#  LOTUS: A (non-)LTE Optimization Tool for Uniform derivation of
Stellar atmospheric parameters

Yangyang Li(李扬洋) Department of Astronomy, University of Florida, Bryant Space
Science Center, Gainesville, FL 32611, USA  Rana Ezzeddine Department of
Astronomy, University of Florida, Bryant Space Science Center, Gainesville, FL
32611, USA  Joint Institute for Nuclear Astrophysics - Center for Evolution of
the Elements, USA

(Received August 23, 2022; Revised January 09, 2023; Accepted January 27,
2023)

###### Abstract

Precise fundamental atmospheric stellar parameters and abundance determination
of individual elements in stars are important for all stellar population
studies. Non-Local Thermodynamic Equilibrium (Non-LTE; hereafter NLTE) models
are often important for such high precision, however, can be computationally
complex and expensive, which renders the models less utilized in spectroscopic
analyses. To alleviate the computational burden of such models, we developed a
robust 1D, NLTE fundamental atmospheric stellar parameter derivation tool,
LOTUS, to determine the effective temperature $T_{\rm eff}$, surface gravity
$\log g$, metallicity [Fe/H] and microturbulent velocity $v_{\mathrm{mic}}$
for FGK type stars, from equivalent width (EW) measurements of Fe i and Fe ii
lines. We utilize a generalized curve of growth method to take into account
the EW dependencies of each Fe i and Fe ii line on the corresponding
atmospheric stellar parameters. A global differential evolution optimization
algorithm is then used to derive the fundamental parameters. Additionally,
LOTUS can determine precise uncertainties for each stellar parameter using a
Markov Chain Monte Carlo (MCMC) algorithm. We test and apply LOTUS on a sample
of benchmark stars, as well as stars with available asteroseismic surface
gravities from the K2 survey, and metal-poor stars from the $Gaia$-ESO and
$R$-process Alliance (RPA) surveys. We find very good agreement between our
NLTE-derived parameters in LOTUS to non-spectroscopic values on average within
$T_{\rm eff}$ $=\pm 30$ K and $\log g$ $=\pm 0.10$ dex for benchmark stars. We
provide open access of our code, as well as of the interpolated pre-computed
NLTE EW grids available on Github github111The software is available on GitHub
https://github.com/Li-Yangyang/LOTUS under a MIT License and version 0.1.1 (as
the persistent version) is archived in Zenodo (Li & Ezzeddine, 2023)., and
documentation with working examples on Readthedocs book.

Astronomical techniques (1684), Spectroscopy (1558); Stellar atmospheres
(1584), Stellar physics (1621), Stellar photospheres (1237); Fundamental
parameters of stars (555), Astrometry (80), Effective temperature (449),
Surface gravity (1669), Metallicity (1031)

††journal: AJ††software: astropy (Astropy Collaboration et al., 2013, 2018),
numpy (van der Walt et al., 2011; Harris et al., 2020), pandas (pandas
development team, 2020), scikit-learn (Buitinck et al., 2013), scipy (Virtanen
et al., 2020), sympy (Meurer et al., 2017), matplotlib (Hunter, 2007), h5py
(Collette, 2013), PyMC3 (Salvatier et al., 2016), theano (Team et al., 2016),
corner (Foreman-Mackey, 2016), numdifftools (Brodtkorb & D’Errico, 2015)

##  1 Introduction

Precise characterization of stellar spectra is a key ingredient for
understanding several fields of modern astrophysics, including the physical
and chemical properties and abundances of stars (Asplund et al., 2009; Jofré
et al., 2019), galactic formation and evolution (Audouze & Tinsley, 1976;
McWilliam, 1997; Kobayashi et al., 2006), as well as macro and micro physical
phenomena near the surface of stars (Miesch & Toomre, 2009; Linsky, 2017).
This accurate level of characterization is also needed for the detection of
extra-solar planets when using radial velocity methods (Vanderburg et al.,
2016).

With the current inflow of stellar spectra from ongoing and future large
observational spectroscopic surveys including, SDSS-V (Kollmeier et al. 2017,
R$\sim$2000 and $\sim$22500), LAMOST (Liu et al. 2020, R$\sim$7500; Cui et al.
2012; Zhao et al. 2012; Deng et al. 2012, R$\sim$1800), APOGEE (Ahumada et al.
2020, R$\sim$22500), RAVE (Steinmetz et al. 2020, R$\sim$7500), GALAH (De
Silva et al. 2015, R$\sim$28000), as well as the upcoming WEAVE (Dalton et al.
2016, R$\sim$5000 and R$\sim$20000), 4MOST (de Jong et al. 2019, R$\sim$20000)
and PLATO (Miglio et al. 2017), stellar spectroscopy will be providing $\sim
10^{5}$ of golden opportunities to study the chemical and dynamical properties
of stars in the Galaxy to help understand its build-up history and evolution.

Atmospheric fundamental stellar parameters, including the effective
temperatyre $T_{\rm eff}$, surface gravity $\log g$, metallicity [Fe/H] and
microturbulent velocity $v_{\mathrm{mic}}$, as well as chemical abundances of
stars, are determined from the observed spectra of a given star by fitting
theoretical synthetic spectra based on assumptions of geometric structures (1D
versus 3D), radiative transfer assumptions (Local Thermodynamic Equilibrium;
hereafter LTE, versus Non-Local Thermodynamic Equilibrium; hereafter NLTE).
Two classical methods are commonly used to derive stellar atmospheric
parameters from stellar spectra: either 1) by iteratively fitting the observed
spectra to synthetic spectral models until a best-fit match is met at the
corresponding stellar parameters, or 2) by measuring chemical abundances
determined from Fe i and Fe ii lines from equivalent widths (EW) measurements,
and employing optimization of excitation and ionization equilibrium by
changing the stellar parameters iteratively until trends with excitation
potential energies ($\chi$) and reduced equivalent widths ($\log(EW/\lambda)$)
of the lines are minimized. While the former method of spectral synthesis
might outperform the latter in crowded spectral regions or spectra dominated
by strong lines ($\log(EW/\lambda)>-4.5$), the EW method generally requires
less calculation time and resources than synthetic spectra, making it a
simpler and more widely applied tool to measure atmospheric stellar parameters
and chemical abundances.

Classical radiative transfer models for deriving stellar parameters and
chemical abundances from observed spectra most often LTE. Under LTE, the gas
and chemical particles throughout the stellar atmosphere satisfy the Saha-
Boltzmann excitation and ionization balance equations. Several stellar
atmospheric parameter tools implementing classical 1D and LTE approximations
for spectroscopic analyses already exist and are widely used (e.g., MATISSE
(Recio-Blanco et al., 2006), MyGIsFOS (Sbordone et al., 2014), the APOGEE
pipeline ASCAP (García Pérez et al., 2016), GALA (Mucciarelli et al., 2013),
DOOp (Cantat-Gaudin et al., 2014), ARES (Sousa et al., 2015), StePar
(Tabernero et al., 2019), FASMA (Tsantaki & Andreasen, 2021) and iSpec
(Blanco-Cuaresma et al., 2014; Blanco-Cuaresma, 2019).

The LTE assumption utilized by all of these tools is, however, not physically
motivated when applied to evolved giants and/or metal-poor stars (Lind et al.,
2012; Ezzeddine et al., 2017; Mashonkina et al., 2017; Amarsi et al., 2020).
Inelastic collisional interactions between atoms and electrons or neutral
hydrogen in the atmospheres of cool stars usually drive the local conditions
in these atmospheres towards LTE. In metal-poor and giant stars, limited
electron donors from metals are not able to induce enough collisions to
maintain collisional equilibrium in the line-forming regions (Hubeny &
Mihalas, 2014), which drive line formation away from LTE (Mihalas & Athay,
1973; Bergemann et al., 2012). Quantified deviations in abundances and stellar
atmospheric parameters from LTE are commonly known as NLTE effects (Asplund,
2005), which are mainly driven by deviations from statistical equilibrium or
kinematic equilibrium.

A small number of radiative transfer codes have started taking NLTE effects
into account for the determination of chemical abundances, including PySME
(Wehrhahn, 2021), which is based on the spectroscopic analysis code
Spectroscopy Made Easy (SME; Piskunov & Valenti 2017). Kovalev et al. (2019)
has implemented NLTE departure coefficients in the synthesis tools, allowing
NLTE spectral synthesis for certain corresponding absorption lines. More
recently, a NLTE version of Turbospectrum (Plez, 2012) has been released
(Gerber et al., 2022), which also has NLTE departure coefficients incorporated
in their 1D, LTE spectral synthesis models. However, both codes allow NLTE
corrections for only some elements via spectral synthesis, and stellar
parameters still need to be derived independently or iteratively via full
spectral fitting, which can be prone to degeneracies. Therefore, a tool that
can automatically derive stellar parameters incorporating NLTE models, taking
into account stellar parameter dependencies, is highly needed which is the
main motivation of this work and paper.

In this work, we present a fast, automatic and robust spectroscopic analysis
tool, LOTUS, which stands for a “(non-)LTE Optimization Tool for Uniform
derivation of Stellar atmospheric parameters”. LOTUS allows the derivation of
$T_{\rm eff}$, $\log g$, [Fe/H] and $v_{\mathrm{mic}}$ based on EW
measurements input of Fe i and Fe ii lines from stellar spectra. Either or
both LTE and NLTE modes can be chosen for the benefit of comparisons. As
compared to traditional full NLTE calculations for each model, LOTUS can
significantly shorten the time of the determination of stellar parameters
using the NLTE assumption from several hours or even days (Hauschildt et al.,
1997) to $\sim 15-30$ mins for each star. A Monte-Carlo Markov Chain (MCMC)
analysis is also implemented to precisely estimate the uncertainties of the
derived parameters. We test and apply LOTUS on several benchmark stars, and
stellar surveys with available non-spectroscopic atmospheric parameters (from
asteroseismology or interferometry)for comparison and validation of our
results.

The rest of the paper is organized as follows: In Section 2, we present a
detailed description of LOTUS, and describe the input models for our NLTE
calculations, as well as a description of the different modules of the code.
In Section 3, we test our code and apply it to derive and compare the derived
parameters of benchmark stars, and stars with non-spectroscopic derived
parameters. In Section 4, we apply the code to a large sample of metal-poor
stars and discuss the NLTE effects obtained via LOTUS. In Section 5, we
present a discussion on the caveats and limitations of the code, and finally,
in Section 6 we present a summary of our results and conclude.

##  2 General description

LOTUS is designed to derive the fundamental atmospheric stellar parameters
$T_{\rm eff}$, $\log g$, [Fe/H] and $v_{\mathrm{mic}}$of FGK type stars, by
implementing observed measurements of EW for Fe i and Fe ii lines as input. An
example of a user input EW linelist is shown in Listing 1 below. The
transition wavelength (obs_wavelength in Å), element and ionization stage (Fe
i or Fe ii), measured EW (obs_ew in mÅ) and excitation potential energy EP
(obs_ep in eV) are required.

⬇

1obs_wavelength,element,obs_ew,obs_ep

24787.8266,FeI,44.2,3.00

34788.7566,FeI,65.5,3.24

44789.6508,FeI,83.3,3.55

56456.3796,FeII,59.2,3.9

6...

Listing 1: Example of an input file format of observed EW measurements for Fe
i and Fe ii lines provided by users for LOTUS. obs_wavelength are in Å, obs_ew
in mÅ, and obs_ep in eV.

LOTUS has three general modules of functionality. In a general overview, (i)
Fe i and Fe ii abundances are derived by interpolating a generalized curve of
growth (GCOG) for each line in a pre-computed grid of theoretical EW in both
LTE and NLTE, following Boeche & Grebel (2016). (ii) the stellar parameters
are then derived by minimizing the slopes for excitation and ionization
equilibrium, iteratively using a global minimization module, and finally,
(iii) uncertainties of the derived atmospheric parameters are estimated
utilizing a Markov Chain Monte Carlo (MCMC) algorithm. We describe each of
these modules in detail in sub-section 2.2 below, after listing the input and
radiative transfer models used in Section 2.1.

Figure 1:  A flow diagram describing the working modules of LOTUS. Three main
modules are used to derive the stellar parameters and their uncertainties: (i)
an interpolation Module, (ii) a Global Minimization Module, and (iii) an
Uncertainty Estimation Module. Input includes EW measurements of Fe i and Fe
ii of the absorption lines measured in the spectra. Users can define the
number of $\sigma$ clipping required to remove outliers (see Section 2.4.3 for
details). Additionally, a halt condition for the value of the smallest
allowable minimization function threshold can also be defined by users (see
Section 2.4.3 for details).

###  2.1 Input Models

####  2.1.1 Stellar Atmosphere Models

LOTUS incorporates 1D, LTE MARCS stellar atmospheric models (Gustafsson et
al., 1975, 2008), covering a wide range of stellar parameters typical for FGK
stars.

Spherical atmospheric models were used for $\log g$$\,<3.5$, otherwise, plane-
parallel models were adopted. The grid of MARCS model atmosphere available
online222https://marcs.astro.uu.se/ offers reasonable coverage for the stellar
parameters, however they exhibit wide gaps in effective temperature (steps of
$\sim 250$ K), surface gravity (steps of $\sim 0.5$ cgs), and metallicity
(steps of $\sim 0.25-0.50$ dex) to optimally explore the parameter space. We
utilize the MARCS interpolation subroutine
iterpol_marcs.f333http://marcs.astro.uu.se/software.php written by Thomas
Masseron, to produce a higher resolution grid, with our final parameter grid
ranging from 4000 K to 6850 K for $T_{\rm eff}$ (steps of 50 K), $\log g$ from
0.0 to 5.0 (steps of 0.1), [Fe/H] from $-3.5$ to $+0.5$ (steps of 0.5) and
$v_{\mathrm{mic}}$ from 0.5 to 3.0 km s-1 (steps of 0.5 km s-1).

####  2.1.2 Iron Model Atom

Computing theoretical NLTE Fe i and Fe ii EWs requires the input of a
comprehensive iron model with up-to-date radiative and collisional atomic
data. For our EW grid calculations, we adopt a well-tested Fe i/Fe ii model
atom containing 846 Fe i and 1027 Fe ii lines Ezzeddine et al. (2016, 2017,
2020). The atom includes absorption line transitions spanning the near-UV to
the near-IR, extending the range of wavelength from $\sim 1000$ to $10^{5}$ Å.
The model also carefully considers hydrogen collision and electron collision
processes from quantum atomic data, particularly implementing ion-pair
production and mutual-neutralization processes from Barklem (2018). Extensive
details on the build-up of the atom and the corresponding atomic data are
presented in Ezzeddine et al. (2016) and Ezzeddine et al. (2020).

####  2.1.3 NLTE Radiative Transfer computations

We utilized the NLTE radiative transfer code MULTI2.3 to solve for statistical
equilibrium populations and derive the theoretical NLTE EW for the Fe i and Fe
ii lines in our atom. The code utilizes the Approximate Lambda Iteration (ALI)
(Rybicki & Hummer, 1991) to iteratively determine the populations using the
comprehensive Fe i/Fe ii model atom described in Section 2.1.2. MULTI2.3 also
solves for LTE populations using the classical Saha and Boltzmann equations,
which is output as a departure coefficient, $b_{i}$, where
$b_{i}=n_{i}(\mathrm{NLTE})/n_{i}(\mathrm{LTE})$ (Wijbenga & Zwaan, 1972),
where $n$ is the level population for the corresponding line transition $i$.

####  2.1.4 Linelist Selection

The linelist selection is crucial for the accurate derivation of Fe i and Fe
ii chemical abundances and stellar parameters using the EW method, especially
for cooler stars (e.g. FGK stars) since they have much denser spectral line
regions containing blended lines. Therefore, we choose a comprehensive list of
Fe i and Fe ii from the $Gaia$-ESO line list (Jofré et al., 2014; Heiter et
al., 2015, 2021), covering the wavelength ranges from 4750 to 6850 Å and from
8500 to 8950 Å. Additional lines from the R-Process Alliance (RPA) survey
(e.g., Hansen et al., 2018; Sakari et al., 2018; Ezzeddine et al., 2020;
Holmbeck et al., 2020) have also been added to account for lines common in
metal-poor stars, with corresponding atomic data and references in (Roederer
et al., 2018). We combine iron lines from both linelists, removing any
duplicates in the process. Our final linelist is presented in Table 2. Future
LOTUS releases should be easily able to extend the linelists to bluer and
redder lines in the UV and IR, respectively.

Figure 2: Computed NLTE EW dependence as a function of $T_{\rm eff}$, $\log
g$, $v_{\mathrm{mic}}$ for the Fe I line at 4070.77Å and EP=3.24 eV (left) and
the Fe II line at 6247.55$\AA$ with EP=3.89 eV (right). Both lines have been
computed at a fixed [Fe/H]$=-2.0$.

###  2.2 Key Modules

Below we describe in detail the key components and modules of the LOTUS
functionalities. An illustrated flow diagram of the workings of the code is
also shown in Figure 1, demonstrating the connection between the different
modules.

####  2.2.1 EW Interpolation Module

Traditional curve of growth (COG) methods to derive chemical abundances
usually employ simplistic models, typically computed at fixed $T_{\rm eff}$,
$\log g$, [Fe/H] and $v_{\mathrm{mic}}$ for each line. For some lines,
however, EW can have strong dependencies on multiple atmospheric stellar
parameters in a given parameter space. Figure 2 demonstrate these
dependencies, where EW variation from our computed NLTE grid are shown as a
function of $T_{\rm eff}$ $\log g$ and $v_{\mathrm{mic}}$ for the Fe I line at
4070.768 Å (left panel), and the Fe II lines at 6247.545 Å (right panel),
respectively. The metallicity for both plots has been fixed at [Fe/H] $=-2.00$
for demonstration purposes. We observe that at a fixed [Fe/H], increasing
$T_{\rm eff}$ will decrease EW of the Fe i line, while EW being mostly
insensitive to $\log g$ variation; For Fe ii lines, however, increasing
$T_{\rm eff}$ will increase EW while increasing $\log g$ will decrease EW. For
both lines, EW will increase as $v_{\mathrm{mic}}$ increases, as
$v_{\mathrm{mic}}$ delays the saturation by spreading absorption into a wider
wavelength band. These EW-stellar parameter dependencies have been
qualitatively proven in Chapter 17.5 of Hubeny & Mihalas (2014). Thus, to take
into account such important dependencies in our codes, which can affect our
derived abundances and thus our stellar parameter derivation, we compute a
Generalized Curve of Growth (GCOG) for each Fe i and Fe ii line in our
linelist. We define the GCOG for any given line $i$ as:

$GCOG_{i}\mathpunct{:}\left(T_{\mathrm{eff}},\mathrm{log}\textit{g},\nu_{mic},\mathrm{EW}\right)\mapsto
A(\mathrm{Fe})_{i}$

A GCOG is thus a generalization of the well-known COG onto a higher
dimensional mapping of EW $\mapsto$ A(Fe) Alternatively, COGi can be obtained
by fixing $T_{\rm eff}$ $\log g$ and $v_{\mathrm{mic}}$ for a given GCOG.
GCOGs have been implemented in previous studies such as Osorio et al. (2015)
and Boeche & Grebel (2016). We thus provide interpolated GCOGs which are
stored as libraries in our code for every line in our linelist (see Section
2.1.4).The GCOGs are then utilize in the optimization module afterward to
derive the Fe i and Fe ii abundances.

###  2.3 Abundance Determination module

To derive the Fe i and Fe ii abundances, we fit multivariate polynomials to
the GCOG of each line, by deriving the relationship between the iron abundance
of the line with $T_{\rm eff}$, $\log g$, $v_{\mathrm{mic}}$ and EW, denoted
as
$A\left(\mathrm{Fe}\right)=P\left(T_{\mathrm{eff}},\mathrm{log}\textit{g},\nu_{mic},\mathrm{EW}\right)$.
The detailed form of $P$ can be written as:

$\sum_{i_{1}+i_{2}+i_{3}+i_{4}\leq
n}a_{i_{1}i_{2}i_{3}i_{4}}\left(T_{\mathrm{eff}}\right)^{i_{1}}\left(\mathrm{log}\textit{g}\right)^{i_{2}}\left(v_{mic}\right)^{i_{3}}\left(\mathrm{EW}\right)^{i_{4}}$
(1)

where $i_{m}$ ($m=1,2,3,4$) is the polynomial power of each of the 3 stellar
parameters ($T_{\rm eff}$, $\log g$ and $v_{\mathrm{mic}}$) as well as EW.
Possible values for $i_{m}$ are positive integers, where the sum of all the
powers should less than or equal to the power degree of the polynomial $n$.
$a_{i_{1}i_{2}i_{3}i_{4}}$ is the product of the polynomial coefficients of
all the variables. The criteria for choosing $n$ depends on the behavior of
theoretical GCOG models within a range of stellar parameters and is described
in more details in Section 2.3.1 below.

Table 1: Interpolation intervals chosen for different stellar types considered in LOTUS. stellar parameter | types | intervals
---|---|---
T${}_{\textrm{eff}}$ (K) | K | [4000, 5200]
| G | [5200, 6000]
| F | [6000, 6850]
logg | supergiant | [0.0, 0.5]
| giant | [0.5, 3.0]
| subgiant | [3.0, 4.0]
| dwarf | [4.0, 5.0]
[Fe/H] | very metal poor | [$-3.5$, $-2.0$]
| metal poor | [$-2.0$, $-0.5$]
| metal rich | [$-0.5$, 0.5]

####  2.3.1 Selection of Interpolator

We choose the linelist utilized to derive stellar parameters to be dependent
on the spectral type of the star, as some lines can be blended or strong in
cool high metallicity stars, whereas these same lines could also be blend-free
and weaker for hotter, metal-poor stars. Therefore, the multivariate
polynomial functions defined in Section 2.3 used to derive the abundances
determined from Fe i and Fe ii lines depend on the choice of linelist for each
spectral type. We thus pay special attention to the choice of interpolator by
identifying the best selection of linelist per spectral type (or stellar
parameters). Therefore, instead of interpolating in the whole parameter space
for all the lines, we pre-define that the GCOGs fit only the abundances
determined from the lines we pre-selected and chose to use within tested
intervals of stellar parameters, according to an initial guess of spectral
types that the users can insert as an input in the code. Our choice of the
intervals of different stellar parameters for each spectral types are listed
in Table 1. For example, if an initial guess is chosen such that the target
star is a metal-poor G giant, the multivariate polynomial will fit the
abundance of each line versus other atmospheric parameters using the grid
points falling into the range of $T_{\rm eff}$ from 5200 K to 6000 K, $\log g$
from 0.0 to 3.0 and [Fe/H] from $-2.0$ to $-0.5$.

In order to choose the best interpolator per spectral type (i.e., the optimal
$n$) among several multivariate polynomials as defined in Equation 1, we use a
Bayesian Information Criteria (BIC) to select the best polynomial function for
each line based on the mean residual differences between the theoretical EWs
at the nodes of our pre-computed NLTE grid (computed at a combination of
$T_{\rm eff}$, $\log g$, [Fe/H], and $v_{\mathrm{mic}}$), to the EWs
interpolated at these parameters. We assume that the optimal model is among
the polynomials with degree=2,3,4,5. The BIC was calculated such as:

$\mathrm{BIC}=n\,\mathrm{ln}\left(\frac{\mathrm{SSR}}{n}\right)+k\,\mathrm{ln}(n)$
(2)

where SSR is the sum of the squared residuals between the theoretical EWs and
the interpolated EWs from models at specific nodes of the grid, and $n$ is
sample size (here we choose $n=4000$ nodes in each spectral type interval).
$k$ is a free parameter (including coefficients and slope intercept), which
can be calculated as k=$C_{d+4}^{d}$, where $d$ is the degree of the
polynomial, and 4 is chosen as the number of dependent variables for each
interpolated EW (namely, $T_{\rm eff}$, $\log g$, [Fe/H] and
$v_{\mathrm{mic}}$).

We thus chose the best interpolator for each spectral type interval as that
with the lowest BIC value. In Fig. 3, we show the differences between the
interpolated EW using the lowest BIC interpolator as compared to the (non-
interpolated) EW directly from MULTI2.3, categorized as a function of stellar
spectral types (x-axis) and metalicities (different panels). We observe that
there exist no clear dependencies between differences and spectral types and
metalicities. The average of differences is within 0.01 for all stellar
spectral types and metalicities. We pre-define the default interpolated EW
uncertainty (also a threshold for the lowest acceptable BIC) in LOTUS as 6
m$\AA$ for each line. However, we also design the code to allow users to input
their acceptable uncertainty limits, in which case LOTUS will drop a given Fe
i or Fe ii from the linelist if the computed BIC is larger than this
uncertainty, and will subsequently be excluded from the lines used to derive
the stellar parameters in the optimization module.

Figure 3: Differences (in mÅ) between the interpolated EWs (using
interpolators chosen at the lowest BIC values) and the EWs from NLTE
theoretical calculations computed directly using MULTI2.3. Each violin plot
shows the distribution of the means of such differences for a random 4000
nodes within the spectral type interval of the pre-computed EW library. Red
lines are marked as the means of the distributions while purple lines are for
the medians. The differences are shown for different metallicity ranges as
indicated in each panel.

####  2.3.2 EP Cut-off

The NLTE abundances derived from low excitation potential Fe i can yield
larger abundances as compared with those derived from high-excitation Fe i and
Fe ii lines, especially using 1D atmospheric models (Amarsi et al., 2016).
Such differences can reach up to 0.45 dex for some Fe i lines, and can affect
our derived stellar parameters as documented in several studies including
Bergemann et al. (2012); Lind et al. (2012) as well as others. We thus follow
previous literature studies by introducing low-excitation potential cut-offs
for Fe i lines with EP(Fe i) $<$ 2.7ev/2.5ev/2.0 eV for stars with
[Fe/H]$<-0.5$, depending on the number of Fe i and Fe ii lines measured in the
stars and the optimization convergence criteria (see Section 2.4); We conduct
no cut-offs for stars with [Fe/H]$>-0.5$.

###  2.4 Optimization Module

Once reliable linelist and interpolators per spectral types of input target
stars have been chosen, as explained in Section 2.3 above, the derived iron
abundances from Fe i and Fe ii lines are fed into the optimization module with
an initial guess of the general type of the target star. We note that users
don’t need to specify an initial guess of each stellar parameter, as it
suffices to only chose an initial guess of the spectral type as an input to
LOTUS, which is then assigned the corresponding interpolation parameters
interval as indicated in Table 1.

####  2.4.1 Optimization Conditions

The general principle of optimization is to adjust stellar parameters
iteratively to derive optimal combinations of stellar parameters that can
satisfy the following three conditions: (i) excitation equilibrium, or
minimizing the trend (i.e., slope) of the Fe i abundances as a function of
excitation potential EP, (ii) ensuring ionization equilibrium or minimizing
the differences between the abundances derived from the Fe i and Fe ii lines,
and (iii) minimizing the trend (i.e., slope) between the abundances derived
from the Fe i lines versus the reduced equivalent widths, REW =
$\log(\mathrm{EW}/\lambda)$.

Therefore, we derive $T_{\rm eff}$ by ensuring excitation equilibrium, $\log
g$ by ensuring ionization equilibrium, and $v_{\mathrm{mic}}$ by minimizing
the trend between Fe i abundances versus line strength (REW). [Fe/H] was then
determined by averaging the abundances derived from the Fe i and Fe ii
abundances.

Figure 4: Iron abundances determined from Fe i (black circles) and Fe ii (red
circles) line versus reduced equivalent widths (upper panel) and excitation
potential energies $\chi$ (lower panel) for selected lines in the metal-poor
benchmark star HD122563. The parameters indicated on the top are the optimal
values derived using the global minimization (differential evolution)
algorithm in LOTUS. Dotted lines are the best linear fits to the Fe i lines in
each panel. The labels at the upper left corner of each panel are the slopes
of the fits and their corresponding standard deviations.

####  2.4.2 Targeted Optimized Object Function

In order to find the best combination of stellar parameters that satisfy the
optimization conditions defined in Section 2.4.1 within our parameter grid, we
first combine these conditions into an object function $\mathcal{F}$, such as:

$\mathcal{F}=\left(\frac{s_{\chi,1}}{\sigma_{\chi,1}}\right)^{2}+\left(\frac{s_{REW,1}}{\sigma_{REW,1}}\right)^{2}+\left(\frac{\bar{A_{1}}-\bar{A_{2}}}{\sigma_{1-2}}\right)^{2}$
(3)

where the subscripts ”1” and ”2” correspond to Fe i and Fe ii, respectively.
$s_{\chi,1}$ is the slope between Fe i abundances and EP, and
$\sigma_{\chi,1}$ is its uncertainty, $s_{REW,1}$ is the slope between the Fe
i abundances and REW, and $\sigma_{REW,1}$ is its uncertainty. $\bar{A_{1}}$
and $\bar{A_{2}}$ are the mean abundances for Fe i and Fe ii, respectively,
while $\sigma_{1-2}$ is the standard deviation of the differences between
$\bar{A_{1}}$ and $\bar{A_{2}}$. A converged solution is obtained at the
combination of $T_{\rm eff}$, $\log g$, [Fe/H] and $v_{\mathrm{mic}}$, which
minimizes $\mathcal{F}$ globally.

####  2.4.3 Global minimization

To find the global minimization fit parameters within our grid, we adopt a
differential evolution algorithm implementing a global minimization search.
The goal is to minimize $\mathcal{F}$ by starting with an initial population
of candidate solutions, which are iteratively improved by retaining the
fittest solutions that yield a lower $\mathcal{F}$ values, until convergence
for the best-fit parameters is met (Storn & Price, 1996). The advantage of a
differential evolution algorithm is that it has the benefit of handling
nonlinear and non-differentiable multi-dimensional objective functions while
requiring few control parameters to steer the minimization. For our code, we
select 100 initial populations (sets of solutions) with a combined rate of
0.3, which is a crossover probability that depends on how fast the algorithm
moves to the next generation of populations. We try different weights between
0.8 and 1.2, to maintain a proper searching radius, at the same time making
sure it does not slow down the convergence speed. We adopt $\mathcal{F}\sim
10^{-5}$ as the absolute tolerance for each iteration. After each iteration,
we perform a 3$\sigma$-clipping on the abundances determined from the Fe i and
Fe ii lines to remove outliers. We adopt 3 iterations of outlier removing in
total as a default, however, this number can be defined by the users depending
on the quality of their EW measurements. An example of HD122563 with derived
abundances of Fe i and Fe ii versus REW and EP at optimal atmospheric
parameters is shown in Figure 4.

###  2.5 Uncertainty Estimation Module

Figure 5: Marginalized posterior distributions of the stellar parameters of
HD122563 based on the log-likelihood function in Equation 6. 1$\sigma$,
2$\sigma$ and 3$\sigma$ uncertainty region are denoted as solid contours in
the two dimensional plot. The histograms show the marginalized posterior
distributions for each parameter, respectively. Blue intersecting lines show
the values obtained from our global optimization module.

Since $\mathcal{F}$ is a function of the stellar parameters, it can be
described as
$\mathcal{F}(\theta)=\mathcal{F}(T_{\mathrm{eff}},log\mathrm{g},$$v_{\mathrm{mic}}$$)$.
We can keep track of how $\mathcal{F}$ changes along the perturbations around
the optimal solution $\theta^{*}$=($T_{\mathrm{eff}}^{*}$,
log$\textit{g}^{*}$, $v_{\mathrm{mic}}$∗), $T_{\mathrm{eff}}^{*}$,
log$\textit{g}^{*}$ and $v_{\mathrm{mic}}$∗ are the parameters at the optimal
solution. Indeed, $\mathcal{F}$ resembles a likelihood function, which can be
used to estimate the uncertainties on each of our derived stellar parameters
from the Hessian Matrix such as:

$SE(\theta^{*})=diag(\sqrt{\mathcal{H}^{-1}(\theta^{*})})$ (4)

where the Hessian Matrix for our objective function can be written as:

$\mathcal{H}(\theta)=\frac{\partial}{\partial\theta_{i}\partial\theta_{j}}\mathcal{F}(\theta),1\leq
i,j\leq 3$ (5)

For [Fe/H], we adopt the standard deviation of the Fe i lines as the
uncertainty.

However, in the above uncertainty framework, one strong assumption is that the
standard errors obtained are symmetric around the mean values. This is only
true if the probability distribution function of the derived parameters is a
normal distribution. Normally, this is not the case. We, therefore, use a
Bayesian framework to robustly determine the uncertainties on our derived
stellar parameters. First, we construct a log-likelihood function using the
same terms as in Equation 3 such as:

$log(\mathcal{L})=-\frac{1}{2}\sum_{i\leq
3}\left[\left(\frac{s_{i}}{n_{i}}\right)^{2}+\log(2\pi n_{i})\right]$ (6)

where $n_{i}$ can be written as:

$n_{i}=\sigma_{i}^{2}+f^{2}s_{i}^{2}$ (7)

where $s_{i}$ represent the slopes $s_{\chi,1}$, $s_{REW,1}$ and
$\bar{A_{1}}-\bar{A_{2}}$ individually, while $\sigma_{i}$ are their
corresponding standard deviations. Introducing $f$ will compensate the
underestimation of the variance of each parameter assuming such an additional
term is proportional to the model itself.

We then perform the Slice Sampling algorithm (Neal, 2003), which is a type of
Markov Chain Monte Carlo (MCMC) implemented in PyMC3, to complete the
estimation of the posterior probability of each parameter. This method adjusts
the step size automatically on every proposed candidate to match the profile
of the posterior distribution without the need to choose a transition
function. Such a framework ensures higher efficiency as compared to classical
MCMC algorithms, such as Metropolis and Gibbs (Metropolis & Ulam, 1949; Geman
& Geman, 1984). For all stellar parameters, we derive a normal distribution
around the mean optimized value obtained from the global minimization module
described in Section 2.4.3, and a standard deviation determined from the
standard errors of the Hessian Matrix.

We use the logarithmic of $f$ as an input variable to the MCMC sampler with a
uniform distribution ranging from $-$10 to 1. In the sampling process, we
consider 4 running chains with each containing 1000 draw steps and 200 tunes
steps. Figure 5 shows the output from our posterior distribution of the
stellar parameters and their uncertainty regions for a benchmark metal-poor
star, HD122563. On the same plot, we also show the optimized parameters
derived using our global optimization module (blue lines intersection), which
agree very well.

##  3 Testing LOTUS

We test LOTUS by deriving the atmospheric stellar parameters of benchmark
stars with well constrained non-spectroscopic and fundamental stellar
parameters, to quantify the precision of our derived parameters and their
uncertainties. Below we present the results of these tests. We list the
derived stellar parameters ($T_{\rm eff}$, $\log g$, [Fe/H] and
$v_{\mathrm{mic}}$) using LOTUS in LTE and NLTE of all the stars considered
from Section 3.1 to 3.4 below, the sources of the EW, the number of Fe i and
Fe ii lines, and the excitation potential cut-offs for each star in Table 3.

Figure 6: Comparison of our derived stellar parameters, $T_{\rm eff}$, $\log
g$ and [Fe/H] using LOTUS to reference literature values derived non-
spectroscopically (for $T_{\rm eff}$ and $\log g$) for HD122564, HD140283 and
Arcturus. The mean NLTE values (red dashed lines) with their 1$\sigma$
confidence intervals (red shadow areas) and our mean LTE values (blue dashed
lines) with their 1$\sigma$ confidence intervals (blue shadow areas), compared
to to reference stellar parameters (black dots with error bars) for references
on the x-axis. References are as follows: Q1996…Quirrenbach et al. (1996);
G1999…Griffin & Lynas-Gray (1999); L2008…Lacour et al. (2008);R2011…Ramírez &
Allende Prieto (2011);C2012…Creevey et al. (2012);F2013…Frebel et al.
(2013);H2015…Heiter et al. (2015);C2015…Creevey et al. (2015);A2016…Amarsi et
al. (2016);K2018…Karovicova et al. (2018);C2019…Creevey et al.
(2019);K2020…Karovicova et al. (2020).

Figure 7: Differences in $\log g$ and $T_{\rm eff}$ between values derived
using LOTUS versus reference values from Hawkins et al. (2016) for five GES
metal-poor stars in their sample. Blue circles are LTE differences, while red
squares are NLTE. Dashed lines in both panels are the zero baselines. Average
systematic offsets are included in the text of each panel.

.

###  3.1 HD122563, HD140283, and Arcturus

The two metal-poor standard stars HD122563, HD140283 and the benchmark giant
Arcturus have been widely analyzed independently in the literature. Their
stellar parameters have therefore been derived spectroscopically (using 1D,
3D, LTE and NLTE assumptions, or a combination of each), as well as using non-
spectroscopic methods and fundamental equations (e.g., using photometric
calibrations, asteroseismology, or interferometric angular diameters). All
three stars are dubbed benchmark stars which have been selected as comparison
standards for the largest stellar surveys, especially in the $Gaia$-ESO
spectroscopic survey (Jofré et al., 2014; Heiter et al., 2015). We adopt EW
measurements of each benchmark star from literature publications as follows:
HD122563 (Frebel et al., 2013), HD140283 (Frebel et al., 2013), Arcturus
(Jofré et al., 2014). Frebel et al. (2013) measured their EW from high-
resolution spectroscopic observations ($R\sim$35,000 in the blue and
$\sim$28,000 in the red) of HD122563 and HD140283, obtained with the MIKE
spectrograph (Bernstein et al., 2003) on the Magellan-Clay telescope at Las
Campanas. A $R\geq$70,000 spectrum was used to derive EW for Arcturus from the
VLT spectrum (Jofré et al., 2014). We derive the stellar parameters of each
star and their uncertainties using LOTUS. We then compare our NLTE and LTE
parameters with several independent determinations from the literature, as
shown in Figure 6.

##### HD122563

We derive $T_{\rm eff}$ = 4620$\pm$59 K, $\log g$ = 1.21$\pm$0.19,
$v_{\mathrm{mic}}$ = 1.89$\pm 0.06$ km s-1 and [Fe/H] = $-$2.76$\pm$0.05 in
NLTE, and $T_{\rm eff}$ = 4528$\pm$42 K , $\log g$ = 0.66$\pm$0.12,
$v_{\mathrm{mic}}$ = 1.84$\pm 0.03$ km s-1 and [Fe/H] = $-$2.98$\pm$0.03.
Creevey et al. (2012) derived $T_{\rm eff}$ = 4598$\pm$41 K using an angular
diameter observed with CHARA interferometry and Palomar interferometeric
observations. Heiter et al. (2015) derived $T_{\rm eff}$ = 4587$\pm$60 K based
on the angular diameters and bolometric fluxe calibrations, and $\log g$ =
1.44$\pm$0.24 from fitting evolutionary tracks. Karovicova et al. (2018)
updated CHARA interferometry with more data and derived an effective
temperature of $T_{\rm eff}$ = 4636$\pm$37 K. Later in Karovicova et al.
(2020), they updated their data reduction pipeline and derived a new $T_{\rm
eff}$ = 4635$\pm$34 K. Our NLTE $T_{\rm eff}$ derived for HD122563 agrees very
well with $T_{\rm eff}$ determined in these studies using interferometric
angular diameters, within $\sim$30 K, while the LTE $T_{\rm eff}$ deviated by
$\sim 100$ K from the reference values.

And for $\log g$ results from the recent updated asteroseismic analysis are in
agreement with the NLTE values in our work, which is close to the upper limit
of 1$\sigma$ confidence interval.

For $\log g$, Creevey et al. (2012) used evolutionary track models to derive
$\log g$ = 1.60$\pm$0.04 for HD122563, while Creevey et al. (2019) utilized
the Hertzsprung telescope (SONG network node) to accurately measure the
surface gravity of HD122563 using asteroseismology for the first time, and
derived $\log g$ = 1.39$\pm$0.01. In their paper they also compare to $Gaia$
DR2 parallax-based $\log g$ = 1.43$\pm$0.03, which shows high consistency
between these methods. Karovicova et al. (2020) also used evolutionary track
models to derive $\log g$ = 1.404$\pm$0.03 for the same star. Our LOTUS $\log
g$ = 1.22 in NLTE matches within $\sim 0.1$ dex the asteroseismic and parallax
$\log g$ in Creevey et al. (2019), whereas the LTE value is 0.6 dex lower.
This gives us strong confidence in LOTUS’ ability to derive NLTE surface
gravities from spectroscopic observations.

We then compare our NLTE and LTE [Fe/H] with those derived by Frebel et al.
(2013) in 1D, LTE and Amarsi et al. (2016) in 3D,NLTE. Our NLTE [Fe/H] agrees
with that determined in both studies within error bars, although Amarsi et al.
(2016) derived a higher [Fe/H] = $-2.5$, which is likely due to considering 3D
effects in their study.

##### HD140283

We derive $T_{\rm eff}$ = 5681$\pm$67 K , $\log g$ = 3.58$\pm$0.16,
$v_{\mathrm{mic}}$ = 2.17$\pm$0.16 km s-1 and [Fe/H] = $-2.64\pm$0.05 in NLTE,
and $T_{\rm eff}$ = 5689$\pm$59 K , $\log g$ = 3.29$\pm$0.17,
$v_{\mathrm{mic}}$ = 2.09$\pm$0.14 km s-1 and [Fe/H] = $-2.72\pm$0.04 in LTE.
Heiter et al. (2015) derived a mean $T_{\rm eff}$ = 5774$\pm$77 K for the sub-
giant in their $Gaia$-ESO benchmark sample from photometric calibrations.
Additionally, Creevey et al. (2015) used the VEGA interferometer on CHARA to
determine $T_{\rm eff}$ = 5534$\pm$103 K (using $A_{V}$ = 0.0 mag) and $T_{\rm
eff}$ =5 647$\pm$105 K (using $A_{V}$ = 0.1 mag). Karovicova et al. (2018)
similarly derived an updated $T_{\rm eff}$ = 5787$\pm$48 K from additional
interferometric data points, and afterwards updating their values to
5792$\pm$55 K in Karovicova et al. (2020). Our LTE and NLTE $T_{\rm eff}$ for
HD140283 agree with the interferometric values derived in Creevey et al.
(2015) within 120 K and Karovicova et al. (2018, 2020) within 80 K.

Heiter et al. (2015) derived $\log g$ = 3.58$\pm$0.11 using fundamental
relations and adopting independently derived parallax for the star. Creevey et
al. (2015) also derived a mean $\log g$ = 3.69$\pm$0.03, similarly from a
combination of parallax and evolutionary track models. Both $\log g$
determined by parallax methods in Heiter et al. (2015) and Creevey et al.
(2015) agree well with our NLTE value to within 0.05 dex. Karovicova et al.
(2020) derived $\log g$ = 3.65$\pm$0.0 from evolutionary models. Our LTE
values is, unexpectedly, 0.3 dex lower.

Similar to HD122563, we compare our [Fe/H] with 1D,LTE and 3D,NLTE abundances
in Frebel et al. (2013) and Amarsi et al. (2016), respectively. Given that
both studies derived their abundances by fixing $T_{\rm eff}$ and $\log g$,
while ours were derived simultaneously using the global optimization method
adopted in LOTUS, we warrant serious direct comparison with their values.
Nevertheless, our NLTE values agree very well with that derived in Frebel et
al. (2013) within 1$\sigma$, whereas is 0.3 dex lower as compared to Amarsi et
al. (2016).

##### Arcturus

We derive $T_{\rm eff}$ = 4306$\pm$41 K, $\log g$ = 1.61$\pm$0.15,
$v_{\mathrm{mic}}$ = 1.79$\pm$0.02 km s-1 and [Fe/H] = $-0.63\pm$0.04 in NLTE,
and $T_{\rm eff}$ = 4364$\pm$47 K , $\log g$ = 1.68$\pm$0.17 ,
$v_{\mathrm{mic}}$ = 1.76$\pm$0.02 km s-1 and [Fe/H] = $-0.64\pm$0.05 in LTE.
For $T_{\rm eff}$ Quirrenbach et al. (1996) used the MkIII Optical
Interferometer on Mt. Wilson to determine Arcturus’ angular diameter and
derived $T_{\rm eff}$ = 4303$\pm$47 K. Griffin & Lynas-Gray (1999) collected
all literature results of interferometry observation up to their study and
derived $T_{\rm eff}$ = 4290$\pm$30 K. Lacour et al. (2008) used the IOTA 3
telescope interferometer in the H band to derive $T_{\rm eff}$ = 4295$\pm$26
K. Additionally, Ramírez & Allende Prieto (2011) fit theoretical spectral
energy distributions (SED) from visible blue bands to mid-infrared to derive
$T_{\rm eff}$ = 4286$\pm$30 K. Finally, Heiter et al. (2015) derived a mean of
4274$\pm$83 K from different interferometric measurements, even though they
warranted against using Arcturus as a benchmark given the large dispersion
they obtained. All interferometric $T_{\rm eff}$ agree very well with our NLTE
$T_{\rm eff}$ to within $\sim 20$ K. Our LTE value is, however, $\sim 80$ K
higher.

Ramírez & Allende Prieto (2011) derived $\log g$ = 1.66$\pm$0.05 from
HIPPARCOS parallax and isocrhone fitting, while Heiter et al. (2015) derived a
fundamental $\log g$ = 1.64$\pm$0.09 based on seismic mass and $\log g$ =
1.82$\pm$0.15 from a compilation of parallax-based measurements. Our NLTE
$\log g$ agrees very well with both results, whereas our LTE values is $0.1$
dex higher.

Griffin & Lynas-Gray (1999) derived [Fe/H] = $-0.68\pm$0.02 by comparing
theoretical 1D, LTE SEDs with observed flux. Ramírez & Allende Prieto (2011)
used a differential abundance analysis relative to the solar spectrum to
derive [Fe/H] = $-0.52\pm$0.04. Our NLTE and LTE [Fe/H] are within 0.05 dex
from each other, and agree well with the values derived in Griffin & Lynas-
Gray (1999) while being $\sim 0.1$ dex as compared to differential abundance
analysis in Ramírez & Allende Prieto (2011).

Figure 8: Same as in Figure 7 for the GES-K2 sample stars from Worley et al.
(2020).  Figure 9: Same as in Figure 7 for the CHARA sample stars from
Karovicova et al. (2020, 2021a, 2021b).

###  3.2 GES Metal-Poor Stars

We also test LOTUS on five metal-poor benchmark stars proposed by Hawkins et
al. (2016) from the $Gaia$-ESO survey (GES). They determined $T_{\rm eff}$ via
the Infrared Flux Method (IRFM) (Casagrande et al., 2011) using multi-band
photometry and $\log g$ by fitting to evolutionary stellar models. The Fe i
and Fe ii EWs for the sample stars were adopted from Hawkins et al. (2016),
who used different EW measurements from different pipelines from the GES
survey to derive their parameters. We use their EPINARBO (EPI) EWs derived
with the FAMA pipeline following Magrini et al. (2013), as those were derived
consistently. We compare our derived $T_{\rm eff}$ and $\log g$ using LOTUS to
those in Hawkins et al. (2016) using the same Fe i and Fe ii lines. We find
that our NLTE parameters are on average within $5\pm 29$ K from their $T_{\rm
eff}$ and $0.11\pm 0.06$ for $\log g$ on average, whereas our LTE parameters
are within $18\pm 22$ K and $0.22\pm 0.08$ dex for $T_{\rm eff}$ and $\log g$
respectively. Star by star comparisons are shown in Figure 7. Our NLTE
parameters agree better with the non-spectroscopic parameters from Hawkins et
al. (2016), as compared to LTE.

A larger $\log g$ dispersion is obtained for HD106038 though with
[Fe/H]=$-1.25$ of $-0.25$ and $-0.45$, for both our NLTE and LTE results,
respectively. With a 3D, Non-LTE analysis, and $Gaia$ EDR3 parallax, Giribaldi
et al. (2021) derived $\log g$=4.29$\pm 0.04$, which is in excellent with our
NLTE $\log g$=4.29$\pm$0.08. Additionally, only 35 Fe i lines used by Hawkins
et al. (2016) were used to derive the stellar parameters in LOTUS which
decreases the accuracy of optimal values (see Section 5 for more details).

###  3.3 GES-K2 Stars

We also test LOTUS by deriving atmospheric stellar parameters of a sample of
Kepler-2 (K2) star sample, which was also observed using a high-resolution
UVES spectrograph on the VLT as part of the GES survey. Worley et al. (2020)
combined the high-resolution spectroscopic observations from UVES, photometry,
and precise asteroseismic data from K2 to derive self-consistent stellar
parameters for these stars, which represent a good non-spectroscopic sample to
compare our stellar parameters derived with LOTUS to.

We adopt the EW measurements from Worley et al. (2020) derived from high-
resolution UVES spectroscopic observations. We chose a total of 52 stars from
their sample. The majority of the stars in the sample are metal-rich with
[Fe/H]$>-0.5$. Only six stars have [Fe/H]$<-0.5$. Worley et al. (2020) used
the IRFM to determine photometrically calibrated $T_{\rm eff}$ for all their
stars following Casagrande et al. (2010, 2011).

The average uncertainties reported in Worley et al. (2020) for $T_{\rm eff}$
and $\log g$ of the GES-K2 stars are $\pm 65$ K and $\pm 0.02$, respectively.
We note that these values are close to our parameter grid resolution. We
derive the stellar parameters for the 52 GES-K2 stars using LOTUS. Our results
for $\log g$ and $T_{\rm eff}$ as compared to Worley et al. (2020) are shown
in Figure 8 as a function of [Fe/H]. We find that the average differences
between the LOTUS parameters are $\bar{\Delta}$$T_{\rm eff}$ = 74$\pm$6 K and
$\bar{\Delta}$$\log g$ = 0.14$\pm$0.01 in LTE, and $\bar{\Delta}$$T_{\rm eff}$
= 16$\pm$6 K, $\bar{\Delta}$$\log g$ = 0.10$\pm$0.01 in NLTE. Both LTE and
NLTE parameters agree well with the photometric and asteroseismic parameters
from Worley et al. (2020) within their error bars, however our NLTE parameter
derivations agree better for both $T_{\rm eff}$ and, particularly for $\log
g$.

###  3.4 CHARA Interferometry Stars

Finally, we apply and test LOTUS on a sample of stars with effective
temperatures derived homogeneously from interferometric angular diameters
observed by CHARA from Karovicova et al. (2020, 2021a, 2021b). Karovicova et
al. (2020) presented a study of interferometric observations of ten late-type
metal-poor dwarfs and giants, whereas Karovicova et al. (2021a, b) showed a
similar analysis for several metal-rich stars. For three of their stars
(namely, HD122563, HD140283, and HD175305), we have already presented their
analysis in Section 3.1 and 3.2. We, therefore, do not include the analysis of
these stars again in this section. EW measurements of the total 12 stars were
adopted from different literature sources including Takeda et al. (2005);
Morel et al. (2014); Heiter et al. (2015); Takeda & Tajitsu (2015); Liu et al.
(2020). The average uncertainties of the interferometric $T_{\rm eff}$
estimated by Karovicova et al. (2020, 2021a, 2021b) are within 1$\%$. The
authors derived their $\log g$ values by fitting Dartmouth isochrones (Dotter
et al., 2008) to their interferometric $T_{\rm eff}$. They thus derive median
uncertainties for $\log g$ of 0.09 for their metal-poor star sample, 0.05 for
their dwarf sample, and 0.07 for the giants/subgiants sample.

We find that on average the differences in $T_{\rm eff}$ and $\log g$ between
the reference values (Karovicova et al., 2020, 2021a, 2021b) and those derived
with LOTUS are within 26 K and 0.01 in NLTE, respectively. The NLTE parameters
derived for all the stars agree within 1$\sigma$ as compared to the reference
values, except for the $\log g$ value of HD121370 with [Fe/H]=0.29, which
deviated by 0.12 for LTE and 0.18 for NLTE. Heiter et al. (2015), however,
reported a seismic $\log g$ for this star of 3.83$\pm$0.02 dex, which agrees
very with our NLTE result of 3.91$\pm$0.06 within 1$\sigma$.

Figure 10: NLTE corrections $\Delta$[Fe/H] versus [Fe/H]LTE determined for
this work’s star sample using LOTUS. Different markers indicate stars from
different studies as indicated. The Yellow dashed line is a linear fit from
Ezzeddine et al. (2017) for stars with [Fe/H]$<$-4.0. The Blue dot-dash line
is our fit to the stars for [Fe/H]$<-0.5$, and the black dotted line is our
fit to the stars with [Fe/H]$<-2.0$.

##  4 NLTE corrections

The stars presented in Section 3 for testing LOTUS on benchmark stars with
$T_{\rm eff}$ and $\log g$ derived using non-spectroscopic methods cover a
limited range of metallicities (mostly with [Fe/H]$>-1.0$), as well as mainly
dwarfs and sub-giant stars. However, NLTE stellar parameter “corrections”
(also known as NLTE effects, defined as $\Delta$ NLTE = parameter(NLTE) -
parameter(LTE)) have been shown in the literature to be more significant and
important for evolved (giants and supergiant) metal-poor stars Lind et al.
(2012); Ezzeddine et al. (2017). Thus, to be able to test our derived NLTE
“corrections” on a larger, more metal-poor sample of giant stars, we derive
LTE and NLTE stellar parameters for the $R$-process Alliance giant metal-poor
star sample from Hansen et al. (2018), who derived the stellar parameters of
107 metal-poor stars ([Fe/H]$<-1.0$) selected based on their $r$-process
enhancement from several surveys. The EW measurements for Fe i and Fe ii lines
were adopted from Hansen et al. (2018), measured from their du Pont
spectroscopic observations. We thus add the RPA sample stars to our test
sample stars presented in Section 3, resulting in a significant sample
covering a wide representative range of stellar parameters from $T_{\rm
eff}$=4000 to 6500 K, $\log g$=0.0 to 4.5, and [Fe/H]=$-3.0$ to $-0.5$. The
derived stellar parameters for the RPA stars, in LTE and NLTE, are also listed
in Table 3.

We derive the NLTE corrections for [Fe/H] (denoted as $\Delta$[Fe/H]) for the
full sample of stars. We plot the results as a function of [Fe/H]LTE in Figure
10. As expected, $\Delta$[Fe/H] increases toward lower metallicities. Such
effects have been shown in multiple previous studies as well (for e.g.,
Mashonkina et al., 2011; Lind et al., 2012; Bergemann et al., 2012; Amarsi et
al., 2016; Ezzeddine et al., 2017). Ezzeddine et al. (2017) derived a linear
relation between the NLTE correction for [Fe/H], $\Delta$[Fe/H], and
[Fe/H](LTE) from 20 ultra metal-poor stars with [Fe/H]$<-4.0$, such as:

$\Delta\mathrm{[Fe/H]}=-0.14\mathrm{[Fe/H]}_{\mathrm{LTE}}-0.15$ (8)

They found that their relationship can also be extended for metal-poor
benchmark stars at $-4.0<$ [Fe/H] $<-2.0$. It is therefore useful to re-derive
this equation using our full stellar sample analyzed uniformly using LOTUS,
for comparison. Following Ezzeddine et al. (2017), we re-derive the relation
between $\Delta$[Fe/H] and [Fe/H](LTE) using our sample of stars . We re-
derive the relation by (i) choosing only the stars with [Fe/H](LTE)$<-0.5$,
and (ii) using the stars with [Fe/H](LTE)$<-2.0$. We thus derive
$\Delta$[Fe/H]=

$\begin{cases}-0.06(\pm 0.01)\mathrm{[Fe/H]}_{\mathrm{LTE}}-0.06(\pm
0.02),&\\\ \mathrm{for~{}[Fe/H]}_{\mathrm{LTE}}<-0.5\\\ -0.16(\pm
0.02)\mathrm{[Fe/H]}_{\mathrm{LTE}}-0.32(\pm 0.06),&\\\
\mathrm{for~{}[Fe/H]}_{\mathrm{LTE}}<-2.0&\end{cases}$ (9)

The two relations from these equations for $\Delta$[Fe/H], as well as that
derived in Ezzeddine et al. (2017), are shown in Figure 10, fit to our test
sample stars from Section 3 as well as the RPA sample. We find that even
though the three relations agree within uncertainties (colored bands in Figure
10), they can, however, yield slightly different NLTE corrections depending on
the metallicity range for which they were fit. For e.g., our relation derived
using stars with [Fe/H]$<-2.0$ underestimates the NLTE [Fe/H] correction as
compared to Ezzeddine et al. (2017) by $\sim 0.1$ dex at [Fe/H] = $-2.0$,
while using the relation derived with [Fe/H]$<-0.5$ can underestimate the NLTE
correction up to 0.2 dex. This demonstrates that while these relations can
provide useful first-order estimates of the NLTE corrections, a complete NLTE
analysis (e.g., using LOTUS) is needed for precise estimation of the
corrections, as the former can be dependent on the incomplete sample of stars
or metallicity range.

Figure 11: Box plots showing the NLTE corrections of stars considered in this
work for stellar parameter $T_{\rm eff}$, $\log g$, [Fe/H], and
$v_{\mathrm{mic}}$ as derived using LOTUS. Box plots are color-coded for two
ranges of $T_{\rm eff}$for each $\log g$range, indicated at the top of each
column. For intervals with only one star from our sample, boxes are replaced
with dots and their error bars.

Similarly, we derive $\Delta$NLTE corrections for $T_{\rm eff}$, $\log g$, and
$v_{\mathrm{mic}}$ for our sample stars. Again, we define the NLTE correction
for $T_{\rm eff}$ as $\Delta$$T_{\rm eff}$ = $T_{\rm eff}$(NLTE) - $T_{\rm
eff}$(LTE), for $\log g$ as $\Delta$$\log g$ = $\log g$(NLTE) - $\log g$(LTE),
and for $v_{\mathrm{mic}}$ as $\Delta$$v_{\mathrm{mic}}$ =
$v_{\mathrm{mic}}$(NLTE) - $v_{\mathrm{mic}}$(LTE). To best represent these
corrections as a function of the other stellar parameters, we divide our
sample into box plots grouped into different $T_{\rm eff}$ and $\log g$ bins,
as a function of [Fe/H] on the x-axis. The results are shown in Figure 11.

In what follows we discuss the NLTE corrections we obtained for each parameter
as a function of the other parameters, namely $T_{\rm eff}$, $\log g$ and
[Fe/H]. We also compare our result to the theoretical NLTE stellar parameter
corrections derived by Lind et al. (2012). We note, however, that our
comparisons are affected by the fact that our analyzed stars do not cover
exactly the same parameter space as theirs, and that our stellar parameters
have been derived by LOTUS simultaneously, i.e., taking into account their
inter-dependencies, as explained in details in Section 2, whereas Lind et al.
(2012) derived their $\Delta$ NLTE corrections for each parameter
independently, by fixing all the others. As shown in Figure 11, we find that
the $T_{\rm eff}$ derived in NLTE are generally higher than those in LTE for
very metal-poor ([Fe/H]$<-2.5$) super-giants and giant stars ($\log g$$<2.0$),
with NLTE corrections up to 100 K, whereas lower $T_{\rm eff}$ are obtained in
NLTE as compared to LTE as $\log g$ and [Fe/H] increases. Lind et al. (2012),
who derived their $T_{\rm eff}$ using both excitation and ionization
equilibrium by fixing gravity and other stellar parameters in the process.
Similarly, they also restrict their Fe i line transitions to certain cutoffs,
choosing only lines with EP$>3.5$ eV. They found that their ionization
$\Delta$$T_{\rm eff}$ yielded lower LTE $T_{\rm eff}$ as compared to NLTE (see
their Figure 5), whereas their excitation $\Delta$$T_{\rm eff}$ yielded
negligible positive corrections for $T_{\rm eff}$$<4500$. More pronounced
negative corrections were obtained for horizontal branches, supergiants, and
extremely metal-poor stars, which are not covered in our sample stars. As
noted above, our derived $T_{\rm eff}$ using LOTUS implement the contribution
from both excitation and ionization equilibrium, by taking into account their
$T_{\rm eff}$-$\log g$ inter-dependencies. In that context, a thorough
comparison of our $\Delta$$T_{\rm eff}$ results to either excitation or
ionization theoretical corrections derived by Lind et al. (2012) are not very
useful, however, similar to their results we generally find that the NLTE
corrections for the bulk of our stars are affected by less than 50 K (and up
to 100 K) in the considered parameter range, which is within our derived
uncertainties.

We also derive $\Delta$$\log g$ for our sample stars. As expected, the NLTE
corrections for $\log g$ increase towards lower gravities, lower
metallicities, and higher temperatures. On average, our corrections are
$\sim+0.3-0.5$ for [Fe/H]$<-2.0$, $\sim+0.1-0.3$ for $-2.0<$[Fe/H]$<-1.0$, for
giants and supergiant stars with $\log g$$<2.0$, with outliers reaching up to
1.0 dex. For stars with $\log g$$>2.0$, the NLTE corrections can be up to
$\sim$0.3 depending on metallicities. These results broadly agree with the
theoretical corrections derived in Lind et al. (2012). It can thus be
concluded that LTE analyses can strongly underestimate the surface gravities
of stars, particularly for warmer metal-poor giants, and should thus be
reliably derived in NLTE for reliable consequent stellar population analyses.

Finally, the NLTE corrections for $v_{\mathrm{mic}}$ are generally small and
are within $2.0$ km s-1 from those derived in LTE. The corrections are mainly
positive for lower metallicity giants and supergiant stars, as in particular
their Fe i lines are more strongly affected by NLTE, which leads to lower
microturbulent velocities in LTE as compared to NLTE. Our results are
generally consistent with the $\Delta$$v_{\mathrm{mic}}$ derived by Lind et
al. (2012) from their theoretical models.

Figure 12: Derived stellar parameter uncertainties as a functions of the
number of Fe I lines and S/N ratios in our sample of stars from Section 4, in
addition to metal-poor stars with high S/N from Ezzeddine et al. (2020).

##  5 Caveats

We have so far described and demonstrated that LOTUS can be used as a reliable
tool to derive NLTE and LTE atmospheric stellar parameters. There are,
however, some caveats that warrant pointing out which can affect the results,
particularly for stars occupying certain parameter spaces in our grids.

##### EW Interpolation

A key component of LOTUS is its interpolation module that expresses the EW as
a function of stellar parameters, using the generalized curve of growth
(GCOG). As explained in Section 2.3.1, we conduct thorough tests to choose the
best polynomial interpolator for each spectral type. However, we find that
some models are not adequate to reliably fit the GCOG, particularly for
parameter regions where EW variations have smaller dependencies on stellar
parameters. This is demonstrated in Figure 2, where the EW of the Fe i line at
4077 Å varies less strongly with $v_{\mathrm{mic}}$ at higher $T_{\rm eff}$
and lower $\log g$. Thus, the iron abundances derived from these interpolated
models can deviate up to 0.5 dex in abundances from those computed directly
from MULTI2.3 output (i.e, non interpolated EWs). Such large offsets are
likely due to lower than optimal orders of polynomials chosen for some
spectral types in these parameter regions (see Section 2.3.1 for details),
where the EW of those lines not being sensitive to the variation of
atmospheric stellar parameters, or being too small (close to zero) at most
atmospheric stellar parameters. We emphasize though, that the number of such
lines is limited and should not impact the statistical properties of the
interpolation performance for the lines considered in our linelist, as shown
in Figure 3.

##### Number of Fe I lines and S/N ratios

The derived atmospheric stellar parameters could be affected by the number of
Fe i and Fe ii lines utilized in the parameter optimization in LOTUS. We,
therefore, investigate the derived uncertainties of the stellar parameters
using LOTUS as a function of the number of Fe I lines and the S/N ratio as
shown in Figure 12. To demonstrate our results over a representative
statistical sample of stars covering a wide range of S/N ratios, we use the
full star sample from Section 4, supplemented by metal-poor stars from
Ezzeddine et al. (2020) which cover higher S/N values (S/N$>$100) than those
in Hansen et al. (2018). We can see in Figure 12 that the uncertainties
derived for each stellar parameter as a function of the number of Fe i and S/N
ratio decrease as a function of increasing the number of Fe i and increasing
the S/N ratio. For stars with $N_{\mathrm{lines}}>100$ or stars with
$N_{\mathrm{lines}}<100$ and S/N$>$100, the uncertainty are $<50$ K for
$T_{\rm eff}$, $<0.1$ dex for $\log g$, $<0.05$ dex for [Fe/H] and $<0.02$ km
s-1 for $v_{\mathrm{mic}}$. For stars with $N_{\mathrm{lines}}<100$ and
S/N$<$60, however, the uncertainties can reach up to 200 K for $T_{\rm eff}$,
0.5 dex for $\log g$, 0.3 dex for [Fe/H] and 0.2 km s-1 for
$v_{\mathrm{mic}}$. It is notable to mention, though, that higher
uncertainties are more strongly correlated to lower S/N ($<40$). We thus
recommend that users try to utilize ”good-quality” EW measurements for their
Fe i (and Fe ii) lines to obtain reliable results and smaller uncertainty
derivation in LOTUS. This is particularly useful if the number of measured EW
lines for a star is too small ($<100$). Additionally, as the number of Fe ii
lines usually detected in cool FGK stellar spectra can be smaller than the
number of Fe i lines (on the order of 5-25 lines, depending on the [Fe/H] of
the star), we moreover recommend that users try to maximize the number of Fe
ii EW line measurements in the stars, if possible, to increase the precision
of the parameter determination. In future work, we plan to test LOTUS on a
sample of low resolution spectroscopic observations (as compared to high-
resolution data for the same stars) to accurately quantify the effects of the
spectral resolution on the results of the stellar parameters derived by LOTUS.

##### K-type stars

The atmospheric stellar parameters, particularly $\log g$, derived for K-type
stars using LOTUS can have larger uncertainties than those derived for other
spectral types. Tsantaki et al. (2019) noted that $\log g$ determined for
K-type stars using ionization balance between Fe i and Fe ii lines are
underestimated depending on the choice of Fe ii lines used in the
optimization. We investigate this effect on our GES-K2 sample, in which most
of the stars are K-type giants or sub-giants. We find that both our NLTE and
LTE results can indeed overestimate the surface gravities up to 0.1 dex as
compared to asteroseismic values, depending on the selection of Fe ii lines.

##### 3D models

Since our atmospheric stellar models are limited to 1D, our determined iron
abundances might suffer from 3D effects due to atmospheric inhomogeneities,
horizontal radiation transfer, as well as the differences in the mean
temperature stratification Amarsi et al. (2016) between 1D and 3D models. The
latter can lead to underestimated abundances derived from Fe i and Fe ii
lines, on average up to $0.1$ dex in 1D, NLTE as compared with Fe abundances
derived using 3D, NLTE. Such effects are, however, more strongly pronounced
for Fe ii lines than Fe i as explained in Amarsi et al. (2016). We find that
adding a $0.1$ dex correction for our 1D, NLTE [Fe/H] for HD122563 brings it
closer to the 3D, NLTE [Fe/H] derived in (Amarsi et al., 2016).

On the other hand, we find that a difference of $0.2$ dex as compared to
Amarsi et al. (2016) is still present when adding the same [Fe/H] correction
for HD140283. This can be explained by the stellar parameter differences
adopted in both studies, as well as the difference between linelists. However,
as noted in Amarsi et al. (2016) and Amarsi et al. (2022), 3D corrections can
nevertheless be smaller than the NLTE corrections determined for low
metallicity evolved stars. Therefore, including 1D, NLTE corrections in the
determination of Fe i and Fe ii lines can significantly improve the derived
stellar parameters as compared to 1D, LTE.

##  6 Summary & Conclusions

We present the open-source code, LOTUS, developed to automatically derive fast
and precise atmospheric stellar parameters ($T_{\rm eff}$, $\log g$, [Fe/H]
and $v_{\mathrm{mic}}$) of stars in 1D, LTE, and 1D, NLTE using Fe i and Fe ii
equivalent width measurement from stellar spectra.

LOTUS implements a generalized curve of growth (GCOG) interpolation to derive
abundances from a pre-computed grid of theoretical NLTE EW in a high-
resolution and dense spectral parameter space. The GCOG takes into account the
EW dependencies on stellar atmospheric parameters. A global differential
evolution optimization algorithm, tailored to the spectral type of the star,
is then used to derive the fundamental stellar parameters. In addition, LOTUS
can be used to estimate precise uncertainties for each stellar parameter using
a well-tested Markov Chain Monte Carlo (MCMC) algorithm.

We tested our code on several benchmark stars and stellar samples with
reliable non-spectroscopic (from asteroseismic, photometric, and
interferometric observations) measurements for a wide range of parameter space
typical for FGK stars. We find that our NLTE-derived stellar parameters for
$T_{\rm eff}$ and $\log g$ are within 30 K and 0.1 dex for benchmark stars
including the metal-poor standard stars, HD140283 and HD122563, as well as
Arcturus. We also test LOTUS on a large sample of $Gaia$-ESO (GES) dwarf stars
from Hawkins et al. (2016) and GES-K2 with asteroseismic gravities from K2, as
well as stars with CHARA interferometric observations. Similarly, we find that
LOTUS performs very well in reproducing the non-spectroscopic $T_{\rm eff}$
and $\log g$ on average within $<20$ K and $<0.1$ dex in NLTE, as compared to
$\sim 70$ K and $\sim 0.2$ dex in LTE.

Moreover, we apply LOTUS on a large sample of metal-poor stars from the
R-Process Alliance (RPA, Hansen et al. 2018). We use the RPA sample as well as
the test sample stars to derive NLTE stellar parameter corrections for our
stars and review the $\Delta$[Fe/H] versus [Fe/H](LTE) relation derived in
Ezzeddine et al. (2017). We find that our NLTE corrections agree with
theoretical corrections predicted by Lind et al. (2012), where general trends
of corrections were found to increasing toward metal-poor evolved stars, as
expected.

We test LOTUS thoroughly for its performance for different spectral types and
parameter space. We find that despite some caveats discussed in Section 5,
LOTUS can overall be reliably used to provide fast and accurate NLTE
derivation for a wide range of stellar parameters, especially metal-poor
giants which can be strongly affected by deviations from LTE. We thus strongly
recommend that the community use it to apply for the spectroscopic analyses of
stars and stellar populations.

We provide open community access to LOTUS, as well as the pre-computed
interpolated LTE and NLTE EW grids available on Github github, with
documentation and working examples on Readthedocs book.

We thank the anonymous referee for their useful comments that heloped improved
the manuscript. R.E. acknowledges support from JINA-CEE (Joint Institute for
Nuclear Astrophysics - Center for the Evolution of the Elements), funded by
the NSF under Grant No. PHY-1430152. Y.L. and R.E. acknowledge support from
NSF grant AST-2206263. The authors acknowledge the University of Florida
Research Computing for providing computational resources and support that have
contributed to the research results reported in this publication. URL: UFRC.

##  Appendix A Linelist of Fe i and Fe ii in LOTUS

Table 2: Fe i and Fe ii linelist selected for LOTUS (see Section 2.1.4 for
details)

Species |  $\lambda$($\AA$) | Elow(ev) | loggf
---|---|---|---
Fe i | 3440.61 | 0.00 |  $-$0.67
Fe i | 3440.99 | 0.05 |  $-$0.96
Fe i | 3447.28 | 2.20 |  $-$1.02
Fe i | 3450.33 | 2.22 |  $-$0.90
Fe i | 3451.91 | 2.22 |  $-$1.00
Fe i | 3476.70 | 0.12 |  $-$1.51
Fe i | 3490.57 | 0.05 |  $-$1.10
Fe i | 3497.84 | 0.11 |  $-$1.55
Fe i | 3540.12 | 2.87 |  $-$0.71
Fe i | 3565.38 | 0.96 |  $-$0.13
Fe i | 3608.86 | 1.01 |  $-$0.10
Fe i | 3618.77 | 0.99 |  $-$0.00
Fe i | 3647.84 | 0.92 |  $-$0.19
Fe i | 3689.46 | 2.94 |  $-$0.17
Fe i | 3719.93 | 0.00 |  $-$0.43
Fe i | 3727.62 | 0.96 |  $-$0.63
Fe i | 3742.62 | 2.94 |  $-$0.81
Fe i | 3758.23 | 0.96 |  $-$0.03
Fe i | 3763.79 | 0.99 |  $-$0.24
Fe i | 3765.54 | 3.24 | 0.48
Fe i | 3786.68 | 1.01 |  $-$2.22
Fe i | 3787.88 | 1.01 |  $-$0.86
Fe i | 3805.34 | 3.30 | 0.31
Fe i | 3808.73 | 2.56 |  $-$1.17
Fe i | 3815.84 | 1.48 | 0.23
Fe i | 3820.43 | 0.86 | 0.12
Fe i | 3825.88 | 0.91 |  $-$0.04
Fe i | 3827.82 | 1.56 | 0.06
Fe i | 3840.44 | 0.99 |  $-$0.51
Fe i | 3841.05 | 1.61 |  $-$0.04
Fe i | 3849.97 | 1.01 |  $-$0.87
Fe i | 3856.37 | 0.05 |  $-$1.29
Fe i | 3865.52 | 1.01 |  $-$0.98
Fe i | 3878.02 | 0.96 |  $-$0.91
Fe i | 3895.66 | 0.11 |  $-$1.67
Fe i | 3899.71 | 0.09 |  $-$1.53
Fe i | 3902.95 | 1.56 |  $-$0.47
Fe i | 3920.26 | 0.12 |  $-$1.75
Fe i | 3922.91 | 0.05 |  $-$1.65
Fe i | 3949.95 | 2.18 |  $-$1.25
Fe i | 3977.74 | 2.20 |  $-$1.12
Fe i | 4005.24 | 1.56 |  $-$0.61
Fe i | 4045.81 | 1.49 | 0.28
Fe i | 4058.22 | 3.21 |  $-$1.18
Fe i | 4063.59 | 1.56 | 0.06
Fe i | 4067.98 | 3.21 |  $-$0.53
Fe i | 4070.77 | 3.24 |  $-$0.87
Fe i | 4071.74 | 1.61 |  $-$0.02
Fe i | 4114.44 | 2.83 |  $-$1.30
Fe i | 4132.06 | 1.61 |  $-$0.68
Fe i | 4134.68 | 2.83 |  $-$0.65
Fe i | 4143.87 | 1.56 |  $-$0.51
Fe i | 4147.67 | 1.49 |  $-$2.10
Fe i | 4150.25 | 3.43 |  $-$1.19
Fe i | 4154.50 | 2.83 |  $-$0.69
Fe i | 4156.80 | 2.83 |  $-$0.81
Fe i | 4157.78 | 3.42 |  $-$0.40
Fe i | 4158.79 | 3.43 |  $-$0.70
Fe i | 4174.91 | 0.91 |  $-$2.97
Fe i | 4175.64 | 2.85 |  $-$0.83
Fe i | 4181.76 | 2.83 |  $-$0.37
Fe i | 4182.38 | 3.02 |  $-$1.18
Fe i | 4184.89 | 2.83 |  $-$0.87
Fe i | 4187.04 | 2.45 |  $-$0.56
Fe i | 4187.80 | 2.42 |  $-$0.55
Fe i | 4191.43 | 2.47 |  $-$0.67
Fe i | 4195.33 | 3.33 |  $-$0.49
Fe i | 4199.10 | 3.05 | 0.16
Fe i | 4202.03 | 1.49 |  $-$0.71
Fe i | 4216.18 | 0.00 |  $-$3.36
Fe i | 4217.55 | 3.43 |  $-$0.48
Fe i | 4222.21 | 2.45 |  $-$0.97
Fe i | 4227.43 | 3.33 | 0.27
Fe i | 4233.60 | 2.48 |  $-$0.60
Fe i | 4238.81 | 3.40 |  $-$0.23
Fe i | 4250.12 | 2.47 |  $-$0.41
Fe i | 4250.79 | 1.56 |  $-$0.71
Fe i | 4260.47 | 2.40 | 0.08
Fe i | 4271.15 | 2.45 |  $-$0.35
Fe i | 4271.76 | 1.49 |  $-$0.16
Fe i | 4282.40 | 2.18 |  $-$0.78
Fe i | 4325.76 | 1.61 | 0.01
Fe i | 4352.73 | 2.22 |  $-$1.29
Fe i | 4375.93 | 0.00 |  $-$3.03
Fe i | 4388.41 | 3.60 |  $-$0.68
Fe i | 4404.75 | 1.56 |  $-$0.14
Fe i | 4415.12 | 1.61 |  $-$0.62
Fe i | 4427.31 | 0.05 |  $-$3.04
Fe i | 4430.61 | 2.22 |  $-$1.66
Fe i | 4432.57 | 3.57 |  $-$1.58
Fe i | 4442.34 | 2.20 |  $-$1.25
Fe i | 4443.19 | 2.86 |  $-$1.04
Fe i | 4447.72 | 2.22 |  $-$1.36
Fe i | 4461.65 | 0.09 |  $-$3.21
Fe i | 4466.55 | 2.83 |  $-$0.60
Fe i | 4484.22 | 3.60 |  $-$0.64
Fe i | 4489.74 | 0.12 |  $-$3.97
Fe i | 4494.56 | 2.20 |  $-$1.14
Fe i | 4514.18 | 3.05 |  $-$1.96
Fe i | 4531.15 | 1.48 |  $-$2.16
Fe i | 4547.85 | 3.55 |  $-$0.82
Fe i | 4574.22 | 3.21 |  $-$2.35
Fe i | 4592.65 | 1.56 |  $-$2.45
Fe i | 4595.36 | 3.30 |  $-$1.76
Fe i | 4602.00 | 1.61 |  $-$3.15
Fe i | 4602.94 | 1.49 |  $-$2.22
Fe i | 4607.65 | 3.27 |  $-$1.33
Fe i | 4619.29 | 3.60 |  $-$1.06
Fe i | 4630.12 | 2.28 |  $-$2.58
Fe i | 4637.50 | 3.28 |  $-$1.29
Fe i | 4643.46 | 3.65 |  $-$1.15
Fe i | 4647.43 | 2.95 |  $-$1.35
Fe i | 4661.97 | 2.99 |  $-$2.50
Fe i | 4668.13 | 3.27 |  $-$1.08
Fe i | 4704.95 | 3.69 |  $-$1.32
Fe i | 4733.59 | 1.49 |  $-$2.99
Fe i | 4736.77 | 3.21 |  $-$0.67
Fe i | 4786.81 | 3.02 |  $-$1.61
Fe i | 4787.83 | 3.00 |  $-$2.62
Fe i | 4788.76 | 3.24 |  $-$1.763
Fe i | 4789.65 | 3.55 |  $-$0.96
Fe i | 4793.96 | 3.05 |  $-$3.43
Fe i | 4794.35 | 2.42 |  $-$3.95
Fe i | 4800.65 | 4.14 |  $-$1.03
Fe i | 4802.88 | 3.64 |  $-$1.51
Fe i | 4807.71 | 3.37 |  $-$2.15
Fe i | 4808.15 | 3.25 |  $-$2.69
Fe i | 4869.46 | 3.55 |  $-$2.42
Fe i | 4871.32 | 2.87 |  $-$0.34
Fe i | 4872.14 | 2.88 |  $-$0.57
Fe i | 4873.75 | 3.30 |  $-$2.96
Fe i | 4875.88 | 3.33 |  $-$1.90
Fe i | 4877.60 | 3.00 |  $-$3.05
Fe i | 4882.14 | 3.42 |  $-$1.48
Fe i | 4885.43 | 3.88 |  $-$0.97
Fe i | 4890.76 | 2.88 |  $-$0.38
Fe i | 4891.49 | 2.85 |  $-$0.11
Fe i | 4896.44 | 3.88 |  $-$1.89
Fe i | 4903.31 | 2.88 |  $-$0.89
Fe i | 4905.13 | 3.93 |  $-$1.73
Fe i | 4907.73 | 3.43 |  $-$1.70
Fe i | 4910.02 | 3.40 |  $-$1.28
Fe i | 4911.78 | 3.93 |  $-$1.75
Fe i | 4918.99 | 2.86 |  $-$0.34
Fe i | 4920.50 | 2.83 | 0.07
Fe i | 4924.77 | 2.28 |  $-$2.11
Fe i | 4938.81 | 2.88 |  $-$1.08
Fe i | 4939.69 | 0.86 |  $-$3.34
Fe i | 4946.39 | 3.37 |  $-$1.11
Fe i | 4950.11 | 3.42 |  $-$1.49
Fe i | 4962.57 | 4.18 |  $-$1.18
Fe i | 4966.09 | 3.33 |  $-$0.79
Fe i | 4969.92 | 4.22 |  $-$0.71
Fe i | 4985.55 | 2.87 |  $-$1.33
Fe i | 4992.79 | 4.26 |  $-$2.35
Fe i | 4994.13 | 0.92 |  $-$3.08
Fe i | 4999.11 | 4.19 |  $-$1.64
Fe i | 5001.86 | 3.88 |  $-$0.01
Fe i | 5002.79 | 3.40 |  $-$1.46
Fe i | 5005.71 | 3.88 |  $-$0.12
Fe i | 5006.12 | 2.83 |  $-$0.61
Fe i | 5012.69 | 4.28 |  $-$1.69
Fe i | 5014.94 | 3.94 |  $-$0.18
Fe i | 5022.24 | 3.98 |  $-$0.33
Fe i | 5023.19 | 4.28 |  $-$1.50
Fe i | 5028.13 | 3.57 |  $-$1.02
Fe i | 5039.25 | 3.37 |  $-$1.52
Fe i | 5044.21 | 2.85 |  $-$2.02
Fe i | 5048.44 | 3.96 |  $-$1.00
Fe i | 5049.82 | 2.28 |  $-$1.35
Fe i | 5051.63 | 0.92 |  $-$2.80
Fe i | 5054.64 | 3.64 |  $-$1.92
Fe i | 5058.50 | 3.64 |  $-$2.83
Fe i | 5060.08 | 0.00 |  $-$5.43
Fe i | 5068.77 | 2.94 |  $-$1.04
Fe i | 5079.22 | 2.20 |  $-$2.07
Fe i | 5079.74 | 0.99 |  $-$3.22
Fe i | 5083.34 | 0.96 |  $-$2.96
Fe i | 5088.15 | 4.15 |  $-$1.68
Fe i | 5107.45 | 0.99 |  $-$3.09
Fe i | 5107.64 | 1.56 |  $-$2.36
Fe i | 5109.65 | 4.30 |  $-$0.98
Fe i | 5115.78 | 3.57 |  $-$2.64
Fe i | 5123.72 | 1.01 |  $-$3.07
Fe i | 5127.36 | 0.92 |  $-$3.31
Fe i | 5131.47 | 2.22 |  $-$2.52
Fe i | 5133.69 | 4.18 | 0.36
Fe i | 5141.74 | 2.42 |  $-$2.24
Fe i | 5150.84 | 0.99 |  $-$3.04
Fe i | 5151.91 | 1.01 |  $-$3.32
Fe i | 5166.28 | 0.00 |  $-$4.20
Fe i | 5171.60 | 1.49 |  $-$1.79
Fe i | 5191.45 | 3.04 |  $-$0.55
Fe i | 5192.34 | 3.00 |  $-$0.42
Fe i | 5194.94 | 1.56 |  $-$2.09
Fe i | 5197.94 | 4.30 |  $-$1.54
Fe i | 5198.71 | 2.22 |  $-$2.13
Fe i | 5202.34 | 2.18 |  $-$1.84
Fe i | 5215.18 | 3.27 |  $-$0.86
Fe i | 5216.27 | 1.61 |  $-$2.15
Fe i | 5217.39 | 3.21 |  $-$1.07
Fe i | 5223.18 | 3.63 |  $-$1.78
Fe i | 5225.53 | 0.11 |  $-$4.79
Fe i | 5228.38 | 4.22 |  $-$1.19
Fe i | 5232.94 | 2.94 |  $-$0.06
Fe i | 5242.49 | 3.63 |  $-$0.97
Fe i | 5243.78 | 4.26 |  $-$1.05
Fe i | 5247.05 | 0.09 |  $-$4.95
Fe i | 5250.21 | 0.12 |  $-$4.93
Fe i | 5250.65 | 2.20 |  $-$2.18
Fe i | 5253.02 | 2.28 |  $-$3.84
Fe i | 5253.46 | 3.28 |  $-$1.58
Fe i | 5262.88 | 3.25 |  $-$2.56
Fe i | 5263.31 | 3.27 |  $-$0.87
Fe i | 5266.56 | 3.00 |  $-$0.39
Fe i | 5281.79 | 3.04 |  $-$0.83
Fe i | 5283.62 | 3.24 |  $-$0.52
Fe i | 5285.13 | 4.43 |  $-$1.66
Fe i | 5288.52 | 3.69 |  $-$1.49
Fe i | 5293.96 | 4.14 |  $-$1.77
Fe i | 5294.55 | 3.64 |  $-$2.76
Fe i | 5295.31 | 4.42 |  $-$1.59
Fe i | 5300.40 | 4.59 |  $-$1.65
Fe i | 5302.30 | 3.28 |  $-$0.74
Fe i | 5307.36 | 1.61 |  $-$2.99
Fe i | 5321.11 | 4.43 |  $-$1.09
Fe i | 5322.04 | 2.28 |  $-$2.80
Fe i | 5324.18 | 3.21 |  $-$0.11
Fe i | 5332.90 | 1.56 |  $-$2.78
Fe i | 5339.93 | 3.27 |  $-$0.63
Fe i | 5341.02 | 1.61 |  $-$1.95
Fe i | 5364.87 | 4.45 | 0.23
Fe i | 5365.40 | 3.57 |  $-$1.02
Fe i | 5367.47 | 4.42 | 0.44
Fe i | 5369.96 | 4.37 | 0.54
Fe i | 5371.49 | 0.96 |  $-$1.64
Fe i | 5373.71 | 4.47 |  $-$0.71
Fe i | 5379.57 | 3.69 |  $-$1.42
Fe i | 5383.37 | 4.31 | 0.65
Fe i | 5386.33 | 4.15 |  $-$1.67
Fe i | 5389.48 | 4.42 |  $-$0.41
Fe i | 5395.22 | 4.45 |  $-$2.07
Fe i | 5397.13 | 0.92 |  $-$1.99
Fe i | 5398.28 | 4.45 |  $-$0.63
Fe i | 5405.77 | 0.99 |  $-$1.85
Fe i | 5410.91 | 4.47 | 0.4
Fe i | 5412.78 | 4.43 |  $-$1.72
Fe i | 5415.20 | 4.39 | 0.64
Fe i | 5417.03 | 4.42 |  $-$1.58
Fe i | 5424.07 | 4.32 | 0.52
Fe i | 5429.70 | 0.96 |  $-$1.88
Fe i | 5434.52 | 1.01 |  $-$2.12
Fe i | 5436.59 | 2.28 |  $-$2.96
Fe i | 5441.34 | 4.31 |  $-$1.63
Fe i | 5445.04 | 4.39 |  $-$0.02
Fe i | 5461.55 | 4.45 |  $-$1.8
Fe i | 5464.28 | 4.14 |  $-$1.40
Fe i | 5466.40 | 4.37 |  $-$0.63
Fe i | 5470.09 | 4.45 |  $-$1.71
Fe i | 5473.90 | 4.15 |  $-$0.72
Fe i | 5483.10 | 4.15 |  $-$1.39
Fe i | 5487.15 | 4.42 |  $-$1.43
Fe i | 5491.83 | 4.19 |  $-$2.19
Fe i | 5493.50 | 4.10 |  $-$1.48
Fe i | 5494.46 | 4.08 |  $-$1.99
Fe i | 5497.52 | 1.01 |  $-$2.85
Fe i | 5501.47 | 0.96 |  $-$3.05
Fe i | 5506.78 | 0.99 |  $-$2.80
Fe i | 5522.45 | 4.21 |  $-$1.45
Fe i | 5525.54 | 4.23 |  $-$1.08
Fe i | 5536.58 | 2.83 |  $-$3.71
Fe i | 5539.28 | 3.64 |  $-$2.56
Fe i | 5543.94 | 4.22 |  $-$1.04
Fe i | 5546.51 | 4.37 |  $-$1.21
Fe i | 5552.69 | 4.95 |  $-$1.89
Fe i | 5554.90 | 4.55 |  $-$0.27
Fe i | 5560.21 | 4.43 |  $-$1.09
Fe i | 5563.60 | 4.19 |  $-$0.75
Fe i | 5569.62 | 3.42 |  $-$0.52
Fe i | 5576.09 | 3.43 |  $-$0.90
Fe i | 5586.76 | 3.37 |  $-$0.11
Fe i | 5587.57 | 4.14 |  $-$1.75
Fe i | 5618.63 | 4.21 |  $-$1.25
Fe i | 5619.60 | 4.39 |  $-$1.60
Fe i | 5624.02 | 4.39 |  $-$1.38
Fe i | 5624.54 | 3.42 |  $-$0.76
Fe i | 5633.95 | 4.99 |  $-$0.23
Fe i | 5635.82 | 4.26 |  $-$1.79
Fe i | 5636.70 | 3.64 |  $-$2.51
Fe i | 5638.26 | 4.22 |  $-$0.72
Fe i | 5641.43 | 4.26 |  $-$1.08
Fe i | 5649.99 | 5.10 |  $-$0.82
Fe i | 5651.47 | 4.47 |  $-$1.90
Fe i | 5652.32 | 4.26 |  $-$1.85
Fe i | 5653.87 | 4.39 |  $-$1.54
Fe i | 5655.18 | 5.06 |  $-$0.60
Fe i | 5661.35 | 4.28 |  $-$1.76
Fe i | 5662.52 | 4.18 |  $-$0.41
Fe i | 5667.52 | 4.18 |  $-$1.58
Fe i | 5679.02 | 4.65 |  $-$0.82
Fe i | 5686.53 | 4.55 |  $-$0.45
Fe i | 5691.50 | 4.30 |  $-$1.45
Fe i | 5696.09 | 4.55 |  $-$1.72
Fe i | 5698.02 | 3.64 |  $-$2.58
Fe i | 5701.54 | 2.56 |  $-$2.22
Fe i | 5705.46 | 4.30 |  $-$1.35
Fe i | 5731.76 | 4.26 |  $-$1.20
Fe i | 5732.30 | 4.99 |  $-$1.46
Fe i | 5741.85 | 4.26 |  $-$1.67
Fe i | 5742.96 | 4.18 |  $-$2.41
Fe i | 5753.12 | 4.26 |  $-$0.62
Fe i | 5760.34 | 3.64 |  $-$2.39
Fe i | 5775.08 | 4.22 |  $-$1.08
Fe i | 5778.45 | 2.59 |  $-$3.43
Fe i | 5784.66 | 3.40 |  $-$2.55
Fe i | 5816.37 | 4.55 |  $-$0.60
Fe i | 5835.10 | 4.26 |  $-$2.27
Fe i | 5837.70 | 4.29 |  $-$2.24
Fe i | 5838.37 | 3.94 |  $-$2.24
Fe i | 5849.68 | 3.69 |  $-$2.89
Fe i | 5853.15 | 1.49 |  $-$5.18
Fe i | 5855.08 | 4.61 |  $-$1.48
Fe i | 5858.78 | 4.22 |  $-$2.16
Fe i | 5883.82 | 3.96 |  $-$1.26
Fe i | 5902.47 | 4.59 |  $-$1.71
Fe i | 5905.67 | 4.65 |  $-$0.69
Fe i | 5916.25 | 2.45 |  $-$2.99
Fe i | 5927.79 | 4.65 |  $-$0.99
Fe i | 5929.68 | 4.55 |  $-$1.31
Fe i | 5930.18 | 4.65 |  $-$0.23
Fe i | 5934.65 | 3.93 |  $-$1.07
Fe i | 5940.99 | 4.18 |  $-$2.05
Fe i | 5956.69 | 0.86 |  $-$4.60
Fe i | 6003.01 | 3.88 |  $-$1.10
Fe i | 6008.56 | 3.88 |  $-$0.98
Fe i | 6012.21 | 2.22 |  $-$4.04
Fe i | 6024.06 | 4.55 |  $-$0.12
Fe i | 6027.05 | 4.08 |  $-$1.09
Fe i | 6056.00 | 4.73 |  $-$0.32
Fe i | 6065.48 | 2.61 |  $-$1.53
Fe i | 6079.01 | 4.65 |  $-$1.02
Fe i | 6082.71 | 2.22 |  $-$3.58
Fe i | 6093.64 | 4.61 |  $-$1.40
Fe i | 6094.37 | 4.65 |  $-$1.84
Fe i | 6096.66 | 3.98 |  $-$1.83
Fe i | 6120.25 | 0.91 |  $-$5.97
Fe i | 6127.91 | 4.14 |  $-$1.40
Fe i | 6136.61 | 2.45 |  $-$1.40
Fe i | 6136.99 | 2.20 |  $-$2.95
Fe i | 6137.69 | 2.59 |  $-$1.40
Fe i | 6151.62 | 2.18 |  $-$3.30
Fe i | 6165.36 | 4.14 |  $-$1.47
Fe i | 6173.33 | 2.22 |  $-$2.88
Fe i | 6187.99 | 3.94 |  $-$1.62
Fe i | 6191.56 | 2.43 |  $-$1.42
Fe i | 6200.31 | 2.61 |  $-$2.43
Fe i | 6213.43 | 2.22 |  $-$2.48
Fe i | 6219.28 | 2.20 |  $-$2.43
Fe i | 6226.73 | 3.88 |  $-$2.12
Fe i | 6229.23 | 2.85 |  $-$2.81
Fe i | 6230.72 | 2.56 |  $-$1.28
Fe i | 6232.64 | 3.65 |  $-$1.24
Fe i | 6240.65 | 2.22 |  $-$3.17
Fe i | 6246.32 | 3.60 |  $-$0.77
Fe i | 6252.56 | 2.40 |  $-$1.69
Fe i | 6265.13 | 2.18 |  $-$2.55
Fe i | 6270.22 | 2.86 |  $-$2.47
Fe i | 6271.28 | 3.33 |  $-$2.70
Fe i | 6297.79 | 2.22 |  $-$2.74
Fe i | 6301.50 | 3.65 |  $-$0.71
Fe i | 6315.81 | 4.08 |  $-$1.63
Fe i | 6322.69 | 2.59 |  $-$2.43
Fe i | 6330.85 | 4.73 |  $-$1.64
Fe i | 6335.33 | 2.20 |  $-$2.18
Fe i | 6336.82 | 3.69 |  $-$0.85
Fe i | 6338.88 | 4.80 |  $-$0.96
Fe i | 6344.15 | 2.43 |  $-$2.92
Fe i | 6355.03 | 2.84 |  $-$2.29
Fe i | 6364.36 | 4.80 |  $-$1.33
Fe i | 6380.74 | 4.19 |  $-$1.38
Fe i | 6393.60 | 2.43 |  $-$1.58
Fe i | 6400.32 | 0.91 |  $-$4.32
Fe i | 6408.02 | 3.69 |  $-$0.99
Fe i | 6411.65 | 3.65 |  $-$0.59
Fe i | 6421.35 | 2.28 |  $-$2.03
Fe i | 6430.85 | 2.18 |  $-$2.01
Fe i | 6475.62 | 2.56 |  $-$2.94
Fe i | 6481.87 | 2.28 |  $-$2.98
Fe i | 6494.98 | 2.40 |  $-$1.27
Fe i | 6496.47 | 4.80 |  $-$0.53
Fe i | 6498.94 | 0.96 |  $-$4.69
Fe i | 6518.37 | 2.83 |  $-$2.44
Fe i | 6533.93 | 4.56 |  $-$1.36
Fe i | 6546.24 | 2.76 |  $-$1.54
Fe i | 6569.21 | 4.73 |  $-$0.38
Fe i | 6574.23 | 0.99 |  $-$5.00
Fe i | 6592.91 | 2.73 |  $-$1.47
Fe i | 6593.87 | 2.43 |  $-$2.42
Fe i | 6597.56 | 4.80 |  $-$0.97
Fe i | 6609.11 | 2.56 |  $-$2.69
Fe i | 6627.54 | 4.55 |  $-$1.59
Fe i | 6648.08 | 1.01 |  $-$5.92
Fe i | 6677.99 | 2.69 |  $-$1.42
Fe i | 6699.14 | 4.59 |  $-$2.10
Fe i | 6703.57 | 2.76 |  $-$3.06
Fe i | 6713.74 | 4.80 |  $-$1.50
Fe i | 6733.15 | 4.64 |  $-$1.15
Fe i | 6739.52 | 1.56 |  $-$4.79
Fe i | 6750.15 | 2.42 |  $-$2.62
Fe i | 6752.71 | 4.64 |  $-$1.20
Fe i | 6786.86 | 4.19 |  $-$1.97
Fe i | 6804.27 | 4.58 |  $-$1.81
Fe i | 6806.84 | 2.73 |  $-$2.13
Fe i | 6810.26 | 4.61 |  $-$0.99
Fe i | 6820.37 | 4.64 |  $-$1.22
Fe i | 6843.66 | 4.55 |  $-$0.73
Fe i | 6855.16 | 4.56 |  $-$0.49
Fe i | 6858.15 | 4.61 |  $-$0.90
Fe i | 6978.85 | 2.48 |  $-$2.50
Fe i | 7495.07 | 4.22 |  $-$0.10
Fe i | 7511.02 | 4.18 | 0.12
Fe i | 7568.90 | 4.28 |  $-$0.88
Fe i | 8220.38 | 4.32 | 0.30
Fe ii | 4173.45 | 2.58 |  $-$2.38
Fe ii | 4178.86 | 2.58 |  $-$2.51
Fe ii | 4233.16 | 2.58 |  $-$2.02
Fe ii | 4303.17 | 2.70 |  $-$2.52
Fe ii | 4385.38 | 2.78 |  $-$2.64
Fe ii | 4416.82 | 2.78 |  $-$2.57
Fe ii | 4491.40 | 2.86 |  $-$2.71
Fe ii | 4508.28 | 2.86 |  $-$2.42
Fe ii | 4515.34 | 2.84 |  $-$2.60
Fe ii | 4522.63 | 2.84 |  $-$2.29
Fe ii | 4549.47 | 2.83 |  $-$1.92
Fe ii | 4555.89 | 2.83 |  $-$2.40
Fe ii | 4576.33 | 2.84 |  $-$2.95
Fe ii | 4583.83 | 2.81 |  $-$1.94
Fe ii | 4620.51 | 2.83 |  $-$3.21
Fe ii | 4923.93 | 2.89 |  $-$1.26
Fe ii | 4993.35 | 2.81 |  $-$3.68
Fe ii | 5197.57 | 3.23 |  $-$2.22
Fe ii | 5234.63 | 3.22 |  $-$2.18
Fe ii | 5256.93 | 2.89 |  $-$4.18
Fe ii | 5264.80 | 3.23 |  $-$3.13
Fe ii | 5276.00 | 3.20 |  $-$2.01
Fe ii | 5316.61 | 3.15 |  $-$1.87
Fe ii | 5316.78 | 3.22 |  $-$2.74
Fe ii | 5325.55 | 3.22 |  $-$3.16
Fe ii | 5414.07 | 3.22 |  $-$3.58
Fe ii | 5425.25 | 3.20 |  $-$3.22
Fe ii | 5534.84 | 3.25 |  $-$2.80
Fe ii | 5991.37 | 3.15 |  $-$3.65
Fe ii | 6084.10 | 3.20 |  $-$3.88
Fe ii | 6113.32 | 3.22 |  $-$4.23
Fe ii | 6149.24 | 3.89 |  $-$2.84
Fe ii | 6247.56 | 3.89 |  $-$2.44
Fe ii | 6369.46 | 2.89 |  $-$4.11
Fe ii | 6432.68 | 2.89 |  $-$3.57
Fe ii | 6456.38 | 3.90 |  $-$2.19

##  Appendix B Derived Stellar Parameters of the Target Stars in This Work

=25mm  LTE NLTE Star Name $T_{\rm eff}$ $\log g$ [Fe/H] $v_{\mathrm{mic}}$
N${}_{\mathrm{Fe_{I}}}$ N${}_{\mathrm{\textup{Fe\,{i}}}}$
$\chi_{\mathrm{Fe_{I}}}$cutoff $T_{\rm eff}$ $\log g$ [Fe/H]
$v_{\mathrm{mic}}$ N${}_{\mathrm{\textup{Fe\,{i}}}}$
N${}_{\mathrm{\textup{Fe\,{ii}}}}$ $\chi_{\mathrm{\textup{Fe\,{i}}}}$cutoff
(K) (cgs) (dex) (km s-1) (ev) (K) (cgs) (dex) (km s-1) (ev) HD122563
4528$\pm$42 0.66$\pm$0.12 $-$2.98$\pm$0.03 1.84$\pm$0.03 72 20 2.7 4620$\pm$59
1.21$\pm$0.19 $-$2.76$\pm$0.05 1.89$\pm$0.06 72 20 2.7 HD140283 5689$\pm$59
3.29$\pm$0.17 $-$2.72$\pm$0.04 2.09$\pm$0.14 96 15 2.0 5681$\pm$67
3.58$\pm$0.16 $-$2.64$\pm$0.05 2.17$\pm$0.16 96 15 2.0 Arcturus 4364$\pm$47
1.68$\pm$0.17 $-$0.64$\pm$0.05 1.76$\pm$0.02 70 8 0.0 4306$\pm$41
1.61$\pm$0.15 $-$0.63$\pm$0.04 1.79$\pm$0.02 70 8 0.0 GES Metal-Poor Stars
(Hawkins et al., 2016) HD102200 6167$\pm$52 3.98$\pm$0.09 $-$1.26$\pm$0.02
0.62$\pm$0.09 33 4 2.5 6057$\pm$75 4.02$\pm$0.09 $-$1.26$\pm$0.04
0.98$\pm$0.28 37 4 2.5 HD106038 6108$\pm$51 4.05$\pm$0.07 $-$1.42$\pm$0.02
0.59$\pm$0.07 35 5 2.5 6124$\pm$60 4.29$\pm$0.08 $-$1.35$\pm$0.03 0.8$\pm$0.18
37 5 2.5 HD175305 5113$\pm$84 2.51$\pm$0.25 $-$1.47$\pm$0.05 1.61$\pm$0.2 45 6
2.5 5059$\pm$70 2.56$\pm$0.2 $-$1.43$\pm$0.04 1.61$\pm$0.17 45 6 2.5 HD201891
6036$\pm$86 4.23$\pm$0.15 $-$1.04$\pm$0.04 0.63$\pm$0.09 44 5 2.5 6047$\pm$81
4.33$\pm$0.14 $-$1.0$\pm$0.04 0.63$\pm$0.09 44 5 2.5 HD298986 6182$\pm$64
3.99$\pm$0.1 $-$1.42$\pm$0.03 0.61$\pm$0.08 37 5 2.5 6182$\pm$137
4.13$\pm$0.19 $-$1.35$\pm$0.07 1.0$\pm$0.33 39 5 2.5 CHARA Interferometry
Stars (Karovicova et al., 2020, 2021a, 2021b) HD131156 5538$\pm$46
4.55$\pm$0.1 $-$0.2$\pm$0.03 0.99$\pm$0.05 90 9 0.0 5501$\pm$47 4.53$\pm$0.1
$-$0.2$\pm$0.03 1.04$\pm$0.05 90 9 0.0 HD146233 5845$\pm$38 4.39$\pm$0.08
0.04$\pm$0.02 0.91$\pm$0.04 68 6 0.0 5788$\pm$39 4.37$\pm$0.08 0.04$\pm$0.03
0.96$\pm$0.04 68 6 0.0 HD186408 5842$\pm$46 4.33$\pm$0.1 0.03$\pm$0.03
1.1$\pm$0.03 96 11 0.0 5783$\pm$49 4.31$\pm$0.09 0.03$\pm$0.03 1.15$\pm$0.04
96 11 0.0 HD186427 5819$\pm$42 4.41$\pm$0.08 0.03$\pm$0.03 0.99$\pm$0.04 97 11
0.0 5771$\pm$45 4.41$\pm$0.09 0.03$\pm$0.03 1.05$\pm$0.04 97 11 0.0 HD190360
5538$\pm$33 4.37$\pm$0.06 0.13$\pm$0.02 0.8$\pm$0.05 49 9 0.0 5485$\pm$40
4.34$\pm$0.08 0.13$\pm$0.03 0.85$\pm$0.05 49 9 0.0 HD161797 5619$\pm$41
4.01$\pm$0.08 0.23$\pm$0.02 1.09$\pm$0.03 88 11 0.0 5536$\pm$30 3.99$\pm$0.06
0.3$\pm$0.02 0.93$\pm$0.03 85 11 0.0 HD207978 6493$\pm$24 3.99$\pm$0.05
$-$0.54$\pm$0.01 1.31$\pm$0.18 63 8 1.2 6407$\pm$41 3.96$\pm$0.14
$-$0.61$\pm$0.03 1.63$\pm$0.16 62 9 1.2 HD121370 6227$\pm$75 3.97$\pm$0.03
0.31$\pm$0.03 1.62$\pm$0.01 $\dagger$ $\dagger$ 0.0 6120$\pm$64 3.91$\pm$0.06
0.3$\pm$0.02 1.62$\pm$0.04 $\dagger$ $\dagger$ 0.0 HD175955 4608$\pm$48
2.69$\pm$0.14 0.07$\pm$0.04 1.03$\pm$0.03 86 14 0.0 4555$\pm$47 2.66$\pm$0.15
0.1$\pm$0.03 1.04$\pm$0.03 86 14 0.0 HD188512 5133$\pm$62 3.52$\pm$0.16
$-$0.22$\pm$0.04 0.83$\pm$0.07 34 7 0.0 5074$\pm$64 3.5$\pm$0.17
$-$0.22$\pm$0.04 0.92$\pm$0.07 34 7 0.0 HD103095 5114$\pm$91 4.37$\pm$0.32
$-$1.39$\pm$0.08 0.66$\pm$0.12 79 9 2.0 5215$\pm$95 4.66$\pm$0.21
$-$1.31$\pm$0.05 0.75$\pm$0.18 82 9 2.0 HD224930 5391$\pm$44 4.14$\pm$0.13
$-$0.9$\pm$0.03 0.79$\pm$0.08 76 11 2.0 5474$\pm$70 4.34$\pm$0.2
$-$0.82$\pm$0.04 0.7$\pm$0.12 81 11 2.0 GES-K2 Stars (Worley et al., 2020)
22074607$-$1055493 4833$\pm$44 2.32$\pm$0.13 $-$1.03$\pm$0.03 1.22$\pm$0.02
138 16 2.7 4778$\pm$42 2.33$\pm$0.13 $-$0.99$\pm$0.03 1.23$\pm$0.02 138 16 2.7
22172723$-$1633039 4597$\pm$28 2.1$\pm$0.1 $-$0.82$\pm$0.02 1.32$\pm$0.01 136
15 2.5 4540$\pm$26 2.08$\pm$0.09 $-$0.81$\pm$0.02 1.36$\pm$0.01 136 15 2.5
22094505$-$1051031 4371$\pm$60 2.04$\pm$0.18 $-$0.5$\pm$0.05 1.57$\pm$0.03 134
13 0.0 4299$\pm$46 1.95$\pm$0.15 $-$0.49$\pm$0.05 1.6$\pm$0.04 133 13 0.0
22075605$-$1535081 4740$\pm$23 3.01$\pm$0.07 $-$0.01$\pm$0.01 1.17$\pm$0.01
151 17 0.0 4696$\pm$21 3.0$\pm$0.06 0.0$\pm$0.01 1.22$\pm$0.02 148 17 0.0
22072959$-$1530438 4957$\pm$19 3.32$\pm$0.05 $-$0.1$\pm$0.01 1.04$\pm$0.02 156
17 0.0 4892$\pm$18 3.27$\pm$0.05 $-$0.1$\pm$0.01 1.09$\pm$0.02 156 17 0.0
22391293$-$1502196 4840$\pm$20 3.08$\pm$0.06 $-$0.07$\pm$0.01 1.21$\pm$0.01
146 16 0.0 4776$\pm$20 3.02$\pm$0.06 $-$0.06$\pm$0.01 1.25$\pm$0.01 146 16 0.0
22390396$-$1500420 4630$\pm$30 2.98$\pm$0.09 $-$0.03$\pm$0.02 1.41$\pm$0.02
123 15 0.0 4586$\pm$28 2.95$\pm$0.09 $-$0.01$\pm$0.02 1.42$\pm$0.02 123 15 0.0
22035226$-$1457037 5015$\pm$15 3.31$\pm$0.04 $-$0.31$\pm$0.01 1.03$\pm$0.01
167 15 0.0 4950$\pm$15 3.26$\pm$0.04 $-$0.31$\pm$0.01 1.07$\pm$0.01 167 15 0.0
22071748$-$1455524 4706$\pm$19 2.71$\pm$0.06 $-$0.3$\pm$0.01 1.22$\pm$0.01 156
17 0.0 4646$\pm$19 2.68$\pm$0.07 $-$0.29$\pm$0.01 1.27$\pm$0.01 151 17 0.0
22033684$-$1449366 4834$\pm$19 2.59$\pm$0.06 $-$0.38$\pm$0.01 1.35$\pm$0.01
154 17 0.0 4742$\pm$17 2.5$\pm$0.06 $-$0.38$\pm$0.01 1.39$\pm$0.01 153 17 0.0
22072768$-$1440392 4601$\pm$25 2.88$\pm$0.08 0.04$\pm$0.02 1.22$\pm$0.02 131
15 0.0 4558$\pm$25 2.86$\pm$0.07 0.06$\pm$0.02 1.21$\pm$0.02 132 15 0.0
22254071$-$1431281 4893$\pm$28 2.6$\pm$0.1 $-$0.34$\pm$0.02 1.56$\pm$0.01 125
11 0.0 4812$\pm$26 2.55$\pm$0.1 $-$0.34$\pm$0.02 1.61$\pm$0.01 125 11 0.0
22243423$-$1430033 4531$\pm$34 2.65$\pm$0.11 0.18$\pm$0.03 1.5$\pm$0.02 94 15
0.0 4497$\pm$33 2.65$\pm$0.11 0.21$\pm$0.03 1.5$\pm$0.02 94 15 0.0
22235672$-$1428420 4755$\pm$17 2.85$\pm$0.06 $-$0.22$\pm$0.01 1.22$\pm$0.01
148 15 0.0 4697$\pm$17 2.82$\pm$0.06 $-$0.21$\pm$0.01 1.26$\pm$0.01 146 15 0.0
22235003$-$1422417 4753$\pm$31 3.35$\pm$0.08 0.3$\pm$0.02 1.23$\pm$0.03 119 14
0.0 4720$\pm$31 3.32$\pm$0.07 0.31$\pm$0.02 1.25$\pm$0.03 119 14 0.0
22175268$-$1344270 4773$\pm$18 2.57$\pm$0.07 $-$0.36$\pm$0.01 1.45$\pm$0.01
153 17 0.0 4702$\pm$17 2.52$\pm$0.07 $-$0.36$\pm$0.01 1.49$\pm$0.01 153 17 0.0
22250508$-$1341415 4741$\pm$20 2.77$\pm$0.07 $-$0.09$\pm$0.01 1.23$\pm$0.01
145 16 0.0 4662$\pm$19 2.69$\pm$0.06 $-$0.08$\pm$0.01 1.25$\pm$0.01 145 16 0.0
22174405$-$1338287 4792$\pm$17 2.81$\pm$0.06 $-$0.34$\pm$0.01 1.21$\pm$0.01
165 13 0.0 4728$\pm$17 2.76$\pm$0.06 $-$0.34$\pm$0.01 1.27$\pm$0.01 158 13 0.0
22185037$-$1257588 4528$\pm$25 2.69$\pm$0.08 $-$0.04$\pm$0.02 1.15$\pm$0.02
137 15 0.0 4491$\pm$25 2.68$\pm$0.08 $-$0.02$\pm$0.02 1.16$\pm$0.02 136 15 0.0
22204635$-$1245072 4804$\pm$23 3.35$\pm$0.06 0.19$\pm$0.01 1.02$\pm$0.02 143
14 0.0 4761$\pm$23 3.32$\pm$0.06 0.2$\pm$0.02 1.04$\pm$0.03 143 14 0.0
22195215$-$1234594 4707$\pm$26 2.72$\pm$0.08 $-$0.08$\pm$0.02 1.3$\pm$0.01 132
14 0.0 4653$\pm$24 2.7$\pm$0.08 $-$0.06$\pm$0.01 1.32$\pm$0.01 132 14 0.0
21563608$-$1202424 4792$\pm$19 3.13$\pm$0.06 $-$0.28$\pm$0.01 1.07$\pm$0.02
161 13 0.0 4738$\pm$19 3.08$\pm$0.06 $-$0.27$\pm$0.01 1.11$\pm$0.02 161 13 0.0
21590887$-$1159078 4678$\pm$26 2.71$\pm$0.08 $-$0.0$\pm$0.02 1.31$\pm$0.01 130
14 0.0 4623$\pm$25 2.68$\pm$0.08 0.02$\pm$0.02 1.32$\pm$0.01 130 14 0.0
22015504$-$1153022 4743$\pm$19 2.82$\pm$0.06 $-$0.25$\pm$0.01 1.29$\pm$0.01
155 16 0.0 4699$\pm$19 2.83$\pm$0.06 $-$0.23$\pm$0.01 1.33$\pm$0.01 150 16 0.0
22013369$-$1141245 4636$\pm$18 2.47$\pm$0.06 $-$0.43$\pm$0.01 1.31$\pm$0.01
152 16 0.0 4575$\pm$16 2.43$\pm$0.06 $-$0.41$\pm$0.01 1.34$\pm$0.01 153 16 0.0
22021848$-$1139147 4638$\pm$30 2.89$\pm$0.09 0.17$\pm$0.02 1.34$\pm$0.02 119
16 0.0 4597$\pm$28 2.87$\pm$0.09 0.19$\pm$0.02 1.35$\pm$0.02 119 16 0.0
22104061$-$1125284 4603$\pm$27 2.79$\pm$0.08 0.04$\pm$0.02 1.29$\pm$0.02 123
15 0.0 4559$\pm$26 2.77$\pm$0.08 0.06$\pm$0.02 1.29$\pm$0.02 123 15 0.0
22074730$-$1059405 4757$\pm$23 3.0$\pm$0.06 0.0$\pm$0.01 1.16$\pm$0.02 149 17
0.0 4712$\pm$21 3.0$\pm$0.06 0.01$\pm$0.01 1.22$\pm$0.02 146 17 0.0
22114557$-$0957433 4885$\pm$18 3.34$\pm$0.05 $-$0.16$\pm$0.01 1.03$\pm$0.02
153 16 0.0 4830$\pm$17 3.29$\pm$0.05 $-$0.16$\pm$0.01 1.06$\pm$0.02 153 16 0.0
22105372$-$0956597 4705$\pm$17 2.86$\pm$0.06 $-$0.37$\pm$0.01 1.09$\pm$0.01
158 16 0.0 4642$\pm$16 2.8$\pm$0.06 $-$0.37$\pm$0.01 1.17$\pm$0.01 148 16 0.0
22083624$-$0948555 4816$\pm$33 3.01$\pm$0.1 0.42$\pm$0.02 1.34$\pm$0.02 106 12
0.0 4769$\pm$33 3.0$\pm$0.09 0.45$\pm$0.02 1.34$\pm$0.02 106 12 0.0
22091180$-$0944335 4849$\pm$17 3.4$\pm$0.05 $-$0.24$\pm$0.01 0.9$\pm$0.02 159
13 0.0 4803$\pm$16 3.37$\pm$0.05 $-$0.23$\pm$0.01 0.93$\pm$0.02 159 13 0.0
22102197$-$0923157 4931$\pm$17 2.67$\pm$0.06 $-$0.2$\pm$0.01 1.32$\pm$0.01 143
15 0.0 4846$\pm$17 2.61$\pm$0.06 $-$0.2$\pm$0.01 1.37$\pm$0.01 142 15 0.0
22013945$-$0909229 4664$\pm$29 3.19$\pm$0.07 0.33$\pm$0.03 1.16$\pm$0.03 107
14 0.0 4634$\pm$29 3.17$\pm$0.07 0.34$\pm$0.03 1.17$\pm$0.03 107 14 0.0
22052550$-$0854435 4845$\pm$17 2.56$\pm$0.06 $-$0.32$\pm$0.01 1.49$\pm$0.01
156 13 0.0 4766$\pm$17 2.51$\pm$0.06 $-$0.32$\pm$0.01 1.53$\pm$0.01 155 13 0.0
22052114$-$0848002 4750$\pm$18 2.64$\pm$0.06 $-$0.36$\pm$0.01 1.22$\pm$0.01
158 15 0.0 4705$\pm$18 2.67$\pm$0.07 $-$0.35$\pm$0.01 1.31$\pm$0.01 145 15 0.0
22055148$-$0840028 4700$\pm$20 2.91$\pm$0.06 $-$0.27$\pm$0.01 1.19$\pm$0.01
162 12 0.0 4646$\pm$19 2.88$\pm$0.06 $-$0.27$\pm$0.01 1.24$\pm$0.01 158 12 0.0
22062074$-$0809079 4694$\pm$25 2.91$\pm$0.07 $-$0.01$\pm$0.02 1.23$\pm$0.02
136 14 0.0 4645$\pm$25 2.89$\pm$0.07 0.01$\pm$0.02 1.24$\pm$0.02 136 14 0.0
22291753$-$0806290 4664$\pm$19 2.9$\pm$0.06 $-$0.3$\pm$0.01 1.19$\pm$0.01 161
15 0.0 4615$\pm$17 2.87$\pm$0.06 $-$0.29$\pm$0.01 1.23$\pm$0.01 158 15 0.0
22122727$-$0719010 4428$\pm$27 2.46$\pm$0.1 $-$0.15$\pm$0.03 1.36$\pm$0.01 139
15 0.0 4389$\pm$27 2.46$\pm$0.09 $-$0.13$\pm$0.02 1.36$\pm$0.02 139 15 0.0
22292970$-$0713347 4833$\pm$19 2.64$\pm$0.06 $-$0.22$\pm$0.01 1.42$\pm$0.01
153 17 0.0 4757$\pm$17 2.59$\pm$0.06 $-$0.21$\pm$0.01 1.46$\pm$0.01 153 17 0.0
22130580$-$0658576 4594$\pm$27 2.78$\pm$0.09 $-$0.03$\pm$0.02 1.37$\pm$0.01
132 14 0.0 4550$\pm$26 2.76$\pm$0.08 $-$0.01$\pm$0.02 1.38$\pm$0.02 132 14 0.0
22092886$-$0617515 4731$\pm$21 3.02$\pm$0.06 $-$0.26$\pm$0.01 1.13$\pm$0.02
160 16 0.0 4693$\pm$22 3.02$\pm$0.06 $-$0.24$\pm$0.01 1.17$\pm$0.02 154 16 0.0
22153043$-$0617291 4942$\pm$16 2.5$\pm$0.06 $-$0.51$\pm$0.01 1.4$\pm$0.01 163
17 0.0 4850$\pm$17 2.44$\pm$0.06 $-$0.52$\pm$0.01 1.49$\pm$0.01 149 17 0.0
22092416$-$0610474 4789$\pm$24 2.7$\pm$0.08 $-$0.0$\pm$0.02 1.36$\pm$0.01 138
16 0.0 4726$\pm$24 2.67$\pm$0.08 0.03$\pm$0.01 1.38$\pm$0.01 139 16 0.0
22085850$-$0608204 4839$\pm$20 2.64$\pm$0.07 $-$0.32$\pm$0.01 1.36$\pm$0.01
148 9 0.0 4758$\pm$20 2.59$\pm$0.07 $-$0.32$\pm$0.01 1.4$\pm$0.01 147 10 0.0
22375413$-$0604257 4770$\pm$27 2.84$\pm$0.08 0.12$\pm$0.02 1.32$\pm$0.01 128
16 0.0 4712$\pm$26 2.81$\pm$0.08 0.13$\pm$0.02 1.36$\pm$0.01 129 16 0.0
22354169$-$0543252 4735$\pm$22 3.0$\pm$0.06 0.1$\pm$0.01 1.1$\pm$0.02 136 15
0.0 4693$\pm$21 3.0$\pm$0.06 0.13$\pm$0.01 1.11$\pm$0.02 139 15 0.0
22362945$-$0540124 4825$\pm$20 3.16$\pm$0.06 $-$0.17$\pm$0.01 1.17$\pm$0.02
150 15 0.0 4769$\pm$19 3.12$\pm$0.06 $-$0.17$\pm$0.01 1.21$\pm$0.02 150 15 0.0
22342769$-$0522505 4645$\pm$22 2.94$\pm$0.07 $-$0.1$\pm$0.01 1.19$\pm$0.02 153
15 0.0 4602$\pm$22 2.93$\pm$0.07 $-$0.09$\pm$0.01 1.21$\pm$0.02 151 15 0.0
22342069$-$0520353 4764$\pm$20 3.28$\pm$0.05 0.04$\pm$0.01 0.97$\pm$0.02 154
16 0.0 4720$\pm$19 3.24$\pm$0.05 0.05$\pm$0.01 0.99$\pm$0.02 154 16 0.0
22344800$-$0516214 4842$\pm$23 3.25$\pm$0.06 0.11$\pm$0.01 1.17$\pm$0.02 136
17 0.0 4790$\pm$21 3.21$\pm$0.06 0.12$\pm$0.01 1.19$\pm$0.02 136 17 0.0
$R$-Process Alliance Stars (Hansen et al., 2018) J03193531$-$3250433
6353$\pm$24 3.0$\pm$0.05 $-$2.97$\pm$0.01 2.81$\pm$0.15 11 5 2.7 6345$\pm$201
3.75$\pm$0.05 $-$2.77$\pm$0.1 2.8$\pm$0.15 11 5 2.7 J02401075$-$1416290
6041$\pm$116 4.4$\pm$0.19 $-$0.89$\pm$0.08 0.87$\pm$0.12 35 9 1.2 5991$\pm$107
4.34$\pm$0.18 $-$0.85$\pm$0.08 0.74$\pm$0.13 35 9 1.2 J00233067$-$1631428
5354$\pm$175 2.93$\pm$0.47 $-$2.53$\pm$0.12 2.12$\pm$0.2 28 13 2.7 5297$\pm$24
3.0$\pm$0.05 $-$2.45$\pm$0.03 1.7$\pm$0.17 28 13 2.7 J01334657$-$2727374
5216$\pm$151 2.46$\pm$0.42 $-$1.77$\pm$0.12 2.23$\pm$0.07 26 6 2.7
5221$\pm$147 2.65$\pm$0.35 $-$1.66$\pm$0.11 2.18$\pm$0.09 26 6 2.7
J00133067$-$1259594 4620$\pm$30 0.07$\pm$0.05 $-$2.78$\pm$0.03 1.82$\pm$0.07
36 9 2.7 4517$\pm$21 0.11$\pm$0.09 $-$2.73$\pm$0.03 1.8$\pm$0.06 36 9 2.7
J19215077$-$4452545 4659$\pm$23 0.1$\pm$0.07 $-$2.55$\pm$0.03 1.77$\pm$0.05 41
7 2.7 4561$\pm$32 0.13$\pm$0.11 $-$2.46$\pm$0.05 1.76$\pm$0.06 41 6 2.7
J23265258$-$0159248 4645$\pm$53 0.22$\pm$0.13 $-$3.13$\pm$0.04 1.94$\pm$0.08
32 15 2.7 4598$\pm$27 0.31$\pm$0.1 $-$3.0$\pm$0.03 1.88$\pm$0.09 32 15 2.7
J00405260$-$5122491 5547$\pm$59 4.01$\pm$0.22 $-$2.2$\pm$0.03 1.29$\pm$0.15 37
10 2.7 5495$\pm$75 3.93$\pm$0.23 $-$2.2$\pm$0.04 1.17$\pm$0.14 37 10 2.7
J15271353$-$2336177 6001$\pm$24 4.0$\pm$0.05 $-$2.16$\pm$0.01 1.64$\pm$0.08 48
13 2.7 6001$\pm$24 4.0$\pm$0.05 $-$2.11$\pm$0.02 1.82$\pm$0.13 48 13 2.7
J01530024$-$3417360 5171$\pm$65 2.96$\pm$0.13 $-$1.73$\pm$0.05 1.45$\pm$0.05
62 14 2.7 5116$\pm$93 2.96$\pm$0.18 $-$1.71$\pm$0.08 1.4$\pm$0.05 62 14 2.7
J16024498$-$1521016 5145$\pm$128 2.95$\pm$0.26 $-$1.99$\pm$0.1 1.69$\pm$0.05
44 13 2.7 5085$\pm$157 2.93$\pm$0.35 $-$1.99$\pm$0.14 1.69$\pm$0.05 44 13 2.7
J20514971$-$6158008 5221$\pm$145 2.97$\pm$0.29 $-$1.94$\pm$0.11 1.53$\pm$0.07
47 14 2.7 5187$\pm$134 3.01$\pm$0.29 $-$1.9$\pm$0.11 1.48$\pm$0.07 47 14 2.7
J16103106+1003055 5354$\pm$200 2.33$\pm$0.51 $-$2.44$\pm$0.13 1.68$\pm$0.21 32
3 1.2 5411$\pm$118 2.83$\pm$0.29 $-$2.26$\pm$0.13 1.5$\pm$0.09 32 3 1.2
J16184302$-$0630558 5293$\pm$103 1.14$\pm$0.29 $-$2.84$\pm$0.05 2.1$\pm$0.09
38 11 1.2 5339$\pm$114 2.1$\pm$0.39 $-$2.54$\pm$0.08 2.39$\pm$0.35 36 11 1.2
J21063474$-$4957500 5365$\pm$23 3.0$\pm$0.05 $-$2.89$\pm$0.02 1.53$\pm$0.12 33
9 2.7 5254$\pm$24 2.99$\pm$0.05 $-$2.88$\pm$0.02 1.26$\pm$0.09 33 9 2.7
J00021668$-$2453494 5140$\pm$160 1.81$\pm$0.48 $-$1.85$\pm$0.11 1.87$\pm$0.15
39 11 2.7 5185$\pm$145 2.24$\pm$0.39 $-$1.71$\pm$0.09 2.03$\pm$0.15 40 11 2.7
J02355867$-$6745520 4661$\pm$108 0.81$\pm$0.25 $-$1.7$\pm$0.08 2.09$\pm$0.12
30 10 2.7 4565$\pm$96 0.77$\pm$0.21 $-$1.66$\pm$0.07 2.14$\pm$0.08 31 10 2.7
J13164824$-$2743351 4821$\pm$95 1.78$\pm$0.3 $-$1.86$\pm$0.08 1.43$\pm$0.06 65
14 2.7 4806$\pm$91 1.96$\pm$0.27 $-$1.79$\pm$0.08 1.48$\pm$0.06 66 14 2.7
J14232679$-$2834200 4882$\pm$200 1.57$\pm$0.53 $-$2.19$\pm$0.17 1.39$\pm$0.08
45 9 2.7 4902$\pm$180 1.87$\pm$0.49 $-$2.08$\pm$0.15 1.43$\pm$0.07 46 9 2.7
J14301385$-$2317388 4352$\pm$51 0.67$\pm$0.13 $-$1.68$\pm$0.04 2.37$\pm$0.04
54 13 2.7 4298$\pm$39 0.65$\pm$0.11 $-$1.64$\pm$0.03 2.43$\pm$0.03 54 13 2.7
J15575183$-$0839549 4585$\pm$71 1.29$\pm$0.29 $-$1.82$\pm$0.07 1.92$\pm$0.06
55 16 2.7 4564$\pm$72 1.42$\pm$0.28 $-$1.74$\pm$0.07 1.96$\pm$0.04 56 16 2.7
J16080681$-$3215592 4531$\pm$27 0.49$\pm$0.18 $-$2.28$\pm$0.03 1.73$\pm$0.02
89 15 1.2 4460$\pm$26 0.63$\pm$0.14 $-$2.25$\pm$0.03 1.81$\pm$0.02 89 15 1.2
J17273886$-$5133298 5068$\pm$143 1.28$\pm$0.41 $-$1.85$\pm$0.08 2.07$\pm$0.16
52 13 2.7 5159$\pm$113 1.87$\pm$0.32 $-$1.67$\pm$0.06 2.28$\pm$0.13 52 13 2.7
J17334285$-$5121550 4864$\pm$153 0.99$\pm$0.37 $-$2.02$\pm$0.1 1.93$\pm$0.11
46 14 2.7 4891$\pm$167 1.22$\pm$0.44 $-$1.88$\pm$0.12 2.04$\pm$0.1 47 14 2.7
J18024226$-$4404426 4654$\pm$89 1.6$\pm$0.3 $-$1.65$\pm$0.08 1.94$\pm$0.04 47
8 2.7 4625$\pm$88 1.7$\pm$0.29 $-$1.57$\pm$0.08 1.97$\pm$0.05 48 8 2.7
J19014952$-$4844359 4602$\pm$26 1.06$\pm$0.11 $-$2.17$\pm$0.03 1.65$\pm$0.01
72 7 0.0 4549$\pm$27 1.14$\pm$0.11 $-$2.12$\pm$0.03 1.73$\pm$0.01 73 7 0.0
J19324858$-$5908019 4427$\pm$102 1.66$\pm$0.3 $-$2.13$\pm$0.08 1.72$\pm$0.08
29 7 2.7 4411$\pm$96 1.77$\pm$0.29 $-$2.09$\pm$0.08 1.75$\pm$0.09 29 7 2.7
J20144608$-$5635300 4828$\pm$115 1.36$\pm$0.39 $-$1.98$\pm$0.09 1.61$\pm$0.16
15 11 2.7 4773$\pm$130 1.53$\pm$0.41 $-$1.95$\pm$0.1 1.84$\pm$0.15 16 11 2.7
J22444701$-$5617540 4395$\pm$107 0.79$\pm$0.23 $-$2.09$\pm$0.08 1.8$\pm$0.09
22 6 2.7 4326$\pm$102 0.79$\pm$0.23 $-$2.09$\pm$0.08 1.95$\pm$0.08 22 6 2.7
J22492756$-$2238289 4768$\pm$105 1.09$\pm$0.31 $-$2.0$\pm$0.08 1.93$\pm$0.12
44 7 2.7 4782$\pm$102 1.38$\pm$0.29 $-$1.89$\pm$0.09 2.11$\pm$0.1 44 7 2.7
J22531984$-$2248555 4577$\pm$87 1.09$\pm$0.29 $-$2.11$\pm$0.07 1.58$\pm$0.07
52 14 2.7 4578$\pm$82 1.31$\pm$0.27 $-$2.03$\pm$0.07 1.66$\pm$0.07 53 14 2.7
J23362202$-$5607498 4459$\pm$106 0.81$\pm$0.24 $-$2.29$\pm$0.07 2.16$\pm$0.17
13 8 2.7 4495$\pm$109 0.9$\pm$0.27 $-$2.23$\pm$0.08 2.4$\pm$0.18 14 8 2.7
J00002259$-$1302275 4835$\pm$117 1.72$\pm$0.47 $-$2.46$\pm$0.1 2.4$\pm$0.33 44
5 0.0 4739$\pm$99 2.03$\pm$0.57 $-$2.52$\pm$0.09 2.52$\pm$0.3 43 5 0.0
J00021222$-$2241388 5180$\pm$137 2.03$\pm$0.43 $-$2.16$\pm$0.07 1.74$\pm$0.21
46 8 2.7 5164$\pm$113 2.34$\pm$0.37 $-$2.05$\pm$0.05 1.78$\pm$0.27 46 8 2.7
J00400685$-$4325183 4458$\pm$156 0.66$\pm$0.45 $-$2.65$\pm$0.13 2.06$\pm$0.14
25 7 2.7 4422$\pm$133 0.65$\pm$0.43 $-$2.55$\pm$0.13 2.04$\pm$0.14 25 8 2.7
J00453930$-$7457294 4727$\pm$37 1.49$\pm$0.17 $-$2.25$\pm$0.04 1.77$\pm$0.02
83 15 1.2 4684$\pm$35 1.65$\pm$0.16 $-$2.2$\pm$0.04 1.76$\pm$0.02 83 15 1.2
J01202234$-$5425582 5133$\pm$131 2.33$\pm$0.44 $-$2.11$\pm$0.08 1.45$\pm$0.16
48 9 2.7 5123$\pm$118 2.59$\pm$0.41 $-$2.01$\pm$0.08 1.39$\pm$0.19 48 9 2.7
J01293113$-$1600454 4678$\pm$133 1.09$\pm$0.41 $-$3.07$\pm$0.09 2.1$\pm$0.16
26 11 2.7 4800$\pm$134 1.76$\pm$0.35 $-$2.84$\pm$0.11 2.18$\pm$0.15 26 11 2.7
J01425422$-$5032488 5140$\pm$73 2.52$\pm$0.23 $-$2.18$\pm$0.06 1.66$\pm$0.06
49 15 2.7 5132$\pm$84 2.74$\pm$0.27 $-$2.08$\pm$0.06 1.6$\pm$0.11 49 15 2.7
J01430726$-$6445174 4582$\pm$66 0.51$\pm$0.25 $-$3.11$\pm$0.05 1.86$\pm$0.1 28
9 2.7 4563$\pm$76 0.9$\pm$0.27 $-$2.95$\pm$0.07 1.79$\pm$0.07 29 9 2.7
J01451951$-$2800583 4445$\pm$59 0.46$\pm$0.25 $-$2.89$\pm$0.05 1.63$\pm$0.03
31 12 2.7 4396$\pm$61 0.51$\pm$0.23 $-$2.8$\pm$0.06 1.61$\pm$0.03 31 12 2.7
J01490794$-$4911429 4691$\pm$72 0.77$\pm$0.24 $-$3.05$\pm$0.05 1.84$\pm$0.07
29 14 2.7 4845$\pm$81 1.61$\pm$0.22 $-$2.79$\pm$0.07 1.98$\pm$0.08 29 14 2.7
J02040793$-$3127556 4556$\pm$43 0.56$\pm$0.2 $-$3.17$\pm$0.04 2.1$\pm$0.06 67
16 1.2 4603$\pm$55 1.15$\pm$0.19 $-$3.01$\pm$0.07 2.24$\pm$0.07 66 16 1.2
J02165716$-$7547064 4531$\pm$64 0.48$\pm$0.26 $-$2.6$\pm$0.06 2.16$\pm$0.04 40
6 2.7 4537$\pm$65 0.7$\pm$0.24 $-$2.44$\pm$0.06 2.15$\pm$0.03 40 11 2.7
J02412152$-$1825376 4270$\pm$25 0.43$\pm$0.14 $-$2.3$\pm$0.02 1.52$\pm$0.03 64
9 1.2 4239$\pm$24 0.45$\pm$0.12 $-$2.31$\pm$0.02 1.71$\pm$0.02 63 10 1.2
J02441479$-$5158241 5223$\pm$120 2.28$\pm$0.4 $-$2.78$\pm$0.08 2.0$\pm$0.1 36
14 2.7 5201$\pm$79 2.7$\pm$0.26 $-$2.64$\pm$0.06 1.94$\pm$0.12 36 14 2.7
J02462013$-$1518419 5047$\pm$265 1.9$\pm$0.73 $-$2.77$\pm$0.2 2.69$\pm$0.22 15
9 2.7 5043$\pm$180 2.31$\pm$0.47 $-$2.61$\pm$0.13 2.62$\pm$0.24 15 9 2.7
J02500719$-$5145148 4575$\pm$37 0.96$\pm$0.18 $-$2.34$\pm$0.04 1.96$\pm$0.03
85 12 1.2 4527$\pm$38 1.11$\pm$0.16 $-$2.29$\pm$0.04 2.01$\pm$0.03 85 12 1.2
J03563703$-$5838281 4614$\pm$99 0.69$\pm$0.34 $-$2.78$\pm$0.08 2.1$\pm$0.06 30
9 2.7 4713$\pm$110 1.36$\pm$0.33 $-$2.55$\pm$0.1 2.07$\pm$0.06 30 9 2.7
J04121388$-$1205050 4601$\pm$57 0.48$\pm$0.25 $-$2.82$\pm$0.06 2.21$\pm$0.05
22 7 1.2 4515$\pm$48 0.57$\pm$0.18 $-$2.78$\pm$0.06 2.33$\pm$0.05 22 7 1.2
J14033542$-$3335257 5040$\pm$127 1.97$\pm$0.32 $-$2.69$\pm$0.09 1.76$\pm$0.11
53 10 2.7 5116$\pm$102 2.48$\pm$0.28 $-$2.49$\pm$0.08 1.7$\pm$0.15 53 10 2.7
J14164084$-$2422000 4555$\pm$95 0.53$\pm$0.33 $-$2.78$\pm$0.07 1.77$\pm$0.06
38 16 2.7 4475$\pm$115 0.64$\pm$0.36 $-$2.7$\pm$0.1 1.77$\pm$0.05 38 16 2.7
J14325334$-$4125494 4729$\pm$127 1.51$\pm$0.36 $-$3.14$\pm$0.1 1.55$\pm$0.12
34 10 2.7 4791$\pm$113 1.95$\pm$0.31 $-$2.99$\pm$0.1 1.62$\pm$0.11 34 10 2.7
J14381119$-$2120085 4458$\pm$50 0.53$\pm$0.27 $-$2.44$\pm$0.04 1.9$\pm$0.03 47
14 2.7 4368$\pm$57 0.61$\pm$0.25 $-$2.41$\pm$0.05 1.91$\pm$0.03 48 13 2.7
J15260106$-$0911388 4697$\pm$119 0.72$\pm$0.38 $-$2.79$\pm$0.08 2.16$\pm$0.13
29 11 2.7 4784$\pm$128 1.37$\pm$0.36 $-$2.55$\pm$0.11 2.13$\pm$0.13 29 11 2.7
J15582962$-$1224344 5298$\pm$175 1.37$\pm$0.38 $-$2.58$\pm$0.09 2.63$\pm$0.22
44 16 2.7 5222$\pm$119 2.09$\pm$0.29 $-$2.39$\pm$0.09 2.73$\pm$0.21 44 16 2.7
J16095117$-$0941174 4620$\pm$58 0.57$\pm$0.24 $-$2.82$\pm$0.04 1.86$\pm$0.05
39 15 2.7 4767$\pm$70 1.39$\pm$0.18 $-$2.55$\pm$0.06 1.91$\pm$0.05 39 15 2.7
J17093199$-$6027271 4525$\pm$55 0.37$\pm$0.24 $-$2.49$\pm$0.06 2.12$\pm$0.05
53 8 1.2 4448$\pm$50 0.4$\pm$0.2 $-$2.41$\pm$0.06 2.11$\pm$0.03 53 8 1.2
J17094926$-$6239285 4611$\pm$123 0.88$\pm$0.43 $-$2.49$\pm$0.1 1.42$\pm$0.09
33 10 2.7 4712$\pm$118 1.47$\pm$0.33 $-$2.26$\pm$0.1 1.35$\pm$0.08 33 10 2.7
J17124284$-$5211479 4745$\pm$174 0.99$\pm$0.5 $-$2.77$\pm$0.13 1.24$\pm$0.12
26 10 2.7 4855$\pm$158 1.61$\pm$0.39 $-$2.54$\pm$0.13 1.28$\pm$0.1 26 10 2.7
J17225742$-$7123000 5019$\pm$113 2.36$\pm$0.33 $-$2.55$\pm$0.1 1.8$\pm$0.09 41
10 1.2 4998$\pm$97 2.58$\pm$0.28 $-$2.47$\pm$0.1 1.7$\pm$0.1 41 10 1.2
J17255680$-$6603395 4666$\pm$66 0.49$\pm$0.27 $-$2.66$\pm$0.05 2.13$\pm$0.05
35 12 2.7 4671$\pm$77 0.99$\pm$0.23 $-$2.5$\pm$0.07 2.05$\pm$0.05 35 12 2.7
J17285930$-$7427532 4760$\pm$136 1.1$\pm$0.57 $-$2.18$\pm$0.09 1.41$\pm$0.13
38 8 2.7 4773$\pm$95 1.44$\pm$0.42 $-$2.07$\pm$0.06 1.45$\pm$0.13 38 8 2.7
J17400682$-$6102129 4594$\pm$91 0.93$\pm$0.33 $-$2.52$\pm$0.07 1.8$\pm$0.05 43
12 2.7 4625$\pm$96 1.32$\pm$0.29 $-$2.37$\pm$0.08 1.8$\pm$0.04 43 12 2.7
J17435113$-$5359333 5198$\pm$147 1.85$\pm$0.43 $-$2.28$\pm$0.07 2.13$\pm$0.24
58 14 2.7 5203$\pm$121 2.37$\pm$0.35 $-$2.12$\pm$0.07 2.13$\pm$0.23 58 12 2.7
J18121045$-$4934495 4526$\pm$79 0.6$\pm$0.29 $-$3.03$\pm$0.06 2.19$\pm$0.09 27
9 2.7 4657$\pm$89 1.31$\pm$0.27 $-$2.78$\pm$0.08 2.2$\pm$0.08 27 9 2.7
J18285086$-$3434203 4706$\pm$93 1.16$\pm$0.3 $-$2.4$\pm$0.07 1.62$\pm$0.07 60
14 2.7 4735$\pm$88 1.51$\pm$0.25 $-$2.25$\pm$0.08 1.64$\pm$0.07 60 14 2.7
J18294122$-$4504000 4572$\pm$92 0.71$\pm$0.34 $-$2.67$\pm$0.08 1.8$\pm$0.05 38
7 2.7 4624$\pm$96 1.2$\pm$0.29 $-$2.48$\pm$0.1 1.73$\pm$0.05 38 7 2.7
J18362318$-$6428124 4700$\pm$90 1.17$\pm$0.28 $-$2.77$\pm$0.07 1.78$\pm$0.07
34 13 2.7 4823$\pm$91 1.77$\pm$0.25 $-$2.54$\pm$0.07 1.79$\pm$0.06 34 13 2.7
J18363613$-$7136597 4574$\pm$150 0.56$\pm$0.43 $-$2.65$\pm$0.12 2.1$\pm$0.1 41
9 2.7 4556$\pm$91 0.58$\pm$0.32 $-$2.46$\pm$0.09 2.02$\pm$0.05 41 13 2.7
J18562774$-$7251331 4641$\pm$65 0.48$\pm$0.32 $-$2.32$\pm$0.06 1.74$\pm$0.05
38 4 2.7 4538$\pm$88 0.56$\pm$0.33 $-$2.26$\pm$0.09 1.75$\pm$0.03 38 4 2.7
J19161821$-$5544454 4449$\pm$21 0.23$\pm$0.17 $-$2.4$\pm$0.02 1.99$\pm$0.09 32
10 2.7 4377$\pm$22 0.3$\pm$0.18 $-$2.38$\pm$0.03 2.12$\pm$0.08 32 10 2.7
J19172402$-$4211240 4568$\pm$88 0.59$\pm$0.32 $-$2.83$\pm$0.07 1.96$\pm$0.08
53 13 2.7 4681$\pm$109 1.25$\pm$0.3 $-$2.59$\pm$0.1 1.99$\pm$0.08 53 13 2.7
J19173310$-$6628545 4608$\pm$160 0.89$\pm$0.52 $-$2.81$\pm$0.12 2.53$\pm$0.13
19 9 2.7 4668$\pm$164 1.35$\pm$0.47 $-$2.63$\pm$0.14 2.49$\pm$0.1 19 9 2.7
J19202070$-$6627202 4426$\pm$31 0.59$\pm$0.21 $-$2.4$\pm$0.03 1.45$\pm$0.03 81
11 1.2 4451$\pm$38 1.04$\pm$0.16 $-$2.34$\pm$0.04 1.6$\pm$0.04 78 11 1.2
J19232518$-$5833410 5029$\pm$209 1.87$\pm$0.69 $-$2.17$\pm$0.13 2.05$\pm$0.36
36 7 2.7 5039$\pm$155 2.21$\pm$0.57 $-$2.06$\pm$0.09 2.14$\pm$0.35 36 7 2.7
J19345497$-$5751400 4841$\pm$204 2.09$\pm$0.66 $-$2.33$\pm$0.17 2.41$\pm$0.14
11 5 2.7 4841$\pm$190 2.4$\pm$0.67 $-$2.23$\pm$0.15 2.29$\pm$0.12 11 5 2.7
J19494025$-$5424113 4648$\pm$129 0.87$\pm$0.41 $-$2.83$\pm$0.1 2.09$\pm$0.1 25
9 2.7 4733$\pm$123 1.47$\pm$0.34 $-$2.62$\pm$0.11 2.08$\pm$0.06 25 9 2.7
J19534978$-$5940001 4708$\pm$45 0.49$\pm$0.19 $-$2.83$\pm$0.04 2.46$\pm$0.05
41 10 1.2 4672$\pm$62 0.96$\pm$0.21 $-$2.65$\pm$0.08 2.24$\pm$0.05 43 10 1.2
J19594558$-$2549075 4523$\pm$72 0.46$\pm$0.29 $-$2.5$\pm$0.05 2.15$\pm$0.05 42
15 2.7 4442$\pm$81 0.52$\pm$0.26 $-$2.45$\pm$0.07 2.16$\pm$0.05 42 15 2.7
J20093393$-$3410273 4410$\pm$39 1.64$\pm$0.15 $-$2.19$\pm$0.02 2.18$\pm$0.08
62 7 1.2 4312$\pm$20 1.77$\pm$0.18 $-$2.22$\pm$0.02 2.19$\pm$0.07 62 7 1.2
J20165357$-$0503592 4546$\pm$105 0.6$\pm$0.33 $-$2.96$\pm$0.09 2.11$\pm$0.11
35 7 2.7 4639$\pm$127 1.21$\pm$0.36 $-$2.74$\pm$0.13 2.13$\pm$0.09 35 7 2.7
J20303339$-$2519500 4378$\pm$17 0.06$\pm$0.05 $-$2.29$\pm$0.02 1.75$\pm$0.03
65 16 2.7 4312$\pm$23 0.12$\pm$0.11 $-$2.24$\pm$0.02 1.83$\pm$0.05 65 16 2.7
J20313531$-$3127319 4658$\pm$107 0.7$\pm$0.34 $-$2.72$\pm$0.08 1.96$\pm$0.09
28 10 2.7 4759$\pm$125 1.36$\pm$0.33 $-$2.49$\pm$0.11 1.98$\pm$0.11 28 10 2.7
J20445584$-$2250597 4330$\pm$44 0.5$\pm$0.23 $-$2.49$\pm$0.03 2.03$\pm$0.03 54
14 2.7 4266$\pm$51 0.5$\pm$0.24 $-$2.49$\pm$0.04 2.21$\pm$0.04 55 14 2.7
J20492765$-$5124440 4503$\pm$67 0.55$\pm$0.28 $-$2.49$\pm$0.06 1.81$\pm$0.04
38 9 2.7 4492$\pm$76 0.87$\pm$0.27 $-$2.39$\pm$0.07 1.83$\pm$0.03 38 9 2.7
J20542346$-$0033097 4414$\pm$57 0.52$\pm$0.27 $-$2.87$\pm$0.05 2.53$\pm$0.06
36 13 2.7 4402$\pm$78 0.76$\pm$0.27 $-$2.77$\pm$0.08 2.49$\pm$0.05 37 13 2.7
J20560913$-$1331176 4615$\pm$53 0.98$\pm$0.2 $-$2.5$\pm$0.04 1.65$\pm$0.02 58
17 2.7 4668$\pm$54 1.41$\pm$0.16 $-$2.34$\pm$0.05 1.63$\pm$0.02 58 17 2.7
J21023752$-$5316132 5198$\pm$289 2.4$\pm$0.94 $-$2.32$\pm$0.22 1.36$\pm$0.36
29 9 2.7 5178$\pm$162 2.6$\pm$0.5 $-$2.22$\pm$0.08 1.22$\pm$0.33 29 9 2.7
J21064294$-$6828266 4830$\pm$255 1.7$\pm$0.76 $-$3.1$\pm$0.21 2.76$\pm$0.17 11
9 2.7 4843$\pm$251 2.08$\pm$0.74 $-$2.97$\pm$0.21 2.79$\pm$0.15 11 9 2.7
J21091825$-$1310062 4746$\pm$106 0.97$\pm$0.35 $-$2.51$\pm$0.08 1.79$\pm$0.06
46 18 2.7 4820$\pm$103 1.53$\pm$0.29 $-$2.31$\pm$0.09 1.8$\pm$0.05 46 18 2.7
J21095804$-$0945400 4493$\pm$77 0.68$\pm$0.3 $-$2.85$\pm$0.06 1.79$\pm$0.07 19
7 2.7 4555$\pm$83 1.15$\pm$0.27 $-$2.66$\pm$0.08 1.77$\pm$0.05 19 7 2.7
J21141350$-$5726363 4515$\pm$67 0.51$\pm$0.24 $-$2.95$\pm$0.06 1.94$\pm$0.05
57 7 2.7 4590$\pm$79 1.12$\pm$0.23 $-$2.74$\pm$0.09 1.96$\pm$0.05 57 7 2.7
J21152551$-$1503309 4505$\pm$72 0.52$\pm$0.33 $-$2.32$\pm$0.05 1.77$\pm$0.06
38 14 2.7 4458$\pm$82 0.69$\pm$0.3 $-$2.29$\pm$0.07 1.86$\pm$0.03 37 10 2.7
J21162185$-$0213420 4418$\pm$25 0.08$\pm$0.06 $-$2.33$\pm$0.03 1.48$\pm$0.04
41 7 2.7 4234$\pm$43 0.45$\pm$0.25 $-$2.44$\pm$0.05 1.86$\pm$0.05 37 2 2.7
J21224590$-$4641030 4743$\pm$123 1.11$\pm$0.41 $-$2.9$\pm$0.09 2.23$\pm$0.13
24 11 2.7 4842$\pm$125 1.75$\pm$0.33 $-$2.68$\pm$0.11 2.25$\pm$0.12 24 11 2.7
J21262525$-$2144243 4362$\pm$61 0.57$\pm$0.26 $-$2.93$\pm$0.06 1.84$\pm$0.04
52 10 2.7 4400$\pm$66 0.96$\pm$0.23 $-$2.78$\pm$0.07 1.82$\pm$0.04 52 10 2.7
J21291592$-$4236219 4602$\pm$104 0.82$\pm$0.38 $-$2.63$\pm$0.08 2.08$\pm$0.07
43 14 2.7 4673$\pm$110 1.34$\pm$0.32 $-$2.44$\pm$0.1 2.05$\pm$0.06 43 14 2.7
J21370807$-$0927347 4507$\pm$119 0.72$\pm$0.5 $-$2.53$\pm$0.1 1.86$\pm$0.09 34
8 2.7 4364$\pm$109 0.63$\pm$0.37 $-$2.52$\pm$0.11 1.84$\pm$0.08 36 8 2.7
J21513595$-$0543398 4489$\pm$71 0.44$\pm$0.24 $-$2.59$\pm$0.06 2.02$\pm$0.04
42 14 2.7 4412$\pm$52 0.49$\pm$0.2 $-$2.55$\pm$0.05 2.08$\pm$0.05 42 14 2.7
J22021636$-$0536483 4695$\pm$58 0.74$\pm$0.25 $-$2.76$\pm$0.05 2.03$\pm$0.07
42 10 1.2 4731$\pm$68 1.31$\pm$0.24 $-$2.57$\pm$0.08 2.06$\pm$0.05 42 10 1.2
J22163596+0246171 4759$\pm$114 1.41$\pm$0.34 $-$2.51$\pm$0.1 1.49$\pm$0.06 49
7 2.7 4761$\pm$104 1.7$\pm$0.28 $-$2.39$\pm$0.1 1.44$\pm$0.05 49 7 2.7
J22595884$-$1554182 4552$\pm$101 0.57$\pm$0.33 $-$2.73$\pm$0.08 2.14$\pm$0.05
44 12 2.7 4543$\pm$118 0.87$\pm$0.37 $-$2.57$\pm$0.11 2.05$\pm$0.05 44 12 2.7
J23022289$-$6833233 5232$\pm$162 2.23$\pm$0.51 $-$2.52$\pm$0.11 1.79$\pm$0.17
39 7 2.7 5227$\pm$144 2.72$\pm$0.49 $-$2.39$\pm$0.1 1.82$\pm$0.29 39 7 2.7
J23044914$-$4243477 4670$\pm$98 1.58$\pm$0.32 $-$2.48$\pm$0.09 0.79$\pm$0.07
26 12 1.2 4634$\pm$91 1.68$\pm$0.27 $-$2.43$\pm$0.09 0.77$\pm$0.07 26 12 1.2
J23130003$-$4507066 4589$\pm$83 0.57$\pm$0.32 $-$2.68$\pm$0.06 1.79$\pm$0.06
35 13 2.7 4675$\pm$100 1.17$\pm$0.31 $-$2.46$\pm$0.09 1.79$\pm$0.07 35 13 2.7
J23310716$-$0223301 4873$\pm$228 1.08$\pm$0.64 $-$2.5$\pm$0.16 2.06$\pm$0.18
12 3 2.7 4938$\pm$201 1.68$\pm$0.56 $-$2.28$\pm$0.16 2.06$\pm$0.2 12 3 2.7

Table 3:  Derived Stellar Atmospheric Parameters of the Target Stars

Note. — ††footnotetext: For HD121370, parameters are obtained with the average
of runs inputting 3 different EW line lists: EPINARBO in Heiter et al. (2015),
BOLOGNA in Heiter et al. (2015) and Takeda et al. (2005). In LTE, there are
N${}_{\mathrm{Fe_{I}}}$=79, 121, 46, N${}_{\mathrm{Fe_{I}I}}$=6, 9, 4 lines in
these three line list respectively; In NLTE, N${}_{\mathrm{Fe_{I}}}$=79, 121,
47, N${}_{\mathrm{Fe_{I}I}}$=6, 9, 4.

(This table is available in machine$-$readable form.)

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