a
program of NSF’s NOIRLab, which is managed by the Association of Universities
for Research in Astronomy (AURA) under a cooperative agreement with the
National Science Foundation, on behalf of the Gemini partnership of Argentina,
Brazil, Canada, Chile, the Republic of Korea, and the United States of
America.

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##  Appendix A Chemical abundances of the studied systems

Table 7 reports the absolute abundances for the 7 DLA systems for which it was
possible to measure the H i column density directly from the fit of the red
damping wing of the Ly$\alpha$ transition. On the other hand, in Table 8 we
list the abundances relative to O for all the systems in our sample.

Table 7: Chemical abundance of elements detected in low ionization systems
where the column density of H i could be estimated.

QSO | $z_{\rm abs}$ | $\rm[C/H]$ | $\rm[O/H]$ | $\rm[Mg/H]$ | $\rm[Al/H]$ | $\rm[Si/H]$ | $\rm[Fe/H]$
---|---|---|---|---|---|---|---
PSO J025-11∗ | $5.7763$ | $-2.29\pm 0.10$ | $-2.82\pm 0.11$ | $-2.25\pm 0.15$ | $-2.22\pm 0.19$ | $-2.15\pm 0.11$ | $-2.75\pm 0.11$
PSO J025-11∗ | $5.8385$ | $>-2.22$ | $>-2.22$ | $>-2.27$ | $-2.27\pm 0.22$ | $-1.97\pm 0.13$ | $-2.25\pm 0.11$
SDSS J0818+1722 | $5.8767$ | $-2.86\pm 0.10$ | $-2.77\pm 0.10$ | $-2.84\pm 0.13$ | $-2.92\pm 0.37$ | $-2.75\pm 0.10$ | $-3.21\pm 0.13$
PSO J007+04∗ | $5.9917$ | $-3.38\pm 0.12$ | $-3.12\pm 0.13$ | $<-3.16$ | $<-2.75$ | $-3.22\pm 0.11$ | $-3.33\pm 0.22$
SDSS J2310+1855∗ | $5.9388$ | $>-3.10$ | $>-2.42$ | $>-3.11$ | $-3.28\pm 0.39$ | $-2.79\pm 0.12$ | $-3.18\pm 0.12$
SDSS J0100+2802 | $6.1434$ | $-2.52\pm 0.10$ | $-2.23\pm 0.10$ | $-2.54\pm 0.10$ | $-2.91\pm 0.15$ | $-2.44\pm 0.10$ | $-2.78\pm 0.10$
PSO J183+05∗ | $6.4041$ | $-2.51\pm 0.12$ | $-2.51\pm 0.11$ | $>-2.13$ | $-2.66\pm 0.12$ | $-2.15\pm 0.10$ | $-2.74\pm 0.10$

141414∗ These systems are PDLA.

Table 8: Chemical abundances relative to oxygen of the elements detected in
the observed low ionization systems.

QSO | $z_{\rm abs}$ | $\rm[C/O]$ | $\rm[Mg/O]$ | $\rm[Al/O]$ | $\rm[Si/O]$ | $\rm[Fe/O]$
---|---|---|---|---|---|---
PSO J308-27 | $5.4400$ | $-0.15\pm 0.04$ | $0.06\pm 0.06$ | $<0.01$ | $0.23\pm 0.07$ | $-0.33\pm 0.06$
PSO J308-27 | $5.6268$ | $-0.05\pm 0.04$ | $0.05\pm 0.06$ | $-0.08\pm 0.13$ | $0.08\pm 0.03$ | $-0.26\pm 0.04$
PSO J023-02 | $5.4869$ | $0.21\pm 0.15$ | $-0.05\pm 0.11$ | $<0.25$ | $<0.29$ | $-0.49\pm 0.10$
PSO J025-11∗ | $5.7763$ | $0.53\pm 0.05$ | $0.57\pm 0.12$ | $0.60\pm 0.17$ | $0.67\pm 0.05$ | $0.07\pm 0.06$
PSO J025-11∗ | $5.8385$ | $\cdots$ | $\cdots$ | $<-0.05$ | $<0.25$ | $<-0.03$
PSO J108+08 | $5.5624$ | $-0.46\pm 0.07$ | $\cdots$ | $<-0.04$ | $<-0.24$ | $<-0.74$
SDSS J0818+1722 | $5.7912$ | $-0.11\pm 0.03$ | $\cdots$ | $\cdots$ | $0.01\pm 0.02$ | $-0.36\pm 0.05$
SDSS J0818+1722 | $5.8767$ | $-0.09\pm 0.04$ | $-0.07\pm 0.09$ | $<0.02$ | $0.02\pm 0.03$ | $-0.44\pm 0.08$
PSO J007+04∗ | $5.9917$ | $-0.26\pm 0.11$ | $<-0.04$ | $<0.37$ | $-0.10\pm 0.09$ | $-0.21\pm 0.22$
SDSS J2310+1855∗ | $5.9388$ | $\cdots$ | $\cdots$ | $<-0.86$ | $<-0.37$ | $<-0.76$
PSO J158-14 | $5.8986$ | $-0.03\pm 0.08$ | $\cdots$ | $-0.10\pm 0.22$ | $0.23\pm 0.08$ | $-0.27\pm 0.08$
PSO J239-07∗ | $5.9918$ | $-0.38\pm 0.13$ | $-0.26\pm 0.13$ | $<0.17$ | $-0.04\pm 0.07$ | $<-0.49$
ULAS J1319+0950∗ | $6.0172$ | $-0.50\pm 0.13$ | $-0.23\pm 0.17$ | $0.15\pm 0.24$ | $-0.25\pm 0.07$ | $-0.29\pm 0.16$
PSO J060+24 | $5.6993$ | $-0.02\pm 0.20$ | $\cdots$ | $0.04\pm 0.25$ | $0.32\pm 0.09$ | $-0.35\pm 0.11$
PSO J065-26 | $5.8677$ | $-0.21\pm 0.03$ | $-0.28\pm 0.05$ | $-0.30\pm 0.16$ | $0.04\pm 0.04$ | $-0.40\pm 0.03$
PSO J065-26∗ | $6.1208$ | $\cdots$ | $\cdots$ | $<0.04$ | $<0.31$ | $<-0.25$
PSO J065-26∗ | $6.1263$ | $>0.66$ | $>0.93$ | $0.83\pm 0.06$ | $0.71\pm 0.04$ | $0.06\pm 0.04$
SDSS J0100+2802 | $5.7974$ | $-0.28\pm 0.04$ | $\cdots$ | $-0.33\pm 0.09$ | $0.11\pm 0.04$ | $-0.32\pm 0.04$
SDSS J0100+2802 | $5.9450$ | $0.39\pm 0.04$ | $0.29\pm 0.05$ | $0.25\pm 0.15$ | $0.51\pm 0.08$ | $0.00\pm 0.06$
SDSS J0100+2802 | $6.1114$ | $-0.52\pm 0.15$ | $-0.50\pm 0.15$ | $-0.89\pm 0.17$ | $-0.50\pm 0.14$ | $-0.85\pm 0.14$
SDSS J0100+2802 | $6.1434$ | $-0.29\pm 0.03$ | $-0.31\pm 0.04$ | $-0.68\pm 0.11$ | $-0.21\pm 0.03$ | $-0.55\pm 0.03$
DELS J1535+1943 | $5.8990$ | $\cdots$ | $\cdots$ | $\cdots$ | $\cdots$ | $\cdots$
PSO J183+05 | $6.0642$ | $0.05\pm 0.07$ | $0.40\pm 0.20$ | $0.27\pm 0.07$ | $0.36\pm 0.04$ | $-0.18\pm 0.05$
PSO J183+05∗ | $6.4041$ | $0.00\pm 0.08$ | $>0.38$ | $-0.15\pm 0.08$ | $0.36\pm 0.05$ | $-0.22\pm 0.05$
WISEA J0439+1634 | $6.2743$ | $0.12\pm 0.21$ | $<-0.30$ | $<0.12$ | $0.20\pm 0.17$ | $<-0.38$
VDES J0224-4711 | $6.1228$ | $-0.20\pm 0.13$ | $-0.23\pm 0.04$ | $<-0.28$ | $0.09\pm 0.06$ | $-0.41\pm 0.06$
PSO J036+03 | $6.0611$ | $-0.15\pm 0.10$ | $0.10\pm 0.14$ | $0.17\pm 0.23$ | $0.39\pm 0.13$ | $<-0.56$
DELS J0923+0402 | $6.3784$ | $-0.46\pm 0.27$ | $-0.61\pm 0.17$ | $<-0.09$ | $-0.27\pm 0.10$ | $<-0.84$

151515∗ These systems are PDLA.

##  Appendix B Description of the studied systems

In this section, we describe in details every O i system that we have
analyzed. For brevity, in the following we refer to them as DLA systems,
although only for 9 of them we have the confirmation that they are actually
DLA. All reported wavelengths are in Å.

### PSO J308-27 $z_{\rm abs}=5.4400$

This system is an intervening DLA, with a separation from the QSO emission
redshift of $\sim 16250$ km s-1. It is characterized by a simple velocity
structure consisting of a single component. We detected the following ions: O
i $1302$, C ii $1334$, Si ii $1304$ and $1526$, Fe ii $2382$ and $2600$, and
Mg ii $2796$,$2803$, as shown in Figure 10. The value of the parameters
obtained from the fit are shown in Table 9. We performed the fit by linking
the $b$ parameter of all ions, and we also derived an upper limit on Al ii at
$1670$.

In the system, we have also detected high ionization lines. At the redshift of
the low ionization lines both Si iv and C iv are detected and have been fitted
by linking the redshift and the Doppler parameter of the two ions (see Fig. 10
and Table 9). The profile of Si iv shows a further component at $\Delta
v\simeq-107.5$ km s-1, which is not considered in the total column density
shown in Table 2.

Finally, we estimated a lower limit of $\log N_{\rm HI}>19.10$ for the H i
column density based on eq. 5.

Table 9: Voigt parameters obtained from the fit of the metal lines in the system at $z_{\rm abs}=5.4400$ in the spectrum of PSO J308-27. Ion | $z_{\rm abs}$ | $\log(N_{\rm X}/{\rm cm^{-2}})$ |  $b$ (km s-1)
---|---|---|---
O i | $5.44005\pm 0.00001$ | $14.09\pm 0.02$ | $11\pm 1$
C ii | $5.44007\pm 0.00002$ | $13.68\pm 0.03$ | $11\pm 1$
Si ii | $5.44010\pm 0.00006$ | $13.14\pm 0.07$ | $11\pm 1$
Al ii | $5.4400$ | $<11.86$ | $11$
Fe ii | $5.44001\pm 0.00006$ | $12.57\pm 0.06$ | $11\pm 1$
Mg ii | $5.44009\pm 0.00003$ | $13.06\pm 0.06$ | $11\pm 1$
Si iv | $5.43757\pm 0.00005$ | $12.81\pm 0.04$ | $27\pm 4$
Si iv | $5.43988\pm 0.00005$ | $12.67\pm 0.05$ | $22\pm 3$
C iv | $5.43988\pm 0.00005$ | $13.41\pm 0.07$ | $22\pm 3$

Figure 10: System at $z_{\rm abs}=5.4400$ in the spectrum of PSO J308-27.
Upper panel: fit of the detected low-ionization metal lines, and region where
Al ii $1670$ absorption would fall. Lower panel: fit of the detected high-
ionization lines.

### PSO J308-27 $z_{\rm abs}=5.6268$

This system is an intervening DLA, with a separation from the QSO emission
redshift of $\sim 7690$ km s-1, which presents a velocity structure
characterized by two components. We detected the following ions: O i $1302$, C
ii $1334$, Si ii $1260$, $1304$ and $1526$, Al ii $1670$, Fe ii $2344$,
$2382$, $2586$ and $2600$, and Mg ii $2796$, $2803$, as shown in Figure 11.
The value of the parameters obtained from the fits of the low ionization lines
are shown in Table 10. We have linked the $b$ parameters of all the ions in
each of the two components, with the exception of that of Mg ii which falls in
the telluric band and is therefore strongly affected by the absorption lines
of the sky (even if they have been partially corrected). Since the Al ii at
$1670$ line is very weak, we performed its fit by linking the redshifts of the
two components with those of Si ii. As regards Mg ii, on the other hand, for
each of the two components we have fixed the redshift to a value equal to that
of Si ii and the parameter $b$ to a value equal to that of the other ions; we
then performed the fit with the column density as the only free parameter.

In this system, we have also detected high ionization lines, which have a
velocity structure characterized by three components of both Si iv and C iv
covering the same velocity range of the low-ionization line profiles (see Fig.
11 and Table 10). We performed the fit of all the components by linking the
redshift and the $b$ parameter of the two ions.

Finally, we estimated a lower limit of $\log N_{\rm HI}>19.79$ for the H i
column density based on eq. 5.

Table 10: Voigt parameters obtained from the fit of the metal lines in the system at $z_{\rm abs}=5.6268$ in the spectrum of PSO J308-27. Ion | $z_{\rm abs}$ | $\log(N_{\rm X}/{\rm cm^{-2}})$ |  $b$ (km s-1)
---|---|---|---
O i | $5.62582\pm 0.00005$ | $14.32\pm 0.03$ | $31\pm 1$
C ii | $5.62597\pm 0.00004$ | $14.06\pm 0.03$ | $31\pm 1$
Si ii | $5.62597\pm 0.00002$ | $13.25\pm 0.01$ | $31\pm 1$
Al ii | $5.62597\pm 0.00002$ | $12.12\pm 0.16$ | $31\pm 1$
Fe ii | $5.62591\pm 0.00009$ | $12.82\pm 0.05$ | $31\pm 1$
Mg ii | $5.62597\pm 0.00000$ | $13.44\pm 0.08$ | $31$
O i | $5.62743\pm 0.00002$ | $14.59\pm 0.04$ | $15.5\pm 0.7$
C ii | $5.62739\pm 0.00002$ | $14.25\pm 0.04$ | $15.5\pm 0.7$
Si ii | $5.62739\pm 0.00001$ | $13.47\pm 0.03$ | $15.5\pm 0.7$
Al ii | $5.62739\pm 0.00001$ | $12.18\pm 0.20$ | $15.5\pm 0.7$
Fe ii | $5.62737\pm 0.00003$ | $13.17\pm 0.03$ | $15.5\pm 0.7$
Mg ii | $5.62739\pm 0.00000$ | $13.43\pm 0.06$ | $15.5$
Si iv | $5.62475\pm 0.00008$ | $12.76\pm 0.07$ | $24\pm 7$
C iv | $5.62475\pm 0.00008$ | $13.29\pm 0.15$ | $24\pm 7$
Si iv | $5.62599\pm 0.00006$ | $12.65\pm 0.07$ | $9\pm 7$
C iv | $5.62599\pm 0.00006$ | $13.13\pm 0.21$ | $9\pm 7$
Si iv | $5.62724\pm 0.00014$ | $12.49\pm 0.13$ | $22\pm 12$
C iv | $5.62724\pm 0.00014$ | $12.84\pm 0.35$ | $22\pm 12$

Figure 11: System at $z_{\rm abs}=5.6268$ in the spectrum of PSO J308-27.
Upper panel: fit of the detected low-ionization metal lines. Lower panel: fit
of the detected high-ionization lines.

### PSO J023-02 $z_{\rm abs}=5.4869$

This system is an intervening DLA composed of a single component, separated
from the QSO emission redshift by $\sim 16310$ km s-1. We detected the
following ions: O i $1302$, C ii $1334$, Fe ii $2382$ and $2600$, and Mg ii
$2796$, as shown in Figure 12. The value of the parameters obtained from the
fit of the low ionization lines are shown in Table 11. The C ii line is
blended with the fine structure line of Si ii* $1264$ at $z=5.8440$, while the
lines of Mg ii fall into the telluric band and only the transition at $2796$
could be observed. We performed the fit by linking the redshift and the $b$
parameter of all ions.We also derived an upper limit on Si ii at $1526$ (Si ii
$1304$ is blended with a C iv $1548$ at $z=4.4656$), and on Al ii at $1670$.

In this system, we did not detect high ionization lines (see Fig. 12) thus we
derived upper limits on Si iv and C iv.

Furthermore, a lower limit on the H i column density of $\log N_{\rm
HI}>19.33$ was estimated from eq. 5.

Table 11: Voigt parameters obtained from the fit of the metal lines in the system at $z_{\rm abs}=5.4869$ in the spectrum of PSO J023-02. Ion | $z_{\rm abs}$ | $\log(N_{\rm X}/{\rm cm^{-2}})$ |  $b$ (km s-1)
---|---|---|---
O i | $5.48698\pm 0.00002$ | $14.32\pm 0.03$ | $13\pm 2$
C ii | $5.48698\pm 0.00002$ | $14.27\pm 0.15$ | $13\pm 2$
Si ii | $5.4869$ | $<13.43$ | $13$
Al ii | $5.4869$ | $<12.33$ | $13$
Fe ii | $5.48698\pm 0.00002$ | $12.64\pm 0.10$ | $13\pm 2$
Mg ii | $5.48698\pm 0.00002$ | $13.18\pm 0.11$ | $13\pm 2$
Si iv | $5.4869$ | $<12.65$ | $26$
C iv | $5.4869$ | $<13.51$ | $26$

Figure 12: System at $z_{\rm abs}=5.4869$ in the spectrum of PSO J023-02.
Upper panel: fit of the detected low-ionization metal lines, and the region
where the absorptions of Si ii $1526$ and Al ii $1670$ would fall. Lower
panel: region where the high ionization lines of Si iv and C iv would fall.

### PSO J023-02 $z_{\rm abs}=5.8441$ PDLA/intrinsic

This system has a separation from the QSO emission redshift of $\sim 250$ km
s-1, and is characterized by a single-component velocity structure. Besides
the common ions of O i $1302$, C ii $1334$, Si ii $1260$, $1304$ and $1526$,
Al ii $1670$ and Fe ii $2344$, $2382$, $2586$ and $2600$, we could detect
relatively rare (at this redshift) transitions of S ii $1250$, $1253$ and
$1259$ and Mn ii $2576$ and $2594$, as shown in Figure 14. The value of the
parameters obtained from the fit of the low ionization lines are shown in the
Table 12. Furthermore, we observed absorption lines due to the fine-structure
transitions C ii* $1335$ and Si ii* $1264$ (Fig. 15), which implies that the
system could be very close to the QSO and possibly part of an outflow. It was
not possible to detect the Mg ii lines as they fall in a region affected by
strong telluric absorption that could not be corrected. The C ii $1334$ line
is blended with an Al ii at $z=4.4657$, while the fine structure line Si ii*
is blended with the C ii line of the previous system at $z=5.4869$. We
performed the fit by linking the $b$ parameters of all the detected ions.

In the system, we also detected high ionization lines due to N v Si iv and C
iv which have a broad velocity structure (see Fig. 14). We performed a fit
with three components, linking the b parameters of these ions in each of them.
Note that this QSO show also a broad absorption line (BAL) system identified
through the C iv absorption in Bischetti et al. (2022).

Finally, we also observed the Ly$\alpha$ absorption line in the proximity
region of the QSO (see Fig. 13), which shows a possible signature of partial
coverage, supporting the hypothesis that the system is arising in a clump of
gas close to the ionizing source. Due to the peculiarity of this system, we
decided to exclude it from the subsequent analysis and to study it in more
details in a future work.

Table 12: Voigt parameters obtained from the fit of the metal lines in the system at $z_{\rm abs}=5.8441$ in the spectrum of PSO J023-02. Ion | $z_{\rm abs}$ | $\log(N_{\rm X}/{\rm cm^{-2}})$ |  $b$ (km s-1)
---|---|---|---
H i | $5.83793\pm 0.00022$ | $14.24\pm 0.16$ | $61\pm 5$
H i | $5.84055\pm 0.00023$ | $14.44\pm 0.14$ | $85\pm 26$
H i | $5.84444\pm 0.00015$ | $14.79\pm 0.05$ | $84\pm 3$
S ii | $5.84412\pm 0.00005$ | $14.55\pm 0.04$ | $26\pm 1$
O i | $5.84419\pm 0.00005$ | $14.35\pm 0.04$ | $26\pm 1$
C ii | $5.84398\pm 0.00003$ | $14.32\pm 0.04$ | $26\pm 1$
$\mbox{C\,{\sc ii}}*$ | $5.84398\pm 0.00003$ | $14.38\pm 0.04$ | $26\pm 1$
Si ii | $5.84408\pm 0.00004$ | $13.14\pm 0.04$ | $26\pm 1$
$\mbox{Si\,{\sc ii}}*$ | $5.84408\pm 0.00004$ | $13.22\pm 0.05$ | $26\pm 1$
Al ii | $5.84421\pm 0.00013$ | $12.84\pm 0.10$ | $26\pm 1$
Fe ii | $5.84404\pm 0.00010$ | $12.95\pm 0.07$ | $26\pm 1$
Mn ii | $5.84403\pm 0.00021$ | $12.45\pm 0.13$ | $26\pm 1$
N v | $5.83801\pm 0.00004$ | $14.52\pm 0.02$ | $44\pm 2$
Si iv | $5.83801\pm 0.00004$ | $13.18\pm 0.08$ | $44\pm 2$
C iv | $5.83801\pm 0.00004$ | $>14.60$ | $44\pm 2$
N v | $5.83987\pm 0.00006$ | $>14.11$ | $28\pm 4$
Si iv | $5.83987\pm 0.00006$ | $13.51\pm 0.05$ | $28\pm 4$
C iv | $5.83987\pm 0.00006$ | $>15.41$ | $28\pm 4$
N v | $5.84329\pm 0.00003$ | $>16.14$ | $66\pm 2$
Si iv | $5.84329\pm 0.00003$ | $>14.87$ | $66\pm 2$
C iv | $5.84329\pm 0.00003$ | $>16.33$ | $66\pm 2$
Figure 13: System at $z_{\rm abs}=5.8441$ in the spectrum of PSO J023-02. Fit
of the H i Ly$\alpha$ absorption line

Figure 14: System at $z_{\rm abs}=5.8441$ in the spectrum of PSO J023-02.
Upper panel: fit of the detected low-ionization metal lines. Lower panel: fit
of the detected high-ionization lines. Figure 15: System at $z_{\rm
abs}=5.8441$ in the spectrum of PSO J023-02. Fit of the detected fine-
structure lines.

### PSO J025-11 $z_{\rm abs}=5.7763$ PDLA

This system is a PDLA with a two-component velocity structure and a separation
from the QSO emission redshift of $\sim 2866$ km s-1. We detected the
following ions: O i $1302$, C ii $1334$, Si ii $1260$, $1304$ and $1526$, Al
ii at $1670$, Fe ii at $2344$, $2382$ and $2600$, and Mg ii at $2796$, as
shown in Figure 16. The value of the parameters obtained from the fit of the
low ionization lines are shown in Table 13. We carried out the fit by linking
the $b$ parameters of all the ions in each of the two components. As for the
Al ii, which falls in a region with low SNR, we have also linked the redshifts
to those of the Si ii. The lines of Mg ii, on the other hand, fall into the
telluric band and are therefore strongly affected by the sky lines, even if
they have been partially corrected; only the transition at $2796$ could be
observed.

Since the system is a PDLA we have also performed the fit of the Ly$\alpha$
absorption line, as described in section 3.4. This line is blended with
another Ly$\alpha$ absorption line present in the spectrum, associated with
the absorption system at $z=5.8385$. From the fit we obtained a column density
$\log N_{\rm HI}=20.35\pm 0.10$, in agreement with the lower limit determined
from the rest equivalent width of Mg ii $2796$ line.

In the system we have also detected high ionization lines, which present a
velocity structure characterized by two components of Si iv and C iv (see Fig.
16 and Table 13). For both components we linked the redshifts and Doppler
parameters of the two ions.

Table 13: Voigt parameters obtained from the fit of the metal lines in the system at $z_{\rm abs}=5.7763$ in the spectrum of PSO J025-11. Ion | $z_{\rm abs}$ | $\log(N_{\rm X}/{\rm cm^{-2}})$ |  $b$ (km s-1)
---|---|---|---
H i | $5.7763$ | $20.35\pm 0.10$ | $40$
O i | $5.77549\pm 0.00007$ | $13.94\pm 0.05$ | $23\pm 1$
C ii | $5.77569\pm 0.00002$ | $14.37\pm 0.03$ | $23\pm 1$
Si ii | $5.77560\pm 0.00002$ | $13.59\pm 0.04$ | $23\pm 1$
Al ii | $5.77560\pm 0.00002$ | $12.47\pm 0.11$ | $23\pm 1$
Fe ii | $5.77544\pm 0.00005$ | $12.96\pm 0.05$ | $23\pm 1$
Mg ii | $5.77560\pm 0.00006$ | $13.54\pm 0.14$ | $23\pm 1$
O i | $5.77736\pm 0.00005$ | $13.90\pm 0.06$ | $10\pm 2$
C ii | $5.77725\pm 0.00003$ | $13.89\pm 0.07$ | $10\pm 2$
Si ii | $5.77730\pm 0.00002$ | $13.08\pm 0.08$ | $10\pm 2$
Al ii | $5.77730\pm 0.00002$ | $11.95\pm 0.59$ | $10\pm 2$
Fe ii | $5.77727\pm 0.00012$ | $12.55\pm 0.11$ | $10\pm 2$
Mg ii | $5.77730\pm 0.00002$ | $13.19\pm 0.19$ | $10\pm 2$
Si iv | $5.77534\pm 0.00007$ | $13.59\pm 0.10$ | $28\pm 3$
C iv | $5.77534\pm 0.00007$ | $14.26\pm 0.05$ | $28\pm 3$
Si iv | $5.77665\pm 0.00014$ | $13.39\pm 0.10$ | $32\pm 6$
C iv | $5.77665\pm 0.00014$ | $13.84\pm 0.10$ | $32\pm 6$

Figure 16: System at $z_{\rm abs}=5.7763$ in the spectrum of PSO J025-11.
Upper panel: fit of the H i Ly$\alpha$ and Ly$\beta$ absorption lines. Middle
panel: fit of the detected low-ionization metal lines. Lower panel: fit of the
detected high-ionization lines.

### PSO J025-11 $z_{\rm abs}=5.8385$ PDLA

This system is a PDLA with a separation from the QSO emission redshift of
$\sim 127$ km s-1. It is characterized by a complex velocity structure. We
detected four components of O i $1302$ and C ii $1334$, six components of Si
ii at $1260$, $1304$ and $1526$, five components of Al ii $1670$, seven
components of Fe ii $2382$ and $2600$ (of which three also detected in Fe ii
$1608$, two also in Fe ii $2374$ and five also in the transition Fe ii
$2586$), and three components of Mg ii $2803$, as shown in Figure 18. The
value of the parameters obtained from the fit of the low ionization lines are
shown in Table 14. We performed the fit by linking the Doppler parameter of
the velocity profile components that matched in redshift. Oxygen, carbon and
magnesium are saturated, therefore their column density was considered a lower
limit. The lines of Mg ii fall in the telluric band and are therefore strongly
affected by the lines of the sky, only three component of the transition at
$2803$ could be observed, which correspond to the last three components of O i
and C ii.

We also performed the fit of the H i Ly$\alpha$ absorption line, resulting in
a column density $\log N_{\rm HI}=21.25\pm 0.10$. This line is blended with
another Ly$\alpha$ absorption line present in the spectrum, due to the
absorption system at $z=5.7763$. The H i fit is in agreement with the lower
limit for the H i column density based on eq. 5.

In the system we have also detected high ionization lines, which have a
velocity structure characterized by three components of Si iv and C iv. We fit
the first two components by linking the $b$ parameter of the two ions, while
the third leaving this parameter free as well.

Table 14: Voigt parameters obtained from the fit of the metal lines in the system at $z_{\rm abs}=5.8385$ in the spectrum of PSO J025-11. Ion | $z_{\rm abs}$ | $\log(N_{\rm X}/{\rm cm^{-2}})$ |  $b$ (km s-1)
---|---|---|---
H i | $5.8385$ | $21.25\pm 0.10$ | $100$
O i | $5.83567\pm 0.00006$ | $14.42\pm 0.05$ | $24\pm 2$
C ii | $5.83578\pm 0.00007$ | $13.88\pm 0.06$ | $24\pm 2$
Si ii | $5.83548\pm 0.00004$ | $13.17\pm 0.04$ | $24\pm 2$
Fe ii | $5.83545\pm 0.00009$ | $12.87\pm 0.14$ | $6$
Al ii | $5.83643\pm 0.00011$ | $12.56\pm 0.12$ | $13\pm 6$
Fe ii | $5.83644\pm 0.00007$ | $13.37\pm 0.08$ | $13\pm 6$
O i | $5.83737\pm 0.00004$ | $>15.45$ | $36\pm 2$
C ii | $5.83756\pm 0.00003$ | $>15.28$ | $36\pm 2$
Si ii | $5.83747\pm 0.00003$ | $14.45\pm 0.02$ | $36\pm 2$
Al ii | $5.83760\pm 0.00010$ | $12.83\pm 0.08$ | $19\pm 2$
Fe ii | $5.83749\pm 0.00004$ | $14.05\pm 0.06$ | $19\pm 2$
Mg ii | $5.83749\pm 0.00000$ | $>14.40$ | $36$
Si ii | $5.83875\pm 0.00012$ | $13.11\pm 0.19$ | $18\pm 11$
Al ii | $5.83875\pm 0.00012$ | $12.29\pm 0.21$ | $18\pm 11$
Fe ii | $5.83875\pm 0.00012$ | $12.87\pm 0.14$ | $18\pm 11$
O i | $5.84023\pm 0.00003$ | $>15.32$ | $35\pm 2$
C ii | $5.84023\pm 0.00002$ | $>14.92$ | $35\pm 2$
Si ii | $5.83967\pm 0.00002$ | $14.36\pm 0.24$ | $8\pm 1$
Al ii | $5.83972\pm 0.00009$ | $13.06\pm 0.46$ | $8\pm 1$
Fe ii | $5.83967\pm 0.00002$ | $14.11\pm 0.08$ | $8\pm 1$
Mg ii | $5.84002\pm 0.00007$ | $>14.10$ | $35\pm 2$
Si ii | $5.84039\pm 0.00008$ | $13.88\pm 0.06$ | $32\pm 3$
Al ii | $5.84030\pm 0.00037$ | $12.53\pm 0.25$ | $32\pm 3$
Fe ii | $5.84035\pm 0.00012$ | $13.54\pm 0.08$ | $32\pm 3$
O i | $5.84243\pm 0.00013$ | $14.11\pm 0.06$ | $39\pm 5$
C ii | $5.84263\pm 0.00009$ | $13.84\pm 0.05$ | $39\pm 5$
Si ii | $5.84251\pm 0.00006$ | $12.83\pm 0.04$ | $24\pm 4$
Fe ii | $5.84251\pm 0.00006$ | $12.65\pm 0.10$ | $24\pm 4$
Mg ii | $5.84267\pm 0.00054$ | $12.55\pm 0.23$ | $39\pm 5$
Si iv | $5.83556\pm 0.00006$ | $13.15\pm 0.04$ | $28\pm 4$
C iv | $5.83549\pm 0.00011$ | $13.73\pm 0.08$ | $28\pm 4$
Si iv | $5.83694\pm 0.00008$ | $12.94\pm 0.07$ | $22\pm 4$
C iv | $5.83663\pm 0.00007$ | $13.88\pm 0.06$ | $22\pm 4$
Si iv | $5.83858\pm 0.00007$ | $12.98\pm 0.05$ | $27\pm 5$
C iv | $5.83851\pm 0.00019$ | $13.11\pm 0.11$ | $19\pm 5$
Figure 17: System at $z_{\rm abs}=5.8385$ in the spectrum of PSO J025-11. Fit
of the H i Ly$\alpha$ and Ly$\beta$ absorption lines.

Figure 18: System at $z_{\rm abs}=5.8385$ in the spectrum of PSO J025-11.
Upper panel: fit of the detected low-ionization metal lines. Lower panel: fit
of the detected high-ionization lines.

### PSO J108+08 $z_{\rm abs}=5.5624$

This system is an intervening DLA composed of a single component, separated
from the QSO emission redshift by $\sim 17400$ km s-1. We detected the
following ions: O i $1302$ and C ii $1334$, as shown in Figure 19. The value
of the parameters obtained from the fit of the low ionization lines are shown
in Table 15. We performed the fit by linking the redshift of these ions and
freezing the parameter $b$ to its minimum value of $5$ km s-1for the visible
region of the spectrum. We also derived an upper limit on Si ii $1304$, Al ii
$1670$, and on Fe ii $2382$. The Mg ii lines fall in a telluric band, and it
was not possible to correct the effect of the sky lines at the wavelength at
which this absorption occurs.

In this system, we did not detect high ionization lines (see Fig. 19) thus we
derived upper limits on Si iv and C iv. The lower limit on the H i column
density derived from eq. 5 is $\log N({\rm HI})>18.85$.

Table 15: Voigt parameters obtained from the fit of the metal lines in the system at $z_{\rm abs}=5.5624$ in the spectrum of PSO J108+08. Ion | $z_{\rm abs}$ | $\log(N_{\rm X}/{\rm cm^{-2}})$ |  $b$ (km s-1)
---|---|---|---
O i | $5.56249\pm 0.00001$ | $13.84\pm 0.03$ | $5$
C ii | $5.56249\pm 0.00001$ | $13.12\pm 0.07$ | $5$
Si ii | $5.5624$ | $<12.42$ | $5$
Al ii | $5.5624$ | $<11.56$ | $6$
Fe ii | $5.5624$ | $<11.91$ | $6$
Si iv | $5.5624$ | $<12.39$ | $26$
C iv | $5.5624$ | $<13.31$ | $26$

Figure 19: System at $z_{\rm abs}=5.5624$ in the spectrum of PSO J108+08.
Upper panel: fit of the detected low-ionization metal lines, and the region
where the absorptions of Si ii $1304$, Al ii $1670$ and Fe ii $2382$ would
fall. Lower panel: region where the high ionization lines of Si iv and C iv
would fall.

### SDSS J0818+1722 $z_{\rm abs}=5.7912$

This system is an intervening DLA with a velocity structure characterized by
three components. The separation from the QSO emission redshift is of $\sim
8950$ km s-1. We detected the following ions: O i $1302$, C ii $1334$, Si ii
$1260$, $1304$ and $1526$, Fe ii $2382$ and $2600$, as shown in Figure 20. The
value of the parameters obtained from the fit of the low ionization lines are
shown in Table 16. We linked the $b$ parameters of all the ions in each of the
three components. The Mg ii lines fall in a telluric band and its column
density cannot be recovered.

As regards the high ionization lines, in this system we detected the C iv
doublet, while we obtained an upper limit for the column density of Si iv,
using the transition at $1402$ and setting the parameter $b$ at $36$ km s-1
like that of C iv (see Fig. 20 and Table 16).

The lower limit on the H i column density derived from eq. 5 is $\log N({\rm
HI})>19.51$.

This system was already identified by Becker et al. (2011) in a high-
resolution spectrum obtained with HIRES at the Keck telescope. They detected O
i, C ii and Si ii, while they did not cover the wavelength region for Fe ii
and Mg ii. The SNR in the regions where C iv and Si iv fall was too low to
detect the lines so they determined upper limits. The total column densities
for the ions in common between their work and this one are in very good
agreement.

Table 16: Voigt parameters obtained from the fit of the metal lines in the system at $z_{\rm abs}=5.7912$ in the spectrum of SDSS J0818+1722. Ion | $z_{\rm abs}$ | $\log(N_{\rm X}/{\rm cm^{-2}})$ |  $b$ (km s-1)
---|---|---|---
O i | $5.79004\pm 0.00013$ | $13.84\pm 0.06$ | $36\pm 2$
C ii | $5.78968\pm 0.00005$ | $13.71\pm 0.02$ | $36\pm 2$
Si ii | $5.78945\pm 0.00003$ | $12.89\pm 0.01$ | $36\pm 2$
Fe ii | $5.78928\pm 0.00033$ | $12.31\pm 0.13$ | $36\pm 2$
O i | $5.79071\pm 0.00005$ | $13.62\pm 0.10$ | $7\pm 6$
C ii | $5.79073\pm 0.00004$ | $13.24\pm 0.06$ | $7\pm 6$
Si ii | $5.79072\pm 0.00004$ | $12.46\pm 0.04$ | $7\pm 6$
Fe ii | $5.79041\pm 0.00021$ | $12.17\pm 0.17$ | $7\pm 6$
O i | $5.79175\pm 0.00002$ | $14.32\pm 0.02$ | $19.1\pm 0.8$
C ii | $5.79166\pm 0.00002$ | $13.84\pm 0.02$ | $19.1\pm 0.8$
Si ii | $5.79166\pm 0.00001$ | $13.04\pm 0.01$ | $19.1\pm 0.8$
Fe ii | $5.79156\pm 0.00006$ | $12.74\pm 0.04$ | $19.1\pm 0.8$
Si iv | $5.7895$ | $<12.58$ | $36$
C iv | $5.78950\pm 0.00013$ | $13.38\pm 0.07$ | $36\pm 10$

Figure 20: System at $z_{\rm abs}=5.7912$ in the spectrum of SDSS J0818+1722.
Upper panel: fit of the detected low-ionization metal lines. Lower panel: fit