# NLTE analysis for Y i and Y ii in atmospheres of F-G-K stars

Sofya Alexeeva CAS Key Laboratory of Optical Astronomy, National Astronomical
Observatories, Beijing, 100101, China
Yu Wang School of Physics, Beijing Institute of Technology, Beijing, 100081,
China
<EMAIL_ADDRESS>Gang Zhao CAS Key Laboratory of Optical Astronomy, National
Astronomical Observatories, Beijing, 100101, China
School of Astronomy and Space Science, University of Chinese Academy of
Sciences, Beijing, 100049, China
Feng Wang School of Physics, Beijing Institute of Technology, Beijing, 100081,
China
Yong Wu Institute of Applied Physics and Computational Mathematics, Beijing
100088, China
HEDPS, Center for Applied Physics and Technology, Peking University, Beijing
100084, China
Jianguo Wang  Institute of Applied Physics and Computational Mathematics,
Beijing 100088, China
Hongliang Yan CAS Key Laboratory of Optical Astronomy, National Astronomical
Observatories, Beijing, 100101, China
School of Astronomy and Space Science, University of Chinese Academy of
Sciences, Beijing, 100049, China
Institute for Frontiers in Astronomy and Astrophysics, Beijing Normal
University, Beijing, 102206, China
Jianrong Shi CAS Key Laboratory of Optical Astronomy, National Astronomical
Observatories, Beijing, 100101, China
School of Astronomy and Space Science, University of Chinese Academy of
Sciences, Beijing, 100049, China

###### Abstract

The non-local thermodynamical equilibrium (NLTE) line formation of Y i and Y
ii is considered in 1D LTE model atmospheres of F-G-K-type stars. The model
atom was constructed with the most up-to-date atomic data, including quantum
cross sections and rate coefficients for transitions in inelastic collisions
of Y i and Y ii with hydrogen atoms. For seven reference stars, we obtained an
agreement between NLTE abundances inferred from the two ionization stages,
while the difference in LTE abundance (Y i – Y ii) can reach up to -0.31 dex.
In the atmospheres of F-G-K-type stars, for both Y i and Y ii lines, the NLTE
abundance corrections are positive. In solar metallicity stars, the NLTE
abundance corrections for Y ii lines do not exceed 0.12 dex, while in
atmospheres of metal-poor stars they do not exceed 0.21 dex. For Y i lines,
the NLTE abundance corrections can reach up to $\sim$0.5 dex. We determined
the yttrium NLTE abundances for a sample of 65 F and G dwarfs and subgiants in
the -2.62 $\leq$ [Fe/H] $\leq$ +0.24 metallicity range, using high-resolution
spectra. For stars with [Fe/H] $\leq$ -1.5, [Y/Fe] versus [Fe/H] diagram
reveals positive trend with an average value of [Y/Fe] $\simeq$ 0\. For metal-
poor stars, among Sr, Y, and Zr, the arrangement [Sr/Fe] $<$ [Y/Fe] $<$
[Zr/Fe] remains consistent. The current study is useful for the Galactic
chemical evolution research. The model atom will be applied for NLTE yttrium
abundance determination in very metal-poor stars studied with LAMOST and
Subaru.

non-LTE line formation, chemical abundance, stars

††journal: ApJ††software: DETAIL (Butler & Giddings, 1985), SynthV_NLTE
(Tsymbal et al., 2019), binmag (Kochukhov, 2010, 2018), MARCS (Gustafsson et
al., 2008)

##  1 Introduction

Yttrium (Y, Z = 39, A = 89) is one of the easily-observable light neutron-
capture elements in B to K-type stars. Yttrium can be produced by stars in
three known types of neutron-capture reactions: rapid (r-) process, strong (or
main) component of the slow (s-) process, and the weak component of the
s-process (Kappeler et al., 1989). Synthesis of yttrium in main component of
the s-process takes place in low- and intermediate-mass stars (1.5–4M$\odot$)
during the double-shell burning stage as a result of thermal pulsations in the
envelopes of asymptotic-branch giants (AGB stars) (Gallino et al., 1998;
Kappeler et al., 2011). About 70-90% of the solar yttrium was produced in main
component. The weak component of the s-process (forming elements up to
A$\sim$90) takes place in the cores of massive (M $\geq$ 8M$\odot$) stars
during convective helium core and carbon shell burning stages (Pignatari et
al., 2010). The astrophysical site for the r-process remains a long-standing
problem of nucleosynthesis (Cowan et al., 2021). During the last several
decades the r-process was associated with type-II supernovae explosions
(Woosley et al., 1994). However, the recent observations showed different
scenarios, such as binary neutron star mergers (see e.g. Watson et al., 2019)
and magneto-rotationally driven supernovae (e.g. Shibagaki et al., 2016) as
the most probable astrophysical r-process sources. One of them, neutron star
mergers, was recently observed and related to the Gravitational Wave event
GW170817, where the yttrium lines were successfully identified in optical
spectra (Vieira et al., 2023). Since the Galactic chemical evolution (GCE)
models underproduce the s-process component of the solar-system abundances of
light neutron-capture elements (Sr-Y-Zr) by about 20–30%, Travaglio et al.
(2004) hypothesized another source of neutron-capture nucleosynthesis in the
Galaxy defined as Light Element Primary Process (LEPP). The need of this
additional LEPP of yet unknown origin for the light isotopes is still highly
debated (Montes et al., 2007; Pignatari et al., 2010; Bisterzo et al., 2014;
Cristallo et al., 2015; Kobayashi et al., 2020). The study of the Galactic
trend of yttrium in stars uniformly distributed over the wide range of
metallicity, from solar to low-metallicity ([Fe/H] $<$ $-$2.0), may indicate
the changes of relative contributions from the processes to the creation of
the element as the Galaxy evolved. The presence of yttrium in stars of
different ages and locations gives a good opportunity to restore the history
of heavy elements enrichment of the interstellar medium and, thus, to provide
constraints on the nucleosynthesis theories.

Many studies have been performed to establish [Y/Fe]–[Fe/H] Galactic trend,
see e.g. Zhao & Magain (1991); Johnson & Bolte (2002); Honda et al. (2004);
François et al. (2007); Nissen & Schuster (2011); Hansen et al. (2012);
Roederer et al. (2014); Bensby et al. (2014); Reggiani et al. (2017);
Baratella et al. (2021); Li et al. (2022). The most of the studies report on a
moderate underabundance in [Y/Fe] in stars with [Fe/H]$<$ $-1$ and a large
dispersion in the [Y/Fe] ratio with decreasing [Fe/H].

All studies determined the yttrium abundance in stars are based on the
assumption of the local thermodynamic equilibrium (LTE). The deviations from
LTE for yttrium lines were not studied so far. However, departures from LTE
are important, especially, for low surface gravities and metal poor
atmospheres. The use of NLTE element abundances is a valuable approach that
strengthens the reliability and accuracy of data interpretation within the
context of the chemical evolution of the Galaxy. NLTE calculations consider
departures from the assumption of LTE and take into account the interactions
between photons, electrons, and atoms in stellar atmospheres. Using NLTE
element abundances in data interpretation improves credibility by offering a
more realistic and comprehensive view of the Galaxy’s chemical processes.

Accurate yttrium abundances in stars of different spectral types and
populations are also important for various astrophysical purposes. For thin
disc stars of different metallicities and solar-type stars accurate yttrium
abundances combined with the other spectroscopic indicator, as magnesium,
provide the method for the estimation of stellar ages, that was a crucial
challenge since the advent of stellar astrophysics. While [Mg/Fe] increases
with age, yttrium shows the opposite behavior meaning that [Y/Mg] can be used
as a sensitive chronometer for Galactic evolution (da Silva et al., 2012;
Nissen, 2015; Tucci Maia et al., 2016; Titarenko et al., 2019; Berger et al.,
2022). Another combinaion of yttrium with europium, as [Y/Eu] abundance ratio,
is a good indicator of the chemical evolution efficiency, because it
characterizes the relative contribution of low- to intermediate-mass stars
with respect to high-mass stars (Recio-Blanco et al., 2021). First peak
s-element yttrium was mainly produced by low- and intermediate mass AGB stars
(Prantzos et al., 2018), while europium is produced by massive stars through
rapid neutron captures (Bisterzo et al., 2014). In RR Lyrae variable stars,
yttrium shows anomalous pattern, which cannot be explained in the framework of
GCE. For example, Clementini et al. (1995); Liu et al. (2013); Gozha et al.
(2020) detected anomalously low (beyond the errors) yttrium abundances in the
atmospheres of the metal-rich RR Lyrae ([Fe/H] $>$ $-$1.0) stars. Clementini
et al. (1995) attributed the anomalous abundances of Y to the departures from
LTE. However, it is not clear why similar effect is not found in normal metal-
poor stars.

There is a significant lack of information regarding NLTE effects for yttrium
in the literature, highlighting the pressing need for precise spectroscopic
analyses utilizing high-resolution observations. This study aims to construct
a comprehensive model atom for Y i –Y ii based on the most up-to-date atomic
data available so far electronic collisions, collisions with hydrogen atoms,
and photoionization cross-section. The model atom is applicable to analysis of
the yttrium lines in F, G, K spectral type stars. As a first application of
the treated model atom, we obtain the yttrium abundances of the reference
stars, with well-determined atmospheric parameters, using an extensive list of
Y i and Y ii lines. The simultaneous presence of lines of the two ionization
stages, Y i and Y ii, in FGK-type stars provides an opportunity to test our
model atom.

In order to draw more dependable conclusions regarding the origin and
evolution of yttrium within the Galactic context, we determine NLTE yttrium
abundances in a sample of 65 well-studied stars that includes F and G dwarfs
and subgiants in a limited range of temperatures, gravities, and
metallicities. For 51 star, Sitnova et al. (2015) have diligently established
precise stellar parameters. Their NLTE abundances for 17 chemical elements
from Li to Eu were presented in Zhao et al. (2016).

The article is organized as follows. Section 2 describes the model atom of Y
i–Y ii, adopted atomic data, and the departures from LTE for Y i–Y ii in model
atmospheres with different stellar parameters. Analysis of the solar Y i–Y ii
lines is presented in Section 3. In Section 4, we determine the Y abundances
of the reference FGK stars. Galactic trend for 65 F and G dwarfs and subgiants
is presented in Section 5. We summarize our conclusions in Section 6.

Figure 1: Grotrian term diagram for Y i. The ionization energy is shown by
solid horizontal line. The dashed lines indicate the transitions, where the
investigated spectral lines arise.  Figure 2: Grotrian term diagram for Y ii.
The ionization energy is shown by solid horizontal line. The dashed lines
indicate the transitions, where the investigated spectral lines arise.

##  2 NLTE line formation for Y i – Y ii

###  2.1 Model atom and atomic data

Yttrium is a transition element displaying chemical properties of rare-earth
elements. Yttrium is a chemical analogue of scandium, and their spectra are
similar. The natural abundance of yttrium is 100% of stable isotope 89Y
(Böhlke et al., 2005), this implies that there is no isotope shift seen in
spectra.

####  2.1.1 Energy levels

Energy levels of Y i : Energy levels of Y i belong to doublet terms of the
4d5s2, 5s2 $nl$ ($nl$ = 5p, 6s, 5d, 6p, 7s), 4d2 5$l$ ($l$ = s, p), 4d5s $nl$
($nl$ = 5p, 6s, 5d, 6p), 4d3, 5p2 5s, and 5s2 $n$f ($n$ = 6–10) electronic
configurations; the quartet terms of 4d2 $nl$ ($nl$ = 5s, 5p, 6s), 4d5s $nl$
($nl$ = 5p, 6s, 5d, 6p, 7s), 4d3, 5p2 $nl$ ($nl$ = 5s, 4d).

Energy levels of Y ii : Energy levels of Y ii belong to singlet terms of the
5s2, 4d$nl$ ($n=$ 5–7, $l\leq$ 3), 4d4f, 4d $n$s ($n=$ 8, 9), 4d2, 5s $nl$
($nl$ = 5p, 6s, 5d, 6p, 4f, 7s, 6d, 8s), 5p2 electronic configurations, the
triplet terms of 4d$nl$ ($n=$ 5–7, $l\leq$ 3), 4d4f, 4d $n$s ($n=$ 8, 9),
4d8d, 4d2, 5s $nl$ ($nl$ = 5p, 5d, 6p, 4f, 6d, 5f), 5p2, additional levels
with configuration 4d5g, and the ground state of Y iii.

Totally, we included 181 and 235 levels for Y i and Y ii taking into account
fine structure, respectively. In order to reduce computational time, we
combine some fine structure levels with higher energies up to 135 and 193
levels for Y i and Y ii, respectively. The energy gaps between the highest
levels and the ionization thresholds are 0.25 and 1.03 eV for Y i and Y ii,
respectively. Fine-structure splitting was included everywhere for the most of
the levels.

Energy levels were taken from the NIST
database111https://www.nist.gov/pml/atomic-spectra-database version 5.9
(Kramida et al., 2022). Energy levels of Y i with 5s2 $n$f ($n$ = 6–10)
electronic configuration were taken from the Kurucz’s
website222http://kurucz.harvard.edu/atoms/3900. The Grotrian term diagrams for
Y i and Y ii in our model atom are shown in Fig. 1 and Fig. 2.

####  2.1.2 Radiative data

The model atom includes 4748 allowed bound-bound ($b-b$) transitions for Y i
and 6837 transitions for Y ii. After combination of some fine structure
levels, the amount of transitions were reduced to 2176 for Y i and 5023 for Y
ii. Semi-empirical oscillator strengths for 377 transitions in Y ii were
adopted from Palmeri et al. (2017). The remaining transition probabilities
were taken from the NIST database (for Y i), and the Kurucz’s website.

Accurate data on the photoionization cross-sections for Y i still remain
undefined. Photo-ionization cross section for the ground state of Y i was
taken from Wijesundera & Kelly (1987), who used many-body perturbation theory.
For the remaining levels of Y i, we calculated photoionization cross-sections
based on formula for inner-shell photoionization and non-hydrogen-like atoms
and ions (Rosmej et al., 2020).

Photo-ionization cross sections for the ground state and 29 lowest levels of Y
ii were provided by Fernández-Menchero et al. (2020), and we employed a
hydrogenic approximation with an effective principal quantum number for the
higher excitation levels of Y ii.

####  2.1.3 Collisions with electrons

No theoretical calculations of the excitation cross sections were performed
for both yttrium neutral atom and singly-ionized yttrium ion. Experiments
based on observation of the optical radiation of excited atoms allow to
directly measure the excitation cross sections (Qij) for spectral lines. We
employed experimental values of the excitation cross sections of spectral
lines of Y i and Y ii presented in Kuchenev & Smirnov (1984); Smirnov (2000,
2002a, 2001, 2002b). For almost all transitions, the dependence of excitation
cross sections on the energy of incident electrons is registered in the energy
range of 0–200 eV. The error of measurement of relative values of the cross
sections varied from 10% for the most intense lines to 20% for low-intensity
ones. For excitation from level $i$ to level $j$, an effective collision
strenghts $\Upsilon_{ij}$ is given by

$\Upsilon_{ij}=g_{i}\dfrac{kT}{E_{H}^{\infty}}\int_{0}^{\infty}Q_{ij}(x)(x+x_{ij})\mathrm{e}^{-x}\,dx,$
(1)

where $g_{i}$ is the statistical weight of the lower level, $k$ the
Boltzmann’s constant, $E_{H}^{\infty}$ the Rydberg unit of energy, $Q_{ij}$
the collision cross-section expressed in unit of $\pi a_{0}^{2}$, $x=E/kT$ the
kinetic energy of electron after excitation and $x_{ij}=E_{ij}/kT$ the
transition energy in unit of $kT$. $\Upsilon_{ij}$ is dimensionless and
symmetric with respect to the transition ($\Upsilon_{ij}$ = $\Upsilon_{ji}$).

For NLTE calculations, we used the collision rate from state $i$ to state $j$
with electrons $C^{e}_{ij}$ in the unit of s-1 defined as

$C^{e}_{ij}=n_{e}A\dfrac{\Upsilon_{ij}}{g_{i}\sqrt{T}}e^{\frac{-E_{ij}}{kT}},$
(2)

where $n_{e}$ is the electron density, and $A$ the constant in unit of cm3 s-1
K1/2

$A=\pi a_{0}^{2}\left(\frac{8E_{H}^{\infty}}{\pi
m_{e}}\right)^{1/2}\left(\frac{E_{H}^{\infty}}{k}\right)^{1/2}=8.629\times
10^{-6},$ (3)

where $a_{0}^{2}$ is Bohr radius and $m_{e}$ the mass of electron.

Totally, we take into account 175 transitions with available experimental
measurements, namely, 9 quartet transitions of Y i from Kuchenev & Smirnov
(1984), 48 doublet transitions of Y i from Smirnov (2000), 41 high-lying
triplet transitions of Y ii from Smirnov (2002a), 32 singlet transitions of Y
ii from Smirnov (2001), and 45 transitions of Y ii from Smirnov (2002b). The
calculated effective collision strengths are given for thirteen temperatures
in the range $T$=2000–20000 K for the states of Y i (Table A.1) and fifteen
temperatures in the range $T$=2000–28000 K for the states of Y ii (Table A.2).

For transitions with non-available experimental data, the electron-impact
excitation was taken into account through the impact parameter method (IPM:
Seaton (1962a)) for the allowed transitions and the effective collision
strength was assumed to be $\Omega_{ij}$ = 1 for forbidden transitions.
Electron impact ionization cross-sections are computed with the formula from
Seaton (1962b).

####  2.1.4 Collisions with hydrogen atoms

For the first time the quantum cross sections and rate coefficients for bound-
bound transitions in inelastic collisions of Y i and Y ii with hydrogen atoms
are used in this study. A simplified model presented by Belyaev & Yakovleva
(2017) is used to estimate rate coefficients for inelastic processes in low-
energy hydrogen collisions. This method relies on the asymptotic approach for
electronic structure calculations and employs the Landau-Zener model for
determining nonadiabatic transition probabilities. The method is physically
reliable but less computationally expensive than a full quantum analysis. The
data for the rate coefficients are involving all levels and all possible
bound-bound and bound-free transitions up to 4$d$ f2P ($E$=5.697 eV) for Y i
and 7$f$ 1H∘ ($E$=11.191 eV) for Y ii. Totally, we included data for 311
bound-free and 20934 bound-bound transitions in the model. The more
information about the calculated rate coefficients can be found in Wang et al.
(2023).

The cross sections of inelastic collisions between atoms and hydrogen atoms
could be estimated by Drawin’s formula (Drawin, 1968), which is an extension
of the classical Thomson model. However, for low-energy atomic collisions, the
Drawin formula compares poorly with the results of the available quantum
mechanical calculations and cannot provide reliable results (Barklem et al.,
2011).

###  2.2 Method of calculations

The departure coefficients, $b_{\rm{i}}$ = $n_{\rm{NLTE}}$ / $n_{\rm{LTE}}$,
where calculated with the code DETAIL (Butler & Giddings, 1985) from the
solution of the system of the radiative transfer and statistical equilibrium
equations using the accelerated $\Lambda$-iteration method (Rybicki & Hummer,
1991). Here, $n_{\rm{NLTE}}$ and $n_{\rm{LTE}}$ are the statistical
equilibrium and thermal (Saha-Boltzmann) number densities, respectively. The
DETAIL opacity package was updated by Przybilla et al. (2011); Mashonkina et
al. (2011a) by including bound-free opacities of neutral and ionized species
for applications of the code to FGK and BA stars. Theoretical NLTE spectra
were calculated with the code synthV_NLTE (Tsymbal et al., 2019) using the
obtained departure coefficients. To examine theoretical stellar spectra and
compare them to observations we employed widget program
binmag333http://www.astro.uu.se/~oleg/binmag.html (Kochukhov, 2018). BinMag
interfaces with mounted code synthV_NLTE allows to obtain the best LTE and
NLTE fits to the observed line profiles automatically to determine chemical
abundances with high precision.

We used classical (1D) plane-parallel model atmospheres from the MARCS model
grid (Gustafsson et al., 2008). For given $T_{\rm eff}$, log $g$, and [Fe/H]
the models were interpolated using a FORTRAN-based routine written by Thomas
Masseron444http://marcs.astro.uu.se/software.php.

We selected the lines of Y i and Y ii, which can be found in spectra of stars
in visual wavelength range and can be suitable for abundance analyses. Table 1
presents the lines together with the adopted line data. The adopted oscillator
strengths were obtained from laboratory measurements. For the most of the
lines of Y i, the oscillator strengths were taken from Kramida et al. (2022).
For three Y i lines at 6023.406, 6222.578, and 6402.007 Å, we adopted the
oscillator strengths from recent experimental work of Li et al. (2018). The
most up-to-date semi-empirical oscillator strengths for Y ii lines were
adopted from Palmeri et al. (2017).

The splitting of the hyperfine components and isotopic shifts were neglected
during the determination of Y abundances. For the Y i and Y ii lines, the
effects due to isotopic splitting and hyperfine structure are insignificant,
since there is only one stable isotope, and the hyperfine splitting factors
are very small, typically less than 1 mÅ (Hannaford et al., 1982; Gough et
al., 1988).

For lines of Y i and Y ii, Radiative, Stark, and Van der Waals damping
constants are presented in Table 1. They were adopted from
VALD3555http://vald.astro.uu.se/~vald3/php/vald.php database (Ryabchikova et
al., 2015).

###  2.3 Departures from LTE for Y i \- Y ii in FGK-type Stars

Figure 3 displays fractions of Y i, Y ii, and Y iii in the model atmospheres
with $T_{\rm eff}$/log$g$/[Fe/H] = 3930/1.11/-0.37 and 6590/3.95/-0.02. In the
model 3930/1.11/-0.37, Y ii is the dominant ionization stage with small
admixtures of Y i (few parts in a thousand) in the line-formation region. In
hotter atmosphere, 6590/3.95/-0.02, Y ii is still the dominant stage and the
fraction of Y iii increases, while Y i becomes the minority species.

Figure 4 shows the departure coefﬁcients for all investigated levels of Y i
and Y ii in the models 5777/4.44/0 and 5780/3.7/-2.46, which represent the
solar atmosphere and metal-poor HD 140283, respectively. The energy levels are
shown by color bars. In deep atmospheric layers, log $\tau_{5000}>$1, where
the gas density is large and collisional processes dominate, the departure
coefﬁcients are equal to unity indicating no deviation from LTE. The Y i
ground state, a2D ($E_{\rm exc}$= 0 eV; $\lambda_{\rm thr}$ = 2006 Å ), and
low-excitation levels, z2P∘ ($E_{\rm exc}$ = 1.305 eV; $\lambda_{\rm thr}$ =
2553 Å ) and a4F ($E_{\rm exc}$ = 1.356 eV; $\lambda_{\rm thr}$ = 2570 Å ),
are subject to UV overionization, which lead to severe depopulation of these
levels in both atmospheres. Population depletion is extended to the remaining
Y i levels due to their coupling to the low-excitation levels. Since Y ii
dominates the element abundance over all atmospheric depths, the Y ii ground
state keeps its LTE populations. The deviations from LTE are stronger in the
metal-poor atmosphere with 5780/3.7/-2.46 compared to solar atmosphere due to
physical conditions, namely, smaller electron number density and stronger
ionization field that lead to stronger overionization of neutral yttrium.

The excited levels of Y ii are overpopulated relative to their LTE populations
in both models, outward log $\tau_{5000}\approx$ 0.3 due to the radiative
pumping of ultraviolet transitions from the ground state. In contrast, the
highly-excited levels of Y ii with energy more than 11 eV and the ground state
of Y iii appear to be strongly depopulated.

To understand the NLTE effects for a given spectral line we analyze the
departure coefﬁcients of the lower ($b_{l}$) and upper ($b_{u}$) levels at the
line-formation depths. In NLTE a given line is stronger compared to LTE, if
$b_{l}>1$ and (or) the line source function is smaller than the Planck
function, that is, $b_{l}>b_{u}$.

First, we consider line of Y i at 4128 Å in the 5777/4.44/0 model. The
departure coefficients for the lower and upper levels for this line are
presented in Figure 5 (upper panel). Its core forms around log
$\tau_{5000}\approx$ -0.6, where the departure coefﬁcient of the lower level
is less than unity, $b_{l}<1$, and $b_{l}<b_{u}$ that lead to the weakening
line and positive abundance correction of $\Delta_{\rm NLTE}$ =
log$\epsilon_{\rm NLTE}$ \- log$\epsilon_{\rm LTE}$ = +0.07 dex. The LTE and
NLTE profiles are also presented.

Second, we consider line of Y ii at 5087 Å in the 4600/1.43/-2.55 model. The
departure coefﬁcients for the lower and upper levels are presented in Figure 5
(bottom panel). The core of the line forms around log $\tau_{5000}\approx$
-0.04, where the departure coefﬁcient of the lower level is less than
departure coefﬁcient of the upper level, $b_{l}<b_{u}$, that leads to larger
source function compared to the Planck function. As a result, the NLTE line is
weaker than LTE, and NLTE correction to the yttrium abundance will be
positive, $\Delta_{\rm NLTE}$ = +0.10 dex.

Figure 6 shows the NLTE abundance corrections for selected Y ii lines at 4398,
4883, 4900, and 5087 Å in three representing model atmospheres with $T_{\rm
eff}$/ log $g$ = 5000/2.0, 5000/4.0, and 6000/4.0, and Vmic = 2 km s-1and
[Y/Fe] = 0 for all of them.

Figure 3: The fractions of Y i, Y ii, and Y iii in the model atmospheres with
different stellar parameters.

Figure 4: Departure coefficients for the Y i levels (left column) and the Y ii
levels (right column) as a function of log $\tau_{5000}$ in the model
atmospheres with 5777/4.44/0 (top row) and 5780/3.7/-2.46 (bottom row).

Figure 5: Departure coefficients as a function of log $\tau_{5000}$ for the
lower and upper levels of Y i line at 4128 Å in the model 5777/4.44/0 (upper
panel) and for the lower and upper levels of Y ii line at 5087 Å in the model
4600/1.43/-2.55 (bottom panel). The line-formation regions are shown by grey
shadow vertical lines. Right panels: theoretical line proﬁles of the
investigated lines calculated with LTE and NLTE for the particular atmospheric
models.

Figure 6: NLTE abundance corrections as functions of [Fe/H] for selected Y ii
lines at 4398, 4883, 4900, and 5087 Å for three sets of stellar parameters
$T_{\rm eff}$/ log $g$ = 5000 / 2.0, 5000 / 4.0, and 6000 / 4.0. Everywhere,
Vmic = 2 km s-1and [Y/Fe] = 0.

##  3 Solar lines of Y i and Y ii

###  3.1 Selection of Y i and Y ii lines

Hannaford et al. (1982) derived the yttrium solar abundance from eight Y i and
41 Y ii solar lines. However, it should be noticed that almost all Y i and
some Y ii lines are blended with lines of other spices. Nonetheless, the
effects of blended lines can be taken into account through the use of spectrum
fitting method. Below, we briefly characterize all lines used in this study.

The Y i line at 4128.304 Å is quite strong in solar spectrum, however, it is
located at the wing of strong Mn ii $\lambda$4128.129 Å, which may affect the
abundance from the Y i line, and it is also blended with three lines Mn i
$\lambda$4128.330, Ce ii $\lambda$4128.36, and Cr i $\lambda$4128.387 Å (Fig.
7).

The Y i lines at 4643.698 and 5630.138 Å are weak and strongly influenced by
the lines of other atoms in solar spectrum. However, in the atmospheres of
cool giants, the strength of the lines increases, while the blending lines
decrease in strength. The Y i line at 4674.848 Å is very weak in solar
spectrum and can be used with caution. It is blended with Ni i
$\lambda$4674.755, Cu i $\lambda$4674.78, C2 $\lambda$4674.831, C2
$\lambda$4674.879, Ca i $\lambda$4674.939, and K i $\lambda$4674.942 Å (Fig.
7). The intensity of the line becomes stronger once more within the
atmospheres of K giants.

The Y i line at 6023.406 Å is very weak in solar-type spectra and it lies in
the wing of the Fe i $\lambda$6024.057 Å line. In spectra of K-type stars, the
line becomes more pronounced and can be utilized for determining abundance by
spectrum fitting, when considering the absorption in the wing of Fe i line.
The Y i line at 6222.578 Å is weak and it is strongly blended by the lines of
Ca i $\lambda$6222.497, Fe ii $\lambda$6222.570, and Si i $\lambda$6222.682 in
solar spectrum. In cooler atmospheres, for example, HD 220009, the Y i
6222.578 Å line becomes more pronounced and can be used for abundance
determination. The Y i line at 6402.007 Å is too weak in solar spectrum and it
lies in the wing of strong Fe i $\lambda$6400.316 Å line. In cooler
atmospheres, the line can be measured reliably. The Y i line at 6435.022 Å is
quite strong in solar spectrum, however, it is blended with two lines CN
$\lambda$6434.894 Å and V i $\lambda$6435.158 Å from both sides (Fig. 7). In
spectra of K-type stars, the line becomes more pronounced, while blending
lines remain weak. It is one of the most reliable Y i lines for abundance
determination. The Y i line at 6437.168 Å is weak blend free line, which can
be found only in the atmospheres of cool giants.

The lines of Y ii at 4883.682, 5087.418, and 5289.815 Å are strong and free
from blends in the spectra of solar-type stars. These lines can be utilized
for determining abundance in metal-poor stars. The line Y ii at 3788.693 Å is
blended with H10 $\lambda$3797 Å, and Ce ii $\lambda$3788.746 Å in solar
spectrum. The line can be measured reliably in metal-poor stars and F-type
stars like Procyon. The line Y ii at 4124.904 Å has blends Cr i
$\lambda$4124.863 Å, and Ce ii $\lambda$4124.870 Å. The Y ii line at 4177.528
Å is blended with two lines Fe i $\lambda$4177.593Å, and Fe ii
$\lambda$4177.686 Å. This line was not used for solar analysis. However, the
blends become less pronounced in HD 84937 due to its low metallicity and hot
temperature. The line Y ii at 4374.933 Å is blended with strong Ti ii
$\lambda$4374.816 Å in solar spectrum (Fig. 7) and weak metallic lines Co i
$\lambda$4374.914, Nd ii $\lambda$4374.920, Mn i $\lambda$4374.947, and Sm ii
$\lambda$4374.975 Å. In VMP stars, weak metallic lines typically have a
negligible impact. The line Y ii at 4398.008 Å is blended with Fe i
$\lambda$4397.971, Nd ii $\lambda$4398.013, Ti i $\lambda$4398.073, and CH
$\lambda$4398.076 Å in solar spectrum (Fig. 7). The line Y ii at 4900.118 Å is
blended with a nearby Ti i line at 4899.91 Å, however, it is insignificant
when rotational velocity is less then 5 km s-1. Small blend of Er ii at
4900.08 Å is less then 2$\%$ relative to Y ii line. The Y ii line at 4982.128
Å lies between two strong lines Ti i 4981.730 Å and 4982.499 Å and has very
weak blending line Mn i $\lambda$4982.085 Å, which is negligible in metal-poor
stars. The line Y ii at 5205.722 Å lies in the wing of strong line of Cr i at
5206.041 Å and has weak blending lines MgH at 5205.755 Å ($\sim$3$\%$).

###  3.2 Solar Yttrium abundance

As a first application of the presented model atom, we derive the solar
yttrium abundance from lines of Y i and Y ii. We used the MARCS model
atmosphere 5777/4.44/0 and a depth-independent microturbulence of 0.9 km s-1.
The solar flux observations were taken from the Kitt Peak Solar Atlas (Kurucz
et al., 1984). The element abundance was determined from line-profile fitting.
The theoretical flux profiles were convolved with a profile that combines a
rotational broadening of 1.8 km s-1 and broadening by macroturbulence with a
radial-tangential profile. For different lines of Y i and Y ii, the most
probable macroturbulence velocity, Vmac, was varied between 2 and 4 km s-1. As
a rule, the uncertainty in fitting the observed profile is less than 0.02 dex
for weak lines and 0.03 dex for strong lines. The quality of the fits is
illustrated in Fig. 7 for the selected lines of Y i and Y ii. Individual line
abundances are presented in Table 1. We analyze the Y i 4128.304 and 4674.848
Å lines but do not include them in the calculations of the mean abundances.

Hereafter, the element abundances are given in the scale, where for hydrogen
log $\epsilon_{\rm H}$ = 12. In LTE, the abundance difference between Y i and
Y ii lines, $\Delta{\rm log~{}\epsilon}$(Y i \- Y ii), amounts to -0.12 dex.
NLTE abundances from the Y i and Y ii lines consistent within 0.07 dex.

Our 1D NLTE solar yttrium abundance obtained from Y ii lines is

${\rm log}~{}\epsilon_{\rm Y}=2.21\pm 0.05.$ (4)

The obtained result is in line with the 3D LTE result of Grevesse et al.
(2015), who obtained log $\epsilon_{\rm Y}$ = 2.21$\pm$0.05. Our result is
also consistent within the error bars with the meteoritic yttrium abundance,
log $\epsilon_{\rm Y}$ = 2.15$\pm$0.02 (Lodders, 2021).

Table 1: Lines of Y i and Y ii used in abundance analysis and solar yttrium
abundances, log $\epsilon$ (cols. 9 – 10).

$\lambda$ | Transition | gl \- gu | $E_{\rm exc}$ | log $gf$ | Ref. | log $\gamma_{\rm r}$ | log $\gamma_{\rm S}/N_{e}$ | log $\gamma_{\rm vW}/N_{H}$ | LTE | NLTE | $\Delta_{\rm NLTE}$
---|---|---|---|---|---|---|---|---|---|---|---
Å |  |  | eV |  |  | rad s-1cm3 | rad s-1cm3 | rad s-1cm3 |  |  |
Y i |  |  |  |  |  |  |  |  |  |  |
4128.304∗ | a2D – y2D∘ | 6 – 6 | 0.066 | 0.378 | 1 | 8.36 | -5.96 | -7.68 | 1.94 | 2.01 | 0.07
4643.698 | a2D – z2F∘ | 4 – 6 | 0.000 | -0.46 | 1 | 7.55 | -6.02 | -7.72 |  $\cdots$ |  $\cdots$ |  $\cdots$
4674.848∗ | a2D – z2F∘ | 6 – 8 | 0.066 | -0.46 | 1 | 7.38 | -6.01 | -7.72 | 2.02 | 2.10 | 0.08
5630.138 | a4F – z4G∘ | 4 – 6 | 1.356 | 0.11 | 2 | 7.83 | -5.85 | -7.76 |  $\cdots$ |  $\cdots$ |  $\cdots$
6023.406 | a2D – z4D∘ | 4 – 4 | 0.000 | -0.99 | 3 | 6.40 | -6.02 | -7.73 |  $\cdots$ |  $\cdots$ |  $\cdots$
6222.578 | a2D – z2D∘ | 4 – 6 | 0.000 | -1.74 | 3 | 6.96 | -5.97 | -7.74 |  $\cdots$ |  $\cdots$ |  $\cdots$
6402.007 | a2D – z2D∘ | 6 – 4 | 0.066 | -1.9 | 3 | 6.99 | -5.27 | -7.74 |  $\cdots$ |  $\cdots$ |  $\cdots$
6435.022 | a2D – z2D∘ | 6 – 6 | 0.066 | -0.82 | 1 | 6.96 | -5.97 | -7.74 | 2.08 | 2.14 | 0.06
6437.168 | a2G – x2F∘ | 10 – 8 | 2.294 | -0.62 | 1 | 8.24 | -5.85 | -7.63 |  $\cdots$ |  $\cdots$ |  $\cdots$
Mean |  |  |  |  |  |  |  |  | 2.08 | 2.14 |
$\sigma$ |  |  |  |  |  |  |  |  | 0.03 | 0.03 |
Y ii |  |  |  |  |  |  |  |  |  |  |
3788.693 | a3D – z3F∘ | 3 – 5 | 0.104 | -0.11 | 4 | 8.30 | -6.23 | -7.80 | 2.13 | 2.13 | 0.00
3950.349 | a3D – z1D∘ | 3 – 5 | 0.104 | -0.45 | 4 | 8.29 | -6.23 | -7.80 |  $\cdots$ |  $\cdots$ |  $\cdots$
4124.904 | a1D – z3F∘ | 5 – 7 | 0.409 | -1.57 | 4 | 8.29 | -6.26 | -7.81 | 2.16 | 2.17 | 0.01
4177.528 | a1D – z3F∘ | 5 – 5 | 0.409 | -0.07 | 4 | 8.30 | -6.26 | -7.80 |  $\cdots$ |  $\cdots$ |  $\cdots$
4235.727 | a3D – z3P∘ | 5 – 5 | 0.130 | -1.59 | 4 | 7.36 | -6.23 | -7.84 |  $\cdots$ |  $\cdots$ |  $\cdots$
4374.933 | a1D – z1D∘ | 5 – 5 | 0.409 | 0.09 | 4 | 8.29 | -6.26 | -7.80 | 2.26 | 2.25 | -0.01
4398.008 | a3D – z3P∘ | 5 – 3 | 0.130 | -1.1 | 4 | 7.44 | -6.23 | -7.83 | 2.22 | 2.25 | 0.03
4682.321 | a1D – z3P∘ | 5 – 5 | 0.409 | -1.5 | 4 | 7.36 | -6.26 | -7.84 |  $\cdots$ |  $\cdots$ |  $\cdots$
4823.304 | a3F – z3D∘ | 5 – 5 | 0.992 | -1.09 | 4 | 8.46 | -6.40 | -7.76 |  $\cdots$ |  $\cdots$ |  $\cdots$
4854.861 | a3F – z3D∘ | 5 – 3 | 0.992 | -0.29 | 4 | 8.46 | -6.40 | -7.76 |  $\cdots$ |  $\cdots$ |  $\cdots$
4883.682 | a3F – z3D∘ | 9 – 7 | 1.084 | 0.1 | 4 | 8.47 | -6.40 | -7.76 | 2.18 | 2.18 | 0.00
4900.118 | a3F – z3D∘ | 7 – 5 | 1.033 | -0.07 | 4 | 8.46 | -6.40 | -7.76 | 2.27 | 2.27 | 0.00
4982.128 | a3F – z3F∘ | 7 – 9 | 1.033 | -1.36 | 4 | 8.31 | -6.40 | -7.81 | 2.18 | 2.19 | 0.01
5087.418 | a3F – z3F∘ | 9 – 9 | 1.084 | -0.19 | 4 | 8.31 | -6.40 | -7.81 | 2.19 | 2.20 | 0.01
5119.110 | a3F – z3F∘ | 5 – 7 | 0.992 | -1.39 | 4 | 8.29 | -6.40 | -7.81 | 2.21 | 2.23 | 0.02
5123.209 | a3F – z1P∘ | 5 – 3 | 0.992 | -1.2 | 4 | 8.30 | -6.40 | -7.78 |  $\cdots$ |  $\cdots$ |  $\cdots$
5200.409 | a3F – z3F∘ | 5 – 5 | 0.992 | -0.67 | 4 | 8.30 | -6.40 | -7.80 | 2.23 | 2.26 | 0.03
5205.722 | a3F – z3F∘ | 7 – 7 | 1.033 | -0.34 | 4 | 8.29 | -6.40 | -7.81 | 2.15 | 2.17 | 0.02
5289.815 | a3F – z3F∘ | 7 – 5 | 1.033 | -1.78 | 4 | 8.30 | -6.40 | -7.80 | 2.13 | 2.16 | 0.03
5402.773 | b1D – z1F∘ | 5 – 7 | 1.839 | -0.35 | 4 | 8.33 | -6.34 | -7.74 |  $\cdots$ |  $\cdots$ |  $\cdots$
5473.384 | a3P – y3P∘ | 3 – 5 | 1.738 | -0.93 | 4 | 8.64 | -6.36 | -7.75 | 2.30 | 2.33 | 0.03
5521.562 | a3P – y3P∘ | 3 – 3 | 1.738 | -1.1 | 4 | 8.64 | -6.36 | -7.75 | 2.24 | 2.25 | 0.01
5544.610 | a3P – y3P∘ | 3 – 1 | 1.738 | -0.99 | 4 | 8.64 | -6.36 | -7.75 |  $\cdots$ |  $\cdots$ |  $\cdots$
5546.008 | a3P – y3P∘ | 5 – 3 | 1.748 | -0.94 | 4 | 8.64 | -6.36 | -7.75 |  $\cdots$ |  $\cdots$ |  $\cdots$
6613.731 | a3P – z3D∘ | 5 – 7 | 1.748 | -0.99 | 4 | 8.47 | -6.36 | -7.76 |  $\cdots$ |  $\cdots$ |  $\cdots$
6795.415 | a3P – z3D∘ | 3 – 5 | 1.738 | -1.22 | 4 | 8.46 | -6.36 | -7.76 | 2.15 | 2.17 | 0.02
7881.878 | b1D – z1P∘ | 5 – 3 | 1.839 | -0.49 | 4 | 8.30 | -6.34 | -7.78 |  $\cdots$ |  $\cdots$ |  $\cdots$
Mean |  |  |  |  |  |  |  |  | 2.20 | 2.21 |
$\sigma$ |  |  |  |  |  |  |  |  | 0.05 | 0.05 |
Y i \- Y ii |  |  |  |  |  |  |  | -0.12 | -0.07 |

Note. — References: (1) Kramida et al. (2022); (2) Shang et al. (2015); (3) Li
et al. (2018); (4) Palmeri et al. (2017). Lines and abundances, which were not
used in mean calculations are marked by (∗). The fitting error (0.03 dex) for
Y i 6435.022 Å line was adopted as $\sigma$. For Y ii lines, $\sigma$ means
standard deviation.

Figure 7: Best NLTE fits (continuous red curve) to the solar flux line
profiles (black circles) of Y i 4128, 4674, 6435 Å and Y ii 4124, 4374, 4398,
4883, 4900, 5087, 5200, 5205, 5289 Å. For each line, the LTE profile (dashed
blue curve) was computed with the yttrium abundance obtained from the NLTE
analysis.

##  4 Yttrium abundances of the selected stars

###  4.1 Stellar Sample, Observations, and Stellar Parameters

Our sample includes 11 bright stars with well-known atmospheric parameters
(Table 2). All of them were established as $Gaia$ FGK benchmark stars with a
range of different metallicities and have been used as reference or test
objects in previous spectroscopic investigations and as targets of
asteroseismological campaigns. The sample includes three FGK dwarfs: HD 22049,
Procyon, and HD 49933, three K giants: Aldebaran (HD 29139), Arcturus (HD
124897), and Pollux (HD 62509), three FG dwarfs with low metallicity: HD
22879, HD 84937, and HD 140283, and two metal-poor giants: HD 122563, HD
220009. Their V magnitudes range from -0.05 to 8.3. Most of the stars are
close to the Sun, and their parameters should be fairly accurate. Below we
comment brieﬂy on some individual stars.

HD 49933 is a solar-type star, with V sin$i\sim 6$ km s-1. The physical
parameters of HD 49933 were obtained previously by different authors with
different methods. However, they display some scatter both in $T_{\rm eff}$
and log $g$. Among the recent determinations, one of the lowest values of
$T_{\rm eff}$(K)/log $g$ = 6476/4.18 were determined by Jönsson et al. (2020),
while the highest ones, 6727/4.50 were presented in Sarmento et al. (2020). We
adopted $T_{\rm eff}$/log $g$ = 6635/4.21, obtained from angular diameter
measurements and bolometric fluxes and from a homogeneous mass determination
based on stellar evolution models (Heiter et al., 2015).

Procyon is a known spectroscopic binary system. The proximity of Procyon to
Earth makes it possible to measure directly its angular diameter. We adopted
$T_{\rm eff}$=6590 K and log $g$=3.95 calculated as average values from eleven
sets of parameters in Ryabchikova et al. (2016).

HD 22879 is a metal poor high-velocity star, with V sin$i\sim 4.2$ km s-1
(Buder et al., 2019), classified by Gray et al. (2001) as G0 V mF2, because
the metallic line spectrum is approximately the strength of the F2 V standard.
We adopted $T_{\rm eff}$(K)/log $g$/[Fe/H]=5893/4.45/-0.86 from spectroscopic
analysis of Casali et al. (2020).

HD 220009 is a K subgiant with high proper motion and rotation velocity V
sin$i\sim 10$ km s-1 (Bernacca & Perinotto, 1970). We adopted $T_{\rm
eff}$/log $g$/[Fe/H] = 4266/1.43/-0.74 from Heiter et al. (2015); Jofré et al.
(2014), whose parameters are in agreement with other studies, where stellar
atmospheric parameters were derived purely spectroscopically (e.g. Steinmetz
et al. (2020)).

The physical parameters for three K giants: Aldebaran (HD 29139), Arcturus (HD
124897), and Pollux (HD 62509) were taken from the sample of Gaia FGK
benchmark stars (Heiter et al., 2015), and the NLTE [Fe/H] values for these
stars were taken from Jofré et al. (2014).

Three metal-poor stars in the -2.55$\leq$[Fe/H]$\leq$-2.12 metallicity range,
HD 84937, HD 122563, and HD 140283, were used for our analysis. Their stellar
parameters are based on numerous photometric measurements and accurate
distances, that is why they are traditionally featured in many NLTE studies,
e.g. Alexeeva & Mashonkina (2015); Sitnova et al. (2016); Mashonkina et al.
(2017); Alexeeva et al. (2018); Mashonkina et al. (2019a); Sitnova et al.
(2022).

Being a subject of scientific interest and also popular science movies for the
last sixty years, HD 22049 ($\epsilon$ Eri) is the closest solar-type star to
the Sun at a distance of 3.220$\pm$0.001 pc (Gaia Collaboration et al., 2021)
with a mass of 0.82$\pm$0.05 M$\odot$ (Baines & Armstrong, 2012). $\epsilon$
Eri is a young (360–720 Myr; Janson et al. (2015)) K2 V star, which displays
relatively high stellar variability and stellar activity, see e.g. Gray &
Baliunas (1995); Bastian et al. (2018); Coffaro et al. (2020); Holzer et al.
(2021). This single star hosts at least one exoplanet with an estimated mass
1.55$\pm$0.24 times that of Jupiter discovered by Hatzes et al. (2000).

The spectrum of Arcturus in the visible spectral range (3772$-$7900 Å) was
obtained in 2019/06/05 (under programm ID 0103.D-0118(A)) with the Echelle
SPectrograph for Rocky Exoplanets and Stable Spectroscopic Observations
(ESPRESSO) spectrograph installed at the Combined-Coude Laboratory of the VLT
and linked to the four 8.2 m Unit Telescopes (Pepe et al., 2021). The spectra
of the remaining stars in the visible spectral range (3781$-$6912 Å) were
obtained with the High-Accuracy Radial velocity Planetary Searcher (HARPS)
echelle spectrograph installed on ESO’s 3.6-m Telescope at La Silla (Mayor et
al., 2003). The extracted and wavelength calibrated spectra were taken from
ESO Archive666http://archive.eso.org/eso/eso$\\_$archive$\\_$main.html. All
spectra were obtained with a high spectral resolving power, $R$, and high
signal-to-noise ratio (S/N; from 186 to 424). The characteristics of the
observed spectra for individual stars are given in Table 3. The normalisation
of stellar spectra to their continuum was performed with the RASSINE $Python$
code (Cretignier et al., 2020).

Table 2: Atmospheric parameters of the reference stars and sources of the
data.

Star | Name | Sp. T. | $T_{\rm eff}$ | log$g$ | [Fe/H] | $\xi_{t}$ | Ref. | [Y/Fe]LTE | [Y/Fe]NLTE
---|---|---|---|---|---|---|---|---|---
|  |  | K | CGS | dex | km s-1 |  |  |
HD 22049 |  $\epsilon$ Eri | K2 V | 5076 | 4.61 | -0.09 | 1.1 | 1, 2 | -0.08$\pm$0.06 | -0.05$\pm$0.03
HD 22879 |  | G0 V mF2 | 5893 | 4.45 | -0.86 | 1.8 | 3 | 0.03$\pm$0.07 | 0.10$\pm$0.06
HD 29139 | Aldebaran | K5+III | 3930 | 1.11 | -0.37 | 1.7 | 1 | -0.20$\pm$0.16 | -0.10$\pm$0.07
HD 49933 |  | F3 V | 6635 | 4.21 | -0.41 | 1.9 | 1, 2 | 0.04$\pm$0.09 | 0.11$\pm$0.09
HD 61421 | Procyon | F5 IV-V | 6590 | 3.95 | -0.02 | 1.8 | 4 | 0.04$\pm$0.04 | 0.07$\pm$0.04
HD 62509 | Pollux | K0 IIIb | 4860 | 2.9 | 0.13 | 1.5 | 1 | -0.18$\pm$0.13 | -0.17$\pm$0.13
HD 84937 |  | F8 V | 6350 | 4.09 | -2.12 | 1.7 | 5 | -0.01$\pm$0.03 | 0.07$\pm$0.03
HD 122563 |  | G8 III | 4600 | 1.43 | -2.55 | 1.6 | 6 | -0.40$\pm$0.08 | -0.28$\pm$0.07
HD 124897 | Arcturus | K1.5 III | 4290 | 1.6 | -0.52 | 1.7 | 1 | -0.21$\pm$0.09 | -0.17$\pm$0.08
HD 140283 |  | F9 V | 5780 | 3.7 | -2.46 | 1.6 | 5 | -0.42$\pm$0.04 | -0.32$\pm$0.04
HD 220009 |  | K1 IV | 4266 | 1.43 | -0.74 | 1.3 | 1, 2 | -0.06$\pm$0.06 | -0.03$\pm$0.07

Note. — Note. References: (1) Heiter et al. (2015); (2) Jofré et al. (2014);
(3) Casali et al. (2020); (4) Ryabchikova et al. (2016); (5) Sitnova et al.
(2015); (6) Mashonkina et al. (2011b). Spectral types are extracted from the
SIMBAD database.

Table 3: Characteristics of observed spectra of the reference stars.

Star | Name | V1 | Telescope/ | Spectral range | $t_{exp}$ | Observing run | $R$ | $S/N$ | Run/Program ID
---|---|---|---|---|---|---|---|---|---
|  | mag | Spectrograph | Å | s | year/month/day |  |  |
HD 22049 |  $\epsilon$ Eri | 3.7 | 1 | 3781-6913 | 30 | 2019/12/01 | 115 000 | 186.3 | 0104.C-0863(A)
HD 22879 |  | 6.7 | 1 | 3781-6913 | 900 | 2005/10/30 | 115 000 | 306.5 | 072.C-0488(E)
HD 29139 | Aldebaran | 0.9 | 1 | 3781-6913 | 15 | 2007/10/22 | 115 000 | 372.0 | 080.D-0347(A)
HD 49933 |  | 5.8 | 1 | 3781-6913 | 279 | 2006/02/11 | 115 000 | 234.8 | 076.C-0279(A)
HD 61421 | Procyon | 0.4 | 1 | 3781-6913 | 10 | 2007/01/11 | 115 000 | 301.8 | 078.D-0492(A)
HD 62509 | Pollux | 1.1 | 1 | 3781-6913 | 8 | 2007/11/06 | 115 000 | 257.6 | 080.D-0347(A)
HD 84937 |  | 8.3 | 1 | 3781-6913 | 2700 | 2007/12/31 | 115 000 | 216.5 | 080.D-0347(A)
HD 122563 |  | 6.2 | 1 | 3781-6913 | 1500 | 2008/02/24 | 115 000 | 318.5 | 080.D-0347(A)
HD 124897 | Arcturus |  $-$0.05 | 2 | 3772-7900 | 15 | 2019/06/05 | 190 000 | 424.5 | 0103.D-0118(A)
HD 140283 |  | 7.2 | 1 | 3781-6913 | 2700 | 2008/03/06 | 115 000 | 267.4 | 080.D-0347(A)
HD 220009 |  | 5.1 | 1 | 3781-6913 | 300 | 2007/09/29 | 115 000 | 332.2 | 080.D-0347(A)

Note. — Notes: 1V is a visual magnitude from the SIMBAD data base.
Telescope/spectrograph: 1 = ESO-3.6/HARPS Echelle; 2 = ESO-VLT-U3/VIS.

###  4.2 Analysis of Y i and Y ii lines in the reference stars

In this section, we derive the yttrium abundances of 11 reference stars using
lines of Y i and Y ii in the visible spectral range. The abundance results on
the individual lines are presented in Table 4. The derived LTE and NLTE [Y/Fe]
ratios are given in Table 2. For six stars where lines of both ionization
stages are available, the NLTE abundances derived from the Y i and Y ii lines
agree within the error bars, while in LTE, the abundance differences can reach
up to -0.31 dex. That is well illustrated by Figure 8. For the most of the
stars, NLTE for Y i gives a smaller line-to-line scatter compared to LTE (see
Table 4).

For the most of the stars, the obtained yttrium NLTE abundance is close to the
solar value. The exceptions are two metal poor stars HD 12256 and HD 140283
with [Y/Fe] = -0.28 dex and -0.32 dex, respectively. Below we give detail
information on individual stars.

$\epsilon$ Eri. This is a solar-type star; therefore the yttrium NLTE
abundance, log$\epsilon$ = 2.05$\pm$0.14, was derived from four Y i lines, and
log$\epsilon$ = 2.10$\pm$0.05 from nine Y ii lines. The NLTE abundance
corrections are significant and positive for Y i lines at 4128, 4674, 6023,
6435 Å, ($\Delta_{\rm NLTE}$ $\sim$0.06 dex), while for Y ii lines, they are
slightly positive ($\Delta_{\rm NLTE}$ $\leq$ 0.03 dex).

HD 22879. NLTE for both Y i and Y ii gives a smaller line-to-line scatter
compared to LTE (Figure 9). NLTE leads to weakened both lines of Y i and Y ii,
and the obtained NLTE abundances from the two ionization stages are consistent
within 0.08 dex.

Aldebaran. Most of the Y i and Y ii lines in the investigated spectral range
are strongly contaminated with blending lines. Even though our line profile
analysis allows to separate pure yttrium lines in the spectra, we limited with
two lines of Y i and three lines of Y ii only. Compared to solar-type
atmosphere, the NLTE effects are stronger in Y i with $\Delta_{\rm NLTE}$
$\leq$0.16 dex, and weaker in Y ii. The NLTE abundances from lines of the two
ionization stages, Y i and Y ii, are consistent, however, we notice quite big
scatter in both LTE and NLTE abundances for Y ii lines.

HD 49933. This is the hottest star in our sample; therefore the NLTE yttrium
abundance, log$\epsilon$ = 1.91$\pm$0.09, was derived from the Y ii lines
only. Totally, ten lines were employed and all of them have slightly positive
NLTE abundance corrections, from 0.00 dex to 0.12 dex.

Procyon. The NLTE effects for the Y ii lines are similar to those found for HD
49933, although they are slightly smaller. We obtained [Y/Fe]NLTE =
0.04$\pm$0.04 and [Y/Fe]LTE = 0.07$\pm$0.04 from eighteen Y ii line.

Pollux. The NLTE abundance corrections are from 0.0 to 0.02 for all
investigated Y ii lines. While, for Y i lines at 6402, and 6435 Å, the
$\Delta_{\rm NLTE}$ $=$ 0.11, and 0.12 dex, respectively. The obtained NLTE
abundances from the two ionization stages are consistent within 0.08 dex
(Figure 9).

HD 84937. This is turn-off VMP star. This star has similar physical parameters
($T_{\rm eff}$ and log$g$) as Procyon, but because of its low metallicity
([Fe/H] = -2.12), the NLTE effects for Y ii lines are stronger compared to
Procyon’s atmosphere and less amount of lines are available for measurement.
The NLTE yttrium abundance, averaged over 6 Y ii lines, is log$\epsilon$ =
0.16$\pm$0.03 and [Y/Fe] = 0.07$\pm$0.03.

HD 122563. In the spectrum of this cool metal-poor giant, we found 12 Y ii
lines only, which can be used for yttrium abundance determination. The NLTE
corrections are positive for all investigated lines and do not exceed 0.21
dex. The Y NLTE abundance, averaged over 12 Y ii lines, is log$\epsilon$ =
-0.62$\pm$0.07 and [Y/Fe] = -0.28$\pm$0.07 that is by 0.12 dex higher compared
to LTE abundance.

Arcturus. The NLTE effects for both Y i and Y ii lines are similar to those
found for Aldebaran. The obtained NLTE abundances from the two ionization
stages are consistent within 0.07 dex. While the LTE abundance based on the Y
i lines is 0.31 dex lower compared with that for Y ii.

HD 140283. In the atmosphere of this VMP subgiant, only few Y ii lines are
avaliable. From six Y ii lines, we derived NLTE yttrium abundance
-0.57$\pm$0.04. The NLTE corrections are positive for all investigated lines
and do not exceed 0.14 dex. The mean NLTE yttrium abundance is higher by 0.10
dex compared to LTE value.

HD 220009. Six lines of Y i and eleven lines of Y ii were examined in the
spectrum of this star. The obtained NLTE abundances from the two ionization
stages are consistent within 0.05 dex (Figure 9), while the LTE abundance
based on the Y i lines is 0.30 dex lower compared with that for Y ii.

Figure 8: [Y/Fe] LTE (left panel) and NLTE (right panel) ratios obtained from
Y i and Y ii lines. The error bars correspond to the dispersion in the single
line measurements about the mean.

Figure 9: Yttrium LTE (open symbols) and NLTE (filled symbols) abundances of
few program stars derived from lines of Y i (circles) and Y ii (squares) in
wide spectral region.  Table 4: NLTE and LTE abundances of the program stars.

$\lambda$ (Å ) | LTE | NLTE | $\Delta$ | LTE | NLTE | $\Delta$ | LTE | NLTE | $\Delta$ | LTE | NLTE | $\Delta$ | LTE | NLTE | $\Delta$ | LTE | NLTE | $\Delta$
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---
| HD22049 | HD22879 | Aldebaran | Pollux | Arcturus | HD220009
Y i |
4128.304 | 1.82 | 1.88 | 0.06 | 1.27 | 1.36 | 0.09 |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$
4643.698 |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ | 0.96 | 1.42 | 0.46
4674.848 | 1.93 | 2.00 | 0.07 | 1.39 | 1.46 | 0.07 |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ | 1.17 | 1.48 | 0.31 | 1.04 | 1.39 | 0.35
5630.138 |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ | 1.26 | 1.48 | 0.22
6023.406 |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$
6222.578 | 2.15 | 2.20 | 0.05 |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ | 1.04 | 1.25 | 0.21
6402.007 |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ | 1.52 | 1.68 | 0.16 | 2.13 | 2.24 | 0.11 | 1.25 | 1.49 | 0.24 | 1.24 | 1.47 | 0.23
6435.022 | 2.08 | 2.13 | 0.05 |  $\cdots$ |  $\cdots$ |  $\cdots$ | 1.54 | 1.70 | 0.16 | 2.14 | 2.26 | 0.12 | 1.13 | 1.37 | 0.24 | 1.09 | 1.32 | 0.23
Mean | 2.00 | 2.05 |  $\cdots$ | 1.33 | 1.41 |  $\cdots$ | 1.53 | 1.69 |  $\cdots$ | 2.14 | 2.25 |  $\cdots$ | 1.18 | 1.45 |  $\cdots$ | 1.11 | 1.39 |  $\cdots$
$\sigma$ | 0.15 | 0.14 |  $\cdots$ | 0.08 | 0.07 |  $\cdots$ | 0.01 | 0.01 |  $\cdots$ | 0.01 | 0.01 |  $\cdots$ | 0.06 | 0.07 |  $\cdots$ | 0.12 | 0.09 |  $\cdots$
Y ii |
4398.008 | 2.00 | 2.03 | 0.03 | 1.49 | 1.56 | 0.07 |  $\cdots$ |  $\cdots$ |  $\cdots$ | 2.16 | 2.16 | 0.00 |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$
4854.861 |  $\cdots$ |  $\cdots$ |  $\cdots$ | 1.36 | 1.43 | 0.07 |  $\cdots$ |  $\cdots$ |  $\cdots$ | 2.07 | 2.07 | 0.00 |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$
4883.682 | 2.17 | 2.20 | 0.03 | 1.36 | 1.44 | 0.08 |  $\cdots$ |  $\cdots$ |  $\cdots$ | 2.08 | 2.08 | 0.00 | 1.63 | 1.67 | 0.04 | 1.50 | 1.54 | 0.04
4900.118 | 2.11 | 2.13 | 0.02 | 1.40 | 1.48 | 0.08 |  $\cdots$ |  $\cdots$ |  $\cdots$ | 2.12 | 2.12 | 0.00 | 1.39 | 1.45 | 0.06 | 1.39 | 1.43 | 0.04
4982.128 |  $\cdots$ |  $\cdots$ |  $\cdots$ | 1.47 | 1.50 | 0.03 |  $\cdots$ |  $\cdots$ |  $\cdots$ | 2.31 | 2.32 | 0.01 | 1.44 | 1.48 | 0.04 | 1.47 | 1.51 | 0.04
5087.418 | 2.01 | 2.03 | 0.02 | 1.40 | 1.44 | 0.04 | 1.73 | 1.75 | 0.02 | 1.96 | 1.97 | 0.01 | 1.43 | 1.46 | 0.03 | 1.41 | 1.44 | 0.03
5119.110 |  $\cdots$ |  $\cdots$ |  $\cdots$ | 1.53 | 1.57 | 0.04 |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ | 1.37 | 1.40 | 0.03
5205.722 |  $\cdots$ |  $\cdots$ |  $\cdots$ | 1.46 | 1.52 | 0.06 |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$
5289.815 | 2.07 | 2.08 | 0.01 | 1.50 | 1.57 | 0.07 | 1.69 | 1.70 | 0.01 | 2.31 | 2.32 | 0.01 | 1.52 | 1.54 | 0.02 | 1.34 | 1.35 | 0.01
5402.773 | 2.08 | 2.08 | 0.00 | 1.32 | 1.36 | 0.04 |  $\cdots$ |  $\cdots$ |  $\cdots$ | 2.06 | 2.06 | 0.00 |  $\cdots$ |  $\cdots$ |  $\cdots$ | 1.35 | 1.35 | 0.00
5473.384 |  $\cdots$ |  $\cdots$ |  $\cdots$ | 1.46 | 1.54 | 0.08 |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ | 1.50 | 1.54 | 0.04 | 1.40 | 1.43 | 0.03
5521.562 |  $\cdots$ |  $\cdots$ |  $\cdots$ | 1.50 | 1.50 | 0.00 |  $\cdots$ |  $\cdots$ |  $\cdots$ | 2.17 | 2.17 | 0.00 |  $\cdots$ |  $\cdots$ |  $\cdots$ | 1.45 | 1.46 | 0.01
5544.610 |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ | 1.84 | 1.92 | 0.08 | 2.37 | 2.39 | 0.02 |  $\cdots$ |  $\cdots$ |  $\cdots$ | 1.49 | 1.54 | 0.05
5546.008 | 2.08 | 2.08 | 0.00 |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$
6613.731 | 2.09 | 2.12 | 0.03 |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$
6795.415 | 2.10 | 2.11 | 0.01 | 1.39 | 1.44 | 0.05 |  $\cdots$ |  $\cdots$ |  $\cdots$ | 2.20 | 2.20 | 0.00 |  $\cdots$ |  $\cdots$ |  $\cdots$ | 1.35 | 1.36 | 0.01
Mean | 2.08 | 2.10 |  $\cdots$ | 1.43 | 1.49 |  $\cdots$ | 1.75 | 1.79 |  $\cdots$ | 2.16 | 2.17 |  $\cdots$ | 1.49 | 1.52 |  $\cdots$ | 1.41 | 1.44 |  $\cdots$
$\sigma$ | 0.05 | 0.05 |  $\cdots$ | 0.07 | 0.06 |  $\cdots$ | 0.08 | 0.12 |  $\cdots$ | 0.13 | 0.13 |  $\cdots$ | 0.09 | 0.08 |  $\cdots$ | 0.06 | 0.07 |  $\cdots$
Y i$-$Y ii | -0.08 | -0.05 |  $\cdots$ | -0.10 | -0.08 |  $\cdots$ | -0.22 | -0.10 |  $\cdots$ | -0.02 | 0.08 |  $\cdots$ | -0.31 | 0.07 |  $\cdots$ | -0.30 | -0.05 |  $\cdots$
| HD49933 | Procyon | HD84937 | HD122563 | HD140283 |
Y ii |
3788.693 |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ | -0.87 | -0.66 | 0.21 | -0.66 | -0.52 | 0.14 |  |  |
4124.904 |  $\cdots$ |  $\cdots$ |  $\cdots$ | 2.26 | 2.29 | 0.03 |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  |  |
4177.528 |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ | 0.03 | 0.16 | 0.13 |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  |  |
4235.727 |  $\cdots$ |  $\cdots$ |  $\cdots$ | 2.21 | 2.25 | 0.04 | 0.11 | 0.19 | 0.08 |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  |  |
4374.933 |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ | 0.07 | 0.17 | 0.10 | -0.82 | -0.72 | 0.10 | -0.73 | -0.64 | 0.09 |  |  |
4398.008 | 1.84 | 1.92 | 0.08 | 2.24 | 2.32 | 0.08 | 0.10 | 0.20 | 0.10 | -0.62 | -0.45 | 0.17 | -0.68 | -0.56 | 0.12 |  |  |
4682.321 |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ | -0.66 | -0.63 | 0.03 |  $\cdots$ |  $\cdots$ |  $\cdots$ |  |  |
4823.304 |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ | -0.80 | -0.67 | 0.13 |  $\cdots$ |  $\cdots$ |  $\cdots$ |  |  |
4854.861 | 1.72 | 1.80 | 0.08 | 2.17 | 2.20 | 0.03 |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  |  |
4883.682 | 1.83 | 1.88 | 0.05 | 2.28 | 2.27 | -0.01 | 0.07 | 0.13 | 0.06 | -0.77 | -0.64 | 0.13 | -0.67 | -0.61 | 0.06 |  |  |
4900.118 |  $\cdots$ |  $\cdots$ |  $\cdots$ | 2.28 | 2.28 | 0.00 | 0.07 | 0.13 | 0.06 | -0.78 | -0.65 | 0.13 | -0.63 | -0.56 | 0.07 |  |  |
4982.128 |  $\cdots$ |  $\cdots$ |  $\cdots$ | 2.23 | 2.25 | 0.02 |  $\cdots$ |  $\cdots$ |  $\cdots$ | -0.60 | -0.54 | 0.06 |  $\cdots$ |  $\cdots$ |  $\cdots$ |  |  |
5087.418 | 1.81 | 1.86 | 0.05 | 2.23 | 2.23 | 0.00 |  $\cdots$ |  $\cdots$ |  $\cdots$ | -0.74 | -0.64 | 0.10 | -0.64 | -0.55 | 0.09 |  |  |
5119.110 | 1.93 | 2.00 | 0.07 | 2.20 | 2.26 | 0.06 |  $\cdots$ |  $\cdots$ |  $\cdots$ | -0.76 | -0.64 | 0.12 |  $\cdots$ |  $\cdots$ |  $\cdots$ |  |  |
5200.409 | 1.88 | 2.00 | 0.12 | 2.26 | 2.34 | 0.08 |  $\cdots$ |  $\cdots$ |  $\cdots$ | -0.73 | -0.57 | 0.16 |  $\cdots$ |  $\cdots$ |  $\cdots$ |  |  |
5205.722 | 1.70 | 1.79 | 0.09 | 2.17 | 2.25 | 0.08 |  $\cdots$ |  $\cdots$ |  $\cdots$ | -0.76 | -0.65 | 0.11 |  $\cdots$ |  $\cdots$ |  $\cdots$ |  |  |
5289.815 | 1.95 | 2.04 | 0.09 | 2.17 | 2.24 | 0.07 |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  |  |
5402.773 | 1.77 | 1.79 | 0.02 |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  |  |
5473.384 |  $\cdots$ |  $\cdots$ |  $\cdots$ | 2.26 | 2.31 | 0.05 |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  |  |
5521.562 |  $\cdots$ |  $\cdots$ |  $\cdots$ | 2.28 | 2.29 | 0.01 |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  |  |
5544.610 |  $\cdots$ |  $\cdots$ |  $\cdots$ | 2.26 | 2.30 | 0.04 |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  |  |
5546.008 | 1.97 | 1.97 | 0.00 | 2.18 | 2.19 | 0.01 |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  |  |
6613.731 |  $\cdots$ |  $\cdots$ |  $\cdots$ | 2.24 | 2.26 | 0.02 |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  |  |
6795.415 |  $\cdots$ |  $\cdots$ |  $\cdots$ | 2.18 | 2.20 | 0.02 |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  |  |
Mean | 1.84 | 1.91 |  $\cdots$ | 2.23 | 2.26 |  $\cdots$ | 0.08 | 0.16 |  $\cdots$ | -0.74 | -0.62 |  $\cdots$ | -0.67 | -0.57 |  $\cdots$ |  |  |
$\sigma$ | 0.09 | 0.09 |  $\cdots$ | 0.04 | 0.04 |  $\cdots$ | 0.03 | 0.03 |  $\cdots$ | 0.08 | 0.07 |  $\cdots$ | 0.04 | 0.04 |  $\cdots$ |  |  |

Note. — Here, $\Delta$ means $\Delta_{NLTE}$.

##  5 Yttrium abundance trend

###  5.1 Stellar sample

We present the NLTE yttrium abundances in a sample consisting of 65 FGK stars,
which are uniformly distributed across the -2.62$\leq$[Fe/H]$\leq$+0.24
metallicity range. This range is relevant to research on the Galactic chemical
evolution. Most of the stars are dwarfs, with a few subgiants added. Stellar
atmosphere parameters and yttrium LTE and NLTE abundances for 61 stars are
given in Table A.3. Other four stars of this sample, HD 49933 (Thin disc), HD
22879 (Thick disc), HD 84937 and HD 140283 (Halo) can be found in Table 2,
where their LTE and NLTE yttrium-to-iron abundance ratios [Y/Fe] are also
presented. For the first 47 stars from Table A.3, we adopted the stellar
parameters from Sitnova et al. (2015). For stars $\\#$ 48–54, the stellar
parameters were adopted from Mashonkina et al. (2003), and, for stars
$\\#$55–61, from Mashonkina et al. (2019b).

The Galactic thin disk stellar population is represented by 28 stars, with
[Fe/H] $\geq$ -0.78. We included 17 thick-disk stars in the
-1.49$\leq$[Fe/H]$\leq$-0.17 range, overlapping with that of the thin-disk and
20 halo stars, which are distributed in the -2.62$\leq$[Fe/H]$\leq$-1.08
range.

For the first 47 stars from Table A.3, we employed high-resolution ($R>$
45,000) and high signal-to-noise ratio S/N $>$ 60 spectra obtained at the 3-m
telescope of the Lick Observatory with the Hamilton spectrograph or taken from
ESPaDOnS777http://www.cadc-ccda.hia-iha.nrc-cnrc.gc.ca/en/search/ archive. The
characteristics of the spectra of the stars $\\#$48–61 are presented in Table
5. The spectra were downloaded from ESO Archive and normalized with the
RASSINE $Python$ code (Cretignier et al., 2020).

We used six lines of Y ii at 4374, 4398, 4883, 4900, 5087, 5205 Å for yttrium
abundance determination in the sample. When fitting the Y ii 4374 Å line, the
Ti ii 4374.813 Å line was taken into account. When fitting the Y ii 5205 Å
line, the Cr i 5206.041 Å line was taken into account. The abundances were
determined using a line-by-line differential approach, comparing them to the
solar reference abundances.

###  5.2 Yttrium Abundance Trend

Halo stars with -2.62$\leq$[Fe/H]$\leq$-1.46 metallicity range show positive
trend (Slope: +0.18$\pm$0.11) from [Y/Fe] $\approx$ -0.07 to 0.14 dex (Figure
10). However, if we remove HD 140283 from the group of stars with this
metallicity range, the positive trend will have slope +0.09$\pm$0.10. Further
NLTE [Y/Fe] determination in very metal poor stars with [Fe/H] $<$ -2.5 would
be helpful for extention the trend towards lower metallicity and studies of
the earliest stages of Galactic yttrium formation. This behaviour argues that
yttrium is mainly produced in supernova type II (massive stars) explosions
(SNe, Kobayashi et al., 2020), and their yields depend on metallicity. The
more metal-rich SNe, the higher yttrium production. A famous star HD 140283,
which has been extensively studied and found to be deficient in $r$-process
elements see e.g. Sitnova et al. (2015); Siqueira-Mello et al. (2015) and
revealed a significant underabundance of Sr, Zr, and Ba compared to Fe ratios
when compared to other stars in the galactic halo, exposes [Y/Fe] = -0.32 dex,
that is lower compared to other stars in our sample.

In the -1.49$\leq$[Fe/H]$\leq$-0.6 metallicity range, the thick disc stars
show negative trend (Slope: -0.26$\pm$0.08) in [Y/Fe] from 0.18 to -0.05 dex.
Thin disc stars at -0.44$\leq$[Fe/H]$\leq$0.24 range also show negative trend
(Slope: -0.32$\pm$0.09) in [Y/Fe] from 0.08 to -0.14 dex. It looks like that
at [Fe/H]$\approx$-1.50 the positive trend turns to negative one. The observed
knee at [Fe/H]$\approx$-1.50 could indicate the onset of the Fe production by
Type Ia SNe (SNe Ia), however, this contradicts with the earlier studies,
where the Galactic trends for different $\alpha$-elements (O, Mg Si, Ca) have
’the knee’ and onset of iron production in SN Ia at [Fe/H] = -0.9. The reason
why we found ’the knee’ at [Fe/H]$\approx$-1.50 instead of [Fe/H] = -0.9 is
not clear.

Figure 10 shows the comparison between our observational data and the
predictions from the GCE models from Kobayashi et al. (2020). The $s$ model
takes into account the $s$-process only (dashed line), and the $s+r$ model
(solid line) takes into account not only the $s$-process, but also high-mass
super-AGB stars explode as electron-capture supernovae (ECSNe), NS–NS/NS–BH
mergers, and core-collapse supernovae induced by strong magnetic ﬁelds and/or
fast rotation (MRSNe). The trend of the $s+r$ model is in excellent agreement
with our observational data at -1.60$\leq$[Fe/H]$\leq$+0.24. However, at
metallicity range -2.62$\leq$[Fe/H]$\leq$-1.60, the $s+r$ model predicts
$\sim$0.23 dex lower [Y/Fe]. This indicates that the input of Y yields needs
to be improved in the GCE model.

We undertake a comparison between yttrium and two other light neutron-capture
elements, namely, strontium (Sr) and zirconium (Zr), which are believed to
have a common origin in nucleosynthesis. The NLTE abundances of Sr and Zr for
our sample stars were taken from Zhao et al. (2016). In Figure 11, we study
the behavior of [Zr/Y] and [Sr/Zr] with metalicity. The [Zr/Y] ratio is close
to the solar value in the thin-disk stars, but it grows steeply in the thick-
disk and halo stars, approaching [Zr/Y] = 0.68 at [Fe/H] = -2.4. Similar
behavior was found for [Zr/Sr] in Zhao et al. (2016). The [Sr/Y] ratio is also
close to the solar value in the thin-disk stars, however, it is decreasing in
the thick-disk and halo stars and reaches [Sr/Y] = -0.37 at [Fe/H] = -2.5. The
difference in behaviour at [Fe/H]$\lesssim$-0.7 between two neighbouring
elements, Y and Zr, was noticed in earlier studies, e.g. Zhao & Magain (1991);
François et al. (2007).

By observing the trends in [Sr/Fe], [Y/Fe], and [Zr/Fe] (Figures 10 and 11),
it becomes evident that the [X/Fe] ratios of these elements increase with
higher Z values in metal-poor stars. Specifically, for Sr, Y, and Zr with Z
values of 38, 39, and 40 respectively, it can be observed that in metal-poor
stars, the order of [Sr/Fe] $<$ [Y/Fe] $<$ [Zr/Fe] holds true. This outcome
could provide valuable insights into unraveling the source of light neutron
capture elements. If the outlined [X/Fe] ratio sequence is rooted in physical
principles, it is reasonable to expect [Rb/Fe] $<$ [Sr/Fe]. This is due to Rb,
with an atomic number of 37, serving as another instance of a light neutron
capture element found in stars (see e.g. Caffau et al., 2021).

Figure 11 shows the average [$<$Sr+Y+Zr$>$/Fe] ratio for our stars as a
function of [Fe/H]. Average [$<$Sr+Y+Zr$>$/Fe] is slightly enhanced in halo
stars with [$<$Sr+Y+Zr$>$/Fe] = 0.16$\pm$0.10 dex, and [$<$Sr+Y+Zr$>$/Fe] =
0.01$\pm$0.10 dex in think disk stars. HD 140283 stands out due to its
pronounced scarcity of all three elements among metal-poor stars and was not
considered in the average value.

The investigation of [Sr/Fe], [Y/Fe], and [Zr/Fe] trends at lower metallicity
down to -4.0 dex will help to better understand the mechanism of the
production of these light neutron capture elements at the early stage of the
galactic evolution.

We compare Y with the heavier neutron-capture elements Barium (Ba) and
Europium (Eu) (Fig. 11). Barium originates from both the $r$-process and the
main components of the $s$-process, whereas Europium is primarily associated
with the $r$-process. It is evident that both patterns, namely [Y/Ba] vs.
[Ba/H] and [Y/Eu] vs. [Eu/H], exhibit significant data dispersion. The
dispersion reduces when examining the relationship between [Y/Ba] and [Eu/Ba].
The [Eu/Ba] ratio depends on the relative contributions of the $s$\- and
$r$-processes to the formation of these elements. The relationship between the
[Y/Ba] ratio and the [Eu/Ba] ratio shows a strong correlation (see Fig. 11),
particular Y and Eu excesses relative to Ba for thick-disk and halo stars. The
found correlation is important for understanding the origin of yttrium.

###  5.3 Comparison with literature

The abundances we obtained align with the existing literature data within the
range of metallicities that overlap with our study, despite the fact that most
studies were performed under the LTE assumption. The reason for this is that
the NLTE abundance corrections for Y ii lines are small within the stellar
parameter range that we are focusing on. Fig. 12 presents the compilation of
literature data from Honda et al. (2004); Hansen et al. (2012); Bensby et al.
(2014); Roederer et al. (2014); Reggiani et al. (2017) obtained under LTE
assumption and our NLTE yttrium-to-iron abundance ratios.

The obtained positive slope for halo stars in metallicity range
-2.62$\leq$[Fe/H]$\leq$-1.46 in this work is different to the result of
Reggiani et al. (2017), who obtained negative slope -0.06$\pm$0.12 for 21
stars in the overlapping metallicity range.

###  5.4 Inﬂuence of NLTE on the Galactic Abundance Trends

As mentioned, this study employs a line-by-line differential analysis method,
comparing each line to the corresponding line in the Sun as a reference. In
this context, we examine the influence of NLTE effects on the determination of
average yttrium abundances [Y/H] and elemental ratios, which varies with the
metallicity of a star. Figure 13 displays the differences between the NLTE and
LTE [Y/H] ratio for all investigated stars. The NLTE abundance corrections do
not exceed 0.11 dex. The disparities between NLTE and LTE are negligible for
stars with [Fe/H]$\sim$0.0, but they become more pronounced as the metallicity
decreases. NLTE abundance corrections for Y ii depend on metallicity and
neglecting NLTE effects distorce the Galactic trends.

Table A.3 demonstrates that NLTE offers an additional benefit through the
reduction of line-to-line scatter, which is observed in the majority of
species and stars when compared to LTE. For example, for HD 94028 in LTE
assumption [Y/Fe] = 0.16$\pm$0.09, while significantly smaller statistical
errors are achieved in NLTE, resulting in [Y/Fe] = 0.26$\pm$0.06.

Table 5: Characteristics of observed spectra.

Star | Telescope/ | Spectral range | Observing run | $R$ | $S/N$ | Run/Program ID
---|---|---|---|---|---|---
| Spectrograph | Å | year/month/day |  |  |
HD 29907 | 2 | 4590-6650 | 2001/03/08 | 51 690 | 298 | 67.D-0086(A)
HD 31128 | 1 | 3781-6913 | 2008/01/16 | 115 000 | 103 | 072.C-0488(E)
HD 59392 | 2 | 4590-6650 | 2020/09/01 | 51 690 | 249 | 67.D-0086(A)
HD 97320 | 1 | 3781-6913 | 2009/03/20 | 115 000 | 160 | 082.C-0212(B)
HD 193901 | 3 | 3772-7900 | 2021/08/23 | 140 000 | 198 | 107.22QS.001
HD 298986 | 2 | 4590-6650 | 2001/03/08 | 51 690 | 264 | 67.D-0086(A)
HD 102200 | 1 | 3781-6913 | 2007/03/10 | 115 000 | 137 | 072.C-0488(E)
HD 3795 | 4 | 3527-9215 | 2017/12/03 | 48 000 | 240 | 0100.A-9022(A)
HD 32923 | 1 | 3781-6913 | 2004/12/24 | 115 000 | 102 | 074.C-0364(A)
HD 40397 | 1 | 3781-6913 | 2016/02/04 | 115 000 | 268 | 192.C-0852(A)
HD 64606 | 4 | 3527-9215 | 2004/03/10 | 48 000 | 229 | 072.C-0033(A)
HD 69611 | 1 | 3781-6913 | 2016/03/06 | 115 000 | 190 | 196.C-0042(A)
HD 114762 | 2 | 4785-6813 | 2001/03/07 | 107 200 | 381 | 67.C-0206(A)
HD 201891 | 2 | 4785-6804 | 2012/10/18 | 66 320 | 109 | 090.B-0605(A)

Note. — Notes: Telescope/spectrograph: 1 = ESO-3.6/HARPS Echelle; 2 = ESO-
VLT-U2/UVES; 3 = ESO-VLT-U1/ESPRESSO; 4 = MPG/ESO-2.2/FEROS

Figure 10:  Stellar NLTE yttrium-to-iron abundance ratios as a function of
metallicity for 65 stars; and the [Y/Fe]–[Fe/H] ratio for the solar
neighborhood models with $s$-process only (dashed line) and with $s-$ and
$r-$processes (solid line) from Kobayashi et al. (2020). Different symbols
correspond to different stellar populations, namely, the thin disk (open
circles), the thick disk (ﬁlled circles), and the halo (asterisks).

Figure 11: NLTE abundance ratios between the neutron-capture elements. The
same symbols are used as in Figure 10. Figure 12:  Our stellar NLTE yttrium-
to-iron abundance ratios as a function of metallicity for 65 stars and
compilation from LTE studies from literature (brown circles). The compilation
was made of data from Honda et al. (2004); Hansen et al. (2012); Bensby et al.
(2014); Roederer et al. (2014); Reggiani et al. (2017). The same symbols are
used as in Figure 10. Figure 13: Differences in differential abundance [Y/H]
between NLTE and LTE for 65 investigated stars.

##  6 Conclusions

For the first time, the departures from LTE for Y i – Y ii in the atmospheres
of FGK stars across wide metallicity range are investigated. We present a new
model atom of Y i – Y ii based on the most up-to-date atomic data including
those for inelastic collisions with neutral hydrogen atoms and electrons.
Collisional excitation and ionization by hydrogen atoms were considered for
all levels. The calculated effective collision strengths for electron impact
excitation of Y i and Y ii are also presented in this study.

With the 1D MARCS solar model atmosphere, we obtain the solar NLTE abundance,
log $\epsilon_{\rm Y}$ = 2.21$\pm$0.05, from 15 lines of Y ii and log
$\epsilon_{\rm Y}$ = 2.14$\pm$0.03 from one line of Y i. In LTE, the abundance
difference between Y i and Y ii amounts to -0.12 dex. Since, we used only one
Y i line, we adopted the solar NLTE abundance log $\epsilon_{\rm Y}$ =
2.21$\pm$0.05 obtained from 15 lines of Y ii only. The obtained result is in
line with the 3D LTE result of Grevesse et al. (2015) and consistent within
the error bars with the meteoritic yttrium abundance from Lodders (2021).

Based on high-S/N, high-resolution spectra, the yttrium NLTE and LTE
abundances were determined for 11 reference stars with reliable atmospheric
parameters, lieing in the following ranges: 3930 K$\leq$ $T_{\rm eff}$ $\leq$
6635 K, 1.1 $\leq$ log $g$ $\leq$ 4.6, and -2.55 $\leq$ [Fe/H] $\leq$ +0.13.
For seven reference stars, including the Sun, we can reach ionization
equilibrium Y i – Y ii in NLTE.

In the models representing the atmospheres of F-G-K-type stars of close-to-
solar metallicity, the NLTE corrections for all Y ii lines, which we analyzed,
are positive and do not exceed 0.12 dex. The exceptions are Y ii lines at 4374
Å and 4883 Å in solar atmosphere and the atmosphere of Procyon, respectively,
for which $\Delta_{\rm NLTE}$ = -0.01 dex. In metal-poor stars, the NLTE
corrections for all Y ii lines are still positive and stronger compared to
solar metallicity stars, but do not exceed $\sim$0.20 dex. For Y i lines, NLTE
effects are stronger compared to Y ii and can reach up to $\sim$0.5 dex. In
metal-poor stars, Y i lines are not available in the spectra. We provide a
grid of the NLTE abundance corrections for Y ii lines at 4398, 4883, 4900, and
5087 Å.

We determined yttrium NLTE abundances for a sample of 65 FGK stars in the
-2.62 $\leq$ [Fe/H] $\leq$ +0.24 metallicity range. We derive line-to-line
differential abundances relative to the Sun using six lines of Y ii at 4374,
4398, 4883, 4900, 5087, 5205 Å. The NLTE leads to smaller line-to-line scatter
for the most of the stars. The NLTE effects in Y ii lines are important for
stars with [Fe/H] $\leq$ -1, and the NLTE–LTE abundance differences are
increasing towards lower metallicity.

Both thick and thin disk stars with -1.5 $\leq$ [Fe/H] $\leq$ +0.24, show
negative trends. Metal-poor halo stars with -2.62$\leq$[Fe/H]$\leq$-1.46 show
positive trend (Slope: +0.18$\pm$0.11) from [Y/Fe] $\approx$ -0.07 to 0.14 dex
The observed slope is in line with the $s+r$ model predicted by Kobayashi et
al. (2020), however, their model predicts by $\sim$0.23 dex lower [Y/Fe].

Our study has facilitated the execution of more precise analyses concerning
Galactic trends and has enabled the presentation of a detailed comparison of
trends in light neutron capture elements (Sr, Y, Zr) in NLTE. For Sr (Z = 38),
Y (Z = 39), and Zr (Z = 40), in metal poor stars, the sequence [Sr/Fe] $<$
[Y/Fe] $<$ [Zr/Fe] applies. This observation could offer key insights into
understanding the origin of light neutron capture elements.

This is the ﬁrst study of NLTE yttrium abundance trend for extensive
metalicity range suitable for the Galactic chemical evolution research. We
plan to use the current model atom for NLTE yttrium abundance determination in
very metal-poor stars studied with LAMOST and Subaru. It will allow us to
obtain [Y/Fe] vs. [Fe/H] trend for stars distributed across the metallicity
down to -4.0 dex to provide observational constrains on GCE models.

We thank the anonymous referee for valuable suggestions and comments. This
work was supported by the National Natural Science Foundation of China under
grant Nos. 11988101, 11890694, 12090044, 11833006, 12022304, 11973052, and
National Key R$\&$D Program of China No. 2019YFA0405500. This research used
the facilities of the Canadian Astronomy Data Centre operated by the National
Research Council of Canada with the support of the Canadian Space Agency. We
employed observations carried out with Shane/Hamilton spectrograph (the Lick
Observatory). Based on observations collected at the European Southern
Observatory under ESO programmes 67.C-0206(A), 67.D-0086(A), 072.C-0488(E),
072.C-0033(A), 074.C-0364(A), 076.C-0279(A), 078.D-0492(A), 080.D-0347(A),
082.C-0212(B), 090.B-0605(A), 0100.A-9022(A), 0103.D-0118(A), 0104.C-0863(A),
192.C-0852(A), 196.C-0042(A), 107.22QS.001. Based on data obtained from the
ESO Science Archive Facility with DOIs:
https://doi.eso.org/10.18727/archive/21;
https://doi.eso.org/10.18727/archive/24;
https://doi.eso.org/10.18727/archive/33;
https://doi.eso.org/10.18727/archive/50. We made use of the NIST, SIMBAD, and
VALD databases. .

##  Appendix A Tables

Table A.1: Effective collision strengths (dimensionless) for selected temperatures in the range $T$=2000–20000 K, for excitation of the states of Y i by electrons.  Transition | $J_{i}-J_{j}$ |  |  |  |  |  |  |  |  $T$ (K) |  |  |  |  |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---
|  | 2000 | 3000 | 4000 | 5000 | 6000 | 7000 | 8000 | 10000 | 12000 | 14000 | 16000 | 18000 | 20000
Effective collision strengths calculated with experimental cross sections from
Kuchenev & Smirnov (1984)
a4F – y4D∘ | 3/2 – 1/2 | 4.31E-4 | 5.64E-4 | 7.13E-4 | 8.66E-4 | 1.02E-3 | 1.18E-3 | 1.33E-3 | 1.65E-3 | 1.96E-3 | 2.28E-3 | 2.60E-3 | 2.92E-3 | 3.25E-3
a4F – y4F∘ | 5/2 – 5/2 | 6.11E-4 | 1.11E-3 | 1.65E-3 | 2.22E-3 | 2.81E-3 | 3.40E-3 | 3.99E-3 | 5.12E-3 | 6.19E-3 | 7.18E-3 | 8.09E-3 | 8.93E-3 | 9.71E-3
a4F – y4D∘ | 5/2 – 5/2 | 7.12E-4 | 9.01E-4 | 1.12E-3 | 1.35E-3 | 1.58E-3 | 1.81E-3 | 2.04E-3 | 2.51E-3 | 2.98E-3 | 3.46E-3 | 3.93E-3 | 4.42E-3 | 4.90E-3
a4F – y4D∘ | 7/2 – 5/2 | 3.46E-3 | 4.38E-3 | 5.44E-3 | 6.54E-3 | 7.67E-3 | 8.80E-3 | 9.94E-3 | 1.22E-2 | 1.45E-2 | 1.68E-2 | 1.92E-2 | 2.15E-2 | 2.39E-2
a4F – x2F∘ | 7/2 – 5/2 | 2.76E-4 | 5.97E-4 | 9.80E-4 | 1.40E-3 | 1.85E-3 | 2.31E-3 | 2.79E-3 | 3.79E-3 | 4.83E-3 | 5.93E-3 | 7.06E-3 | 8.25E-3 | 9.48E-3
a4F – y4D∘ | 7/2 – 7/2 | 2.77E-4 | 5.99E-4 | 9.82E-4 | 1.40E-3 | 1.85E-3 | 2.31E-3 | 2.79E-3 | 3.79E-3 | 4.84E-3 | 5.93E-3 | 7.07E-3 | 8.25E-3 | 9.48E-3
a4F – z2G∘ | 9/2 – 7/2 | 1.18E-2 | 9.20E-3 | 8.90E-3 | 9.20E-3 | 9.73E-3 | 1.04E-2 | 1.11E-2 | 1.26E-2 | 1.42E-2 | 1.58E-2 | 1.74E-2 | 1.91E-2 | 2.08E-2
a4F – y4D∘ | 9/2 – 7/2 | 2.53E-3 | 3.82E-3 | 5.18E-3 | 6.57E-3 | 7.97E-3 | 9.38E-3 | 1.08E-2 | 1.36E-2 | 1.65E-2 | 1.94E-2 | 2.23E-2 | 2.52E-2 | 2.82E-2
z4P∘ – f4D | 5/2 – 7/2 | 2.00E-3 | 2.22E-3 | 2.61E-3 | 3.04E-3 | 3.51E-3 | 4.00E-3 | 4.51E-3 | 5.56E-3 | 6.62E-3 | 7.69E-3 | 8.76E-3 | 9.81E-3 | 1.08E-2
Effective collision strengths calculated with experimental cross sections from
Smirnov (2000)
a2D – z2D∘ | 3/2 – 5/2 | 5.69E-3 | 9.14E-3 | 1.29E-2 | 1.70E-2 | 2.12E-2 | 2.56E-2 | 3.02E-2 | 3.94E-2 | 4.89E-2 | 5.83E-2 | 6.78E-2 | 7.71E-2 | 8.64E-2
a2D – z2D∘ | 3/2 – 3/2 | 1.50E-2 | 2.75E-2 | 4.18E-2 | 5.76E-2 | 7.43E-2 | 9.17E-2 | 1.09E-1 | 1.45E-1 | 1.82E-1 | 2.18E-1 | 2.54E-1 | 2.90E-1 | 3.25E-1
a2D – z2F∘ | 3/2 – 5/2 | 1.22E-2 | 2.38E-2 | 3.66E-2 | 5.02E-2 | 6.46E-2 | 7.96E-2 | 9.52E-2 | 1.28E-1 | 1.62E-1 | 1.97E-1 | 2.33E-1 | 2.70E-1 | 3.08E-1
a2D – y2D∘ | 3/2 – 3/2 | 7.25E-2 | 1.26E-1 | 1.85E-1 | 2.45E-1 | 3.08E-1 | 3.73E-1 | 4.38E-1 | 5.73E-1 | 7.11E-1 | 8.51E-1 | 9.94E-1 | 1.14E-0 | 1.28E-0
a2D – y2P∘ | 3/2 – 3/2 | 5.81E-3 | 1.11E-2 | 1.68E-2 | 2.28E-2 | 2.90E-2 | 3.53E-2 | 4.19E-2 | 5.56E-2 | 6.99E-2 | 8.48E-2 | 1.00E-1 | 1.16E-1 | 1.33E-1
a2D – y2F∘ | 3/2 – 5/2 | 9.93E-2 | 1.54E-1 | 2.10E-1 | 2.69E-1 | 3.29E-1 | 3.92E-1 | 4.55E-1 | 5.87E-1 | 7.22E-1 | 8.61E-1 | 1.00E-0 | 1.15E-0 | 1.29E-0
a2D – y2P∘ | 3/2 – 1/2 | 9.07E-3 | 1.75E-2 | 2.68E-2 | 3.66E-2 | 4.66E-2 | 5.69E-2 | 6.73E-2 | 8.85E-2 | 1.10E-1 | 1.33E-1 | 1.55E-1 | 1.79E-1 | 2.03E-1
a2D – y2D∘ | 3/2 – 5/2 | 5.07E-3 | 9.23E-3 | 1.37E-2 | 1.84E-2 | 2.33E-2 | 2.84E-2 | 3.36E-2 | 4.42E-2 | 5.52E-2 | 6.64E-2 | 7.79E-2 | 8.95E-2 | 1.01E-1
a2D – x2P∘ | 3/2 – 1/2 | 1.05E-2 | 2.24E-2 | 3.60E-2 | 5.05E-2 | 6.55E-2 | 8.09E-2 | 9.68E-2 | 1.30E-1 | 1.64E-1 | 1.99E-1 | 2.36E-1 | 2.73E-1 | 3.12E-1
a2D – x2P∘ | 3/2 – 3/2 | 2.20E-3 | 3.72E-3 | 5.42E-3 | 7.26E-3 | 9.22E-3 | 1.13E-2 | 1.34E-2 | 1.79E-2 | 2.25E-2 | 2.74E-2 | 3.25E-2 | 3.78E-2 | 4.32E-2
a2D – x2F∘ | 3/2 – 5/2 | 4.15E-3 | 4.65E-3 | 5.49E-3 | 6.49E-3 | 7.60E-3 | 8.79E-3 | 1.00E-2 | 1.26E-2 | 1.53E-2 | 1.80E-2 | 2.06E-2 | 2.33E-2 | 2.59E-2
a2D – x2D∘ | 3/2 – 3/2 | 2.78E-3 | 3.89E-3 | 5.09E-3 | 6.34E-3 | 7.63E-3 | 8.95E-3 | 1.03E-2 | 1.30E-2 | 1.58E-2 | 1.87E-2 | 2.16E-2 | 2.45E-2 | 2.75E-2
a2D – x2D∘ | 3/2 – 5/2 | 4.29E-4 | 7.88E-4 | 1.16E-3 | 1.55E-3 | 1.94E-3 | 2.34E-3 | 2.74E-3 | 3.56E-3 | 4.39E-3 | 5.25E-3 | 6.11E-3 | 6.99E-3 | 7.88E-3
a2D – w2D∘ | 3/2 – 3/2 | 1.88E-3 | 2.96E-3 | 4.13E-3 | 5.33E-3 | 6.54E-3 | 7.75E-3 | 8.93E-3 | 1.12E-2 | 1.34E-2 | 1.54E-2 | 1.73E-2 | 1.91E-2 | 2.07E-2
a2D – z2D∘ | 5/2 – 5/2 | 6.11E-2 | 9.85E-2 | 1.39E-1 | 1.83E-1 | 2.29E-1 | 2.78E-1 | 3.27E-1 | 4.28E-1 | 5.32E-1 | 6.35E-1 | 7.39E-1 | 8.41E-1 | 9.43E-1
a2D – z2F∘ | 5/2 – 5/2 | 1.88E-3 | 3.67E-3 | 5.64E-3 | 7.74E-3 | 9.96E-3 | 1.23E-2 | 1.47E-2 | 1.98E-2 | 2.51E-2 | 3.05E-2 | 3.62E-2 | 4.19E-2 | 4.77E-2
a2D – z2F∘ | 5/2 – 7/2 | 1.64E-2 | 3.18E-2 | 4.82E-2 | 6.51E-2 | 8.23E-2 | 9.98E-2 | 1.18E-1 | 1.54E-1 | 1.91E-1 | 2.29E-1 | 2.68E-1 | 3.08E-1 | 3.48E-1
a2D – y2D∘ | 5/2 – 3/2 | 2.20E-2 | 3.85E-2 | 5.62E-2 | 7.48E-2 | 9.40E-2 | 1.14E-1 | 1.34E-1 | 1.75E-1 | 2.17E-1 | 2.60E-1 | 3.04E-1 | 3.49E-1 | 3.94E-1
a2D – y2P∘ | 5/2 – 3/2 | 1.24E-2 | 2.38E-2 | 3.61E-2 | 4.89E-2 | 6.22E-2 | 7.59E-2 | 9.00E-2 | 1.20E-1 | 1.50E-1 | 1.83E-1 | 2.16E-1 | 2.50E-1 | 2.86E-1
a2D – y2F∘ | 5/2 – 5/2 | 4.09E-2 | 6.33E-2 | 8.66E-2 | 1.11E-1 | 1.36E-1 | 1.62E-1 | 1.88E-1 | 2.43E-1 | 2.99E-1 | 3.57E-1 | 4.16E-1 | 4.76E-1 | 5.37E-1
a2D – y2D∘ | 5/2 – 5/2 | 8.52E-2 | 1.55E-1 | 2.31E-1 | 3.11E-1 | 3.93E-1 | 4.79E-1 | 5.67E-1 | 7.47E-1 | 9.33E-1 | 1.12E-0 | 1.32E-0 | 1.52E-0 | 1.72E-0
a2D – y2F∘ | 5/2 – 7/2 | 1.75E-1 | 2.47E-1 | 3.21E-1 | 3.99E-1 | 4.78E-1 | 5.61E-1 | 6.45E-1 | 8.21E-1 | 1.00E-0 | 1.19E-0 | 1.39E-0 | 1.59E-0 | 1.79E-0
a2D – x2P∘ | 5/2 – 3/2 | 3.30E-2 | 5.58E-2 | 8.15E-2 | 1.09E-1 | 1.39E-1 | 1.70E-1 | 2.02E-1 | 2.69E-1 | 3.40E-1 | 4.14E-1 | 4.91E-1 | 5.71E-1 | 6.53E-1
a2D – x2F∘ | 5/2 – 5/2 | 5.19E-4 | 5.82E-4 | 6.87E-4 | 8.13E-4 | 9.53E-4 | 1.10E-3 | 1.26E-3 | 1.58E-3 | 1.92E-3 | 2.26E-3 | 2.59E-3 | 2.92E-3 | 3.25E-3
a2D – x2D∘ | 5/2 – 3/2 | 7.86E-4 | 1.10E-3 | 1.44E-3 | 1.80E-3 | 2.16E-3 | 2.54E-3 | 2.92E-3 | 3.70E-3 | 4.50E-3 | 5.31E-3 | 6.13E-3 | 6.97E-3 | 7.81E-3
a2D – x2F∘ | 5/2 – 7/2 | 8.14E-3 | 1.10E-2 | 1.42E-2 | 1.75E-2 | 2.10E-2 | 2.45E-2 | 2.82E-2 | 3.58E-2 | 4.36E-2 | 5.15E-2 | 5.93E-2 | 6.70E-2 | 7.46E-2
a2D – x2D∘ | 5/2 – 5/2 | 2.13E-3 | 3.90E-3 | 5.78E-3 | 7.70E-3 | 9.65E-3 | 1.16E-2 | 1.36E-2 | 1.77E-2 | 2.19E-2 | 2.61E-2 | 3.04E-2 | 3.48E-2 | 3.93E-2
a2D – w2P∘ | 5/2 – 3/2 | 3.27E-4 | 6.24E-4 | 9.67E-4 | 1.34E-3 | 1.73E-3 | 2.13E-3 | 2.55E-3 | 3.41E-3 | 4.31E-3 | 5.24E-3 | 6.19E-3 | 7.16E-3 | 8.16E-3
a2D – w2F∘ | 5/2 – 7/2 | 7.47E-2 | 7.99E-2 | 8.32E-2 | 8.59E-2 | 8.86E-2 | 9.11E-2 | 9.36E-2 | 9.81E-2 | 1.02E-1 | 1.06E-1 | 1.10E-1 | 1.13E-1 | 1.17E-1
a2F – x2P∘ | 5/2 – 3/2 | 4.33E-4 | 7.66E-4 | 1.16E-3 | 1.60E-3 | 2.09E-3 | 2.62E-3 | 3.19E-3 | 4.41E-3 | 5.74E-3 | 7.18E-3 | 8.71E-3 | 1.03E-2 | 1.20E-2
a2F – x2F∘ | 5/2 – 5/2 | 2.13E-3 | 2.45E-3 | 2.98E-3 | 3.61E-3 | 4.32E-3 | 5.10E-3 | 5.92E-3 | 7.67E-3 | 9.52E-3 | 1.14E-2 | 1.33E-2 | 1.53E-2 | 1.72E-2
a2F – x2D∘ | 5/2 – 3/2 | 1.34E-3 | 1.93E-3 | 2.58E-3 | 3.28E-3 | 4.02E-3 | 4.80E-3 | 5.61E-3 | 7.30E-3 | 9.08E-3 | 1.09E-2 | 1.29E-2 | 1.48E-2 | 1.69E-2
a2F – w2D∘ | 5/2 – 3/2 | 1.67E-3 | 2.69E-3 | 3.82E-3 | 5.02E-3 | 6.26E-3 | 7.50E-3 | 8.75E-3 | 1.12E-2 | 1.36E-2 | 1.59E-2 | 1.81E-2 | 2.01E-2 | 2.21E-2
a2F – w2F∘ | 5/2 – 7/2 | 9.91E-3 | 1.07E-2 | 1.13E-2 | 1.18E-2 | 1.22E-2 | 1.27E-2 | 1.32E-2 | 1.41E-2 | 1.49E-2 | 1.57E-2 | 1.64E-2 | 1.71E-2 | 1.78E-2
a2F – x2F∘ | 7/2 – 7/2 | 3.94E-3 | 5.49E-3 | 7.23E-3 | 9.12E-3 | 1.11E-2 | 1.33E-2 | 1.55E-2 | 2.03E-2 | 2.53E-2 | 3.05E-2 | 3.57E-2 | 4.10E-2 | 4.62E-2
a2F – x2D∘ | 7/2 – 5/2 | 1.69E-3 | 3.18E-3 | 4.80E-3 | 6.51E-3 | 8.30E-3 | 1.02E-2 | 1.21E-2 | 1.61E-2 | 2.03E-2 | 2.48E-2 | 2.94E-2 | 3.42E-2 | 3.91E-2
b2D – x2D∘ | 3/2 – 3/2 | 5.94E-4 | 8.55E-4 | 1.15E-3 | 1.46E-3 | 1.80E-3 | 2.14E-3 | 2.51E-3 | 3.27E-3 | 4.08E-3 | 4.91E-3 | 5.78E-3 | 6.68E-3 | 7.60E-3
b2D – w2D∘ | 3/2 – 3/2 | 1.23E-3 | 1.99E-3 | 2.83E-3 | 3.72E-3 | 4.64E-3 | 5.57E-3 | 6.50E-3 | 8.33E-3 | 1.01E-2 | 1.18E-2 | 1.35E-2 | 1.50E-2 | 1.65E-2
b2D – w2F∘ | 3/2 – 5/2 | 7.07E-5 | 1.71E-4 | 2.98E-4 | 4.43E-4 | 6.00E-4 | 7.66E-4 | 9.41E-4 | 1.31E-3 | 1.71E-3 | 2.13E-3 | 2.58E-3 | 3.04E-3 | 3.52E-3
b2D – x2D∘ | 5/2 – 5/2 | 5.77E-5 | 1.09E-4 | 1.64E-4 | 2.23E-4 | 2.84E-4 | 3.48E-4 | 4.14E-4 | 5.52E-4 | 6.98E-4 | 8.51E-4 | 1.01E-3 | 1.17E-3 | 1.34E-3
b2D – w2D∘ | 5/2 – 5/2 | 1.43E-3 | 2.46E-3 | 3.57E-3 | 4.71E-3 | 5.88E-3 | 7.07E-3 | 8.28E-3 | 1.07E-2 | 1.31E-2 | 1.55E-2 | 1.78E-2 | 2.00E-2 | 2.22E-2
b2D – w2P∘ | 5/2 – 3/2 | 2.08E-4 | 4.07E-4 | 6.43E-4 | 9.05E-4 | 1.19E-3 | 1.48E-3 | 1.80E-3 | 2.46E-3 | 3.17E-3 | 3.92E-3 | 4.71E-3 | 5.53E-3 | 6.38E-3
b2D – w2F∘ | 5/2 – 7/2 | 8.41E-2 | 9.10E-2 | 9.58E-2 | 1.00E-1 | 1.04E-1 | 1.09E-1 | 1.13E-1 | 1.20E-1 | 1.27E-1 | 1.34E-1 | 1.41E-1 | 1.47E-1 | 1.53E-1
a2G – z2H∘ | 9/2 – 11/2 | 3.02E-4 | 1.34E-3 | 3.14E-3 | 5.56E-3 | 8.43E-3 | 1.16E-2 | 1.50E-2 | 2.21E-2 | 2.93E-2 | 3.63E-2 | 4.29E-2 | 4.92E-2 | 5.51E-2
a2G – y2G∘ | 9/2 – 9/2 | 7.25E-4 | 2.14E-3 | 4.05E-3 | 6.22E-3 | 8.50E-3 | 1.08E-2 | 1.31E-2 | 1.75E-2 | 2.17E-2 | 2.57E-2 | 2.95E-2 | 3.31E-2 | 3.65E-2
a2G – z2G∘ | 7/2 – 7/2 | 5.52E-3 | 9.70E-3 | 1.42E-2 | 1.90E-2 | 2.38E-2 | 2.86E-2 | 3.34E-2 | 4.27E-2 | 5.15E-2 | 5.99E-2 | 6.81E-2 | 7.59E-2 | 8.36E-2
a2G – z2H∘ | 7/2 – 9/2 | 2.29E-4 | 9.96E-4 | 2.33E-3 | 4.14E-3 | 6.35E-3 | 8.85E-3 | 1.16E-2 | 1.74E-2 | 2.34E-2 | 2.93E-2 | 3.50E-2 | 4.05E-2 | 4.56E-2
a2G – y2G∘ | 7/2 – 7/2 | 9.69E-4 | 2.41E-3 | 4.21E-3 | 6.20E-3 | 8.28E-3 | 1.04E-2 | 1.24E-2 | 1.65E-2 | 2.03E-2 | 2.39E-2 | 2.73E-2 | 3.05E-2 | 3.36E-2
Table A.2: Effective collision strengths for selected temperatures in the range $T$=2000–28000 K, for excitation of the states of Y ii by electrons.  Transition | $J_{i}-J_{j}$ |  |  |  |  |  |  |  |  $T$ (K) |  |  |  |  |  |  |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---
|  | 2000 | 3000 | 4000 | 5000 | 6000 | 7000 | 8000 | 10000 | 12000 | 14000 | 16000 | 18000 | 20000 | 24000 | 28000
Effective collision strengths calculated with experimental cross sections from
Smirnov (2002a)
y3P∘ – 7s 3D | 2 – 3 | 2.42E-08 | 2.01E-06 | 2.07E-05 | 8.93E-05 | 2.46E-04 | 5.21E-04 | 9.33E-04 | 2.19E-03 | 4.02E-03 | 6.35E-03 | 9.12E-03 | 1.23E-02 | 1.57E-02 | 2.32E-02 | 3.13E-02
z3P∘ – g3D | 0 – 1 | 6.25E-17 | 1.31E-12 | 2.14E-10 | 4.88E-09 | 4.08E-08 | 1.91E-07 | 6.20E-07 | 3.36E-06 | 1.08E-05 | 2.55E-05 | 4.96E-05 | 8.47E-05 | 1.32E-04 | 2.63E-04 | 4.44E-04
z3P∘ – g3D | 1 – 2 | 1.96E-16 | 4.08E-12 | 6.67E-10 | 1.52E-08 | 1.26E-07 | 5.91E-07 | 1.92E-06 | 1.04E-05 | 3.32E-05 | 7.84E-05 | 1.53E-04 | 2.60E-04 | 4.05E-04 | 8.08E-04 | 1.36E-03
z3P∘ – g3D | 2 – 3 | 3.67E-16 | 7.43E-12 | 1.20E-09 | 2.71E-08 | 2.25E-07 | 1.05E-06 | 3.39E-06 | 1.83E-05 | 5.84E-05 | 1.38E-04 | 2.68E-04 | 4.57E-04 | 7.11E-04 | 1.42E-03 | 2.39E-03
z3P∘ – e3P | 1 – 2 | 1.47E-18 | 1.08E-13 | 3.31E-11 | 1.10E-09 | 1.18E-08 | 6.63E-08 | 2.46E-07 | 1.61E-06 | 5.87E-06 | 1.52E-05 | 3.16E-05 | 5.70E-05 | 9.24E-05 | 1.97E-04 | 3.47E-04
z3P∘ – e3P | 0 – 1 | 2.16E-19 | 1.80E-14 | 5.97E-12 | 2.07E-10 | 2.30E-09 | 1.31E-08 | 4.95E-08 | 3.30E-07 | 1.21E-06 | 3.16E-06 | 6.60E-06 | 1.19E-05 | 1.93E-05 | 4.12E-05 | 7.29E-05
z3D∘ – f3P | 2 – 1 | 1.51E-17 | 4.43E-13 | 8.74E-11 | 2.22E-09 | 1.99E-08 | 9.82E-08 | 3.31E-07 | 1.89E-06 | 6.26E-06 | 1.51E-05 | 3.00E-05 | 5.18E-05 | 8.13E-05 | 1.64E-04 | 2.80E-04
z3D∘ – f3P | 3 – 2 | 2.67E-17 | 7.24E-13 | 1.37E-10 | 3.40E-09 | 3.01E-08 | 1.46E-07 | 4.89E-07 | 2.76E-06 | 9.07E-06 | 2.18E-05 | 4.30E-05 | 7.41E-05 | 1.16E-04 | 2.34E-04 | 3.96E-04
z3P∘ – e3P | 1 – 1 | 1.16E-18 | 9.65E-14 | 3.19E-11 | 1.11E-09 | 1.23E-08 | 7.02E-08 | 2.65E-07 | 1.76E-06 | 6.49E-06 | 1.69E-05 | 3.53E-05 | 6.37E-05 | 1.04E-04 | 2.21E-04 | 3.90E-04
z1D∘ – e3F | 2 – 2 | 3.18E-18 | 1.95E-13 | 5.55E-11 | 1.76E-09 | 1.83E-08 | 1.00E-07 | 3.66E-07 | 2.33E-06 | 8.32E-06 | 2.12E-05 | 4.37E-05 | 7.79E-05 | 1.25E-04 | 2.62E-04 | 4.58E-04
z3P∘ – e3P | 2 – 2 | 6.33E-18 | 4.63E-13 | 1.43E-10 | 4.74E-09 | 5.10E-08 | 2.86E-07 | 1.06E-06 | 6.95E-06 | 2.53E-05 | 6.55E-05 | 1.36E-04 | 2.46E-04 | 3.99E-04 | 8.49E-04 | 1.50E-03
z3P∘ – e3P | 1 – 0 | 1.13E-18 | 9.18E-14 | 2.99E-11 | 1.03E-09 | 1.13E-08 | 6.42E-08 | 2.41E-07 | 1.60E-06 | 5.85E-06 | 1.52E-05 | 3.17E-05 | 5.70E-05 | 9.24E-05 | 1.96E-04 | 3.44E-04
z3F∘ – e3F | 3 – 3 | 1.28E-18 | 1.06E-13 | 3.51E-11 | 1.22E-09 | 1.35E-08 | 7.68E-08 | 2.89E-07 | 1.92E-06 | 7.05E-06 | 1.83E-05 | 3.83E-05 | 6.91E-05 | 1.12E-04 | 2.39E-04 | 4.21E-04
z3F∘ – e3F | 2 – 2 | 1.18E-18 | 7.23E-14 | 2.06E-11 | 6.51E-10 | 6.78E-09 | 3.71E-08 | 1.36E-07 | 8.64E-07 | 3.09E-06 | 7.87E-06 | 1.62E-05 | 2.89E-05 | 4.65E-05 | 9.75E-05 | 1.70E-04
z3P∘ – e3S | 2 – 1 | 1.90E-17 | 1.18E-12 | 3.33E-10 | 1.05E-08 | 1.09E-07 | 5.93E-07 | 2.16E-06 | 1.37E-05 | 4.86E-05 | 1.23E-04 | 2.53E-04 | 4.49E-04 | 7.19E-04 | 1.50E-03 | 2.59E-03
y3P∘ – g3D | 1 – 2 | 2.04E-16 | 3.05E-12 | 4.23E-10 | 8.69E-09 | 6.77E-08 | 3.01E-07 | 9.41E-07 | 4.82E-06 | 1.49E-05 | 3.42E-05 | 6.51E-05 | 1.09E-04 | 1.67E-04 | 3.26E-04 | 5.39E-04
z1D∘ – e3G | 2 – 3 | 8.58E-19 | 7.45E-14 | 2.50E-11 | 8.73E-10 | 9.72E-09 | 5.59E-08 | 2.12E-07 | 1.43E-06 | 5.29E-06 | 1.39E-05 | 2.93E-05 | 5.33E-05 | 8.73E-05 | 1.88E-04 | 3.36E-04
z3D∘ – e3F | 2 – 3 | 6.16E-18 | 3.65E-13 | 1.02E-10 | 3.18E-09 | 3.29E-08 | 1.79E-07 | 6.52E-07 | 4.14E-06 | 1.47E-05 | 3.75E-05 | 7.71E-05 | 1.37E-04 | 2.21E-04 | 4.63E-04 | 8.08E-04
z3D∘ – e3F | 1 – 2 | 2.50E-18 | 1.54E-13 | 4.37E-11 | 1.38E-09 | 1.44E-08 | 7.89E-08 | 2.88E-07 | 1.84E-06 | 6.57E-06 | 1.68E-05 | 3.45E-05 | 6.16E-05 | 9.91E-05 | 2.08E-04 | 3.63E-04
z3D∘ – e3F | 3 – 4 | 7.91E-18 | 4.38E-13 | 1.18E-10 | 3.62E-09 | 3.69E-08 | 1.99E-07 | 7.18E-07 | 4.51E-06 | 1.60E-05 | 4.04E-05 | 8.28E-05 | 1.47E-04 | 2.36E-04 | 4.93E-04 | 8.59E-04
z3F∘ – e3G | 4 – 5 | 8.87E-18 | 8.00E-13 | 2.75E-10 | 9.76E-09 | 1.10E-07 | 6.34E-07 | 2.41E-06 | 1.63E-05 | 6.05E-05 | 1.59E-04 | 3.34E-04 | 6.04E-04 | 9.85E-04 | 2.11E-03 | 3.73E-03
z3D∘ – f3D | 3 – 1 | 5.64E-19 | 7.34E-14 | 3.03E-11 | 1.20E-09 | 1.45E-08 | 8.80E-08 | 3.48E-07 | 2.50E-06 | 9.66E-06 | 2.61E-05 | 5.64E-05 | 1.04E-04 | 1.73E-04 | 3.81E-04 | 6.88E-04
z3D∘ – f3D | 3 – 3 | 9.21E-19 | 1.25E-13 | 5.33E-11 | 2.16E-09 | 2.66E-08 | 1.65E-07 | 6.60E-07 | 4.82E-06 | 1.89E-05 | 5.18E-05 | 1.13E-04 | 2.10E-04 | 3.49E-04 | 7.73E-04 | 1.40E-03
z3D∘ – e3G | 3 – 3 | 1.37E-18 | 1.19E-13 | 3.98E-11 | 1.39E-09 | 1.55E-08 | 8.92E-08 | 3.38E-07 | 2.28E-06 | 8.48E-06 | 2.23E-05 | 4.71E-05 | 8.56E-05 | 1.40E-04 | 3.03E-04 | 5.42E-04
z1D∘ – e3D | 2 – 2 | 2.87E-19 | 3.84E-14 | 1.61E-11 | 6.42E-10 | 7.80E-09 | 4.77E-08 | 1.90E-07 | 1.37E-06 | 5.31E-06 | 1.44E-05 | 3.12E-05 | 5.80E-05 | 9.65E-05 | 2.14E-04 | 3.90E-04
z3F∘ – e3D | 3 – 3 | 1.68E-19 | 3.02E-14 | 1.46E-11 | 6.39E-10 | 8.26E-09 | 5.27E-08 | 2.16E-07 | 1.62E-06 | 6.46E-06 | 1.78E-05 | 3.90E-05 | 7.28E-05 | 1.22E-04 | 2.70E-04 | 4.92E-04
z3F∘ – e3D | 2 – 1 | 1.11E-18 | 1.17E-13 | 4.33E-11 | 1.60E-09 | 1.85E-08 | 1.09E-07 | 4.20E-07 | 2.89E-06 | 1.09E-05 | 2.88E-05 | 6.09E-05 | 1.11E-04 | 1.82E-04 | 3.92E-04 | 6.97E-04
z3F∘ – e3D | 3 – 2 | 7.10E-19 | 9.49E-14 | 3.97E-11 | 1.59E-09 | 1.93E-08 | 1.18E-07 | 4.69E-07 | 3.38E-06 | 1.31E-05 | 3.57E-05 | 7.74E-05 | 1.44E-04 | 2.39E-04 | 5.31E-04 | 9.68E-04
y3P∘ – e3P | 2 – 2 | 1.19E-18 | 8.75E-14 | 2.70E-11 | 8.99E-10 | 9.68E-09 | 5.43E-08 | 2.02E-07 | 1.33E-06 | 4.84E-06 | 1.26E-05 | 2.62E-05 | 4.73E-05 | 7.69E-05 | 1.64E-04 | 2.91E-04
z3F∘ – e3D | 4 – 3 | 7.40E-19 | 1.33E-13 | 6.45E-11 | 2.82E-09 | 3.64E-08 | 2.32E-07 | 9.53E-07 | 7.16E-06 | 2.85E-05 | 7.87E-05 | 1.72E-04 | 3.21E-04 | 5.37E-04 | 1.19E-03 | 2.17E-03
y3P∘ – e3G | 2 – 3 | 4.14E-19 | 3.61E-14 | 1.21E-11 | 4.24E-10 | 4.72E-09 | 2.72E-08 | 1.03E-07 | 6.96E-07 | 2.59E-06 | 6.82E-06 | 1.44E-05 | 2.62E-05 | 4.30E-05 | 9.30E-05 | 1.67E-04
z3D∘ – e3D | 3 – 3 | 7.14E-19 | 1.28E-13 | 6.22E-11 | 2.72E-09 | 3.51E-08 | 2.24E-07 | 9.21E-07 | 6.91E-06 | 2.76E-05 | 7.60E-05 | 1.66E-04 | 3.11E-04 | 5.19E-04 | 1.16E-03 | 2.10E-03
z3D∘ – e3D | 1 – 1 | 6.08E-19 | 6.41E-14 | 2.38E-11 | 8.81E-10 | 1.02E-08 | 5.99E-08 | 2.31E-07 | 1.59E-06 | 5.98E-06 | 1.58E-05 | 3.35E-05 | 6.11E-05 | 1.00E-04 | 2.16E-04 | 3.85E-04
z3D∘ – e3D | 2 – 2 | 4.01E-19 | 5.37E-14 | 2.25E-11 | 8.98E-10 | 1.09E-08 | 6.69E-08 | 2.66E-07 | 1.92E-06 | 7.45E-06 | 2.03E-05 | 4.39E-05 | 8.16E-05 | 1.36E-04 | 3.02E-04 | 5.50E-04
z3D∘ – e3D | 2 – 1 | 5.50E-19 | 5.81E-14 | 2.15E-11 | 7.97E-10 | 9.20E-09 | 5.42E-08 | 2.09E-07 | 1.44E-06 | 5.42E-06 | 1.43E-05 | 3.04E-05 | 5.54E-05 | 9.07E-05 | 1.96E-04 | 3.49E-04
y3P∘ – e3S | 1 – 1 | 2.39E-18 | 1.48E-13 | 4.21E-11 | 1.33E-09 | 1.38E-08 | 7.52E-08 | 2.74E-07 | 1.74E-06 | 6.20E-06 | 1.58E-05 | 3.24E-05 | 5.77E-05 | 9.25E-05 | 1.93E-04 | 3.36E-04
z1F∘ – f3D | 3 – 3 | 2.91E-19 | 3.96E-14 | 1.69E-11 | 6.86E-10 | 8.45E-09 | 5.23E-08 | 2.10E-07 | 1.53E-06 | 6.03E-06 | 1.65E-05 | 3.60E-05 | 6.71E-05 | 1.12E-04 | 2.48E-04 | 4.50E-04
y3P∘ – e3S | 2 – 1 | 6.46E-18 | 4.02E-13 | 1.14E-10 | 3.59E-09 | 3.73E-08 | 2.04E-07 | 7.42E-07 | 4.72E-06 | 1.68E-05 | 4.27E-05 | 8.78E-05 | 1.56E-04 | 2.51E-04 | 5.24E-04 | 9.09E-04
z3D∘ – e3D | 3 – 2 | 5.23E-19 | 6.99E-14 | 2.93E-11 | 1.17E-09 | 1.42E-08 | 8.71E-08 | 3.46E-07 | 2.50E-06 | 9.71E-06 | 2.64E-05 | 5.73E-05 | 1.06E-04 | 1.77E-04 | 3.93E-04 | 7.18E-04
y3P∘ – e3D | 1 – 2 | 1.12E-19 | 1.50E-14 | 6.29E-12 | 2.52E-10 | 3.06E-09 | 1.88E-08 | 7.46E-08 | 5.39E-07 | 2.10E-06 | 5.71E-06 | 1.24E-05 | 2.30E-05 | 3.84E-05 | 8.54E-05 | 1.56E-04
z1F∘ – e3D | 3 – 2 | 1.49E-19 | 2.00E-14 | 8.37E-12 | 3.35E-10 | 4.07E-09 | 2.50E-08 | 9.93E-08 | 7.17E-07 | 2.79E-06 | 7.61E-06 | 1.65E-05 | 3.07E-05 | 5.12E-05 | 1.14E-04 | 2.08E-04
Effective collision strengths calculated with experimental cross sections from
Smirnov (2001)
a1S – y1P∘ | 0–1 | 5.40E-19 | 1.19E-13 | 6.31E-11 | 2.88E-09 | 3.82E-08 | 2.48E-07 | 1.03E-06 | 7.86E-06 | 3.16E-05 | 8.75E-05 | 1.92E-04 | 3.58E-04 | 5.99E-04 | 1.33E-03 | 2.41E-03
a1D – y1P∘ | 2–1 | 1.45E-18 | 3.22E-13 | 1.70E-10 | 7.78E-09 | 1.03E-07 | 6.71E-07 | 2.78E-06 | 2.12E-05 | 8.54E-05 | 2.37E-04 | 5.19E-04 | 9.71E-04 | 1.62E-03 | 3.61E-03 | 6.56E-03
z1D∘ – g1D | 2–2 | 1.11E-18 | 1.42E-13 | 5.71E-11 | 2.21E-09 | 2.62E-08 | 1.57E-07 | 6.14E-07 | 4.32E-06 | 1.65E-05 | 4.40E-05 | 9.39E-05 | 1.72E-04 | 2.82E-04 | 6.10E-04 | 1.09E-03
z3P∘ – f1D | 2–2 | 5.16E-18 | 4.51E-13 | 1.51E-10 | 5.25E-09 | 5.82E-08 | 3.33E-07 | 1.25E-06 | 8.35E-06 | 3.06E-05 | 7.94E-05 | 1.66E-04 | 2.98E-04 | 4.83E-04 | 1.03E-03 | 1.81E-03
z3F∘ – g1D | 2–2 | 8.28E-19 | 1.05E-13 | 4.25E-11 | 1.64E-09 | 1.95E-08 | 1.17E-07 | 4.57E-07 | 3.22E-06 | 1.23E-05 | 3.28E-05 | 7.00E-05 | 1.28E-04 | 2.11E-04 | 4.56E-04 | 8.10E-04
z1P∘ – g1D | 1–2 | 7.60E-19 | 9.67E-14 | 3.90E-11 | 1.51E-09 | 1.79E-08 | 1.07E-07 | 4.20E-07 | 2.95E-06 | 1.13E-05 | 3.01E-05 | 6.43E-05 | 1.18E-04 | 1.93E-04 | 4.18E-04 | 7.44E-04
z1D∘ – f1D | 2–2 | 1.64E-18 | 1.44E-13 | 4.82E-11 | 1.68E-09 | 1.86E-08 | 1.06E-07 | 4.01E-07 | 2.67E-06 | 9.79E-06 | 2.54E-05 | 5.30E-05 | 9.55E-05 | 1.55E-04 | 3.29E-04 | 5.79E-04
z3D∘ – g1D | 1–2 | 5.31E-19 | 6.76E-14 | 2.72E-11 | 1.05E-09 | 1.25E-08 | 7.51E-08 | 2.94E-07 | 2.07E-06 | 7.88E-06 | 2.11E-05 | 4.50E-05 | 8.25E-05 | 1.36E-04 | 2.93E-04 | 5.22E-04
z1P∘ – f1S | 1–0 | 3.97E-18 | 4.14E-13 | 1.53E-10 | 5.63E-09 | 6.49E-08 | 3.82E-07 | 1.47E-06 | 1.01E-05 | 3.78E-05 | 9.96E-05 | 2.10E-04 | 3.81E-04 | 6.22E-04 | 1.33E-03 | 2.36E-03
z3F∘ – f1D | 2–2 | 1.56E-18 | 1.36E-13 | 4.57E-11 | 1.59E-09 | 1.76E-08 | 1.01E-07 | 3.81E-07 | 2.53E-06 | 9.30E-06 | 2.42E-05 | 5.04E-05 | 9.08E-05 | 1.47E-04 | 3.13E-04 | 5.51E-04
z1P∘ – f1D | 1–2 | 1.92E-18 | 1.68E-13 | 5.63E-11 | 1.96E-09 | 2.18E-08 | 1.24E-07 | 4.69E-07 | 3.12E-06 | 1.15E-05 | 2.98E-05 | 6.22E-05 | 1.12E-04 | 1.82E-04 | 3.86E-04 | 6.80E-04
z3D∘ – f1S | 1–0 | 6.88E-19 | 7.19E-14 | 2.65E-11 | 9.77E-10 | 1.13E-08 | 6.63E-08 | 2.55E-07 | 1.75E-06 | 6.56E-06 | 1.73E-05 | 3.65E-05 | 6.63E-05 | 1.08E-04 | 2.32E-04 | 4.11E-04
a1D – z1F∘ | 2–3 | 1.44E-19 | 6.77E-14 | 5.15E-11 | 2.92E-09 | 4.47E-08 | 3.22E-07 | 1.44E-06 | 1.23E-05 | 5.32E-05 | 1.56E-04 | 3.58E-04 | 6.94E-04 | 1.20E-03 | 2.80E-03 | 5.32E-03
z1F∘ – e1G | 3–4 | 3.93E-18 | 3.59E-13 | 1.23E-10 | 4.37E-09 | 4.91E-08 | 2.84E-07 | 1.08E-06 | 7.35E-06 | 2.74E-05 | 7.24E-05 | 1.53E-04 | 2.79E-04 | 4.58E-04 | 9.92E-04 | 1.77E-03
b1D – y1P∘ | 2–1 | 1.83E-19 | 4.05E-14 | 2.15E-11 | 9.85E-10 | 1.31E-08 | 8.52E-08 | 3.54E-07 | 2.71E-06 | 1.09E-05 | 3.04E-05 | 6.68E-05 | 1.25E-04 | 2.10E-04 | 4.69E-04 | 8.56E-04
z1D∘ – e1D | 2–2 | 1.19E-19 | 2.25E-14 | 1.12E-11 | 4.92E-10 | 6.39E-09 | 4.10E-08 | 1.69E-07 | 1.27E-06 | 5.10E-06 | 1.41E-05 | 3.11E-05 | 5.85E-05 | 9.84E-05 | 2.22E-04 | 4.09E-04
a1S – z1P∘ | 0–1 | 3.51E-20 | 2.07E-14 | 1.77E-11 | 1.07E-09 | 1.72E-08 | 1.28E-07 | 5.92E-07 | 5.24E-06 | 2.33E-05 | 6.99E-05 | 1.63E-04 | 3.19E-04 | 5.55E-04 | 1.31E-03 | 2.49E-03
z1F∘ – f1D | 3–2 | 3.38E-18 | 2.96E-13 | 9.93E-11 | 3.47E-09 | 3.85E-08 | 2.20E-07 | 8.31E-07 | 5.55E-06 | 2.04E-05 | 5.30E-05 | 1.11E-04 | 2.00E-04 | 3.25E-04 | 6.92E-04 | 1.22E-03
z3D∘ – e1D | 1–2 | 4.01E-20 | 7.63E-15 | 3.78E-12 | 1.67E-10 | 2.17E-09 | 1.39E-08 | 5.72E-08 | 4.32E-07 | 1.73E-06 | 4.82E-06 | 1.06E-05 | 1.99E-05 | 3.36E-05 | 7.57E-05 | 1.40E-04
z3D∘ – e1D | 2–2 | 1.19E-19 | 2.26E-14 | 1.12E-11 | 4.95E-10 | 6.43E-09 | 4.12E-08 | 1.70E-07 | 1.28E-06 | 5.14E-06 | 1.43E-05 | 3.14E-05 | 5.91E-05 | 9.95E-05 | 2.24E-04 | 4.15E-04
a3D – z1P∘ | 1–1 | 1.69E-20 | 9.93E-15 | 8.50E-12 | 5.17E-10 | 8.29E-09 | 6.18E-08 | 2.85E-07 | 2.52E-06 | 1.12E-05 | 3.37E-05 | 7.84E-05 | 1.54E-04 | 2.68E-04 | 6.32E-04 | 1.20E-03
a3D – z1P∘ | 2–1 | 3.20E-20 | 1.88E-14 | 1.61E-11 | 9.79E-10 | 1.57E-08 | 1.17E-07 | 5.40E-07 | 4.78E-06 | 2.13E-05 | 6.38E-05 | 1.49E-04 | 2.92E-04 | 5.07E-04 | 1.20E-03 | 2.28E-03
y3P∘ – e1F | 2–3 | 1.66E-19 | 2.44E-14 | 1.06E-11 | 4.34E-10 | 5.35E-09 | 3.30E-08 | 1.32E-07 | 9.52E-07 | 3.69E-06 | 9.96E-06 | 2.14E-05 | 3.95E-05 | 6.53E-05 | 1.43E-04 | 2.57E-04
y1P∘ – h1D | 1–2 | 1.79E-15 | 1.17E-11 | 1.07E-09 | 1.73E-08 | 1.15E-07 | 4.55E-07 | 1.31E-06 | 6.00E-06 | 1.73E-05 | 3.79E-05 | 6.99E-05 | 1.15E-04 | 1.74E-04 | 3.34E-04 | 5.50E-04
a3D – z1D∘ | 1–2 | 4.10E-21 | 4.10E-15 | 4.55E-12 | 3.22E-10 | 5.70E-09 | 4.55E-08 | 2.20E-07 | 2.06E-06 | 9.49E-06 | 2.89E-05 | 6.79E-05 | 1.34E-04 | 2.33E-04 | 5.46E-04 | 1.03E-03
a3D – z1D∘ | 2–2 | 7.91E-21 | 7.91E-15 | 8.77E-12 | 6.21E-10 | 1.10E-08 | 8.77E-08 | 4.23E-07 | 3.98E-06 | 1.83E-05 | 5.58E-05 | 1.31E-04 | 2.58E-04 | 4.49E-04 | 1.05E-03 | 1.99E-03
a3F – z1F∘ | 4–3 | 2.71E-20 | 1.27E-14 | 9.70E-12 | 5.51E-10 | 8.43E-09 | 6.08E-08 | 2.73E-07 | 2.33E-06 | 1.01E-05 | 2.96E-05 | 6.80E-05 | 1.32E-04 | 2.28E-04 | 5.36E-04 | 1.02E-03
a1D – z1D∘ | 2–2 | 2.84E-20 | 2.84E-14 | 3.16E-11 | 2.24E-09 | 3.96E-08 | 3.16E-07 | 1.53E-06 | 1.43E-05 | 6.60E-05 | 2.01E-04 | 4.73E-04 | 9.32E-04 | 1.62E-03 | 3.81E-03 | 7.19E-03
z1F∘ – e1D | 3–2 | 3.80E-19 | 7.23E-14 | 3.59E-11 | 1.58E-09 | 2.06E-08 | 1.32E-07 | 5.45E-07 | 4.12E-06 | 1.66E-05 | 4.61E-05 | 1.02E-04 | 1.91E-04 | 3.22E-04 | 7.29E-04 | 1.35E-03
a3F – z1P∘ | 2–1 | 9.84E-21 | 5.79E-15 | 4.96E-12 | 3.02E-10 | 4.86E-09 | 3.63E-08 | 1.67E-07 | 1.48E-06 | 6.63E-06 | 1.99E-05 | 4.64E-05 | 9.13E-05 | 1.59E-04 | 3.77E-04 | 7.20E-04
a3P – z1F∘ | 2–3 | 4.68E-21 | 2.20E-15 | 1.68E-12 | 9.55E-11 | 1.46E-09 | 1.06E-08 | 4.75E-08 | 4.05E-07 | 1.76E-06 | 5.18E-06 | 1.19E-05 | 2.32E-05 | 4.01E-05 | 9.43E-05 | 1.80E-04
b1D – z1F∘ | 2–3 | 1.18E-20 | 5.56E-15 | 4.25E-12 | 2.41E-10 | 3.70E-09 | 2.67E-08 | 1.20E-07 | 1.03E-06 | 4.46E-06 | 1.31E-05 | 3.01E-05 | 5.87E-05 | 1.02E-04 | 2.39E-04 | 4.56E-04
Effective collision strengths calculated with experimental cross sections from
Smirnov (2002b)
a3D – y3P∘ | 1 – 1 | 1.11E-19 | 3.35E-14 | 2.03E-11 | 1.00E-09 | 1.40E-08 | 9.43E-08 | 4.02E-07 | 3.18E-06 | 1.31E-05 | 3.72E-05 | 8.29E-05 | 1.57E-04 | 2.66E-04 | 6.05E-04 | 1.12E-03
a3D – y3P∘ | 2 – 2 | 2.90E-20 | 1.59E-14 | 1.31E-11 | 7.74E-10 | 1.22E-08 | 8.98E-08 | 4.09E-07 | 3.56E-06 | 1.56E-05 | 4.63E-05 | 1.07E-04 | 2.09E-04 | 3.63E-04 | 8.55E-04 | 1.63E-03
a3D – y3P∘ | 1 – 0 | 3.09E-20 | 1.78E-14 | 1.50E-11 | 9.04E-10 | 1.44E-08 | 1.06E-07 | 4.87E-07 | 4.26E-06 | 1.88E-05 | 5.59E-05 | 1.29E-04 | 2.53E-04 | 4.38E-04 | 1.03E-03 | 1.95E-03
a3D – y3P∘ | 2 – 1 | 3.96E-19 | 1.19E-13 | 7.24E-11 | 3.58E-09 | 4.99E-08 | 3.36E-07 | 1.43E-06 | 1.13E-05 | 4.68E-05 | 1.32E-04 | 2.95E-04 | 5.61E-04 | 9.49E-04 | 2.16E-03 | 3.99E-03
a3D – y3P∘ | 3 – 2 | 1.24E-19 | 6.80E-14 | 5.59E-11 | 3.32E-09 | 5.23E-08 | 3.84E-07 | 1.75E-06 | 1.52E-05 | 6.70E-05 | 1.99E-04 | 4.59E-04 | 8.96E-04 | 1.55E-03 | 3.67E-03 | 6.99E-03
a1S – z3D∘ | 0 – 1 | 9.15E-21 | 3.71E-15 | 2.61E-12 | 1.41E-10 | 2.07E-09 | 1.46E-08 | 6.39E-08 | 5.28E-07 | 2.24E-06 | 6.47E-06 | 1.46E-05 | 2.81E-05 | 4.79E-05 | 1.10E-04 | 2.04E-04
a3D – z3D∘ | 2 – 3 | 2.27E-20 | 1.19E-14 | 9.57E-12 | 5.60E-10 | 8.74E-09 | 6.38E-08 | 2.89E-07 | 2.49E-06 | 1.09E-05 | 3.19E-05 | 7.33E-05 | 1.42E-04 | 2.45E-04 | 5.72E-04 | 1.08E-03
a3D – z3D∘ | 1 – 2 | 1.73E-20 | 8.49E-15 | 6.61E-12 | 3.79E-10 | 5.84E-09 | 4.23E-08 | 1.90E-07 | 1.62E-06 | 7.05E-06 | 2.07E-05 | 4.74E-05 | 9.20E-05 | 1.59E-04 | 3.70E-04 | 6.99E-04
a3D – z3D∘ | 3 – 3 | 9.01E-20 | 4.73E-14 | 3.80E-11 | 2.22E-09 | 3.47E-08 | 2.54E-07 | 1.15E-06 | 9.89E-06 | 4.31E-05 | 1.27E-04 | 2.92E-04 | 5.66E-04 | 9.75E-04 | 2.28E-03 | 4.30E-03
a3D – z3D∘ | 1 – 1 | 9.53E-20 | 3.87E-14 | 2.72E-11 | 1.46E-09 | 2.16E-08 | 1.52E-07 | 6.66E-07 | 5.50E-06 | 2.34E-05 | 6.75E-05 | 1.53E-04 | 2.93E-04 | 5.00E-04 | 1.15E-03 | 2.13E-03
a3D – z3D∘ | 2 – 2 | 7.21E-20 | 3.54E-14 | 2.76E-11 | 1.58E-09 | 2.44E-08 | 1.76E-07 | 7.94E-07 | 6.78E-06 | 2.94E-05 | 8.64E-05 | 1.98E-04 | 3.84E-04 | 6.62E-04 | 1.54E-03 | 2.92E-03
a3D – z3D∘ | 2 – 1 | 5.42E-20 | 2.20E-14 | 1.55E-11 | 8.32E-10 | 1.23E-08 | 8.62E-08 | 3.79E-07 | 3.13E-06 | 1.33E-05 | 3.84E-05 | 8.68E-05 | 1.67E-04 | 2.84E-04 | 6.52E-04 | 1.21E-03
a3D – z3D∘ | 3 – 2 | 4.84E-20 | 2.38E-14 | 1.85E-11 | 1.06E-09 | 1.64E-08 | 1.19E-07 | 5.33E-07 | 4.56E-06 | 1.98E-05 | 5.81E-05 | 1.33E-04 | 2.58E-04 | 4.45E-04 | 1.04E-03 | 1.96E-03
a3D – z3F∘ | 3 – 4 | 6.73E-17 | 5.36E-12 | 1.67E-09 | 5.53E-08 | 5.90E-07 | 3.29E-06 | 1.21E-05 | 7.89E-05 | 2.86E-04 | 7.39E-04 | 1.54E-03 | 2.78E-03 | 4.52E-03 | 9.68E-03 | 1.72E-02
a3D – z3F∘ | 2 – 3 | 3.68E-20 | 2.66E-14 | 2.52E-11 | 1.63E-09 | 2.72E-08 | 2.09E-07 | 9.83E-07 | 8.99E-06 | 4.10E-05 | 1.25E-04 | 2.95E-04 | 5.87E-04 | 1.03E-03 | 2.49E-03 | 4.83E-03
a3D – z3F∘ | 1 – 2 | 9.82E-21 | 8.22E-15 | 8.34E-12 | 5.61E-10 | 9.63E-09 | 7.53E-08 | 3.59E-07 | 3.34E-06 | 1.54E-05 | 4.72E-05 | 1.12E-04 | 2.22E-04 | 3.91E-04 | 9.42E-04 | 1.82E-03
a3D – z3F∘ | 2 – 2 | 4.65E-21 | 3.90E-15 | 3.95E-12 | 2.66E-10 | 4.56E-09 | 3.57E-08 | 1.70E-07 | 1.58E-06 | 7.30E-06 | 2.24E-05 | 5.30E-05 | 1.05E-04 | 1.85E-04 | 4.46E-04 | 8.62E-04
a3D – z3F∘ | 3 – 3 | 1.42E-20 | 1.02E-14 | 9.69E-12 | 6.26E-10 | 1.05E-08 | 8.04E-08 | 3.78E-07 | 3.46E-06 | 1.58E-05 | 4.81E-05 | 1.14E-04 | 2.26E-04 | 3.98E-04 | 9.60E-04 | 1.86E-03
a3D – z3F∘ | 3 – 2 | 2.05E-21 | 1.71E-15 | 1.74E-12 | 1.17E-10 | 2.01E-09 | 1.57E-08 | 7.50E-08 | 6.98E-07 | 3.21E-06 | 9.85E-06 | 2.33E-05 | 4.64E-05 | 8.17E-05 | 1.97E-04 | 3.80E-04
a1D – z3D∘ | 2 – 2 | 1.47E-20 | 7.23E-15 | 5.63E-12 | 3.23E-10 | 4.98E-09 | 3.61E-08 | 1.62E-07 | 1.39E-06 | 6.03E-06 | 1.77E-05 | 4.06E-05 | 7.88E-05 | 1.36E-04 | 3.17E-04 | 6.00E-04
a1D – z3D∘ | 2 – 1 | 1.38E-20 | 5.61E-15 | 3.94E-12 | 2.12E-10 | 3.14E-09 | 2.20E-08 | 9.67E-08 | 8.00E-07 | 3.40E-06 | 9.82E-06 | 2.22E-05 | 4.27E-05 | 7.30E-05 | 1.68E-04 | 3.12E-04
a1D – z3F∘ | 2 – 3 | 1.78E-21 | 1.29E-15 | 1.22E-12 | 7.87E-11 | 1.32E-09 | 1.01E-08 | 4.76E-08 | 4.35E-07 | 1.99E-06 | 6.06E-06 | 1.43E-05 | 2.85E-05 | 5.02E-05 | 1.21E-04 | 2.35E-04
a1D – z3F∘ | 2 – 2 | 5.93E-21 | 4.97E-15 | 5.04E-12 | 3.40E-10 | 5.83E-09 | 4.56E-08 | 2.18E-07 | 2.03E-06 | 9.34E-06 | 2.86E-05 | 6.79E-05 | 1.35E-04 | 2.38E-04 | 5.73E-04 | 1.11E-03
a3D – z3P∘ | 1 – 2 | 9.33E-21 | 3.80E-15 | 2.67E-12 | 1.44E-10 | 2.13E-09 | 1.49E-08 | 6.57E-08 | 5.43E-07 | 2.31E-06 | 6.66E-06 | 1.51E-05 | 2.89E-05 | 4.93E-05 | 1.13E-04 | 2.12E-04
a1S – z3P∘ | 0 – 1 | 3.21E-20 | 7.74E-15 | 4.19E-12 | 1.93E-10 | 2.58E-09 | 1.68E-08 | 6.99E-08 | 5.36E-07 | 2.17E-06 | 6.06E-06 | 1.34E-05 | 2.53E-05 | 4.27E-05 | 9.66E-05 | 1.79E-04
a3D – z3P∘ | 2 – 2 | 1.00E-19 | 4.08E-14 | 2.87E-11 | 1.54E-09 | 2.28E-08 | 1.60E-07 | 7.04E-07 | 5.82E-06 | 2.47E-05 | 7.14E-05 | 1.61E-04 | 3.10E-04 | 5.29E-04 | 1.22E-03 | 2.28E-03
a3D – z3P∘ | 3 – 2 | 2.56E-19 | 1.04E-13 | 7.34E-11 | 3.95E-09 | 5.84E-08 | 4.10E-07 | 1.80E-06 | 1.49E-05 | 6.33E-05 | 1.83E-04 | 4.14E-04 | 7.94E-04 | 1.35E-03 | 3.12E-03 | 5.83E-03
a3D – z3P∘ | 1 – 1 | 2.05E-19 | 4.93E-14 | 2.67E-11 | 1.23E-09 | 1.64E-08 | 1.07E-07 | 4.46E-07 | 3.42E-06 | 1.38E-05 | 3.87E-05 | 8.55E-05 | 1.61E-04 | 2.72E-04 | 6.17E-04 | 1.14E-03
a3D – z3P∘ | 2 – 1 | 5.53E-19 | 1.33E-13 | 7.21E-11 | 3.33E-09 | 4.43E-08 | 2.89E-07 | 1.20E-06 | 9.23E-06 | 3.73E-05 | 1.04E-04 | 2.31E-04 | 4.36E-04 | 7.36E-04 | 1.67E-03 | 3.09E-03
a3D – z3P∘ | 1 – 0 | 2.01E-20 | 8.07E-15 | 5.73E-12 | 3.14E-10 | 4.72E-09 | 3.38E-08 | 1.51E-07 | 1.29E-06 | 5.66E-06 | 1.68E-05 | 3.91E-05 | 7.70E-05 | 1.35E-04 | 3.23E-04 | 6.28E-04
a1D – z3P∘ | 2 – 2 | 2.13E-20 | 8.70E-15 | 6.12E-12 | 3.30E-10 | 4.88E-09 | 3.42E-08 | 1.51E-07 | 1.25E-06 | 5.30E-06 | 1.53E-05 | 3.46E-05 | 6.65E-05 | 1.14E-04 | 2.62E-04 | 4.90E-04
a3F – z3D∘ | 3 – 3 | 8.76E-21 | 4.61E-15 | 3.71E-12 | 2.17E-10 | 3.40E-09 | 2.48E-08 | 1.13E-07 | 9.72E-07 | 4.25E-06 | 1.25E-05 | 2.88E-05 | 5.60E-05 | 9.67E-05 | 2.26E-04 | 4.29E-04
a3F – z3D∘ | 2 – 1 | 3.90E-20 | 1.58E-14 | 1.12E-11 | 6.02E-10 | 8.89E-09 | 6.25E-08 | 2.75E-07 | 2.28E-06 | 9.68E-06 | 2.80E-05 | 6.36E-05 | 1.22E-04 | 2.09E-04 | 4.81E-04 | 8.96E-04
a3F – z3D∘ | 4 – 3 | 3.99E-20 | 2.10E-14 | 1.69E-11 | 9.90E-10 | 1.55E-08 | 1.13E-07 | 5.13E-07 | 4.43E-06 | 1.94E-05 | 5.72E-05 | 1.31E-04 | 2.56E-04 | 4.41E-04 | 1.03E-03 | 1.96E-03
a3F – z3D∘ | 3 – 2 | 3.46E-20 | 1.70E-14 | 1.33E-11 | 7.62E-10 | 1.18E-08 | 8.52E-08 | 3.84E-07 | 3.29E-06 | 1.43E-05 | 4.21E-05 | 9.66E-05 | 1.88E-04 | 3.24E-04 | 7.59E-04 | 1.44E-03
a3F – z3F∘ | 4 – 4 | 8.99E-21 | 6.65E-15 | 6.35E-12 | 4.12E-10 | 6.88E-09 | 5.28E-08 | 2.48E-07 | 2.26E-06 | 1.02E-05 | 3.09E-05 | 7.25E-05 | 1.43E-04 | 2.49E-04 | 5.93E-04 | 1.13E-03
a3F – z3F∘ | 2 – 2 | 8.24E-22 | 6.91E-16 | 7.02E-13 | 4.73E-11 | 8.12E-10 | 6.36E-09 | 3.04E-08 | 2.83E-07 | 1.31E-06 | 4.02E-06 | 9.53E-06 | 1.90E-05 | 3.35E-05 | 8.09E-05 | 1.57E-04
a3F – z3F∘ | 3 – 3 | 4.01E-21 | 2.90E-15 | 2.75E-12 | 1.78E-10 | 2.98E-09 | 2.29E-08 | 1.08E-07 | 9.90E-07 | 4.52E-06 | 1.38E-05 | 3.27E-05 | 6.52E-05 | 1.15E-04 | 2.78E-04 | 5.41E-04
a3F – z3F∘ | 4 – 3 | 1.88E-21 | 1.36E-15 | 1.29E-12 | 8.36E-11 | 1.40E-09 | 1.08E-08 | 5.07E-08 | 4.65E-07 | 2.12E-06 | 6.49E-06 | 1.54E-05 | 3.06E-05 | 5.40E-05 | 1.31E-04 | 2.54E-04
a3P – y3P∘ | 2 – 2 | 6.96E-21 | 3.83E-15 | 3.16E-12 | 1.88E-10 | 2.96E-09 | 2.19E-08 | 9.98E-08 | 8.71E-07 | 3.85E-06 | 1.14E-05 | 2.65E-05 | 5.20E-05 | 9.05E-05 | 2.15E-04 | 4.12E-04
a3P – y3P∘ | 1 – 0 | 2.14E-21 | 1.23E-15 | 1.04E-12 | 6.30E-11 | 1.00E-09 | 7.45E-09 | 3.42E-08 | 3.00E-07 | 1.33E-06 | 3.97E-06 | 9.22E-06 | 1.81E-05 | 3.14E-05 | 7.42E-05 | 1.41E-04
a3P – z3D∘ | 2 – 3 | 9.36E-21 | 4.93E-15 | 3.98E-12 | 2.33E-10 | 3.65E-09 | 2.67E-08 | 1.21E-07 | 1.05E-06 | 4.60E-06 | 1.36E-05 | 3.13E-05 | 6.09E-05 | 1.05E-04 | 2.47E-04 | 4.70E-04
a3P – z3D∘ | 1 – 2 | 7.12E-21 | 3.51E-15 | 2.74E-12 | 1.58E-10 | 2.44E-09 | 1.77E-08 | 7.97E-08 | 6.84E-07 | 2.98E-06 | 8.79E-06 | 2.02E-05 | 3.94E-05 | 6.81E-05 | 1.60E-04 | 3.04E-04
a3P – z3D∘ | 1 – 1 | 4.15E-21 | 1.69E-15 | 1.19E-12 | 6.44E-11 | 9.53E-10 | 6.70E-09 | 2.95E-08 | 2.45E-07 | 1.05E-06 | 3.03E-06 | 6.89E-06 | 1.33E-05 | 2.27E-05 | 5.24E-05 | 9.80E-05
a3P – z3D∘ | 2 – 1 | 1.10E-20 | 4.48E-15 | 3.16E-12 | 1.71E-10 | 2.52E-09 | 1.78E-08 | 7.82E-08 | 6.49E-07 | 2.77E-06 | 8.03E-06 | 1.82E-05 | 3.51E-05 | 6.02E-05 | 1.39E-04 | 2.60E-04

Table A.3: Atmospheric parameters of the sample stars and yttrium LTE and NLTE abundances.  $\\#$ | Star | $T_{\rm eff}$ | log$g$ | [Fe/H] | $\xi_{t}$ | Pop. | [Y/Fe]LTE | $\sigma_{\rm LTE}$ | [Y/Fe]NLTE | $\sigma_{\rm NLTE}$ | $N_{\rm lines}$
---|---|---|---|---|---|---|---|---|---|---|---
|  | K | CGS | dex | km s-1 |  |  |  |  |  |
1 | HD 19373 | 6045 | 4.24 | 0.10 | 1.20 | Thin disk | -0.11 | 0.05 | -0.11 | 0.05 | 4
2 | HD 22484 | 6000 | 4.07 | 0.01 | 1.10 | Thin disk | -0.06 | 0.06 | -0.08 | 0.05 | 3
3 | HD 24289 | 5980 | 3.71 | -1.94 | 1.10 | Halo | -0.03 | 0.08 | 0.07 | 0.07 | 4
4 | HD 30562 | 5900 | 4.08 | 0.17 | 1.30 | Thin disk | -0.05 | 0.05 | -0.07 | 0.05 | 3
5 | HD 30743 | 6450 | 4.20 | -0.44 | 1.80 | Thin disk | 0.04 | 0.05 | 0.08 | 0.05 | 3
6 | HD 34411 | 5850 | 4.23 | 0.01 | 1.20 | Thin disk | -0.08 | 0.05 | -0.08 | 0.05 | 3
7 | HD 43318 | 6250 | 3.92 | -0.19 | 1.70 | Thin disk | -0.02 | 0.02 | -0.02 | 0.02 | 2
8 | HD 45067 | 5960 | 3.94 | -0.16 | 1.50 | Thin disk | -0.04 | 0.04 | -0.04 | 0.04 | 5
9 | HD 45205 | 5790 | 4.08 | -0.87 | 1.10 | Thick disk | -0.04 | 0.02 | 0.03 | 0.04 | 3
10 | HD 52711 | 5900 | 4.33 | -0.21 | 1.20 | Thin disk | -0.04 | 0.02 | -0.04 | 0.02 | 4
11 | HD 58855 | 6410 | 4.32 | -0.29 | 1.60 | Thin disk | 0.06 | 0.02 | 0.08 | 0.00 | 3
12 | HD 59374 | 5850 | 4.38 | -0.88 | 1.20 | Thick disk | -0.02 | 0.06 | 0.04 | 0.06 | 5
13 | HD 59984 | 5930 | 4.02 | -0.69 | 1.40 | Thin disk | -0.17 | 0.05 | -0.12 | 0.04 | 4
14 | HD 62301 | 5840 | 4.09 | -0.70 | 1.30 | Thick disk | -0.12 | 0.06 | -0.08 | 0.05 | 5
15 | HD 64090 | 5400 | 4.70 | -1.73 | 0.70 | Halo | -0.07 | 0.06 | -0.01 | 0.03 | 3
16 | HD 69897 | 6240 | 4.24 | -0.25 | 1.40 | Thin disk | -0.05 | 0.06 | -0.03 | 0.05 | 4
17 | HD 74000 | 6225 | 4.13 | -1.97 | 1.30 | Halo | 0.07 | 0.05 | 0.16 | 0.02 | 4
18 | HD 76932 | 5870 | 4.10 | -0.98 | 1.30 | Thick disk | 0.11 | 0.05 | 0.20 | 0.03 | 4
19 | HD 82943 | 5970 | 4.37 | 0.19 | 1.20 | Thin disk | -0.20 | 0.01 | -0.21 | 0.02 | 4
20 | HD 89744 | 6280 | 3.97 | 0.13 | 1.70 | Thin disk | 0.05 | 0.07 | 0.03 | 0.04 | 3
21 | HD 90839 | 6195 | 4.38 | -0.18 | 1.40 | Thin disk | 0.03 | 0.04 | 0.05 | 0.03 | 4
22 | HD 92855 | 6020 | 4.36 | -0.12 | 1.30 | Thin disk | -0.05 | 0.02 | -0.05 | 0.02 | 2
23 | HD 94028 | 5970 | 4.33 | -1.47 | 1.30 | Thick disk | 0.16 | 0.09 | 0.26 | 0.06 | 6
24 | HD 99984 | 6190 | 3.72 | -0.38 | 1.80 | Thin disk | 0.07 | 0.04 | 0.09 | 0.04 | 4
25 | HD 100563 | 6460 | 4.32 | 0.06 | 1.60 | Thin disk | 0.04 | 0.02 | 0.03 | 0.04 | 3
26 | HD 102870 | 6170 | 4.14 | 0.11 | 1.50 | Thin disk | -0.06 | 0.06 | -0.07 | 0.06 | 4
27 | HD 103095 | 5130 | 4.66 | -1.26 | 0.90 | Halo | -0.02 | 0.03 | 0.04 | 0.01 | 3
28 | HD 105755 | 5800 | 4.05 | -0.73 | 1.20 | Thin disk | -0.07 | 0.03 | -0.02 | 0.02 | 4
29 | HD 106516 | 6300 | 4.44 | -0.73 | 1.50 | Thick disk | -0.03 | 0.05 | 0.02 | 0.04 | 3
30 | HD 108177 | 6100 | 4.22 | -1.67 | 1.10 | Halo | 0.00 | 0.03 | 0.09 | 0.04 | 6
31 | HD 110897 | 5920 | 4.41 | -0.57 | 1.20 | Thin disk | -0.11 | 0.05 | -0.07 | 0.04 | 4
32 | HD 114710 | 6090 | 4.47 | 0.06 | 1.10 | Thin disk | 0.10 | 0.04 | 0.09 | 0.04 | 4
33 | HD 115617 | 5490 | 4.40 | -0.10 | 1.10 | Thin disk | -0.18 | 0.05 | -0.17 | 0.06 | 3
34 | HD 134088 | 5730 | 4.46 | -0.80 | 1.10 | Thick disk | -0.04 | 0.03 | 0.01 | 0.05 | 3
35 | HD 134169 | 5890 | 4.02 | -0.78 | 1.20 | Thin disk | -0.12 | 0.04 | -0.06 | 0.03 | 4
36 | HD 138776 | 5650 | 4.30 | 0.24 | 1.30 | Thin disk | -0.24 | 0.05 | -0.24 | 0.05 | 3
37 | HD 142091 | 4810 | 3.12 | -0.07 | 1.20 | Thin disk | -0.26 | 0.02 | -0.26 | 0.02 | 2
38 | HD 142373 | 5830 | 3.96 | -0.54 | 1.40 | Thin disk | -0.17 | 0.07 | -0.13 | 0.07 | 4
39 | BD+07 4841 | 6130 | 4.15 | -1.46 | 1.30 | Halo | 0.19 | 0.05 | 0.29 | 0.05 | 6
40 | BD+09 0352 | 6150 | 4.25 | -2.09 | 1.30 | Halo | -0.03 | 0.14 | 0.05 | 0.13 | 2
41 | BD+24 1676 | 6210 | 3.90 | -2.44 | 1.50 | Halo | -0.12 | 0.14 | -0.04 | 0.11 | 2
42 | BD+29 2091 | 5860 | 4.67 | -1.91 | 0.80 | Halo | -0.19 | 0.02 | -0.10 | 0.03 | 4
43 | BD+37 1458 | 5500 | 3.70 | -1.95 | 1.00 | Halo | 0.14 | 0.06 | 0.24 | 0.08 | 4
44 | BD+66 0268 | 5300 | 4.72 | -2.06 | 0.60 | Halo | -0.13 | 0.04 | -0.06 | 0.04 | 3
45 | BD-04 3208 | 6390 | 4.08 | -2.20 | 1.40 | Halo | -0.05 | 0.03 | 0.03 | 0.03 | 1
46 | BD-13 3442 | 6400 | 3.95 | -2.62 | 1.40 | Halo | 0.05 | 0.03 | 0.16 | 0.03 | 1
47 | G090-003 | 6007 | 3.90 | -2.04 | 1.30 | Halo | -0.13 | 0.04 | -0.04 | 0.06 | 4
48 | HD 29907 | 5500 | 4.64 | -1.55 | 0.60 | Halo | -0.09 | 0.07 | -0.03 | 0.07 | 3
49 | HD 31128 | 5980 | 4.49 | -1.49 | 1.20 | Thick disc | 0.03 | 0.05 | 0.14 | 0.04 | 5
50 | HD 59392 | 6010 | 4.02 | -1.59 | 1.40 | Halo | 0.14 | 0.05 | 0.22 | 0.04 | 4
51 | HD 97320 | 6110 | 4.27 | -1.18 | 1.40 | Thick disc | 0.05 | 0.07 | 0.14 | 0.06 | 5
52 | HD 193901 | 5780 | 4.46 | -1.08 | 0.90 | Halo | -0.12 | 0.04 | -0.05 | 0.03 | 5
53 | HD 298986 | 6130 | 4.30 | -1.34 | 1.40 | Halo | -0.12 | 0.05 | -0.03 | 0.05 | 4
54 | HD 102200 | 6115 | 4.20 | -1.24 | 1.40 | Thick disc | -0.04 | 0.06 | 0.04 | 0.05 | 6
55 | HD 3795 | 5475 | 3.85 | -0.61 | 1.00 | Thick disc | 0.06 | 0.08 | 0.06 | 0.07 | 4
56 | HD 32923 | 5710 | 4.03 | -0.26 | 1.20 | Thin disc | 0.03 | 0.05 | 0.03 | 0.04 | 4
57 | HD 40397 | 5550 | 4.39 | -0.17 | 1.00 | Thick disc | -0.02 | 0.06 | -0.01 | 0.07 | 3
58 | HD 64606 | 5280 | 4.63 | -0.68 | 1.00 | Thick disc | -0.16 | 0.09 | -0.14 | 0.08 | 4
59 | HD 69611 | 5940 | 4.17 | -0.60 | 1.20 | Thick disc | -0.04 | 0.04 | 0.01 | 0.03 | 4
60 | HD 114762 | 5930 | 4.18 | -0.71 | 1.20 | Thick disc | -0.17 | 0.04 | -0.12 | 0.04 | 4
61 | HD 201891 | 5900 | 4.29 | -0.97 | 1.20 | Thick disc | -0.19 | 0.06 | -0.13 | 0.05 | 4

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