# Enrichment of the Galactic disc with neutron-capture elements: Gd, Dy, and
Th

T. Mishenina1 , M. Pignatari2,3,4,5 *, T. Gorbaneva1, B. Côté9,5,2 $\dagger$ ,
A. Yagüe López2,10 $\dagger$, F.-K. Thielemann6,7, C. Soubiran8
1Astronomical Observatory, Odessa National University, Shevchenko Park, 65014,
Odessa, Ukraine
2 Konkoly Observatory, Research Centre for Astronomy and Earth Sciences
(CSFK), Eötvös Loránd Research Network (ELKH),
Konkoly Thege Miklós út 15-17, H-1121 Budapest, Hungary
3 CSFK, MTA Centre of Excellence, Budapest, Konkoly Thege Miklós út 15-17,
H-1121, Hungary
4 E.A. Milne Centre for Astrophysics, Dept of Physics & Mathematics,
University of Hull, HU6 7RX, United Kingdom
5 Joint Institute for Nuclear Astrophysics - Center for the Evolution of the
Elements, USA
6 Department of Physics, University of Basel, Klingelbergstrabe 82, 4056
Basel, Switzerland
7 GSI Helmholtzzentrum für Schwerionenforschung, Planckstrasse 1, D-64291
Darmstadt, Germany
8 Laboratoire d’Astrophysique de Bordeaux, Univ. Bordeaux - CNRS, B18N, allée
Geoffroy Saint-Hilaire, 33615 Pessac, France
9 Department of Physics and Astronomy, University of Victoria, Victoria, BC
V8P 5C2, Canada
10 Computer, Computational and Statistical Sciences (CCS) Division, Center for
Theoretical Astrophysics, Los Alamos National
Laboratory, Los Alamos, NM 87545, USA
tmishenina@ukr.net;*<EMAIL_ADDRESS>NuGrid collaboration,
http://www.nugridstars.org

(Accepted 2021 xxx. Received 2021 xxx; in original form 2021 xxx)

###### Abstract

The study of the origin of heavy elements is one of the main goals of nuclear
astrophysics. In this paper, we present new observational data for the heavy
$r$-process elements gadolinium (Gd, Z=64), dysprosium (Dy, Z=66) and thorium
(Th, Z=90) in a sample of 276 Galactic disc stars ( –1.0$<$[Fe/H]$<$+0.3). The
stellar spectra have a high resolution of 42,000 and 75,000, and the signal-
to-noise ratio higher than 100. The LTE abundances of Gd, Dy and Th have been
determined by comparing the observed and synthetic spectra for three Gd lines
(149 stars), four Dy lines (152 stars) and the Th line at 4019.13 Å (170
stars). For about 70% of the stars in our sample Gd and Dy are measured for
the first time, and Th for 95% of the stars. Typical errors vary from 0.07 to
0.16 dex. This paper provides the first extended set of Th observations in the
Milky Way disc. Together with europium (Eu, Z = 63) data from our previous
studies, we have compared these new observations with nucleosynthesis
predictions and Galactic Chemical Evolution simulations. We confirm that
[Gd/Fe] and [Dy/Fe] show the same behavior of Eu. We study with GCE
simulations the evolution of [Th/Fe] in comparison with [Eu/Fe], showing that
unlike Eu either the Th production is metallicity dependent in case of a
unique source of the r-process in the Galaxy, or the frequency of the Th-rich
r-process source is decreasing with the increasing of [Fe/H].

###### keywords:

stars: abundances – stars: late-type – Galaxy: disc – Galaxy: evolution

††pagerange: Enrichment of the Galactic disc with neutron-capture elements:
Gd, Dy, and Th–4††pubyear: 2021

##  1 Introduction

The nucleosynthesis of heavy neutron-capture elements in stars and their
observations is one of the main research drivers for modern nuclear
astrophysics. In this context, the origin of the rapid neutron capture process
(r-process, e.g., Cowan et al., 2021, and references therein) is still a major
matter of debate. Among others, the most favoured $r$-process sites are
neutron-star mergers (e.g. Eichler et al., 1989; Freiburghaus, Rosswog &
Thielemann, 1999; Goriely et al., 2015; Thielemann et al., 2017; Rosswog et
al., 2018) and neutron star-black hole mergers (e.g. Lattimer & Schramm, 1974;
Surman et al., 2008; Fernández, Foucart & Lippuner, 2020), certain rare
classes of fast-rotating supernovae with powerful magnetic fields (e.g.
Symbalisty, Schramm & Wilson, 1985; Cameron, 2003; Nishimura et al., 2006;
Winteler et al., 2012; Nishimura et al., 2017; Mösta et al., 2018;
Obergaulinger, Just & Aloy, 2018; Reichert et al., 2021), as well as
hypernovae or collapsars (e.g. Cameron, 2003; Siegel, Barnes & Metzger, 2019;
Thielemann, Wehmeyer & Wu, 2020; Zenati et al., 2020; Brauer et al., 2021). In
the past, core-collapse supernovae (CCSNe) have been considered as the
dominant source of the $r$-process, initially by suggesting neutron-rich
innermost ejecta (e.g. Hillebrandt, Takahashi & Kodama, 1976), later arguing
for fast $(\alpha,n)$-reactions in explosive burning of He shells (e.g.
Truran, Cowan & Cameron, 1978; Thielemann, Arnould & Hillebrandt, 1979; Cowan,
Cameron & Truran, 1985), and afterwards turning to high entropy conditions in
neutrino-driven winds during the core-collapse and explosion phase (e.g.
Woosley et al., 1994; Takahashi, Witti & Janka, 1994; Hoffman, Woosley & Qian,
1997; Ning, Qian & Meyer, 2007; Farouqi et al., 2010; Arcones & Thielemann,
2013). At present, realistic CCSN simulations do not provide the right
conditions to produce a complete $r$-process pattern, while still a mild weak
$r$-process production could be possible (see e.g., Wanajo, Janka & Kubono,
2011; Curtis et al., 2019; Cowan et al., 2021; Ghosh, Wolfe & Fröhlich, 2021).

Stellar spectroscopic observations can be used to derive fundamental
constraints for theoretical simulations. In particular, a large number of
works in the past decade has been made to define the composition of old
$r$-process rich stars, formed in the early Milky Way Galaxy (e.g. Sneden et
al., 2003; Simmerer et al., 2004; Beers & Christlieb, 2005; Barklem et al.,
2005; Yong et al., 2013; Roederer et al., 2014; Sakari et al., 2018;
Mashonkina & Christlieb, 2014; Hansen et al., 2018). Such an importance is
primarily due to the possibility to trace contributions of one or several
stellar sites of production of these elements within the early Galaxy
timescales, before global gas mixing might actually take place (e.g. Hansen et
al., 2020). Therefore, stellar observations can be used to test directly
$r$-process predictions from different stellar sites (Farouqi et al., 2021) –
for instance, those resulting from neutron-star mergers (Ji, Drout & Hansen,
2019) or from magnetorotational hypernovae Yong et al. (2021). This includes
to study the role of progenitors of satellite galaxies on the early galactic
chemical enrichment (e.g. Gudin et al., 2021).

As the Galaxy evolves, new stars are forming enriched by previous stellar
generations. Compared to the early Galaxy, different stellar sources need to
be taken into account for the production of neutron-capture elements during
the chemical evolution of the Galaxy (GCE, e.g., Prantzos et al., 2018;
Kobayashi, Karakas & Lugaro, 2020). At present in the Milky Way there are two
main processes responsible for the production of heavy elements. In addition
to the $r$-process, the slow neutron capture process (s-process, e.g.,
Käppeler et al., 2011) is responsible for about half of the abundances beyond
iron in the solar system. The s-process elements are mainly produced in
massive stars (e.g. The, El Eid & Meyer, 2007; Pignatari et al., 2010;
Frischknecht et al., 2016; Limongi & Chieffi, 2018) and in Asymptotic Giant
Branch (AGB) stars (e.g. Gallino et al., 1998; Busso, Gallino & Wasserburg,
1999; Bisterzo et al., 2014; Cristallo et al., 2015; Karakas & Lugaro, 2016;
Battino et al., 2019). In order to take into account the $r$-process
contribution in GCE calculations, these yields are often derived from the
solar residual method: the $r$-process abundance pattern is obtained from the
solar composition after removing the $s$-process contribution, and then it is
assumed to be the same for all metallicities (e.g., Travaglio et al., 2004;
Prantzos et al., 2018). Alternatively, a large range of theoretical
$r$-process yields may be adopted. GCE models and simulations are crucial
tools to better understand the evolution of $r$-process elements in galaxies
(e.g., Wehmeyer, Pignatari & Thielemann 2015; Naiman et al. 2018; van de Voort
et al. 2020). In particular, the [Eu/Fe] vs [Fe/H] trend in the Galactic disc
has been targeted several times to probe the enrichment timescales and
contribution of neutron star mergers and rare classes of core-collapse
supernovae. Studies have suggested that neutron star mergers alone cannot
reproduce the decreasing trend of Eu when assuming a merger delay-time
probability distribution (DTD) in the form of $t^{-1}$ (e.g., Côté et al.
2017a, 2019a; Hotokezaka, Beniamini & Piran 2018; Haynes & Kobayashi 2019;
Simonetti et al. 2019). Such an issue, however, can be lifted by implying
metallicity-dependent DTDs (e.g., Simonetti et al. 2019), imposing shorter
delay times for mergers relative to Type Ia supernovae (e.g., Matteucci et al.
2014; Wehmeyer, Pignatari & Thielemann 2015; Côté et al. 2017a; Cavallo,
Cescutti & Matteucci 2021; Wanajo, Hirai & Prantzos 2021), or adopting
different treatments for how $r$-process elements are mixed and distributed
within the Galaxy (e.g., Schönrich & Weinberg 2019; Banerjee, Wu & Yuan 2020;
Beniamini & Hotokezaka 2020). Another solution to recover the [Eu/Fe] trend is
to involve additional sources alongside neutron star mergers for Eu, such as
rare supernovae originating from massive stars (e.g., Côté et al. 2019a;
Siegel, Barnes & Metzger 2019; Kobayashi, Karakas & Lugaro 2020; Cavallo,
Cescutti & Matteucci 2021; Greggio, Simonetti & Matteucci 2021; Farouqi et al.
2021).

Europium is the most extensively studied chemical element produced via the
$r$-process in the Galactic disc (according to (e.g. Bisterzo et al., 2014),
the solar $s$-process contribution is about 6 %). Europium abundance in the
Galactic disc has been investigated by many researchers (e.g. Mashonkina &
Gehren, 2001; Reddy et al., 2003; Bensby et al., 2005; Mishenina et al., 2013,
etc.). On the other hand, there are only a limited amount of stars with
available several $r$-process elements measured together from the same
analysis. For instance, in Guiglion et al. (2018) gadolinium and dysprosium
were examined together with europium and barium within the frameworks of the
AMBRE Project based on high-resolution FEROS, HARPS and UVES spectra from the
ESO archive. The contribution by the $s$-process to the Gd and Dy solar
abundances is estimated to be 15.4 % and 15.0 %, respectively (Bisterzo et
al., 2014), i.e., indicating a dominant $r$-process contribution. Gd, and Dy
abundances in thin and thick discs were investigated by Guiglion et al. (2018)
and in solar twins by Spina et al. (2018). Th abundances and the ratios Th/Eu
were obtained for thin disc stars to estimate the age of the disc (del Peloso,
da Silva & Arany-Prado, 2005). The Th abundance is also measured for samples
of solar twins stars (Unterborn, Johnson & Panero, 2015; Botelho et al.,
2019). As a continuation of our previous research focused on studying of the
Galactic disc enrichment with neutron-capture elements Mishenina et al. (2013,
2017, 2019a, 2019b), this paper aims to investigate the abundance distribution
of the $r$-process elements Gd, Dy and Th. Our study includes new Gd and Dy
measurements for nearly 70 % of the stars in our sample. For more than 90 % of
stars we present new Th values, and the GCE of the Milky Way disk is done for
the first time taking into account both actinide (Th) and lanthanide (Eu, Gd
and Dy) observations.

The paper is organized as follows. The observations and the definition of the
main stellar parameters are described in §2. The abundance determinations and
the error analysis are presented in §3. The analysis of the behaviour of
elemental abundances in the pattern of the theory of nucleosynthesis and the
chemical evolution of the Galaxy is reported in §4. Conclusions are drawn in
§5.

##  2 Observations and atmospheric parameters

The present study was carried out on an initial list of 276 stars and based on
the spectra and atmospheric parameters by Mishenina et al. (2013). The 1.93-m
telescope at the Observatoire de Haute-Provence (OHP, France) and the echelle-
type spectrograph ELODIE Baranne et al. (1996) were employed to obtain spectra
at the resolving power R = 42,000 in the wavelength range from 4400 to 6800 Å
and with the signal-to noise (S/N) better than 100 at 5500 Å. We also used
additional spectra from the OHP spectroscopic archive Moultaka et al. (2004)
collected with the SOPHIE spectrograph Perruchot et al. (2008) and covering a
similar wavelength range at the spectral resolution R = 75,000. The complex
pre-processing of images available on-line and enabling to obtain
spectroscopic data in a digital form was carried out immediately during
observations Katz et al. (1998). The subsequent processing of the studied
spectra was performed using the DECH30 software package developed by G.A.
Galazutdinov (see http://www.gazinur.com/DECH-software.html). DECH software
provides all stages of the CCD echelle spectral image processing, including
bias/background subtraction, flat-field correction (separation), extraction of
one-dimensional spectrum from two-dimensional images, diffuse light
correction, spectrum addition and exclusion of cosmic-ray features. The
programme enables to locate a fiducial continuum, to measure equivalent widths
(EWs) of lines by several methods, to determine line positions and shifts and
much more besides. In this case, we worked with spectra in the FITS format,
using such options as normalisation of individual spectra to the local
continuum, identification of spectral lines, development of the dispersion
curve, measurements of the line depths and equivalent widths (EWs),
elimination of cosmic-ray effects, selection of individual parts of the
spectrum, etc. The measured line depths were subsequently used to determine
the effective temperature ($T_{\rm eff}$) while the EWs of the neutral and
ionised iron lines were measured by the Gaussian profile fitting and employed
to derive atmospheric parameters (the surface gravity, $\log\,g$, and micro-
turbulent velocity, V${\rm t}$).

The stellar atmospheric parameters for the stars under examination in this
work were determined by us in previous studies. The procedures employed to
derive the effective temperatures $T_{\rm eff}$, surface gravities $\log\,g$
and microturbulent velocity V${\rm t}$ for the target stars had been described
in detail in Mishenina & Kovtyukh (2001) and Mishenina et al. (2004, 2008). In
particular, the effective temperatures $T_{\rm eff}$ were determined by
calibrating the line-depth ratios for the pairs of spectral lines that have
different low-level excitation potentials with the application of the
technique introduced and developed by Kovtyukh et al. (2003). For most of
metal-poor stars in our sample, $T_{\rm eff}$ were assumed by adjusting the
far-wings of the Hα line (Mishenina & Kovtyukh, 2001). In Mishenina et al.
(2004), we showed that the temperature scales adopted in Mishenina & Kovtyukh
(2001); Kovtyukh et al. (2003) are consistent. The surface gravities,
$\log\,g$, were computed from the ionisation equilibrium, which means that
similar iron abundances should be obtained from the neutral iron (Fe I) and
singly ionised iron (Fe II) lines. In our case, the difference between these
values does not exceed 0.03 dex. The microturbulent velocity, V${\rm t}$, was
derived by factoring out correlations between the iron abundances from Fe I
lines and the equivalent widths (EW) of those Fe I lines. We adopted the iron
abundance determined from the Fe I lines as the metallicity, [Fe/H]. As is
known (e.g Thévenin & Idiart, 1999; Shchukina & Trujillo Bueno, 2001;
Mashonkina et al., 2011; Bergemann et al., 2012), the lines of neutral iron
are influenced by the deviations from the LTE in the solar and stellar
spectra, and hence, these deviations also affect the iron abundances
determined from those lines. However, within the temperature and metallicity
ranges of our target stars, the NLTE corrections is less than 0.1 dex (e.g
Mashonkina et al., 2011). Thus, both in the case of accepted [Fe/H] as the
iron abundance from Fe I lines and also in the case of using the ionization
equilibrium method for iron to derived $\log\,g$, this correction does not
exceed the errors in determining of these parameters.

The list of parameter values obtained, as well as their comparison with the
results of other authors, has been given in Mishenina et al. (2004, 2008,
2013). The estimated accuracy of our parameter determinations is as follows:
$\Delta$($T_{\rm eff}$)= $\pm$100 K, $\Delta$($\log\,g$)= $\pm$0.2dex,
$\Delta$(V${\rm t}$) = $\pm$0.2km s-1 and $\Delta$([Fe/H]) = $\pm$0.1dex. In
this paper, we have compared our parameters with those obtained recently in
the studies by Guiglion et al. (2018) and Spina et al. (2018), wherein
gadolinium and dysprosium abundances were determined, and also those in the
studies by del Peloso, da Silva & Arany-Prado (2005), who reported europium
and thorium abundances (five stars in common with our sample) and Unterborn,
Johnson & Panero (2015) for one star in common with our sample; (see Table 1).
To compare with our findings, we chose the data reported by Guiglion et al.
(2018) for the stars in common with the highest S/N among those available in
on-line catalogs. We obtained average differences and errors for 36 stars in
common by deducting our data from those by Guiglion et al. (2018) (see Table
1). Then, we sorted out the data with $T_{\rm eff}$ from 5100 K to 6300 K and
surface gravities within 3.5 $<$ $\log\,g$$<$ 5.0 (for 26 stars in common) as
such ranges of parameter values had been chosen by the authors as criteria for
the selection of stars for further analysis; the resulting differences are
slightly smaller (Table 1). In general, we see a good agreement between our
findings and those from the literature, as well as a good consistency with the
estimated accuracy in parameter determinations adopted earlier. As we can see
from Table 1, the mean difference $\Delta$$T_{\rm eff}$ between our effective
temperature and that obtained by other authors, does not exceed 25 K, and the
rms deviations are within 100 K. A mean difference in gravity values
$\Delta$$\log\,g$ does not exceed 0.10, with the rms deviation is only
slightly exceeding (0.22), adopted earlier (0.2). In terms of metallicity, the
mean value does not exceed $\Delta$([Fe/H])= 0.05 $\pm$0.07 dex.

Table 1: Comparison of parameters and Eu, Gd, Dy, and Th abundance determinations taken from the literature with our results for the $n$ stars common with our stellar sample. Our data for Eu abundances are from Mishenina et al. (2013).  Reference |  $\Delta$($T_{\rm eff}$) |  $\Delta$($\log\,g$) |  $\Delta$([Fe/H]) |  $\Delta$([Eu/Fe]) |  $\Delta$([Gd/Fe]) |  $\Delta$([Dy/Fe]) |  $\Delta$([Th/Fe]) | n
---|---|---|---|---|---|---|---|---
Guiglion et al. | -14.7 | 0.09 | 0.01 | 0.09 | 0.09 | 0.14 | – | 36
2018 |  $\pm$99.4 |  $\pm$0.22 |  $\pm$0.07 |  $\pm$0.16 |  $\pm$0.18 |  $\pm$0.16 | – |
Guiglion et al. | 12.1 | 0.06 | 0.0 | 0.09 | 0.03 | 0.10 | – | 26
2018 |  $\pm$93 |  $\pm$0.21 |  $\pm$0.07 |  $\pm$0.15 |  $\pm$0.13 |  $\pm$0.13 | – |
Spina et al. | 14.8 | 0.06 | 0.04 | –0.03 | –0.03 | –0.04 | – | 6 (4)
2018 |  $\pm$25 |  $\pm$0.1 |  $\pm$0.05 |  $\pm$0.04 |  $\pm$0.04 |  $\pm$0.05 | – |
del Peloso et al. | -16.4 | 0.04 | 0.05 | 0.05 | – | – | -0.23 | 5 (4)
2005 |  $\pm$55 |  $\pm$0.08 |  $\pm$0.08 |  $\pm$0.08 | – | – |  $\pm$0.14 |
Morell et al. | -3.8 | 0.02 | -0.02 | – | – | – | -0.11 | 5 (5)
1992 |  $\pm$85 |  $\pm$0.20 |  $\pm$0.04 | – | – | – |  $\pm$0.12 |
Unterborn et al. | 23 | 0.05 | 0.04 | – | – | – | 0.48 | 1(1)
2015 | – | – | – | – | – | – | – |
Botelho et al. | -15.6 | -0.05 | -0.04 | 0.02 | – | – | -0.09 | 5(3)
2019 |  $\pm$28 |  $\pm$0.11 |  $\pm$0.05 |  $\pm$0.04 | – | – |  $\pm$0.15 |

We adopt the kinematic classification of the stars into the thin and thick
discs and Hercules stream, as previously described in Mishenina et al. (2013).
TM: To determine the components of spatial velocity (U, V, W) and the
belonging of stars to different galactic populations, the Hipparhos catalog
was used. Since the stars in our sample are bright and tend to have Gaia
astrometric errors equivalent to those of the Hipparcos observations, we have
not updated our classification with respect to the latest astrometric data
from the Gaia Data Release 2 (Gaia Collaboration et al., 2018). Some stars are
even too bright to be measured by Gaia. Our previous sample of 276 stars in
total consists of 21 stars belonging to the thick disc, 212 of those in the
thin disc, 16 stars related to the Hercules stream and 27 unclassified stars.

##  3 Abundance determination

The abundances of Dy, Gd and Th were derived in the Local Thermodynamical
Equilibrium (LTE) approximation with a new modified STARSP LTE spectral
synthesis code Tsymbal (1996) using the models by Castelli & Kurucz (2004).
For each star, the model was chosen by standard interpolation for $T_{\rm
eff}$ and $\log\,g$. The metalicity [Fe/H] and the turbulent velocity V${\rm
t}$ are not interpolated, in terms of metallicity, a model close to [Fe/H] of
stars in $\pm$0.2 dex was selected and the turbulent velocity V${\rm t}$
determined for each star was used. For Gd II lines 4037.89, 4085.56, 4483.33Å,
and Dy II lines 4073.12, 4077.97, 4103.31, and 4449.70 Å, and Th II 4019.12 Å
the oscillator strengths log gf were adopted from last version (2016) of the
VALD database (Kupka F. et al., 1999). In contrast to the considered Gd and Dy
lines, the 4019.129 Å Th line is a complex blend with a contribution to its
intensity from the Th and Co abundances at almost the same wavelength (e.g.
del Peloso, da Silva & Arany-Prado, 2005; Mashonkina, Christlieb & Eriksson,
2014; Botelho et al., 2019). Using a list of VALD lines, which includes atomic
and molecular lines, to describe the Th line in the solar spectrum, we found a
noticeable discrepancy between the observed and calculated spectra in the
region of Fe lines; to eliminate this, we corrected the log gf Fe I oscillator
strengths with an appropriate fit. The values of the oscillator strength
adopted by us for the Th and Co lines follow the VALD list, namely, the values
of log gf = -0.228 for the Th II line (Nilsson et al., 2002) and log gf =
-2.270 for the Co I line (Lawler, Whaling & Grevesse, 1990), in our case, they
are presented with a detailed contributions of the hyperfine structure. A list
of our main atomic and molecular lines employed in the thorium 4019 Å line
region are given in Table 2. For the Sun, and two stars with stellar
parameters ($T_{\rm eff}$, $\log\,g$, [Fe/H]) HD 22879 (5825; 4.42; -0.91),
and HD (5373; 4.30; 0.25) the predominant lines in the region are shown in
Fig. 1. Examples of fitting several Gd, Dy and Th lines in the stellar spectra
are presented in Fig. 2.

Table 2: List of lines in the thorium 4019 Å line region  Species | lambda, Å | Elow, ev | log gf | source
---|---|---|---|---
Ce II | 4018.820 | 1.55 | -0.959 | VALD
Nd II | 4018.820 | 0.06 | -0.890 | VALD
Fe I | 4018.887 | 4.26 | -2.781 | solar fit
Ce II | 4018.900 | 1.01 | -1.219 | VALD
Ce II | 4018.927 | 0.63 | -1.679 | VALD
V I | 4018.929 | 2.58 | -0.556 | VALD
Pr II | 4018.963 | 0.20 | -1.029 | VALD
13CH | 4018.965 | 0.46 | -3.253 | VALD
Mn I | 4018.987 | 4.35 | -1.883 | VALD
Fe I | 4019.002 | 4.32 | -2.700 | solar fit
Fe I | 4019.042 | 2.61 | -3.100 | solar fit
V II | 4019.044 | 3.75 | -1.231 | VALD
Ce II | 4019.057 | 1.01 | -0.529 | VALD
Mn I | 4019.066 | 4.67 | -0.522 | VALD
Ni I | 4019.067 | 1.94 | -3.399 | VALD
13CH | 4019.074 | 0.46 | -3.245 | VALD
Co I | 4019.110 | 2.28 | -3.287 | VALD
Co I | 4019.118 | 2.28 | -3.173 | VALD
Co I | 4019.120 | 2.28 | -2.876 | VALD
Co I | 4019.125 | 2.28 | -3.492 | VALD
Co I | 4019.126 | 2.28 | -3.298 | VALD
Th II | 4019.129 | 0.00 | -0.227 | VALD
Co I | 4019.129 | 2.87 | -5.163 | VALD
V I | 4019.134 | 1.80 | -2.149 | VALD
Co I | 4019.135 | 2.28 | -3.287 | VALD
Co I | 4019.135 | 2.28 | -3.474 | VALD
Co I | 4019.138 | 2.28 | -3.173 | VALD
Co I | 4019.140 | 2.28 | -3.298 | VALD
Co I | 4019.143 | 2.87 | -5.142 | VALD
Co I | 4019.210 | 2.87 | -4.821 | VALD
---
Figure 1: Observed (squares) and calculated spectra in the region of Th II
line for Sun, HD 22879 (5825; 4.42; -0.91), and HD 75732 (5373; 4.30; 0.25).
The contributions of various elements to the profile of the thorium line are
marked on the panel.
---
Figure 2: Observed (points) and calculated spectra in the region of Gd II, Dy
II and Th II lines for stars HD 42018 (5787;4.5;–0.07) and HD 202108
(5712;4.2;–0.21).

In order to calculate the synthetic spectrum and the Th abundance, we used the
relevant abundances of chemical elements obtained by Mishenina et al. (2013),
including nickel. In particular, to take into account the blend due to cobalt,
as a first approximation we estimated its abundance from the scaled solar
cobalt value. Then, we further refined from the profile fit of the cobalt line
at a wavelength of 4020.89 Å, which was calculated factoring in the hyperfine
structure (HFS). We finally derived the Th abundance by taking into account
the contribution of cobalt in the blend Th-Co. Therefore, our results obtained
for thorium should not be overestimated because of local contribution from
other elements. Examples of fitting Co line in the stellar spectra are shown
in Fig. 8. The abundance of europium was determined by us early and for
further analysis in this study, we use those obtained in Mishenina et al.
(2013). In that study the Eu abundance was derived from the Eu II lines at
6645 Å, taking into account the hyperfine structure Ivans et al. (2006). The
solar abundances of Dy, Gd and Th are determined using the STARSP code Tsymbal
(1996) from the lines in the spectra of the Moon and asteroids obtained with
the ELODIE spectrograph with the line parameters being the same as in the
stellar spectra: log A(Gd) = 1.08$\pm$0.05 and log A(Dy) = 1.10$\pm$0.05,
which coincide with Asplund et al. (2009) (log A(Gd)⊙ = 1.07$\pm$0.04, log
A(Dy)⊙ = 1.10$\pm$0.04), and our solar log A(Th) = 0.08$\pm$0.08 is consistent
with the value log A(Th)⊙ = 0.08 reported for the Sun in Mashonkina,
Christlieb & Eriksson (2014), the value of Asplund et al. (2009) is log A(Th)⊙
= 0.02$\pm$0.10.

The stellar parameters and obtained Gd, Dy and Th abundances with the
statistical uncertainties associated from line-to-line abundance variation
(standard deviation or rms derivation) are given in Table LABEL:ncapt.

###  3.1 Errors in abundance determinations

The total errors in Gd, Dy, Th abundance determinations mainly result from the
errors in sampling the parameter values and fitting the synthetic spectra to
observational ones (0.05 dex in Gd and Dy, and 0.08 for Th). To determine the
systematic errors in the elemental abundances, resulting from uncertainties in
the atmospheric parameters, we derived the elemental abundance of four stars
with different set of stellar parameters ($T_{\rm eff}$ in K, $\log\,g$,
V${\rm t}$ in km s-1 , [Fe/H]): HD154345 (5503,4.30,1.3,-0.21), HD82106
(4827,4.10,1.1,-0.11), HD75732 (5373,4.30,1.1,0.25), and HD201891
(5850,4.40,1.0,-0.96) for several models with modified parameters
($\Delta$$T_{\rm eff}$= +100 K, $\Delta$$\log\,g$= +0.2, $\Delta$V${\rm t}$=
+0.1). The impact of the parameter uncertainties on the accuracy of elemental
abundance determinations, as exemplified by the stars with different $T_{\rm
eff}$ and metallicities, is presented in Table 3.

Table 3:  Abundance errors due to atmospheric parameter uncertainties, for four stars with different set of stellar parameters ($T_{\rm eff}$, $\log\,g$, V${\rm t}$, [Fe/H]): HD154345 (5503,4.30,1.3,-0.21), HD82106 (4827,4.10,1.1,-0.11), HD75732 (5373,4.30,1.1,0.25), and HD201891 (5850,4.40,1.0,-0.96).  |  | HD1545345 |  |  |
---|---|---|---|---|---
AN | El |  $\Delta$ $T_{\rm eff}$+ |  $\Delta$ $\log\,g$+ |  $\Delta$ V${\rm t}$+ | tot+
64 | GdII | 0.07 | 0.10 | 0.01 | 0.12
68 | DyII | 0.09 | 0.08 | 0.02 | 0.13
90 | ThII | 0.10 | 0.11 | 0.0 | 0.16
|  | HD82106 |  |  |
64 | GdII | 0.07 | 0.06 | 0.00 | 0.10
68 | DyII | 0.10 | 0.12 | 0.01 | 0.15
90 | ThII | 0.05 | 0.06 | 0.0 | 0.11
|  | HD75732 |  |  |
64 | GdII | 0.06 | 0.10 | 0.01 | 0.12
68 | DyII | 0.10 | 0.09 | 0.01 | 0.14
90 | ThII | 0.10 | 0.06 | 0.0 | 0.14
|  | HD201891 |  |  |
64 | GdII | 0.02 | 0.04 | 0.02 | 0.08
68 | DyII | 0.05 | 0.03 | 0.01 | 0.07
90 | ThII | 0.12 | 0.06 | 0.0 | 0.15

As can be seen from Table 3, uncertainties in $T_{\rm eff}$ and $\log\,g$
contribute maximally to the total error. Total errors due to parameter
uncertainties and the measured spectra vary from 0.07 dex to 0.15 dex for Gd
and Dy, and from 0.11 to 0.16 dex for Th abundance.

To verify our selection of stellar parameters, we present correlations between
Gd, Dy and Th abundances and atmospheric parameters $T_{\rm eff}$ and
$\log\,g$ (see Figs. 3, 4). As can be seen in Figures 3, 4, there is no
correlation between the elemental abundances and chosen parameters.

---
Figure 3: Dependence of [El/Fe] vs. $T_{\rm eff}$
---
Figure 4: Dependence of [El/Fe] vs. $\log\,g$

A comparison between the abundance determinations obtained in this study and
the data reported by other authors is given in Table 1 (see in §2). Also Fig.
5 shows our [Eu/Fe], [Gd/Fe], and [Dy/Fe] data and ones from Guiglion et al.
(2018) and Spina et al. (2018) as a function of [Fe/H]. For these Figures we
selected the data of Guiglion et al. (2018) with $T_{\rm eff}$ from 5100 K to
6300 K and surface gravities within 3.5 $<$ $\log\,g$$<$ 5.0. Such ranges of
parameter values are the same chosen by the authors for further analysis. The
Fig. 6 presents our [Th/Fe] determinations and those by del Peloso, da Silva &
Arany-Prado (2005), Morell, Kallander & Butcher (1992), Unterborn, Johnson &
Panero (2015) and Botelho et al. (2019).

---
Figure 5: [Eu/Fe], [Gd/Fe], and [Dy/Fe] as a function of [Fe/H]. Stars
associated to the thin and thick discs are marked as black and red open
circles, respectively. Selected data are taken from Guiglion et al. (2018)
(points), and ones from Spina et al. (2018) (asterisks).
---
Figure 6: [Th/Fe] as a function of [Fe/H]. Our measurements associated to the
thin and thick discs are marked as black circles and red open circles,
respectively. In comparison, observations by del Peloso, da Silva & Arany-
Prado (2005) (blue open circles), Morell, Kallander & Butcher (1992) (blue
open asterisks), Unterborn, Johnson & Panero (2015) (blue asterisks) and
Botelho et al. (2019) (green semi-full circles) are shown.
---
Figure 7: For our stellar sample, the velocities along the Z axis
($\sqrt{U^{2}+W^{2}}$) are shown with respect to [Th/Fe] and [Th/Eu]. The full
sample is divided between thick and thin disk stars.

Table 1 shows the mean differences and rms errors for the values of thorium
abundance obtained by us and other authors for stars in common. We have 5
common stars with Morell, Kallander & Butcher (1992), for which the parameters
and content of thorium are determined: $\Delta$([Th/Fe]) (our – Morell) = 0.11
$\pm$0.12 dex, the shift is within the error limits. We also have 5 stars in
common with del Peloso, da Silva & Arany-Prado (2005), for which parameters
have been determined, and 4 of them have definitions of thorium abundance. The
mean difference is $\Delta$([Th/Fe]) (our-Peloso)= 0.23 $\pm$0.14 dex and it
is larger than the resulting error. In addition, there is one star HD 76932
also shared with Morell, Kallander & Butcher (1992) and del Peloso, da Silva &
Arany-Prado (2005). Our thorium abundance for HD 76932 is [Th/Fe] = 0.57 dex,
Morell, Kallander & Butcher (1992) and del Peloso, da Silva & Arany-Prado
(2005) give [Th/Fe] = 0.35dex and [Th/Fe] = 0.30 dex, respectively. There is
one common star, namely HD 146233, with Unterborn, Johnson & Panero (2015), it
is also was studied by Botelho et al. (2019). For HD 146233 the Th
measurements are varying significantly between different works. We obtain
[Th/Fe] =–0.09 dex, Unterborn, Johnson & Panero (2015) gives [Th/Fe] =0.28 dex
and in Botelho et al. (2019) [Th/Fe] =0.15 dex. We have 5 stars in common with
the Botelho et al. (2019), but among them only 3 stars with measurements of Th
abundance. The mean difference and rms between our data and those of Botelho
et al. (2019) is $\Delta$([Th/Fe]) (our – Botelho) = -0.09 $\pm$0.15. This
value (shift) has opposite sign in comparison with those obtained for
comparison of Morell, Kallander & Butcher (1992), and del Peloso, da Silva &
Arany-Prado (2005), but it is within the limits of errors. From a comparison
with Morell, Kallander & Butcher (1992), del Peloso, da Silva & Arany-Prado
(2005), and Botelho et al. (2019), the obtained rms of the mean difference are
0.12, 0.14 and 0.15, respectively. At the same time, the del Peloso, da Silva
& Arany-Prado (2005) data show a systematic shift relative to our data (0.23),
since the mean difference is greater than the scatter. The maximum difference
in thorium abundance between our values and these for del Peloso, da Silva &
Arany-Prado (2005) reaches 0.4 dex for the star HD 22879. However, this
discrepancy is contributed also by a difference of 0.15 dex in metallicity
obtained by us ([Fe/H] = -0.91) and ([Fe/H] = -0.76) del Peloso, da Silva &
Arany-Prado (2005). Fig. 8 (top panel) presents the synthetic spectra for the
star HD 22879 calculated in this work (blue solid line) and that with the data
(stellar parameters, chemical abundances and line list) of del Peloso, da
Silva & Arany-Prado (2005) (red solid line). The black solid line shows the
calculation from our data (parameters, abundance), but adapted to the Peloso’s
line list. Blue asterisks shows the calculation based on Peloso’s data
(parameters, abundances) with our line list in the thorium region. Circles are
the corresponding observational spectrum. The bottom panel shows a description
of the observed spectrum by our synthetic spectrum in a wider spectral region
with the thorium line. We observe a difference in the synthetic calculations
for our data and those of del Peloso, da Silva & Arany-Prado (2005) in the
region of the iron, nickel, manganese lines at the maximum intensity of this
spectral peculiarity due to the difference in oscillator strengths of lines,
assumed abundances of elements and the absence of the iron line in the del
Peloso, da Silva & Arany-Prado (2005) list. In the part of profile with the
thorium-cobalt lines, we see that using our data and different line lists
gives similar trends, and different stellar parameters and abundances make a
significant contribution to the result, in this case, an increase in the
thorium abundance compared to that obtained by del Peloso, da Silva & Arany-
Prado (2005) is required. In general, the differences between the data
obtained in different works are mostly due to the different lists of used
lines in the thorium line region and different parameters and elemental
abundances measured in different works.

---
Figure 8: Top panel: comparison of the synthetic spectrum calculations for our
data and those of Peloso et al. (2005)(see details in the text); bottom panel:
comparison of our synthetic computation with observations, in the region of Th
II line for a wider range of the spectrum.

##  4 Results and comparison with Galactic chemical evolution models

The Milky Way disk stars with the metallicity range covered from this study
are formed from interstellar matter enriched by several generations of stars.
Therefore, these observations cannot be directly compared with theoretical
stellar models, and Galactic chemical evolution (GCE) simulations must be used
to study the evolution history that allowed to build the chemical inventory
observed today (e.g., Tinsley, 1980; Gibson et al., 2003; Kobayashi, Karakas &
Lugaro, 2020; Matteucci, 2021, and references therein). In this work we focus
on the r-process elements Eu, Gd, Dy and Th. Although the main stellar source
of the r-process in the Galaxy is still matter of debate, from decades the
r-process was typically considered to produce the same abundances
independently from the metallicity of the stellar progenitors. The close
similarity between the solar residual (where the residual is derived by
subtracting the s-process contribution from the solar abundances of heavy
elements beyond iron, e.g., Arlandini et al., 1999; Bisterzo et al., 2014;
Prantzos et al., 2020) and the abundance patterns measured in r-process-rich
metal-poor stars drove and supported such a scenario. Indeed, while there is a
significant abundance scatter among different r-process enriched stars for
lighter elements in the mass region Sr-Ru, the abundances appear to better
align with the solar residual for Ba and heavier elements up to Pb (e.g.,
Sneden, Cowan & Gallino, 2008; Cowan et al., 2021). Within this heavier mass
region, GCE simulations could carry the same r-process signature across the
evolution of the Galaxy, where the main remaining uncertainties are the source
frequency and the quantitative r-process yields associated to each stellar
source (e.g., Matteucci et al. 2014; Wehmeyer, Pignatari & Thielemann 2015;
Côté et al. 2018a; Hotokezaka, Beniamini & Piran 2018). A larger observational
scatter between different r-process rich stars has been measured for the
actinides elements Th and U, which are highly affected by varying the
conditions in r-process theoretical calculations (Eichler et al., 2019; Cowan
et al., 2021). However, a significant variation is also seen beyond Ba once a
larger sample of metal-poor stars is considered (Roederer et al., 2010),
suggesting that the r-process production does not yield a unique and robust
pattern, and a degree of variation should be expected. The observation of
actinide-boost stars has further questioned those classical paradigms (e.g.,
Roederer et al., 2010; Holmbeck et al., 2018; Farouqi et al., 2021).

At least for metal-poor halo stars in the Galaxy, it is still matter of debate
if only one r-process source would be able to explain the early large
variations observed in stars for Eu and other heavy r-process element
abundances with respect to iron or $\alpha$-elements. As already pointed out
by Qian & Wasserburg (2007) and followed up by Hansen, Montes & Arcones
(2014), it is actually more plausible that at least two different types of
r-process sources were active, contributing with different frequency and
timescale. Here we discuss the aspect that two processes contribute to the
lanthanide and actinide r-process elements. On the other hand, observations
from old metal-poor stars would not exclude that today there is one source
with possible abundance variations, dominating the r-process contribution to
GCE (e.g., Wehmeyer, Pignatari & Thielemann, 2015; Côté et al., 2019a; Farouqi
et al., 2021, and references therein).

If we consider the r-process lanthanides discussed in this work, i.e., Eu, Gd
and Dy, we have seen in Figure 5 that their abundance trends with respect to
Fe are similar. In particular, we cannot identify if the observed abundance
scatter is due to the GCE contribution from multiple r-process sources and/or
some different production in the region, or if such a dispersion can be simply
due to observation uncertainties.

On the other hand, it may be interesting to study the evolution of Th (an
actinides element) with respect to Eu. In this context, we have performed GCE
models to compare with our new observations. The simulations are made using
the Python code OMEGA+ (Côté et al. 2017b, 2018b), which is part of the open-
source JINAPyCEE package111https://github.com/becot85/JINAPyCEE. It consists
of a two-zone model that includes a one-zone GCE model surrounded by a large
gas reservoir representing the circumgalactic medium. These two zones are
interacting via galactic inflows and outflows, where inflows transfer gas from
the circumgalactic medium to the central GCE model (the galaxy), and outflows
transfer gas from the galaxy to the circumgalactic medium. In this work, we
use the yields of Nomoto, Kobayashi & Tominaga (2013), Cristallo et al.
(2015), and Iwamoto et al. (1999) for massive stars, low-and intermediate-mass
stars, and Type Ia supernovae, and we use the same galaxy evolution parameters
as the best model found in Côté et al. (2019b), which reproduced various
observational constraints such as the current star formation rate, gas inflow
rate, supernova rates, total stellar mass, and total gas mass. Recent
developments have allowed to take into account radioactivity throughout the
GCE calculations (Côté et al. 2019b; Trueman et al. 2022), using the numerical
solver presented in Yagüe López et al. (2022) to properly follow radioactive
decay on timescales shorter than the lifetime of the Milky Way. This numerical
solver was modified in OMEGA+ to include the terms for material moving between
the two simulated zones along with decay in an unsplit fashion.

Our results are shown in Figure 9, and our goal is to address the relative
timescales at which Eu (as a representative of the r-process production of
lanthanides including Dy and Gd) and Th (as a representative of the actinides)
are produced within the Galactic disc with a simple approach. Given this goal,
all Eu and Th yields in our models have been included artificially in order to
freely explore which scenarios could give rise to the GCE trends provided by
our data. The black solid lines assume that all Eu and Th come from one
source, with a short delay time typical of CCSNe sources. Here Eu and Th
yields are the same in all events, regardless of metallicity. In this case,
while our prediction is acceptable for [Eu/Fe], the predicted trend for
[Th/Fe] does not decrease as steeply as the observational data, a feature that
can also be seen with [Th/Eu]. The relatively flat [Th/Eu] trend shows that
the decay of Th (the 232Th half-life is 14.1 billion years) plays an
insignificant role in shaping our predictions, meaning that Th decay would not
explain the different degrees at which Th and Eu decrease with respect to
metallicity.

The dashed orange and solid green lines in Figure 9 explore two different
scenarios matching the Th and Eu trends simultaneously. The dashed orange line
still assumes one prompt r-process source and a constant yield for Eu, but
assumes metallicity-dependent Th yields where Th is boosted by a factor of 4.5
at low metallicity relative to high metallicity, with a continuous decrease
between $Z=0.001$ and 0.02. The solid green line, on the other hand, combines
two r-process sources — neutron star mergers with long delay times, and exotic
SNe or collapsars with short delays (see also e.g., Côté et al. 2019a; Haynes
& Kobayashi 2019; Siegel, Barnes & Metzger 2019; Molero et al. 2021; Farouqi
et al. 2021). In this case, Th and Eu yields are kept constant as a function
of metallicity for both sources. However, the frequency of the short-delay
source is assumed to be metallicity dependent, such that its rate is three
times higher than the long-delay source at $Z<0.001$, and becomes negligible
$Z>0.01$. Such a computational experiment would boost the Th production at low
metallicity as we may expect. A type of exotic SNe that would fit these
assumptions are magneto-rotational (MHD) supernovae. MHD supernovae were
originally proposed as a source of a strong r-process (e.g., Winteler et al.,
2012). However, it was later shown by Mösta et al. (2018) that a strong
r-process can only be obtained with (unlikely) very extreme pre-collapse
magnetic fields, which are required to eject neutron-rich matter stemming from
the electron capture during the collapse to high densities. If sufficient
rotation exists also weaker pre-collape magnetic fields can be enhanced by the
magneto-rotational instability (MRI), lead to a successful explosion and a
highly magnetized neutron star (magnetar), but during the delay encountered
before the MRI had its impact, neutrino absorptions enhance the electron
fraction and limit the reach of the r-process. On the other hand, black-hole
accretion disk outflows can lead to highly r-process enriched matter with
$Y_{e}$-values in the ejecta just in the range leading to an actinide boost,
as observed in many r-II stars (see the detailed discussion in Farouqi et al.,
2021). As the collapsar behavior leading to black holes requires the core-
collapse of quite massive progenitors, their frequency is expected to be much
higher at low metallicities. The reason is that low-metallicity progenitors
have lower opacities, experience - as a consequence - less mass loss during
their stellar evolution and possess at the point of core collapse
significantly higher masses, favoring the collapse to a black hole.

Both scenarios shown in Figure 9 lead to an enhancement of Th production in
the early Universe, and would both be consistent with the observation of
metal-poor actinide-boost stars. From this timescale experiment, it is
unfortunately not possible to distinguish between one r-process source with
metallicity-dependent yields, multiple r-process sources with metallicity-
dependent rates, or a combination of the two. The variations observed in
metal-poor stars between r-process elements and the existence of the actinide-
boost stars seem to point more toward the second or third scenarios mentioned
above (e.g., Roederer et al., 2010; Farouqi et al., 2021) that, as we have
seen, it would be consistent with observations at higher metallicities in the
Galactic disk. Nevertheless, the fact that [Th/Fe] decreases more steeply than
[Eu/Fe] suggests that Th and Eu had a different production history, with Th
being more efficiently synthesized at low metallicity than at high
metallicity, as compared to Eu.

---
Figure 9: Predicted evolution of [Eu/Fe], [Th/Fe], and [Th/Eu] as a function
of [Fe/H] in the Galactic disc, using OMEGA+. In each panel, the solid black
line assumes one r-process site with a prompt delay, assuming constant Eu and
Th yields for all enrichment events. The dashed orange line is the same as the
black line, but assuming Z-dependent Th yields. The solid green line assumes
two r-process sites, one with a prompt delay and one with a long-lasting
delay-time distribution, where the contribution of the prompt site declines
with increasing metallicity.

##  5 Conclusions

In this work, we presented and discussed the abundance measurements of Gd, Dy
and Th for 276 disc stars. The analysis is based on LTE assumptions. Typical
uncertainties are 0.10 dex for Gd (with a range between 0.08 and 0.12 dex),
0.11 for Dy (between 0.07 and 0.15 dex) and 0.12 dex for Th (with a range
between 0.09 and 0.15 dex). The major sources of these uncertainties in the
analysis are the stellar surface temperature and gravities.

The [Dy/Fe] and [Gd/Fe] ratios show the same trend of [Eu/Fe] in the galactic
disk. Due to the present observation uncertainties, it is not possible to use
the evolution of Dy and Gd with respect to Eu to disentangle a contribution
from different r-process components. On the other hand, [Th/Fe] shows a
steeper decrease than the [Eu/Fe] with respect to [Fe/H].

By using GCE models we have explored possible solutions to explain those
trends. We found that the observations may be better reproduced by one
r-process source but with metallicity-dependent Th yields, or by multiple
r-process sources with metallicity-dependent rates for the Th-rich source. We
would rather support this second scenario, since it would also be compatible
with observations of both actinides boost r-process rich metal-poor stars and
not boosted.

## Acknowledgements

This article was based on observations collected at OHP Observatory, France.
MP acknowledges significant support to NuGrid from NSF grant PHY-1430152 (JINA
Center for the Evolution of the Elements) and STFC (through the University of
Hull’s Consolidated Grant ST/R000840/1), and access to viper, the University
of Hull High Performance Computing Facility. MP acknowledges the support from
the ”Lendület-2014” Programme of the Hungarian Academy of Sciences (Hungary).
FKT acknowledges support from the European Research Council (FP7) under ERC
Advanced Grant Agreement 321263 FISH. BC, AY and MP acknowledges support from
the ERC Consolidator Grant (Hungary) funding scheme (project RADIOSTAR, G.A.
n. 724560) and from the National Science Foundation (USA) under grant No.
PHY-1430152 (JINA Center for the Evolution of the Elements). This article is
based upon work from the ChETEC COST Action (CA16117), supported by COST
(European Cooperation in Science and Technology). We thank the ChETEC-INFRA
project funded from the European Union’s Horizon 2020 research and innovation
programme (grant agreement No 101008324), and the IReNA network supported by
NSF AccelNet. MP also thank the UK network BRIDGCE. TM is grateful to the
Laboratoire d’Astrophysique de l’Universite de Bordeaux for their kind
hospitality.

## Data Availability

The data underlying this article will be shared on reasonable request to the
corresponding author.

## References

  * Arcones & Thielemann (2013) Arcones A., Thielemann F. K., 2013, Journal of Physics G Nuclear Physics, 40, 013201
  * Arlandini et al. (1999) Arlandini C., Käppeler F., Wisshak K., Gallino R., Lugaro M., Busso M., Straniero O., 1999, ApJ, 525, 886
  * Asplund et al. (2009) Asplund M., Grevesse N., Sauval A. J., Scott P., 2009, ARA&A, 47, 481
  * Banerjee, Wu & Yuan (2020) Banerjee P., Wu M.-R., Yuan Z., 2020, ApJ, 902, L34
  * Baranne et al. (1996) Baranne A. et al., 1996, A&AS, 119, 373
  * Barklem et al. (2005) Barklem P. S. et al., 2005, A&A, 439, 129
  * Battino et al. (2019) Battino U. et al., 2019, MNRAS, 489, 1082
  * Beers & Christlieb (2005) Beers T. C., Christlieb N., 2005, ARA&A, 43, 531
  * Beniamini & Hotokezaka (2020) Beniamini P., Hotokezaka K., 2020, MNRAS, 496, 1891
  * Bensby et al. (2005) Bensby T., Feltzing S., Lundström I., Ilyin I., 2005, A&A, 433, 185
  * Bergemann et al. (2012) Bergemann M., Lind K., Collet R., Magic Z., Asplund M., 2012, MNRAS, 427, 27
  * Bisterzo et al. (2014) Bisterzo S., Travaglio C., Gallino R., Wiescher M., Käppeler F., 2014, ApJ, 787, 10
  * Botelho et al. (2019) Botelho R. B. et al., 2019, MNRAS, 482, 1690
  * Brauer et al. (2021) Brauer K., Ji A. P., Drout M. R., Frebel A., 2021, ApJ, 915, 81
  * Busso, Gallino & Wasserburg (1999) Busso M., Gallino R., Wasserburg G. J., 1999, ARA&A, 37, 239
  * Cameron (2003) Cameron A. G. W., 2003, ApJ, 587, 327
  * Castelli & Kurucz (2004) Castelli F., Kurucz R. L., 2004, ArXiv Astrophysics e-prints, astro-ph/0405087
  * Cavallo, Cescutti & Matteucci (2021) Cavallo L., Cescutti G., Matteucci F., 2021, MNRAS, 503, 1
  * Côté et al. (2017a) Côté B., Belczynski K., Fryer C. L., Ritter C., Paul A., Wehmeyer B., O’Shea B. W., 2017a, ApJ, 836, 230
  * Côté et al. (2019a) Côté B. et al., 2019a, ApJ, 875, 106
  * Côté et al. (2018a) Côté B. et al., 2018a, ApJ, 855, 99
  * Côté et al. (2019b) Côté B., Lugaro M., Reifarth R., Pignatari M., Világos B., Yagüe A., Gibson B. K., 2019b, ApJ, 878, 156
  * Côté et al. (2017b) Côté B., O’Shea B. W., Ritter C., Herwig F., Venn K. A., 2017b, ApJ, 835, 128
  * Côté et al. (2018b) Côté B., Silvia D. W., O’Shea B. W., Smith B., Wise J. H., 2018b, ApJ, 859, 67
  * Cowan, Cameron & Truran (1985) Cowan J. J., Cameron A. G. W., Truran J. W., 1985, ApJ, 294, 656
  * Cowan et al. (2021) Cowan J. J., Sneden C., Lawler J. E., Aprahamian A., Wiescher M., Langanke K., Martínez-Pinedo G., Thielemann F.-K., 2021, Reviews of Modern Physics, 93, 015002
  * Cristallo et al. (2015) Cristallo S., Straniero O., Piersanti L., Gobrecht D., 2015, ApJS, 219, 40
  * Curtis et al. (2019) Curtis S., Ebinger K., Fröhlich C., Hempel M., Perego A., Liebendörfer M., Thielemann F.-K., 2019, ApJ, 870, 2
  * del Peloso, da Silva & Arany-Prado (2005) del Peloso E. F., da Silva L., Arany-Prado L. I., 2005, A&A, 434, 301
  * Eichler et al. (1989) Eichler D., Livio M., Piran T., Schramm D. N., 1989, Nature, 340, 126
  * Eichler et al. (2019) Eichler M., Sayar W., Arcones A., Rauscher T., 2019, ApJ, 879, 47
  * Farouqi et al. (2010) Farouqi K., Kratz K.-L., Pfeiffer B., Rauscher T., Thielemann F.-K., Truran J. W., 2010, ApJ, 712, 1359
  * Farouqi et al. (2021) Farouqi K., Thielemann F.-K., Rosswog S., Kratz K.-L., 2021, arXiv e-prints, arXiv:2107.03486
  * Fernández, Foucart & Lippuner (2020) Fernández R., Foucart F., Lippuner J., 2020, MNRAS, 497, 3221
  * Freiburghaus, Rosswog & Thielemann (1999) Freiburghaus C., Rosswog S., Thielemann F.-K., 1999, ApJ, 525, L121
  * Frischknecht et al. (2016) Frischknecht U. et al., 2016, MNRAS, 456, 1803
  * Gaia Collaboration et al. (2018) Gaia Collaboration et al., 2018, A&A, 616, A11
  * Gallino et al. (1998) Gallino R., Arlandini C., Busso M., Lugaro M., Travaglio C., Straniero O., Chieffi A., Limongi M., 1998, ApJ, 497, 388
  * Ghosh, Wolfe & Fröhlich (2021) Ghosh S., Wolfe N., Fröhlich C., 2021, arXiv e-prints, arXiv:2107.13016
  * Gibson et al. (2003) Gibson B. K., Fenner Y., Renda A., Kawata D., Lee H.-c., 2003, PASA, 20, 401
  * Goriely et al. (2015) Goriely S., Bauswein A., Just O., Pllumbi E., Janka H. T., 2015, MNRAS, 452, 3894
  * Greggio, Simonetti & Matteucci (2021) Greggio L., Simonetti P., Matteucci F., 2021, MNRAS, 500, 1755
  * Gudin et al. (2021) Gudin D. et al., 2021, ApJ, 908, 79
  * Guiglion et al. (2018) Guiglion G., de Laverny P., Recio-Blanco A., Prantzos N., 2018, A&A, 619, A143
  * Hansen et al. (2020) Hansen C. J. et al., 2020, A&A, 643, A49
  * Hansen, Montes & Arcones (2014) Hansen C. J., Montes F., Arcones A., 2014, ApJ, 797, 123
  * Hansen et al. (2018) Hansen T. T. et al., 2018, ApJ, 858, 92
  * Haynes & Kobayashi (2019) Haynes C. J., Kobayashi C., 2019, MNRAS, 483, 5123
  * Hillebrandt, Takahashi & Kodama (1976) Hillebrandt W., Takahashi K., Kodama T., 1976, A&A, 52, 63
  * Hoffman, Woosley & Qian (1997) Hoffman R. D., Woosley S. E., Qian Y.-Z., 1997, ApJ, 482, 951
  * Holmbeck et al. (2018) Holmbeck E. M. et al., 2018, ApJ, 859, L24
  * Hotokezaka, Beniamini & Piran (2018) Hotokezaka K., Beniamini P., Piran T., 2018, International Journal of Modern Physics D, 27, 1842005
  * Ivans et al. (2006) Ivans I. I., Simmerer J., Sneden C., Lawler J. E., Cowan J. J., Gallino R., Bisterzo S., 2006, ApJ, 645, 613
  * Iwamoto et al. (1999) Iwamoto K., Brachwitz F., Nomoto K., Kishimoto N., Umeda H., Hix W. R., Thielemann F.-K., 1999, ApJS, 125, 439
  * Ji, Drout & Hansen (2019) Ji A. P., Drout M. R., Hansen T. T., 2019, ApJ, 882, 40
  * Käppeler et al. (2011) Käppeler F., Gallino R., Bisterzo S., Aoki W., 2011, Reviews of Modern Physics, 83, 157
  * Karakas & Lugaro (2016) Karakas A. I., Lugaro M., 2016, ApJ, 825, 26
  * Katz et al. (1998) Katz D., Soubiran C., Cayrel R., Adda M., Cautain R., 1998, A&A, 338, 151
  * Kobayashi, Karakas & Lugaro (2020) Kobayashi C., Karakas A. I., Lugaro M., 2020, ApJ, 900, 179
  * Kovtyukh et al. (2003) Kovtyukh V. V., Soubiran C., Belik S. I., Gorlova N. I., 2003, A&A, 411, 559
  * Kupka F. et al. (1999) Kupka F., Piskunov N.E., Ryabchikova T.A., Stempels H. C., Weiss W. W., 1999, A&AS, 138
  * Lattimer & Schramm (1974) Lattimer J. M., Schramm D. N., 1974, ApJ, 192, L145
  * Lawler, Whaling & Grevesse (1990) Lawler J. E., Whaling W., Grevesse N., 1990, Nature, 346, 635
  * Limongi & Chieffi (2018) Limongi M., Chieffi A., 2018, VizieR Online Data Catalog, J/ApJS/237/13
  * Mashonkina & Christlieb (2014) Mashonkina L., Christlieb N., 2014, A&A, 565, A123
  * Mashonkina, Christlieb & Eriksson (2014) Mashonkina L., Christlieb N., Eriksson K., 2014, A&A, 569, A43
  * Mashonkina & Gehren (2001) Mashonkina L., Gehren T., 2001, A&A, 376, 232
  * Mashonkina et al. (2011) Mashonkina L., Gehren T., Shi J. R., Korn A. J., Grupp F., 2011, A&A, 528, A87
  * Matteucci (2021) Matteucci F., 2021, A&A Rev., 29, 5
  * Matteucci et al. (2014) Matteucci F., Romano D., Arcones A., Korobkin O., Rosswog S., 2014, MNRAS, 438, 2177
  * Mishenina et al. (2017) Mishenina T. et al., 2017, MNRAS, 469, 4378
  * Mishenina et al. (2019a) Mishenina T., Pignatari M., Gorbaneva T., Bisterzo S., Travaglio C., Thielemann F. K., Soubiran C., 2019a, MNRAS, 484, 3846
  * Mishenina et al. (2019b) Mishenina T., Pignatari M., Gorbaneva T., Travaglio C., Côté B., Thielemann F. K., Soubiran C., 2019b, MNRAS, 489, 1697
  * Mishenina & Kovtyukh (2001) Mishenina T. V., Kovtyukh V. V., 2001, A&A, 370, 951
  * Mishenina et al. (2013) Mishenina T. V., Pignatari M., Korotin S. A., Soubiran C., Charbonnel C., Thielemann F. K., Gorbaneva T. I., Basak N. Y., 2013, A&A, 552, A128
  * Mishenina et al. (2008) Mishenina T. V., Soubiran C., Bienaymé O., Korotin S. A., Belik S. I., Usenko I. A., Kovtyukh V. V., 2008, A&A, 489, 923
  * Mishenina et al. (2004) Mishenina T. V., Soubiran C., Kovtyukh V. V., Korotin S. A., 2004, A&A, 418, 551
  * Molero et al. (2021) Molero M. et al., 2021, MNRAS, 505, 2913
  * Morell, Kallander & Butcher (1992) Morell O., Kallander D., Butcher H. R., 1992, A&A, 259, 543
  * Mösta et al. (2018) Mösta P., Roberts L. F., Halevi G., Ott C. D., Lippuner J., Haas R., Schnetter E., 2018, ApJ, 864, 171
  * Moultaka et al. (2004) Moultaka J., Ilovaisky S. A., Prugniel P., Soubiran C., 2004, PASP, 116, 693
  * Naiman et al. (2018) Naiman J. P. et al., 2018, MNRAS, 477, 1206
  * Nilsson et al. (2002) Nilsson H., Zhang Z. G., Lundberg H., Johansson S., Nordström B., 2002, A&A, 382, 368
  * Ning, Qian & Meyer (2007) Ning H., Qian Y. Z., Meyer B. S., 2007, ApJ, 667, L159
  * Nishimura et al. (2017) Nishimura N., Sawai H., Takiwaki T., Yamada S., Thielemann F.-K., 2017, ApJ, 836, L21
  * Nishimura et al. (2006) Nishimura S., Kotake K., Hashimoto M.-a., Yamada S., Nishimura N., Fujimoto S., Sato K., 2006, ApJ, 642, 410
  * Nomoto, Kobayashi & Tominaga (2013) Nomoto K., Kobayashi C., Tominaga N., 2013, ARA&A, 51, 457
  * Obergaulinger, Just & Aloy (2018) Obergaulinger M., Just O., Aloy M. A., 2018, Journal of Physics G Nuclear Physics, 45, 084001
  * Perruchot et al. (2008) Perruchot S. et al., 2008, in Proc. SPIE, Vol. 7014, Ground-based and Airborne Instrumentation for Astronomy II, p. 70140J
  * Pignatari et al. (2010) Pignatari M., Gallino R., Heil M., Wiescher M., Käppeler F., Herwig F., Bisterzo S., 2010, ApJ, 710, 1557
  * Prantzos et al. (2020) Prantzos N., Abia C., Cristallo S., Limongi M., Chieffi A., 2020, MNRAS, 491, 1832
  * Prantzos et al. (2018) Prantzos N., Abia C., Limongi M., Chieffi A., Cristallo S., 2018, MNRAS, 476, 3432
  * Qian & Wasserburg (2007) Qian Y. Z., Wasserburg G. J., 2007, Phys. Rep., 442, 237
  * Reddy et al. (2003) Reddy B. E., Tomkin J., Lambert D. L., Allende Prieto C., 2003, MNRAS, 340, 304
  * Reichert et al. (2021) Reichert M., Obergaulinger M., Eichler M., Aloy M. Á., Arcones A., 2021, MNRAS, 501, 5733
  * Roederer et al. (2010) Roederer I. U., Cowan J. J., Karakas A. I., Kratz K.-L., Lugaro M., Simmerer J., Farouqi K., Sneden C., 2010, ApJ, 724, 975
  * Roederer et al. (2014) Roederer I. U., Preston G. W., Thompson I. B., Shectman S. A., Sneden C., Burley G. S., Kelson D. D., 2014, AJ, 147, 136
  * Rosswog et al. (2018) Rosswog S., Sollerman J., Feindt U., Goobar A., Korobkin O., Wollaeger R., Fremling C., Kasliwal M. M., 2018, A&A, 615, A132
  * Sakari et al. (2018) Sakari C. M. et al., 2018, ApJ, 868, 110
  * Schönrich & Weinberg (2019) Schönrich R. A., Weinberg D. H., 2019, MNRAS, 487, 580
  * Shchukina & Trujillo Bueno (2001) Shchukina N., Trujillo Bueno J., 2001, ApJ, 550, 970
  * Siegel, Barnes & Metzger (2019) Siegel D. M., Barnes J., Metzger B. D., 2019, Nature, 569, 241
  * Simmerer et al. (2004) Simmerer J., Sneden C., Cowan J. J., Collier J., Woolf V. M., Lawler J. E., 2004, ApJ, 617, 1091
  * Simonetti et al. (2019) Simonetti P., Matteucci F., Greggio L., Cescutti G., 2019, MNRAS, 486, 2896
  * Sneden, Cowan & Gallino (2008) Sneden C., Cowan J. J., Gallino R., 2008, ARA&A, 46, 241
  * Sneden et al. (2003) Sneden C. et al., 2003, ApJ, 591, 936
  * Spina et al. (2018) Spina L. et al., 2018, MNRAS, 474, 2580
  * Surman et al. (2008) Surman R., McLaughlin G. C., Ruffert M., Janka H.-T., Hix W. R., 2008, ApJ, 679, L117
  * Symbalisty, Schramm & Wilson (1985) Symbalisty E. M. D., Schramm D. N., Wilson J. R., 1985, ApJ, 291, L11
  * Takahashi, Witti & Janka (1994) Takahashi K., Witti J., Janka H.-T., 1994, A&A, 286, 857
  * The, El Eid & Meyer (2007) The L.-S., El Eid M. F., Meyer B. S., 2007, ApJ, 655, 1058
  * Thévenin & Idiart (1999) Thévenin F., Idiart T. P., 1999, ApJ, 521, 753
  * Thielemann, Arnould & Hillebrandt (1979) Thielemann F.-K., Arnould M., Hillebrandt W., 1979, A&A, 74, 175
  * Thielemann et al. (2017) Thielemann F. K., Eichler M., Panov I. V., Wehmeyer B., 2017, Annual Review of Nuclear and Particle Science, 67, 253
  * Thielemann, Wehmeyer & Wu (2020) Thielemann F.-K., Wehmeyer B., Wu M.-R., 2020, in Journal of Physics Conference Series, Vol. 1668, Journal of Physics Conference Series, p. 012044
  * Tinsley (1980) Tinsley B. M., 1980, Fund. Cosmic Phys., 5, 287
  * Travaglio et al. (2004) Travaglio C., Gallino R., Arnone E., Cowan J., Jordan F., Sneden C., 2004, ApJ, 601, 864
  * Trueman et al. (2022) Trueman T. C. L., Côté B., Yagüe López A., den Hartogh J., Pignatari M., Soós B., Karakas A. I., Lugaro M., 2022, ApJ, 924, 10
  * Truran, Cowan & Cameron (1978) Truran J. W., Cowan J. J., Cameron A. G. W., 1978, ApJ, 222, L63
  * Tsymbal (1996) Tsymbal V., 1996, 108, 198
  * Unterborn, Johnson & Panero (2015) Unterborn C. T., Johnson J. A., Panero W. R., 2015, ApJ, 806, 139
  * van de Voort et al. (2020) van de Voort F., Pakmor R., Grand R. J. J., Springel V., Gómez F. A., Marinacci F., 2020, MNRAS, 494, 4867
  * Wanajo, Hirai & Prantzos (2021) Wanajo S., Hirai Y., Prantzos N., 2021, MNRAS, 505, 5862
  * Wanajo, Janka & Kubono (2011) Wanajo S., Janka H.-T., Kubono S., 2011, ApJ, 729, 46
  * Wehmeyer, Pignatari & Thielemann (2015) Wehmeyer B., Pignatari M., Thielemann F. K., 2015, MNRAS, 452, 1970
  * Winteler et al. (2012) Winteler C., Käppeli R., Perego A., Arcones A., Vasset N., Nishimura N., Liebendörfer M., Thielemann F. K., 2012, ApJ, 750, L22
  * Woosley et al. (1994) Woosley S. E., Wilson J. R., Mathews G. J., Hoffman R. D., Meyer B. S., 1994, ApJ, 433, 229
  * Yagüe López et al. (2022) Yagüe López A., García-Hernández D. A., Ventura P., Doherty C. L., den Hartogh J. W., Jones S. W., Lugaro M., 2022, A&A, 657, A28
  * Yong et al. (2021) Yong D. et al., 2021, Nature, 595, 223
  * Yong et al. (2013) Yong D. et al., 2013, ApJ, 762, 26
  * Zenati et al. (2020) Zenati Y., Siegel D. M., Metzger B. D., Perets H. B., 2020, MNRAS, 499, 4097

## Appendix A

We presented the stellar parameters and the Gd, Dy, Th abundances with errors
in Table A1.

Table 4: Stellar parameters and abundances of Gd, Dy, and Th. HD/BD |  $T_{\rm eff}$, K | $\log\,g$ | [Fe/H] | V${\rm t}$ | [Gd/Fe] | stand. deviation | [Dy/Fe] | stand. deviation | [Th/Fe]
---|---|---|---|---|---|---|---|---|---
thin disc |  |  |  |  |  |  |  |  |
166 | 5514 | 4.6 | 0.16 | 0.6 | – | – | – | – | 0.06
1562 | 5828 | 4.0 | -0.32 | 1.2 | 0.14 | 0.04 | 0.12 | 0.05 | 0.31
1835 | 5790 | 4.5 | 0.13 | 1.1 | – | – | – | – | –
3651 | 5277 | 4.5 | 0.15 | 0.6 | 0.05 | 0.07 | 0.05 | 0.05 | -0.08
4256 | 5020 | 4.3 | 0.08 | 1.1 | – | – | – | – | –
4307 | 5889 | 4.0 | -0.18 | 1.1 | – | – | – | – | –
4614 | 5965 | 4.4 | -0.24 | 1.1 | 0.18 | 0.03 | 0.19 | 0.05 | 0.03
5294 | 5779 | 4.1 | -0.17 | 1.3 | 0.19 | 0.00 | 0.11 | 0.03 | 0.26
6660 | 4759 | 4.6 | 0.08 | 1.4 | – | – | – | – | –
7590 | 5962 | 4.4 | -0.10 | 1.4 | 0.15 | 0.04 | 0.16 | 0.05 | 0.19
7924 | 5165 | 4.4 | -0.22 | 1.1 | 0.19 | 0.00 | 0.22 | 0.04 | 0.16
8648 | 5790 | 4.2 | 0.12 | 1.1 | – | – | 0.14 | 0.06 | -0.05
9407 | 5666 | 4.45 | 0.05 | 0.8 | 0.09 | 0.06 | -0.02 | 0.03 | 0.12
9826 | 6074 | 4.0 | 0.10 | 1.3 | -0.03 | 0.00 | -0.10 | 0.06 | -0.08
10086 | 5696 | 4.3 | 0.13 | 1.2 | – | – | – | – | –
10307 | 5881 | 4.3 | 0.02 | 1.1 | – | – | – | – | -0.10
10476 | 5242 | 4.3 | -0.05 | 1.1 | – | – | – | – | -0.13
10780 | 5407 | 4.3 | 0.04 | 0.9 | 0.16 | 0.06 | -0.02 | 0.03 | -0.12
11007 | 5980 | 4.0 | -0.20 | 1.1 | 0.13 | 0.05 | 0.15 | 0.06 | 0.29
11373 | 4783 | 4.65 | 0.08 | 1.0 | – | – | – | – | –
12846 | 5766 | 4.5 | -0.24 | 1.2 | 0.29 | 0.04 | 0.19 | 0.07 | 0.33
13507 | 5714 | 4.5 | -0.02 | 1.1 | 0.09 | – | 0.12 | 0.05 | -0.01
14374 | 5449 | 4.3 | -0.09 | 1.1 | 0.06 | – | 0.07 | 0.06 | 0.18
16160 | 4829 | 4.6 | -0.16 | 1.1 | 0.21 | – | 0.21 | 0.00 | 0.25
17674 | 5909 | 4.0 | -0.14 | 1.1 | 0.06 | 0.06 | 0.06 | 0.12 | 0.28
17925 | 5225 | 4.3 | -0.04 | 1.1 | – | – | – | – | –
18632 | 5104 | 4.4 | 0.06 | 1.4 | – | – | – | – | –
18803 | 5665 | 4.55 | 0.14 | 0.8 | 0.03 | 0.07 | -0.03 | 0.05 | -0.12
19019 | 6063 | 4.0 | -0.17 | 1.1 | 0.22 | – | 0.21 | 0.06 | 0.16
19373 | 5963 | 4.2 | 0.06 | 1.1 | -0.06 | 0.02 | -0.02 | 0.05 | 0.01
20630 | 5709 | 4.5 | 0.08 | 1.1 | 0.07 | 0.04 | 0.00 | 0.03 | -0.06
22049 | 5084 | 4.4 | -0.15 | 1.1 | – | – | – | – | –
22484 | 6037 | 4.1 | -0.03 | 1.1 | 0.12 | 0.03 | 0.07 | 0.02 | 0.15
22556 | 6155 | 4.2 | -0.17 | 1.1 | – | – | – | – | –
24053 | 5723 | 4.4 | 0.04 | 1.1 | 0.06 | 0.04 | 0.05 | 0.05 | 0.13
24238 | 4996 | 4.3 | -0.46 | 1.0 | 0.28 | – | 0.31 | 0.07 | 0.23
24496 | 5536 | 4.3 | -0.13 | 1.5 | 0.18 | 0.03 | 0.14 | 0.05 | 0.02
25665 | 4967 | 4.7 | 0.01 | 1.2 | – | – | – | – | –
25680 | 5843 | 4.5 | 0.05 | 1.1 | – | – | – | – | –
26923 | 5920 | 4.4 | -0.03 | 1.0 | 0.12 | 0.06 | 0.12 | 0.05 | -0.10
28005 | 5980 | 4.2 | 0.23 | 1.1 | -0.03 | 0.04 | -0.06 | 0.03 | 0.14
28447 | 5639 | 4.0 | -0.09 | 1.1 | 0.14 | 0.04 | 0.17 | 0.03 | 0.08
29150 | 5733 | 4.3 | 0.00 | 1.1 | 0.06 | 0.01 | 0.04 | 0.02 | -0.13
29310 | 5852 | 4.2 | 0.08 | 1.4 | – | – | – | – | –
29645 | 6009 | 4.0 | 0.14 | 1.3 | -0.07 | 0.05 | -0.09 | 0.04 | -0.12
30495 | 5820 | 4.4 | -0.05 | 1.3 | – | – | – |  | –
33632 | 6072 | 4.3 | -0.24 | 1.1 | 0.11 | 0.04 | 0.19 | 0.04 | 0.28
34411 | 5890 | 4.2 | 0.10 | 1.1 | – | – | – | – |
37008 | 5016 | 4.4 | -0.41 | 0.8 | 0.18 | – | 0.26 | – | 0.18
37394 | 5296 | 4.5 | 0.09 | 1.1 | – | – | – | – | –
38858 | 5776 | 4.3 | -0.23 | 1.1 | 0.19 | 0.09 | 0.18 | 0.07 | 0.12
39587 | 5955 | 4.3 | -0.03 | 1.5 | 0.11 | 0.03 | 0.05 | 0.03 | 0.20
40616 | 5881 | 4.0 | -0.22 | 1.1 | 0.17 | 0.04 | 0.15 | 0.03 | 0.16
41330 | 5904 | 4.1 | -0.18 | 1.2 | 0.15 | 0.05 | 0.19 | 0.06 | 0.32
41593 | 5312 | 4.3 | -0.04 | 1.1 | -0.02 | 0.11 | 0.01 | 0.08 | -0.14
42618 | 5787 | 4.5 | -0.07 | 1.0 | 0.11 | 0.03 | 0.17 | 0.05 | 0.01
42807 | 5719 | 4.4 | -0.03 | 1.1 | 0.09 | 0.08 | 0.06 | 0.05 | 0.05
43587 | 5927 | 4.1 | -0.11 | 1.3 | 0.01 | 0.06 | 0.07 | 0.05 | 0.30
43856 | 6143 | 4.1 | -0.19 | 1.1 | 0.19 | 0.04 | 0.09 | 0.04 | –
43947 | 6001 | 4.3 | -0.24 | 1.1 | 0.06 | 0.04 | 0.12 | 0.03 | 0.33
45088 | 4959 | 4.3 | -0.21 | 1.2 | 0.33 | 0.07 | 0.21 | 0.00 | 0.25
47752 | 4613 | 4.6 | -0.05 | 0.2 | – | – | – | – | -0.13
48682 | 5989 | 4.1 | 0.05 | 1.3 | -0.08 | 0.09 | -0.05 | 0.04 | 0.07
50281 | 4712 | 3.9 | -0.20 | 1.6 | – | – | – | – | –
50692 | 5911 | 4.5 | -0.10 | 0.9 | 0.11 | 0.06 | 0.12 | 0.03 | 0.24
51419 | 5746 | 4.1 | -0.37 | 1.1 | 0.32 | 0.11 | 0.25 | 0.08 | 0.39
51866 | 4934 | 4.4 | 0.00 | 1.0 | – | – | – | – | –
53927 | 4860 | 4.64 | -0.22 | 1.2 | 0.17 | 0.04 | 0.27 | 0.00 | 0.11
54371 | 5670 | 4.2 | 0.06 | 1.2 | – | – | – | – | –
55575 | 5949 | 4.3 | -0.31 | 1.1 | 0.18 | 0.04 | 0.21 | 0.06 | 0.35
58595 | 5707 | 4.3 | -0.31 | 1.2 | 0.20 | 0.08 | 0.21 | 0.04 | 0.30
59747 | 5126 | 4.4 | -0.04 | 1.1 | -0.04 | 0.07 | -0.01 | – | -0.04
61606 | 4956 | 4.4 | -0.12 | 1.3 | – | – | – | – | –
62613 | 5541 | 4.4 | -0.10 | 1.1 | 0.14 | 0.08 | 0.11 | 0.08 | 0.14
63433 | 5693 | 4.35 | -0.06 | 1.9 | 0.08 | 0.00 | 0.23 | 0.03 | 0.15
64468 | 5014 | 4.2 | 0.00 | 1.2 | 0.07 | 0.00 | -0.02 | 0.06 | -0.13
64815 | 5864 | 4.0 | -0.33 | 1.1 | 0.28 | 0.08 | 0.23 | 0.08 | –
65874 | 5936 | 4.0 | 0.05 | 1.3 | – | – | – | – | –
66573 | 5821 | 4.6 | -0.53 | 1.1 | 0.38 | 0.06 | 0.37 | 0.05 | 0.45
68638 | 5430 | 4.4 | -0.24 | 1.1 | 0.14 | 0.06 | 0.09 | 0.05 | 0.23
70923 | 5986 | 4.2 | 0.06 | 1.1 | 0.00 | 0.05 | -0.07 | 0.05 | 0.06
71148 | 5850 | 4.2 | 0.00 | 1.1 | – | – | – | – | -0.13
72760 | 5349 | 4.1 | 0.01 | 1.1 | – | – | – | – | –
72905 | 5884 | 4.4 | -0.07 | 1.5 | – | – | – | – | –
73344 | 6060 | 4.1 | 0.08 | 1.1 | 0.02 | 0.04 | -0.11 | 0.05 | -0.06
73667 | 4884 | 4.4 | -0.58 | 0.9 | 0.42 | 0.06 | 0.28 | 0.05 | 0.55
75732 | 5373 | 4.3 | 0.25 | 1.1 | -0.07 | 0.04 | -0.13 | 0.06 | 0.02
75767 | 5823 | 4.2 | -0.01 | 0.9 | – | – | – | – | –
76151 | 5776 | 4.4 | 0.05 | 1.1 | – | – | – | – | –
79969 | 4825 | 4.4 | -0.05 | 1.0 | – | – | – | – | –
82106 | 4827 | 4.1 | -0.11 | 1.1 | 0.08 | 0.07 | 0.04 | 0.04 | 0.25
82443 | 5334 | 4.4 | -0.03 | 1.3 | -0.03 | 0.08 | 0.10 | 0.03 | 0.10
87883 | 5015 | 4.4 | 0.00 | 1.1 | – | – | – | – | –
88072 | 5778 | 4.3 | 0.00 | 1.1 | 0.05 | 0.03 | 0.07 | 0.03 | 0.02
89251 | 5886 | 4.0 | -0.12 | 1.1 | – | – | 0.14 | 0.08 | –
89269 | 5674 | 4.4 | -0.23 | 1.1 | 0.19 | 0.05 | 0.09 | 0.05 | 0.17
91347 | 5931 | 4.4 | -0.43 | 1.1 | 0.24 | 0.05 | 0.26 | 0.03 | 0.50
94765 | 5077 | 4.4 | -0.01 | 1.1 | 0.15 | 0.06 | 0.01 | 0.04 | -0.07
95128 | 5887 | 4.3 | 0.01 | 1.1 | 0.06 | 0.00 | 0.02 | 0.03 | 0.01
97334 | 5869 | 4.4 | 0.06 | 1.2 | -0.02 | 0.04 | -0.04 | 0.03 | 0.06
97658 | 5136 | 4.5 | -0.32 | 1.2 | 0.29 | 0.07 | 0.27 | 0.04 | 0.21
98630 | 6060 | 4.1 | 0.22 | 1.4 | – | – | – | – | –
101177 | 5932 | 4.1 | -0.16 | 1.1 | 0.13 | 0.07 | 0.14 | 0.03 | 0.25
102870 | 6055 | 4.0 | 0.13 | 1.4 | -0.09 | 0.05 | -0.04 | 0.05 | 0.09
105631 | 5416 | 4.4 | 0.16 | 1.2 | – | – | – | – | –
107705 | 6040 | 4.2 | 0.06 | 1.4 | – | – | – | – | –
108954 | 6037 | 4.4 | -0.12 | 1.1 | – | – | – | – | 0.21
109358 | 5897 | 4.2 | -0.18 | 1.1 | 0.14 | 0.05 | 0.12 | 0.03 | 0.32
110463 | 4950 | 4.5 | -0.05 | 1.2 | – | – | – | – | –
110833 | 5075 | 4.3 | 0.00 | 1.1 | – | – | – | – | –
111395 | 5648 | 4.6 | 0.10 | 0.9 | 0.02 | 0.09 | -0.05 | 0.00 | –
112758 | 5203 | 4.2 | -0.56 | 1.1 | – |  | – | – | –
114710 | 5954 | 4.3 | 0.07 | 1.1 | -0.05 | 0.04 | -0.03 | 0.05 | -0.05
115383 | 6012 | 4.3 | 0.11 | 1.1 | -0.06 | 0.03 | 0.01 | 0.03 | 0.01
115675 | 4745 | 4.45 | 0.02 | 1.0 | – | – | – | – | –
116443 | 4976 | 3.9 | -0.48 | 1.1 | – | – | – | – | 0.35
116956 | 5386 | 4.55 | 0.08 | 1.2 | 0.06 | 0.06 | -0.01 | 0.03 | -0.21
117043 | 5610 | 4.5 | 0.21 | 0.4 | -0.02 | 0.03 | -0.14 | 0.03 | -0.09
119802 | 4763 | 4.0 | -0.05 | 1.1 | – | – | – | – | –
122064 | 4937 | 4.5 | 0.07 | 1.1 | – | – | – | – | -0.05
124642 | 4722 | 4.65 | 0.02 | 1.3 | – | – | – | – | –
125184 | 5695 | 4.3 | 0.31 | 0.7 | – | – | – | – | –
126053 | 5728 | 4.2 | -0.32 | 1.1 | 0.19 | 0.05 | 0.16 | 0.05 | 0.46
127506 | 4542 | 4.6 | -0.08 | 1.2 | – | – | – | – | –
128311 | 4960 | 4.4 | 0.03 | 1.3 | 0.16 | 0.05 | 0.00 | 0.03 | –
130307 | 4990 | 4.3 | -0.25 | 1.4 | 0.27 | 0.05 | 0.23 | 0.03 | –
130948 | 5943 | 4.4 | -0.05 | 1.3 | – | – | – | – | –
131977 | 4683 | 3.7 | -0.24 | 1.8 | – | – | – | – | –
135599 | 5257 | 4.3 | -0.12 | 1.0 | 0.07 | 0.04 | 0.11 | 0.05 | 0.21
137107 | 6037 | 4.3 | 0.00 | 1.1 | 0.05 | 0.03 | 0.05 | 0.04 | -0.13
139777 | 5771 | 4.4 | 0.01 | 1.3 | 0.11 | 0.00 | 0.08 | 0.05 | –
139813 | 5408 | 4.5 | 0.00 | 1.2 | – | – | – | – | –
140538 | 5675 | 4.5 | 0.02 | 0.9 | – | – | – | – | –
141004 | 5884 | 4.1 | -0.02 | 1.1 | 0.12 | 0.03 | 0.08 | 0.06 | 0.04
141272 | 5311 | 4.4 | -0.06 | 1.3 | 0.16 | 0.03 | 0.09 | 0.03 | 0.00
142267 | 5856 | 4.5 | -0.37 | 1.1 | – | – | – | – | –
144287 | 5414 | 4.5 | -0.15 | 1.1 | 0.22 | 0.05 | 0.21 | 0.03 | 0.19
145675 | 5406 | 4.5 | 0.32 | 1.1 | -0.05 | 0.05 | -0.10 | 0.03 | 0.10
146233 | 5799 | 4.4 | 0.01 | 1.1 | 0.14 | 0.03 | 0.13 | 0.02 | -0.09
149661 | 5294 | 4.5 | -0.04 | 1.1 | 0.16 | 0.07 | 0.09 | 0.05 | -0.14
149806 | 5352 | 4.55 | 0.25 | 0.4 | – | – | – | – | –
151541 | 5368 | 4.2 | -0.22 | 1.3 | – | – | – | – | –
153525 | 4810 | 4.7 | -0.04 | 1.0 | – | – | – | – | –
154345 | 5503 | 4.3 | -0.21 | 1.3 | 0.18 | 0.05 | 0.11 | 0.04 | 0.35
156668 | 4850 | 4.2 | -0.07 | 1.2 | 0.17 | 0.04 | 0.22 | 0.07 | 0.16
156985 | 4790 | 4.6 | -0.18 | 1.0 | – |  | – |  | 0.17
158633 | 5290 | 4.2 | -0.49 | 1.3 | 0.20 | 0.08 | 0.19 | 0.04 | 0.51
160346 | 4983 | 4.3 | -0.10 | 1.1 | – | – | – | – | –
161098 | 5617 | 4.3 | -0.27 | 1.1 | – | – | – | – | –
164922 | 5392 | 4.3 | 0.04 | 1.1 | – | – | – | – | –
165173 | 5505 | 4.3 | -0.05 | 1.1 | 0.15 | 0.06 | 0.09 | – | -0.03
165341 | 5314 | 4.3 | -0.08 | 1.1 | – | – | – | – | -0.03
165476 | 5845 | 4.1 | -0.06 | 1.1 | – | – | – | – | –
165670 | 6178 | 4.0 | -0.10 | 1.5 | – | – | – | – | –
165908 | 5925 | 4.1 | -0.60 | 1.1 | 0.25 | 0.04 | 0.30 | 0.06 | –0.37
166620 | 5035 | 4.0 | -0.22 | 1.0 | – | – | – | – | –
171314 | 4608 | 4.65 | 0.07 | 1.0 | – | – | – | – | –
174080 | 4764 | 4.55 | 0.04 | 1.0 | – | – | – | – | 0.08
175742 | 5030 | 4.5 | -0.03 | 2.0 | – | – | – | – | –
176377 | 5901 | 4.4 | -0.17 | 1.3 | 0.14 | 0.07 | 0.18 | 0.02 | 0.11
176841 | 5841 | 4.3 | 0.23 | 1.1 | – | – | – | – | -0.11
178428 | 5695 | 4.4 | 0.14 | 1.0 | – | – | – | – | -0.17
180161 | 5473 | 4.5 | 0.18 | 1.1 | – | – | – | – | –
182488 | 5435 | 4.4 | 0.07 | 1.1 | – | – | – | – | 0.05
183341 | 5911 | 4.3 | -0.01 | 1.3 | – | – | – | – | –
184385 | 5536 | 4.45 | 0.12 | 0.9 | 0.00 | 0.05 | -0.03 | 0.05 | –
185144 | 5271 | 4.2 | -0.33 | 1.1 | 0.10 | 0.05 | 0.06 | 0.03 | 0.37
185414 | 5818 | 4.3 | -0.04 | 1.1 | 0.04 | 0.04 | 0.08 | 0.02 | -0.14
186408 | 5803 | 4.2 | 0.09 | 1.1 | – | – | – | – | -0.22
186427 | 5752 | 4.2 | 0.02 | 1.1 | – | – | – | – | -0.10
187897 | 5887 | 4.3 | 0.08 | 1.1 | -0.01 | 0.05 | -0.02 | 0.06 | -0.01
189087 | 5341 | 4.4 | -0.12 | 1.1 | – | – | – | – | 0.01
189733 | 5076 | 4.4 | -0.03 | 1.5 | 0.13 | 0.04 | 0.13 | 0.05 | –
190007 | 4724 | 4.5 | 0.16 | 0.8 | – | – | – | – | –
190406 | 5905 | 4.3 | 0.05 | 1.0 | – | – | – | – | 0.07
190470 | 5130 | 4.3 | 0.11 | 1.0 | 0.00 | 0.06 | -0.10 | 0.05 | -0.14
190771 | 5766 | 4.3 | 0.13 | 1.5 | – | – | – | – | –
191533 | 6167 | 3.8 | -0.10 | 1.5 | – | – | – | – | 0.19
191785 | 5205 | 4.2 | -0.12 | 1.2 | 0.12 | 0.04 | 0.08 | 0.06 | 0.26
195005 | 6075 | 4.2 | -0.06 | 1.3 | – | – | – | – | 0.08
195104 | 6103 | 4.3 | -0.19 | 1.1 | – | – | – | – | –
197076 | 5821 | 4.3 | -0.17 | 1.2 | 0.09 | 0.05 | 0.11 | 0.05 | 0.29
199960 | 5878 | 4.2 | 0.23 | 1.1 | – | – | – | – | –
200560 | 5039 | 4.4 | 0.06 | 1.1 | – | – | – | – | –
202108 | 5712 | 4.2 | -0.21 | 1.1 | 0.16 | 0.08 | 0.19 | 0.03 | 0.35
202575 | 4667 | 4.6 | -0.03 | 0.5 | – | – | – | – | 0.20
203235 | 6071 | 4.1 | 0.05 | 1.3 | – | – | – | – | –
205702 | 6020 | 4.2 | 0.01 | 1.1 | 0.06 | 0.07 | -0.01 | 0.05 | 0.21
206860 | 5927 | 4.6 | -0.07 | 1.8 | 0.09 | 0.07 | 0.10 | – | 0.16
208038 | 4982 | 4.4 | -0.08 | 1.0 | – | – | – | – | –
208313 | 5055 | 4.3 | -0.05 | 1.0 | – | – | – | – | –
208906 | 5965 | 4.2 | -0.80 | 1.7 | 0.44 | 0.13 | 0.39 | 0.05 | 0.57
210667 | 5461 | 4.5 | 0.15 | 0.9 | 0.12 | 0.05 | 0.03 | 0.03 | –
210752 | 6014 | 4.6 | -0.53 | 1.1 | 0.40 |  | 0.41 | 0.04 | –
211472 | 5319 | 4.4 | -0.04 | 1.1 | 0.04 | 0.03 | 0.06 | 0.03 | 0.06
214683 | 4747 | 4.6 | -0.46 | 1.2 | – | – | – | – | 0.53
216259 | 4833 | 4.6 | -0.55 | 0.5 | – | – | – | – | –
216520 | 5119 | 4.4 | -0.17 | 1.4 | – | – | – | – | –
217014 | 5763 | 4.3 | 0.17 | 1.1 | -0.08 | 0.08 | 0.02 | 0.05 | -0.10
217813 | 5845 | 4.3 | 0.03 | 1.5 | 0.04 | 0.00 | 0.02 | 0.00 | –
218868 | 5547 | 4.45 | 0.21 | 0.4 | – | – | – | – | -0.19
219538 | 5078 | 4.5 | -0.04 | 1.1 | – | – | – | – | –
219623 | 5949 | 4.2 | 0.04 | 1.2 | – | – | – | – | -0.12
220140 | 5144 | 4.6 | -0.03 | 2.4 | – | – | – | – | –
220182 | 5364 | 4.5 | -0.03 | 1.2 | – | – | – | – | –
220221 | 4868 | 4.5 | 0.16 | 0.5 | 0.09 | 0.04 | 0.06 | 0.03 | -0.04
221851 | 5184 | 4.4 | -0.09 | 1.0 | 0.16 | 0.07 | 0.12 | 0.03 | –
222143 | 5823 | 4.45 | 0.15 | 1.1 | – | – | – | – | –
224465 | 5745 | 4.5 | 0.08 | 0.8 | – | – | – | – | –
263175 | 4734 | 4.5 | -0.16 | 0.5 | 0.16 | 0.03 | 0.14 | 0.04 | 0.13
BD12063 | 4859 | 4.4 | -0.22 | 0.6 | 0.19 | 0.00 | 0.21 | 0.05 | 0.34
BD124499 | 4678 | 4.7 | 0.00 | 0.5 | – | – | – | – | –
thick disc |  |  |  |  |  |  |  |  |
245 | 5400 | 3.4 | -0.84 | 0.7 | 0.38 | 0.12 | 0.47 | 0.05 | 0.46
3765 | 5079 | 4.3 | 0.01 | 1.1 | 0.06 | 0.07 | 0.07 | 0.05 | -0.01
5351 | 4378 | 4.6 | -0.21 | 0.5 | – | – | – | – | 0.33
6582 | 5350 | 4.5 | -0.83 | 0.4 | 0.28 | 0.06 | 0.22 | 0.06 | 0.60
13783 | 5350 | 4.1 | -0.75 | 1.1 | – | – | – | – | 0.57
18757 | 5741 | 4.3 | -0.25 | 1.0 | 0.15 | 0.03 | 0.16 | 0.05 | 0.32
22879 | 5825 | 4.42 | -0.91 | 0.9 | 0.41 | 0.03 | 0.38 | 0.03 | 0.58
65583 | 5373 | 4.6 | -0.67 | 0.7 | 0.37 | 0.06 | 0.34 | 0.08 | 0.49
76932 | 5840 | 4.0 | -0.95 | 1.0 | – | – | – | – | 0.57
106516 | 6165 | 4.4 | -0.72 | 1.1 | – | – | – | – | –
110897 | 5925 | 4.2 | -0.45 | 1.1 | 0.15 | 0.06 | 0.16 | 0.05 | 0.42
135204 | 5413 | 4.0 | -0.16 | 1.1 | – | – | – |  | 0.03
152391 | 5495 | 4.3 | -0.08 | 1.3 | 0.13 | 0.06 | 0.07 | 0.05 | 0.10
157089 | 5785 | 4.0 | -0.56 | 1.0 | – | – | – | – | 0.43
157214 | 5820 | 4.5 | -0.29 | 1.0 | – | – | – | – | 0.21
159062 | 5414 | 4.3 | -0.40 | 1.0 | 0.34 | 0.03 | 0.23 | 0.05 | 0.27
165401 | 5877 | 4.3 | -0.36 | 1.1 | – | – | – | – | 0.13
190360 | 5606 | 4.4 | 0.12 | 1.1 | -0.02 | 0.03 | 0.04 | – | 0.15
201889 | 5600 | 4.1 | -0.85 | 1.2 | 0.40 | 0.03 | 0.41 | 0.05 | 0.57
201891 | 5850 | 4.4 | -0.96 | 1.0 | 0.45 | 0.03 | 0.37 | 0.03 | 0.58
204521 | 5809 | 4.6 | -0.66 | 1.1 | 0.40 | 0.03 | 0.36 | 0.05 | 0.58
Hercules stream |  |  |  |  |  |  |  |  |
13403 | 5724 | 4.0 | -0.31 | 1.1 | 0.20 | 0.03 | 0.19 | 0.05 | 0.48
19308 | 5844 | 4.3 | 0.08 | 1.1 | -0.03 | 0.03 | -0.04 | 0.02 | 0.14
23050 | 5929 | 4.4 | -0.36 | 1.1 | 0.23 | 0.07 | 0.22 | 0.02 | 0.43
30562 | 5859 | 4.0 | 0.18 | 1.1 | – | – | – | – | –
64606 | 5250 | 4.2 | -0.91 | 0.8 | 0.33 | 0.05 | 0.35 | 0.05 | 0.73
68017 | 5651 | 4.2 | -0.42 | 1.1 | – | – | – | – | –
81809 | 5782 | 4 | -0.28 | 1.3 | 0.18 | 0.03 | 0.15 | 0.03 | 0.25
107213 | 6156 | 4.1 | 0.07 | 1.6 | -0.05 | 0.07 | -0.10 | 0.04 | 0.15
139323 | 5204 | 4.6 | 0.19 | 0.7 | -0.09 | 0.06 | 0.04 | 0.03 | -0.02
139341 | 5242 | 4.6 | 0.21 | 0.9 | – | – | – | – | –
144579 | 5294 | 4.1 | -0.70 | 1.3 | 0.35 | 0.03 | 0.35 | 0.04 | 0.67
159222 | 5834 | 4.3 | 0.06 | 1.2 | 0.01 | 0.05 | 0.00 | 0.06 | -0.04
159909 | 5749 | 4.1 | 0.06 | 1.1 | – | – | – | – | –
215704 | 5418 | 4.2 | 0.07 | 1.1 | – | – | – | – | –
218209 | 5705 | 4.5 | -0.43 | 1.0 | 0.32 | 0.03 | 0.32 | 0.05 | 0.50
221354 | 5242 | 4.1 | -0.06 | 1.2 | 0.06 |  | 0.09 |  | 0.08
nonclassified |  |  |  |  |  |  |  |  |
4628 | 4905 | 4.6 | -0.36 | 0.5 | – | – | 0.24 | 0.05 | –
4635 | 5103 | 4.4 | 0.07 | 0.8 | 0.05 | 0.10 | 0.11 | 0.10 | 0.15
10145 | 5673 | 4.4 | -0.01 | 1.1 | – | – | – | – | –
12051 | 5458 | 4.55 | 0.24 | 0.5 | – | – | – | – | –
13974 | 5590 | 3.8 | -0.49 | 1.1 | 0.14 | 0.03 | 0.07 | 0.03 | 0.31
17660 | 4713 | 4.75 | 0.17 | 1.3 | – | – | – | – | –
20165 | 5145 | 4.4 | -0.08 | 1.1 | – | – | – | – | –
24206 | 5633 | 4.5 | -0.08 | 1.1 | 0.10 | 0.00 | 0.12 | 0.05 | 0.20
32147 | 4945 | 4.4 | 0.13 | 1.1 | 0.02 | 0.04 | -0.01 | 0.03 | 0.29
45067 | 6058 | 4.0 | -0.02 | 1.2 | – | – | – | – | –
84035 | 4808 | 4.8 | 0.25 | 0.5 | – | – | – | – | –
86728 | 5725 | 4.3 | 0.22 | 0.9 | – | – | – | – | –
90875 | 4788 | 4.5 | 0.24 | 0.5 | – | – | – | – | –
117176 | 5611 | 4.0 | -0.03 | 1.0 | 0.10 | 0.05 | 0.11 | 0.03 | 0.25
117635 | 5230 | 4.3 | -0.46 | 0.7 | – | – | – | – | –
154931 | 5910 | 4.0 | -0.10 | 1.1 | – | – | – | – | –
159482 | 5620 | 4.1 | -0.89 | 1.0 | – | – | – | – | –
168009 | 5826 | 4.1 | -0.01 | 1.1 | – | – | – | – | –
173701 | 5423 | 4.4 | 0.18 | 1.1 | -0.01 | 0.07 | -0.02 | 0.05 | 0.14
182736 | 5430 | 3.7 | -0.06 | 1.0 | 0.10 | 0.03 | 0.11 | 0.04 | 0.23
184499 | 5750 | 4.0 | -0.64 | 1.5 | 0.31 | 0.00 | 0.33 | 0.03 | 0.66
184768 | 5713 | 4.2 | -0.07 | 1.1 | – | – | – | – | –
186104 | 5753 | 4.2 | 0.05 | 1.1 | – | – | – | – | –
215065 | 5726 | 4.0 | -0.43 | 1.1 | 0.27 | 0.03 | 0.18 | 0.04 | 0.35
219134 | 4900 | 4.2 | 0.05 | 0.8 | – | – | – | – | –
219396 | 5733 | 4.0 | -0.10 | 1.2 | 0.09 | 0.03 | 0.15 | 0.05 | 0.32
224930 | 5300 | 4.1 | -0.91 | 0.7 | 0.33 | 0.05 | 0.20 | 0.02 | 0.61


11institutetext: Australian Centre for Field Robotics, University of Sydney
<EMAIL_ADDRESS>
# Experimental Evaluation of a Hierarchical Operating Framework for Ground
Robots in Agriculture

Stuart Eiffert Stuart Eiffert and Nathan Wallace contributed equally to this
work; corresponding author: He Kong Nathan D. Wallace⋆ He Kong  Navid
Pirmarzdashti  and Salah Sukkarieh

###### Abstract

For mobile robots to be effectively applied to real world unstructured
environments—such as large scale farming—they require the ability to generate
adaptive plans that account both for limited onboard resources, and the
presence of dynamic changes, including nearby moving individuals. This work
provides a real world empirical evaluation of our proposed hierarchical
framework for long-term autonomy of field robots, conducted on University of
Sydney’s Swagbot agricultural robot platform. We demonstrate the ability of
the framework to navigate an unstructured and dynamic environment in an
effective manner, validating its use for long-term deployment in large scale
farming, for tasks such as autonomous weeding in the presence of moving
individuals.

###### Keywords:

Field Robotics, Navigation, Dynamic Path Planning

##  1 Introduction

Mobile robots are seeing increasing application in real world environments.
However, for longer term deployments, the planning of the robot’s operation
must take its resource constraints into account, which, for applications such
as large scale farming, may include energy and other materials necessary to
perform tasks around the farm—such as herbicide for weed spraying.
Consideration of these constraints is especially important due to the often
broad scale of the areas the robot is expected to operate over.

Additionally, to achieve robust autonomy, the robot must be able to adapt any
mission level plan in response to the presence of both unknown and dynamic
elements in these unstructured environments. Currently, autonomous field
robots are limited to use in more structured environments, including row crops
[1] or orchards [2], where dynamic elements such as moving individuals are not
a critical consideration. These approaches generally make use of reactive
planners, which can adapt to unforeseen static obstacles. Planning in the
presence of moving individuals, however, requires an understanding of how they
might respond to the planned motion of the robot, in order to avoid the
‘frozen-robot problem’ [3] which would otherwise occur in the presence of
crowds and herds.

To address the above challenges, in our prior work [4], we have proposed a
hierarchical framework for long-term and robust deployment of field ground
robots in large-scale farming. In this paper, we present a real world
evaluation of the former framework which integrates a local, interaction-aware
dynamic path planner with a longer term resource aware mission planner to
achieve long-term autonomy in unstructured and dynamic environments. Through
trials conducted on the University of Sydney’s Swagbot agricultural robot
platform, we demonstrate that our framework is able to navigate an
unstructured environment in an energy-efficient manner in the presence of
moving individuals, enabling the completion of tasks such as weed spraying in
farm environments.

##  2 Technical Approach

In our previous work [4], we developed a hierarchical framework for off-road,
multi-objective robot navigation in the presence of both moving individuals
and static obstacles. The performance of this framework was validated using
simulated trials, in which moving agents were modelled using the ORCA
reciprocal collision avoidance model of motion [5]. In the present work, we
further extend this hierarchical framework—shown in Fig. 1—to include the
operation of an actuated weeding arm, and evaluate its use in a real world
agricultural environment, in the context of a spraying a set of pre-identified
weeds in the presence of moving individuals.

Figure 1: System overview of the hierarchical framework, illustrating the
communication between each planner, the failsafe collision module, and the
high level controller. Mission objectives are provided externally to the long-
term planner.

The hierarchical framework is composed of a few key components: an object
detection and tracking module, a long-term planner, a local dynamic planner, a
high level switching controller, and a path tracker. The multimodal perception
solution used in this work utilises both LIDAR and RGB for object detection,
as per our simulated work in [4]. However, due to limited sensor field of
view, as shown in Fig. 2, detection is not possible directly behind the robot.
The tracking module used has been updated to be aware of the sensor field of
view, ensuring that updating of tracked object confidence based on missed
observations is performed at a slower rate when it enters the blind spot, in
order to maintain object permanence.

The long-term planner is based on [6]–[9], in which an energy efficient path
is generated by searching over a Probabilistic Roadmap of the environment to
find the lowest cost paths between all the goal waypoints—determined using a
learnt energy cost of motion metric—and by then solving an asymmetric
Travelling Salesman problem over this emergent graph to yield the optimal plan
(alternatively, the long-term plan can also be generated using our recent work
in [10] on the orienteering problem with replenishment, accounting for when,
where, and for how long to recharge resources). This plan takes into
consideration the topography of the area, the slip conditions of the terrain,
and any previously known non-traversable areas. The local dynamic planner used
in this work is adapted from our prior work in [11, 12], using generative
Recurrent Neural Networks (RNNs) and Monte Carlo Tree Search (MCTS). A high
level controller switches between planning modes based on proximity to
detected moving individuals, static obstacles, and waypoints.

Figure 2: Swagbot Robotic Platform used for testing. (a) Photo of Swagbot with
actuated weeder extended. (b) Top-down illustration of sensor FOV, and the
blind spot arising due to the front-mounted sensor installation.

##  3 Experimental Evaluation

Real world empirical evaluation of our approach has been conducted on the
University of Sydney’s Swagbot agricultural robot platform; a four-wheeled
independently driven and steered electric ground vehicle capable of
omnidirectional motion, which was designed for use in environments with uneven
terrain. Testing was performed at the University’s Arthursleigh Farm—pictured
in Fig. 3—and involved the continuous navigation between updated sets of
externally provided mission waypoints across an unstructured field 2 ha in
size. At each waypoint the robot was required to accurately spray a pre-
located weed, operating in the presence of both moving individuals and unknown
obstacles. Each iteration of the trial began at a home waypoint, where a set
of 5-8 objective waypoints were supplied to the robot.

As per Section 2, an optimal energy-efficient path was then computed and used
as the reference path for online local planning during navigation to each
objective. Upon returning to base, a new set of waypoints were supplied and
the trial repeated. A total of 3 sets of waypoints were reused, with testing
continuing until the robot exhausted its energy resources. An overview map of
the testing area showing the repeated route of the robot is illustrated in
Fig. 4. Total time of the trial was 2hr44mins, covering a distance of 5.49km,
including 37 distinct interactions with groups of moving agents. For the
purposes of this trial, people—rather than livestock—were used as agents, both
for safety, and due to the availability of a response prediction model of
person-robot interactions from our prior work. Performance was determined
using metrics of: (1) number of near-collisions with moving individuals; (2)
average speed between waypoints; (3) deviation from the reference path.

Figure 3: Satellite imagery of the Arthursleigh Farm test site, where the
experiments were conducted. Terrain topography indicated by the contour lines,
and spatial extent indicated by grid lines spaced at 20m intervals. Figure 4:
Complete course, showing repeated route of the robot during the trial, all
waypoints, and detected agents. The reference path (dark blue) is overlayed
with the actual taken path, differentiating between when the long-term planner
module (light blue) and dynamic planning module (purple) were each in use.

##  4 Results

Figure 5: Histogram of distances to closest agent by planner mode, shown as a
percentage of occurrence of times when an agent was within 8m. Dynamic
planning mode is able to successfully take over from the long-term planner
when in the presence of other agents and avoid collisions. Mode handover is
dependent both on proximity of agents to the robot and to the prior planned
path, resulting in the overlap shown.

Figure 6: Navigation around moving individuals, highlighting when the dynamic
planning module was in use (purple). (a) the robot initially attempts to pass
between agents, but instead takes wider route as the agents continue their
path down. (b) less desirable behaviour, where tracking of nearby agents
failed when the robot was facing away. Both examples show the robot returning
to the reference path when clear of agents.

###  4.1 Dynamic Collision Avoidance

Throughout the trial 9.42% of time was spent in dynamic planning mode (a total
of 15.5 minutes). Switching between dynamic and long-term planning modes is
handled by the high level controller as shown in Fig. 1, dependent on
proximity of detected agents both to the robot and the prior output of the
path tracker module. As shown in Fig. 6, this allows the robot to continue in
long-term mode even when in close proximity to nearby agents if the current
planned path will not result in a collision. Fig. 6 also demonstrates the
ability of the dynamic planning mode to successfully avoid collisions and
navigate around dynamic agents. The robot was able to maintain an average
distance of 3.36m from all agents whilst in dynamic mode. Fig. 6 (a) shows an
example of this desired behaviour, whilst example (b) shows the single
occasion in which an agent came within the fail-safe distance of 1.5m,
reaching a minimum distance of 1.30m before the robot stopped. During this
interaction the robot turned on the spot without realising that a person was
present in its ‘blind spot’. This occurred both as a result of limited sensor
field of view and inconsistent implementations of motor controller between
prior simulated work in [4] and this experiment. In [4], planning was done
using a non-holonomic simulated robot configured for Ackermann motion,
limiting motion to forward direction only. However, the real world robot is
capable of omnidirectional motion, and while the planner constrained the robot
to drive forwards, preventing it from travelling into its blind spot, it could
nevertheless still turn on the spot whilst tracking both the dynamic and long-
term paths.

Figure 7: Distances from the offline computed energy optimal reference path
throughout the trial, by planner mode. Both the long-term and dynamic mode
tend to remain close to the reference, however the dynamic planner can deviate
significantly in order to navigate around nearby moving individuals, as shown
by the protracted tail. Figure 8: Comparison of overall velocity (VelOverall)
and velocity along the reference path (Vel2Goal) when in long-term planning
mode (a) versus dynamic planning (b) illustrating the impact of nearby moving
individuals on the robot’s ability to follow the reference path. The average
VelOverall in dynamic mode is less than half of that achieved in long-term
mode. Additionally, the ratio of Vel2Goal to VelOverall is significantly less
in dynamic mode, with over 35% of time spent travelling away from the optimal
direction.

###  4.2 Navigation Efficiency

Fig. 7 illustrates how significant deviations from the prior optimal path can
occur whilst navigating through groups of individuals, although for the most
part the dynamic planner tends to remain close to the reference path when
possible. This is desirable since keeping close to the long-term reference
path will retain the energy efficiency merits and minimise resource usage.
Similarly, a comparison of the velocity of the robot along the optimal path,
compared to its overall velocity, allows an analysis of how much energy is
required navigating around dynamic obstacles. Fig. 8 highlights the impact
that the presence of moving individuals has on the efficiency of the robot’s
navigation. As shown in (a), when in long-term planning mode, almost all of
the robot’s velocity is directed along the optimal path, with average velocity
towards goal of 1.32 m/s nearly matching average overall velocity of 1.37 m/s.
However when dynamically navigating around moving agents the robot achieves an
overall velocity of only 0.60 m/s. Additionally, a significant amount of
energy is directed away from the optimal path, as shown in (b). Over 35% of
motion is directed away from the local goal resulting in an average velocity
towards goal of 0.44m/s, which is 33.3% of that achieved in long-term mode.

##  5 Discussion

This work has shown that the proposed system allows for safe operation of a
mobile robot around moving individuals during the completion of tasks such as
weeding an agricultural field. Overall, the presented results have
successfully demonstrated the implementation of our hierarchical framework in
the real world. These results validate the hierarchical framework for use in
large scale farming, allowing the safe and efficient operation in dynamic and
unstructured environments.

However, a number of outstanding challenges remain in order to extend the
proposed system for long-term autonomy. Improved perception around moving
individuals is required, including the ability to better detect and track
agents on a robotic platform with a limited field of view, and the proper
integration of the planner’s dynamics and the real world platform dynamics.
Additionally, real applications of long-term autonomy require inclusion of a
recharging station, rather than simply designating a base waypoint as such as
was done in this work. Whilst other works [13] have shown how this can be
applied to mobile robots in agriculture, it will need to be included in the
proposed hierarchical framework in future. Based on the results discussed in
Section 4.2, an understanding of how dynamic adjustments to the offline
computed optimal path influence energy usage and navigation efficiency should
also be considered. This suggests the need for consideration of crowd or herd
density during extended operation, to ensure mobile robots are able to
effectively reach a recharging station when required.

## References

  * [1] A. Bechar and C. Vigneault, Agricultural robots for field operations. Part 2: Operations and systems, Biosystems Engineering, Vol. 153, pp. 110–128, 2017.
  * [2] R. F. Carpio et al., A navigation architecture for Ackermann vehicles in precision farming, IEEE Robotics and Automation Letters, Vol. 5, No. 2, pp. 1103–1110, 2020
  * [3] P. Trautman, and A. Krause, Unfreezing the robot: Navigation in dense, interacting crowds, IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), pp. 797–803, 2010.
  * [4] S. Eiffert, N. Wallace, H. Kong, N. Pirmarzdashti, and S. Sukkarieh, A hierarchical framework for long-term and robust deployment of field ground robots in large-Scale farming, Proc. of IEEE CASE, pp. 948–954, Hong Kong, 2020.
  * [5] J. Van Den Berg, S. J. Guy, M. Lin, and D. Manocha, Reciprocal n-body collision avoidance, Proc. of the 14th Int. Symposium ISRR, Springer Tracts in Advanced Robotics, Vol. 70, pp. 3–19, 2011.
  * [6] N. Wallace, H. Kong, A. Hill, and S. Sukkarieh, Receding horizon estimation and control with structured noise blocking for mobile robot slip compensation, Proc. of IEEE ICRA, pp. 1169–1175, Montreal, Canada, 2019.
  * [7] N. Wallace, H. Kong, A. Hill, and S. Sukkarieh, Structured noise blocking strategies for receding horizon estimation and control of mobile robots with slip, Proc. of Australasian Conf. on Robotics and Auto. (ACRA), pp. 1–10, 2018.
  * [8] N. Wallace, H. Kong, A. Hill, and S. Sukkarieh, Experimental validation of structured receding horizon estimation and control for mobile ground robot slip Compensation, Proc. of the 12th Conf. on Field and Service Robotics, pp. 1–16, 2019.
  * [9] N. Wallace, H. Kong, A. Hill, and S. Sukkarieh, Motion cost characterisation of an omnidirectional WMR on uneven terrains, Proc. of the 12th IFAC CAMS and 1st IFAC WROCO, Vol. 52, No. 22, pp. 31–36, Daejeon, Korea, 2019.
  * [10] N. Wallace, H. Kong, A. Hill, and S. Sukkarieh, The orienteering problem with replenishment, Proc. of the IEEE CASE, pp. 973–978,, Hong Kong, 2020.
  * [11] S. Eiffert, H. Kong, N. Pirmarzdashti, and S. Sukkarieh, Path planning in dynamic environments using Generative RNNs and Monte Carlo tree search, Proc. of IEEE ICRA, pp. 10263–10269, Paris, France, 2020.
  * [12] S. Eiffert and S. Sukkarieh, Predicting responses to a robot’s future motion using generative recurrent neural networks, Proc. of ACRA, 2019.
  * [13] L. Varandas, P. Gaspar, M. Aguiar, Standalone Docking Station with Combined Charging Methods for Agricultural Mobile Robots, World Academy of Science, Engineering and Technology, Open Science Index 145, International Journal of Mechanical and Mechatronics Engineering, Vol. 13, No. 1, pp. 38–42, 2019.