11institutetext:  Department of Astronomy, University of Geneva, Chemin Pegasi
51, 1290 Versoix, Switzerland 11email<EMAIL_ADDRESS>22institutetext:
Institute of Astronomy, Kharkiv National University, Sumska 35, Kharkiv,
61022, Ukraine 33institutetext: European Southern Observatory, Karl-
Schwarzschild Str. 2, 85748 Garching bei München, Germany 44institutetext:
European Southern Observatory, Alonso de Córdova 3107, Casilla 19001,
Vitacura, Santiago, Chile 55institutetext: Centre de Recherche Astrophysique
de Lyon, Univ. Claude Bernard Lyon 1, 9 Av. Charles André, 69230 St Genis
Laval, France

# The $\alpha$-element enrichment of gas in distant galaxies

Anna Velichko The $\alpha$-element enrichment of gas in distant galaxiesThe
$\alpha$-element enrichment of gas in distant galaxiesThe $\alpha$-element
enrichment of gas in distant galaxiesThe $\alpha$-element enrichment of gas in
distant galaxies Annalisa De Cia The $\alpha$-element enrichment of gas in
distant galaxiesThe $\alpha$-element enrichment of gas in distant galaxiesThe
$\alpha$-element enrichment of gas in distant galaxiesThe $\alpha$-element
enrichment of gas in distant galaxies Christina Konstantopoulou The
$\alpha$-element enrichment of gas in distant galaxiesThe $\alpha$-element
enrichment of gas in distant galaxies Cédric Ledoux The $\alpha$-element
enrichment of gas in distant galaxiesThe $\alpha$-element enrichment of gas in
distant galaxies Jens-Kristian Krogager The $\alpha$-element enrichment of gas
in distant galaxiesThe $\alpha$-element enrichment of gas in distant galaxies
Tanita Ramburuth-Hurt The $\alpha$-element enrichment of gas in distant
galaxiesThe $\alpha$-element enrichment of gas in distant galaxies

(Received date / Accepted date )

###### Abstract

Context.  The chemical evolution of distant galaxies cannot be assessed from
observations of individual stars, in contrast to the case of nearby galaxies.
On the other hand, the study of the interstellar medium (ISM) offers an
alternative way to reveal important properties of the chemical evolution of
distant galaxies. The chemical enrichment of the ISM is produced by all the
previous generations of stars and it is possible to precisely determine the
metal abundances in the neutral ISM in galaxies. The chemical abundance
patterns in the neutral ISM are determined by the gas metallicity, presence of
dust (the depletion of metals into dust grains), and possible deviations due
to specific nucleosynthesis, for example, $\alpha$-element enhancements.

Aims.  We aim to derive the metallicities, dust depletion, and
$\alpha$-element enhancements in the neutral ISM of gas-rich mostly-metal-poor
distant galaxies (Damped Lyman-$\alpha$ absorbers, DLAs). Furthermore, we aim
to constrain the distribution of $\alpha$-element enhancements with
metallicity in these galaxies.

Methods. We collected a literature sample of column density measurements of O,
Mg, Si, S, Ti, Cr, Fe, Ni, Zn, P, and Mn in the neutral ISM of DLAs at
redshifts of $0.60<z<3.40$. We used this sample to define a golden sample of
DLAs with constrained observations of Ti and at least one other
$\alpha$-element. By studying the abundance patterns, we determined the amount
of dust depletion, solely based on the observed relative abundances of the
$\alpha$-elements. We then used the abundances of Fe-peak elements to
determine the overall metallicity of each system, after correcting for dust
depletion. In addition, we studied the deviations from the basic (linear)
abundance patterns. We divided our sample into two groups of galaxies based on
the widths of their absorption lines ($\Delta v_{90}$ above or below 100 $\rm
km\,s^{-1}$), which may be considered as a proxy for their dynamical mass. We
characterised the distribution of the $\alpha$-element enhancements as a
function of metallicity for the galaxy population as a whole, by fitting a
piecewise function (plateau, decline, plateau) to the data.

Results. We observed systematic deviations from the basic abundance patterns
for O, Mg, Si, S, Ti, and Mn, which we interpreted as $\alpha$-element
enhancements and a Mn underabundance. The distribution of the $\alpha$-element
enhancements with metallicity is different in the high-$\Delta v_{90}$ and
low-$\Delta v_{90}$ groups of galaxies. We constrained the metallicity of the
$\alpha$-element knee for the high-$\Delta v_{90}$ and low-$\Delta v_{90}$
groups of galaxies to be $-$1.02$\pm$0.15 dex and $-$1.84$\pm$0.11 dex,
respectively. The average $\alpha$-element enhancement at the high-plateau is
[$\alpha$/Fe]=0.38$\pm$0.07 dex. On the other hand, Mn shows an underabundance
in all DLAs in the golden sample of $-$0.36$\pm$0.07 dex, on average.

Conclusions. We have constrained, for the first time, the distribution of the
$\alpha$-element enhancement with metallicity in the neutral ISM in distant
galaxies. Less massive galaxies show an $\alpha$-element knee at lower
metallicities than more massive galaxies. This can be explained by a lower
star formation rate in less massive galaxies. If this collective behaviour can
be interpreted in the same way as it is for individual systems, this would
suggest that more massive and metal-rich systems evolve to higher
metallicities before the contribution of SN-Ia to [$\alpha$/Fe] levels out
that of core-collapse SNe. This finding may plausibly be supported by
different SFRs in galaxies of different masses. Overall, our results offer
important clues to the study of chemical evolution in distant galaxies.

###### Key Words.:

ISM: abundances – dust, extinction – quasars: absorption lines – galaxies:
evolution

##  1 Introduction

The outcome of the evolutionary history of galaxies is recorded in the
interstellar abundances of chemical elements. Observations of the interstellar
medium (ISM) in galaxies of various types, differing in terms of mass, size,
metallicity, and their respective evolutionary stages, may provide a key to
understanding the processes taking place in galaxies (Maiolino & Mannucci
2019).

In the Milky Way (MW) and nearby galaxies, one of the ways to trace their
evolutionary process is from observations of the detailed abundances of
chemical elements in individual stars (McWilliam 1997; Tolstoy et al. 2009).
Although it is impossible to obtain information about individual stars in
distant galaxies, the chemical properties of their interstellar medium (ISM)
can be analysed in great detail. The chemical abundance patterns in the ISM is
the result of enrichment produced by all the previous generations of stars.
These patterns make up a snapshot of the evolutionary history of the galaxy.

One of the techniques to determine element abundances in the gas of faint
high-redshift galaxies is based on the detection of its imprint on the
spectrum of a background sources which may be a quasi-stellar object (QSO) or
gamma-ray burst (GRB) afterglow (Prochaska & Wolfe 1999; Prochaska et al.
2007; Ledoux et al. 2002a; Vreeswijk et al. 2004; De Cia et al. 2012). Damped
Lyman-$\alpha$ absorbers (DLA) are defined as systems with high column
densities of neutral hydrogen (N(H I)$\geq 2\times 10^{20}$ cm-2) that appear
in absorption in QSOs or GRBs spectra.

The use of DLAs to study galaxies is important for several reasons. First, due
to the fact that they are observed in absorption, there is no selection effect
with respect to luminosity of the DLA-galaxies and presumably masses. Hence,
it is possible to detect in this way both the faintest low-mass and bright
high-mass galaxies. In our study, it is important to cover a wide range of
galaxies as much as possible in terms of masses.

Secondly, due to the fact that hydrogen in DLAs is mainly in a neutral state
(HI), the HI atoms shield the gas against ionisation (e.g. Viegas 1995), and
other elements are also mainly in their dominant states, while the other
states are negligible. For example, it is known that under such conditions,
oxygen and nitrogen, like hydrogen, are neutral (OI, NI), while elements such
as C, Mg, Si, Fe, and S are predominantly singly ionised (CII, MgII, etc.,
see, e.g. Hernandez et al. 2020). Therefore, there is no need to apply
ionisation corrections, which, in turn, can introduce large uncertainties.
This makes it possible to accurately determine the element abundances from the
column densities.

Third, unlike emission spectra, in which only very strong spectral lines can
be detected, absorption spectra provide very detailed chemical composition
even for faint high-z galaxies since, in this case, it is possible to make
measurements from very weak line profiles.

The $\alpha$-element enhancement, [$\alpha$/Fe], and its evolution with the
metallicity [M/H] is a strong diagnostic of the chemical evolution of galaxies
(e.g. Tinsley 1979; Hill et al. 1995; Chiappini et al. 1997; Tolstoy et al.
2009; Kobayashi et al. 2020a; Matteucci 2021). More details about
[$\alpha$/Fe] evolution with metallicity are discussed in Section 5.1. Until
recently, the [$\alpha$/Fe] has mostly been observed in stars in the local
group (e. g. McWilliam 1997; Tolstoy et al. 2009; Matteucci 2021). Cullen et
al. (2021) observed [$\alpha$/Fe] in nearby galaxies from a combination of
stellar and gas metallicities. In the gas, the measurements of [$\alpha$/Fe]
are additionally complicated by the presence of dust, which dramatically
alters the observed abundances. Large fractions of refractory metals are
missing from the gas-phase and are instead incorporated into dust grains, a
phenomenon called dust depletion (e.g. Field 1974; Savage & Sembach 1996;
Jenkins 2009; De Cia et al. 2016). When dust depletion is negligible, it has
been possible in the past to observe $\alpha$-element enhancement in a few
least dusty, typically metal-poor DLA systems (Dessauges-Zavadsky et al. 2002;
Ledoux et al. 2002b; Dessauges-Zavadsky et al. 2006; Cooke et al. 2011; Becker
et al. 2012; De Cia et al. 2016). Recently, Ramburuth-Hurt et al. (2023)
studied the depletion patterns of individual gas components within DLA systems
and discovered $\alpha$-element enhancements for systems with a wide range of
dust depletions. In this study, we analyse the abundance patterns of a sample
of DLAs out to z$\sim$4, correct for dust depletion, and measure the
$\alpha$-element enhancements in the gas in the DLA galaxies. Furthermore, we
split our sample in a group of lower-mass galaxies and one of higher-mass
galaxies to investigate the evolution of the [$\alpha$/Fe] distribution with
metallicity for these groups.

We refer to metal relative abundances [X/Y] defined as:

${\rm[X/Y]=log\,\frac{N(X)}{N(H)}-log\,\frac{N(X)_{\odot}}{N(H)_{\odot}}},$
(1)

where N(X)⊙, N(Y)⊙ are column densities from Asplund et al. (2021), following
the recommendations of Lodders & Palme (2009), as reported in Table 1 of
Konstantopoulou et al. (2022).

##  2 Features of the nucleosynthesis of the elements under study

###  2.1 The $\alpha$-elements

The study of the distribution of [$\alpha$/Fe] with metallicity, [M/H], is
fundamental to understand the chemical evolution of galaxies (e.g. Tinsley
1979; Hill et al. 1995; Chiappini et al. 1997; Tolstoy et al. 2009; Kobayashi
et al. 2020a; Matteucci 2021) and can provide important information on the
star-formation history (SFH) in a galaxy. It is well known that
$\alpha$-elements (i.e. those that can be created by the $\alpha$-process,
e.g. O, Mg, Si, S, Ca, Ti) are mainly produced inside massive stars (${\rm
M\geqslant 8M_{\odot}}$) with lifetimes lower than 30 Myr. They are
subsequently released into the interstellar medium (ISM) via core-collapse
Type II supernovae. As a result, the ejected matter is enriched in
$\alpha$-elements relative to Fe, until after about 1 billion years most SNe
Ia begin to explode and produce more iron (Tinsley 1979).

Schematically, in simplified form, this behaviour can be plotted in
coordinates [$\alpha$/Fe] – [M/H], as shown in Fig. 1. During the first phase,
when only core-collapse SNe (CCSNe) contribute to the abundance of elements,
[$\alpha$/Fe] is about constant and forms a plateau. The level of the
high-$\alpha$ plateau depends on the initial mass function (IMF, McWilliam
1997) because a larger number of massive stars produce more $\alpha$-elements.
In addition, the IMF may become more ”top-heavy” with increasing star
formation (Köppen et al. 2007).

Although $\alpha$-elements enrichment is dominated by CCSNe, SNe Ia also can
partially contribute to the abundances depending on the element. For instance,
O and Mg are produced almost exclusively by CCSNe, while Si, S, Ca and Ti in
the given order have an increasing contribution from SNe Ia, so that about 1/3
of titanium contained in the Sun has been produced in SNe Ia (Andrews et al.
2017). In addition, according to Woosley & Weaver (1995); Cayrel et al.
(2004), O is mainly produced by central helium burning with some contribution
of neon burning; Mg is mostly product of hydrostatic carbon burning in a shell
and explosive neon burning; Si and Ca are formed in both the oxygen burning
and neon burning shells; Ti by explosive oxygen burning. As a result of these
differences in the formation of $\alpha$-elements, the level of the
high-$\alpha$ plateau can systematically differ by 0.15 dex, if oxygen is not
taken into account (Cayrel et al. 2004; Petitjean et al. 2008).

After SNe Ia start to explode, the abundance of $\alpha$-elements relative to
iron gradually decreases, and the transition point from one regime to another
is commonly referred to as the ’$\alpha$-element knee’ (McWilliam 1997). The
position of the knee is sensitive to the early star formation rate (SFR).
Observations at different redshifts show that the SFR increases with galactic
mass (Katsianis et al. 2016). If the SFR is high, then more metals have time
to form during the first phase, resulting in a knee located at a higher [M/H]
(e.g. Tinsley 1979; McWilliam 1997). The position of the $\alpha$-element knee
has been measured in stars in local galaxies, and it seems to depend on the
mass of the galaxy, i.e. the knee is at lower metallicities for lower stellar
masses (de Boer et al. 2014). Because [$\alpha$/Fe] are decreasing after the
knee, the plateau is followed by a decay with a certain slope. According to
Andrews et al. (2017), the latter can be sensitive to the gas outflow rate.

Then, after a certain period of time, the third phase of the [$\alpha$/Fe]
evolution begins, when the contribution in the chemical yields of the SNe Ia
compensates those of the CCSNe. At this point, the [$\alpha$/Fe] reaches a
plateau at a value close to zero. In the case of the MW, the transition point
is at [M/H] = $-$0.2 (McWilliam 1997), and the low-$\alpha$ plateau level is
at [$\alpha$/Fe] = 0.05. To distinguish between the two knees mentioned above,
we call them high-$\alpha$ and low-$\alpha$ knee for transition points from
the high-$\alpha$ plateau to the decay and from the decay to the low-$\alpha$
plateau, respectively.

Figure 1 shows the curves [$\alpha$/Fe] – [M/H] we obtained using the release
DR17 of the Apache Point Observatory Galactic Evolution Experiment (APOGEE,
Majewski et al. (2017)) data for satellite galaxies of the MW: Large and Small
Magellanic Clouds (LMC and SMC, respectively), Sagittarius Dwarf Galaxy (Sgr),
Fornax (Fnx), and the now fully disrupted Gaia Sausage/Enceladus (GSE) system.
We selected stars belonging the galaxies according to the lists from
Hasselquist et al. (2021). For comparison, the curve for the MW given by
McWilliam (1997) is also shown. For details on APOGEE DR17 data fitting, we
refer to Appendix C.

Of course, this piecewise model is simplified compared to the natural
behaviour. In fact, the evolution of galaxies of different types, sizes, and
masses have their own peculiarities. For example, dwarf galaxies often have
several separate bursts of star formation in their evolutionary history, in
contrast to the more or less stable star formation in large galaxies such as
the MW (Tolstoy et al. 2009; Atek et al. 2022). Such a discontinuous star
formation manifests itself in the [$\alpha$/Fe]–[M/H] behaviour in the form of
bump on a low-$\alpha$ plateau (see e.g. the modelled tracks in Fig. 4 from
Hasselquist et al. 2021). We see such a bump (or a hint of it) in the
behaviour of [$\alpha$/Fe] for the all considered dwarf galaxies (see dark
gray curves in Fig. 16). The abundances of $\alpha$-elements follow each other
fairly well, that is, they make up a fairly homogeneous group; however, there
are small differences in their production, such as the location of synthesis
and dependencies on stellar mass and metallicity.

###  2.2 Zinc

Zinc is a volatile element that is often used as a tracer of metallicity in
the ISM of various objects, assuming that it is not captured in dust grains.
In reality, the depletion of Zn is non-negligible. Therefore, the evaluation
of metallicity using Zn can be erroneous, especially in highly dusty
environments.

Zinc is often considered to be an ideal tracer of iron-peak elements, because
in the Solar neighborhood [Zn/Fe] is about 0.0 for [Fe/H] between $-$2 and 0
dex (e.g. Nissen et al. 2004; Saito et al. 2009). However, the nucleosynthetic
nature of Zn is complex since it is neither an iron-peak nor an
$\alpha$-element. At [Fe/H] less than $-$2 dex [Zn/Fe] increases towards lower
metallicities up to $\approx$0.5 dex (Nissen et al. 2007). For the red giants
in the MW bulge, at [Fe/H] ¿ 0 dex [Zn/Fe] shows a decrease down to
$\approx-$0.5 dex (Barbuy et al. 2015). In dwarf galaxies the behaviour
[Zn/Fe] versus [Fe/H] is different from that observed in the MW due to the
different star formation history. Instead of a plateau, dwarf galaxies show a
constant decreasing [Zn/Fe] over the entire observed metallicity range
(Skúladóttir et al. 2017; Hirai et al. 2018). This difference between the
behaviour of [Zn/Fe] in massive and dwarf galaxies can be explained by the
complicated production of Zn.

According to (Bensby et al. 2003; Nissen & Schuster 2011; Mishenina et al.
2011; Barbuy et al. 2015; Duffau et al. 2017), the relation [Zn/Fe] versus
[M/H] tends to behave partially like an [$\alpha$/Fe] but with a smaller
amplitude. Sitnova et al. (2022) showed from non-LTE calculations for the MW
stars that Zn and Mg do not strictly follow each other. Nevertheless, [Zn/Fe]
is decreasing with metallicity because of various contributions from core-
collapse SNe and SNe Ia, and their different timescales (as for
$\alpha$-elements).

De Cia et al. (2024) analysed element abundances in the neutral ISM of the
Small and Large Magellanic Clouds and observed a potential tendency of a
deviation of Zn with respect to Fe up to 0.2 dex at lower metallicities and
down to $-$0.2 dex at higher metallicities. If confirmed, this might be in
agreement with the behaviour derived from stellar measurements described
above. However, this still needs to be verified with further investigations
with more data.

###  2.3 Phosphorus

Phosphorus is thought to be mainly produced in massive stars during their
hydrostatic carbon and neon burning phases (Woosley & Weaver 1995). SNe Ia
produce less significant amount of P compared to massive stars (Leung & Nomoto
2018). Little or no P is produced in AGB stars (Karakas & Lugaro 2016).
According to Maas et al. (2019, 2022), the behaviour of P with metallicity in
the MW is most similar to that of the $\alpha$-elements, especially Mg. Over
the [Fe/H] range from $-$1.0 to 0.2 dex [P/Fe] decreases from $\sim$0.6 dex to
$\sim-$0.2. This is in agreement with the assumption that P is likely mostly
produced in CCSNe.

###  2.4 Iron group elements Cr, Fe, and Ni

Iron-group elements such as Cr, Fe, Ni are mostly produced by SNe Ia (Nomoto
et al. 1997; Kobayashi et al. 2020a, b). From observations of the MW stars
[Cr/Fe] increases with metallicity from $\sim-$0.5 to $\sim$0 in the range
$\sim-$4.2¡[Fe/H]¡$\sim-$1.5 (Frebel 2010; Xing et al. 2019; Cayrel et al.
2004). From the APOGEE data, [Cr/Fe] and [Ni/Fe] are around 0 within the range
of [Fe/H] from $\sim-$1.5 to $\sim$0.5 dex (Lim et al. 2022). Bensby et al.
(2003) find for thin and thick disk stars in the Solar neighborhood a slight
overabundance of Ni with respect to Fe at metallicities below 0 and a small
increase of [Ni/Fe] up to 0.1 dex above [Fe/H] = 0.

In nearby dwarf galaxies, LMC, SMC, Fnx, Sgr, GSE and Sculptor, Ni follows the
MW trend in the metal-poor regime while for [Fe/H] $\geq-$1.5 it becomes
underabundant down to $-$0.2 dex (e.g, Tolstoy et al. 2009; Van der Swaelmen
et al. 2013; Lemasle et al. 2014; Hasselquist et al. 2021). From the abundance
measurements in the neutral ISM of LMC and LMC, Ni is slightly underabundant
relative to Fe at lower metallicities and increases up to 0 or a bit above at
higher metallicities, while [Cr/Fe] is about 0 dex in the entire range of
[Fe/H] (De Cia et al. 2024).

###  2.5 Manganese

Manganese is an iron-group element. Despite extensive studies by many authors
(e.g. Seitenzahl et al. 2013; Eitner et al. 2020), the production of Mn
remains uncertain. [Mn/Fe] has a different evolution compared to both other
iron-peak elements and $\alpha$-elements (Mishenina et al. 2015). Compared to
$\alpha$-elements, core-collapse SNe produce much less Mn. Hence, at low
metallicities, Mn deficiency with respect to Fe (or Mn underabundance) is
observed. When type Ia SNe start exploding and producing more Mn (Nomoto et
al. 1997), the underabundance gradually disappears with an increasing [Fe/H]
(e.g. Mishenina et al. 2015; Prantzos 2005; Mikolaitis et al. 2017, for the
MW).

Moreover, according to Bergemann & Gehren (2008), in stellar atmospheres Mn
abundances may be affected by deviations from the LTE in such a way that the
measured values may be underestimated by up to 0.5–0.6 dex. However, Mishenina
et al. (2015) did not confirm these deviations which is explained by the lack
of high-quality atomic data and, hence, the inability to build an adequate
model of Mn atoms. Nevertheless, this should not affect the values obtained
from ISM.

Figure 1: Piecewise approximation of the $\alpha$-element behaviour in nearby
dwarf galaxies SMC, LMC, GSE, Fnx, and Sgr from the APOGEE data (see details
in Fig. 16).

##  3 Data and sample

###  3.1 Column densities

For the analysis, we utilised the column density measurements of O, Mg, Si, S,
Ti, Cr, Fe, Ni, Zn, P, and Mn for the QSO-DLA sample taken from the work by
Konstantopoulou et al. (2022). After removing duplicate entries
Konstantopoulou et al. (2023) finalised a sample of 108 DLAs with a
measurement of Zn. Among them, 37 QSO-DLAs are from De Cia et al. (2016),
which is a homogeneous sample of high-resolution ($R=\lambda/\Delta\lambda$ =
35000 – 58000) spectra taken with the Very Large Telescope (VLT) Ultraviolet
and Visual Echelle Spectrograph (UVES). The signal-to-noise ratios (S/N) of
these spectra are in the ranges 14–33 pixel-1 and 54–10 pixel-1 in the blue
and red spectroscopic arm of UVES, respectively. The data were supplemented by
Konstantopoulou et al. (2022), wherever possible, with new column density
measurements of Ti and Ni from UVES/VLT spectra using the Voigt-profile fit
method (Krogager 2018). 71 QSO-DLAs are from the large compilation by Berg et
al. (2015a) published during the period between 1994 and 2004, with a minimum
resolution restriction of $R>$ 10000, but typically $R\sim$ 40000\. The S/N
for the spectra is up to $\sim$50 pixel-1, with the typical spectrum having an
S/N of $\sim$10 pixel-1 (Berg et al. 2015a, b). In order to homogenise the
measurements taken from different sources, Konstantopoulou et al. (2022)
corrected the column densities to the newest possible oscillator strengths for
both of the samples.

The sample described above has been supplemented with one QSO-DLA (Q1210+175)
from De Cia et al. (2016), which is not included the work of Konstantopoulou
et al. (2022) due to the lack of measurements for zinc; however UVES data
covering absorption lines of Ti were indeed available. In addition, there is
one QSO-DLA (Q1232+082) from the list provided by Konstantopoulou et al.
(2022), for which there was no Ti measurement, but it turned out to be
possible. In this system, the Ti II $\lambda$1910 line can be slightly
blended, but we consider the column density to be reliable. In this paper we
measure Ti and Ni for these additional two systems, using the method described
in Konstantopoulou et al. (2022). In additional, we provide column densities
of Ti and Ni, where is possible, for other DLAs from the list from De Cia et
al. (2016) (see Table 5). Velocity profiles are shown in Figs. 19, 20. In
total, our sample contains 110 QSO-DLAs.

From the list of 110 QSO-DLAs described above, we have selected 24 objects for
which there are column density measurements of Ti and at least one more
$\alpha$-element (Mg, Si, S, and O). We did not take into account those
objects for which only limits have been calculated. We refer to this subsample
as the ”golden” sample. The need for this selection is explained in Section 4.
15 QSO-DLAs in the golden sample are from the list of De Cia et al. (2016),
while the remaining 9 QSO-DLAs are from the compilation by Berg et al. (2015a)
(see references in Table 1). All the data for the golden sample is high
quality, with resolution of at least 35000 and high S/N.

The results of this work are based on the golden sample. For the rest of the
sample, we do a minimal analysis and report the abundance patterns in the
appendix.

###  3.2 Velocity widths

In addition to the column densities, our analysis uses information about the
velocity widths of the absorption lines, $\Delta v_{90}$, namely, the velocity
intervals encompassing 90$\%$ of the integrated optical depths. This quantity
is computed as $c[\lambda(95\%)-\lambda(5\%)]/\lambda_{0}$, where
$\lambda(5\%)$ and $\lambda(95\%)$ are the wavelengths corresponding to the
5th and 95th percentiles of the apparent optical depth distribution,
respectively, and $\lambda_{0}$ is the first moment of this distribution, as
defined by Ledoux et al. (2006).

One of the advantages of the DLA absorption spectrum is that it is produced by
low-ionisation atoms dominated by galactic-scale motions governed by gravity
(unlike highly ionised atoms which can make up the hot ejected gas).
Therefore, these spectra are well suited for determining the dynamical
velocity, which can be a proxy for their mass (Ledoux et al. 2006; Prochaska
et al. 2008; Christensen et al. 2014; Arabsalmani et al. 2018). Thus, by
measuring $\Delta v_{90}$ in DLAs, we can get an insight in a statistical
sense on the mass of the galaxies responsible for the absorption lines. In
this work, we adopted the values of $\Delta v_{90}$ from Ledoux et al. (2006);
Herbert-Fort et al. (2006); Noterdaeme et al. (2008); Jorgenson et al. (2010);
Rafelski et al. (2012); Neeleman et al. (2013); Berg et al. (2015a) (see
Table. 1).

##  4 Method

The major challenge in properly determining the total (gas + dust) element
abundances in the ISM is to correct account for the depletion by dust. To
measure the total ISM metallicity, it is highly important to estimate the
fraction of atoms of different elements withdrawn from the gas phase and
incorporated into dust grains.

De Cia et al. (2016) have developed an effective method to characterise the
dust depletion in the ISM of the MW and QSO-DLAs based on the analysis of the
relative abundances, that allows to derive the total (gas + dust) metallicity.
Based on this, De Cia et al. (2021) have built the so-called ”relative” method
to derive the total metallicty in the neutral ISM in the MW. The total
abundance [X/H]tot can be derived as follows:

${\rm[M/H]_{tot}=[X/H]-\delta_{X}},$ (2)

where [X/H] is the observed abundance of element X, and ${\rm\delta_{X}}$ is
its dust depletion. The ’minus’ sign in the formula 2 is due to the fact that
the value of ${\rm\delta_{X}}$ is negative in its classical notation (e.g. De
Cia et al. 2016).

The method is aimed at deriving the total metallicity [M/H]tot and overall
strength of depletion [Zn/Fe]fit from the distribution of element abundances
[X/H] depending on their refractory index, $B2_{X}$. The latter represents how
strongly an element is incorporated into the dust. This linear dependence is
defined as follows:

$y=a+bx,$ (3)

where

$\displaystyle x$ $\displaystyle=B2_{X},$ (4) $\displaystyle y$
$\displaystyle={\rm log}\,N(X)-{\rm
log}\,N(H)-X_{\odot}+12-A2_{X}\sim{\rm[X/H]},$ (5) $\displaystyle a$
$\displaystyle={\rm[M/H]_{tot}},$ (6) $\displaystyle b$
$\displaystyle={\rm[Zn/Fe]_{fit}}.$ (7)

The coefficient $A2_{X}$ is the normalisation of the depletion sequences of
each element after subtracting the correction for nucleosynthesis effects such
as $\alpha$-element enhancement or Mn underabundance. In general it could be
assumed to be zero, implying no dust depletion at [Zn/Fe]=0 (De Cia et al.
2016). The depletion factor [Zn/Fe]fit represents the overall strength of
depletion and it is derived from several different metals. 111Despite using
all available metals, [Zn/Fe] still has a somewhat privileged role in the
analysis, i.e. the relations of ${\rm\delta_{X}}$ with [Zn/Fe]
(Konstantopoulou et al. 2022).

The $A2_{X}$ and $B2_{X}$ coefficient have been adopted from Konstantopoulou
et al. (2022). To derive these coefficients, these authors used a large
collection of column density measurements of 18 metals with different
refractory properties located in various environments such as MW, the
Magellanic Clouds, and DLAs.

A few remarks should be made. First, due to their nucleosynthesis
peculiarities, some elements may have systematic deviations from abundance
patterns that we expect from depletion effects. The best-known and most
prominent examples are $\alpha$-element enhancement and Mn underabundance
(e.g. McWilliam 1997; Mishenina et al. 2015).

Second, $\delta_{X}$ is a linear function of the overall strength of depletion
characterised by the parameter [Zn/Fe]fit in the relative method. The
difference from the observed parameter [Zn/Fe] is that [Zn/Fe]fit is derived
from the abundances of all available metals or their subset.

Here, we consider the application of the method on the example of the QSO-DLA
source Q0405–443c (see Fig. 2). The left panel shows the linear fit to all the
element abundances. For the linear fit, we took into account error bars on
both axes and did not include elements for which only the limits have been
measured. The values of [X/H] have a fairly large scatter relative to the best
fit curve, which could not be explained by the 3$\sigma$ confidence interval
(shown as the gray area in Fig. 2). This scatter is likely caused by the
nucleosynthesis peculiarities of $\alpha$-elements and Mn. This becomes
evident from the right panel of Fig. 2, where the elements have been divided
into three subsets: $\alpha$-elements (Ti, Si, S), elements of the iron group
(Fe, Ni, Cr) and others. We do not include Zn to the iron group since its
abundances does not always follow those of Fe, Ni and Cr, especially in dwarf
galaxies (see Hirai et al. 2018).

Figure 2:  Linear fitting over the entire data set of [X/H] (left panel). The
elements (right panel) are divided into three groups: $\alpha$-elements (blue
triangles), Fe-group elements (red diamonds), and other metals (purple
circles). The blue dashed line shows linear fitting over solely the
$\alpha$-element abundances, the red solid line is the blue dashed line
shifted to the value averaged over Fe-group elements. The gray filled areas
show 3$\sigma$ confidence intervals. The total metallicity [M/H]tot is shown
by intersection of gray dashed lines.

Despite small differences in the nucleosynthetic origin of various
$\alpha$-elements (see Sect. 1, Tolstoy et al. 2009), their abundance pattern
is fairly uniform, unlike other metals (Prantzos 2005, see also the discussion
in Sect. 5.1). It is important to separate $\alpha$-elements from other metals
for the further analysis. With this assumption, the best way to derive the
slope [Zn/Fe]fit of the linear fit to the abundance pattern is from the total
amount of $\alpha$-element measurements available.

For the correct application of this method, it is important to have an
abundance measurement of titanium and at least one other $\alpha$-element.
This provides sufficient dynamical range in the $x$-axis for a more confident
fit because titanium is the most refractory among other $\alpha$-elements. In
six cases among the golden sample systems, the preferred slope of the linear
fit to the abundance patterns would be negative. However, a negative slope is
not physical because dust depletion only removes metals from the gas-phase. We
limited the possible slopes to be non-negative, using the same methodology in
De Cia et al. (2024).

To obtain the total metallicity of the system, we shifted the linear fit
obtained solely from the $\alpha$-elements to the weighted mean of the Fe, Cr,
and Ni abundances, and derived the y-intercept. This is shown in Fig. 2 with a
red line. The value of the shifted straight line at $B2_{X}$=0 is the total
metallicity [M/H]tot of the system. In this example, for Q0405-443c, we
derived [M/H]tot = $-$1.12$\pm$0.12.

We derived the uncertainty on the slope [Zn/Fe]fit from the Python procedure
we used for the linear fit to the abundance patterns. To calculate the
uncertainty of the normalisation [M/H]tot, we took into account the
uncertainty, $\sigma_{\alpha_{\rm fit}}$, derived from the fitting procedure,
the uncertainty of the weighted mean of the Fe-group element abundances,
$\sigma_{\rm theFe}$, and the uncertainty of hydrogen, $\sigma_{\rm H_{\rm
tot}}$ as follows:

$\sigma_{\rm[M/H]_{tot}}=\sqrt{\sigma^{2}_{\alpha_{\rm fit}}+\sigma^{2}_{\rm
Fe}+\sigma^{2}_{\rm H_{\rm tot}}}.$ (8)

In addition to the metallicity and amount of dust depletion, we can further
study any peculiarities due to nucleosynthesis by characterising any
deviations of the observed abundances from the main trend (red curve). We
derived the relative abundances of different elements [X/H]nucl due to
nucleosynthesis, after correcting for dust depletion as follows:

${\rm[X/H]_{nucl}=[X/H]-y(B2_{X})}.$ (9)

Hence, we obtain:

${\rm[X/Fe]_{nucl}=[X/H]_{nucl}-[Fe/H]_{nucl}}.$ (10)

##  5 Results and discussion

We analysed the abundance patterns of 110 DLAs, in particular, 24 DLAs in the
golden sample. In most cases, we find a satisfactory fit to the data. These
are shown in Figs. 14 and 15. Tables 1 and 4 contain the resulting data for
the golden sample: total (gas+dust) metallicities, [M/H]tot, the overall
strength of dust depletion, [Zn/Fe]fit, and the relative abundances due to
nucleosynthesis, [X/Fe]nucl, which are the deviations from the abundance
patterns after taking dust depletion into account.

We divided the golden sample into two parts by velocity widths: $\Delta
v_{90}<100$$\rm km\,s^{-1}$ and $\Delta v_{90}\geq 100$$\rm km\,s^{-1}$ which
we refer to as low- and high-$\Delta v_{90}$ subsamples, respectively. Figure
3 shows the distribution of QSO-DLAs by $\Delta v_{90}$. The dividing point
has been chosen in such a way that the two subsamples roughly contains a
comparable number of systems: there are 15 and 9 QSO-DLAs in low- and
high-$\Delta v_{90}$ subsamples, respectively. Using 70 DLA or sub-DLA systems
Ledoux et al. (2006) have shown a correlation between metallicity and velocity
widths which is probably the consequence of an underlying mass-metallicity
relation (Christensen et al. 2014). Thus, the low-$\Delta v_{90}$ sub-sample
is expected to have overall lower galaxy masses than the high-$\Delta v_{90}$
sub-sample. According to Arabsalmani et al. (2018), the threshold velocity
width of 100 $\rm km\,s^{-1}$ corresponds to the stellar mass of the galaxy
$M^{*}$ of about 109M⊙.

Figure 3: Distribution of the golden sample by velocity widths.

Figure 4 shows the distribution of the golden sample by the total metallicity.
We see that [M/H]tot varies from $-$2.0 to $-$0.5. The metallicity ranges for
the two subsamples mostly overlap, although the distributions are different:
vertical lines show the weighted mean which is $-$1.36 and $-$0.97 for the
low- and high-$\Delta v_{90}$ subsamples, respectively.

Figure 4: Distribution of the golden sample by metallicity [M/H] for low
(shown by blue) and high (orange) $\Delta v_{90}$ subsamples.

The strength of dust depletion [Zn/Fe]fit shown in Fig. 5 is in the range from
0.0 to 0.55, with the two subsamples displaying only a very small systematic
difference in distribution of 0.01 (see vertical lines in Fig. 5 that show the
weighted mean).

Figure 5: Distribution of the golden sample by dust depletion [Zn/Fe]fit for
low (shown by blue) and high (orange) $\Delta v_{90}$ subsamples.

Figure 6 displays a broad correlation between the total metallicity and the
strength of dust depletion with quite a large scatter. Similar relations have
been derived by other authors (De Cia et al. 2024; Noterdaeme et al. 2008;
Ledoux et al. 2002a). Hence, the amount of dust in DLAs overall depends on the
gas metallicity. This is in agreement with an assumption that significant
amount of dust is built through grain-growth in the ISM depending on the gas
metallicity, density, and temperature (Dwek 2016; Mattsson et al. 2014; De Cia
et al. 2013). From Fig. 6, it might appear that low-$\Delta v_{90}$ systems
show larger [Zn/Fe]fit compared to high-$\Delta v_{90}$ galaxies. In fact,
this is a shift in metallicity (see Fig. 4), while [Zn/Fe]fit values are
similarly distributed in low- and high-$\Delta v_{90}$ galaxies, as shown in
Fig. 5. The data for the MW do not strongly follow the dust-metallicity
relation showing steeper slope than DLAs. The possible cause of this is that
the MW disk has higher pressure and higher density of colder gas compared to
more diffuse warm neutral medium in DLAs (see De Cia et al. 2024). As a
result, dust is expected to grow more easily in the MW.

Figure 6: Relation between the total metallicity, [M/H]tot and the strength of
dust depletion, [Zn/Fe]fit, in the neutral ISM of DLAs. Large blue and orange
triangles show the data for the golden sample with low- and high-$\Delta
v_{90}$, respectively. The small gray diamonds are the data for the non-golden
sample. The solid line shows a linear fit to all the data including
uncertainties on both axes, [Zn/Fe]fit = 0.33$\pm$0.03$\times$[M/H]tot \+
0.69$\pm$0.03 . The shaded area represents the 3$\sigma$ confidence interval.
Figure 7: Total metallicity [M/H]tot in the ISM of QSO-DLAs from the golden
sample. Large purple diamonds are the values derived from solely
$\alpha$-elements (this work, the basic result). Small green triangles show
the values derived from fitting the iron-group elements + Zn. Small orange
crosses and small blue stars are the determinations given by De Cia et al.
(2016) and De Cia et al. (2018), respectively.

We compared our most solid derivation of the total metallicity, [M/H]tot, for
the golden sample with alternative ways of estimating the metallicity, to test
their robustness. First, we compared our results to the total metallicity
based on the fit of the abundance pattern of only the Fe-group elements and Zn
(green triangles in Fig. 7). This reveals that in most cases, the estimates
based only on the Fe-group are slightly lower than the fiducial value, on
average by 0.06 dex. The values of total metallicity determined by De Cia et
al. (2016) and De Cia et al. (2018) (yellow crosses and blue stars in Fig. 7)
generally demonstrae a greater similarity to the metallicity we determined
using only the Fe-group elements and Zn. This reflects the fact the
methodologies of De Cia et al. (2016) and De Cia et al. (2018) based their
results more heavily on Fe-group elements and Zn. In this work, however, the
methodology is refined to separate the effects of metallicity, dust depletion,
and nucleosynthesis, and thus more robust. One outstanding example is the case
of Q1232+082, for which we measure a total metallicity, which is 1 dex lower
than the estimate of De Cia et al. (2016). This is due to high
$\alpha$-element enhancement (0.5 dex, see Fig. 14) in this case, combined
with the absence of measurements of Ti in the work of De Cia et al. (2016). As
a result, the slope of the linear fitting is steeper which leads to the zero
intercept at a higher value of [M/H]tot.

Table 1: Collection of data for QSO-DLAs in the golden sample. The values of
logN(HI) were taken from Konstantopoulou et al. (2022) or De Cia et al.
(2016).

QSO | $z_{abs}$ | logN(HI) | [M/H]tot | [Zn/Fe]fit | $\Delta v_{90}$ | Ref.
---|---|---|---|---|---|---
Q0058$-$292 | 2.671 | 21.10 $\pm$ 0.10 |  $-$1.36 $\pm$ 0.23 | 0.32 $\pm$ 0.10 | 34a | 1,2
Q0100+130 | 2.309 | 21.35 $\pm$ 0.08 |  $-$1.62 ${}^{+0.22}_{-0.21}$ | 0.09${}^{+0.10}_{-0.09}$ | 37a | 1,2
Q0102$-$190a | 2.370 | 21.00 $\pm$ 0.08 |  $-$2.00 ${}^{+0.23}_{-0.12}$ | 0.00${}^{+0.11}_{-0.00}$ | 17a | 1,2
Q0405$-$443a | 1.913 | 20.80 $\pm$ 0.10 |  $-$0.78 $\pm$ 0.21 | 0.27 $\pm$ 0.07 | 98a | 1,2
Q0405$-$443c | 2.595 | 21.05 $\pm$ 0.10 |  $-$1.12 $\pm$ 0.20 | 0.25 $\pm$ 0.07 | 79a | 1,2
Q0528$-$250a | 2.141 | 20.98 $\pm$ 0.05 |  $-$1.62 ${}^{+0.17}_{-0.09}$ | 0.00${}^{+0.08}_{-0.00}$ | 105a | 1,2
Q0528$-$250b | 2.811 | 21.35 $\pm$ 0.07 |  $-$0.85 $\pm$ 0.17 | 0.39 $\pm$ 0.07 | 304a | 1,2
Q0841+129a | 1.864 | 21.00 $\pm$ 0.10 |  $-$1.58 ${}^{+0.22}_{-0.19}$ | 0.04${}^{+0.08}_{-0.04}$ | 32a | 1,2
Q1117$-$134 | 3.350 | 20.95 $\pm$ 0.10 |  $-$1.60 ${}^{+0.25}_{-0.15}$ | 0.00${}^{+0.10}_{-0.00}$ | 44a | 1,2
Q1157+014 | 1.944 | 21.80 $\pm$ 0.10 |  $-$1.49 $\pm$ 0.20 | 0.24 $\pm$ 0.07 | 89a | 1,2
Q1223+178 | 2.466 | 21.40 $\pm$ 0.10 |  $-$1.48 $\pm$ 0.20 | 0.16 $\pm$ 0.07 | 91a | 1,2
Q2206$-$199a | 1.921 | 20.67 $\pm$ 0.05 |  $-$0.53 $\pm$ 0.14 | 0.21 $\pm$ 0.06 | 136a | 1,2
Q2243$-$605 | 2.331 | 20.65 $\pm$ 0.05 |  $-$1.03 $\pm$ 0.15 | 0.09 $\pm$ 0.07 | 173a | 1,2
SDSS1249$-$0233 | 1.781 | 21.45 $\pm$ 0.15 |  $-$1.15 $\pm$ 0.29 | 0.18 $\pm$ 0.11 | 152b | 3
Q2230+025 | 1.864 | 20.83 $\pm$ 0.05 |  $-$0.72 $\pm$ 0.22 | 0.29 $\pm$ 0.10 | 148a | 3
HE1104$-$1805 | 1.662 | 20.85 $\pm$ 0.01 |  $-$1.02 $\pm$ 0.20 | 0.44 $\pm$ 0.10 | 50c | 3
Q0027$-$1836 | 2.402 | 21.75 $\pm$ 0.10 |  $-$1.80 $\pm$ 0.19 | 0.33 $\pm$ 0.07 | 44d | 3
Q1210+17 | 1.892 | 20.63 $\pm$ 0.08 |  $-$0.74 $\pm$ 0.20 | 0.30 $\pm$ 0.09 | 62a | 3
FJ0812+32 | 2.067 | 21.00 $\pm$ 0.10 |  $-$1.57 ${}^{+0.23}_{-0.14}$ | 0.00${}^{+0.09}_{-0.00}$ | 26e,∗ | 3
J1135$-$0010 | 2.207 | 22.05 $\pm$ 0.10 |  $-$0.97 $\pm$ 0.24 | 0.55 $\pm$ 0.09 | 168f | 3
Q2231$-$00 | 2.066 | 20.53 $\pm$ 0.08 |  $-$1.23 ${}^{+0.25}_{-0.14}$ | 0.00${}^{+0.11}_{-0.00}$ | 145a | 3
J1200+4015 | 3.220 | 20.65 $\pm$ 0.15 |  $-$0.66 $\pm$ 0.26 | 0.12 $\pm$ 0.07 | 127g | 3
Q1210+175 | 1.892 | 20.70 $\pm$ 0.08 |  $-$0.60 $\pm$ 0.20 | 0.52 $\pm$ 0.07 | 62a |  $\star$,1
Q1232+082 | 2.338 | 20.90 $\pm$ 0.08 |  $-$1.65 $\pm$ 0.23 | 0.15 $\pm$ 0.10 | 85a |  $\star$,1

  * Notes: The values of $\Delta v_{90}$ have been taken from a – Ledoux et al. (2006); b – Herbert-Fort et al. (2006); c – Neeleman et al. (2013); d – Noterdaeme et al. (2008); e – Jorgenson et al. (2010); f – Christensen et al. (2019); g – Berg et al. (2015a). Symbol ∗ designates a very poorly studied system, for which it is not clear what the extent of the metal-line profile is. Only lower limit has been determined. Column densities are taken from (1) De Cia et al. (2016), (2) Konstantopoulou et al. (2022), (3) Berg et al. (2015a) (corrected by Konstantopoulou et al. 2022, to the newest oscillator strengths, see Sec. 3.1), and ($\star$) this work.

###  5.1 $\alpha$-elements

The total $\alpha$-element abundances [$\alpha$/Fe]nucl for each object has
been obtained by calculating an average weighted by the uncertainties over all
available individual $\alpha$-element (Ti, Si, S, Mg, and O) values
[X/Fe]nucl. Looking at the $\alpha$-element enhancement [$\alpha$/Fe], as
calculated from the fitting described in Sect. 4, for our entire sample does
not yield any obvious relation as seen for individual galaxies in Fig. 1. This
is expected as the DLA population probes a large range of different galaxies
(e.g. Fynbo et al. 2008; Krogager et al. 2017) that will have heterogeneous
enrichment histories (see also Dvorkin et al. 2015). However, when splitting
our sample into bins of $\Delta v_{90}$, a correlation is apparent.

In Fig. 8, we show [$\alpha$/Fe] for our golden sample as a function of total
metallicity in the low- and high-$\Delta v_{90}$ subsamples (as blue and
orange points, respectively). Since $\Delta v_{90}$ is a proxy of galactic
mass, it is reasonable to expect some difference between the high-$\alpha$
knee positions for these two groups of systems (see discussion in Section
5.1). It is evident that the orange points tend to cluster at larger
metallicities than the blue points, as expected from the correlation between
$\Delta v_{90}$ and metallicity (Ledoux et al. 2006). Yet, the two subsamples
also seem to follow a similar anti-correlation between [$\alpha$/Fe] versus
[M/H]tot. This is illustrated in the simplest case by a linear fit to the two
subsamples (Case 4). For both subsamples, we find consistent slopes of
$-$0.19$\pm$0.15 and $-$0.16$\pm$0.22 for the low- and high-$\Delta v_{90}$
subsamples, respectively, with an offset in metallicity of $\sim$0.7 dex.

Both of the inferred slopes are slightly lower than the slope inferred for the
MW ($-$0.3, see McWilliam 1997), yet consistent within the considerable
uncertainties that are dominated by scatter in the data. Upon further
inspection, there tends to be a slight flattening of the two relations: the
relation for the low-$\Delta v_{90}$ subsample appears reach a low-alpha
plateau at higher metallicities, $\gtrsim-1$, whereas the high-$\Delta v_{90}$
subsample tends towards a high-$\alpha$ plateau at low metallicity,
$\lesssim-1.2$. This behaviour follows the expectation from the MW and local
dwarf galaxies (see Fig. 1 and McWilliam 1997). The presence of a plateau in
the data would indeed bias the slopes towards lower values. We consider four
possibilities for fitting the data, which are shown in Fig. 8 and reported in
Table 2:

  * •

Case 1: Motivated by the behaviour of [$\alpha$/Fe] in the MW and local dwarf
galaxies, we fit our data with a three-piecewise function (high-$\alpha$
plateau + decline + low-$\alpha$ plateau) with five parameters. Due to the
strong spread of values and a small number of points, an attempt to set all
parameters as free leads to a large uncertainty in fitting. As a first guess,
we left the position of the $\alpha$-element knee free to vary and we fixed
the other parameters according to the values defined for the MW by McWilliam
(1997): the level of high-$\alpha$ plateau [$\alpha$/Fe]nucl is 0.35, the
slope is $-$0.3, and the level of low-$\alpha$ plateau is 0.05 (see Table 2).

  * •

Case 2: We fixed the slope and the low-$\alpha$ plateau at the values of
McWilliam (1997) and fit the data with the three-piecewise functions to find
the high-$\alpha$ knee positions and the high-$\alpha$ plateau levels.

  * •

Case 3: Since the paucity of observational data of [$\alpha$/Fe]nucl hampers
our capability to constrain all the five parameters of a three-piecewise
function, we tested the results by applying a two-piecewise function
(high-$\alpha$ plateau + decline) with all three parameters remaining free.

  * •

Case 4: Fitting the data with a linear function of the form: [$\alpha$/Fe]
$=\alpha_{0}$ $+$ slope $\times$ [M/H]tot.

Because of the large scatter of points, the values of all the parameters vary
from case to case, but they are consistent within the error bars (see Table
2). For the high-$\Delta v_{90}$ subsample, we can clearly determine the
high-$\alpha$ plateau, high-$\alpha$ knee, and slope. However, the low-alpha
knee and low-alpha plateau cannot be constrained due to the lack of points at
metallicities lower than $-$0.5 dex. For the low-$\Delta v_{90}$ subsample,
the plateau seems to be less clearly constrained, unlike the high-$\Delta
v_{90}$ one (see also Fig. 17 in the appendix to assess the variations between
different $\alpha$-elements). Overall, all the models show systematic
differences between the low- and high-$\Delta v_{90}$ subsamples in the
[$\alpha$/Fe]nucl – [M/H]tot plane. These are probably due to different
chemical evolution phases and properties (e.g. SFR and SFH) of galaxies with
different stellar masses.

To compare these four cases, we computed the reduced $\chi^{2}$
($\chi^{2}_{\nu}$) values and report them in Table 2. From the values, it was
impossible to choose a preferred model because the difference in
$\chi^{2}_{\nu}$ should be larger than $\sim$1 (or $\sim$2$\sigma$) to state
that a given model is better over another.

Figure 8: $\alpha$-elements abundances for low-$\Delta v_{90}$ (blue open triangles) and high $\Delta v_{90}$ (orange open diamonds) QSO-DLA systems. Case 1: Data have been approximated by three-piecewise function: high-$\alpha$ plateau + decline + low-$\alpha$ plateau. The five parameters of the function are: levels of high- and low-$\alpha$ plateaus, and the slope and positions of the high- and low-$\alpha$ knees. During the fitting, only the position of the high-$\alpha$ knee is considered to be free, while the other parameters are fixed and set to values given for the MW. The gray dashed curve shows behaviour for the MW as determined by McWilliam (1997). Case 2: The level of the high-$\alpha$ plateau and position of the high-$\alpha$ knee are allowed to vary. Case 3: Fitting the data with a two-piecewise function. Case 4: Fitting the data with a linear function. Two filled points at the lower right panel indicate median values in [M/H]tot and average values in [$\alpha$/Fe]nucl show the systematic difference between the two subsamples. All the parameters and their uncertainties are shown in Table 2. Table 2: Parameters of the piecewise function fitting $\alpha$-element enhancement in the low- and high-$\Delta v_{90}$ subsamples. Case 1 is shown in Fig. 8. Case |  $\alpha$ knee | Plateau level | Slope | $\chi^{2}_{\nu}$
---|---|---|---|---
| [M/H]tot, dex | [$\alpha$/Fe]nucl, dex |  |
High $\Delta v_{90}$
1 |  $-$1.03$\pm$0.15 | 0.35∗ |  $-$0.30∗ | 0.39
2 |  $-$1.01$\pm$0.28 | 0.34$\pm 0.05$ |  $-$0.30∗ | 0.45
3 |  $-$0.82$\pm$0.66 | 0.31$\pm$0.04 |  $-$0.26$\pm$0.81 | 0.60
4 | … | … |  $-$0.16$\pm$0.22 | 0.37
Low $\Delta v_{90}$
1 |  $-$1.87$\pm 0.11$ | 0.35∗ |  $-$0.30∗ | 0.58
2 |  $-$1.80$\pm 0.32$ | 0.32$\pm 0.09$ |  $-$0.30∗ | 0.60
3 |  $-$1.56$\pm$0.38 | 0.25$\pm$0.04 |  $-$0.21$\pm$0.11 | 0.71
4 | … | … |  $-$0.19$\pm$0.15 | 0.62
∗ – fixed parameters |
Figure 9: $\alpha$-element overabundance with respect to Fe as a function of
the total metallicity for the non-golden sample. Two points are out of the
range of the figure at ([M/H]tot, [$\alpha$/Fe]) = ($-$1.93$\pm$0.15,
0.82$\pm$0.09) and ($-$0.76$\pm$0.13, $-$0.63$\pm$0.08).

For a comparison with the results shown above, we applied the same fitting
technique to the APOGEE stellar data in nearby dwarf galaxies. This is shown
in Figs 1 and 16. It is only for Sgr that the data allow for full three-
piecewise function to be traced and the high-$\alpha$ knee is at
[M/H]=$-$1.92$\pm$0.05. From the data, it is impossible to determine the
position of the high-$\alpha$ knee for the SMC, LMC, and Fnx galaxies. Nidever
et al. (2020) constrained it to be at [Fe/H]$\lesssim-$2.2 for both LMC and
SMC, despite the fact that LMS is 10 times more massive than SMC. The
abundances derived by Van der Swaelmen et al. (2013) from high-resolution
spectra at VLT with the FLAMES/GIRAFFE multifibre spectrograph show higher
$\alpha$-element enhancement for the LMC. Also, there is some hint that the
knee is at higher metallicity of $\approx-$1.5.

Hendricks et al. (2014) reported that the high-$\alpha$ knee for Fnx dwarf
galaxy is at [Fe/H]$\approx-$1.9, which was determined from abundance
measurements of Mg using VLT/GIRAFFE spectra. The position of the knee is less
clearly defined for Si and Ti, but apparently it is more clearly seen at
metallicities below $-$1.8. From the APOGEE data, there are no signs of the
presence of high-$\alpha$ plateau at metallicities above $-$2.0 (see Figs. 1
and 16). We derived the position of the high-$\alpha$ knee for GSE to be at
[M/H] of $-$1.21$\pm$0.01.

The high-$\alpha$ knee is challenging to determine even in local galaxies
because it requires measuring reliable $\alpha$-element abundances for a
statistically significant number of faint metal-poor stars. Furthermore, there
are some discrepancies among different observations (Nidever et al. 2020;
Hendricks et al. 2014; Van der Swaelmen et al. 2013) that causes additional
confusion in trying to interpret the results. Compared to GSE and Sgr, the
high-$\alpha$ knee in LMC is more metal-poor (Nidever et al. 2020) even though
LMC is more massive than the progenitors of GSE and Sgr (see Table 3). This
can be explained by the differences in the early evolution of the Magellanic
Clouds from that of many other local galaxies (Nidever et al. 2020).
Obviously, Local Group galaxies do not fully fit the simplified picture where
faint, low-mass galaxies show lower enrichment efficiencies. Their
evolutionary histories depend on several factors such as the total stellar
mass, amount of gas, interaction with the MW, efficiency in producing metals,
and so on. However, it is not the goal of this paper to reconcile the stellar
observations in nearby galaxies.

Table 3:  Stellar M∗ and dynamical Md masses of nearby galaxies or their progenitors in cases of GSE and Sgr. The data are from O – D’Onghia & Fox (2016), L – Limberg et al. (2022), W – Walker et al. (2006), B-C – Bermejo-Climent et al. (2018). galaxy | M∗, (M⊙) | Md, (M⊙)
---|---|---
SMC | 3$\times$108, O | 2.4$\times$109, O
LMC | 3$\times$109, O | 1.7$\times$10${}^{1}0$, O
GSE | 1.3$\times$109, L | …
Sgr |  $\sim$109, B-C | …
Fnx |  $\sim$107, B-C | 108 – 109, W

Figure 10 shows the distribution of [X/Fe]nucl for different $\alpha$-elements
in QSO-DLAs from the golden sample – except for oxygen, for which only one
measurement is available. The weighted averages of [X/Fe]nucl (gray vertical
lines in Fig. 10) vary between the elements within 0.05 dex with standard
deviation (filled areas in Fig. 10) between 0.1 and 0.2. Thus, the abundance
patterns of different $\alpha$-elements are fairly uniform and a splitting
sample based on available elements is not expected to produce sufficiently
different [$\alpha$/Fe]nucl versus [M/H]tot behaviour. This also can be seen
from Fig. 17, where we show the fitting of [X/Fe]–[M/H]tot for Ti, S, and Si
(if available), with three-piecewise functions. For the high-$\Delta v_{90}$
subsample, the high-$\alpha$ plateau varies from [$\alpha$/Fe]tot =
0.31$\pm$0.03 to 0.36$\pm$0.02, while the position of the knee is within
[M/H]tot = $-1.09\pm 0.13$ – $-0.80\pm 0.18$. For the low-$\Delta v_{90}$
subsample, the parameter determination is less stable due to lack of data,
especially at low metallicities. From [Si/Fe]nucl , the parameters are not
constrained, while from Ti and S the plateau is 0.39$\pm$0.02 and
0.25$\pm$0.02 and the knee is $-1.84\pm 0.44$ and $-1.34\pm 0.11$.

Figure 10:  Distribution of [X/Fe]nucl for Ti, Si, S, and Mg for the golden
sample. Gray vertical lines show the weighted average, while the filled areas
correspond to the standard deviation.

###  5.2 Manganese

The distribution of [Mn/Fe]nucl with metallicity is shown in Fig. 11. The top
panels shows the results for the golden sample. There is a clear Mn
underabundance for all DLAs with weighted mean values of $-$0.33$\pm$0.07 and
$-$0.39$\pm$0.07 for the high- and low-$\Delta v_{90}$ subsamples,
respectively. We do not see a hint of an increase of [Mn/Fe]nucl with
metallicity up to [Fe/H]tot=$-$0.53 dex. This is contrary to our expectations
because it is clear from the behaviour of $\alpha$-elements in Fig. 1 that in
some DLAs, Type Ia SNa should contribute to the nucleosynthesis, which, in
turn, should lead to an increase in the abundance of manganese relative to
iron. In addition, observations of stellar abundances of Mn both in the MW and
in nearby galaxies show increasing [Mn/Fe]nucl toward higher metallicity
starting from [Fe/H]$\sim-$1.5 dex (see gray dashed curve in Fig. 11 for the
averaged behaviour in the MW). From the analysis of elemental abundances in
the neutral ISM of the SMC, De Cia et al. (2024) observed consistent
[$\alpha$/Fe]nucl enhancement and [Mn/Fe]nucl under-abundance at an
approximately constant level throughout the whole range of metallicity, which
can be explained by contribution from recent core-collapse SNe.

For the non-golden sample, a hint of increase of [Mn/Fe]nucl is seen starting
from [M/H]${}_{\rm tot}\approx-$0.7 dex (lower panel of Fig. 11). For the
consistency of this comparison, the figure has been supplemented with the data
for the golden sample, but in this case the [Mn/Fe]nucl and [M/H]tot values
has been determined according to the methodology used for the non-golden
sample. We approximated the entire data set with a two-piecewise function
consisting of a plateau and an increase. The best-fitting parameters are the
following: the plateau is at the level of [Mn/Fe]${}_{\rm nucl}=-0.35\pm$0.02,
the knee position is at [M/H]${\rm{}_{tot}}=-0.69\pm$0.13 and the slope is
0.34$\pm$0.10.

Figure 11: Manganese abundances in the ISM of DLAs. Upper panel: Mn abundances
for the golden sample for low-$\Delta v_{90}$ (blue open triangles) and
high-$\Delta v_{90}$ (orange open diamonds). Horizontal color lines show the
weighted average values of $-$0.39$\pm$0.10 and $-$0.33$\pm$0.04 for the low-
and high- $\Delta v_{90}$ subsamples, respectively. Lower panel: Mn abundances
for the non-golden sample (magenta open diamonds) as well as for the golden
sample (symbols as on the upper panel) with [Mn/Fe]nucl and [M/H]tot being
derived according to the methodology used for the non-golden sample. Two
points are out of the range of the figure at ([M/H]tot, [Mn/Fe]) =
($-$1.32$\pm$0.22, $-$0.63$\pm$0.16), and ($-$1.34$\pm$0.08,
$-$0.66$\pm$0.15). In both panels, the gray dashed curve shows typical
behaviour for the MW taken from Mishenina et al. (2015).

###  5.3 Phosphorus

Figure 12: Phosphorus abundances in the ISM of DLAs for low-$\Delta v_{90}$
(blue open triangles) and high $\Delta v_{90}$ (orange open diamonds).

Konstantopoulou et al. (2023) found a most reliable value of refractory index
$B2_{\rm P}$ for DLAs equal to $-$0.26$\pm$0.08, which we used in this study.
For Q1232+082, we find that the column density measurement for the bluest
spectral component of the PII $\lambda$1152 line profile is unreliable because
of strong contamination (De Cia et al. 2016). Thus, we excluded it from the
calculation of the total N(PII). The new total column density is
12.88$\pm$0.28, which is lower than the previous value by 0.35 dex.

Among six DLAs for which there are measurements of P, four do not show
significant enhancement ([P/Fe]${}_{\rm nucl}\leq$0.30 dex), while the rest
have values higher than 0.45 dex. However, in all these cases the PII column
densities were measured only from one line ($\lambda$ 1152$\AA$ or 963$\AA$),
which is located in the Ly-$\alpha$ forest (De Cia et al. 2016). In general,
it is necessary to fit multiple lines of the same ion simultaneously to obtain
reliable measurements of the column density and avoid contaminations from
other sources. In particular, contamination from HI lines are very likely
within the Ly-$\alpha$ forest (bluer than Ly-$\alpha$). In addition, the
systems with high $\Delta v_{90}$ are even more likely to be contaminated,
because they have a broader velocity profile. Thus, we did not find the
current data to be reliable enough to robustly assess the [P/Fe]nucl.
Nevertheless, the methodology in this paper shows the potential for discovery
in this field.

###  5.4 Zinc

Zn and Fe are often assumed to follow each other in nucleosytnhesis in studies
of DLAs with metallicities between 1/100th of Solar and Solar, so that the
observed gas-phase [Zn/Fe] is interpreted as a pure tracer of dust (e.g. De
Cia et al. 2016; De Cia 2018; Konstantopoulou et al. 2022). However, according
to (Bensby et al. 2003; Nissen & Schuster 2011; Mishenina et al. 2011; Barbuy
et al. 2015; Duffau et al. 2017), the relation [Zn/Fe] versus [M/H] in stars
in this metallicity range tends to behave partially like an [$\alpha$/Fe], but
with a smaller amplitude. Sitnova et al. (2022) showed from non-LTE
calculations for the MW stars that Zn and Mg do not strictly follow each
other. [Zn/Fe] is decreasing with metallicity because of various contributions
from core-collapse SNe and SNe Ia, and their different timescales (as for
$\alpha$-elements).

Our measurements of [Zn/Fe]nucl are reliable only for the golden sample
because Zn is not included in the fit for to the abundance patterns. Figure 13
shows the [Zn/Fe]nucl with metallicity for the golden sample, where the
strength of depletion is calculated only from $\alpha$-elements, without
involving Zn. The distribution partially resembles the behaviour of
[$\alpha$/Fe]nucl, but with smaller amplitudes ([Zn/Fe]nucl up to 0.2 dex). We
observe a potential decrease of [Zn/Fe]nucl, which is not unlike that of
Sitnova et al. (2022). The low- and high-$\Delta v_{90}$ subsamples form
separate sequences: one at lower and one at higher metallicities. For the non-
golden sample, it is not meaningful to analyse the [Zn/Fe]nuclbecause it is
distributed around zero by construction (see Fig. 18).

Figure 13: Zinc abundances in the ISM of DLAs for the golden sample for
low-$\Delta v_{90}$ (blue open triangles) and high $\Delta v_{90}$ (orange
open diamonds).

###  5.5 Additional caveats

This work is based on the assumption that we know well the refractory
behaviour of different metals, namely, according to the refractory index
$B2_{X}$. These coefficients were calculated by Konstantopoulou et al. (2022)
and De Cia et al. (2016) based on the observed depletion sequences, that is,
how the depletion vary with the overall amount of dust. This was derived after
taking an assumption on the $\alpha$-element enhancement and Mn underabundance
to focus on and characterise the properties of dust depletion. Our results on
the $\alpha$-elements and Mn are independent from the initial assumptions of
Konstantopoulou et al. (2022) and De Cia et al. (2016), for the following
reasons. First, this paper uses additional data with respect to
Konstantopoulou et al. (2022) and De Cia et al. (2016). Second, the
enhancement of $\alpha$-elements and deficiency of Mn are observed for DLA
systems with [Zn/Fe]$\sim 0$ (e.g. Fig. 3 of De Cia et al. 2016), so there is
no assumption in this regime (the $\alpha$-plateau at low metallicities).
Third, the assumed $\alpha$-knee results of Konstantopoulou et al. (2022) and
De Cia et al. (2016) were at the same metallicity as for the MW ([M/H]
$\sim-1.2$) and the same for all systems. These works made an overall
statistical correction for $\alpha$-elements to the whole sample, without
studying the details of individual systems. Eventually, the $\alpha$-knee that
we find are at $[M/\mbox{H}]_{\rm tot}\sim-1.0$ and $[M/\mbox{H}]_{\rm
tot}\sim-1.8$, different than previous assumptions. Finally, we measured
different $\alpha$-knees for different samples of galaxies, which make
physical sense.

###  5.6 Testing the robustness of the results on the $\alpha$-elements.

To derive the depletion coefficients $B2_{X}$ for $\alpha$-elements,
Konstantopoulou et al. (2022) applied corrections to account for the effect of
$\alpha$-element enhancement. To do so, they adopted the shape of a standard
nucleosynthetic curve taken from De Cia et al. (2016) (see also Section 5.1).
To demonstrate that the assumption made by De Cia et al. (2016) and
Konstantopoulou et al. (2022) has no (or minimal) impact on our present
results, we tested our calculations using an alternative set of $B2_{X}$
coefficients; for instance, considering that no assumption on $\alpha$-element
nucleosynthesis had ever been made. For this purpose, we adopted the $B2_{X}$
coefficients of Konstantopoulou et al. (2022), but before the correction for
$\alpha$-element enhancement was made. The test coefficients should not be
considered as more solid, because they describe dust depletion without taking
any potential $\alpha$-element enhancements into account. Nevertheless, they
are useful to check the robustness of our results and test that the
assumptions that went into the calculation of the $B2_{X}$ does not
substantially affect our results.

With the test calculations, the values of $B2_{X}$ turn out to be
systematically shifted downward by 0.11–0.20 depending on the element (S, Mg,
O, Si, and Ti). With the test coefficients the $\alpha$-element enhancement is
either the same or slightly higher compared to the reference values. However,
the difference can become more prominent, up to 0.10 dex, if the slope of the
dust depletion [Zn/Fe]fit is steep. In average the difference of
[$\alpha$/Fe]${\rm nucl}$ calculated with the test and standard $B2_{X}$
coefficients is 0.03 for both low- and high-$\Delta v_{90}$ subsamples.
Despite these differences, we reproduced the same $\alpha$-element behaviour
as in Fig. 8, but with slightly different fitting parameters: in case of test
calculations, the position of the high-$\alpha$ knee is at [M/H]tot lower by
0.02 and 0.09 dex for low- and high-$\Delta v_{90}$ subsamples, respectively.
The $\alpha$-plateau becomes slightly higher compared to the reference values
by 0.1 and 0.05 dex for low- and high-$\Delta v_{90}$ subsamples,
respectively. The two subsamples are still clearly separated and the
assumption used by Konstantopoulou et al. (2022) has hardly any impact on our
results.

For the golden sample, measurements of Ti are derived from the weak TiII
$\lambda$1910 absorption line. If there is a contamination of the line, the
column density of Ti could be overestimated and this may lead to an
underestimation of the metallicity. We test our main results by deriving
[M/H]tot and [Zn/Fe]fit for the golden sample in the same way as for the non-
gold sample, namely, based on only iron-group elements (Fe, Ni, Cr) and Zn and
without using Ti and other $\alpha-$elements. There are some differences in
metallicities (0.15 dex in average) only for the high-$\Delta v_{90}$
subsample, while for the low-$\Delta v_{90}$ subsample the estimates are the
same. Thus, our conclusions are holding regardless of the Ti measurements.

##  6 Conclusions

In this paper, we study abundance patterns of the neutral ISM in 110 QSO-DLA
systems. We characterise the strength of depletion [Zn/Fe]fit and measure the
total (dust + gas) metallicities [M/H]tot. In addition, from the deviations of
the observed abundances from the linear fits to the abundance patterns, we
derive [X/Fe]nucl for O, Mg, Si, S, Ti, Cr, Fe, Ni, Zn, P, and Mn. These are
relative abundances with respect to Fe, after taking dust depletion into
account and, thus, directly comparable to stellar relative abundances. We
analyse the behaviour of [$\alpha$/Fe]nucl, [Mn/Fe]nucl, and [Zn/Fe]nucl
depending on the total metallicity.

The main analysis is based on 24 QSO-DLAs (the golden sample) for which there
are measurements of column densities of Ti and at least one other
$\alpha$-element. We separated our golden sample into two groups, one with
$\Delta v_{90}$ ¡ 100 $\rm km\,s^{-1}$ (low $\Delta v_{90}$) and the other
with $\Delta v_{90}$ ¿ 100 $\rm km\,s^{-1}$ (high $\Delta v_{90}$). This
separation is aimed at creating two subsamples of galaxies: one with a higher
and one with lower average stellar mass. In addition, we made a minimal
analysis for a non-golden sample for which the depletion by dust and the total
metallicity have been obtained from a linear fitting abundances of Zn and the
iron-group elements Fe, Cr, and Ni.

For the golden sample, we found that less massive galaxies show an
$\alpha$-element knee at lower metallicities than more massive galaxies. If
this collective behaviour can be interpreted as for individual systems, this
would suggest that more massive and metal-rich systems evolve to higher
metallicities before the contribution of SN-Ia levels out the [$\alpha$/Fe]
enhancement created by core-collapse SNe. This is possibly explained by
different SFR in galaxies of different masses.

For the golden sample, there is a clear manganese under-abundance at about
constant level up to [M/H]tot = $-$0.53 dex with average values of [Mn/Fe]nucl
equal to $-$0.33$\pm$0.07 and $-$0.39$\pm$0.07 for the high- and low-$\Delta
v_{90}$ subsamples, respectively. This is not fully consistent with our
expectations since (according to the behaviour of $\alpha$-elements) in some
QSO-DLAs, SNe Ia contribute to abundance pattern that, in turn, should lead to
increase of [Mn/Fe]nucl. It is only for the non-golden sample that [Mn/Fe]nucl
increases starting from [M/H]tot = $-$0.69 dex.

We traced slight effects in the behaviour of [Zn/Fe]nucl with the total
metallicity that resemble the behaviour of [$\alpha$/Fe]nucl but with a
smaller amplitude. This is in agreement with several works on stellar relative
abundances (Bensby et al. 2003; Nissen & Schuster 2011; Mishenina et al. 2011;
Barbuy et al. 2015; Duffau et al. 2017). A systematic bias by [M/H]tot between
high- and low-$\Delta v_{90}$ subsamples is observed. These effects can be
obtained only for the golden sample. Otherwise, by construction of the method
[Zn/Fe]nucl should be approximately Solar.

Measurements of phosphorus should be treated with caution, since in all cases
the column densities were measured only from one line ($\lambda$ 1152$\AA$ or
963$\AA$), which is located in the Ly-$\alpha$ forest (bluer than
Ly-$\alpha$). Probably, because of this, all DLAs in the high-$\Delta v_{90}$
subsample have inexplicably high values of [P/Fe]nucl, higher than 0.45 dex. A
wider velocity profile is more likely to be contaminated and lead to erroneous
measurement. The low-$\Delta v_{90}$ DLAs do not show significant enhancement
of P, with [P/Fe]${}_{\rm nucl}\leq$0.15 dex.

Studying the chemical properties of the neutral ISM in a sample of QSO-DLAs
enables us to trace the collective behaviour of element abundances that can be
interpreted as for individual systems. A homogeneous set of $\alpha$-element
abundances (Ti and at least one other $\alpha$-element) provides a powerful
tool for estimating the strength of depletion [Zn/Fe]fit and the total
metallicity [M/H]tot in the ISM of QSO-DLAs, as well as the more subtle
deviations in the relative abundances due to the nucleosynthesis of specific
stellar populations. This opens a new window into the study of the chemical
evolution of distant galaxies.

###### Acknowledgements.

We thank the anonymous referee for the useful and constructive comments that
improved this manuscript. A.V., A.D.C., C.K., J.K.K. and T.R.H. acknowledge
support by the Swiss National Science Foundation under grant 185692 funding
the “Interstellar One” project.

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##  Appendix A Element abundances in the golden sample

Table 4: Element abundances derived after taking into account the dust depletion. QSO |  [O/Fe]nucl |  [Mg/Fe]nucl |  [Si/Fe]nucl |  [S/Fe]nucl |  [Ti/Fe]nucl |  [Cr/Fe]nucl |  [Ni/Fe]nucl |  [P/Fe]nucl |  [Mn/Fe]nucl |  [Zn/Fe]nucl
---|---|---|---|---|---|---|---|---|---|---
Q0058$-$292 | … |  0.26$\pm$0.04 |  0.23$\pm$0.05 |  0.27$\pm$0.04 |  0.29$\pm$0.12 |  0.07$\pm$0.05 |  0.00$\pm$0.09 | … | … |  $-$0.09$\pm$0.05
Q0100$+$130 | … |  0.31$\pm$0.07 | … |  0.32$\pm$0.04 |  0.32$\pm$0.12 |  0.01$\pm$0.04 | … |  $-$0.05$\pm$0.06 |  $-$0.48$\pm$0.07 |  0.04$\pm$0.05
Q0102$-$190a | … | … | … |  0.17$\pm$0.04 |  0.37$\pm$0.13 |  0.06$\pm$0.05 |  $-$0.10$\pm$0.08 | … |  $-$0.49$\pm$0.07 |  0.01$\pm$0.09
Q0405$-$443a | … | … |  0.04$\pm$0.04 | … |  0.04$\pm$0.06 |  0.00$\pm$0.05 |  $-$0.10$\pm$0.05 | … |  $-$0.41$\pm$0.07 |  $-$0.25$\pm$0.06
Q0405$-$443c | … | … |  0.19$\pm$0.04 |  0.19$\pm$0.04 |  0.18$\pm$0.08 |  0.03$\pm$0.05 |  $-$0.09$\pm$0.05 |  $-$0.02$\pm$0.06 |  $-$0.38$\pm$0.07 |  0.01$\pm$0.05
Q0528$-$250a | … | … |  0.41$\pm$0.04 |  0.33$\pm$0.04 |  0.45$\pm$0.09 |  0.03$\pm$0.05 |  0.05$\pm$0.05 | … |  $-$0.30$\pm$0.08 |  0.25$\pm$0.06
Q0528$-$250b | … |  0.05$\pm$0.04 |  0.33$\pm$0.04 |  0.10$\pm$0.04 |  0.05$\pm$0.08 |  $-$0.07$\pm$0.04 |  0.01$\pm$0.05 | … |  $-$0.31$\pm$0.06 |  $-$0.03$\pm$0.05
Q0841$+$129a | … | … | … |  0.13$\pm$0.06 |  0.13$\pm$0.08 | … |  $-$0.10$\pm$0.05 | … |  $-$0.43$\pm$0.07 |  $-$0.14$\pm$0.12
Q1117$-$134 | … | … |  0.20$\pm$0.04 | … |  0.29$\pm$0.08 |  $-$0.03$\pm$0.06 |  ¡$-$0.10 | … | … |  0.14$\pm$0.07
Q1157$+$014 | … |  0.25$\pm$0.05 |  0.22$\pm$0.04 | … |  0.23$\pm$0.06 |  0.02$\pm$0.04 |  $-$0.09$\pm$0.05 |  0.15$\pm$0.07 |  $-$0.36$\pm$0.06 |  0.06$\pm$0.05
Q1223$+$178 | … |  0.41$\pm$0.06 |  0.12$\pm$0.04 |  0.17$\pm$0.04 |  0.20$\pm$0.08 |  $-$0.03$\pm$0.04 |  $-$0.16$\pm$0.07 | … |  $-$0.48$\pm$0.07 |  $-$0.19$\pm$0.05
Q2206$-$199a | … |  0.14$\pm$0.06 |  0.25$\pm$0.04 |  0.23$\pm$0.04 |  0.22$\pm$0.06 |  $-$0.04$\pm$0.04 |  0.01$\pm$0.05 |  0.46$\pm$0.07 |  $-$0.38$\pm$0.07 |  $-$0.01$\pm$0.05
Q2243$-$605 | … | … |  0.31$\pm$0.04 |  0.34$\pm$0.04 |  0.34$\pm$0.07 |  $-$0.06$\pm$0.05 |  0.06$\pm$0.05 |  0.54$\pm$0.06 |  $-$0.26$\pm$0.07 |  0.17$\pm$0.05
SDSS1249$-$0233 | … | … | … |  0.27$\pm$0.06 |  0.27$\pm$0.12 |  0.13$\pm$0.05 |  0.01$\pm$0.07 | … |  $-$0.40$\pm$0.07 |  0.24$\pm$0.07
Q2230$+$025 | … | … |  0.22$\pm$0.06 |  0.22$\pm$0.06 |  0.22$\pm$0.11 |  $-$0.10$\pm$0.06 |  0.13$\pm$0.07 | … |  $-$0.31$\pm$0.07 |  0.06$\pm$0.07
HE1104$-$1805 |  0.32$\pm$0.20 | … |  0.30$\pm$0.04 | … |  0.30$\pm$0.09 |  $-$0.00$\pm$0.04 |  $-$0.15$\pm$0.05 | … |  $-$0.18$\pm$0.15 |  0.01$\pm$0.05
Q0027$-$1836 | … |  0.73$\pm$0.06 |  0.44$\pm$0.05 |  0.35$\pm$0.04 |  0.39$\pm$0.08 |  0.09$\pm$0.04 |  $-$0.07$\pm$0.05 | … |  $-$0.29$\pm$0.07 |  0.23$\pm$0.05
Q1210$+$17 | … | … |  0.08$\pm$0.05 |  0.07$\pm$0.04 |  0.06$\pm$0.10 |  $-$0.04$\pm$0.05 |  $-$0.14$\pm$0.07 | … |  $-$0.44$\pm$0.06 |  $-$0.17$\pm$0.07
FJ0812$+$32 | … | … |  0.20$\pm$0.04 | … |  0.25$\pm$0.07 |  0.03$\pm$0.04 |  $-$0.09$\pm$0.05 | … |  $-$0.32$\pm$0.07 |  0.06$\pm$0.05
J1135$-$0010 | … | … |  0.36$\pm$0.05 | … |  0.36$\pm$0.07 |  0.08$\pm$0.04 |  0.12$\pm$0.05 | … |  $-$0.35$\pm$0.06 |  0.06$\pm$0.06
Q2231$-$00 | … | … |  0.37$\pm$0.05 |  0.62$\pm$0.15 |  0.44$\pm$0.10 |  $-$0.15$\pm$0.06 |  $-$0.11$\pm$0.07 | … |  $-$0.32$\pm$0.07 |  0.21$\pm$0.07
J1200$+$4015 | … | … | … |  0.31$\pm$0.06 |  0.31$\pm$0.07 |  $-$0.10$\pm$0.06 |  0.06$\pm$0.07 | … | … |  0.17$\pm$0.07
Q1210$+$175 | … |  0.28$\pm$0.09 | … |  0.02$\pm$0.08 |  0.11$\pm$0.06 | … |  $-$0.02$\pm$0.05 | … |  $-$0.33$\pm$0.08 | …
Q1232$+$082 | … |  0.60$\pm$0.09 |  0.53$\pm$0.08 |  0.39$\pm$0.08 |  0.46$\pm$0.10 | … |  $-$0.03$\pm$0.06 |  0.26$\pm$0.18 |  $-$0.14$\pm$0.13 | …
Figure 14: Abundance patterns for the golden sample of QSO-DLA (see Sec. 3).
Blue dashed curve is fitting to the $\alpha$-elements, shown by blue open
triangles. Red curve is shifted blue one to the value averaged through Ni, Cr,
and Fe. The intersection of the gray dashed lines at $B2_{X}=0$ shows the
metallicity [M/H]tot of each system. Gray areas show 1$\sigma$ confidence
intervals.

##  Appendix B Element abundances in the non-golden sample

(a)  Figure 15: Abundance patterns for the non-golden sample of QSO-DLA (see
Sec. 3). Total metallicity [M/H]tot and the dust depletion [Zn/Fe]fit have
been derived from fitting iron-group elements and Zn. (b)  Figure 15:
continued. (c)  Figure 15: continued.

##  Appendix C Dwarf galaxies

Figure 16:  Chemical abundances of $\alpha$-elements taken from the APOGEE
DR17 catalog for dwarf galaxies (color points with $x,y$ error bars), with
Hasselquist et al. (2021) selection. Color solid curves show the approximation
of the data points by piecewise functions consisting of two or three straight
lines representing the average behaviour of $\alpha$-elements relative to
iron. Dark gray solid curves have been obtained by averaging the data in each
metallicity bin. Typically, the bin width is equal to 0.1 dex, but in some
ranges where there are too few stars, it is increased up to 0.2 dex. For
comparison, the behaviour typical for the MW is shown by gray dashed curve
(McWilliam (1997)).

##  Appendix D Fitting the data

Figure 17:  [X/Fe]nucl for three $\alpha$-elements Ti, Si and S. The data are
fitted by three-piecewise functions as for Case 2 to find the level of the
high-$\alpha$ plateau and the position of the high-$\alpha$ knee.

##  Appendix E Abundances of zinc for the non-golden sample

Figure 18: Zinc abundances in the ISM of QSO-DLAs for the non-golden sample.

##  Appendix F New column densities

Figure 19: Velocity profiles of selected low-ionisation transition lines from the DLA system at $z_{\rm abs}$ = 1.892 towards Q 1210+175. Figure 20: Velocity profiles of selected low-ionisation transition lines from the DLA system at $z_{\rm abs}$ = 2.338 towards Q 1232+082. QSO | $z_{\rm abs}$ | log $N$(FeII) | log $N$(NiII) | log $N$(TiII)
---|---|---|---|---
Q0102$-$190b | 2.92648 | 13.80$\pm$0.02 |  $<$13.05 |  $<$12.38
Q0112+030 | 2.42299 | 14.85$\pm$0.02 | 13.57$\pm$0.06 | 12.48$\pm$0.16
Q0112$-$306a | 2.41844 | 13.42$\pm$0.04 | … |  $<$12.28
Q0112$-$306b | 2.70163 | 14.81$\pm$0.03 | 13.65$\pm$0.01 | …
Q0135$-$273a | 2.10735 | 14.58$\pm$0.03 |  $<$13.35 |  $<$12.50
Q0135$-$273b | 2.80004 | 14.77$\pm$0.03 | 13.46$\pm$0.06 |  $<$12.51
Q0336$-$017 | 3.06209 | 14.79$\pm$0.02 | 13.42$\pm$0.05 |  $<$11.92
Q0450$-$131 | 2.06658 | 14.24$\pm$0.02 | 13.34$\pm$0.04 |  $<$12.65
Q0913+072 | 2.61843 | 13.10$\pm$0.02 |  $<$12.42 |  $<$12.02
Q1036$-$229 | 2.77779 | 14.76$\pm$0.01 | 13.71$\pm$0.02 |  $<$12.16
Q1108$-$077b | 3.60767 | 13.88$\pm$0.02 |  $<$12.35 |  $<$12.25
Q1210+175 | 1.89177 | 14.90$\pm$0.02 | 13.67$\pm$0.02 | 12.31$\pm$0.03
Q1232+082 | 2.33771 | 14.52$\pm$0.01 | 13.30$\pm$0.03 | 12.43$\pm$0.09
Q1337+113a | 2.50792 | 13.40$\pm$0.02 |  $<$12.85 |  $<$12.55
Q1337+113b | 2.79584 | 14.33$\pm$0.02 | 13.20$\pm$0.06 | …
Q1340$-$136 | 3.11835 | 13.93$\pm$0.02 | 12.89$\pm$0.05 | …
Q1409+095b | 2.45593 | 13.74$\pm$0.02 |  $<$12.66 |  $<$12.32
Q1451+123b | 2.46921 | 13.38$\pm$0.02 |  $<$13.22 |  $<$12.58
Q1451+123c | 3.17112 | 13.35$\pm$0.09 | 13.30$\pm$0.06 |  $<$13.11
Q2059$-$360a | 2.50734 | 13.50$\pm$0.03 |  $<$12.79 |  $<$12.29
Q2059$-$360b | 3.08261 | 14.48$\pm$0.02 | 13.02$\pm$0.06 |  $<$12.29
Q2152+137b | 3.31599 | 14.50$\pm$0.02 |  $<$12.88 |  $<$12.51
Q2206$-$199b | 2.07622 | 13.34$\pm$0.01 | 12.24$\pm$0.09 |  $<$11.59
Q2230+025 | 1.86427 | 15.35$\pm$0.01 | 14.04$\pm$0.07 |  $<$12.45
Q2231$-$002 | 2.06615 | 14.92$\pm$0.01 | 13.61$\pm$0.01 | …
Q2332$-$094b | 3.05722 | 14.37$\pm$0.01 | 13.19$\pm$0.11 |  $<$12.51
Q2344+125 | 2.53787 | 14.01$\pm$0.01 | 12.58$\pm$0.08 |  $<$12.30
Q2348$-$011a | 2.42695 | 14.83$\pm$0.01 | 13.74$\pm$0.02 |  $<$12.52
Q2348$-$011b | 2.61473 | 14.65$\pm$0.01 | 13.34$\pm$0.05 | …
Q2359$-$022b | 2.15368 | 13.78$\pm$0.04 |  $<$13.22 |  $<$12.60
Table 5: Column densities for the DLAs that are absent in the list compiled by
Konstantopoulou et al. (2022).