6822, were discovered more recently on ground-based wide-field CCD images
(Hwang et al., 2011; Huxor et al., 2013).

Our analysis of the clusters SC6 and SC7 was discussed in Larsen et al.
(2018a). As for most other clusters that we have reanalysed here, the
metallicities have increased by about 0.1 dex (mainly due to the revised
microturbulence prescription), but we recover our previous result that the
$\alpha$-element abundances for SC7 are close to scaled-solar while SC6
exhibits the $\alpha$-enhanced abundance patterns that are characteristic of
other metal-poor GCs in our sample.

In addition to SC6 and SC7, we here include the cluster Hubble VII although
the analysis of its spectrum posed some difficulties. When plotting the
abundance measurements as a function of wavelength, the spectral windows with
wavelengths $\lambda>5200$ Å tended to yield higher Fe abundances than the
bluer windows. Specifically, using only windows with $\lambda<5200$ Å we found
$\mathrm{[Fe/H]}=-1.77$ (with an rms of 0.13 dex) while for $\lambda>5200$ Å
we found $\mathrm{[Fe/H]}=-1.58$ (rms 0.23 dex). Such a trend could
potentially be caused by a mismatch between the HRD of the actual cluster and
that used in the modelling, for example if an incorrect age were assumed.
However, the trend persisted even if an age as young as 5 Gyr was assumed: in
this case we still found a difference of 0.16 dex between the
$\mathrm{[Fe/H]}$ values for $\lambda<5200$ Å and $\lambda>5200$ Å.

As Hubble VII is projected onto the main body of NGC 6822, where the
background is more complicated, one might suspect poor background subtraction
as a possible culprit. We compared our HIRES spectrum with a spectrum obtained
with the Keck Cosmic Web Imager (KCWI) and found the two spectra to be very
similar (apart from the lower spectral resolution of KCWI). Hence, we have not
been able to identify a satisfactory explanation for the difficulties with the
analysis of Hubble VII, and the results should therefore be considered more
uncertain than for the other clusters in our sample. Nevertheless, our
analysis agrees fairly well with that of Colucci & Bernstein (2011) who
measured $\mathrm{[Fe/H]}=-1.61\pm 0.02$, just 0.06 dex higher than our value
(or 0.08 dex when compared with our LTE analysis). In both cases, these are
significantly higher iron abundances than the value measured by Cohen &
Blakeslee (1998). Colucci & Bernstein (2011) also found an approximately
scaled-solar Ca abundance of $\mathrm{[Ca/Fe]}=+0.01\pm 0.07$, which is
similar to our measurement of $\mathrm{[Ca/Fe]}=+0.07\pm 0.04$ ($+0.06$ in
LTE). Nevertheless, the detailed abundance patterns remain somewhat puzzling,
as we find Si and Ti to be enhanced while Mg is depleted ($-0.03$ dex). We
also find a slightly higher Ba abundance than Colucci & Bernstein (2011),
$\mathrm{[Ba/Fe]}=+0.35\pm 0.08$ dex ($+0.48$ in LTE) vs. their
$\mathrm{[Ba/Fe]}=+0.22\pm 0.13$. Hubble VII thus appears worthy of further
study.

##### M31

Table 9: Comparison of our LTE measurements for M31 GCs with literature data.

|  | 006-058 | 012-064 | 163-217 | 171-222 | 225-280 | 358-219
---|---|---|---|---|---|---|---
$\mathrm{[Fe/H]}$ | This work | $-0.54$ | $-1.73$ | $-0.15$ | $-0.23$ | $-0.35$ | $-2.25$
| C2014 | $-0.73$ | $-1.61$ | $-0.49$ | $-0.45$ | $-0.66$ | $-2.21$
| S2016 | $-0.69$ | $-1.60$ | $-0.42$ | $-0.52$ | $-0.64$ | …
$\mathrm{[Na/Fe]}$ | This work | $+0.46$ | $+0.24$ | $+0.65$ | $+0.58$ | $+0.54$ | $+0.34$
| C2014 | $+0.52$ | $+0.62$ | $+0.72$ | $+0.73$ | … | …
| S2016 | $+0.39$ | … | $+0.57$ | $+0.57$ | … | …
$\mathrm{[Mg/Fe]}$ | This work | $+0.34$ | $+0.05$ | $+0.22$ | $+0.27$ | $+0.27$ | $+0.18$
| C2014 | $+0.32$ | $-0.08$ | $+0.25$ | $+0.18$ | $+0.45$ | $-0.03$
| S2016 | $+0.43$ | $-0.14$ | $+0.22$ | $+0.37$ | $+0.24$ | …
$\mathrm{[Si/Fe]}$ | This work | $+0.32$ | $+0.71$ | $+0.29$ | $+0.25$ | $+0.36$ | $+0.42$
| C2014 | $+0.48$ | $+0.35$ | $+0.25$ | $+0.45$ | $+0.49$ | …
| S2016 | $+0.37$ | $+0.43$ | $+0.19$ | $+0.27$ | $+0.32$ | …
$\mathrm{[Ca/Fe]}$ | This work | $+0.25$ | $+0.33$ | $+0.11$ | $+0.11$ | $+0.15$ | $+0.34$
| C2014 | $+0.25$ | $+0.40$ | $+0.28$ | $+0.27$ | $+0.40$ | $+0.27$
| S2016 | $+0.31$ | … | $+0.27$ | $+0.30$ | $+0.34$ | …
$\mathrm{[Ti/Fe]}$ | This work | $+0.29$ | $+0.18$ | $+0.27$ | $+0.23$ | $+0.38$ | $+0.18$
| C2014 | $+0.22$ | $+0.34$ | $+0.25$ | $-0.06$ | $+0.29$ | $+0.23$
| S2016 | $+0.43$ | … | $+0.22$ | $+0.35$ | $+0.39$ | …
141414For C2014 we give $\mathrm{[Ti/Fe]}$ as the weighted average of Ti i and
Ti ii.

Since the initial discovery of 140 ‘nebulous objects …provisionally identified
as globular clusters’ by Hubble (1932), the M31 GC system has been the subject
of numerous studies. We do not attempt to review the literature here, but only
note that the spectroscopic observations analysed here were made prior to the
identification of about 100 GCs in the PAndAS survey, mostly located in the
outer halo of M31 (Huxor et al., 2014). Many of these are, in any case,
relatively extended, and therefore less efficiently observed with a single-
slit spectrograph such as HIRES.

The M31 GCs in our sample span a NLTE metallicity range from
$\mathrm{[Fe/H]}=-2.8$ (EXT8) to $\mathrm{[Fe/H]}=-0.1$ (163-217). They all
show enhanced abundances of Si, Ca, and Ti relative to scaled-solar
composition, although EXT8 is extremely Mg-deficient (Larsen et al., 2020). In
general, the abundance patterns tend to align with those observed in Milky Way
GCs of similar metallicities. From integrated-light spectroscopy, the inner
$\sim 10\arcmin$ of M31 itself are dominated by old, $\alpha$-enhanced
($[\alpha/\mathrm{Fe}]\simeq 0.25$) stars with near-solar metallicities,
associated with a bulge or bar-like component (Saglia et al., 2009, 2018).
Hence, the enhanced $\alpha$-element abundances of the metal-rich GCs are
similar to those seen in metal-rich stars in the central regions of M31 and
may trace the same components at larger galactocentric distances. The three
most metal-rich M31 GCs in our sample are located at projected distances of
$7\aas@@fstack{\prime}8$ (171-222), $13\aas@@fstack{\prime}2$ (163-217), and
$20\aas@@fstack{\prime}5$ (225-280).

The clusters analysed here are among the brightest GCs in M31, and many of
them have been included in several spectroscopic studies in the past. In
addition to the comparison with the low-dispersion metallicity measurements in
Fig. 6, it is of interest to compare with previous analyses that made use of
high-dispersion spectroscopy and analysis techniques similar to ours. In Table
9 we compare our LTE abundance measurements with those published by Colucci et
al. (2014, C2014), also using HIRES observations (but from different runs than
those used here) and Sakari et al. (2016, S2016) (using APOGEE $H$-band
observations). We do not include the errors on the measurements in Table 9 but
they typically amount to $\sim\pm 0.1$ dex (see Tables 13-15 and the original
references).

As noted by C2014, their measurements of $\mathrm{[Fe/H]}$ show a systematic
difference with respect to low-resolution studies in the sense that their
[Fe/H] values tend to be lower for metal-rich GCs. As discussed above (Sect.
3.9), we instead find excellent agreement between our iron abundances and
those measured by Caldwell et al. (2011) at all metallicities, so that our
$\mathrm{[Fe/H]}$ values are systematically higher than those of C2014 and
S2016 at the high-metallicity end. At low metallicities (012-064 and 358-219),
all three studies agree well on $\mathrm{[Fe/H]}$.

Despite the systematic differences in the iron abundances, we generally find
similar abundance ratios to those measured by C2014 and S2016. There are some
occasional outliers, such as $\mathrm{[Na/Fe]}$ and $\mathrm{[Si/Fe]}$ for
012-064 (where our measurements differ by 0.3-0.4 dex from those of C2014 and
S2016) and $\mathrm{[Mg/Fe]}$ for 225-280, where the value measured by C2014
is about 0.2 dex higher, but otherwise the three studies mostly agree within
$\sim 0.1$ dex.

##### M33

The characterisation of the M33 GC system is, to a large extent, still a work
in progress. Part of the difficulty stems from the fact that the GC population
is relatively sparse (certainly when compared to that of M31), and most of the
clusters appear projected onto the highly structured disc of M33. This
difficulty is compounded by the presence of a large number of intermediate-age
clusters which may easily be confused with ancient GCs, especially if
reddened. Indeed, the prevalence of clusters with blue colours compared to
Galactic GCs was noted already in early studies (Hiltner, 1960; Kron & Mayall,
1960) and was later confirmed by larger samples (Melnick & D’Odorico, 1978;
Christian & Schommer, 1982).

Our sample of M33 GCs mostly consists of clusters with resolved HST photometry
from Sarajedini et al. (2000), to which we have added CBF 28 (Chandar et al.,
1999) and the cluster HM33-B from Huxor et al. (2009). We had planned to
include several additional GC candidates from Beasley et al. (2015) which
however turned out to be Galactic foreground stars, as confirmed by their non-
zero parallaxes and proper motions listed in the Gaia DR2 catalogue (IDs 1115,
1138, 1322, 1965, 2001, and 2145 in Beasley et al. 2015). The observations of
the four clusters R14, U77, CBF 28, and HM33-B are published here for the
first time, while analysis of data for H38, M9, R12, and U49 was included in
Larsen et al. (2018a).

Despite the suggestion that the M33 GCs are several Gyr younger than their
Milky Way counterparts (Sarajedini et al., 2000), most of them have enhanced
$\alpha$-element abundances similar to those seen in GCs in other galaxies.
However, it is interesting to note that HM33-B appears chemically more similar
to Fornax 4 and NGC 6822-SC7 in some respects (we discuss this further in
Sect. 5), and is also one of a few GCs located well outside the main body of
M33 (Huxor et al., 2009). This is reminiscent of the behaviour of stars in the
outer M31 halo, which also tend to have abundances more similar to those seen
in dwarf galaxies (Gilbert et al., 2020).

##### NGC 2403

At a distance of about 3.2 Mpc (Freedman & Madore, 1988; Radburn-Smith et al.,
2011), this low-mass Sc-type spiral (similar to M33) is the only galaxy in our
sample that is located outside the Local Group. A list of five cluster
candidates was given by Tammann & Sandage (1968), of which one had a red
colour consistent with it being a GC. The cluster included in our sample, F46,
was first identified by Battistini et al. (1984), who listed a relatively blue
colour ($B-V=0.47$) and suggested that it might be an intermediate-age object.
However, according to SDSS DR12 photometry (Alam et al., 2015), F46 has
$(g-z)_{0}=0.92\pm 0.02$, which is quite normal for an old GC with a
metallicity around $\mathrm{[Fe/H]}\simeq-1.5$ (Vanderbeke et al., 2013).

The spectrum of F46 is of good quality, despite the relatively modest
integration time (Table 11) and most elemental abundances are well
constrained. It helps that the cluster is very compact and the spectrum was
obtained on a night with good seeing ($0\aas@@fstack{\prime\prime}8$ FWHM), so
that slit losses were minimised. The cluster is moderately metal-poor
($\mathrm{[Fe/H]}=-1.71\pm 0.03$) and the $\alpha$-elements are mostly
enhanced, with the exception of $\mathrm{[Mg/Fe]}$ which is _sub_ -solar. In
this respect F46 resembles several other clusters with metallicities around
$\mathrm{[Fe/H]}\approx-1.7$.

We can use the velocity broadening obtained from the spectral analysis to
constrain the virial mass and mass-to-light ratio of F46. Correcting the total
broadening in Table 11 for an instrumental broadening of 3.4 km s-1 (Larsen et
al., 2020), the line-of-sight velocity broadening is
$\sigma_{\mathrm{1D}}=11.7$ km s-1. We used an HST/ACS archival image in the
F555W filter (Progr. ID 10402, P.I. R. Chandar) to estimate the half-light
radius of F46 by measuring the flux in concentric apertures. Visually, the
cluster can be traced out to a radius of about 50 pixels
($2\aas@@fstack{\prime\prime}5$) in the ACS image, and within this radius the
total magnitude is about $m_{\mathrm{F555W}}=17.8$, slightly brighter than the
value of $V=17.96$ given by Battistini et al. (1984). The ACS photometry may
however be affected by multiple cosmic-ray hits in the single exposure.
Correcting the measurement in the ACS image for a foreground extinction of
$A_{V}=0.11$ mag (NED) we get $M_{V}=-9.8$. Half of the flux is contained
within a radius of 6 ACS pixels or $0\aas@@fstack{\prime\prime}30$,
corresponding to a half-light radius of $r_{h}=4.6$ pc at a distance of 3.2
Mpc. Subtracting the half-light radius of the ACS point-spread function (about
1.5 pixels; Bohlin, 2016) in quadrature decreases $r_{h}$ by about 0.15 pc.
The dynamical mass is then

$M_{\mathrm{dyn}}=10\frac{\sigma_{\mathrm{1D}}^{2}r_{h}}{G}\simeq 1.4\times
10^{6}\,M_{\odot}$ (10)

and the mass-to-light ratio is $M_{\mathrm{dyn}}/L_{V}\simeq
2.0\,M_{\odot}/L_{V,\odot}$, which is a typical value for an old GC at this
metallicity (Strader et al., 2011). For an age of $10^{8}-10^{9}$ years, as
suggested by Battistini et al. (1984), the $V$-band mass-to-light ratio would
be only 5%–15% of that at 10 Gyr (e.g. Bruzual & Charlot, 2003), in strong
contrast to the measured value. We conclude that F46 is indeed most likely a
relatively metal-poor, old GC.

Figure 7: Integrated-light abundances of $\alpha$-elements relative to iron
(Table 13). Large symbols show our measurements, with symbol colours and
shapes encoding information about the host galaxies as indicated in the
legend. Error bars indicate $\sigma_{\langle X\rangle}$ or $S_{X}$, whichever
is larger. Olive coloured small triangles: NLTE measurements for Milky Way
field stars (Bergemann et al., 2017b; Mashonkina et al., 2017b, 2019;
Mishenina et al., 2017; Zhao et al., 2016). Orange points: Milky Way bulge
stars (Bensby et al., 2017). Grey points in panel with [Si/Fe]: LTE
measurements for Milky Way field stars (Suda et al., 2008).  Figure 8: Sodium
abundances (NLTE). Symbols for our integrated-light measurements are the same
as in Fig. 7. References for Milky Way GCs (open circles), Milky Way field
star LTE data (grey points) and NLTE data (olive coloured triangles), and
field stars in the Fornax dwarf (small red circles) are given in the text.

###  4.2 Abundance trends

Having discussed the individual GC systems, we next turn to a more general
discussion of the abundance trends and comparison with existing measurements
of individual stars. In Fig. 7-10 we plot the measurements in Tables 13-15 as
a function of $\mathrm{[Fe/H]}$. In each figure, the symbols for our
integrated-light measurements are colour-coded according to the type of host
galaxy, using the same scheme as in Fig. 1. Red symbols indicate GCs belonging
to dwarf spheroidals and ellipticals (NGC 147, NGC 185, NGC 205, and the
Fornax dSph) and teal-colour symbols indicate dwarf irregulars (NGC 6822 and
WLM). The Milky Way, M31, and M33 GCs are shown with black, violet, and blue
squares, respectively, and the single GC in NGC 2403 is represented by an
orange square.

##### The $\alpha$-elements

Figure 7 shows the $\alpha$-element abundance ratios ($\mathrm{[Mg/Fe]}$,
$\mathrm{[Si/Fe]}$, $\mathrm{[Ca/Fe]}$, and $\mathrm{[Ti/Fe]}$). Although the
classification of Ti as an $\alpha$-element may be questionable (Woosley &
Weaver, 1995), it usually tends to trace other $\alpha$-elements (such as Mg
and Si) fairly closely (Conroy et al., 2014; Parikh et al., 2019), and here we
group it together with the $\alpha$-elements. For Mg, Ca, and Ti we include
NLTE measurements for Milky Way field stars (Zhao et al., 2016; Mashonkina et
al., 2017b, 2019; Mishenina et al., 2017) and additionally, for Mg, data for
326 thick-disc stars from Bergemann et al. (2017b). For Si (where our
measurements are LTE values) we show literature data from the Stellar
Abundances for Galactic Archeology (SAGA) database (Suda et al., 2008). The
increasing scatter at metallicities below $\mathrm{[Fe/H]}=-2$ for the
literature [Si/Fe] data is caused partly by larger measurement uncertainties,
although uncertainties are not provided for all stars. We also include
measurements for microlensed Milky Way bulge stars from Bensby et al. (2017)
and literature data for individual stars in Galactic GCs (Roediger et al.,
2014, R2014), the latter indicated with open circles.

Perhaps the most notable feature of Fig. 7 is the high degree of uniformity of
the abundance patterns for Si, Ca, and Ti. All three elements are enhanced
relative to scaled-solar composition with mean abundance ratios of
$\langle\mathrm{[Si/Fe]}\rangle=+0.32\pm 0.01$,
$\langle\mathrm{[Ca/Fe]}\rangle=+0.21\pm 0.01$, and
$\langle\mathrm{[Ti/Fe]}\rangle=+0.35\pm 0.01$. The dispersions of the
$\mathrm{[Ca/Fe]}$ and $\mathrm{[Ti/Fe]}$ values are only 0.09 dex and 0.10
dex, respectively, while the $\mathrm{[Si/Fe]}$ values have a larger
dispersion (0.17 dex), driven at least in part by the larger uncertainties.
Above $\mathrm{[Fe/H]}\approx-0.5$, $\mathrm{[Ca/Fe]}$ shows a declining trend
towards higher metallicities while Ti and Si remain elevated throughout the
entire metallicity range. We thus confirm the $\alpha$-element like behaviour
of Ti.

Overall, the abundance ratios [Si/Fe], [Ca/Fe], and [Ti/Fe] for our sample are
fairly similar to those seen in the R2014 data and in the Milky Way field
stars. The larger differences for Mg are discussed in more detail below. We
note that the NLTE corrections tend to slightly decrease our [Ca/Fe] values
and increase the [Ti/Fe] values (Table 7). There may indeed be a tendency for
our abundances for these elements to be slightly offset in the corresponding
directions from the R2014 data, which are generally based on LTE analyses of
individual GC member stars. Slight offsets could, however, also be caused by
other effects, such as differences in the atomic data and adopted solar
abundance scales (Sect. 3.5.2). In their compilation, R2014 did not attempt to
homogenise the data to account for such differences.

Superimposed on the general homogeneity of the $\alpha$-element abundance
patterns are some higher-order differences. Two GCs, Fornax 4 and NGC
6822-SC7, have consistently low $\alpha$-element abundances. As discussed in
Larsen et al. (2018a), this mirrors the tendency for the ‘knee’ in the
$\alpha$-element versus [Fe/H] relation to occur at a lower metallicity in
dwarf galaxies than in the Milky Way. Our present sample includes an
additional cluster with a hint of this behaviour, HM33-B, albeit at lower
significance. This cluster has relatively low $\mathrm{[Mg/Fe]}$ and
$\mathrm{[Ca/Fe]}$ ratios although the $\mathrm{[Si/Fe]}$ and
$\mathrm{[Ti/Fe]}$ ratios are more similar to those of the Galactic stars at
this metallicity. The S/N ratio of the HM33-B spectrum is relatively low, and
the uncertainties on the abundances thus relatively large, and obtaining a
better spectrum of this cluster would be desirable. At metallicities below
those of Fornax 4, NGC 6822-SC7, and HM33-B, $\mathrm{[Fe/H]}<-1.3$, there is
a small but systematic difference between the mean $\alpha$-element abundance
ratios for the GCs in spirals and those in dwarf galaxies. For the metal-poor
GCs in spirals we find
$\langle\mathrm{[Si/Fe]}\rangle_{\mathrm{MP,spir}}=+0.40\pm 0.02$,
$\langle\mathrm{[Ca/Fe]}\rangle_{\mathrm{MP,spir}}=+0.28\pm 0.01$, and
$\langle\mathrm{[Ti/Fe]}\rangle_{\mathrm{MP,spir}}=+0.38\pm 0.01$, while the
corresponding mean values for GCs in the dwarf galaxies are
$\langle\mathrm{[Si/Fe]}\rangle_{\mathrm{MP,dwarf}}=+0.35\pm 0.03$,
$\langle\mathrm{[Ca/Fe]}\rangle_{\mathrm{MP,dwarf}}=+0.23\pm 0.01$, and
$\langle\mathrm{[Ti/Fe]}\rangle_{\mathrm{MP,dwarf}}=+0.36\pm 0.01$. Hence, the
GCs in the spiral galaxies are systematically more $\alpha$-enhanced by about
0.04 dex.

For Mg the situation is more complicated than for the other $\alpha$-elements.
The $\mathrm{[Mg/Fe]}$ ratio has the largest dispersion of the
$\alpha$-elements ($\sigma_{\mathrm{[Mg/Fe]}}=0.19$ dex) and a number of GCs
scatter well below the relation followed by the field stars. The tendency for
the integrated-light $\mathrm{[Mg/Fe]}$ measurements to fall below those of
the other $\alpha$-elements has been noted in several previous studies of
extragalactic GCs (Colucci et al., 2009, 2014; Larsen et al., 2012, 2018a;
Sakari et al., 2015) and it has been suggested that it may be caused by
internal Mg spreads in the clusters similar to those observed in some Galactic
GCs. One difficulty with this interpretation is the relatively large fraction
of clusters with integrated-light measurements that appear to be affected
(Larsen et al., 2018a), and another is that the Mg spreads observed in
Galactic GCs appear insufficient produce the observed effect (Pancino et al.,
2017). In the context of galactic chemical evolution, low [Mg/Fe] values can
be produced by a variety of mechanisms, such as gas inflows or extended star
formation histories (Buck, 2020; Buck et al., 2021), but are usually expected
to be accompanied by a general deficit of the $\alpha$-elements, unlike the
situation for the GCs. Hence there is currently no satisfactory explanation
for these unusually low Mg abundances. Apart from Fornax 4, NGC 6822-SC7, and
HM33-B, which are also deficient in other $\alpha$-elements, it is interesting
to note that the clusters with strongly depleted Mg abundances are mainly
found at $\mathrm{[Fe/H]}<-1.5$. Indeed, the most Mg-deficient cluster, EXT8,
is also the most metal-poor cluster in our sample.

##### Sodium

Our integrated-light measurements of $\mathrm{[Na/Fe]}$ are shown in Fig. 8
along with Galactic field star samples that include NLTE corrections (Gehren
et al., 2004, 2006; Mishenina et al., 2017; Mashonkina et al., 2017b; Zhao et
al., 2016) and the larger LTE field star samples of Venn et al. (2004, V2004)
and Ishigaki et al. (2013, I2013). Also included are (LTE) data for field
stars in the Fornax dwarf spheroidal galaxy (Letarte et al., 2010, L2010) and
average $\mathrm{[Na/Fe]}$ values for individual stars in Galactic GCs
(C2009). The latter include NLTE corrections from Gratton et al. (1999).

The behaviour of $\mathrm{[Na/Fe]}$ as a function of metallicity and
environment is rather complex and the Na abundances in GCs are, furthermore,
affected by intra-cluster abundance spreads associated with multiple
populations. The latter most likely account for the tendency for the GC
$\mathrm{[Na/Fe]}$ values to lie above the bulk of the field star
measurements, especially at low and high metallicities. At intermediate
metallicities, $-1.5\la\mathrm{[Fe/H]}\la-1.0$, the offset of the integrated-
light measurements with respect to the field star NLTE literature data is less
evident. However, it is worth noting that the trends of $\mathrm{[Na/Fe]}$ vs.
$\mathrm{[Fe/H]}$ in the NLTE corrected field samples are quite different from
those seen in the larger samples of V2004 and I2013: the latter display a
larger scatter in $\mathrm{[Na/Fe]}$ at $\mathrm{[Fe/H]}\la-1$ and reach lower
$\mathrm{[Na/Fe]}$ values at intermediate metallicities. Given that our NLTE
corrections for Na tend to be negative, which also tends to be the case for
individual stars (Gehren et al., 2004; Takeda et al., 2003), a NLTE correction
would most likely shift the V2004 and I2013 data to lower [Na/Fe] values. The
tendency for [Na/Fe] to reach significantly sub-solar values at low to
intermediate metallicities is characteristic of halo populations (I2013; Zhao
et al. 2016), which are less well represented at intermediate metallicities in
the NLTE comparison samples, but may provide a more direct comparison with the
GC measurements.

The $\approx+0.3$ dex offset between our integrated-light $\mathrm{[Na/Fe]}$
values and the average values from C2009, discussed above for 47 Tuc (Sect.
3.8), is also evident in Fig. 8. If shifted downwards by 0.3 dex, the trend of
$\mathrm{[Na/Fe]}$ vs. $\mathrm{[Fe/H]}$ seen in the C2009 data would closely
match that seen in our integrated-light measurements, including the transition
from the scatter around scaled-solar abundance ratios in the range
$\mathrm{[Fe/H]}<-1$ to a tighter sequence at super-solar $\mathrm{[Na/Fe]}$
values at higher metallicities. We recall that a difference of 0.1 dex between
our [Na/Fe] values and those measured by C2009 is explained by the different
solar abundance scales, but this still leaves 0.2 dex unaccounted for. One
possibility could be the use of significantly over-estimated NLTE corrections
in the C2009 analysis. Their work relies on the NLTE model atom by Gratton et
al. (1999), who employed empirically-calibrated collision rates based on the
Drawin & Felenbok (1965) formula. Our analysis, however, relies on state-of-
the-art ab initio data for Na$+$H collisions that are available from detailed
quantum-mechanical calculations. As Lind et al. (2011) demonstrated
previously, the differences in the collisional rates may account for up to
$+0.2$ dex difference in NLTE abundances. In particular, Lind et al. (2011)
also hint a significant difference between their results and those by Gratton
et al. (1999), in the sense that the latter study leads to positive NLTE
corrections, in contrast with predictions with more accurate H collision data
(see also Asplund 2005). Our NLTE corrections for Na lines are negative and
are in agreement with the Lind et al. (2011) findings, which suggests that the
NLTE Na abundances from C2009 are over-estimated.

While it is tempting to interpret strongly elevated integrated-light
$\mathrm{[Na/Fe]}$ values as evidence of multiple populations in the GCs, this
must be tempered by the caveat that the Na abundances of field stars in other
galaxies may differ from those observed in the Milky Way. In Fig. 8, this is
evident from the difference between the Na abundances of stars in the Fornax
dSph and those in the Milky Way. Similarly sub-solar [Na/Fe] abundance ratios
are observed in field stars in other Local Group dwarf galaxies such as
Sagittarius (Sbordone et al., 2007; Hasselquist et al., 2017), Draco (Cohen &
Huang, 2009), Ursa Minor (Cohen & Huang, 2010) and Sculptor (Salgado et al.,
2019), while massive early-type galaxies are often found to exhibit super-
solar $\mathrm{[Na/Fe]}$ ratios that correlate with velocity dispersion
(Conroy et al., 2014; Worthey et al., 2014; La Barbera et al., 2017). In the
nuclear regions of M31, Na enhancements as high as
$\mathrm{[Na/Fe]}\approx+1.0$ dex have been measured (Conroy & van Dokkum,
2012). As in previous studies (Colucci et al., 2014; Sakari et al., 2016), we
find the metal-rich GCs in M31 to be quite Na-rich, too, albeit not reaching
the extreme enhancement found by Conroy & van Dokkum (2012).

##### Iron-peak elements: Sc, Cr, Mn, Ni

Figure 9: Abundances of iron-peak elements (Table 14). Symbols for our
measurements are the same as in Fig. 7. NLTE abundances for Mn in Milky Way
field stars are from Eitner et al. (2020).

Our measurements of the iron-peak elements are shown in Fig. 9. Corrections
for NLTE effects are included for Mn and Ni. For field stars we include NLTE
Mn abundances from Eitner et al. (2019). While our integrated-light
measurements do not include NLTE corrections for Cr, we have included NLTE
data for field dwarfs from Bergemann & Cescutti (2010). These do not differ
strongly from the LTE data from I2013.

The iron-peak elements mostly tend to follow the trends observed in Milky Way
samples and display only moderate departures from scaled-solar abundance
patterns. The $\mathrm{[Sc/Fe]}$ ratios tend to be moderately enhanced
compared to scaled-solar composition in both the GC and field star
measurements, with the exception of Fornax 4, NGC 6822-SC7, and HM33-B. A few
of the most metal-poor GCs (mainly associated with NGC 147) also show hints of
sub-solar [Sc/Fe] values, but these measurements all have fairly large
uncertainties. Manganese is moderately sub-solar over most of the metallicity
range (by about 0.2 dex), but the strongly depleted $\mathrm{[Mn/Fe]}$ ratios
typically seen at low metallicities in LTE analyses of Mn I lines, which can
be as low as $\mathrm{[Mn/Fe]}\approx-1.0$ (Bonifacio et al., 2009), are not
present in our NLTE analysis. Our integrated-light $\mathrm{[Mn/Fe]}$ ratios
closely follow those seen in NLTE analyses of Milky Way field stars, with the
GCs that deviate from the general trend tending to have large uncertainties.

Nickel is slightly enhanced relative to scaled-solar composition over most of
the metallicity range, again with the exception of the clusters Fornax 4, NGC
6822-SC7, and HM33-B, which have clearly sub-solar [Ni/Fe]. The NLTE
corrections for Ni are significant at low metallicities, reaching 0.2 dex at
$\mathrm{[Fe/H]}=-2.5$ (see e.g. Table 7), which causes an offset between the
integrated-light GC measurements and the LTE field star data. Hence our GC
analysis does not show the slightly sub-solar [Ni/Fe] values that are
typically quoted in the literature for halo stars (Gratton & Sneden 1987;
I2013). It should be pointed out, however, that none of the Galactic chemical
evolution models reproduces the observational trends across the entire
metallicity range. The models by Kobayashi et al. (2019) underpredict the
observed [Ni/Fe] values below [Fe/H] $\approx-0.7$, and the same trend is seen
in the results by Palla (2021). It is not clear yet whether a contribution
from rotating massive stars (e.g. Limongi & Chieffi, 2018) could explain this
discrepancy.

##### Heavy elements: Cu, Zn, Zr, Ba, Eu

Figure 10: Abundances of heavy elements (Table 15). Symbols for our
measurements are the same as in Fig. 7.

Figure 10 shows our measurements of the elements beyond the iron-peak, which
are thought to be produced mainly via the (slow and rapid) neutron-capture
processes. Our LTE measurements for Cu, Zn, Zr, and Eu are plotted together
with Milky Way field star data from Frebel (2010, F2010), I2013, Bensby et al.
(2017, B2017), and Van der Swaelmen et al. (2016, VdS2016), as indicated in
the legends.

The GC data generally align well with the field stars, and there are no
obvious differences between the abundance patterns for GCs in different types
of galaxies, apart from the overall lower metallicities of the GCs in the
dwarf galaxies. We note that neither Fornax 4, NGC 6822-SC7, or HM33-B are
conspicuous outliers in any of these plots, in contrast to the situation for
some $\alpha$\- and iron-peak elements.

The top panel in Fig. 10 reveals a strong correlation between
$\mathrm{[Cu/Fe]}$ vs. $\mathrm{[Fe/H]}$, which has long been observed in
field stars (Sneden et al. 1991; I2013). However, recent work suggests that it
may be caused mainly by NLTE effects (Andrievsky et al., 2018). Zinc is mildly
enhanced at the lowest metallicities and approaches scaled-solar abundances at
near-solar metallicities, again consistent with the behaviour of the field
stars (Bensby et al., 2017; da Silveira et al., 2018).

The measurements of Zr and Eu are more challenging due to the weakness of the
lines and are only available for a subset of the clusters, mainly the more
metal-rich ones. At $\mathrm{[Fe/H]}\la-1$, the GCs resemble the field stars
in being somewhat enhanced in $\mathrm{[Zr/Fe]}$ on average, although the
uncertainties on individual measurements are large. At higher metallicities,
the tendency for Zr to be enhanced is still apparent in the GCs, while the
Galactic (disc) stars approach scaled-solar composition. Measurements of Zr in
the bulge are scarce, but Johnson et al. (2012) tentatively suggested that
there may be two sequences, one being characterised by
$\mathrm{[Zr/Fe]}\approx+0.25$ and the other by
$\mathrm{[Zr/Fe]}\approx-0.10$. The metal-rich GCs would then appear to align
with the Zr-rich sequence. For $\mathrm{[Eu/Fe]}$, one can recognise the same
pattern observed in field stars, with a roughly constant level of Eu
enhancement at lower metallicities ($\mathrm{[Fe/H]}\la-1$) and a decrease at
higher metallicities that is also seen in Galactic bulge giants (Johnson et
al., 2012; Van der Swaelmen et al., 2016). However, the decrease is more
pronounced for the GCs, which reach [Eu/Fe] values even below those typical of
the disc stars at high metallicities. While the Eu measurements are
challenging, we note that the metal-rich Milky Way bulge GC NGC 6553 has
abundance patterns measured from individual stars that resemble our
integrated-light measurements with a roughly solar [Eu/Fe] and enhanced
$\alpha$-element abundances (Barbuy et al., 1999; Alves-Brito et al., 2006).
We do not recover the very high [Eu/Fe] values for the Fornax GCs from the
analysis in Larsen et al. (2012). These were driven in part by the Eu ii 4205
Å line that is not included in the present analysis.

The second panel from the bottom of Fig. 10 shows our integrated-light NLTE
measurements for Ba together with NLTE field star data (Mashonkina et al.,
2017b; Mishenina et al., 2017; Zhao et al., 2016). When synthesising the Ba ii
lines, we assumed the $r$-process isotopic ratios of McWilliam (1998). For
$s$-process dominated isotopic mixture, the Ba abundances would be higher by
about 0.1 dex, owing to the more dominant contribution from 138Ba which lacks
hyperfine splitting. In previous versions of our analysis, the integrated-
light $\mathrm{[Ba/Fe]}$ ratios were found to be slightly higher compared to
literature data for field stars (Larsen et al., 2014, 2018a). A slight hint of
this tendency may still be present in Fig. 10, especially for the M33 GCs, but
the integrated-light GC measurements mostly fall within the envelope defined
by the field stars.

###  4.3 Comparison with individual stars in host galaxies

Figure 11: Mean $\alpha$-element abundance ratios for GCs and field stars in
NGC 147, NGC 185 (Vargas et al., 2014), and Fornax (Letarte et al., 2010).

For a few galaxies other than the Milky Way, we can directly compare our
integrated-light GC measurements with data for field stars for a subset of
elements. In Fig. 11 we compare our integrated-light measurements of
[$\alpha$/Fe] (the average of [Mg/Fe], [Si/Fe], [Ca/Fe], and [Ti/Fe]) for GCs
in NGC 147, NGC 185, and the Fornax dSph with literature data for individual
stars in these systems (Letarte et al., 2010; Vargas et al., 2014). This
figure illustrates how the GCs complement data for individual stars: while
$\alpha$-element abundances can be measured for individual RGB stars in the
Andromeda satellites, the scatter is large (mainly due to measurement
uncertainties) and the field stars are preferentially more metal-rich than the
GCs. In the Fornax dSph, abundance measurements for individual stars are more
accurate, but the distinct difference in the metallicities of field stars and
GCs remains evident. For all three galaxies, the GCs trace the mean trends
seen in the field stars quite well.

##  5 Discussion

Figure 12: Principal components analysis of the abundance measurements, showing the first four principal components. Figure 13: Second, third, and fourth PC as a function of the first PC for each cluster. Symbols are the same as in Fig. 7. Table 10: Projections of abundance measurement onto principal component vectors. Cluster | PC1 | PC2 | PC3 | PC4
---|---|---|---|---
NGC 0104 | $0.675$ | $-0.290$ | $-0.051$ | $-0.033$
NGC 0362 | $0.331$ | $0.289$ | $-0.153$ | $0.143$
NGC 6254 | $-0.080$ | $0.132$ | $-0.333$ | $0.053$
NGC 6388 | $0.893$ | $0.087$ | $0.176$ | $0.001$
NGC 6752 | $-0.308$ | $-0.143$ | $-0.104$ | $-0.032$
NGC 7078 | $-0.887$ | $0.135$ | $-0.092$ | $-0.221$
NGC 7099 | $-0.840$ | $-0.056$ | $0.054$ | $-0.066$
N147 HII | $-0.107$ | $-0.840$ | $-0.073$ | $0.182$
N147 HIII | $-0.974$ | $-0.422$ | $0.926$ | $0.362$
N147 PA-1 | $-0.857$ | $-0.196$ | $0.398$ | $-0.252$
N147 PA-2 | $-0.516$ | $-0.258$ | $-0.078$ | $0.145$
N147 SD7 | $-0.540$ | $0.044$ | $-0.105$ | $-0.082$
N185 FJJ-III | $-0.329$ | $-0.423$ | $-0.046$ | $-0.255$
N185 FJJ-V | $-0.415$ | $0.085$ | $-0.027$ | $-0.011$
N185 FJJ-VIII | $-0.395$ | $-0.255$ | $-0.197$ | $0.283$
N205 HubbleI | $0.024$ | $0.106$ | $-0.139$ | $-0.059$
N205 HubbleII | $0.083$ | $-0.057$ | $-0.101$ | $-0.007$
N6822 SC6 | $-0.249$ | $0.017$ | $-0.103$ | $0.210$
N6822 SC7 | $0.214$ | $1.057$ | $0.229$ | $0.453$
N6822 HVII | $-0.241$ | $0.380$ | $0.194$ | $-0.228$
M33 M9 | $-0.272$ | $0.006$ | $-0.432$ | $0.029$
M33 R12 | $0.511$ | $0.158$ | $-0.157$ | $0.239$
M33 U49 | $0.036$ | $-0.366$ | $-0.534$ | $0.179$
M33 R14 | $0.380$ | $0.152$ | $-0.008$ | $-0.050$
M33 U77 | $-0.428$ | $-0.007$ | $-0.393$ | $0.195$
M33 CBF28 | $0.293$ | $0.178$ | $0.082$ | $0.017$
M33 HM33B | $0.187$ | $0.863$ | $0.106$ | $-0.390$
WLM GC | $-0.449$ | $-0.072$ | $0.114$ | $0.183$
Fornax 3 | $-0.901$ | $0.243$ | $-0.156$ | $-0.231$
Fornax 4 | $0.134$ | $0.649$ | $0.234$ | $0.344$
Fornax 5 | $-0.687$ | $-0.196$ | $0.369$ | $-0.231$
M31 006-058 | $0.898$ | $-0.236$ | $0.079$ | $-0.031$
M31 012-064 | $-0.291$ | $0.112$ | $-0.140$ | $-0.404$
M31 019-072 | $0.732$ | $-0.216$ | $0.156$ | $0.041$
M31 058-119 | $0.434$ | $0.250$ | $-0.065$ | $-0.144$
M31 082-114 | $0.725$ | $-0.494$ | $-0.223$ | $-0.013$
M31 163-217 | $1.297$ | $-0.313$ | $0.379$ | $-0.035$
M31 171-222 | $1.231$ | $-0.240$ | $0.226$ | $-0.069$
M31 174-226 | $0.425$ | $0.146$ | $-0.131$ | $-0.231$
M31 225-280 | $1.093$ | $-0.152$ | $0.170$ | $-0.216$
M31 338-076 | $0.336$ | $0.059$ | $-0.175$ | $0.036$
M31 358-219 | $-0.795$ | $-0.101$ | $0.176$ | $-0.063$
N2403 F46 | $-0.372$ | $0.183$ | $-0.054$ | $0.260$

The general homogeneity of the $\alpha$-element abundance patterns among the
GCs in our sample, with at most minor differences between GCs in dwarf
galaxies and in spirals, was noted in Sect. 4.2. Indeed, the similarity is not
restricted to the $\alpha$-elements, but also extends to most other elements.
Three clusters, namely Fornax 4, NGC 6822-SC7, and HM33-B, have significantly
different abundance patterns than the rest. From inspection of Figs. 7-10,
these three clusters have clearly depleted abundances of Na, Mg, Si, Ca, Ti,
Sc, Ni, and possibly also Zn and Eu, compared to the other GCs in our sample.
On the other hand, Cr and Mn do not appear to vary in a correlated way with
these elements.

A more quantitative way to gain insight into correlations between abundances
of different elements is via a Principal Components Analysis (PCA). We used
the scikit-learn package (Pedregosa et al., 2011) in Python to carry out a PCA
for the abundance measurements [Fe/H], [Na/Fe], [Mg/Fe], [Si/Fe], [Ca/Fe],
[Ti/Fe], [Sc/Fe], [Cr/Fe], [Mn/Fe], [Ni/Fe], [Zn/Fe], and [Ba/Fe]. For these
elements, measurements are available for all clusters except EXT8 (whose
features are very weak owing to the low metallicity) and M33 H38 (which has a
low S/N). Errors on the principal component (PC) vectors were estimated via a
Monte-Carlo simulation in which the PCs were recomputed from 1000 random
realisations of the dataset. The first four PCs of the dataset are shown in
Fig. 12, ordered according to their contributions to the total variance of the
dataset. It is clear, and fairly unsurprising, that the first PC, which
accounts for more than half of the variance, mainly traces metallicity. The
second PC, accounting for 17% of the variance, involves all of the abundance
ratios in which the three GCs mentioned above are deficient, also including
Zn. This again shows very clearly that variations in the $\alpha$-elements are
strongly correlated with variations in [Na/Fe], [Sc/Fe], [Ni/Fe], and [Zn/Fe].

Table 10 lists, for each cluster, the projection of the abundance measurements
onto the first four PC vectors. Hence the first column (PC1) indicates
metallicity and the second column (PC2) indicates variations in the
$\alpha$-elements and their related elements. We note that PC2 is defined such
that a positive increase in this component corresponds to a decrease in the
$\alpha$-element abundances. It is again evident that PC2 has the strongest
positive contribution in Fornax 4, HM33-B, and NGC 6822-SC7. The PCA clearly
confirms that HM33-B shares similar abundance patterns with Fornax 4 and with
NGC 6822-SC7.

While the first and second PC have clear astrophysical interpretations, this
is less clear for the higher-order PCs. Fig. 13 graphically illustrates the
data in Table 10 by plotting PC2, PC3, and PC4 as a function of PC1. The three
$\alpha$-deficient GCs are clearly identifiable as outliers in the top panel.
PC3 shows a U-shaped variation with PC1, implying a similar U-shaped variation
of [Na/Fe] with [Fe/H] and an inverse variation of [Ba/Fe]. This tendency for
the most metal-poor and metal-rich clusters to have relatively high [Na/Fe]
and relatively low [Ba/Fe] ratios is indeed visible in Figs. 8 and 10. PC4
accounts for less than 6% of the variance, and probably does not trace
significant physical variations in the dataset.

The relation between [Na/Fe] and the $\alpha$-elements has previously been
discussed in the literature, with conflicting conclusions. Several studies
have found significant correlations between [Na/Fe] and [$\alpha$/Fe] similar
to that reported here (Fulbright 2002; I2013), yet no such correlation was
found by V2004 in their analysis of a compilation of literature data.
Evidently the relationship between Na and the $\alpha$-elements is complex, as
can be appreciated from the fact that relatively metal-rich field stars in
dwarf galaxies reach much lower [Na/Fe] values than Galactic stars of
comparable metallicities (e.g. Fig. 8).

Similar remarks may be made about the Ni-Na correlation, which has received
considerable attention in the literature and is thought to be linked to the
production of both elements in Type II SN nucleosynthesis (Nissen & Schuster,
1997; Cohen & Huang, 2010; Letarte et al., 2010; Lemasle et al., 2014). The
two abundance ratios, [Ni/Fe] and [Na/Fe], are also correlated in our dataset
though PC2, but cannot here be separated in an unambiguous way from the
general correlation of both elements with the $\alpha$-element abundances.

The identification of the cluster HM33-B in the above analysis is reminiscent
of the idea of chemical tagging, which seeks to establish relations between
stars or star clusters based on their chemical composition (Freeman & Bland-
Hawthorn, 2002). Given the small variation in the various abundance ratios at
low metallicities, it seems clear that prospects for tagging GCs are most
promising for clusters that have metallicities higher than the knee in host
galaxies that are sufficiently massive to host GCs, that is,
$\mathrm{[Fe/H]}\ga-1.5$. Similar conclusions were reached in previous work
that explored the chemical association of GCs with halo substructure in M31
(Sakari et al., 2014, 2015) and the Milky Way (Horta et al., 2020).

###  5.1 Enrichment time scales and IMF

As discussed in the introduction, the integrated light of massive early-type
galaxies is usually dominated by old stellar populations with enhanced
$\alpha$-element abundances. When broken down by individual elements the
picture becomes more complex. The lighter $\alpha$-elements (O, Mg) become
increasingly enhanced for higher velocity dispersions (i.e. more massive
systems), whereas Ca is typically found to be only slightly enhanced relative
to scaled-solar composition, or not at all (Conroy et al., 2014; Worthey et
al., 2014). These differences reflect differences in nucleosynthetic origin,
with the light $\alpha$-elements being produced predominantly by hydrostatic
burning in massive stars, while Ca and Ti are also produced in explosive
nucleosynthesis and have significant contributions from type Ia SNe (Woosley &
Weaver, 1995; McWilliam et al., 2013; Kobayashi et al., 2020). Data for the
integrated light of dwarf galaxies are more scarce, but indicate Mg abundances
close to scaled-solar values, thus extending the trend of decreasing
[$\alpha$/Fe] ratio with decreasing galaxy mass towards lower masses (Gorgas
et al., 1997; Şen et al., 2018).

Abundance measurements for GCs provide a complementary insight into the
behaviour of the various abundances at lower metallicities compared to the
dominant field star component, and hence at an earlier stage of chemical
enrichment (Sect. 4.3). In metal-poor GCs, we find that Ca participates in the
general level of $\alpha$-element enhancement, but at higher metallicities it
tends to decrease towards scaled-solar values and thus approaches the
behaviour seen in integrated galaxy light. Most of the GCs have metallicities
below the knee in the relation of [$\alpha$/Fe], and at these relatively low
metallicities any differences in the mean abundance patterns between dwarf
galaxies and the large Local Group spirals are very minor.

In the time-delay model for chemical evolution (Tinsley, 1979; Matteucci &
Greggio, 1986), the abundance ratios at early times, for stars with
metallicities below the knee, are expected to depend mainly on the Type II SN
yields (see Figure 10 in Vincenzo et al. 2015 for an illustration). The high
degree of similarity of the abundance patterns observed for metal-poor GCs in
different environments may therefore not be surprising. However, since the
detailed yields do depend on the masses of the Type II SN progenitors (in
addition to their metallicity and spin), abundance ratios can, in principle,
provide constraints on the shape of the initial mass function (IMF) (Matteucci
& Brocato, 1990; Nissen et al., 1994; McWilliam, 1997; Wyse, 1998; Tolstoy et
al., 2003). According to chemical evolution models, the $\alpha$-element
abundance patterns of metal-poor stars in the solar neighbourhood are
consistent with an early IMF slope similar to, or slightly steeper, than that
of the classical Salpeter (1955) IMF (Tsujimoto et al., 1997; Wyse, 1998;
Hopkins, 2018). By way of illustration, Wyse & Gilmore (1992) calculated that
a change in IMF slope from $-2.3$ to $-1.1$ (where the Salpeter (1955) slope
is $-2.35$) would lead to an increase in $\mathrm{[O/Fe]}$ by about 0.4 dex
for stars in the Galactic bulge. The details may differ at lower metallicities
and for other $\alpha$-elements, with the effect on Mg, Si, and Ca expected to
be about half that on [O/Fe] (Vincenzo et al., 2015). Very roughly, a
difference in mean [$\alpha$/Fe] ratio of about 0.04 dex between dwarf and
spiral galaxies (Sect. 4.2) might then correspond to a difference in IMF slope
of about 0.2, suggesting that the early IMF in the dwarf galaxies in our
sample did not differ substantially from the Salpeter (1955) IMF.

The effects of IMF variations on models for chemical evolution have been
explored theoretically for dwarf galaxies (Recchi et al., 2014), including the
Sagittarius dSph (Vincenzo et al., 2015), with particular attention to
predictions for the Integrated Galactic IMF (IGIMF) theory (Weidner & Kroupa,
2005). In this theory, the IMF is coupled to the star formation rate (SFR),
with lower SFRs leading to a deficit of high-mass stars and a corresponding
lowering of the $\alpha$-element abundances. The SFRs at early times are
generally not well constrained for the dwarf galaxies in our sample. However,
the fact that these galaxies were able to form GCs suggests relatively high
SFRs. The brightest GCs in each galaxy reach $M_{V}\sim-8$ or brighter,
corresponding to masses greater than $2.7\times 10^{5}\,M_{\odot}$ (for
$M/L_{V}=2\,M_{\odot}/L_{V,\odot}$), which translates to SFRs of about
$0.8\,M_{\odot}\,\mathrm{yr}^{-1}$ or higher in the IGIMF theory (Vincenzo et
al., 2015). At such relatively high SFRs, the IGIMF theory predicts only minor
differences compared with models that assume classical IMFs. Comparing models
with SFRs of 0.5 $M_{\odot}\,\mathrm{yr}^{-1}$ and 100
$M_{\odot}\,\mathrm{yr}^{-1}$, Recchi et al. (2014) found a difference of only
0.015 dex in the predicted [$\alpha$/Fe] ratios on the plateau below the knee.
These arguments are thus consistent with the similarity of the
$\alpha$-element abundance ratios for GCs in dwarf and spiral galaxies, which
suggest that only minor differences in the IMF shape are allowed at low
metallicities.

The relatively minor differences in the abundance ratios at low metallicities
are in contrast to the more pronounced differences observed at higher
metallicities, such as a deficit of hydrostatic elements relative to explosive
elements in relatively metal-rich field stars in the Sagittarius dSph
(McWilliam et al., 2013). The latter may suggest that the later stages of
chemical evolution were characterised by a steeper, more top-light IMF as
predicted in the IGIMF theory for the lower SFRs expected at later times
(Vincenzo et al., 2015). At lower metallicities, the abundances of stars in
Sagittarius are more similar to those observed in the Milky Way halo (and to
our GC measurements), consistent with a normal IMF at earlier times (Hansen et
al., 2018). It is again worth recalling that some metal-poor GCs also show
very low Mg abundances, but linking this to IMF variations is made more
difficult by the fact that only some GCs are affected, and by the possibility
that Mg is affected by multiple populations.

###  5.2 Enrichment processes

Figure 14: Abundances of heavy elements with respect to the average of the
$\alpha$-elements. Symbols for our measurements as in Fig. 7.

In Fig. 14 we compare the abundances of Fe, Ba, and Eu, taken as
representative tracers of Type Ia SN, $s$-process, and $r$-process
nucleosynthesis, respectively. In the literature it is customary to plot these
elements relative to Mg, taking the latter as a tracer of Type II SN
nucleosynthesis (e.g. Skúladóttir & Salvadori, 2020). We have here replaced Mg
with an error-weighted average of the $\alpha$-element abundances (Mg, Si, Ca,
and Ti) to reduce the uncertainties, and to alleviate the impact of the
anomalously low $\mathrm{[Mg/Fe]}$ values seen in some GCs. As shown in Fig.
7, this approach is justified by the fairly similar dependencies of the
various $\alpha$-element abundances on metallicity, even though the heavier
elements (in particular Ca and Ti) have a more complicated nucleosynthetic
history.

The top panel in Fig. 14 shows [Fe/$\alpha$] vs. $\mathrm{[Fe/H]}$ and is, of
course, equivalent to the mean of the panels in Fig. 7, with the vertical axis
inverted, and leads to the same conclusion: for the most part, the GCs are
preferentially enriched in the $\alpha$-elements compared to scaled-solar
composition, consistent with enrichment on time scales shorter than those
characteristic of Type Ia SNe. Indeed, Fig. 14 suggests the alternative, but
equivalent and perhaps more intuitive formulation that the metal-poor GCs are
deficient in iron, due to the still ‘missing’ contribution from SN Ia
nucleosynthesis. As previously discussed, the main exceptions are Fornax 4,
NGC 6822-SC7, and HM33-B. While Fig. 14 shows an average of all four
$\alpha$-elements, the scatter is similar to those of [Ca/Fe] and [Ti/Fe]
alone, $\sigma_{[\mathrm{Fe}/\alpha]}=0.09$ dex, suggesting that at least part
of the dispersion is real.

Similar to [Fe/$\alpha$], the Ba and Eu abundance ratios, defined with respect
to either iron (Fig. 10) or the $\alpha$-elements (Fig. 14), display no
obvious differences depending on the host galaxy. In particular, the apparent
enhancement in [Ba/Fe] noted for the M33 GCs (Sect. 4.2) becomes less clear
relative to the $\alpha$-elements. To be more quantitative, we computed the
average [Ba/Fe] for the M33 GCs and for other GCs in a similar metallicity
range ($-2<\mathrm{[Fe/H]}<-0.8$). We found
$\langle\mathrm{[Ba/Fe]}\rangle_{\mathrm{M33}}=+0.25\pm 0.03$ for the M33 GCs
and $\langle\mathrm{[Ba/Fe]}\rangle_{\mathrm{other}}=+0.21\pm 0.01$ for the
other GCs, which is only a marginally significant difference. With respect to
the $\alpha$-elements, we instead found
$\langle[\mathrm{Ba}/\alpha]\rangle_{\mathrm{M33}}=-0.01\pm 0.03$ and
$\langle[\mathrm{Ba}/\alpha]\rangle_{\mathrm{other}}=0.00\pm 0.01$, which
confirms the visual impression from Fig. 14 that no significant difference is
present.

As noted in the introduction, the n-capture element abundances are often found
to differ significantly between field stars in classical dSph galaxies and the
Milky Way. However, at low metallicities, these differences are typically less
pronounced (Reichert et al., 2020), in agreement with our results for the GCs.
Ultra-faint dwarfs exhibit a larger scatter in the n-capture element
abundances that may reflect stochasticity in the enrichment processes
dominated by a few rare events (Ji et al., 2016; Marshall et al., 2019; Molero
et al., 2021). It is noteworthy that no GC in our sample exhibits the strongly
enhanced [Eu/Fe] abundance ratios, up to $\mathrm{[Eu/Fe]}>1$, recently found
for metal-poor stars in the Small and Large Magellanic Cloud (SMC and LMC;
Reggiani et al., 2021). These authors suggested that the Eu enhancement in the
SMC and LMC stars might result from a more gradual early chemical enrichment
history that would have allowed for a more substantial contribution from
delayed $r$-process enrichment due to neutron star mergers. By comparison with
our sample, the Magellanic Clouds would appear to have been fairly unique in
this respect, even when compared with relatively isolated, irregular galaxies
such as NGC 6822 and WLM. A few GCs are consistent with a more moderate Eu
enhancement of $\mathrm{[Eu/Fe]}\simeq 0.6-0.7$, as reported for the Gaia
Sausage (Aguado et al., 2021) and the Galactic GCs NGC 1261 and NGC 6934
(Koch-Hansen et al., 2021; Marino et al., 2021). Due to the challenging nature
of the Eu measurements in the integrated light, independent confirmation of
the results for individual clusters would be desirable. However, our
measurement of $\mathrm{[Eu/Fe]}=+0.63\pm 0.04$ for the Galactic GC NGC 362 is
fairly similar to the literature value of $\mathrm{[Eu/Fe]}=+0.57\pm 0.02$
(Shetrone & Keane, 2000; Pritzl et al., 2005).

The [Eu/Ba] ratio, plotted in the lower panel in Fig. 14, is frequently used
as an indicator of the importance of $r$\- versus $s$-process enrichment. The
$r$\- and $s$-process reference ratios are from McWilliam (1997). Our
integrated-light measurements mostly lie between the solar system and pure
$r$-process value, but there is a significant scatter. Some GCs, particularly
those towards the metal-rich end, even reach sub-solar [Eu/Ba] ratios,
implying a more important $s$-process contribution. Overall, these results are
similar to those found for Galactic GCs and field stars in the corresponding
metallicity range (McWilliam, 1997; Gratton et al., 2004). While Ba is indeed
considered a classical tracer of the $s$-process (according to Bisterzo et al.
(2014), about 85% of the Ba in the solar system is attributed to the
$s$-process), Ba production via the $r$-process becomes increasingly important
at early times (Pagel & Tautvaisiene, 1997; Cescutti et al., 2006). Europium
is, instead, a fairly pure $r$-process element, with a contribution of only 6%
from the $s$-process in the solar system (Bisterzo et al., 2014). The
identification of AGB stars as an important $s$-process production site is
fairly uncontroversial, but $s$-process elements are also produced in massive
stars, so the yields remain not well constrained, as the predictions depend on
different parameters in the models, such as rotation, metallicity, and the
size of the convective 13C pocket (Cescutti et al., 2006; Prantzos et al.,
2018; Limongi & Chieffi, 2018; Kobayashi et al., 2020). The details of the
$r$-process are even more uncertain, and it appears increasingly likely that
there are at least two $r$-process sources of which one operates on relatively
short time scales ($\la 10^{8}$ yr) and is likely linked to massive stars,
while the other involves a delay of up to several Gyr and may involve neutron-
star mergers (Skúladóttir & Salvadori, 2020; Molero et al., 2021). Therefore,
the variation in the relative abundances of Ba and Eu as a function of time
and metallicity may be expected to be rather more complicated than for the
[$\alpha$/Fe] ratio. Some of the difficulties encountered when modelling the
evolution of n-capture elements have been more fully discussed by Tautvaišienė
et al. (2021).

Internal variations in the abundances of neutron-capture elements have been
observed in NGC 7078 (M15) and a few other GCs (Roederer, 2011), although some
cases remain controversial (Cohen, 2011). It is reasonable to wonder how this
might affect the comparison of n-capture elements in GCs and field stars. In
NGC 7078, which is the clearest and best studied case, the member stars fall
into two groups with Ba, La, and Eu abundances differing by 0.2–0.4 dex, but
both groups have abundance patterns indicative of $r$-process enrichment.
Interestingly, both groups independently show the Na-O anti-correlation that
is generally associated with multiple populations in GCs (Sneden et al., 1997;
Worley et al., 2013). While the Na spreads in GCs cause clear systematic
differences between field stars and mean GC abundances (Fig. 8), internal
spreads in n-capture element abundances appear to be relatively rare, and in
any case do not make NGC 7078 a significant outlier in the relevant relations.
A satisfactory explanation for the spreads in n-capture elements in GCs is
even more elusive than for the light element abundance variations. The
possibility that $r$-process self-enrichment in GCs may be caused by neutron-
star mergers has been discussed in the literature (e.g. Zevin et al., 2019),
but it seems clear from Fig. 10 that such processes do not leave any
significant signature in the form of a detectable offset in [Eu/Fe] between
GCs and field stars (see also Sakari et al., 2013).

###  5.3 The extremely metal-poor GC M31 EXT8

By far the most metal-poor GC in our sample is M31 EXT8. The spectroscopic
observations of this cluster were previously discussed in Larsen et al. (2020)
and its CMD was discussed in Larsen et al. (2021).

The metallicity reported here ($\mathrm{[Fe/H]}=-2.81\pm 0.04$) is about 0.1
dex higher than that found in Larsen et al. (2020), mainly due to the
application of NLTE corrections (our LTE value is $\mathrm{[Fe/H]}=-2.88$; see
Appendix D). As the NLTE corrections also lead to an increase in the
metallicites of the other clusters (albeit less so at higher metallicities),
the differential change with respect to other GCs in our sample is even
smaller. In any case, the slight increase does not change the conclusion that
M31 EXT8 is, by a considerable margin, the most metal-poor GC currently known.
It was already noted in previous analysis that the [Mg/Fe] is peculiarly low,
while the other $\alpha$-element abundances are fairly typical of Milky Way
field stars at the corresponding metallicity. We note that the [Mg/Fe]
measurement in Larsen et al. (2020) was based on the Mg $b$ triplet, while the
measurement here is obtained from the weaker Mg i lines that were also used
for other clusters in our sample. Nevertheless, we recover the low [Mg/Fe]
value previously found.

At the low metallicity of EXT8, the uncertainties on most abundance ratios are
relatively large owing to the weakness of the spectral features. There is a
suggestion that [Ni/Fe] is somewhat enhanced, but it is not very unusual
compared to the Milky Way data when the $\sim 0.2$ dex NLTE correction is
accounted for. The [Ba/Fe] value, which has a small uncertainty, is also
relatively high, and falls near the upper envelope of $\mathrm{[Ba/Fe]}$
values for Galactic halo field stars (Fig. 10). However, [Mg/Fe] remains the
most significant outlier in abundance space.

###  5.4 Outlook: Refining the analysis techniques

While the analysis presented herein has been updated and improved in a variety
of ways, it is certainly not definitive. When comparing with model
predictions, it is clearly important to eliminate systematic biases in the
analysis as much as possible. Even when comparing differentially with other
datasets, LTE vs. LTE is not necessarily a like-with-like comparison, owing to
the fact that different stellar types and spectral features are affected in
different ways by NLTE effects (e.g. Eitner et al., 2019). Here we have
applied NLTE corrections for many lines and elements to integrated-light
analysis for the first time, and we find that our NLTE abundances for the GCs
generally agree well with the corresponding NLTE values for metal-poor Milky
Way field stars.

As for individual stars, some elements are more strongly affected by NLTE
effects than others. In some cases, application of NLTE corrections can lead
to quantitatively different trends with metallicity and different
astrophysical implications. A case in point is [Mn/Fe] which displays a strong
increasing trend as a function of metallicity in LTE, but remains
approximately flat in NLTE. As discussed in Eitner et al. (2020), the flat
trend of slightly sub-solar [Mn/Fe] ratios can be reproduced in galactic
chemical evolution models in which the Type Ia SN contribution to Mn
production is mainly due to sub-Chandrasekhar mass progenitors, with a
significant contribution from core collapse SNe as well. In contrast, the
steeper trend found in LTE would support Type Ia SN progenitors with near-
Chandrasekhar masses.

A similar case to Mn may be Cu. We have not here included NLTE corrections for
this element, and our integrated-light analysis (Fig. 10) shows the trend of
increasing [Cu/Fe] with metallicity that is also commonly observed in field
stars. This is often taken as evidence that Cu behaves as a secondary element,
produced by the weak $s$-process in massive stars (Romano & Matteucci, 2007).
However, NLTE analyses of Cu tend to find a much shallower trend with
metallicity that more closely resembles the behaviour expected for a primary
element (Yan et al., 2015; Korotin et al., 2018; Shi et al., 2018). Hence, Cu
is another case for which the details of the analysis have important
consequences for the astrophysical interpretation, and it might therefore be
worthwhile to compute integrated-light NLTE corrections for Cu. Taken
together, the abundances of Mn, Zn, and Cu may provide important constraints
on Type Ia SN models, in particular the role of the double-detonation scenario
in which detonation of a helium-rich surface layer may lead to increased
production of these three elements (Lach et al., 2020).

Of course, correction for NLTE effects addresses just one of several
approximations made in classical abundance analysis. Another is the assumption
that the physical properties of stellar atmospheres are time-independent and
depend only on the depth in the atmosphere. In the last decade, significant
progress has been made in the computation of 3-dimensional radiation-
hydrodynamic models (e.g. Magic et al., 2013) and the resulting stellar
spectra, from which it is clear that the effects on the derived abundances can
be significant at the level of 0.1 dex or more for some elements (Bergemann et
al., 2019; Semenova et al., 2020; Amarsi et al., 2019). One appealing aspect
of 3-D radiation-hydrodynamic models is that convective motions are explicitly
accounted for, which eliminates the mixing length, micro-, and macro-turbulent
velocities as free parameters in the analysis.

##  6 Summary and conclusions

We have presented homogeneous integrated-light abundance measurements for a
sample of 45 GCs, including NLTE corrections for several elements. The sample
includes clusters in most Local Group galaxies that host GC systems, although
it is mostly limited to the brighter half of the GC luminosity function and to
relatively compact clusters that are better suited for measurements of their
integrated light with single-slit echelle spectrographs. Compared with
previously published analyses of a subset of the data, the current analysis
has been updated in a number of ways, including a critical revision of the
line list, a modified prescription for the assignment of microturbulent
velocities, and the use of ATLAS12 model atmospheres with self-consistent
chemical composition.

Our main results can be summarised as follows:

  * •

We have extended the formalism for integrated-light NLTE corrections developed
by Eitner et al. (2019) to account for simultaneous fitting of multiple
spectral lines.

  * •

To first order, GCs in different galaxies have very similar abundance
patterns. Metal-poor GCs ($\mathrm{[Fe/H]}\la-1.5)$ have enhanced
$\alpha$-element abundances in all galaxies, and the overall scatter in the
$\alpha$-element abundances is less than 0.1 dex. As in previous studies, we
find peculiarly low [Mg/Fe] values for a fraction of the metal-poor GCs.

  * •

The similarity of the $\alpha$-element abundances indicates that the GC formed
in environments with similar IMFs. There is possibly a small offset of about
0.04 dex between the mean $\alpha$-element abundances of GCs in dwarf galaxies
and in the spirals, which we estimate translates to a variation in the IMF
slope of at most 0.2 dex.

  * •

From a principal components analysis, the $\alpha$-element abundance
variations are found to be correlated with variations in [Na/Fe], [Sc/Fe],
[Ni/Fe], and [Zn/Fe]. These correlations are driven mainly by three clusters:
Fornax 4, NGC 6822-SC7, and HM33-B. Fornax 4 and NGC 6822-SC7 are the most
metal-rich GCs in their respective host galaxies, and the similarity of the
abundance patterns of HM33-B to the two other clusters may suggest an
accretion origin for HM33-B.

  * •

The n-capture element abundances are also fairly uniform across our sample. We
find no GCs with strongly enhanced $r$-process signatures, as reported for
metal-poor stars in the Magellanic Clouds (Reggiani et al., 2021) and in
ultra-faint dwarfs such as Reticulum II (Ji et al., 2016; Roederer et al.,
2016)

  * •

In view of the very similar abundance patterns at low metallicities, and in
agreement with previous studies, we conclude that chemical tagging of GCs is
likely to work best at metallicities above $\mathrm{[Fe/H]}\approx-1.5$, where
differences between the chemical composition of stellar populations in host
dwarf galaxies become more apparent.

  * •

We measure a line-of-sight velocity dispersion of about 11.7 km s-1 and a
corresponding mass-to-light ratio of $M_{\mathrm{dyn}}/L_{V}\simeq
2.0\,M_{\odot}/L_{V,\odot}$ for the cluster F46 in NGC 2403, consistent with
the value expected for a moderately metal-poor old GC.

Beyond the results summarised above, the analysis presented here may also
serve as a reference for future studies of larger samples of GCs beyond the
Local Group. With the next generation of 30-40 m class telescopes, it will be
possible to obtain high S/N spectra for GCs well beyond the Local Group,
including in galaxies with rich GC systems (such as the Sombrero galaxy and
NGC 5128), of which a substantial fraction will fall in the more metal-rich
regime where interesting differences may be expected.

###### Acknowledgements.

JS acknowledges support from the Packard Foundation. AJR was supported by
National Science Foundation Grant AST-1616710 and as a Research Corporation
for Science Advancement Cottrell Scholar. MB is supported through the Lise
Meitner grant from the Max Planck Society. We acknowledge support by the
Collaborative Research centre SFB 881 (projects A5, A10), Heidelberg
University, of the Deutsche Forschungsgemeinschaft (DFG, German Research
Foundation). This project has received funding from the European Research
Council (ERC) under the European Union’s Horizon 2020 research and innovation
programme (Grant agreement No. 949173). Funding for the Sloan Digital Sky
Survey (SDSS) has been provided by the Alfred P. Sloan Foundation, the
Participating Institutions, the National Aeronautics and Space Administration,
the National Science Foundation, the U.S. Department of Energy, the Japanese
Monbukagakusho, and the Max Planck Society. The SDSS Web site is
http://www.sdss.org/. The SDSS is managed by the Astrophysical Research
Consortium (ARC) for the Participating Institutions. The Participating
Institutions are The University of Chicago, Fermilab, the Institute for
Advanced Study, the Japan Participation Group, The Johns Hopkins University,
Los Alamos National Laboratory, the Max-Planck-Institute for Astronomy (MPIA),
the Max-Planck-Institute for Astrophysics (MPA), New Mexico State University,
University of Pittsburgh, Princeton University, the United States Naval
Observatory, and the University of Washington. This research has made use of
ESASky, developed by the ESAC Science Data Centre (ESDC) team and maintained
alongside other ESA science mission’s archives at ESA’s European Space
Astronomy Centre (ESAC, Madrid, Spain). Some of the data presented herein were
obtained at the W. M. Keck Observatory, which is operated as a scientific
partnership among the California Institute of Technology, the University of
California and the National Aeronautics and Space Administration. The
Observatory was made possible by the generous financial support of the W. M.
Keck Foundation. The authors wish to recognize and acknowledge the very
significant cultural role and reverence that the summit of Maunakea has always
had within the indigenous Hawaiian community. We are most fortunate to have
the opportunity to conduct observations from this mountain. We thank A.
Wasserman for assistance with the HIRES observations and J. van Eijck for help
with selection of lines for NLTE analysis. We are grateful to the anonymous
referee for carefully reading the manuscript and delivering a timely report
which contained several useful suggestions.

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##  Appendix A Observations

Table 11: Observations

Cluster | Instrument | Date (UT) | Range (Å) |  Texp (s) | S/N | $V$ | RA, Dec (J2000.0)
---|---|---|---|---|---|---|---
NGC 104 | UVES |  22 Jul 20151 | 4150 - 6200 | $2\times 1500$ | 546 |  3.958 | 00:24:05.67 |  $-$72:04:52.68
| UVES |  6 Aug 20192 | 5660 - 9460 | $2\times 1500$ |  583⋆ |  |  |
NGC 362 | UVES |  22 Jul 20151 | 4150 - 6200 | $1\times 1500$ | 408 |  6.408 | 01:03:14.26 |  $-$70:50:55.68
| UVES |  6 Aug 20192 | 5660 - 9460 | $2\times 1500$ |  596⋆ |  |  |
NGC 6254 | UVES |  22-23 Jul 20151 | 4150 - 6200 | $8\times 1800$ | 373 |  6.608 | 16:57:09.05 |  $-$04:06:01.18
| UVES |  6-7 Aug 20192 | 5660 - 9460 | $8\times 1800$ |  466⋆ |  |  |
NGC 6388 | UVES |  22 Jul 20151 | 4150 - 6200 | $2\times 1200$ | 561 |  6.728 | 17:36:17.23 |  $-$44:44:07.88
| UVES |  6 Aug 20192 | 5660 - 9460 | $2\times 1200$ |  635⋆ |  |  |
NGC 6752 | UVES |  23 Jul 20151 | 4150 - 6200 | $4\times 1800$ | 617 |  5.408 | 19:10:52.11 |  $-$59:59:04.48
| UVES |  7 Aug 20192 | 5660 - 9460 | $4\times 1800$ |  677⋆ |  |  |
NGC 7078 | UVES |  22 Jul 20151 | 4150 - 6200 | $2\times 1800$ | 580 |  6.208 | 21:29:58.33 |  $+$12:10:01.28
| UVES |  6 Aug 20192 | 5660 - 9460 | $2\times 1800$ |  563⋆ |  |  |
NGC 7099 | UVES |  23 Jul 20151 | 4150 - 6200 | $4\times 1800$ | 440 |  7.198 | 21:40:22.12 |  $-$23:10:47.58
| UVES |  7 Aug 20192 | 5660 - 9460 | $4\times 1800$ |  380⋆ |  |  |
M31 006-058 | HIRES |  2-3 Oct 20072 | 3900 - 8350 | $10\times 1800$ | 329 |  15.509 | 00:40:26.49 |  $+$41:27:26.79
M31 012-064 | HIRES |  19 Oct 20072 | 3550 - 6300 | $4\times 1800$ | 190 |  15.099 | 00:40:32.47 |  $+$41:21:44.29
M31 019-072 | HIRES |  18 Oct 20072 | 3550 - 6300 | $4\times 1800$ | 285 |  14.939 | 00:40:52.53 |  $+$41:18:53.49
M31 058-119 | HIRES |  1 Oct 20072 | 3900 - 8350 | $9\times 1800$ | 394 |  14.979 | 00:41:53.01 |  $+$40:47:09.79
M31 082-144 | HIRES |  19 Oct 20072 | 3550 - 6300 | $4\times 1800$ | 108 |  15.549 | 00:42:15.84 |  $+$41:01:14.39
M31 163-217 | HIRES |  3 Oct 20072 | 3900 - 8350 | $7\times 1800$ | 386 |  15.059 | 00:43:17.64 |  $+$41:27:44.99
M31 171-222 | HIRES |  3 Oct 20072 | 3900 - 8350 | $5\times 1800$ | 305 |  15.229 | 00:43:25.61 |  $+$41:15:37.19
M31 174-226 | HIRES |  18 Oct 20072 | 3550 - 6300 | $4\times 1800$ | 139 |  15.479 | 00:43:30.30 |  $+$41:38:56.29
M31 225-280 | HIRES |  1 Oct 20072 | 3900 - 8350 | $7\times 1800$ | 618 |  14.169 | 00:44:29.56 |  $+$41:21:35.39
M31 338-076 | HIRES |  18 Oct 20072 | 3550 - 6300 | $4\times 1800$ | 316 |  14.259 | 00:40:58.87 |  $+$40:35:47.89
M31 358-219 | HIRES |  2 Oct 20072 | 3900 - 8350 | $8\times 1800$ | 300 |  15.229 | 00:43:17.86 |  $+$39:49:13.29
M31 EXT8 | HIRES |  25 Oct 20193 | 3850 - 8170 | $2\times 1200$ | 216 |  15.609 | 00:53:14.53 |  $+$41:33:24.59
M33 H38 | HIRES |  26 Oct 19984 | 3730 - 6170 | $7\times 1800$ | 44 |  17.2510 | 01:33:52.12 |  $+$30:29:03.619
M33 M9 | HIRES |  26 Oct 19984 | 3730 - 6170 | $9\times 1800$ | 81 |  17.1210 | 01:34:30.22 |  $+$30:38:12.719
M33 R12 | HIRES |  25 Oct 19984 | 3730 - 6170 | $7\times 1800$ | 94 |  16.3810 | 01:34:08.01 |  $+$30:38:38.019
M33 U49 | HIRES |  25 Oct 19984 | 3730 - 6170 | $8\times 1800$ | 57 |  16.2510 | 01:33:45.01 |  $+$30:47:46.719
M33 R14 | HIRES |  01 Nov 20182 | 3900 - 8160 | $4\times 1800$ | 142 |  16.4810 | 01:34:02.44 |  $+$30:40:40.619
M33 U77 | HIRES |  25 Oct 20192 | 3850 - 8170 | $6\times 1800$ | 91 |  17.1910 | 01:33:28.68 |  $+$30:41:34.919
M33 CBF28 | HIRES |  25 Oct 20192 | 3850 - 8170 | $4\times 1800$ | 216 |  16.3711 | 01:34:01.91 |  $+$30:39:45.911
M33 HM33B | HIRES |  25 Oct 20192 | 3850 - 8170 | $6\times 1800$ | 32 |  17.7612 | 01:36:02.12 |  $+$29:57:49.412
N147 Hodge II | HIRES |  25 Sep 20165 | 3930 - 8170 | $5\times 1800$ | 39 |  18.0613 | 00:33:13.6 |  $+$48:28:48.713
N147 Hodge III | HIRES |  05 Oct 20155 | 3610 - 8170 | $4\times 1800$ | 96 |  16.5813 | 00:33:15.2 |  $+$48:27:23.113
N147 PA1 | HIRES |  05 Oct 20155 | 3970 - 8170 | $1800+865$ | 92 |  16.9613 | 00:32:35.3 |  $+$48:19:48.013
|  |  25 Sep 20165 |  | $2\times 1800$ |  |  |  |
N147 PA2 | HIRES |  25 Sep 20165 | 3930 - 8170 | $5\times 1800$ | 112 |  17.3713 | 00:33:43.3 |  $+$48:38:45.013
N147 SD7 | HIRES |  05 Oct 20155 | 3610 - 8170 | $4\times 1800$ | 103 |  17.0013 | 00:32:22.2 |  $+$48:31:27.013
N185 FJJ-III | HIRES |  25 Sep 20172 | 3850 - 8170 | $4\times 1800$ | 79 |  16.5813 | 00:39:03.8 |  $+$48:19:57.513
N185 FJJ-V | HIRES |  25 Sep 20172 | 3850 - 8170 | $4\times 1800$ | 100 |  16.7113 | 00:39:13.4 |  $+$48:23:04.913
N185 FJJ-VIII | HIRES |  26 Sep 20172 | 3850 - 8170 | $5\times 1800$ | 91 |  17.5713 | 00:39:23.7 |  $+$48:18:45.113
N205 Hubble I | HIRES |  25 Sep 20172 | 3850 - 8170 | $4\times 1800$ | 163 |  16.914 | 00:40:30.70 |  $+$41:36:55.720
N205 Hubble II | HIRES |  25 Sep 20172 | 3850 - 8170 | $4\times 1800$ | 183 |  16.714 | 00:40:31.88 |  $+$41:39:17.020
N6822 Hubble VII | HIRES |  25 Sep 20172 | 3850 - 8170 | $2\times 1800$ | 168 |  15.7915 | 19:44:55.8 |  $-$14:48:56.215
N6822 SC6 | HIRES |  25 Sep 20165 | 3930 - 8170 | $2\times 1800$ | 142 |  15.9715 | 19:45:37.0 |  $-$14:41:10.815
N6822 SC7 | HIRES |  05 Oct 20155 | 3610 - 8170 | $1800+1139$ | 181 |  15.4215 | 19:46:00.7 |  $-$14:32:35.015
WLM-GC | UVES | 29 Jul - | 4170 - 6200 | $12\times 1475$ | 205 |  16.0616 | 00:01:49.54 |  $-$15:27:31.020
|  |  02 Aug 20066 |  |  |  |  |  |
Fornax 3 | UVES |  19 Nov 20067 | 4170 - 6210 | $4\times 2400$ | 264 |  12.6117 | 02:39:52.5 |  $-$34:16:0821
Fornax 4 | UVES |  19-20 Nov 20067 | 4170 - 6210 | $4\times 2400$ | 192 |  13.5717 | 02:40:09.0 |  $-$34:32:2421
Fornax 5 | UVES |  20 Nov 20067 | 4170 - 6210 | $4\times 2400$ | 144 |  13.4217 | 02:42:21.15 |  $-$34:06:04.721
NGC 2403 F46 | HIRES |  25 Oct 20192 | 3850 - 8170 | $2\times 1800+1200$ | 121 |  17.818 | 07:36:29.17 |  $+$65:40:33.520

151515The S/N values are given per Å at 5000 Å, except for entries marked with
a star (⋆) for which they are given at 6000 Å.

Spectroscopy: (1) Larsen et al. (2017); (2) this work; (3) Larsen et al.
(2020); (4) Larsen et al. (2002b); (5) Larsen et al. (2018a); (6) Larsen et
al. (2014); (7) Larsen et al. (2012); Integrated magnitudes and coordinates:
(8) Harris (1996, 2010 revision); (9) Revised Bologna Catalogue v5.0 (Galleti
et al. 2004); (10) Sarajedini et al. (1998); (11) Chandar et al. (1999); (12)
Huxor et al. (2009); (13) Veljanoski et al. (2013); (14) Sharina et al.
(2006); (15) Veljanoski et al. (2015); (16) Sandage & Carlson (1985); (17)
Webbink (1985); (18) Sect. 4.1; (19) Beasley et al. (2015); (20) Gaia EDR3
(Brown et al. 2021) via ESASky; (21) Mackey & Gilmore (2003).

##  Appendix B Spectral windows

Table 12: Windows used for spectral fitting.

Elem. Range (Å) Elem. Range (Å) Fe 4573.0–4600.0 Sc 4739.0–4758.0 Fe
4600.0–4618.0 Sc 5026.0–5036.0 Fe 4631.0–4660.0 Sc 5521.0–5531.0 Fe
4671.0–4686.0 Sc 5638.0–5690.0 Fe 4705.0–4714.0 Sc 6206.0–6216.0 Fe
4724.0–4750.0 Ti 4500.0–4519.5 Fe 4866.0–4883.0 Ti 4551.0–4570.0 Fe
4886.0–4896.0 Ti 4586.5–4596.0 Fe 4897.0–4915.0 Ti 4638.0–4660.0 Fe
4915.0–4929.0 Ti 4680.0–4698.0 Fe 4936.0–4944.0 Ti 4802.0–4821.0 Fe
4944.0–4953.0 Ti 4975.0–5000.0 Fe 4952.0–4962.0 Ti 5000.0–5030.0 Fe
4963.0–4976.0 Ti 5060.0–5075.0 Fe 4975.0–4998.0 Ti 5331.0–5341.0 Fe
5008.0–5017.0 Ti 5376.0–5386.0 Fe 5045.0–5064.0 Ti 5510.0–5520.0 Fe
5066.0–5115.0 Ti 5860.0–5875.0 Fe 5118.0–5150.0 Ti 5912.0–5922.0 Fe
5250.0–5259.0 Cr 4535.0–4550.0 Fe 5271.0–5289.0 Cr 4611.0–4631.0 Fe
5300.0–5345.0 Cr 4646.0–4657.0 Fe 5358.0–5375.0 Cr 4703.0–4723.0 Fe
5378.0–5400.0 Cr 4751.0–4761.0 Fe 5400.0–5420.0 Cr 4796.0–4806.0 Fe
5420.0–5460.0 Cr 4824.0–4834.0 Fe 5460.0–5475.5 Cr 4866.0–4876.0 Fe
5494.0–5510.0 Cr 4931.0–4947.0 Fe 5529.0–5539.0 Cr 5063.0–5096.0 Fe
5566.5–5590.0 Cr 5117.0–5127.0 Fe 5610.0–5630.0 Cr 5270.0–5281.0 Fe
5682.0–5714.0 Cr 5292.0–5302.0 Fe 5858.5–5865.0 Cr 5341.0–5353.0 Fe
5970.0–5980.0 Cr 5407.0–5413.0 Fe 6001.0–6019.0 Cr 5783.0–5793.0 Fe
6021.0–6029.5 Cr 6325.0–6335.0 Fe 6053.0–6082.0 Cr 6973.0–6983.0 Fe
6131.0–6140.0 Mn 4750.0–4790.0 Fe 6144.0–6160.0 Mn 6010.0–6030.0 Fe
6170.0–6185.0 Ni 4600.0–4610.0 Na 5677.0–5695.0 Ni 4644.0–4654.0 Na
6149.0–6166.0 Ni 4681.0–4691.0 Mg 4347.0–4357.0 Ni 4709.0–4719.0 Mg
4565.0–4576.0 Ni 4824.0–4835.0 Mg 4700.0–4707.0 Ni 4899.0–4909.0 Mg
5523.0–5531.5 Ni 4931.0–4942.0 Mg 5705.0–5715.0 Ni 4975.0–4985.0 Si
5661.0–5671.0 Ni 5075.0–5089.0 Si 5685.0–5695.0 Ni 5098.0–5108.0 Si
5767.0–5777.0 Ni 5141.0–5151.0 Si 6150.0–6160.0 Ni 5472.0–5482.0 Si
6232.0–6250.0 Ni 5707.0–5717.0 Si 7400.0–7427.0 Ni 6103.0–6113.0 Ca
4420.0–4440.0 Ni 6172.0–6182.0 Ca 4451.0–4461.0 Cu 5101.0–5112.0 Ca
4573.0–4590.0 Cu 5777.0–5787.0 (DIB) Ca 5255.0–5268.0 Zn 4717.0–4727.0 Ca
5347.0–5357.0 Zn 4805.0–4815.0 Ca 5507.0–5517.0 Zr 6124.0–6147.0 Ca
5576.0–5602.0 Ba 4551.0–4560.0 Ca 5852.0–5862.0 Ba 4929.0–4939.0 Ca
6098.0–6127.0 Ba 5849.0–5859.0 Ca 6151.0–6174.0 Ba 6135.0–6145.0 Ba
6492.0–6502.0 Eu 4431.0–4441.0 Eu 6640.0–6650.0

161616The Cu window at 5777 Å- 5787 Å is affected by a diffuse interstellar
absorption band.

##  Appendix C NLTE abundance measurements

Tables 13-15 list the average abundance measurements from our analysis, based
on DSEP isochrones and empirical horizontal branches. The measurements in
these Tables include NLTE corrections on the abundance measurements when
available.

Table 13: Results for Fe, Na, Mg, Si, Ca, and Ti.

Cluster [Fe/H] $\sigma_{\langle\mathrm{Fe}\rangle}$ $S_{\mathrm{Fe}}$ N
[Na/Fe] $\sigma_{\langle\mathrm{Na}\rangle}$ $S_{\mathrm{Na}}$ N [Mg/Fe]
$\sigma_{\langle\mathrm{Mg}\rangle}$ $S_{\mathrm{Mg}}$ N [Si/Fe]
$\sigma_{\langle\mathrm{Si}\rangle}$ $S_{\mathrm{Si}}$ N [Ca/Fe]
$\sigma_{\langle\mathrm{Ca}\rangle}$ $S_{\mathrm{Ca}}$ N [Ti/Fe]
$\sigma_{\langle\mathrm{Ti}\rangle}$ $S_{\mathrm{Ti}}$ N NGC 0104 $-0.735$
0.008 0.019 39 $+0.237$ 0.038 0.065 2 $+0.404$ 0.027 0.058 4 $+0.376$ 0.023
0.044 6 $+0.238$ 0.018 0.030 9 $+0.412$ 0.015 0.026 14 NGC 0362 $-1.073$ 0.009
0.019 39 $-0.207$ 0.043 0.005 2 $+0.169$ 0.030 0.027 4 $+0.155$ 0.026 0.051 6
$+0.140$ 0.019 0.028 9 $+0.417$ 0.016 0.033 14 NGC 6254 $-1.485$ 0.009 0.018
39 $-0.204$ 0.048 0.009 2 $+0.295$ 0.031 0.050 4 $+0.279$ 0.032 0.051 6
$+0.260$ 0.020 0.048 9 $+0.422$ 0.017 0.034 14 NGC 6388 $-0.537$ 0.008 0.025
39 $+0.202$ 0.038 0.090 2 $+0.113$ 0.028 0.073 4 $+0.218$ 0.023 0.060 6
$+0.040$ 0.018 0.047 9 $+0.262$ 0.016 0.027 14 NGC 6752 $-1.704$ 0.009 0.014
39 $+0.064$ 0.043 0.037 2 $+0.312$ 0.030 0.074 4 $+0.408$ 0.028 0.016 6
$+0.326$ 0.018 0.022 9 $+0.361$ 0.016 0.028 14 NGC 7078 $-2.293$ 0.010 0.020
38 $-0.057$ 0.091 0.002 2 $+0.147$ 0.035 0.031 4 $+0.471$ 0.065 0.115 3
$+0.262$ 0.022 0.031 9 $+0.431$ 0.021 0.046 12 NGC 7099 $-2.243$ 0.010 0.020
39 $-0.035$ 0.082 0.025 2 $+0.295$ 0.035 0.039 4 $+0.456$ 0.054 0.084 5
$+0.260$ 0.022 0.023 9 $+0.372$ 0.020 0.020 14 N147 HII $-1.441$ 0.029 0.059
37 $+0.250$ 0.119 0.048 2 $+0.201$ 0.165 0.120 4 $+0.679$ 0.115 0.062 2
$+0.253$ 0.062 0.050 8 $+0.661$ 0.134 0.080 6 N147 HIII $-2.363$ 0.024 0.041
34 $+0.408$ 0.146 … 1 $+0.069$ 0.120 0.123 3 $+0.152$ 0.274 … 1 $+0.299$ 0.052
0.060 6 $+0.370$ 0.084 0.067 8 N147 PA-1 $-2.216$ 0.023 0.042 34 $+0.281$
0.218 … 1 $+0.209$ 0.110 0.101 4 $+0.574$ 0.363 0.159 2 $+0.178$ 0.051 0.039 7
$+0.379$ 0.089 0.076 8 N147 PA-2 $-1.919$ 0.017 0.026 38 $+0.110$ 0.127 0.019
2 $+0.337$ 0.084 0.061 4 $+0.150$ 0.127 0.232 2 $+0.332$ 0.036 0.042 9
$+0.426$ 0.052 0.064 11 N147 SD7 $-1.887$ 0.017 0.037 37 $-0.184$ 0.179 0.316
2 $+0.368$ 0.095 0.156 3 $+0.549$ 0.066 0.105 4 $+0.198$ 0.035 0.061 9
$+0.435$ 0.054 0.051 10 N185 FJJ-III $-1.754$ 0.020 0.031 36 $+0.323$ 0.114 …
1 $+0.472$ 0.076 0.147 5 $+0.419$ 0.099 0.142 6 $+0.342$ 0.045 0.067 9
$+0.443$ 0.059 0.082 11 N185 FJJ-V $-1.780$ 0.017 0.031 36 $-0.114$ 0.162 … 1
$+0.186$ 0.070 0.123 5 $+0.329$ 0.091 0.157 5 $+0.289$ 0.035 0.040 9 $+0.412$
0.052 0.077 11 N185 FJJ-VIII $-1.749$ 0.017 0.026 37 $+0.026$ 0.123 0.010 2
$-0.049$ 0.077 0.080 5 $+0.286$ 0.088 0.166 4 $+0.317$ 0.036 0.043 9 $+0.387$
0.056 0.070 11 N205 HubbleI $-1.410$ 0.012 0.025 37 $-0.124$ 0.073 0.072 2
$+0.417$ 0.041 0.060 5 $+0.301$ 0.048 0.025 6 $+0.236$ 0.026 0.031 9 $+0.386$
0.028 0.048 12 N205 HubbleII $-1.348$ 0.011 0.023 37 $+0.014$ 0.063 0.012 2
$+0.318$ 0.040 0.054 5 $+0.315$ 0.046 0.083 6 $+0.218$ 0.024 0.043 9 $+0.326$
0.027 0.030 12 N6822 SC6 $-1.689$ 0.015 0.025 37 $+0.015$ 0.104 0.031 2
$+0.255$ 0.058 0.076 5 $+0.043$ 0.111 0.144 2 $+0.206$ 0.034 0.044 9 $+0.282$
0.046 0.063 12 N6822 SC7 $-1.130$ 0.011 0.019 36 $-0.663$ 0.084 0.041 2
$-0.235$ 0.050 0.027 4 $-0.010$ 0.045 0.085 6 $-0.047$ 0.025 0.033 9 $-0.006$
0.031 0.066 12 N6822 HVII $-1.666$ 0.014 0.035 36 $+0.049$ 0.079 0.014 2
$-0.031$ 0.059 0.059 5 $+0.283$ 0.050 0.114 6 $+0.073$ 0.030 0.040 9 $+0.264$
0.038 0.075 12 M33 H38 $-1.090$ 0.023 0.051 30 $-0.262$ 0.153 … 1 $+0.144$
0.136 0.208 2 … … … … $+0.324$ 0.076 0.146 5 $+0.393$ 0.058 0.086 11 M33 M9
$-1.634$ 0.019 0.027 30 $-0.014$ 0.123 0.054 2 $-0.090$ 0.129 0.051 2 $+0.489$
0.256 0.006 2 $+0.220$ 0.051 0.067 7 $+0.472$ 0.046 0.056 13 M33 R12 $-0.861$
0.014 0.023 30 $-0.151$ 0.064 0.084 2 $+0.161$ 0.082 0.096 2 $+0.196$ 0.101
0.140 3 $+0.202$ 0.037 0.050 7 $+0.346$ 0.031 0.043 14 M33 U49 $-1.333$ 0.024
0.036 30 $-0.098$ 0.141 0.068 2 $+0.304$ 0.183 0.054 2 $+0.453$ 0.209 0.040 2
$+0.149$ 0.069 0.132 6 $+0.526$ 0.058 0.060 14 M33 R14 $-1.020$ 0.013 0.021 37
$+0.004$ 0.063 0.001 2 $+0.162$ 0.046 0.031 5 $+0.350$ 0.043 0.041 6 $+0.209$
0.028 0.039 9 $+0.230$ 0.036 0.048 12 M33 U77 $-1.797$ 0.020 0.038 35 $-0.285$
0.232 … 1 $+0.147$ 0.093 0.187 4 $+0.329$ 0.129 0.056 2 $+0.400$ 0.043 0.070 8
$+0.446$ 0.061 0.049 12 M33 CBF28 $-1.128$ 0.011 0.019 35 $+0.046$ 0.051 0.142
2 $+0.209$ 0.034 0.065 5 $+0.181$ 0.037 0.045 6 $+0.201$ 0.023 0.015 9
$+0.312$ 0.024 0.039 12 M33 HM33B $-1.218$ 0.032 0.068 33 $-0.087$ 0.199 0.479
2 $-0.267$ 0.197 0.234 4 $+0.365$ 0.188 0.061 3 $-0.000$ 0.083 0.162 9
$+0.300$ 0.109 0.136 11 WLM GC $-1.849$ 0.014 0.029 37 $+0.021$ 0.151 0.009 2
$+0.038$ 0.064 0.073 4 $+0.185$ 0.305 … 1 $+0.255$ 0.034 0.056 9 $+0.407$
0.032 0.056 14 Fornax 3 $-2.284$ 0.013 0.021 39 $-0.073$ 0.202 … 1 $-0.071$
0.057 0.099 4 $+0.642$ 0.219 0.161 2 $+0.154$ 0.034 0.056 8 $+0.290$ 0.030
0.042 13 Fornax 4 $-1.237$ 0.010 0.019 39 $-0.390$ 0.074 0.003 2 $-0.069$
0.044 0.043 4 $+0.065$ 0.075 0.122 4 $+0.033$ 0.025 0.027 9 $+0.162$ 0.023
0.025 13 Fornax 5 $-2.058$ 0.016 0.027 39 $+0.319$ 0.138 … 1 $+0.048$ 0.078
0.080 4 $+0.669$ 0.620 … 1 $+0.208$ 0.040 0.055 9 $+0.309$ 0.040 0.079 11 M31
006-058 $-0.527$ 0.009 0.018 37 $+0.300$ 0.039 0.044 2 $+0.341$ 0.026 0.035 5
$+0.311$ 0.026 0.029 6 $+0.216$ 0.020 0.026 8 $+0.369$ 0.017 0.035 13 M31
012-064 $-1.708$ 0.016 0.021 38 $+0.111$ 0.101 0.090 2 $+0.016$ 0.078 0.086 4
$+0.688$ 0.082 0.051 4 $+0.283$ 0.039 0.089 8 $+0.289$ 0.039 0.066 12 M31
019-072 $-0.693$ 0.010 0.025 38 $+0.299$ 0.045 0.040 2 $+0.246$ 0.034 0.091 4
$+0.213$ 0.039 0.055 5 $+0.206$ 0.023 0.043 8 $+0.432$ 0.019 0.048 14 M31
058-119 $-0.985$ 0.009 0.023 37 $-0.013$ 0.045 0.079 2 $+0.191$ 0.028 0.125 5
$+0.329$ 0.029 0.026 6 $+0.172$ 0.021 0.022 8 $+0.319$ 0.019 0.038 13 M31
082-114 $-0.689$ 0.016 0.037 36 $+0.339$ 0.079 0.229 2 $+0.386$ 0.065 0.146 4
$+0.387$ 0.068 0.069 5 $+0.239$ 0.037 0.030 8 $+0.406$ 0.047 0.079 12 M31
163-217 $-0.132$ 0.009 0.028 37 $+0.518$ 0.039 0.073 2 $+0.224$ 0.025 0.047 5
$+0.274$ 0.025 0.080 6 $+0.083$ 0.019 0.058 9 $+0.329$ 0.017 0.040 13 M31
171-222 $-0.217$ 0.009 0.024 37 $+0.441$ 0.039 0.036 2 $+0.290$ 0.027 0.109 5
$+0.235$ 0.027 0.063 6 $+0.083$ 0.020 0.034 8 $+0.295$ 0.018 0.036 13 M31
174-226 $-1.012$ 0.013 0.024 38 $+0.091$ 0.079 0.091 2 $+0.214$ 0.054 0.033 4
$+0.319$ 0.073 0.042 5 $+0.254$ 0.033 0.030 8 $+0.396$ 0.030 0.050 12 M31
225-280 $-0.342$ 0.009 0.026 34 $+0.399$ 0.038 0.159 2 $+0.242$ 0.024 0.117 5
$+0.348$ 0.024 0.075 6 $+0.118$ 0.018 0.060 9 $+0.442$ 0.016 0.039 13 M31
338-076 $-1.065$ 0.010 0.023 38 $+0.025$ 0.059 0.178 2 $+0.244$ 0.038 0.149 4
$+0.246$ 0.050 0.049 5 $+0.226$ 0.025 0.033 8 $+0.362$ 0.021 0.043 14 M31
358-219 $-2.199$ 0.013 0.023 36 $+0.202$ 0.086 0.121 2 $+0.165$ 0.044 0.074 5
$+0.369$ 0.082 0.105 5 $+0.300$ 0.027 0.034 8 $+0.307$ 0.030 0.043 12 M31 EXT8
$-2.808$ 0.024 0.043 28 … … … … $-0.344$ 0.220 0.015 2 $+0.547$ 0.316 … 1
$+0.269$ 0.055 0.075 8 $+0.335$ 0.082 0.088 10 N2403 F46 $-1.707$ 0.019 0.027
34 $-0.172$ 0.153 … 1 $-0.228$ 0.099 0.079 4 $+0.237$ 0.113 0.171 4 $+0.215$
0.042 0.066 8 $+0.303$ 0.062 0.083 10

171717 The listed abundances include NLTE corrections for Fe, Na, Mg, Ca, and
Ti. The columns $\sigma_{\langle\mathrm{X}\rangle}$ list the uncertainties on
the mean abundances of elements $X$ from propagation of the measurement
errors, while the columns $S_{X}$ give the standard errors on the means
estimated from the dispersions of the measurements. The columns labelled N
list the number of individual measurements.

Table 14: Results for Sc, Cr, Mn, and Ni.

Cluster [Sc/Fe] $\sigma_{\langle\mathrm{Sc}\rangle}$ $S_{\mathrm{Sc}}$ N
[Cr/Fe] $\sigma_{\langle\mathrm{Cr}\rangle}$ $S_{\mathrm{Cr}}$ N [Mn/Fe]
$\sigma_{\langle\mathrm{Mn}\rangle}$ $S_{\mathrm{Mn}}$ N [Ni/Fe]
$\sigma_{\langle\mathrm{Ni}\rangle}$ $S_{\mathrm{Ni}}$ N NGC 0104 $+0.197$
0.028 0.067 5 $-0.029$ 0.014 0.033 17 $-0.188$ 0.037 0.041 2 $+0.060$ 0.015
0.053 14 NGC 0362 $+0.133$ 0.031 0.050 5 $-0.025$ 0.015 0.037 17 $-0.255$
0.039 0.110 2 $-0.087$ 0.017 0.051 14 NGC 6254 $+0.238$ 0.036 0.056 4 $-0.124$
0.019 0.043 17 $-0.338$ 0.042 0.050 2 $+0.023$ 0.020 0.046 14 NGC 6388
$+0.145$ 0.028 0.075 5 $-0.063$ 0.014 0.038 17 $-0.147$ 0.038 0.006 2 $-0.015$
0.016 0.074 14 NGC 6752 $+0.130$ 0.034 0.060 4 $-0.111$ 0.017 0.025 17
$-0.248$ 0.040 0.012 2 $+0.072$ 0.017 0.041 14 NGC 7078 $+0.119$ 0.041 0.014 3
$-0.267$ 0.030 0.041 12 $-0.139$ 0.057 0.182 2 $+0.115$ 0.029 0.066 13 NGC
7099 $+0.129$ 0.041 0.066 4 $-0.176$ 0.027 0.046 13 $-0.203$ 0.056 0.032 2
$+0.097$ 0.028 0.059 14 N147 HII $+0.318$ 0.128 0.220 2 $+0.026$ 0.088 0.110
12 $-0.033$ 0.147 0.307 2 $+0.191$ 0.106 0.148 11 N147 HIII $-0.190$ 0.199
0.097 2 $+0.130$ 0.116 0.231 6 $+0.333$ 0.125 0.304 2 $-0.341$ 0.118 0.259 5
N147 PA-1 $-0.406$ 0.319 0.107 2 $-0.026$ 0.076 0.101 8 $+0.118$ 0.125 … 1
$+0.233$ 0.175 0.039 3 N147 PA-2 $+0.021$ 0.083 0.133 2 $+0.019$ 0.055 0.091
10 $-0.126$ 0.125 0.087 2 $+0.106$ 0.072 0.094 10 N147 SD7 $-0.183$ 0.112
0.098 2 $-0.022$ 0.056 0.083 14 $-0.316$ 0.111 0.130 2 $+0.172$ 0.059 0.094 12
N185 FJJ-III $+0.096$ 0.127 0.126 2 $+0.221$ 0.053 0.114 12 $-0.081$ 0.135 … 1
$+0.259$ 0.063 0.093 12 N185 FJJ-V $-0.093$ 0.097 0.173 2 $-0.147$ 0.062 0.092
11 $-0.004$ 0.096 0.121 2 $+0.197$ 0.055 0.092 12 N185 FJJ-VIII $+0.177$ 0.092
0.012 2 $-0.054$ 0.049 0.063 15 $-0.060$ 0.078 0.101 2 $+0.130$ 0.055 0.091 13
N205 HubbleI $+0.278$ 0.052 0.045 4 $-0.038$ 0.028 0.047 17 $-0.200$ 0.052
0.078 2 $-0.020$ 0.032 0.057 14 N205 HubbleII $+0.334$ 0.058 0.148 2 $-0.066$
0.024 0.042 17 $-0.247$ 0.050 0.045 2 $+0.072$ 0.027 0.065 14 N6822 SC6
$+0.188$ 0.084 0.062 2 $-0.066$ 0.043 0.051 15 $-0.334$ 0.085 0.056 2 $-0.053$
0.053 0.063 13 N6822 SC7 $-0.292$ 0.061 0.035 3 $-0.128$ 0.026 0.036 17
$-0.301$ 0.051 0.038 2 $-0.217$ 0.030 0.056 14 N6822 HVII $-0.065$ 0.072 0.164
3 $+0.087$ 0.032 0.085 17 $-0.027$ 0.059 0.225 2 $+0.034$ 0.043 0.100 14 M33
H38 $+0.022$ 0.107 0.104 3 $+0.626$ 0.158 0.161 3 $-0.303$ 0.113 0.257 2
$+0.118$ 0.073 0.100 12 M33 M9 $+0.202$ 0.087 0.049 2 $-0.298$ 0.126 0.393 4
$-0.276$ 0.106 0.078 2 $-0.014$ 0.063 0.058 13 M33 R12 $+0.090$ 0.063 0.098 3
$-0.411$ 0.111 0.148 3 $-0.132$ 0.061 0.154 2 $-0.007$ 0.036 0.069 13 M33 U49
$+0.352$ 0.095 0.026 3 $+0.135$ 0.190 0.507 3 $+0.014$ 0.101 0.148 2 $+0.067$
0.078 0.112 10 M33 R14 $+0.119$ 0.061 0.036 3 $-0.056$ 0.030 0.050 17 $-0.151$
0.057 0.023 2 $+0.003$ 0.035 0.069 14 M33 U77 $+0.328$ 0.105 0.128 2 $+0.049$
0.056 0.089 13 $-0.165$ 0.113 0.064 2 $-0.001$ 0.068 0.064 12 M33 CBF28
$+0.050$ 0.049 0.061 4 $-0.084$ 0.022 0.026 18 $-0.257$ 0.047 0.053 2 $-0.062$
0.024 0.049 14 M33 HM33B $-0.227$ 0.193 0.051 2 $+0.210$ 0.079 0.117 16
$-0.137$ 0.226 … 1 $-0.197$ 0.105 0.092 12 WLM GC $+0.159$ 0.073 0.089 3
$+0.019$ 0.046 0.071 10 $-0.262$ 0.079 0.111 2 $+0.131$ 0.044 0.095 13 Fornax
3 $+0.109$ 0.066 0.120 3 $-0.216$ 0.048 0.046 12 $-0.258$ 0.100 0.256 2
$-0.003$ 0.051 0.079 12 Fornax 4 $-0.134$ 0.049 0.062 3 $-0.108$ 0.025 0.034
15 $-0.275$ 0.049 0.053 2 $-0.163$ 0.023 0.051 15 Fornax 5 $-0.119$ 0.112
0.226 3 $-0.004$ 0.057 0.087 11 $-0.286$ 0.114 … 1 $+0.151$ 0.052 0.093 13 M31
006-058 $+0.224$ 0.032 0.077 5 $-0.012$ 0.017 0.031 15 $-0.157$ 0.039 0.074 2
$+0.014$ 0.017 0.059 15 M31 012-064 $+0.344$ 0.075 0.147 3 $-0.071$ 0.043
0.062 13 $-0.336$ 0.086 0.177 2 $+0.031$ 0.051 0.076 14 M31 019-072 $+0.190$
0.040 0.036 5 $-0.037$ 0.019 0.037 16 $-0.182$ 0.043 0.066 2 $+0.054$ 0.020
0.064 15 M31 058-119 $+0.138$ 0.037 0.090 5 $-0.078$ 0.021 0.048 15 $-0.251$
0.042 0.098 2 $+0.016$ 0.019 0.061 15 M31 082-114 $+0.327$ 0.091 0.118 2
$-0.068$ 0.044 0.066 15 $-0.326$ 0.092 0.111 2 $+0.245$ 0.044 0.079 15 M31
163-217 $+0.136$ 0.031 0.076 5 $-0.057$ 0.017 0.039 15 $-0.030$ 0.040 0.028 2
$+0.108$ 0.016 0.074 15 M31 171-222 $+0.219$ 0.033 0.082 5 $-0.028$ 0.017
0.041 15 $-0.015$ 0.041 0.049 2 $+0.096$ 0.017 0.068 15 M31 174-226 $+0.235$
0.069 0.056 3 $-0.033$ 0.031 0.041 16 $-0.267$ 0.063 0.151 2 $+0.059$ 0.037
0.074 14 M31 225-280 $+0.163$ 0.030 0.125 5 $-0.004$ 0.016 0.053 15 $-0.103$
0.039 0.004 2 $+0.112$ 0.016 0.085 15 M31 338-076 $+0.077$ 0.046 0.095 5
$-0.075$ 0.022 0.037 16 $-0.280$ 0.047 0.046 2 $-0.008$ 0.023 0.057 15 M31
358-219 $-0.029$ 0.060 0.021 3 $-0.163$ 0.049 0.053 9 $-0.237$ 0.083 0.067 2
$+0.047$ 0.042 0.073 12 M31 EXT8 $+0.442$ 0.118 0.148 2 $-0.234$ 0.163 0.149 5
$+1.155$ 0.167 … 1 $+0.462$ 0.089 0.218 8 N2403 F46 $-0.063$ 0.103 0.133 2
$-0.041$ 0.057 0.084 13 $-0.313$ 0.109 0.076 2 $+0.210$ 0.057 0.112 12

181818 The listed abundances include NLTE corrections for Mn and Ni. See notes
to Table 13 for further explanations.

Table 15: Results for Cu, Zn, Zr, Ba, and Eu.

Cluster [Cu/Fe] $\sigma_{\langle\mathrm{Cu}\rangle}$ $S_{\mathrm{Cu}}$ N
[Zn/Fe] $\sigma_{\langle\mathrm{Zn}\rangle}$ $S_{\mathrm{Zn}}$ N [Zr/Fe]
$\sigma_{\langle\mathrm{Zr}\rangle}$ $S_{\mathrm{Zr}}$ N [Ba/Fe]
$\sigma_{\langle\mathrm{Ba}\rangle}$ $S_{\mathrm{Ba}}$ N [Eu/Fe]
$\sigma_{\langle\mathrm{Eu}\rangle}$ $S_{\mathrm{Eu}}$ N NGC 0104 $-0.049$
0.060 … 1 $+0.113$ 0.044 0.046 2 $+0.224$ 0.065 … 1 $+0.133$ 0.025 0.070 5
$+0.225$ 0.050 0.006 2 NGC 0362 $-0.330$ 0.067 … 1 $-0.098$ 0.048 0.066 2
$+0.396$ 0.076 … 1 $+0.303$ 0.025 0.053 5 $+0.625$ 0.047 0.021 2 NGC 6254
$-0.588$ 0.076 … 1 $-0.005$ 0.056 0.008 2 $-0.130$ 0.150 … 1 $+0.328$ 0.028
0.049 5 $+0.188$ 0.090 … 1 NGC 6388 $-0.102$ 0.060 … 1 $-0.159$ 0.050 0.076 2
$+0.294$ 0.063 … 1 $+0.120$ 0.024 0.066 5 $-0.055$ 0.071 … 1 NGC 6752 $-0.441$
0.065 … 1 $+0.098$ 0.045 0.029 2 $+0.295$ 0.134 … 1 $+0.153$ 0.027 0.077 5
$+0.390$ 0.054 0.093 2 NGC 7078 … … … … $-0.189$ 0.103 0.060 2 … … … …
$+0.259$ 0.030 0.036 5 $+0.531$ 0.109 0.082 2 NGC 7099 $-0.437$ 0.114 … 1
$-0.080$ 0.077 0.092 2 … … … … $-0.052$ 0.032 0.145 5 $+0.332$ 0.110 … 1 N147
HII $-0.425$ 0.362 … 1 $+0.655$ 0.731 … 1 $+0.452$ 0.458 … 1 $-0.224$ 0.176
0.308 3 … … … … N147 HIII $+0.386$ 0.228 … 1 $+0.179$ 0.392 … 1 … … … …
$-0.615$ 0.107 0.092 5 … … … … N147 PA-1 $-0.203$ 0.292 … 1 $+0.026$ 0.405 … 1
… … … … $+0.048$ 0.086 0.083 5 … … … … N147 PA-2 $-0.840$ 0.350 … 1 $+0.307$