# Searching For Transiting Planets Around Halo Stars. I. Sample Selection and
Validation

Jared R. Kolecki  Department of Astronomy, The Ohio State University,
Columbus, Ohio 43210, USA  Ji Wang (王吉) Department of Astronomy, The Ohio
State University, Columbus, Ohio 43210, USA  Jennifer A. Johnson  Department
of Astronomy, The Ohio State University, Columbus, Ohio 43210, USA  Joel C.
Zinn  NSF Astronomy and Astrophysics Postdoctoral Fellow.  Department of
Astronomy, The Ohio State University, Columbus, Ohio 43210, USA  Department of
Astrophysics, American Museum of Natural History, Central Park West at 79th
Street, New York, NY 10024, USA  Ilya Ilyin  Leibniz-Institute for
Astrophysics Potsdam (AIP), An der Sternwarte 16, D-14482 Potsdam, Germany
Klaus G. Strassmeier  Leibniz-Institute for Astrophysics Potsdam (AIP), An der
Sternwarte 16, D-14482 Potsdam, Germany

(Received January 18, 2021; Revised May, June 2021)

###### Abstract

By measuring the elemental abundances of a star, we can gain insight into the
composition of its initial gas cloud—the formation site of the star and its
planets. Planet formation requires metals, the availability of which is
determined by the elemental abundance. In the case where metals are extremely
deficient, planet formation can be stifled. To investigate such a scenario
requires a large sample of metal-poor stars and a search for planets therein.
This paper focuses on the selection and validation of a halo star sample. We
select $\sim$17,000 metal-poor halo stars based on their Galactic kinematics,
and confirm their low metallicities ($\rm{[Fe/H]}<-0.5$), using spectroscopy
from the literature. Furthermore, we perform high-resolution spectroscopic
observations using LBT/PEPSI and conduct detailed metallicity ([Fe/H])
analyses on a sample of 13 previously known halo stars that also have hot
kinematics. We can use the halo star sample presented here to measure the
frequency of planets and to test planet formation in extremely metal-poor
environments. The result of the planet search and its implications will be
presented and discussed in a companion paper by Boley et al.

Halo stars, Exoplanets, Metallicity

††journal: AJ††software: APOGEE data reduction pipeline (Nidever et al.,
2015), ASPCAP (García Pérez et al., 2016)), Astropy (Price-Whelan et al.,
2018), MOOG (Sneden, 1973), PyMOOGi (Adamow, 2017), SciPy (Virtanen et al.,
2020), SDS (Strassmeier et al., 2018)

##  1 Introduction

When and under what conditions did the first planet form? The oldest planetary
system that we know of is $\sim$11.2 Gyr old (Kepler-444, Campante et al.,
2015; Mack et al., 2018), with a host star metallicity of $\rm{[Fe/H]}=-0.52$.
The first generation of stars and planets is expected to have metallicities
similar to or below that of Kepler-444. Such a metal-poor environment poses
challenges for planet formation. For gas giant planets, core mass growth via
accretion halts in the extremely metal-poor regime, resulting in a strong
dependence of planet occurrence rate on stellar metallicity—known as the
planet-metallicity correlation (e.g., Fischer & Valenti, 2005). For
terrestrial planets, the planet-metallicity correlation is weaker (Wang &
Fischer, 2015) and period-dependent (Wilson et al., 2018; Petigura et al.,
2018). Therefore, metallicity is a key to regulate planet formation. More
interestingly, some elements (e.g., $\alpha$-elements) may play a bigger role
than others (Adibekyan et al., 2012; Bashi & Zucker, 2019).

The abundance of the elements increases as the Milky Way evolves. Among the
stellar populations in the Milky Way, halo stars are the most metal-poor on
average and therefore serve as an ideal test ground for planet formation in
metal-poor environments. However, identifying halo stars is difficult because
halo stars are relatively rare in the solar neighborhood, representing of
order 1% of the local population; discovering them has historically been
laborious; and detailed characterization via high-resolution spectroscopy has
been time-consuming (see Carney & Latham (1987) and associated works).

The Gaia mission (Gaia Collaboration et al., 2016) significantly changed the
landscape of the study of halo stars, because we can use it to identify metal-
poor stars based on their kinematics, thanks to the well-known correlation
between the two (Eggen et al., 1962). Gaia’s astrometric and radial velocity
measurements of one billion stars in the Milky Way provide an efficient way of
identifying halo stars. As such, we set out to identify stars with halo
kinematics using the Gaia DR2 data (Gaia Collaboration et al., 2018). The
kinematically selected halo stars are then validated using data from the
APOGEE spectroscopic survey (Majewski et al., 2017) and other photometric
surveys to check the purity of the sample.

Many of the halo stars are in the field of view of the Transiting Exoplanet
Survey Satellite (TESS, Ricker et al., 2015). Searching for transiting planets
around halo stars are therefore made possible by the Gaia and TESS missions.
Our halo sample is much larger than previous samples used for planetary
searches via radial velocity (Sozzetti et al., 2006; Faria et al., 2016).
Since $>70\%$ stars in our sample have [Fe/H]$<-$1, our search will likely
result in planetary systems that are more metal-poor than the current record
holder at [Fe/H]=$-0.84$ (Anglada-Escudé et al., 2014). The methods and
results of the planet search are described in a companion paper (Boley et al.
2021).

It is of interest to determine the absolute amount of metal deficiency of the
protoplanetary disk as input into simulations of planet formation in disks
(e.g., Johnson & Li, 2012). However, halo stars in the literature can have
values that differ by $\sim$ a factor of two, even when all studies use high-
resolution/high signal-to-noise data (e.g., Jofré et al., 2014). Among the
sources of systematic differences in the studies, the validity of using
ionization equilibrium in LTE to determine gravity (Thévenin & Idiart, 1999)
is another area where Gaia information is crucial. Gaia parallaxes resolve the
question of whether a star is a subgiant or main-sequence star. We therefore
consider a selection of well-studied halo stars from the literature with new
spectra and analyses in this work.

The paper is organized as follows: Section 2 outlines the process and criteria
used to select a sufficiently pure sample of halo dwarf stars, while Section 3
offers verification of the success of the sample selection. Section 4 details
the observation and data reduction process used to generate the spectra used
in Section 5 to analyze the iron abundances of selected halo stars from the
literature. The results of this analysis are discussed and compared with other
papers in Section 6.

##  2 Sample Selection

Gaia DR2 ID | pmRA (mas/yr) | pmDEC (mas/yr) | $T_{mag}$ | $M/M_{\odot}$ | $L/L_{\odot}$ | [M/H] from TIC
---|---|---|---|---|---|---
688442476835805312 | 66.074 | -114.073 | 13.068 | 1.11 | 0.92 | -1.52
800209689226496128 | -234.096 | -159.769 | 14.759 | 0.61 | 0.04 | -1.11
1021587525024433152 | -46.409 | -55.106 | 14.499 | 1.26 | 0.59 | -1.82
808143181016203264 | 60.511 | -128.934 | 14.341 | 1.03 | 0.63 | -1.43
Table 1: Selected entries from this paper’s final halo catalog. The entire
catalog is available electronically as a csv file, featuring additional
columns not present in this print version of the table.

Stars were selected preferentially from the CTLv0801 (Stassun et al., 2018,
2019) to have dwarf-like radii (raddflag = 1); have Gaia DR2 parallaxes and
proper motions (PMFlag == ‘gaia2’; PARFlag == ‘gaia2’; gaiaqflag == 1); be
within 1kpc according to the TICv8, which uses the Bailer-Jones et al. (2018)
method to calculate distance (Stassun et al., 2019) (this is to ensure that
the kinematic cut described below is valid, which was designed based on a
simulation of the nearest 1kpc stars); and be outside of the ecliptic plane
($|\texttt{lat}|>6$) to ensure candidates are observable by TESS. Note that,
although the majority of targets from the CTL have $T<13$, the Cool Dwarf list
extends to $T=16$ (for a description of this special list, see Muirhead et
al., 2018).

Additional stars were selected by an equivalent search in the TICv8 (Stassun
et al., 2018, 2019) for stars with $13\leq T<15$ (otherwise the same cuts as
for the CTL are applied), effectively extending the magnitude limit of the
halo dwarf search to $T<15$.

To select stars with halo-like kinematics, we ran a Milky Way Galaxia (Sharma
et al., 2011) simulation of stars within 1kpc. We designed a kinematic cut to
choose halo stars based on only proper motion using this simulation, so that a
Gaia radial velocity was not required. Our Galaxia simulations were run using
the default parameters, which are described in Sharma et al. (2011). In
particular, the Galaxia stellar halo geometry follows the Besançon model of an
oblate spheroid, with density proportional to
$\left(\frac{\mathrm{Max}(a_{c},a)}{R_{\odot}}\right)^{n}$, where
$a^{2}=R^{2}+\frac{z^{2}}{\epsilon^{2}}$, $a_{c}=500\ \mathrm{pc}$,
$\epsilon=0.76$, and $n=-2.44$ (Robin et al., 2003), with $R$ and $z$ denoting
Galactocentric cylindrical radius and height above the plane in pc. Following
Bond et al. (2010), the Galaxia halo velocity distribution is assumed to be an
ellipsoid with $\sigma_{R}=141\ \mathrm{km}\,\mathrm{s}^{-1}$ and
$\sigma_{\theta}=\sigma_{\phi}=75\ \mathrm{km}\,\mathrm{s}^{-1}$, which
describes well the observed SDSS halo velocity distribution within 10kpc
(Smith et al., 2009) as well that of Gaia halo stars (Posti et al., 2018).

The resulting kinematic selection was applied to the CTL/TIC sample, such that
$v_{\delta}<0\ \mathrm{km}/\mathrm{s}$ and either $v_{\alpha}<-230\
\mathrm{km}/\mathrm{s}$, $v_{\alpha}>210\ \mathrm{km}/\mathrm{s}$, or
$v_{\delta}<-\sqrt{(1-((v_{\alpha}+10)\times 220)^{2})}\times 230\
\mathrm{km}/\mathrm{s}$.

Finally, stars were selected to fall below the binary sequence of a MIST 13
Gyr $\rm{[Fe/H]}=-1.0$ (Dotter, 2016; Choi et al., 2016) isochrone in
$J-K_{\rm{s}}$–$L$ space, where the luminosity, $L$, is adopted from the TIC.
The final number of halo dwarf candidates selected in this way is 16940. The
stars passing the kinematic cuts versus those passing the additional binary
main sequence cut are shown in Figure 1. An excerpt from the final sample is
displayed in Table 1. The entire catalog is available electronically in csv
format.

Figure 1: Color-luminosity diagram demonstrating our H-R Diagram selection
criteria. Dwarf halo candidates passing kinematic selection criteria are shown
as a black contour, representing the 95% percentile. The binary main sequence
of a $\rm{[Fe/H]}=-1$ isochrone is shown as the dashed curve, and the
distribution of the dwarf halo candidates falling below this sequence and
therefore chosen as our final sample, is shown as the blue contour.

##  3 Sample Validation

Our sample selection can be tested by looking at the subset of stars with full
3-D kinematics or with metallicities. While the goal of the sample is to
locate metal-poor stars, confirming that the proper-motion selected stars fall
into kinematically hot populations when radial velocities are added is also
valuable, given the correlation between the two properties.

###  3.1 Galactic Velocity Distribution

We calculated the Galactic space velocity (Johnson & Soderblom, 1987) for the
780 stars in the halo sample that had available Gaia DR2 radial velocity data
and the 61 stars in the sample with APOGEE radial velocity data. Because
radial velocity data are not used our selection procedure, we can further
verify the validity of our selection with the galactic space velocity
distribution of the subsample with radial velocity data. The Toomre diagram
(Sandage & Fouts, 1987) in Figure 2 shows that the galactic space velocities
of these stars are all above 200 km/s. We note that the distribution is
consistent with that from the literature that studied metal-poor halo stars,
which have $V_{\mathrm{tot}}>180\ \mathrm{km}\,\mathrm{s}^{-1}$ (e.g., Nissen
& Schuster, 2010; Schuster et al., 2012).

Figure 2: A projection of the stars’ 3-dimensional space velocity onto a
2-dimensional plane, where the x-axis represents velocity in the direction of
galactic rotation (V), and the y-axis represents the magnitude of the vector
sum of radial velocity (U) and velocity perpendicular to the galactic plane
(W). A star’s total velocity is represented by its distance from the origin
point (0,0). For this reason, iso-velocity lines are shown in gray for
readability. All velocities are reported relative to the local standard of
rest. Error bars are approximately 3 km/s along either axis and thus are not
visible on the scale of the plot.

###  3.2 Metallicity Distribution

In addition to the 3-D kinematic verification of the sample, we can also
directly measure the degree to which it is indeed metal-poor by appealing to
independent metallicities from the literature, which have been compiled by the
TIC.

We analyzed the distribution of the TIC metallicities, which are available for
roughly 11% (n = 1,897) of the sample, yielded an overall purity estimate of
$70\%$, the proportion of TIC metallicities which are below the low
metallicity threshold of $\rm{[Fe/H]}=1.0$. We note that while the fraction of
stars in the halo sample which have TIC metallicities is relatively small, the
roughly 2,000 data points available should provide a metallicity distribution
which is sufficiently representative of that of the entire halo sample. The
distribution of these TIC metallicities is shown in Figure 3.

It should be noted the metallicities in the TIC/CTL are compiled from
literature spectroscopic values, and are therefore heterogeneous. In order of
preference, metallicities for the catalogue are adopted from: SPOCS (Brewer et
al., 2016); PASTEL (Soubiran et al., 2016); Gaia-ESO DR3 (Gilmore et al.,
2012); TESS-HERMES DR1 (Sharma et al., 2018); GALAH DR2 (Buder et al., 2018);
APOGEE-2 DR14 (Abolfathi et al., 2018); LAMOST DR4 (Luo et al., 2015); RAVE
DR5 (Kunder et al., 2017); and Geneva-Copenhagen DR3 (Holmberg et al., 2009),
as described in Stassun et al. (2019). While the TIC metallicities may not be
self-consistent and may have a few tenths dex uncertainties, it provides a
representative distribution of the halo dwarf candidate sample metallicities.

Figure 3: The distribution of TIC metallicity values (n = 1,897) of stars in
the sample we selected. From the distribution, we estimate our complete sample
to have a purity of roughly 70%, as both distributions show 70% of their stars
having $\rm{[Fe/H]}<-1.0$.

##  4 Observations of Halo Stars Showing Discrepancies in Stellar Properties

Some of our kinematically-selected halo stars have been previously known and
studied (Reddy et al., 2006; Sozzetti et al., 2009; Boesgaard et al., 2011).
However, there are discrepancies in derived stellar properties such as
effective temperature and surface gravity, both among the literature, and when
the literature is compared to the results of this paper. Table 2 shows
effective temperature, surface gravity, and [Fe/H] values derived by previous
studies. Notable anomalies include the following:

  * •

BD+51 1696, the star measured by the greatest number of studies we compared
with, shows significant spread in both Teff and log(g) between studies.

  * •

In many cases, Boesgaard et al. (2011) derives surface gravities
characteristic of post-main-sequence stars, despite the selection process of
this paper being designed to limit the sample to main sequence dwarfs.

This motivates us to observe 13 previously-known halo stars using the PEPSI
spectrograph (Strassmeier et al., 2015) at the Large Binocular Telescope (LBT,
$2\times 8.4$ m on Mt. Graham, Arizona, USA). The higher spectral resolution
(R=120,000) and a homogeneous abundance analysis, in addition to the external
constraints from the Gaia DR2 data, help to reconcile the discrepancies and
lead to a more accurate determination of stellar properties. We detail the
PEPSI observations and our abundance measurements below.

LBT PEPSI observations were made on March 25, May 15, June 23 and 25, 2019 UT
with 200 $\mu$m fiber ($R=130\,000$ and $1.75^{\prime\prime}$ on sky) in two
spectral regions 4800 - 5441 Å and 6278 - 7419 Å (cross-dispersers (CD) 3 and
5) with 10–60 min integration time depending on the star brightness. A typical
signal-to-noise ratio achieved is 350 in CD5 and 260 in CD3 for a star V=9.7
in one hour integration time with two LBT mirrors. The whole sample has
signal-to-noise ratio ranging from 100 to 600.

Star | Teff (K) | log(g) ([cm/s2]) | [Fe/H]
---|---|---|---
BD+18 3423 | 5943 (S), 5760 (R) | 4.43 (S), 4.59 (R) | -1.00 (S), -0.87 (R)
BD+20 2594 | 5886 (R) | 4.60 (R) | -0.94 (R)
BD+20 3603 | 5908 (B) | 3.61 (B) | -2.18 (B)
BD+25 1981 | 6745 (A) | 4.42 (A) | -1.45 (A)
BD+34 2476 | 6248 (B) | 3.72 (B) | -1.94 (B)
BD+36 2165 | 6052 (B) | 3.78 (B) | -1.71 (B)
BD+42 2667 | 5665 (R), 5793 (A) | 3.92 (R), 3.90 (A) | -1.34 (R), -1.48 (A)
BD+51 1696 | 5852 (B), 5315 (R), 5377 (A) | 4.19 (B), 4.74 (R), 3.90 (A) | -1.21 (B), -1.50 (R), -1.38 (A)
BD+75 839 | 5704 (R) | 4.13 (R) | -0.95 (R)
HD 64090 | 5384 (S), 5500 (B) | 4.70 (S), 4.73 (B) | -1.75 (S), -1.77 (B)
HD 108177 | 6105 (B) | 3.91 (B) | -1.77 (B)
HD 160693 | 5648 (R) | 4.48 (R) | -0.54 (R)
HD 194598 | 5875 (B) | 4.20 (B) | -1.23 (B)
Table 2: Effective temperatures derived by APOGEE DR16 (Jönsson et al., 2020),
Boesgaard et al. (2011), Reddy et al. (2006), and Sozzetti et al. (2009), as
marked by the first letter of the citation.

###  4.1 Data Reduction

The data reduction is done using the Spectroscopic Data Systems (SDS) with its
pipeline adapted to the PEPSI data calibration flow and image specific
content. Its description is given in Strassmeier et al. (2018).

The specific steps of image processing include bias subtraction and variance
estimation of the source images, super-master flat field correction for the
CCD spatial noise, échelle orders definition from the tracing flats, scattered
light subtraction, wavelength solution using ThAr images, optimal extraction
of image slices and cosmic ray removal, wavelength calibration and merging
slices in each order, normalization to the master flat field spectrum to
remove CCD fringes and blaze function, a global 2D fit to the continuum of the
normalized image, and rectification of all spectral orders in the image to a
1D spectrum for a given cross-disperser.

The spectra from two sides of the telescope are averaged with weights into one
spectrum and corrected for the barycentric velocity of the Solar system. The
wavelength scale is preserved for each pixel as given by the wavelength
solution without rebinning. The wavelength solution uses about 3000 ThAr lines
and has an uncertainty of the fit at the image center of 4 m/s.

##  5 Abundance Analysis

###  5.1 PEPSI spectra

To determine the metallicities and stellar parameters of the stars observed
with PEPSI, we first calculated the equivalent widths (EW) of absorption lines
in each star’s spectrum. This was done using an automated program which
displays graphs and measurements from fits of a Voigt and Gaussian
distribution, along with its direct measurement of the observed data. From
this we chose the method which most closely fit the data trend. This manual
screening allows for the best measurements to be kept for all lines,
mitigating the effects of noise, contamination, and improper line fitting. If
these effects are too great, the program allows us to discard the measurement
from the final data.

To streamline this process, if all three EW measurements (Gaussian, Voigt, and
raw) are within 20% of each other, usually the result of a clean, isolated
line feature, the program automatically takes the average of the three and
uses the result as that line’s EW. On the other hand, if both curve fitting
functions fail, the line is automatically discarded without prompting the
user. This latter scenario usually occurs where a line is weak enough that it
is completely drowned out by noise and is indistinguishable from the
continuum.

Line information was compiled from the NIST Atomic Spectra Database (Kramida
et al., 2020). A small section of the PEPSI spectrum for the star HD 160693 is
shown in Figure 4 with line features annotated with their corresponding
species and equivalent width.

For each star, we chose to keep only lines for which EW $>5\text{m\,\AA}$, to
minimize the effects of noise on weak lines in our measurements. Furthermore,
manual sigma-clipping based on each individual line’s derived abundance was
performed after the initial analysis to remove lingering outlying
measurements, after which the process was repeated. This was done twice. A
complete list of our final EW measurements can be found in Table 4.

Figure 4: A range of the PEPSI B-band spectrum of HD 160693, with iron line
features annotated with their corresponding equivalent width.

###  5.2 Iterative MOOG Analysis

To derive abundances and stellar atmospheric parameters, we used a program
written by the authors which combines
PyMOOGi111https://github.com/madamow/pymoogi (Adamow, 2017), which is a Python
implementation of the Fortran code
MOOG222http://www.as.utexas.edu/~chris/moog.html (Sneden, 1973), with several
Python functions designed to iteratively derive stellar parameters,
abundances, and the uncertainties thereof.

We used the ATLAS9 model atmospheres computed for the APOGEE survey (Mészáros
et al., 2012), and the PyKMOD atmosphere
interpolator333https://github.com/kolecki4/PyKMOD to create the model stellar
atmospheres for our analysis. To convert the resulting abundance values into
quantities relative to solar, we took the solar iron abundance
$\rm{[Fe/H]}_{\odot}=7.48$ as stated in Palme et al. (2014).

####  5.2.1 Temperature and Surface Gravity

We used Gaia DR2 (Gaia Collaboration et al., 2018), 2MASS (Skrutskie et al.,
2006), and WISE (Wright et al., 2010) photometry compared against Dartmouth
theoretical isochrones444http://stellar.dartmouth.edu/models/ (Dotter et al.,
2007) to derive Teff and log(g). The photometry was queried from its
respective databases using Astroquery, a module of the Astropy software
library (Price-Whelan et al., 2018). We used distances computed by Bailer-
Jones et al. (2018) to convert these values from apparent to absolute
magnitude.

The process is as follows: the star’s photometric profile is compared against
the synthetic photometry for each age and equivalent evolutionary phase (EEP)
at a fixed [Fe/H] from the Dartmouth isochrones. From this comparison, a
2-dimensional grid of residuals is created in the age-EEP plane. Thus, each
point on the grid represents the sum of the differences of magnitudes at each
pass band between those observed of the star and those from the given point on
the isochrone.

From the absolute minimum point on this grid, we define the area around this
point for which the residuals are within 10% of the minimum as valid points in
the grid from which to extract Teff and log(g) values. The averages of the
resulting temperature and gravity distributions are taken as the parameters
derived from the given metallicity, with the standard deviation of the mean
being taken as the uncertainty.

####  5.2.2 Microturbulence

To determine a value for the microturbulence parameter ($\xi$), we sought to
remove the correlation between reduced equivalent width (REW) and abundance
for Fe I lines. This was done by calculating the slope of this correlation for
a fixed set of microturbulence values (ranging from 0 to 4 km/s), and linearly
interpolating the microturbulence value at which the resulting slope is 0.

In the case where this process did not succeed (for example, if there is no
point where the slope value crosses 0 along the range of microturbulence
values), we chose to follow the convention used by Boesgaard et al. (2011),
which is to simply set microturbulence equal to 1.5 km/s.

####  5.2.3 Details of the Iteration Program

The process first assumes a metallicity of $\rm{[Fe/H]}=-1.0$. From here, it
gets Teff and log(g) values according to Section 5.2.1, and interpolates a
model atmosphere from the grid with these photometric parameters and a
microturbulence set to 1.5 km/s. Then, it runs MOOG with this model atmosphere
and the line list for a given star.

It then reads the MOOG output, gathering the metallicity data and a value for
[Fe/H], and then repeats, now using isochrones of the output [Fe/H] to derive
new parameters for the model atmosphere. Convergence is reached and the
process ends when the metallicity output by MOOG is the same (to within 0.1
dex, the precision of the isochrone grid) as that used to derive that run’s
stellar parameters.

Note that the initial metallicity choice is arbitrary. It is simply used as an
initial guess for the iteration process, which lasts a variable amount of time
based on how accurate this initial guess is.

After the process converges on a solution for [Fe/H], we calculate the
microturbulence as outlined in Section 5.2.2, re-deriving stellar parameters
as necessary as the microturbulence affects the metallicity. At this point,
the program proceeds with the uncertainty analysis.

###  5.3 Uncertainty Analysis

Uncertainty in the microturbulence parameter was determined by perturbing the
microturbulence until the slope of the REW-abundance correlation fell outside
of the uncertainty range.

All other uncertainties, including those for Teff, log(g), and abundances were
calculated using iteration of the process outlined in Section 3.2 of Epstein
et al. (2010). The method used by those authors creates a matrix of partial
derivatives of parameters with respect to one another and uses various
equations to account for the effects of uncertainties in each parameter on the
uncertainties of all the others.

Since, by the methodology outlined in Section 5.2.1, the uncertainty in
metallicity can affect the uncertainty in Teff and log(g), and by the
methodology outlined here, the reverse is also true, we are required to
iterate these calculations repeatedly, using the output uncertainties from one
run as the input uncertainties of the next.

Initial uncertainties were simply taken as the standard deviation of the mean
value derived for each parameter, and the calculations taken from Epstein et
al. were repeated until the [Fe/H] uncertainty was changed by less than 0.01
dex from one iteration to the next.

###  5.4 Results

Star | Teff (K) | log(g) ([cm/s2]) |  $\xi$ (km/s) | [Fe I/H] | [Fe II/H]
---|---|---|---|---|---
BD+18 3423 | 6204 $\pm$ 70 | 4.19 $\pm$ 0.01 | 0.86 $\pm$ 0.21 | -0.874 $\pm$ 0.099 | -0.893 $\pm$ 0.103
BD+20 2594 | 6160 $\pm$ 40 | 4.29 $\pm$ 0.01 | 0.42 $\pm$ 0.29 | -0.838 $\pm$ 0.067 | -0.886 $\pm$ 0.079
BD+20 3603 | 6544 $\pm$ 20 | 4.32 $\pm$ 0.01 | 1.52 $\pm$ 0.28 | -1.982 $\pm$ 0.116 | -2.088 $\pm$ 0.140
BD+25 1981 | 6774 $\pm$ 20 | 4.18 $\pm$ 0.02 | 1.52 $\pm$ 0.24 | -1.551 $\pm$ 0.140 | -1.387 $\pm$ 0.150
BD+34 2476 | 6595 $\pm$ 40 | 4.11 $\pm$ 0.01 | 1.34 $\pm$ 0.21 | -1.884 $\pm$ 0.110 | -1.941 $\pm$ 0.145
BD+36 2165 | 6470 $\pm$ 20 | 4.19 $\pm$ 0.01 | 0.86 $\pm$ 0.23 | -1.359 $\pm$ 0.053 | -1.411 $\pm$ 0.046
BD+42 2667 | 6314 $\pm$ 30 | 4.32 $\pm$ 0.01 | 0.56 $\pm$ 0.27 | -1.265 $\pm$ 0.086 | -1.328 $\pm$ 0.091
BD+51 1696 | 5793 $\pm$ 20 | 4.57 $\pm$ 0.01 | 1.5 $\pm$ 0.71 | -1.424 $\pm$ 0.084 | -1.416 $\pm$ 0.096
BD+75 839 | 6320 $\pm$ 70 | 4.21 $\pm$ 0.05 | 1.10 $\pm$ 0.13 | -0.769 $\pm$ 0.158 | -1.151 $\pm$ 0.164
HD 64090 | 5607 $\pm$ 10 | 4.67 $\pm$ 0.01 | 1.5 $\pm$ 0.78 | -1.650 $\pm$ 0.074 | -1.846 $\pm$ 0.107
HD 108177 | 6410 $\pm$ 40 | 4.33 $\pm$ 0.01 | 0.59 $\pm$ 0.30 | -1.479 $\pm$ 0.113 | -1.502 $\pm$ 0.160
HD 160693 | 5951 $\pm$ 30 | 4.29 $\pm$ 0.01 | 1.5 $\pm$ 0.52 | -0.610 $\pm$ 0.052 | -0.613 $\pm$ 0.078
HD 194598 | 6243 $\pm$ 80 | 4.36 $\pm$ 0.02 | 1.5 $\pm$ 0.40 | -1.131 $\pm$ 0.192 | -1.243 $\pm$ 0.209
Table 4: Stellar Parameters of Selected Sample Stars

We found the stars to fall within a temperature range of $5600\leq$ Teff $\leq
6800$ and a surface gravity range of $4.1\leq log(g)\leq 4.7$. Detailed
stellar parameter and abundance results for each star can be found in Table 4.
The stars also fall well within the expected metallicity values given their
halo classification, as we found them to fall within the range
$-2.0<\rm{[Fe/H]}<-0.6$.

Figure 5: A plot of log(g) versus $(G-Rp)$ color, overlayed with isochrones of
6, 8, 10, and 12 Gyr for each metallicity.

##  6 Discussion

###  6.1 Using Photometric vs Spectroscopic Parameters

One method of deriving stellar parameters involves using the spectroscopic
abundance analysis, adjusting them until the following conditions are met:

1\. Effective Temperature: The star should be in excitation equilibrium, i.e.
the correlation between abundance derived from each line and excitation
potential (EP) should be removed.

2\. Surface Gravity: The star should be in ionization balance, i.e. the
abundances of Fe I and Fe II should be within 1$\sigma$ of each other.

3\. Microturbulence: There should be no correlation between the abundance
derived from each line and reduced equivalent width
($log(\frac{\text{EW}}{\lambda})$).

We followed this method for microturbulence, but our Teff and log(g) values
were derived photometrically from isochrones. However, for every star except
BD+75 839, the resulting log(g) led to ionization balance.

Also, the resulting Teff led to excitation equilibrium for many of the stars,
such that the slope of the EP-abundance regression line was equal to 0 at the
1-sigma level for four stars, and at the 3-sigma for seven, where sigma is
defined as the standard deviation of the linear regression fit assuming normal
distribution of residuals.

Two stars (HD 64090 and HD 160693) featured slopes which were 4-sigma away
from zero. Notably however, these two stars were also unable to achieve
microturbulence convergence.

####  6.1.1 Comparison with Previous Results

For the six stars in common with Reddy et al. (2006), the mutual discrepancy
between metallicities is on average 0.06 dex, which we consider to be
reasonably identical within a margin of error. Their process of determining
stellar parameters was similar to ours in that it also does not rely on
spectroscopy for Teff and log(g). They use $(b-y)$ and $(V-K_{\mathrm{s}})$ to
derive Teff, whereas we use magnitudes, rather than colors, and use $G$, $Bp$,
$Rp$, $J$, $H$, $K_{\mathrm{s}}$, $W1$, $W2$, $W3$, and $W4$.

For surface gravities, they make use of Hipparcos astrometry whereas we use
the same photometric method for log(g) as was used for Teff. And lastly, for
microturbulence, they use a previously-calculated relation between other
parameters and $\xi$ for metal-poor dwarfs, where we in this case use the
spectroscopic approach for microturbulence.

We also compared our results with those for the seven stars our sample shares
with Boesgaard et al. (2011). In the paper, they determined the stellar
parameters spectroscopically according to the conditions in Section 6.1. Their
metallicities are systematically lower than ours by an average of 0.19 dex,
except in the case of BD+51 1696, where theirs is higher by 0.23 dex.

Although similar stellar parameter convergence conditions (ionization balance,
excitation equilibrium, microturbulence convergence) were met to a degree of
uncertainty in both papers, it can be seen in Tables 2 and 4 that the
resulting parameters are in many cases quite different, especially surface
gravity.

From these discrepancies we can assume the importance of the additional
photometric constraints on the parameters.

Based on the available information, it seems that the spectroscopic method can
lead to cases where there are multiple points in the Teff-log(g)-$\xi$
parameter space where the convergence conditions are met. This leaves the
chance that, if additional constraints are not used, any given analysis may
not necessarily converge on the correct point, leading to parameters which
conflict with other stellar data.

###  6.2 The Negligibility of non-LTE Corrections

We investigated the magnitude of the effects of the LTE assumption on our
final abundance measurements. We accessed data from Bergemann et al. (2012)
via a web tool by M. Kovalev et al. (2018), and discovered that all
corrections for lines we tested were within our metallicity uncertainty
thresholds, thus making them negligible corrections to our measurements.

##  7 Summary and Conclusion

In this paper we discuss our selection process for metal-poor halo stars,
detailing kinematic and photometric criteria resulting in a final sample of
$\sim 16,940$ stars, where $\rm{[Fe/H]}<-1.0$ for roughly $70\%$ of the stars
included based on comparison to literature metallicities.

We also present a re-analysis of 13 halo stars from the literature using new
observations taken with the high-resolution PEPSI spectrograph, attempting to
rectify discrepancies of stellar properties in the literature. We measure the
metallicity of these stars to an accuracy of roughly
$\sigma(\rm{[Fe/H]})=0.1~{}\text{dex}$. In this process, we also used Gaia,
2MASS, and WISE photometry to derive accurate effective temperature and
surface gravity values using Dartmouth theoretical isochrones.

In summary, given the overall fidelity of our sample, the halo dwarf
candidates presented here will prove to be useful targets for planet studies
in metal-poor host systems with TESS. An analysis of the sample in the context
of planet occurrence rates in this metal-poor regime is described in Boley et
al. 2021, the companion to this paper.

JCZ supported by an NSF Astronomy and Astrophysics Postdoctoral Fellowship
under award AST-2001869. This work has made use of data from the European
Space Agency (ESA) mission Gaia (https://www.cosmos.esa.int/gaia), processed
by the Gaia Data Processing and Analysis Consortium (DPAC,
https://www.cosmos.esa.int/web/gaia/dpac/consortium). Funding for the DPAC has
been provided by national institutions, in particular the institutions
participating in the Gaia Multilateral Agreement. This research made use of
Astropy,555http://www.astropy.org a community-developed core Python package
for Astronomy (Astropy Collaboration et al., 2013, 2018). PEPSI was made
possible by funding through the State of Brandenburg (MWFK) and the German
Federal Ministry of Education and Research (BMBF) through their
Verbundforschung grants 05AL2BA1/3 and 05A08BAC. The LBT is an international
collaboration among institutions in the United States, Italy and Germany. LBT
Corporation partners are: The University of Arizona on behalf of the Arizona
Board of Regents; Istituto Nazionale di Astrofisica, Italy; LBT
Beteiligungsgesellschaft, Germany, representing the Max-Planck Society, The
Leibniz Institute for Astrophysics Potsdam, and Heidelberg University; The
Ohio State University, representing OSU, University of Notre Dame, University
of Minnesota and University of Virginia. Funding for the Sloan Digital Sky
Survey IV has been provided by the Alfred P. Sloan Foundation, the U.S.
Department of Energy Office of Science, and the Participating Institutions.
SDSS-IV acknowledges support and resources from the Center for High
Performance Computing at the University of Utah. The SDSS website is
www.sdss.org. SDSS-IV is managed by the Astrophysical Research Consortium for
the Participating Institutions of the SDSS Collaboration including the
Brazilian Participation Group, the Carnegie Institution for Science, Carnegie
Mellon University, Center for Astrophysics — Harvard & Smithsonian, the
Chilean Participation Group, the French Participation Group, Instituto de
Astrofísica de Canarias, The Johns Hopkins University, Kavli Institute for the
Physics and Mathematics of the Universe (IPMU) / University of Tokyo, the
Korean Participation Group, Lawrence Berkeley National Laboratory, Leibniz
Institut für Astrophysik Potsdam (AIP), Max-Planck-Institut für Astronomie
(MPIA Heidelberg), Max-Planck-Institut für Astrophysik (MPA Garching), Max-
Planck-Institut für Extraterrestrische Physik (MPE), National Astronomical
Observatories of China, New Mexico State University, New York University,
University of Notre Dame, Observatário Nacional / MCTI, The Ohio State
University, Pennsylvania State University, Shanghai Astronomical Observatory,
United Kingdom Participation Group, Universidad Nacional Autónoma de México,
University of Arizona, University of Colorado Boulder, University of Oxford,
University of Portsmouth, University of Utah, University of Virginia,
University of Washington, University of Wisconsin, Vanderbilt University, and
Yale University.

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Table 4: Table of PEPSI equivalent widths

Line Information | Equivalent Width for Given Star [mÅ]
---|---
|  |  |  | BD+18 | BD+20 | BD+20 | BD+25 | BD+34 | BD+36 | BD+42 | BD+51 | BD+75 | HD | HD | HD | HD
Element |  $\lambda$ [Å] | EP [eV] | log($gf$) | 3423 | 2594 | 3603 | 1981 | 2476 | 2165 | 2667 | 1696 | 839 | 64090 | 108177 | 160693 | 194598
Fe I | 4745.8 | 3.65 | -1.27 | … | 23.91 | … | … | … | … | … | … | … | … | 5.81 | … | …
Fe I | 4771.7 | 2.2 | -3.23 | 11.71 | … | … | … | … | … | … | … | 11.4 | … | … | 25.29 | …
Fe I | 4772.83 | 3.02 | -2.19 | 28.42 | … | … | … | … | … | 14.16 | … | … | … | 8.71 | … | …
Fe I | 4779.44 | 3.41 | -2.02 | 6.56 | 7.01 | … | … | … | … | … | … | … | … | … | … | …
Fe I | 4786.81 | 3.02 | -1.61 | … | 30.34 | … | … | … | 9.26 | 15.46 | … | … | 23.91 | 7.5 | 54.96 | …
Fe I | 4788.76 | 3.24 | -1.76 | … | … | … | … | … | 7.71 | 7.65 | … | … | 9.5 | 5.04 | 43.47 | …
Fe I | 4789.65 | 3.55 | -0.96 | 37.14 | … | … | 8.59 | 7.03 | 14.4 | … | … | … | 26.11 | 11.05 | 60.75 | 28.97
Fe I | 4791.25 | 3.27 | -2.44 | … | 9.4 | … | … | … | … | … | … | … | … | … | … | …
Fe I | 4798.26 | 4.19 | -1.17 | … | … | … | … | … | … | … | … | … | 6.76 | 7.43 | … | …
Fe I | 4799.41 | 3.64 | -2.19 | … | 6.36 | … | … | … | … | … | … | … | … | … | … | …
Fe I | 4800.65 | 4.14 | -1.03 | 14.06 | … | … | … | … | … | … | … | … | … | … | … | …
Fe I | 4807.71 | 3.37 | -2.15 | 6.22 | … | … | … | … | … | … | … | … | … | … | … | …
Fe I | 4817.78 | 2.22 | -3.44 | 6.27 | 6.52 | … | … | … | … | … | 5.78 | 7.45 | … | … | 20.91 | 7.29
Fe I | 4840.32 | 4.15 | -1.37 | 15.44 | 18.34 | … | … | … | … | 5.59 | … | 18.61 | 7.76 | … | … | 14.73
Fe I | 4843.14 | 3.4 | -1.79 | 13.01 | … | … | … | … | … | … | … | … | 8.5 | … | … | 11.55
Fe I | 4844.01 | 3.55 | -2.05 | … | 7.08 | … | … | … | … | … | … | … | … | … | … | 9.61
Fe I | 4848.88 | 2.28 | -3.14 | 11.0 | … | … | … | … | … | … | … | 8.74 | … | … | 21.66 | …
Fe I | 4859.74 | 2.88 | -0.76 | … | … | 22.16 | … | … | … | … | … | 72.53 | 70.49 | 34.51 | … | 55.71
Fe I | 4871.32 | 2.87 | -0.36 | 94.34 | 97.44 | 34.28 | 43.09 | 44.82 | 62.12 | 72.72 | 103.84 | 110.34 | 100.73 | 58.46 | 134.97 | 83.21
Fe I | 4872.14 | 2.88 | -0.57 | 78.32 | 78.33 | 26.47 | 35.35 | 26.95 | 50.2 | 57.8 | 83.18 | 88.31 | 77.35 | 47.04 | 110.34 | 64.51
Fe I | 4875.88 | 3.33 | -1.97 | 12.49 | 14.03 | … | … | … | … | … | … | 14.61 | 6.09 | … | … | …
Fe I | 4881.72 | 3.3 | -1.78 | 14.65 | … | … | … | … | … | 5.37 | … | … | … | … | … | 8.38
Fe I | 4889.0 | 2.2 | -2.55 | … | … | … | … | … | 10.15 | … | … | … | … | 5.23 | … | …
Fe I | 4891.49 | 2.85 | -0.11 | 111.2 | 117.93 | 49.41 | 62.54 | 51.27 | 76.5 | 87.48 | 131.74 | 139.1 | 127.0 | 72.98 | 168.85 | 107.42
Fe I | 4903.31 | 2.88 | -0.93 | 72.72 | 75.65 | 17.02 | 25.24 | 17.54 | 38.19 | 48.75 | 73.17 | 79.84 | 71.12 | 33.83 | 105.26 | 61.37
Fe I | 4920.5 | 2.83 | 0.07 | 134.03 | 148.25 | 61.51 | 76.55 | 61.6 | 89.51 | 101.31 | 169.58 | 177.64 | 159.56 | 83.6 | 218.67 | 120.04
Fe I | 4927.42 | 3.57 | -2.07 | 7.2 | … | … | … | … | … | … | … | … | … | … | 23.43 | 5.78
Fe I | 4938.81 | 2.88 | -1.08 | 62.52 | 65.44 | … | 18.69 | 14.07 | 29.05 | 40.53 | 63.04 | 69.52 | 59.05 | 30.85 | 94.06 | …
Fe I | 4942.46 | 4.22 | -1.41 | 16.6 | 17.7 | … | … | … | … | 6.46 | … | 19.92 | 7.46 | … | … | 8.59
Fe I | 4957.3 | 2.85 | -0.41 | … | … | 70.77 | … | … | … | … | … | … | … | … | … | …
Fe I | 4962.57 | 4.18 | -1.18 | 11.07 | 11.81 | … | … | … | … | 6.7 | 10.57 | … | … | … | … | 7.59
Fe I | 4968.7 | 3.64 | -1.74 | 10.96 | 12.1 | … | … | … | … | … | … | 8.51 | … | … | 32.74 | 9.11
Fe I | 4973.1 | 3.96 | -0.92 | 30.15 | 32.63 | … | 7.06 | … | 10.04 | 15.94 | … | … | 18.35 | 9.29 | 60.25 | 23.31
Fe I | 4985.25 | 3.93 | -0.56 | … | 44.99 | … | … | 6.31 | 17.37 | … | … | … | 40.16 | 14.02 | 67.79 | …
Fe I | 4986.22 | 4.22 | -1.37 | 7.15 | … | … | … | … | … | … | … | … | … | … | … | 11.72
Fe I | 4991.87 | 4.22 | -1.89 | … | … | … | … | … | … | … | … | … | … | … | 8.35 | …
Fe I | 4994.13 | 0.91 | -3.08 | 60.37 | … | 9.78 | 10.76 | 10.06 | 26.5 | … | … | … | 62.06 | 28.73 | 82.09 | …
Fe I | 5002.79 | 3.4 | -1.53 | … | 21.66 | … | … | … | 6.34 | 9.5 | … | … | 10.3 | 6.2 | … | …
Fe I | 5006.12 | 2.83 | -0.61 | 87.01 | 88.24 | 27.47 | 33.97 | 29.46 | 53.98 | 64.69 | 91.09 | 97.35 | 83.33 | 50.79 | 115.72 | 76.32
Fe I | 5021.59 | 4.26 | -0.68 | … | … | … | … | … | … | … | 8.2 | … | 5.18 | … | 43.13 | 8.9
Fe I | 5022.79 | 2.99 | -2.2 | 23.42 | … | … | … | … | 8.78 | … | … | … | … | 9.0 | … | …
Fe I | 5029.62 | 3.41 | -2.0 | 7.65 | … | … | … | … | … | … | … | … | … | … | … | …
Fe I | 5039.25 | 3.37 | -1.57 | 23.65 | 26.86 | … | 7.98 | … | 7.5 | … | … | … | 12.64 | 6.16 | 63.26 | 23.21
Fe I | 5041.76 | 1.48 | -2.2 | … | … | 25.8 | 41.25 | 28.64 | 48.25 | … | … | … | 83.97 | 38.49 | … | …
Fe I | 5048.44 | 3.96 | -1.03 | 13.79 | 15.48 | … | … | … | … | … | 13.31 | … | 7.79 | … | … | …
Fe I | 5051.63 | 0.91 | -2.79 | 72.0 | 74.84 | 17.85 | 17.83 | 17.22 | 39.41 | 52.08 | 73.18 | 78.21 | 72.27 | 42.05 | 106.32 | 64.5
Fe I | 5056.84 | 4.26 | -1.94 | … | … | … | … | … | … | … | … | … | 5.15 | … | 12.15 | …
Fe I | 5065.19 | 3.64 | -1.51 | … | … | … | … | … | 20.68 | … | … | … | … | … | … | …
Fe I | 5074.75 | 4.22 | -0.23 | 53.47 | 55.03 | 9.87 | 20.26 | 10.84 | 23.81 | 33.03 | 48.97 | 58.34 | 40.32 | 19.17 | 81.82 | 46.8
Fe I | 5079.74 | 0.99 | -3.22 | 47.88 | … | 6.52 | 6.32 | 6.64 | … | … | … | … | 50.52 | 18.33 | 63.97 | …
Fe I | 5083.34 | 0.96 | -2.96 | 62.52 | 64.78 | 10.88 | 11.57 | 12.78 | 31.33 | … | … | 69.25 | 64.36 | 32.93 | 84.45 | …
Fe I | 5090.77 | 4.26 | -0.44 | 32.68 | 34.97 | … | 7.24 | … | 11.33 | 15.41 | 26.12 | … | 16.47 | 9.28 | 60.36 | 24.18
Fe I | 5107.45 | 0.99 | -3.09 | … | … | … | … | … | … | … | … | … | 53.81 | … | … | …
Fe I | 5121.64 | 4.28 | -0.81 | 22.61 | 24.59 | … | … | … | 6.33 | 9.69 | 16.65 | 25.87 | 11.77 | 6.74 | 57.18 | 20.66
Fe I | 5126.19 | 4.26 | -1.06 | 17.49 | 16.84 | … | … | … | … | 6.14 | … | 19.06 | 8.29 | … | 43.2 | …
Fe I | 5131.47 | 2.22 | -2.52 | 25.91 | … | … | … | … | 7.71 | 11.98 | … | … | 20.85 | 5.17 | 52.63 | …
Fe I | 5137.38 | 4.18 | -0.43 | 39.25 | 44.57 | 6.4 | 13.2 | 6.77 | 15.09 | 22.68 | … | 48.43 | 31.01 | 16.43 | 61.45 | 35.93
Fe I | 5139.46 | 2.94 | -0.51 | … | … | … | 67.72 | … | … | … | … | … | … | … | … | …
Fe I | 5142.93 | 0.96 | -3.07 | 57.51 | … | 7.11 | … | 7.23 | 19.08 | … | … | … | 49.85 | 15.72 | … | 44.7
Fe I | 5145.09 | 2.2 | -2.88 | 9.18 | … | … | … | … | … | … | … | … | 6.03 | … | … | …
Fe I | 5150.84 | 0.99 | -3.04 | 56.46 | … | 7.75 | 9.04 | 7.47 | 26.11 | … | … | … | 55.77 | 21.1 | 82.55 | …
Fe I | 5191.45 | 3.04 | -0.55 | 81.72 | 85.81 | 21.17 | 36.94 | 31.54 | 48.4 | 57.26 | 82.5 | 90.26 | 73.82 | 43.15 | 116.99 | 70.19
Fe I | 5194.94 | 1.56 | -2.09 | 74.43 | 74.84 | 19.21 | 24.39 | 24.1 | 44.06 | 54.9 | … | 78.41 | 74.36 | 44.82 | 94.94 | 65.24
Fe I | 5198.71 | 2.22 | -2.13 | 46.0 | … | 6.14 | 8.07 | 6.42 | 16.55 | 23.56 | … | 51.54 | 38.6 | 15.54 | 72.51 | …
Fe I | 5216.27 | 1.61 | -2.15 | 68.63 | 67.94 | 16.14 | 22.4 | 16.43 | 38.2 | 48.02 | 67.49 | 71.81 | 68.32 | 34.06 | 83.55 | 62.54
Fe I | 5217.92 | 3.64 | -1.72 | … | … | … | … | … | … | … | … | … | … | … | 23.2 | …
Fe I | 5227.19 | 1.56 | -1.23 | … | … | 57.91 | 73.33 | 53.74 | 86.02 | 97.46 | … | … | 136.77 | 76.45 | … | 119.4
Fe I | 5232.94 | 2.94 | -0.06 | 112.07 | 117.43 | 48.99 | 62.03 | 49.7 | 76.82 | 95.95 | 130.86 | 138.0 | 125.58 | 70.99 | 171.82 | 103.27
Fe I | 5243.78 | 4.26 | -1.12 | 14.24 | 13.95 | … | … | … | 5.06 | … | … | … | 6.42 | … | … | 11.3
Fe I | 5249.1 | 4.47 | -1.46 | … | … | … | … | … | … | … | … | … | … | … | 12.38 | …
Fe I | 5250.65 | 2.2 | -2.18 | 49.19 | 50.66 | 6.97 | 9.51 | 6.04 | 20.38 | 25.95 | … | … | 44.32 | 18.22 | 76.89 | …
Fe I | 5263.31 | 3.27 | -0.88 | 52.22 | 56.17 | 8.11 | 15.25 | 9.03 | 20.55 | 30.08 | … | 62.35 | 44.68 | 24.12 | 83.84 | 43.75
Fe I | 5266.55 | 3.0 | -0.39 | 90.93 | 94.44 | 30.74 | 44.01 | 32.28 | 55.72 | 69.06 | 99.47 | 106.86 | 92.62 | 52.92 | 132.83 | 86.05
Fe I | 5269.54 | 0.86 | -1.32 | 139.63 | 148.5 | 87.84 | 91.56 | 89.25 | 107.52 | 115.91 | 195.96 | 192.7 | 210.94 | 104.01 | 222.9 | 133.64
Fe I | 5273.16 | 3.29 | -0.99 | … | … | … | 19.04 | … | … | 18.42 | … | … | 25.42 | … | … | …
Fe I | 5280.36 | 3.64 | -1.82 | 6.12 | 6.77 | … | … | … | … | … | 5.08 | 8.41 | … | … | 21.48 | …
Fe I | 5283.62 | 3.24 | -0.53 | 78.11 | 79.69 | 20.47 | 26.21 | 22.69 | 43.53 | 53.35 | 82.63 | 88.85 | 70.51 | 39.15 | 119.43 | 69.63
Fe I | 5293.96 | 4.14 | -1.84 | … | … | … | … | … | … | … | … | … | … | … | 10.79 | …
Fe I | 5295.31 | 4.42 | -1.67 | … | … | … | … | … | … | … | … | … | … | … | 10.95 | …
Fe I | 5302.3 | 3.28 | -0.72 | 61.32 | 64.31 | 11.32 | 19.42 | 11.11 | 26.23 | 34.52 | 58.44 | 69.8 | 56.39 | 22.92 | 87.26 | 55.43
Fe I | 5322.04 | 2.28 | -2.8 | 11.72 | 13.41 | … | … | … | … | … | … | … | 8.2 | … | … | 8.73
Fe I | 5328.53 | 1.56 | -1.85 | … | … | 24.83 | 29.08 | 24.21 | 44.31 | 62.23 | 90.02 | 104.43 | … | 44.05 | … | 75.62
Fe I | 5339.93 | 3.27 | -0.72 | 66.34 | 68.81 | 14.1 | 24.22 | 16.01 | 32.78 | 43.2 | 72.66 | 77.94 | 66.11 | 28.12 | 100.25 | 63.71
Fe I | 5361.62 | 4.42 | -1.41 | 6.99 | … | … | … | … | … | … | … | … | … | … | 20.61 | 6.28
Fe I | 5364.87 | 4.45 | 0.23 | 56.4 | 57.61 | 11.95 | 23.01 | 12.69 | 25.7 | 32.99 | 50.5 | 60.11 | 42.8 | 21.29 | 85.93 | 47.87
Fe I | 5367.47 | 4.42 | 0.44 | 61.26 | 65.15 | 14.85 | 30.0 | 15.42 | 36.21 | 40.67 | 57.48 | 69.13 | 51.06 | 27.9 | 93.46 | 52.63
Fe I | 5371.49 | 0.96 | -1.65 | 121.69 | 124.19 | 69.85 | 74.24 | 70.63 | 91.45 | 100.52 | 141.71 | 146.97 | 146.45 | 88.47 | 183.75 | 112.16
Fe I | 5387.48 | 4.14 | -2.03 | … | … | … | … | … | … | … | … | … | … | … | 10.0 | …
Fe I | 5395.22 | 4.45 | -2.15 | … | … | … | … | … | … | … | … | … | … | … | 6.25 | …
Fe I | 5398.28 | 4.45 | -0.71 | 24.96 | 22.7 | … | … | … | 5.81 | 7.84 | … | 22.3 | 8.67 | 5.13 | 41.73 | 15.8
Fe I | 5409.13 | 4.37 | -1.27 | 10.16 | 9.9 | … | … | … | … | … | 6.21 | 10.31 | … | … | 26.97 | …
Fe I | 5412.78 | 4.43 | -1.72 | … | … | … | … | … | … | … | … | … | … | … | 6.41 | …
Fe I | 5415.2 | 4.39 | 0.64 | 72.72 | 73.96 | 20.42 | 46.14 | 26.22 | 41.52 | 49.0 | 70.69 | 81.4 | 58.4 | 36.36 | 107.92 | 63.53
Fe I | 5429.7 | 0.96 | -1.88 | 113.05 | … | 56.91 | … | … | … | … | … | 135.87 | … | … | … | 101.72
Fe I | 6230.72 | 2.56 | -1.28 | … | 75.92 | … | 26.94 | … | … | … | 85.09 | … | … | 35.41 | 103.37 | …
Fe I | 6232.64 | 3.65 | -1.22 | … | 21.81 | … | … | … | … | … | 24.0 | … | … | 5.38 | 53.38 | …
Fe I | 6246.32 | 3.6 | -0.88 | 47.63 | 49.97 | … | 11.78 | 5.72 | 22.85 | 22.5 | 45.03 | 54.34 | 31.09 | 17.06 | 79.33 | 39.93
Fe I | 6254.26 | 2.28 | -2.43 | 41.36 | 46.45 | … | 9.41 | 5.3 | 13.71 | 20.55 | 36.57 | 48.02 | 29.89 | 12.16 | 83.31 | 34.12
Fe I | 6265.13 | 2.18 | -2.55 | 29.88 | 32.93 | … | … | … | 12.48 | 14.35 | 31.2 | 38.16 | 26.88 | 8.48 | 61.66 | 24.82
Fe I | 6271.28 | 3.33 | -2.7 | … | … | … | … | … | … | … | … | … | … | … | 8.77 | …
Fe I | 6297.79 | 2.22 | -2.74 | … | … | … | … | … | … | 10.11 | … | 25.8 | 16.49 | … | 44.78 | …
Fe I | 6311.5 | 2.83 | -3.14 | … | … | … | … | … | … | … | … | … | … | … | 9.16 | …
Fe I | 6315.81 | 4.08 | -1.66 | … | 5.8 | … | … | … | … | … | … | … | … | … | 19.03 | …
Fe I | 6322.68 | 2.59 | -2.43 | 22.39 | 24.56 | … | … | … | … | … | … | 21.35 | 14.2 | … | 47.66 | 17.92
Fe I | 6335.33 | 2.2 | -2.18 | 42.75 | 45.45 | … | 6.91 | 7.98 | 16.03 | 23.7 | 43.4 | 48.18 | 40.32 | 14.86 | 69.96 | 38.44
Fe I | 6358.63 | 4.14 | -1.66 | 13.49 | … | … | … | … | … | … | … | … | … | … | … | …
Fe I | 6362.88 | 4.19 | -1.93 | … | … | … | … | … | … | … | … | … | … | … | 11.66 | …
Fe I | 6380.74 | 4.19 | -1.38 | 8.93 | 9.95 | … | … | … | … | … | 7.0 | 10.96 | … | … | 26.4 | …
Fe I | 6411.65 | 3.65 | -0.72 | 55.59 | 57.66 | 9.44 | 16.09 | 8.62 | 24.7 | 28.94 | 51.68 | 64.2 | 39.1 | 22.03 | 86.66 | 47.79
Fe I | 6421.35 | 2.28 | -2.03 | 51.19 | 54.44 | 8.08 | 10.89 | 7.71 | 25.17 | 29.54 | 53.3 | 59.53 | 44.97 | 20.33 | 80.75 | 44.82
Fe I | 6462.71 | 0.91 | -2.17 | 111.95 | 118.53 | 35.47 | 61.83 | 51.95 | 68.61 | 74.57 | 107.31 | 127.47 | … | 62.35 | 162.69 | 91.61
Fe I | 6469.19 | 4.83 | -0.81 | 8.85 | 10.94 | … | … | … | … | … | 6.32 | 9.63 | 6.75 | … | 24.57 | …
Fe I | 6481.87 | 2.28 | -2.98 | 11.86 | 17.6 | … | … | … | … | 6.05 | 14.34 | … | 17.01 | 8.1 | 35.66 | 13.54
Fe I | 6495.74 | 4.83 | -0.92 | 5.98 | 6.07 | … | … | … | … | … | … | … | … | … | 14.93 | …
Fe I | 6533.93 | 4.56 | -1.43 | … | 10.2 | … | … | … | … | … | … | 6.64 | … | … | 13.28 | …
Fe I | 6569.21 | 4.73 | -0.45 | 21.93 | 28.97 | … | … | … | 5.6 | 6.43 | 14.5 | 20.96 | 9.35 | … | 41.69 | 13.92
Fe I | 6575.02 | 2.59 | -2.71 | 11.91 | 12.37 | … | … | … | … | … | … | 14.36 | 10.66 | … | … | …
Fe I | 6592.91 | 2.73 | -1.47 | 52.35 | 55.56 | 7.76 | 10.89 | 8.94 | 26.93 | 30.0 | 53.43 | 63.27 | 44.46 | 21.48 | 80.02 | 42.6
Fe I | 6597.56 | 4.8 | -1.05 | 6.26 | 8.17 | … | … | … | … | … | … | 7.38 | … | … | 17.64 | …
Fe I | 6752.71 | 4.64 | -1.2 | … | … | … | … | … | … | … | … | … | … | … | 13.29 | …
Fe I | 6786.86 | 4.19 | -2.02 | … | … | … | … | … | … | … | … | … | … | … | 8.9 | …
Fe I | 6804.0 | 4.65 | -1.5 | … | … | … | … | … | … | … | … | … | … | … | 5.36 | …
Fe I | 6820.37 | 4.64 | -1.29 | 5.31 | 5.53 | … | … | … | … | … | … | 5.68 | … | … | 16.6 | …
Fe I | 6839.83 | 2.56 | -3.35 | … | … | … | … | … | … | … | … | … | … | … | 10.08 | …
Fe I | 6842.69 | 4.64 | -1.29 | 5.72 | 5.67 | … | … | … | … | … | … | … | … | … | 15.29 | …
Fe I | 6858.15 | 4.61 | -0.93 | 8.97 | 8.84 | … | … | … | … | … | 6.43 | 9.2 | … | … | 23.25 | …
Fe I | 6885.75 | 4.65 | -1.35 | … | … | … | … | … | … | … | … | … | … | … | 13.56 | …
Fe I | 6945.2 | 2.42 | -2.48 | 23.27 | 26.11 | … | … | … | … | … | 23.58 | 48.61 | 38.05 | … | 54.17 | 22.53
Fe I | 6978.85 | 2.48 | -2.5 | 29.39 | 22.71 | … | … | … | 7.35 | 13.13 | 22.02 | 26.6 | 18.43 | … | 51.25 | 23.38
Fe I | 7016.39 | 4.15 | -1.21 | 10.17 | 19.33 | … | … | … | … | … | 7.94 | … | … | … | 24.14 | …
Fe I | 7038.22 | 4.22 | -1.25 | 12.83 | 12.54 | … | … | … | … | … | … | 13.17 | … | … | 31.47 | …
Fe I | 7090.38 | 4.23 | -1.16 | 13.03 | 13.0 | … | … | … | 6.81 | … | 9.89 | 15.77 | 5.69 | … | 31.6 | …
Fe I | 7132.99 | 4.08 | -1.63 | … | 7.51 | … | … | … | … | … | … | 7.9 | 7.02 | … | 18.99 | …
Fe I | 7223.66 | 3.02 | -2.21 | 13.73 | 14.1 | … | … | … | … | … | 13.08 | … | … | … | 36.3 | …
Fe I | 7320.68 | 4.56 | -1.16 | … | … | … | … | … | … | … | 5.39 | … | … | … | … | …
Fe I | 7401.68 | 4.19 | -1.35 | 5.86 | 5.97 | … | … | … | … | … | 5.99 | 6.36 | 6.72 | … | 18.08 | …
Fe II | 4923.92 | 2.89 | -1.21 | … | … | 61.07 | 98.8 | 68.36 | 85.16 | 87.14 | … | … | 67.26 | 74.75 | … | 87.54
Fe II | 4993.35 | 2.81 | -3.7 | 14.69 | … | … | … | … | … | 6.15 | … | … | 5.18 | … | … | …
Fe II | 5018.44 | 2.89 | -1.35 | 128.21 | 123.3 | 70.3 | … | 78.67 | 94.38 | 93.62 | 88.48 | 110.97 | 70.94 | 91.68 | 174.78 | 104.18
Fe II | 5169.03 | 2.89 | -0.87 | 171.52 | 170.11 | 84.76 | 118.12 | 92.37 | 128.49 | 127.63 | 148.12 | 166.03 | 123.73 | 118.06 | 224.53 | 144.14
Fe II | 5197.57 | 3.23 | -2.05 | 56.14 | 52.55 | 13.19 | … | 16.92 | 32.42 | 34.12 | … | … | 14.72 | 23.82 | 64.5 | 42.88
Fe II | 5234.62 | 3.22 | -2.21 | 62.39 | 58.04 | 15.36 | 39.93 | 20.25 | 35.53 | 38.73 | … | … | 19.49 | 26.8 | 67.6 | 52.91
Fe II | 5264.8 | 3.23 | -3.23 | 18.58 | 23.48 | … | 7.75 | … | 7.05 | … | … | … | … | … | … | …
Fe II | 5276.0 | 3.2 | -1.9 | … | … | 17.82 | 46.79 | 21.28 | 39.31 | 41.56 | 35.51 | … | 25.65 | 30.82 | … | 49.99
Fe II | 5284.1 | 2.89 | -3.2 | 29.55 | … | … | 10.24 | … | 11.65 | 13.07 | 11.24 | … | 5.97 | … | … | 19.82
Fe II | 5325.55 | 3.22 | -3.26 | 21.1 | 14.11 | … | 6.55 | … | 6.09 | … | 5.33 | … | … | … | … | …
Fe II | 5414.07 | 3.22 | -3.48 | 9.52 | … | … | … | … | … | … | … | … | … | … | 13.45 | 7.44
Fe II | 5425.25 | 3.2 | -3.4 | 14.01 | … | … | … | … | 5.85 | 5.72 | … | … | … | … | … | 16.31
Fe II | 6238.39 | 3.89 | -2.8 | 16.23 | 15.9 | … | 8.26 | … | 7.01 | 5.82 | 5.35 | 9.93 | … | … | 27.33 | …
Fe II | 6247.56 | 3.89 | -2.4 | 27.82 | 23.2 | … | 13.69 | 5.7 | 14.11 | 12.21 | 9.97 | 17.34 | … | 6.38 | 34.77 | 17.85
Fe II | 6416.92 | 3.89 | -2.9 | 15.78 | 12.79 | … | 6.44 | … | 5.89 | 6.11 | 6.04 | 8.18 | … | … | 21.65 | …
Fe II | 6432.68 | 2.89 | -3.5 | 15.87 | 13.75 | … | 6.64 | … | 5.44 | 6.33 | 6.27 | 10.64 | … | … | 21.88 | …
Fe II | 6456.38 | 3.9 | -2.2 | 37.7 | 27.7 | 6.36 | 14.96 | 8.33 | 18.17 | 21.76 | 14.16 | 24.18 | 6.24 | 11.05 | 44.9 | 26.26
Fe II | 6516.08 | 2.89 | -3.37 | 21.96 | 19.68 | … | 16.21 | … | 8.53 | 10.31 | 10.51 | 16.72 | … | 17.13 | 58.95 | 16.44
Fe II | 7222.39 | 3.89 | -3.4 | … | … | … | … | … | … | … | … | … | … | … | 14.85 | …
Fe II | 7224.48 | 3.89 | -3.4 | … | … | … | … | … | … | … | … | … | … | … | 11.17 | …

Note. — Only those lines that we were able to measure for at least one star
are listed. The line information section includes element, wavelength,
excitation potential, and line strength data. Lines measured as weaker than
the 5mÅ cutoff are not included in this table.


# Danish National Election 2022 Twitter Data on Likes, Retweets, and Botscores
for the purpose of exploring Coordinated Inauthenthic Behavior

Laura Jahn1 and Rasmus K. Rendsvig2

1,2: Center for Information and Bubble Studies, University of Copenhagen
1<EMAIL_ADDRESS>ORCID: 0000-0002-5475-8496
2<EMAIL_ADDRESS>ORCID: 0000-0002-5475-8496

This note primarily contains the README.md from the GitHub repository of the
same name, with a few additional comments and references. We upload the note
for visibility, hoping that other researchers may find the data of use.

The repository contains code related to the dataset on the Danish National
Election 2022, available at Harvard Dataverse. See the directory _Data from
Danish Twitter on National Election 2022_ in the Harvard repository.

We cluster Twitter users into bins of users that showed exactly the same
liking/retweeting behavior over the period. To investigate whether any of
these bins exhibited _coordinated inauthentic behavior_ , we were interested
in whether bin size correlated with

  * $\circ$

user account deletion/suspension (we bought some likes at some point, and saw
that the user accounts disappeared rather quickly)

  * $\circ$

high bot scores from Botometer / Botometer Lite.

We didn’t find significant correlations. Neither, and somewhat surprisingly,
between Botometer and Botometer Lite scores.

### Dates for Data Collection

  * $\circ$

November 1, 2022: Election date.

  * $\circ$

October 7, 2022 and 30 days forward: we scraped with the query _#dkpol
-is:retweet OR #fv22 -is:retweet OR #fv2022 -is:retweet_. See Pull-
All_fv22/parameters.py.

  * $\circ$

Late January to Mid February 2023: we looked up user account information and
botscores.

Botometer guidelines suggest that we should have looked up botscores runningly
as they are somewhat time sensitive. Checking for correlations with botscores,
however, came as an afterthought to the general data collection.

### Code on Dataset

To use the code in the GitHub repository on the dataset, clone the repo and
download the dataset, extract Data from the directory Data from Danish Twitter
on National Election 2022/Raw Data/Pull-All_fv22.zip and place the Pull-
All_fv22 directory in the repo root.

### Much more Information

For much more information on the research motivation for creating this dataset
and undertaking the analysis, please see the introduction to the PhD thesis
_Curbing Amplification Online: Towards Improving the Quality of Information
Spread on Social Media Using Agent-Based Models and Twitter Data_ by Laura
Jahn, University of Copenhagen, 2023 [1]. A related paper extensively
discussing data collection and preliminary analysis on the same type of data
(likes) can be found on arXiv [3] and the corresponding GitHub repository [2].

## Dataset components

The dataset contains the following:

### 1\. /Raw Data/Pull-All_fv22.zip

#### Tweet IDs, Liking Users and Retweeting Users live scraped from Oct. 7th
and 30 days forward

Runningly, we collected the user identities of liking and retweeting users,
with the algorithm described in [3] using the code from this repo.

The dataset contains the collected data, time stamped. I.e., for every ~5
minutes in the scrape period, there is a file of the last 48 hours’ tweet IDs,
and lists of liking and retweeting users. See the linked-to repo for
information on the directory and file structure.

This repo contains code to process these rather raw files. In addition to this
readme, you can also go through the file analysis/Pull-fv22-treatment.py for a
bit of practical code.

_Note:_ The dataset does not contain e.g. tweet text, as this cannot to shared
in batch without violating Twitter’s terms and conditions.

## 2\. /Preprocessed Data

_Note:_ We have uploaded the processed data as it can take quite some RAM to
conclude the processing. We ran out of memory on 128 GB RAM Linux machine, so
we supplemented it with an additional 2 TB NVMe disk, allocated to swap space.
One treatment ended up using ~590 GB of that.

### 2.0 /Preprocessed Data

Preprocessed using code from this repo, see below.

The binarymatrices.zip file contains two Tweet IDs $\times$ User IDs matrices
(one for likes, one for retweets), with a $1$ in $(i,j)$ if user $j$
liked/retweeted tweet $i$, else $0$.

  * $\circ$

Processed using binarymatrices.sh

### 2.1 /Preprocessed Data/Botscores

Contains botscores for every liking user / retweeting user observed during the
live scrape, according to Botometer v4 and Botometer Lite.

Collected using botscores_v4.sh and botscores_lite.sh

### 2.2 /Preprocessed Data/Clusters

Contains analyses of the binary matrices, where users have been grouped if
they share the exact same liking / retweeting behavior. As described in [3].

The clustering/binning was done using /analysis/binning.sh.

### 2.3 /Preprocessed Data/Later Users and Tweets Lookups

  * $\circ$

latercounts.pkl: look up of all tweets to get their like and retweet counts,

  * $\circ$

laterusers.pkl: look up of all user profiles e.g. whether it still exists, has
been suspended, error codes, etc.

### 2.4 /Preprocessed Data/Likers Retweeters Pagination

To improve the live scraped data, we have since used Twitter’s updated API
allowing for pagination to re-collect the liking and retweeting users.

This data should, if no users were deleted or unliked, contain the same
information as the live scraped data.

See the section _Disclaimer for Article II_ in the PhD thesis [1] for more
information.

This paginated data was collected using the twarc2 package, using the scripts
analysis/twarc-lookup-liking-users.sh and analysis/twarc-lookup-retweeting-
users.sh. As we had multiple bearer tokens available, we split the user lists
using twarc-split-user-list.py into sublists so we could collect data in
parallel.

## Testing for Correlations: Conclusions

Again, we were mostly interested in whether the correlation in
liking/retweeting behavior among users correlated with

  * $\circ$

user account deletion/suspension, creation date, and/or

  * $\circ$

high bot scores from Botometer / Botometer lite.

We did not find any significant correlations: The size of a user’s cluster of
identically liking/retweeting users did not correlate with the user’s
Botometer scores or Botometer Lite scores, and the size of a cluster did not
correlate with how many of its users had disappeared. Also, Botometer and
Botometer Lite scores did not correlate with one another.

### To replicate:

1\. Run analysis/features-frame.py: Collects tweet and user information,
including botscores, user cluster sizes, deletions, etc.

In a bit more detail, the feature frames we created to check for correlated
features included the following:

  * $\circ$

binsize: size of bin/cluster the user is grouped into

  * $\circ$

user-ID

  * $\circ$

error_title: result from user look-ups

  * $\circ$

error_detail

  * $\circ$

name

  * $\circ$

created_at: creation date of user account

  * $\circ$

protected: whether user account is private

  * $\circ$

verified: whether user account is verified

  * $\circ$

followers_count: number of followers of user

  * $\circ$

following_count: number of accounts the user follows

  * $\circ$

tweet_count: number of posted tweets by user

  * $\circ$

listed_count: number of public lists that user is a member of

  * $\circ$

screenname - Botscores

  * $\circ$

All 8 raw, universal Botometer v4 botscores, such as *overall*, *fake
follower*, *astroturf*

  * $\circ$

Botometer Lite score

2\. Run analysis/correlation-coeff.py: Loads the feature frame and inspects
data, e.g.:

  * $\circ$

slices dataframe to filter for users in large bins,

  * $\circ$

computes the Pearson correlation coefficient across all columns,

  * $\circ$

plots histograms comparing users’ different features, e.g. bin size and bot
scores.

## References

  * [1] Jahn, Laura.  Curbing Amplification Online: Towards Improving the Quality of Information Spread on Social Media Using Agent-Based Models and Twitter Data.  PhD Thesis, University of Copenhagen, 2023.
  * [2] Jahn, Laura and Rendsvig, Rasmus K.  Get-twitter-likers-data.  github.com/humanplayer2/get-twitter-likers-data/, 2022.
  * [3] Jahn, Laura and Rendsvig, Rasmus K.  Towards Detecting Inauthentic Coordination in Twitter Likes Data.  arXiv, https://doi.org/10.48550/arXiv.2305.07384, 2023.