# The APO-K2 Catalog. I. 7500 Red Giants with Fundamental Stellar Parameters from APOGEE DR17 Spectroscopy and K2-GAP Asteroseismology

Jessica Schonhut-Stasik, Joel C. Zinn, Keivan G. Stassun, Marc Pinsonneault, Jennifer A. Johnson, Jack T. Warfield, Dennis Stello, Yvonne Elsworth, Rafael A. García, Savita Mathur, et al.

► To cite this version:

Jessica Schonhut-Stasik, Joel C. Zinn, Keivan G. Stassun, Marc Pinsonneault, Jennifer A. Johnson, et al.. The APO-K2 Catalog. I. 7500 Red Giants with Fundamental Stellar Parameters from APOGEE DR17 Spectroscopy and K2-GAP Asteroseismology. The Astronomical Journal, 2024, 167, 10.3847/1538-3881/ad0b13. insu-04843547

HAL Id: insu-04843547

https://insu.hal.science/insu-04843547v1

Submitted on 17 Dec 2024

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# The APO-K2 Catalog. I. ~7500 Red Giants with Fundamental Stellar Parameters from APOGEE DR17 Spectroscopy and K2-GAP Asteroseismology

Jessica Schonhut-Stasik<sup>1,26</sup> ID, Joel C. Zinn<sup>2,3,27</sup> ID, Keivan G. Stassun<sup>1</sup> ID, Marc Pinsonneault<sup>4</sup> ID, Jennifer A. Johnson<sup>4,5</sup> ID, Jack T. Warfield<sup>6</sup> ID, Dennis Stello<sup>7,8,9,10</sup> ID, Yvonne Elsworth<sup>11,12</sup>, Rafael A. García<sup>13</sup> ID, Savita Mathur<sup>14,15</sup> ID, Benoit Mosser<sup>16</sup> ID, Marc Hon<sup>17</sup> ID, Jamie Tayar<sup>18</sup> ID, Guy S. Stringfellow<sup>19</sup> ID, Rachael L. Beaton<sup>20,21</sup> ID, Henrik Jönsson<sup>22</sup> ID, and Dante Minniti<sup>23,24,25</sup> ID

Received 2023 April 19; revised 2023 September 23; accepted 2023 October 8; published 2024 January 9

## Abstract

We present a catalog of fundamental stellar properties for ~7500 evolved stars, including stellar radii and masses, determined from the combination of spectroscopic observations from the Apache Point Observatory Galactic Evolution Experiment, part of the Sloan Digital Sky Survey IV, and asteroseismology from K2. The resulting APO-K2 catalog provides spectroscopically derived temperatures and metallicities, asteroseismic global parameters, evolutionary states, and asteroseismically derived masses and radii. Additionally, we include kinematic information from Gaia. We investigate the multidimensional space of abundance, stellar mass, and velocity with an eye toward applications in Galactic archaeology. The APO-K2 sample has a large population of low-metallicity stars (~288 with [M/H] ≤ −1), and their asteroseismic masses are larger than astrophysical estimates. We argue that this may reflect offsets in the adopted fundamental temperature scale for metal-poor stars rather than metallicity-dependent issues with interpreting asteroseismic data. We characterize the kinematic properties of the population as a function of α enhancement and position in the disk and identify those stars in the sample that are candidate components of the Gaia-Enceladus merger. Importantly, we characterize the selection function for the APO-K2 sample as a function of metallicity, radius, mass, $v_{max}$, color, and magnitude referencing Galactic simulations and target selection criteria to enable robust statistical inferences with the catalog.

Unified Astronomy Thesaurus concepts: Galactic archaeology (2178); Stellar astronomy (1583); Asteroseismology (73); Spectroscopy (1558); Stellar kinematics (1608)

Supporting material: machine-readable tables

## 1. Introduction

Galactic archaeology probes the Galaxy's stars as a fossil record, investigating their histories to determine the formation and evolution of the Milky Way. Studying these fossils is best achieved using extensive data sets—that well represent the Galaxy's stellar population—over a broad parameter space comprising stellar ages, abundances, and kinematics; this data reveals the *when*, *what*, and *where* of the Milky Way's formation. The gathering of these data sets has grown

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<footnote n="1"><sup>1</sup> Vanderbilt University, Department of Physics & Astronomy, 6301 Stevenson Center Lane, Nashville, TN 37235, USA; jessica.stasik@vanderbilt.edu</footnote>

<footnote n="2"><sup>2</sup> Department of Astrophysics, American Museum of Natural History, Central Park West at 79th Street, New York, NY 10024, USA</footnote>

<footnote n="3"><sup>3</sup> Department of Physics and Astronomy, California State University, Long Beach, Long Beach, CA 90840, USA</footnote>

<footnote n="4"><sup>4</sup> Department of Astronomy, The Ohio State University, McPherson Laboratory, 140 West 18th Avenue, Columbus, OH 43210, USA</footnote>

<footnote n="5"><sup>5</sup> Center for Cosmology and AstroParticle Physics, Physics Research Building, 190 West Woodruff Avenue, Columbus, OH 43210, USA</footnote>

<footnote n="6"><sup>6</sup> Department of Astronomy, The University of Virginia, 530 McCormick Road, Charlottesville, VA 22904, USA</footnote>

<footnote n="7"><sup>7</sup> School of Physics, University of New South Wales, NSW 2052, Australia</footnote>

<footnote n="8"><sup>8</sup> Sydney Institute for Astronomy (SIfA), School of Physics, University of Sydney, NSW 2006, Australia</footnote>

<footnote n="9"><sup>9</sup> ARC Centre of Excellence for All Sky Astrophysics in 3 Dimensions (ASTRO 3D), Australia</footnote>

<footnote n="10"><sup>10</sup> Stellar Astrophysics Centre, Department of Physics and Astronomy, Aarhus University, DK-8000 Aarhus C, Denmark</footnote>

<footnote n="11"><sup>11</sup> Stellar Astrophysics Centre, Department of Physics and Astronomy, Aarhus University, Ny Munkegade 120, DK-8000 Aarhus C, Denmark</footnote>

<footnote n="12"><sup>12</sup> School of Physics and Astronomy, University of Birmingham, Edgbaston, Birmingham, B15 2TT, UK</footnote>

<footnote n="13"><sup>13</sup> Université Paris-Saclay, Université Paris Cité, CEA, CNRS, AIM, 91191, Gif-sur-Yvette, France</footnote>

<footnote n="14"><sup>14</sup> Instituto de Astrofísica de Canarias (IAC), E-38205 La Laguna, Tenerife, Spain</footnote>

<footnote n="15"><sup>15</sup> Universidad de La Laguna (ULL), Departamento de Astrofísica, E-38206 La Laguna, Tenerife, Spain</footnote>

<footnote n="16"><sup>16</sup> LESIA, Observatoire de Paris, Université PSL, CNRS, Sorbonne Université, Université de Paris, F-92195 Meudon, France</footnote>

<footnote n="17"><sup>17</sup> Institute for Astronomy, University of Hawaiiʻi, 2680 Woodlawn Drive, Honolulu, HI 96822, USA</footnote>

<footnote n="18"><sup>18</sup> Department of Astronomy, University of Florida, Bryant Space Science Center, Stadium Road, Gainesville, FL 32611, USA</footnote>

<footnote n="19"><sup>19</sup> Center for Astrophysics and Space Astronomy, University of Colorado at Boulder, 389 UCB, Boulder, CO 80309-0389, USA</footnote>

<footnote n="20"><sup>20</sup> Space Telescope Science Institute, Baltimore, MD 21218, USA</footnote>

<footnote n="21"><sup>21</sup> Department of Physics and Astronomy, Johns Hopkins University, Baltimore, MD 21218, USA</footnote>

<footnote n="22"><sup>22</sup> Materials Science and Applied Mathematics, Malmö University, SE-205 06 Malmö, Sweden</footnote>

<footnote n="23"><sup>23</sup> Departamento de Física, Universidade Federal de Santa Catarina, Trindade 88040-900, Florianópolis, Brazil</footnote>

<footnote n="24"><sup>24</sup> Instituto de Astrofísica, Facultad de Ciencias Exactas, Universidad Andres Bello, Avenida Fernández Concha 700, Santiago, Chile</footnote>

<footnote n="25"><sup>25</sup> Vatican Observatory, I-V00120 Vatican City State, Italy</footnote>

<footnote n="26"><sup>26</sup> Neurodiversity Inspired Science and Engineering Graduate Fellow.</footnote>

<footnote n="27"><sup>27</sup> NSF Astronomy and Astrophysics Postdoctoral Fellow.</footnote>
considerably in the last decade, with a stream of space- and ground-based telescopes providing asteroseismic, spectroscopic, and kinematic measurements determining the ages, compositions, and positions of hundreds of thousands of stars. These data have enabled increasingly detailed descriptions of the Milky Way's stellar building blocks.

In terms of stellar targets, red giant stars are particularly beneficial for Galactic archaeology (e.g., Stello et al. 2015). Due to their high luminosities, red giants can be seen to greater distances than less evolved stars, providing a better understanding of the edge of our Galaxy. Furthermore, their solar-like oscillations can be observed in a longer cadence than is necessary to observe similar oscillations in dwarfs and subgiants. Asteroseismic, spectroscopic, and kinematic catalogs of giant stars already exist for various samples.

CoRoT (Baglin et al. 2006), Kepler (Borucki et al. 2010), K2 (Howell et al. 2014), and TESS (Ricker et al. 2014) have been transformational for taking the once-boutique field of asteroseismology into the era of large data sets. There are now large catalogs of asteroseismic data for red giants available from Kepler (with ~16,000 stars from Yu et al. 2018; see also Pinsonneault et al. 2018), K2 (~19,000, Zinn et al. 2022), and TESS (~158,000, Hon et al. 2021; ~1700, Mackereth et al. 2021). Spectroscopic data for millions of stars from large-scale surveys such as the Apache Point Observatory Galactic Evolution Experiment (APOGEE; Majewski et al. 2017), GALAH (Buder et al. 2021), and LAMOST (Cui et al. 2012) complement asteroseismic data by providing the temperatures and metallicities needed for detailed stellar physics and Galactic archaeological studies. To these survey data, Gaia (Gaia Collaboration et al. 2016) has also been groundbreaking in adding precise kinematic information for over one billion stars. Here, we present a catalog at the intersection of a subset of these surveys, drawing together asteroseismology from K2, spectroscopy from APOGEE, and kinematics from Gaia, and demonstrate its unique potential for stellar physics and applications to Galactic archaeology.

We can learn *when* stellar populations formed in our Galaxy using precise asteroseismic stellar ages (e.g., Miglio et al. 2009; Sharma et al. 2016; Silva Aguirre et al. 2018; Rendle et al. 2019; Mackereth et al. 2021). Such age estimates rely on asteroseismic masses in combination with stellar models, metallicities, and temperatures. When performing population asteroseismology on large samples of solar oscillators, it is common to reduce the dimensionality of the oscillation pattern by using two global seismic parameters for faster processing instead of performing detailed mode-by-mode analysis on all targets. These asteroseismic global parameters are the large frequency separation ($\Delta\nu$, related to the mean density) and the frequency of maximum power ($\nu_{max}$, related to $\log(g)$ and $T_{eff}$) (Brown et al. 1991; Kjeldsen & Bedding 1995). These global parameters can, in turn, provide the input to calculate high-precision stellar masses and radii using scaling relations (see Section 2.2). These scaling relations, and the resulting ages, depend explicitly on the temperature measurements; therefore, spectroscopic surveys provide a powerful complement to time-domain asteroseismology.

Spectroscopic data measures stellar abundances, powerfully describing *what* the Galaxy's stellar composition is. An example of the symbiosis between asteroseismic and spectroscopic measurements is the study of the distribution of $\alpha$-element abundances. As stars formed in our Galaxy, the

proportion of metals increased through a series of supernovae (SNe), providing an increasingly metal-rich medium for star formation and altering the proportions of $\alpha$ elements to other elements (hereafter, $[\alpha/Fe]$) (e.g., Burbidge et al. 1957; Timmes et al. 1995). Therefore, the most metal-poor old stars present an excellent probe of the nucleosynthesis pathways in the early Galaxy.

A major prediction from early models is a single-valued function of the $\alpha$ elements as a function of $[Fe/H]$ (e.g., Gilmore et al. 1989). However, with the support of spectroscopic measurements, data have shown a double-valued function (Fuhrmann 1998; Prochaska et al. 2000; Bensby et al. 2003), even in the Galactic bar (Queiroz et al. 2021). There are many proposed mechanisms for this $[\alpha/Fe]-[Fe/H]$ bimodality, such as radial migration (Sellwood & Binney 2002; Schönrich & Binney 2009; Nidever et al. 2014; Weinberg et al. 2017; Sharma et al. 2021), two separate episodes of star formation (Chiappini et al. 1997; Haywood et al. 2016; Lian et al. 2020), and stars forming throughout the Galaxy in clumpy bursts (Clarke et al. 2019). Adding asteroseismic ages provides further information, allowing us to test models of the $[\alpha/Fe]-[Fe/H]$ bimodality thanks to their precision, large sample sizes, and a relatively large range of distances compared to that of isochronal aging techniques. Samples from Kepler, K2, and TESS are promising for continued work to constrain these models (e.g., Silva Aguirre et al. 2018; Mackereth et al. 2019a; Rendle et al. 2019; Warfield et al. 2021).

With stellar position and orbital parameters derived from astrometry, we can determine *where* stars formed and to which Milky Way component they belong (the halo, thick disk, thin disk, or bulge), separate out populations such as globular clusters (Kruijssen et al. 2019; Massari et al. 2019; Forbes 2020; Pérez-Villegas et al. 2020; Callingham et al. 2022), and determine if the stars originated as part of an accretion event by considering the Galactic halo. As the Milky Way developed its structure, it accreted much smaller galaxies, and in some cases, the Milky Way is still actively accreting. For example, the tidal disruption of the Sagittarius dwarf galaxy is ongoing (Ibata et al. 1994; Limberg et al. 2023), the Magellanic Clouds appear to be on their first infall (Besla et al. 2007), and there are dozens of globular cluster streams currently encircling our Galaxy (Bonaca et al. 2020). These accreted bodies come with unique kinematic profiles, and they share integrals of motion (Helmi & de Zeeuw 2000; Font et al. 2011; Simpson et al. 2019) even several billion years later, allowing us, in some cases, to identify their stellar components. These stars also share chemical abundance values, aiding in their identification (Freeman & Bland-Hawthorn 2002; Venn et al. 2004; Lee et al. 2015; Grunblatt et al. 2021).

Combining the abundances, masses, radii, velocities, and positions of evolved stars allows us to assemble a catalog containing the essential data to address the significant questions in Galactic archaeology. Furthermore, combining these parameters can improve the precision of other diagnostic criteria. For example, evolutionary states can be inferred to higher precision by correlating spectroscopic and asteroseismic properties (Jönsson et al. 2020), as it is otherwise difficult to separate shell H-burning red giant branch (RGB) stars from core He-burning red clump (RC) stars. It is also challenging to infer parameters for RGB stars, such as ages, with spectroscopic information alone (e.g., Soderblom 2010).
Another problem our extensive data set can explore is the purported conflict between astrophysical priors and asteroseismic masses for low-metallicity halo stars (Epstein et al. 2014), first identified in early Kepler data (Pinsonneault et al. 2014). Although more recent investigations have called this result into question (Miglio et al. 2016; Sharma et al. 2016; Valentini et al. 2019), others have supported an inflation of the metal-poor asteroseismic mass scale (Zinn et al. 2019; Matsuno et al. 2021). With a larger sample of asteroseismic, metal-poor stars available in K2 compared to Kepler, the catalog presented here is a timely addition to this debate.

Our catalog introduces the first APOGEE and K2 combination and includes data from the third data release of Gaia (DR3). Because the K2 fields sample very different populations from those seen in the original Kepler field, we can gain powerful insights into the formation history of the Milky Way. This paper presents the results from the dedicated targeting efforts of the fourth phase of the Sloan Digital Sky Survey (SDSS-IV; Beaton et al. 2021) to observe the K2 fields. The resulting APO-K2 catalog contains the combined data sets for 7672 evolved Milky Way stars, combining spectroscopic (APOGEE DR17; Abdurro'uf et al. 2022), asteroseismic (K2 Galactic Archaeology Program (K2-GAP); Stello et al. 2015), and astrometric (Gaia DR3; Gaia Collaboration et al. 2023) data, with a well-understood selection function (Sharma et al. 2022, hereafter S22). In Section 2, we discuss the data and the construction of the catalog. Section 3 presents the final sample, including a discussion of metallicity, the selection function, and a comparison between the APO-K2 and APOKASC-2 (Pinsonneault et al. 2018) samples. In Section 4, we investigate the stellar masses in the low-metallicity regime, the kinematic properties, and the [α/Fe]–[Fe/H] bimodality seen in the data set; we also identify halo stars and potential Gaia-Enceladus-Sausage (GES) members (Helmi et al. 2018; Mackereth et al. 2019b). Section 5 presents the conclusions. The publication of asteroseismic ages for this sample will follow in a companion paper (J. T. Warfield et al. 2024, in preparation), as will a detailed analysis of sample abundances and multiplicity (J. Schonhut-Stasik et al. 2024, in preparation).

## 2. Sample Data

Our catalog uses asteroseismic data from the K2 Galactic Archaeology Program (K2-GAP DR3; Zinn et al. 2022), spectroscopic data from APOGEE DR17 (Abdurro'uf et al. 2022), and astrometric data from Gaia DR3 (cross-matched from EDR3, included in APOGEE DR17; Abdurro'uf et al. 2022). Our initial sample was compiled by cross-matching K2-GAP DR3 with APOGEE DR17 (Section 2.1). Having combined these sources we calculated fundamental asteroseismic parameters (Section 2.2), incorporated spectroscopic parameters (Section 2.3), and collated astrometric values (Section 2.4), resulting in the APO-K2 catalog.

### 2.1. Cross-match

The K2-GAP DR3 catalog is the base of our cross-match, which has been analyzed in various works (Stello et al. 2017; Zinn et al. 2020, 2022). The complete list of K2-GAP targets observed by K2 contains 121,715 stars. From here, a cross-match with APOGEE DR17 was performed. Around 32% of the K2-GAP stars were also observed in APOGEE (39,319 stars); by then cross-matching those stars with the asteroseismic

measurements, we arrive at a sample of 8581 stars (7% of those observed for K2-GAP).

The primary axis for our cross-match between the K2-GAP and APOGEE DR17 catalogs was their associated Two Micron All Sky Survey (2MASS) IDs, which came from the Ecliptic Plane Input Catalog (EPIC; Huber et al. 2016), compiled to support target selection and management for the K2 mission. Prior to the match, we sorted the APOGEE DR17 targets by signal-to-noise ratio (S/N), dropping rows with lower S/N where multiple entries for the same target were available. We also only considered APOGEE targets that had a metallicity measurement. Dropping low-S/N entries ensured that each entry in the K2-GAP catalog received a single spectroscopic match, with the highest available S/N observation. To show which stars were dropped, we created a flag for the cross-match (apo-crossmatch_flag) and set the value to 1 where no drop was made and 0 otherwise. A minority of stars were observed in multiple K2 campaigns (10% of the sample), and were noted in the final catalog as having observations in multiple campaigns. Gaia EDR3 data was already in the APOGEE DR17 table, and so no stars were dropped by adding this information, which was later updated to include DR3 values.

### 2.2. Asteroseismic Data

Asteroseismic detections for thousands of stars became possible with missions such as CoRoT (Auvergne et al. 2009; De Ridder et al. 2009) and Kepler (Huber et al. 2009; Stello et al. 2013). However, these missions had limited sky coverage, selecting stars primarily for planet hunting (Sharma et al. 2016, 2017). In Kepler, this resulted in only a fraction of the available oscillating targets observed, at a given combination of age, metallicity, and distance (Silva Aguirre et al. 2018).

The Kepler mission targeted a field in the Cygnus and Lyra constellations, with a four-year nominal mission, to find Earth-like planets around Sun-like stars. Conveniently, Kepler's precise photometry also allowed for the study of asteroseismic variability in thousands of cool stars, the long cadence of Kepler being particularly advantageous, with 29.4 minute observations ideal for studying the oscillation periods of red giants (e.g., Bedding et al. 2010).

Following the failure of the second of Kepler's four reaction wheels in 2013 May, the Kepler spacecraft began a second mission, K2. The spacecraft was repurposed using solar wind for partial stabilization, allowing the telescope to continue to observe, although the acquisition of Kepler's original field was no longer possible due to the lack of stable pointing. Therefore, unlike the fixed original field, K2 observed 18 regions across a 360° ecliptic field of view for ~80 days at a time (Howell et al. 2014). Each K2 campaign covered 115.64 deg²—over 21 CCD modules, each made up of 1024 × 2200 pixel CCDs (2"/98 pixel scale); there were slight gaps between the CCDs and between each of the 21 modules.

The K2 mission had several scientific objectives proposed through guest observer programs. The international collaboration of K2-GAP (Stello et al. 2015) created a dedicated program to target red giants far beyond the solar neighborhood, which provided a trove of new asteroseismic data by detecting oscillations, with an aim to study the formation and evolution of the Milky Way. Roughly 25% of the observed K2 targets were allocated to K2-GAP.
K2 performed 18 full observing campaigns before a lack of fuel forced retirement in 2018. In Zinn et al. (2022, hereafter Z22), the authors presented K2-GAP for campaigns C1–C8 and C10–C18.<fnref n="28" /> The Z22 catalog represents the largest asteroseismic sample of red giants, with both $v_{max}$ and $\Delta v$, in the literature to date.

Our catalog includes K2-GAP asteroseismic data from C1–C8 and C10–C18, and was analyzed by members of the Kepler Asteroseismic Science Consortium (KASC).<fnref n="29" /> The K2-GAP lightcurves were reduced and calibrated in a manner appropriate for asteroseismology (see Z22, where the interested reader can find a full explanation). Briefly, each star in the sample received analysis from six independent pipelines, which returned asteroseismic parameters. The final asteroseismic values were the average of the pipeline values, with an outlier rejection algorithm applied. For stars observed in multiple campaigns, a weighted average of the averaged pipeline values from each campaign served as the final parameters.

The final two asteroseismic parameters in the APO-K2 catalog are the frequency of maximum oscillation power ($v_{max}$) and the large frequency separation ($\Delta v$); we only adopted stars that had a measurement of both these values in K2-GAP. We determined asteroseismic masses and radii by combining these parameters with scaling relations via radius and mass coefficients ($\kappa_R$ and $\kappa_M$, respectively; Sharma et al. 2016):

$$ \frac{R}{R_{\odot}} \approx \left( \frac{v_{\max}}{v_{\max, \odot}} \right) \left( \frac{\Delta v}{f_{\Delta v} \Delta v_{\odot}} \right)^{-2} \left( \frac{T_{\text{eff}}}{T_{\text{eff}, \odot}} \right)^{1/2} \\ \equiv \kappa_R \left( \frac{T_{\text{eff}}}{T_{\text{eff}, \odot}} \right)^{1/2} \quad (1) $$

$$ \frac{M}{M_{\odot}} \approx \left( \frac{v_{\max}}{v_{\max, \odot}} \right)^3 \left( \frac{\Delta v}{f_{\Delta v} \Delta v_{\odot}} \right)^{-4} \left( \frac{T_{\text{eff}}}{T_{\text{eff}, \odot}} \right)^{3/2} \\ \equiv \kappa_M \left( \frac{T_{\text{eff}}}{T_{\text{eff}, \odot}} \right)^{3/2} . \quad (2) $$

As the scaling relations were originally calibrated to the Sun, extra calibrations (with the help of stellar models) were needed to make these relations appropriate for red giant stars, as frequency spacings are impacted by stellar structure (White et al. 2011), and therefore not simply related to the mean density. In the above, $f_{\Delta v}$ represents a model-dependent correction to the observed $\Delta v$ values. Its value depends, in part, on the temperature and metallicity of the star. In K2-GAP DR3 (Z22), the EPIC served as the source for this temperature and metallicity. With APOGEE DR17 temperatures and metallicities in hand, we updated $f_{\Delta v}$ using asfgrid (Sharma et al. 2016) with its low-mass, low-metallicity extension (Stello & Sharma 2022), in accordance with the treatment described in Z22, including $\alpha$-dependent corrections to the metallicities. In the APOKASC publications, the so-far-published K2-GAP work, and this work, our asteroseismic parameters adopt the method described in APOKASC-2, which is an empirical calibration against fundamental data to set the $v_{max}$ zero-point

(see Z22 for more details). Our catalog includes masses and radii calculated using $f_{\Delta v}$ and $v_{max}$ values that have been updated since their initial publication in Z22. For $v_{max}$, the empirical evolutionary-state corrections from Z22 were removed and reapplied using the spectroscopic evolutionary states used here; the solar reference value, $v_{max, \odot}$, for both RGB and RC stars was taken to be 3076 µHz. The $f_{\Delta v}$ values were similarly recalculated with our new spectroscopic evolutionary states and updated APOGEE DR17 temperatures and metallicity. We include the updated $f_{\Delta v}$ and an associated flag to indicate the quality of those values, the mass and radius coefficients, the stellar masses and radii, and their associated errors in Table 2.

We note that the K2-GAP DR3 asteroseismic data were calibrated using Gaia-based distances inferred from bulk stellar motions from Gaia DR2 (Gaia Collaboration et al. 2018) according to the methodology described in Schönrich et al. (2019) accounting for selection functions according to Schönrich & Aumer (2017). This technique corrects for bias in parallax, and indicates ≈10 µas positional variations in the Gaia parallax zero-point across the K2 campaigns. The Gaia DR3 parallaxes corrected according to the Gaia team's recommendations (Lindegren et al. 2021) appear to still suffer from position-dependent parallax bias in K2 asteroseismic red giant samples (Khan et al. 2023), with a range in the bias of ≈40 µas across the K2 campaigns. A comparison of the K2-GAP DR3 asteroseismic radius scale to the Gaia DR3 radius scale computed according to Zinn et al. (2017) with parallax corrections from the Gaia team shows a 1.5% offset in the sense that the Gaia DR3 radii are smaller. Assuming this offset for a mass calibration via the $v_{max}$ solar reference value (see Z22) would suggest a 4.5% downward revision of the asteroseismic masses. Such an offset is within the 2% systematic uncertainty in the $v_{max}$ scale reported by Z22, and so while we note the possibility of a downward revision to the radius/mass scale here, we did not recalibrate the asteroseismic data to the Gaia DR3 parallaxes, particularly given indications of position-dependent Gaia DR3 parallax bias at a similar level.

## 2.3. Spectroscopic Data

Through detailed studies of the stars in the Milky Way, APOGEE (Majewski et al. 2017) is unraveling the compositional form of our Galaxy. APOGEE uses a high-resolution (R ~ 22,500) infrared spectrograph (Wilson et al. 2019) operating in the H band. For Northern Hemisphere observations, APOGEE is mounted on the Sloan Foundation 2.5 m telescope (Gunn et al. 2006) at Apache Point Observatory, New Mexico. In the Southern Hemisphere the 40 inch Irénée Du Pont telescope (Bowen & Vaughan 1973) at Las Campanas Observatory, Chile, houses the instrument.

APOGEE data were reduced, wavelength-calibrated, and co-added according to Nidever et al. (2015). Spectroscopic parameters were calculated using the APOGEE Stellar Parameters and Chemical Abundances Pipeline (ASPCAP; Holtzman et al. 2015; García Pérez et al. 2016) and calibrated according to Holtzman et al. (2018), with the model grids and the interpolation method described by Jönsson et al. (2020). APOGEE primarily targeted K2 evolved stars (RGB and RC) as they are intrinsically luminous with significant flux in the infrared, allowing high-S/N observations at large distances. K2-GAP stars that were not already observed in the GALAH survey (Buder et al. 2021) were prioritized, although

<footnote n="28">²⁸ Some differences between campaigns are worth noting: C3 had a slightly shifted field of view due to a late change in roll angle; therefore, some of the proposed targets were unobservable. During C10, a permanent failure of one of the CCD modules occurred, resulting in stars in this and all subsequent campaigns being observed partially, or not at all. C18 had very few seismic detections. C9 was not used as it was a dense field chosen for microlensing, nor C19, which had very few asteroseismic detections due to its short duration.</footnote>

<footnote n="29">²⁹ https://kasoc.phys.au.dk</footnote>
overlapping stars at lower priority were also observed. About half of the targets observed by APOGEE reside in the disk of the Milky Way ($b \le 16^{\circ}$), with the remaining targets split between the bulge and the halo. Information on K2 object targeting can be found in Zasowski et al. (2017), Beaton et al. (2021), and Santana et al. (2021); the latter two papers include information on the relative weighting of the different classes of targets.

In this work, we use APOGEE data obtained during SDSS-IV (Blanton et al. 2017) and analyzed in the 17th (and final) data release (Abdurro’uf et al. 2022) of SDSS-IV (hereafter DR17). DR17 contains 675,000 APOGEE targets over an additional two years of SDSS observations, in both hemispheres, compared to DR16 (Jönsson et al. 2020). The cumulative nature of SDSS data sets means that DR17 contains a reprocessing of all data obtained, processed, and released in previous data releases. Although many beneficial, and significant, updates appeared in DR17 we only detail changes to the data release and reduction process relevant to this work. These changes primarily affect the abundances, because APOGEE uses the infrared flux method (IRFM) as an absolute standard for effective temperature, and asteroseismology for the absolute standard for log(g). For instance, ASPCAP was updated for DR17, with new sets of spectral synthesis grids including non-local thermodynamic equilibrium effects for Na, Mg, K, and Ca, which will be considered more in an upcoming APO-K2 abundance paper (J. Schonhut-Stasik et al. 2024, in preparation).

In the APOKASC samples (Pinsonneault et al. 2014, 2018), asteroseismic evolutionary states were employed to differentiate between RGB and RC stars. For the purposes of this work, we adopted spectroasteroseismic evolutionary states. These were calculated by a similar method to that described in Warfield et al. (2021), and depended on recalculating the temperature, surface gravity, and abundance dependent cut performed in Warfield et al. (2021). Therefore, these evolutionary states relied on values of $T_{\text{eff}}$, log(g), and elemental abundances from APOGEE DR17, and were trained on the asteroseismically derived RGB and RC classifications from APOKASC-3 (M. Pinsonneault et al. 2024, in preparation). Ultimately, we assigned stars to the RGB if their uncalibrated surface gravity is$^{30}$ log(g)$_{SPEC}$ < 2.30, or, where log(g)$_{SPEC}$ ≥ 2.30, if

$$[\text{C/N}] \times 10^3 < 59.15 - 3.455 (155.1[\text{Fe/H}]_{\text{SPEC}} + \Delta T). \quad (3)$$

In this equation, $\Delta T = T_{\text{eff}}^{(\text{SPEC})} - T_{\text{ref}}$ is the difference between the star’s uncalibrated effective temperature and its “reference” temperature, calculated from a fit to the ridgeline of known RGB stars in the APOKASC-3 data set, which we define as

$$T_{\text{ref}} = 4427.18 - 399.5[\text{Fe/H}]_{\text{SPEC}} + 553.17(\log(g) - 2.5). \quad (4)$$

Although these new evolutionary states show promise in that they are reliable in classifying the stars accurately, there is a harder boundary in the log(g) space than we see when using asteroseismology-only derived evolutionary states. For example, there are few RC stars above a log(g) of 2.2 and this should be considered when dealing with stars in this domain.

## 2.4. Astrometric Data

The largest ever source of precise astrometric data is the Gaia mission (Gaia Collaboration et al. 2016), which was launched in 2013 and measured the six-dimensional spatial and velocity distribution of nearly two billion stars in the Milky Way. The astrometric information in this work was obtained from Gaia DR3 (Gaia Collaboration et al. 2023) by selecting the 2MASS ID using the Gaia team-provided Gaia DR2–2MASS cross-match (Marrese et al. 2019) and Gaia DR2–Gaia DR3 ID cross-match (Torra et al. 2021).

## 3. Results

In this section we begin by exploring the selection function (Section 3.1). We then describe in detail the catalog provided in this work (Section 3.2). In Section 3.3 we discuss the overall metallicity as a function of K2 campaign, before finishing with an exploration of the sample in terms of evolutionary states (Sections 3.4 and 3.5).

### 3.1. Selection Function

This section investigates the multiple layers of targeting and selection that led to the APO-K2 sample, so that interested readers may consider completeness when using our catalog. The APO-K2 sample is fundamentally comprised of K2-GAP DR3, cross-matched with APOGEE DR17, which therefore includes selection and targeting choices made by both K2-GAP and APOGEE DR17. Because there were no stars lost in the cross-match between APOGEE DR17 and Gaia DR3, the Gaia aspect of the selection function is irrelevant. In what follows, we consider known aspects of both of these selection functions in turn.

Although the purpose here is to understand the completeness of the APO-K2 sample, we stop short of comparing it to a true, underlying Galactic stellar population; instead we compare it to a set of simulated stars that are drawn from a parent mock Galactic stellar population, as generated by the Galaxia code (Sharma et al. 2011). These simulated stars are drawn according to the K2-GAP selection function in color and magnitude, and then have an expected asteroseismic selection function applied to only keep stars with greater than 90% expected probability of having detectable asteroseismic signals (Sharma et al. 2022).

Some important assumptions were made in the creation of this simulated sample that could affect our inferences on the completeness of the APO-K2 catalog: for example, the assumed metallicity of the thin and thick disks (discussed further in our interpretation of Figure 2) and the choices related to star formation history (which directly impact the distribution of $\kappa_M$, and as a consequence, mass).

#### 3.1.1. K2-GAP Selection

The targets for the K2-GAP sample were chosen with a color cut. Broadly, the cut removed mostly dwarfs, with ($J - K_s$) < 0.5, corresponding to dwarfs with $M_{K_s} > 1$. This cut did exclude some giants, such as those on the horizontal branch (the blue extension of the RC); however, these are mostly rare, metal-poor stars, and are too hot to support solar-like oscillations.

For C1, C2, and C3, the 2MASS H-band magnitude was used to select in brightness. For later campaigns, an

<footnote>$^{30}$ In the APOGEE catalog, the “SPEC” subscript marks the uncalibrated version of the parameter.</footnote>
approximation of the V-band magnitude measured from the 2MASS J and Ks bands was used, as per Equation (5) below. This cut was chosen for later campaigns because K2 collected data in the Kp band, which is significantly bluer than the H-band, and more consistent with the V band (see Sharma et al. 2022 for more details):

$$V_{JK_s} = K_s + 2.0(J - K_s + 0.14) + 0.382 \exp[(J - K_s - 0.2)/0.50]. \quad (5)$$

### 3.1.2. APOGEE Selection

By cross-matching with APOGEE we inserted elements of the APOGEE selection function into our catalog. Beaton et al. (2021) discussed the prioritization scheme for targeting in each field of the K2 program. This provides a meaningful comparison between targeted and observed stellar populations, and can be used to judge the completeness of our sample, especially in parameter spaces that may have been affected by our cross-match.

### 3.1.3. Comparing Targeting and Selection Functions

We compared our sample of APO-K2 stars to the K2-GAP stars and the simulated stars from S22.31 We note that the values of asteroseismic mass and radius that we report are the average over a number of pipelines from Z22, whereas the K2-GAP data only used the SYD pipeline (Huber et al. 2009), which may cause a small difference in the inferred selection function when mapping from K2 data to APO-K2.

From here we investigate four parameter spaces: mass versus radius (Figure 1), mass versus metallicity (Figure 2), color versus magnitude (Figure 3), and magnitude versus $v_{max}$ (Figure 4). In each space, depending on the relative density being computed, we cut down the larger sample to match the limits of the smaller sample.32 We created two 10 × 10 grids in the investigated parameter space; for example, in the mass versus radius regime we binned in a 10 × 10 grid of mass and radius. We populated these grids with the relative density of stars, one corresponding to the ratio of the observed K2 sample to the simulated sample, and one corresponding to the ratio of the APO-K2 sample to the observed K2 sample. This first ratio allowed us to determine which stars were lost due to unknown aspects of the asteroseismic selection function (e.g., due to unexpectedly low S/N in the data as compared to the Sharma et al. 2022 simulations) and the second ratio allowed us to determine which were lost from the APO-K2 catalog due to the APOGEE selection function. When considering the simulated sample we multiplied the number of stars in each bin by 0.1, to compensate for how the simulated stars were oversampled by a factor of 10 to reduce Poisson noise (see explanation in Sharma et al. 2022). In all the density plots (the top row of Figures 1–4) gray areas cover bins where “nan” or “inf” values were calculated; this occurred when one of the samples had no stars in that bin. The resulting relative densities ($D$) were calculated and multiplied by a scaling factor (the second term in

Equations (6) and (7)) that is specific to the parameter space. These scalings allow the reader to plainly see the differences in the bins. These equations are shown below, for the density of the observed K2 sample relative to the simulated sample,

$$D = \frac{N_{i(\text{K2-GAP})}}{N_{i(\text{sim})}} \times \frac{N_{\text{sim}}}{N_{\text{K2-GAP}}} \quad (6)$$

and for the density of the APO-K2 sample relative to the observed K2 sample,

$$D = \frac{N_{i(\text{APO-K2})}}{N_{i(\text{K2-GAP})}} \times \frac{N_{\text{K2-GAP}}}{N_{\text{APO-K2}}}, \quad (7)$$

where the first term represents the relative density between the samples for a given bin (i). Another scaling was applied to all bins, to more easily see structure in the selection function (Equation (8)), using the value of $x = 0.6$ (for the mass–radius space) and $x = 1.0$ (for the other parameter spaces). This change in the denominator will incline the scaling toward a log scale at $<-0.6$ and $>0.6$, and $<-1.0$ and $>1.0$, respectively.

$$\hat{D} = \operatorname{arcsinh}\left[\frac{D-1}{x}\right]. \quad (8)$$

One of the key distributions when considering Galactic archaeology is mass. The mass distribution we would expect to see would be indicative of the star formation history and the lifetime of stars as a function of mass and metallicity (Wu et al. 2017). In terms of individual mass limits we expect a couple of clear boundaries. For example, there would be no massive stars above 5 $M_{\odot}$ because they would be too hot at the surface gravities probed by K2 to sustain solar-like oscillations. The lowest-mass stars we expect would correspond to the age of the Galaxy, discussed further in Section 4.1. Higher or lower masses than these bounds likely reflect mergers, binary mass transfer, or mass loss.

Figure 1 shows density plots in mass [$M_{\odot}$] versus radius [$R_{\odot}$] and histograms for these parameters. The color bar on the density plot indicates the scaled fractional density of stars. The scaling factor described in the second term of Equation (6) for the left-hand plot is (538,414/95,503) ~ 5.6 (the number of K2-GAP stars/the number of simulated stars) and the scaling factor is (13,723/8460) ~ 1.6 (the number of APO-K2 stars/ the number of K2-GAP stars) on the right (Equation (7)). In the top left density plot, for the K2-GAP/simulated stars, we see few simulated stars in the low-mass regime. This is likely due to the uncertainties on mass adopted by the simulation, as they correspond to the median uncertainties for the data (Sharma et al. 2011). We used the temperatures, the $\kappa_M$ values, a 3% uncertainty on temperature (in alignment with the EPIC temperature), and the SYD $\kappa_M$ errors to compute the fractional error on mass for the simulated stars. Over the whole simulated sample, the fractional mass error is around 24%, but 51% when the sample was cut to $M < 1 M_{\odot}$ stars. Therefore, as the simulation adopts median uncertainties from the data, the simulation errors for mass are underestimated, likely causing the deficit in mass we see in the low-mass regime for the simulated sample; this is also seen at the low-mass end of the mass histogram. One could argue that the abundance of low-mass stars seen in the sample that are absent in the simulated data may be the result of mass loss (including mass transfer and binary interaction that the simulation does not account for), as discussed in works that investigate inferred mass loss from

<footnote n="31">31 github.com/sanjibs/k2gap and http://www.physics.usyd.edu.au/k2gap/. We used `data_name='Galaxia-K2-sydai2-mrtd5'` for the simulated stars, and `data_name='k2-sydai2'` for the K2 observed stars, being mindful to choose only stars within the campaigns we use in APO-K2 by selecting on campaign number with “cno.”</footnote>

<footnote n="32">32 For example, when calculating the number density between the K2-GAP and simulated samples for mass and radius, we cut the simulated data to match the maximum and minimum K2-GAP masses and radii.</footnote>
<figure><img src="image_3.png" /><figcaption>**Figure 1.** A collection of plots describing the completeness of our sample through an analysis of the selection function, by first comparing the simulated and K2-GAP samples, then the K2-GAP and APO-K2 samples. Top left: a 10 × 10 grid showing the scaled fractional density of K2-GAP stars compared to the simulated sample in the mass [*M*⊙] vs. radius [*R*⊙] space. The title displays the number of stars in each of the samples overall; these values correspond to the scaling relation in the second term of Equation (7). The color bar shows the varying scaled density in each bin from an overabundance of simulated stars in red to an overabundance of K2-GAP stars in blue, as compared to expectations. Because *D̂* contains an asinh scale, the color bar is centered around 0, which corresponds to an equal number of stars in both bins. The gray area, bordered in white, demarcates bins with real numbers allocated, against those that were calculated to have “nan” or “inf” values, due to the bins being populated by no star in either the simulated or the K2-GAP sample. Top right: the same as the top left but for the density of APO-K2 stars over K2-GAP stars, with an abundance of APO-K2 stars shown in green and an abundance of K2-GAP stars again shown in blue. Bottom left: three histograms showing the distribution in radius within 2 < *R* [*R*⊙] < 30 of each sample (when cut on radius and mass): the simulated sample (red), the K2-GAP sample (blue), and the APO-K2 sample (green). Bottom right: the same as the bottom left but showing the distribution of masses over 0 < *M* [*M*⊙] < 2. In all plots, the simulated stars have been multiplicied by a scaling factor of 0.1, to account for the oversampling discussed in S22.</figcaption></figure>

asteroseismic data (Miglio et al. 2012, 2021; Kallinger et al. 2018; Howell et al. 2022; Tailo et al. 2022; J. Roberts et al. 2024, in preparation); however, due to the level of uncertainty in the simulated sample at low masses, we do not wish to draw this conclusion here.

Looking to the top right plot, of the relative APO-K2 stars/K2-GAP stars, we see more APO-K2 stars at lower masses and smaller radii (this is represented by the green bump on the left of the plot). This may be the result of a combination of the different temperatures (APOGEE versus EPIC) and asteroseismic scales (K2-GAP versus SYD) being used to calculate the masses and radii in these samples. To investigate the extent to which temperatures were the cause, we recalculated the mass, using mean raw APOGEE temperatures and mean EPIC temperatures (used for the K2-GAP sample). The resulting temperature difference corresponds to a difference of ~6% in mass.

On the bottom left, in the radius histogram, we see a bump at 10 *R*⊙ that does not appear in the observed samples. This likely represents clump stars, which are underrepresented in the data, as

it can be difficult to detect oscillations in RCs (Mosser et al. 2018) with their lower oscillation amplitudes (Yu et al. 2018). The extent of this bump in the histogram is due to the relatively long lifetime stars spend in the RC relative to the RGB. RC stars have a similar core mass, which dictates their similar radii to one another (however they do not share the same envelope mass).

Figure 2 shows the density plots for mass [*M*⊙] and metallicity [dex]. In this case, we used [M/H] values<fnref n="33" /> for the simulated stars, and [Fe/H] for APO-K2 and the K2-GAP samples, as [Fe/H] was unavailable for the simulated sample.<fnref n="34" /> For the relative density of the K2-GAP/simulated sample we see a bimodal distribution separated by an area where the relative number of observed stars is higher. The bimodal

<footnote n="33">³³ When discussing abundances in this work we use the standard notation: [X/Fe] = log₁₀((X/Fe)/log₁₀(Fe⊙)).</footnote>

<footnote n="34">³⁴ [M/H] is the average bulk metallicity in APOGEE, while [Fe/H] involves a selected subset of iron lines. In practice, the two agree closely for most APOGEE stars, since optical metallicity values track iron abundances (see https://www.sdss3.org/dr10/irspec/aspcap.php for more information).</footnote>
<figure><img src="image_4.png" /><figcaption>**Figure 2.** Same as Figure 1 but in mass [$M_\odot$] vs. metallicity [dex] space. The scaling values can be determined from the plot titles. The metallicity histogram (bottom left) ranges within $-2.5 < [M/H] [dex] < 0.5$, and the mass histogram (bottom right) ranges within $0 < [M_\odot] < 4$. See Figure 1 for more general information.</figcaption></figure>

distribution is ultimately due to the assumed metallicity of the thin and thick disks in the *Galaxia* model used to create the simulated stars, which we see in the distribution of the simulated sample's metallicities (a lower-metallicity peak corresponding to the thick disk and a higher-metallicity peak corresponding to the thin disk).

On the right-hand side, showing the relative density of K2-GAP stars/APO-K2 stars, we see fewer gray bins, indicating that these bins are now populated. This demonstrates that although these stars were observed in K2-GAP they did not appear in the simulated sample, resulting in the gray area on the left-hand density plot.

In the mass histogram, again we see a wealth of lower-mass stars ($\approx 0.6-1 M_\odot$) in the APO-K2 sample, and that more stars were observed at lower masses in K2 than were found in the simulated sample. Note the difference in mass range for the density plots between Figures 1 and 2. The mass range in Figure 1 is purposely more condensed to show the detail toward smaller masses.

In Figure 3, we show the color–magnitude space. These plots clearly show color cuts enforced by the K2-GAP target selection, where C1 and C2 have a maximum magnitude of 7 in the H band, and all other campaigns have a maximum magnitude of $V_{JK} = 9$ (see Table 1 of S22). This is evident both in the histograms and in the top left density plot, which shows many more simulated bright

stars at the top. In the right-hand histogram we see very good agreement between the simulated stars and the observed K2-GAP stars. This is due to the selection function for targeting taking place in the V band, and these cuts being easily replicated in the simulation. In the top left density plot for the K2-GAP/simulated sample we see an abundance of simulated stars in the column of bins corresponding to $\sim 0.77$ in J–K. This corresponds to the peak in the bottom left histogram, representing the RC stars. We note that the *Galaxia* simulation does not include extinction, so the blue edge may be due to the cutoff in J–Ks observation: the simulated sample is not seeing some stars that would be reddened and pass the J–Ks cut. This lack of extinction is also evident in the histograms, which show the RC stars appearing redder and more smeared out in the K2-GAP color histogram compared to the cleaner peak in the simulated sample. Finally, the simulations assume a color dependence for the amplitude of oscillation, which may cause a mismatch between the assumed and actual color distributions.

Figure 4 shows the $v_{max}$ versus magnitude space. S22 plotted their selection function in this same parameter space (bottom right-hand plot of Figure 10 in S22), and the top left density plot in this figure shows similar results, confirming consistency in our work. We see more faint, high-$v_{max}$ K2-GAP stars, and in the density plot on the right, we see a shift in the distribution, imposed by the APOGEE selection. In the upper right corner of this plot, we see
<figure><img src="image_5.png" /><figcaption>**Figure 3.** Same as Figure 1 but in color (J-K) vs. magnitude ($V_{mag}$) space. Again, the scaling value can be determined from the plot titles. The color histogram (bottom left) ranges within $0.5 < JK_s < 1.3$, and the magnitude histogram (bottom right) ranges within $8.5 < V_{mag} < 16$. See Figure 1 for more general information.</figcaption></figure>

fewer APO-K2 stars, corresponding to fewer of the seismically low-S/N stars. The histograms also show an overabundance of stars at lower $v_{max}$ values corresponding to stars that are difficult to measure due to there being few modes for low $v_{max}$, which sit at the limit of resolution of the K2-GAP lightcurves (Z22). The histograms between the K2-GAP stars and the simulated stars match well in the $v_{max}$ and magnitude space because the selection of stars for the K2-GAP sample was based on the ability to determine pulsations, and the simulated sample were selection-function matched to the catalog (provided in S22) and designed to determine the completeness of the K2-GAP observed stars.

The selection function plots for individual campaigns can be found on the companion GitHub. It is important to consider the selection function over each campaign due to potential differences (discussed in S22), such as in lightcurve duration, pointing accuracy, and variation in crowding. For those interested in studying completeness in the sample, both in individual campaigns and as a whole, the GitHub also includes tabulated values of the density plots with files for the bin edges, and for the fractional densities of the K2-GAP/simulated and APO-K2/K2-GAP samples.

## 3.2. The APO-K2 Catalog

The public catalog distributed with this publication contains a row for each star. In this paper the catalog is broken down

into four distinct tables. Table 1 includes the EPIC, APOGEE, and Gaia DR3 ID numbers; the K2 campaign number; the coordinates in R.A. and decl. as well as the Galactic coordinates; the spectroastroseismic evolutionary states<fnref n="35" />; and the calibrated $T_{eff}$ and log(g) from APOGEE, with their associated errors.

Table 2 contains the asteroseismic parameters for the stars including $v_{max}$, $\Delta v$, $f_{\Delta v}$, mass, radius, and the corresponding mass and radius coefficients, all with their respective errors. There is also a flag that pertains to $f_{\Delta v}$, for which an integer value of 0 indicates no issue with the calculation, an integer value of 1 indicates that $f_{\Delta v}$ was computed by extrapolating beyond the bounds of the $f_{\Delta v}$ grid, and an integer value of 2 indicates that $f_{\Delta v}$ could not be computed due to a lack of $\Delta v$.

Table 3 contains elemental abundance information from APOGEE and magnitude and color information from the EPIC. The abundance information given is the [M/H], [Fe/H], and [α/M], with their associated errors from APOGEE. There is also a flag indicating whether a source is high-[α/M] (1) or low-[α/M] (0), with an extra condition for stars that are close to the dividing line (within $2\sigma$) and/or have [Fe/H] $< -1$ ($-1$). The magnitude information includes the $V_{JK}$ magnitude,

<footnote n="35">³⁵ Asteroseismic evolutionary states for the K2-GAP sample can be found in Zinn et al. (2022).</footnote>
<figure><img src="image_6.png" /><figcaption>**Figure 4.** Same as Figure 1 but in magnitude ($V_{mag}$) vs. $v_{max}$ [$\mu$Hz] space. The scaling values can be determined from the plot titles. The $v_{max}$ histogram (bottom left) ranges within $0 < v_{max}$ [$\mu$Hz] < 240, and the magnitude histogram (bottom right) ranges within $8.5 < V_{mag} < 16$. See Figure 1 for more general information.</figcaption></figure>

calculated using the J- and Ks-band magnitudes (also included); the J - Ks color; and the associated error for each, with the $V_{JK}$ error calculated using the standard propagation of uncertainty.

The final table (Table 4) contains kinematic and orbital information for the stars. The corrected parallax and error from Gaia DR3 are given, together with the following parameters computed with the Gala module (Price-Whelan 2017; Price-Whelan et al. 2022; for other references, see Section 4.3): Galactic eccentricity, $|Z_{max}|$ (the farthest point from the Galactic plane reached by the star in its orbit), angular momentum, total energy, and the U, V, and W components of the velocity. Each parameter also comes with an associated error. The final flag provided is the DR3 flag, which is nonzero if either of the following is true: the star is flagged in the non_single_star column of DR3, or the fidelity_v2 value from Rybizki et al. (2022) is ≤0.5 or unavailable.

The APO-K2 catalog can be found as an electronic table in this paper and on the companion GitHub.<fnref n="36" /> A frozen version of the data in this table can be found at Zenodo using the following DOI: https://doi.org/10.5281/zenodo.8373233. The public catalog contains all information needed to recreate the plots in this paper. The GitHub and the paper's website<fnref n="37" /> also contain supplemental plots, including the selection

function density plots for the individual K2 campaigns, and their density matrices as .csv files. In future, further extensions to the APO-K2 catalog will be placed here. Furthermore, in the interest of accessibility, alternative text<fnref n="38" /> for the plots can be found at these sources, as well as author information, and relevant conference presentations. The APOKASC-2 data used in this paper can be found directly at http://vizier.u-strasbg.fr/viz-bin/VizieR-3?-source=J/ApJS/215/19, or by way of Pinsonneault et al. (2018).

### 3.3. Sample Metallicity

K2 sampled multiple Galactic lines of sight providing a broad overview of the metallicity distribution of the Milky Way. Overall, our catalog provides a range of metallicities for evolved stars, particularly in campaigns of high and low Galactic latitudes.

Figure 5 shows the [M/H] distribution for each K2 campaign. Each histogram contains all stars observed in the campaign, including those that appear in multiple campaigns. The bottom right histogram shows the metallicity distribution for the APOKASC-2 sample. C10 boasts the lowest mean metallicity with $\langle [M/H] \rangle = -0.50$ [dex] at $b = 59^\circ 6$.<fnref n="39" /> The highest average metallicity is in C11 ($\langle [M/H] \rangle = -0.05$ [dex]

<footnote n="36">³⁶ https://github.com/Jessstella/APO-K2</footnote>

<footnote n="37">³⁷ https://www.jesscastasik.com/apo-k2</footnote>

<footnote n="38">³⁸ For those who may be blind or visually impaired.</footnote>

<footnote n="39">³⁹ Where *b* is the average Galactic latitude for the field.</footnote>
<table><caption>Table 1
Basic Positional and Stellar Parameter Data for Each of the Stars in the APO-K2 Catalog</caption><thead><tr><th>EPIC ID</th><th>APOGEE ID</th><th>Gaia DR3 ID</th><th>Campaign</th><th>R.A.<br>(deg)</th><th>Decl.<br>(deg)</th><th>b<br>(deg)</th><th>l<br>(deg)</th><th>Evol</th><th>T<sub>eff</sub><br>(K)</th><th>σ<sub>T<sub>eff</sub></sub><br>(K)</th><th>log(g)<br>(dex)</th><th>σ<sub>log(g)</sub><br>(dex)</th></tr></thead><tbody><tr><td>211705076</td><td>2M08374542+1558546</td><td>657961231375051264</td><td>5, 16, 18</td><td>129.4393</td><td>15.9818</td><td>30.56</td><td>209.68</td><td>RGB</td><td>4664</td><td>7</td><td>2.872</td><td>0.021</td></tr><tr><td>212873074</td><td>2M13305142-0302596</td><td>3637132654493312384</td><td>17</td><td>202.7143</td><td>-3.0499</td><td>58.36</td><td>321.95</td><td>RGB</td><td>4789</td><td>11</td><td>2.782</td><td>0.029</td></tr><tr><td>204651310</td><td>2M16593864-2127129</td><td>4126325130252374656</td><td>11</td><td>254.911</td><td>-21.4536</td><td>12.79</td><td>0.4</td><td>RGB</td><td>4667</td><td>7</td><td>3.027</td><td>0.02</td></tr><tr><td>212386819</td><td>2M13364485-1513074</td><td>3606298775037819264</td><td>6</td><td>204.1869</td><td>-15.2187</td><td>46.25</td><td>318.84</td><td>RC</td><td>4761</td><td>8</td><td>2.474</td><td>0.022</td></tr><tr><td>228774437</td><td>2M12441419-0751315</td><td>3675439948842715520</td><td>10</td><td>191.0591</td><td>-7.8588</td><td>54.97</td><td>299.82</td><td>RC</td><td>5006</td><td>9</td><td>2.847</td><td>0.021</td></tr><tr><td>212349887</td><td>2M13394793-1608035</td><td>3605235169336614400</td><td>6</td><td>204.9497</td><td>-16.1343</td><td>45.17</td><td>319.52</td><td>RC</td><td>4828</td><td>9</td><td>2.457</td><td>0.024</td></tr><tr><td>204970434</td><td>2M16494197-2001358</td><td>4130505439095442944</td><td>2</td><td>252.4249</td><td>-20.0266</td><td>15.51</td><td>0.14</td><td>RGB</td><td>4827</td><td>14</td><td>2.415</td><td>0.035</td></tr><tr><td>228909546</td><td>2M12254205-0306337</td><td>3693228260274665600</td><td>10</td><td>186.4252</td><td>-3.1094</td><td>59.13</td><td>290.33</td><td>RC</td><td>4725</td><td>8</td><td>2.378</td><td>0.022</td></tr><tr><td>201698245</td><td>2M11284829+0336340</td><td>3812520972624745216</td><td>1</td><td>172.2012</td><td>3.6095</td><td>59.3</td><td>259.34</td><td>RGB</td><td>4665</td><td>10</td><td>2.239</td><td>0.032</td></tr><tr><td>201495451</td><td>2M10544228+0027166</td><td>3804835077108840704</td><td>14</td><td>163.6762</td><td>0.4546</td><td>51.32</td><td>251.66</td><td>RC</td><td>4662</td><td>7</td><td>2.43</td><td>0.021</td></tr><tr><td>206384822</td><td>2M22300191-0652342</td><td>2622798470238605184</td><td>3</td><td>337.508</td><td>-6.8762</td><td>-50.83</td><td>57.51</td><td>RGB</td><td>4179</td><td>5</td><td>1.824</td><td>0.02</td></tr><tr><td>247512035</td><td>2M05024943+2217174</td><td>3418251294206034816</td><td>13</td><td>75.706</td><td>22.2882</td><td>-11.71</td><td>180.16</td><td>RC</td><td>4677</td><td>7</td><td>2.433</td><td>0.021</td></tr><tr><td>211623551</td><td>2M08413695+1451547</td><td>609605736481635200</td><td>5, 16, 18</td><td>130.404</td><td>14.8652</td><td>30.98</td><td>211.29</td><td>RC</td><td>5032</td><td>10</td><td>2.757</td><td>0.022</td></tr><tr><td>251566284</td><td>2M13291268-0202116</td><td>3638370116175271808</td><td>17</td><td>202.3029</td><td>-2.0366</td><td>59.45</td><td>321.75</td><td>RGB</td><td>4941</td><td>9</td><td>2.975</td><td>0.023</td></tr><tr><td>248856910</td><td>2M10595542+1204552</td><td>3871633230290062208</td><td>14</td><td>164.981</td><td>12.082</td><td>59.85</td><td>237.38</td><td>RGB</td><td>4800</td><td>8</td><td>2.49</td><td>0.022</td></tr><tr><td>212328705</td><td>2M13362612-1642100</td><td>3603874691200483584</td><td>6</td><td>204.1088</td><td>-16.7028</td><td>44.83</td><td>318.21</td><td>RGB</td><td>4806</td><td>9</td><td>2.592</td><td>0.025</td></tr><tr><td>228902151</td><td>2M12271983-0314176</td><td>3693539215906675968</td><td>10</td><td>186.8326</td><td>-3.2382</td><td>59.08</td><td>291.16</td><td>RC</td><td>4958</td><td>10</td><td>2.426</td><td>0.027</td></tr><tr><td>212342710</td><td>2M13353650-1619290</td><td>3603970421727041152</td><td>6</td><td>203.9021</td><td>-16.3247</td><td>45.25</td><td>318.07</td><td>RC</td><td>4699</td><td>7</td><td>2.445</td><td>0.021</td></tr><tr><td>211342712</td><td>2M08532503+1040506</td><td>598595708076959872</td><td>5</td><td>133.3543</td><td>10.6807</td><td>31.89</td><td>217.15</td><td>RGB</td><td>4638</td><td>7</td><td>2.214</td><td>0.023</td></tr><tr><td>248833327</td><td>2M11001398+1129143</td><td>3871457922609751296</td><td>14</td><td>165.0583</td><td>11.4873</td><td>59.58</td><td>238.43</td><td>RGB</td><td>4582</td><td>7</td><td>2.584</td><td>0.024</td></tr><tr><td>211418744</td><td>2M08501827+1155212</td><td>604967244817098240</td><td>[5, 16, 18]</td><td>132.5762</td><td>11.9226</td><td>31.73</td><td>215.45</td><td>RC</td><td>4743</td><td>8</td><td>2.353</td><td>0.023</td></tr><tr><td>248828012</td><td>2M10575784+1121231</td><td>3871441365511075968</td><td>14</td><td>164.491</td><td>11.3564</td><td>59.04</td><td>238.02</td><td>RC</td><td>4725</td><td>8</td><td>2.444</td><td>0.022</td></tr><tr><td>247487137</td><td>2M04574880+2205410</td><td>3412369491113446912</td><td>13</td><td>74.4534</td><td>22.0947</td><td>-12.75</td><td>179.61</td><td>RC</td><td>4844</td><td>9</td><td>2.498</td><td>0.024</td></tr><tr><td>211380313</td><td>2M08521656+1119380</td><td>604696730596495744</td><td>5, 18</td><td>133.069</td><td>11.3272</td><td>31.91</td><td>216.32</td><td>RGB</td><td>4391</td><td>6</td><td>2.122</td><td>0.021</td></tr><tr><td>228973349</td><td>2M12283232-0158166</td><td>3693965688979458304</td><td>10</td><td>187.1347</td><td>-1.9713</td><td>60.38</td><td>291.29</td><td>RC</td><td>4879</td><td>9</td><td>2.51</td><td>0.025</td></tr><tr><td>212357017</td><td>2M13374476-1556555</td><td>3605438063591567872</td><td>6</td><td>204.4365</td><td>-15.9488</td><td>45.48</td><td>318.91</td><td>RGB</td><td>4729</td><td>8</td><td>2.928</td><td>0.02</td></tr><tr><td>204964919</td><td>2M16461562-2003089</td><td>4130449814981630208</td><td>2</td><td>251.5651</td><td>-20.0525</td><td>16.14</td><td>359.61</td><td>RGB</td><td>4560</td><td>9</td><td>2.714</td><td>0.024</td></tr><tr><td>251541831</td><td>2M13223736-0235249</td><td>3638103763778784768</td><td>17</td><td>200.6557</td><td>-2.5903</td><td>59.35</td><td>318.34</td><td>RC</td><td>4922</td><td>9</td><td>2.628</td><td>0.023</td></tr><tr><td>247418635</td><td>2M05021404+2132500</td><td>3409186130072687872</td><td>13</td><td>75.5585</td><td>21.5472</td><td>-12.25</td><td>180.69</td><td>RGB</td><td>4386</td><td>6</td><td>1.96</td><td>0.021</td></tr><tr><td>248404489</td><td>2M10501626-0016330</td><td>3806259563141801344</td><td>14</td><td>162.5678</td><td>-0.2758</td><td>50.02</td><td>251.21</td><td>RGB</td><td>4217</td><td>5</td><td>1.991</td><td>0.019</td></tr><tr><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td></tr></tbody></table>

Notes. The EPIC ID, APOGEE ID, and Gaia DR3 ID are given in the first three columns and drawn from their respective catalogs. The campaign number corresponds to the K2 campaign of observation; if the star was observed in more than one campaign then all campaigns are listed. The R.A. and decl. are given in degrees as are the Galactic latitude and longitude. The “Evol” column contains the derived evolutionary state of the star with “RC” corresponding to red clump stars and “RGB” corresponding to red giant branch stars. The T<sub>eff</sub> [K] and σ<sub>T<sub>eff</sub></sub> [K] columns provide the calibrated effective temperatures from APOGEE and the log(g) [dex] and σ<sub>log(g)</sub> [dex] columns are the calibrated surface gravities from APOGEE. Note that the full data set shown in Tables 1–4 is available in machine-readable format. These versions only show an example for the reader. (This table is available in machine-readable form.)
<table><caption>**Table 2**
The Asteroseismic Values for the Stars in the Sample</caption><thead><tr><th>EPIC ID</th><th>ν<sub>max</sub><br>(μHz)</th><th>σ<sub>ν<sub>max</sub></sub><br>(μHz)</th><th>Δν<br>(μHz)</th><th>σ<sub>Δν</sub><br>(μHz)</th><th>f<sub>Δν</sub></th><th>σ<sub>f<sub>Δν</sub></sub></th><th>f<sub>Δν</sub> Flag</th><th>κ<sub>M</sub></th><th>σ<sub>κ<sub>M</sub></sub></th><th>Mass<br>(M<sub>☉</sub>)</th><th>σ<sub>Mass</sub><br>(M<sub>☉</sub>)</th><th>κ<sub>R</sub></th><th>σ<sub>κ<sub>R</sub></sub></th><th>Radius<br>(R<sub>☉</sub>)</th><th>σ<sub>Radius</sub><br>(R<sub>☉</sub>)</th></tr></thead><tbody><tr><td>211705076</td><td>98.008</td><td>0.574</td><td>9.267</td><td>0.091</td><td>1.024</td><td>0.0008</td><td>0</td><td>1.463</td><td>0.063</td><td>1.061</td><td>0.069</td><td>6.776</td><td>0.139</td><td>6.089</td><td>0.125</td></tr><tr><td>212873074</td><td>49.941</td><td>0.411</td><td>5.198</td><td>0.019</td><td>1.0261</td><td>0.0009</td><td>0</td><td>1.955</td><td>0.056</td><td>1.476</td><td>0.05</td><td>10.974</td><td>0.121</td><td>9.992</td><td>0.111</td></tr><tr><td>204651310</td><td>148.608</td><td>1.503</td><td>12.949</td><td>0.032</td><td>1.0158</td><td>0.0012</td><td>0</td><td>1.338</td><td>0.043</td><td>0.971</td><td>0.033</td><td>5.262</td><td>0.059</td><td>4.73</td><td>0.053</td></tr><tr><td>212386819</td><td>32.987</td><td>1.205</td><td>3.952</td><td>0.069</td><td>0.9978</td><td>0.0006</td><td>0</td><td>1.686</td><td>0.219</td><td>1.262</td><td>0.196</td><td>12.54</td><td>0.634</td><td>11.385</td><td>0.575</td></tr><tr><td>228774437</td><td>89.247</td><td>1.575</td><td>7.56</td><td>0.093</td><td>0.9932</td><td>0.0005</td><td>0</td><td>2.495</td><td>0.18</td><td>2.012</td><td>0.189</td><td>9.273</td><td>0.281</td><td>8.632</td><td>0.261</td></tr><tr><td>212349887</td><td>31.614</td><td>0.702</td><td>3.97</td><td>0.035</td><td>0.9981</td><td>0.0007</td><td>0</td><td>1.457</td><td>0.11</td><td>1.113</td><td>0.097</td><td>11.908</td><td>0.338</td><td>10.886</td><td>0.309</td></tr><tr><td>204970434</td><td>25.992</td><td>0.701</td><td>2.979</td><td>0.036</td><td>1.0214</td><td>0.0023</td><td>0</td><td>2.554</td><td>0.241</td><td>1.951</td><td>0.217</td><td>17.386</td><td>0.63</td><td>15.892</td><td>0.576</td></tr><tr><td>228909546</td><td>31.082</td><td>0.639</td><td>3.69</td><td>0.153</td><td>0.9972</td><td>0.0009</td><td>0</td><td>1.857</td><td>0.329</td><td>1.374</td><td>0.37</td><td>13.557</td><td>1.158</td><td>12.261</td><td>1.048</td></tr><tr><td>201698245</td><td>27.508</td><td>0.835</td><td>3.05</td><td>0.115</td><td>1.0242</td><td>0.0057</td><td>0</td><td>2.757</td><td>0.486</td><td>2.0</td><td>0.511</td><td>17.558</td><td>1.427</td><td>15.778</td><td>1.283</td></tr><tr><td>201495451</td><td>32.034</td><td>0.489</td><td>4.081</td><td>0.039</td><td>0.9984</td><td>0.0004</td><td>0</td><td>1.359</td><td>0.081</td><td>0.985</td><td>0.075</td><td>11.423</td><td>0.279</td><td>10.262</td><td>0.251</td></tr><tr><td>206384822</td><td>11.93</td><td>0.295</td><td>1.951</td><td>0.011</td><td>1.0444</td><td>0.0018</td><td>0</td><td>1.343</td><td>0.104</td><td>0.826</td><td>0.068</td><td>18.61</td><td>0.506</td><td>15.827</td><td>0.43</td></tr><tr><td>247512035</td><td>33.972</td><td>0.707</td><td>4.218</td><td>0.063</td><td>0.9983</td><td>0.0004</td><td>0</td><td>1.42</td><td>0.123</td><td>1.034</td><td>0.117</td><td>11.339</td><td>0.413</td><td>10.202</td><td>0.372</td></tr><tr><td>211623551</td><td>90.875</td><td>1.456</td><td>7.487</td><td>0.065</td><td>0.9932</td><td>0.0005</td><td>0</td><td>2.738</td><td>0.162</td><td>2.225</td><td>0.163</td><td>9.626</td><td>0.227</td><td>8.984</td><td>0.212</td></tr><tr><td>251566284</td><td>133.479</td><td>1.389</td><td>10.884</td><td>0.136</td><td>1.0116</td><td>0.0008</td><td>0</td><td>1.943</td><td>0.114</td><td>1.536</td><td>0.131</td><td>6.691</td><td>0.181</td><td>6.188</td><td>0.168</td></tr><tr><td>248856910</td><td>39.742</td><td>0.658</td><td>3.662</td><td>0.029</td><td>1.0025</td><td>0.0031</td><td>0</td><td>4.0</td><td>0.236</td><td>3.029</td><td>0.214</td><td>17.595</td><td>0.403</td><td>16.038</td><td>0.368</td></tr><tr><td>212328705</td><td>54.207</td><td>0.785</td><td>5.761</td><td>0.039</td><td>1.0272</td><td>0.0007</td><td>0</td><td>1.657</td><td>0.085</td><td>1.257</td><td>0.077</td><td>9.696</td><td>0.192</td><td>8.844</td><td>0.176</td></tr><tr><td>228902151</td><td>30.078</td><td>1.011</td><td>4.233</td><td>0.125</td><td>0.9932</td><td>0.0079</td><td>0</td><td>0.971</td><td>0.151</td><td>0.772</td><td>0.164</td><td>9.967</td><td>0.677</td><td>9.233</td><td>0.627</td></tr><tr><td>212342710</td><td>36.614</td><td>0.648</td><td>4.274</td><td>0.061</td><td>0.9977</td><td>0.0004</td><td>0</td><td>1.686</td><td>0.131</td><td>1.237</td><td>0.13</td><td>11.9</td><td>0.4</td><td>10.733</td><td>0.361</td></tr><tr><td>211342712</td><td>16.67</td><td>0.867</td><td>2.347</td><td>0.004</td><td>1.0305</td><td>0.0016</td><td>0</td><td>1.749</td><td>0.273</td><td>1.258</td><td>0.197</td><td>17.963</td><td>0.936</td><td>16.094</td><td>0.839</td></tr><tr><td>248833327</td><td>42.672</td><td>0.279</td><td>5.133</td><td>0.038</td><td>1.0352</td><td>0.0004</td><td>0</td><td>1.283</td><td>0.046</td><td>0.907</td><td>0.046</td><td>9.618</td><td>0.156</td><td>8.566</td><td>0.139</td></tr><tr><td>211418744</td><td>26.583</td><td>0.443</td><td>3.286</td><td>0.051</td><td>0.9992</td><td>0.0003</td><td>0</td><td>1.846</td><td>0.147</td><td>1.374</td><td>0.151</td><td>14.616</td><td>0.515</td><td>13.244</td><td>0.467</td></tr><tr><td>248828012</td><td>31.432</td><td>1.087</td><td>4.065</td><td>0.211</td><td>0.998</td><td>0.0033</td><td>0</td><td>1.304</td><td>0.303</td><td>0.964</td><td>0.332</td><td>11.296</td><td>0.236</td><td>10.216</td><td>1.118</td></tr><tr><td>247487137</td><td>36.982</td><td>1.312</td><td>4.165</td><td>0.043</td><td>0.995</td><td>0.0009</td><td>0</td><td>1.927</td><td>0.22</td><td>1.479</td><td>0.185</td><td>12.659</td><td>0.52</td><td>11.592</td><td>0.476</td></tr><tr><td>211380313</td><td>15.885</td><td>0.283</td><td>2.169</td><td>0.059</td><td>1.0315</td><td>0.003</td><td>0</td><td>2.075</td><td>0.251</td><td>1.375</td><td>0.248</td><td>20.044</td><td>1.147</td><td>17.476</td><td>1.0</td></tr><tr><td>228973349</td><td>35.42</td><td>0.321</td><td>4.342</td><td>0.079</td><td>0.9976</td><td>0.0005</td><td>0</td><td>1.433</td><td>0.111</td><td>1.113</td><td>0.132</td><td>11.157</td><td>0.418</td><td>10.253</td><td>0.385</td></tr><tr><td>212357017</td><td>108.613</td><td>1.046</td><td>9.474</td><td>0.061</td><td>1.0187</td><td>0.0006</td><td>0</td><td>1.823</td><td>0.071</td><td>1.35</td><td>0.067</td><td>7.185</td><td>0.116</td><td>6.501</td><td>0.105</td></tr><tr><td>204964919</td><td>64.729</td><td>1.655</td><td>...</td><td>...</td><td>...</td><td>...</td><td>2</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td></tr><tr><td>251541831</td><td>43.795</td><td>0.574</td><td>4.63</td><td>0.022</td><td>0.9937</td><td>0.0005</td><td>0</td><td>2.096</td><td>0.092</td><td>1.648</td><td>0.082</td><td>12.133</td><td>0.196</td><td>11.199</td><td>0.182</td></tr><tr><td>247418635</td><td>10.032</td><td>0.165</td><td>1.489</td><td>0.191</td><td>1.0287</td><td>0.0202</td><td>0</td><td>2.357</td><td>1.215</td><td>1.559</td><td>1.268</td><td>26.884</td><td>6.913</td><td>23.425</td><td>6.024</td></tr><tr><td>248404489</td><td>16.014</td><td>0.45</td><td>2.389</td><td>0.014</td><td>1.0416</td><td>0.002</td><td>0</td><td>1.444</td><td>0.126</td><td>0.9</td><td>0.083</td><td>16.654</td><td>0.507</td><td>14.228</td><td>0.433</td></tr><tr><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td></tr></tbody></table>

**Notes.** The EPIC ID is used as the main identifier in this and subsequent tables. From left to right we provide the frequency of maximum power ($\nu_{max}$) [μHz], the large frequency separation ($\Delta\nu$) [μHz], the $\Delta\nu$ correction factor ($f_{\Delta\nu}$), and the $f_{\Delta\nu}$ flag. Note that the $\Delta\nu$ values provided here have already had the $f_{\Delta\nu}$ applied and therefore these correction factors are not needed in Equations (1) and (2). Explanation of this flag can be found in Section 3.2. We also include the asteroseismic mass and radius coefficients, along with the stellar mass [$M_{\odot}$] and stellar radius [$R_{\odot}$] computed when using these values with the APOGEE temperatures, and their associated errors. Note that the full data set shown in Tables 1–4 is available in machine-readable format. These versions only show an example for the reader.

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

at $b = 9^{\circ}1$). This is in contrast to the APOKASC-2 histogram with a mean metallicity of $-0.02$ [dex] (at $b = 13^{\circ}5$); all of the K2 histograms have lower mean metallicity than the Kepler field.

Kepler's objective of observing nearby, solar-metallicity dwarf stars likely contributed to its observing relatively few metal-poor stars. In contrast, the K2-GAP sample was selected with completeness of the evolved stars in mind, a sample ideal for Galactic archaeology. Apart from the observing selection function, the field choice itself is a determinative factor in the resulting metallicity distributions of Kepler versus K2: the K2 sample is, on average, farther away from the Galactic plane than the stars in the Kepler field. This is evident in Figures 5 and 6, as the stars at higher and lower Galactic latitude are generally more metal-poor.

### 3.4. Sample Overview

Our final APO-K2 sample contains 7672 unique stars with spectroscopic, asteroseismic, and astrometric data. The sample includes a total of 8460 observations across multiple campaigns, in which sometimes the same star was observed

in more than one campaign. When they are separated into evolutionary states, we have 2465 unique RC stars and 5207 unique RGB stars. The extensive overlap (see Section 2.1) between the APOGEE catalog and K2-GAP is due to the priority ordering for target selection (see Table 3 of S22). Targets were chosen for observation in K2-GAP according to criteria such as the 2MASS and SDSS color and membership in existing spectroscopic survey catalogs, with each criterion given a priority ranking. This selection method gave the highest priority to APOGEE targets; APOGEE, in turn, prioritized observing spectra of K2-GAP stars resulting in the large overlap we see.

The sample reaches $\sim 60^{\circ}$ above and below the plane of the Milky Way, and explores the Galactic center. The positions of these stars relative to the plane of the Milky Way are shown in Figure 6. Color represents [Fe/H] for each star in our sample (from APOGEE), with the color bar scaled between $-1.0$ and $0.5$ [dex]; the actual maximum and minimum values of [Fe/H] are $-2.45$ and $0.51$ [dex], respectively. This scaling shows the relatively metal-rich state of the Kepler field in comparison to K2 and the metal-rich state of C2, C7, C11, and C15 relative to the other campaigns; we discussed campaign-specific metallicities in
<table><caption>**Table 3**

Elemental Abundance and Magnitude Information for Each of the Stars in the Sample</caption><thead><tr><th>EPIC ID</th><th>[M/H]<br>(dex)</th><th>σ<sub>[M/H]</sub><br>(dex)</th><th>[Fe/H]<br>(dex)</th><th>σ<sub>[Fe/H]</sub><br>(dex)</th><th>[α/M]</th><th>σ<sub>[α/M]</sub></th><th>α Flag</th><th>V<sub>mag</sub><br>(mag)</th><th>σ<sub>Vmag</sub><br>(mag)</th><th>J<br>(mag)</th><th>σ<sub>J</sub><br>(mag)</th><th>K<sub>s</sub><br>(mag)</th><th>σ<sub>Ks</sub><br>(mag)</th><th>J − K<sub>s</sub></th><th>σ<sub>J − Ks</sub></th></tr></thead><tbody><tr><td>211705076</td><td>0.0019</td><td>0.006</td><td>−0.0087</td><td>0.0072</td><td>0.072</td><td>0.005</td><td>−1</td><td>9.402</td><td>0.875</td><td>7.555</td><td>0.02</td><td>6.913</td><td>0.026</td><td>0.642</td><td>0.033</td></tr><tr><td>212873074</td><td>−0.2655</td><td>0.0084</td><td>−0.2752</td><td>0.0098</td><td>0.0575</td><td>0.0079</td><td>0</td><td>7.027</td><td>0.812</td><td>5.143</td><td>0.017</td><td>4.488</td><td>0.036</td><td>0.655</td><td>0.04</td></tr><tr><td>204651310</td><td>0.1912</td><td>0.0055</td><td>0.1745</td><td>0.0068</td><td>0.0274</td><td>0.0044</td><td>0</td><td>9.782</td><td>0.788</td><td>7.647</td><td>0.019</td><td>6.91</td><td>0.018</td><td>0.737</td><td>0.026</td></tr><tr><td>212386819</td><td>−0.0508</td><td>0.006</td><td>−0.0572</td><td>0.0071</td><td>0.01</td><td>0.0053</td><td>0</td><td>9.494</td><td>0.824</td><td>7.644</td><td>0.019</td><td>7.001</td><td>0.024</td><td>0.643</td><td>0.031</td></tr><tr><td>228774437</td><td>0.0398</td><td>0.0056</td><td>0.032</td><td>0.0065</td><td>−0.0191</td><td>0.0052</td><td>0</td><td>9.181</td><td>0.842</td><td>7.536</td><td>0.026</td><td>6.968</td><td>0.023</td><td>0.568</td><td>0.035</td></tr><tr><td>212349887</td><td>−0.2352</td><td>0.0064</td><td>−0.2454</td><td>0.0074</td><td>0.0469</td><td>0.0061</td><td>0</td><td>9.756</td><td>0.93</td><td>7.78</td><td>0.026</td><td>7.094</td><td>0.02</td><td>0.686</td><td>0.033</td></tr><tr><td>204970434</td><td>−0.4503</td><td>0.01</td><td>−0.4612</td><td>0.0115</td><td>0.2651</td><td>0.0101</td><td>1</td><td>13.355</td><td>1.235</td><td>11.327</td><td>0.023</td><td>10.624</td><td>0.021</td><td>0.703</td><td>0.031</td></tr><tr><td>228909546</td><td>−0.0284</td><td>0.006</td><td>−0.0343</td><td>0.0072</td><td>−0.0026</td><td>0.0052</td><td>0</td><td>9.507</td><td>0.918</td><td>7.555</td><td>0.026</td><td>6.877</td><td>0.021</td><td>0.678</td><td>0.033</td></tr><tr><td>201698245</td><td>−0.6215</td><td>0.0091</td><td>−0.6287</td><td>0.0103</td><td>0.2823</td><td>0.0092</td><td>1</td><td>12.718</td><td>1.122</td><td>10.769</td><td>0.022</td><td>10.092</td><td>0.021</td><td>0.677</td><td>0.03</td></tr><tr><td>201495451</td><td>0.0292</td><td>0.0059</td><td>0.0166</td><td>0.0072</td><td>0.0114</td><td>0.0049</td><td>0</td><td>10.013</td><td>1.122</td><td>7.97</td><td>0.027</td><td>7.262</td><td>0.026</td><td>0.708</td><td>0.037</td></tr><tr><td>206384822</td><td>0.1197</td><td>0.0061</td><td>0.1094</td><td>0.0078</td><td>0.0864</td><td>0.0042</td><td>1</td><td>11.795</td><td>1.288</td><td>9.338</td><td>0.022</td><td>8.508</td><td>0.023</td><td>0.83</td><td>0.032</td></tr><tr><td>247512035</td><td>0.0788</td><td>0.0058</td><td>0.072</td><td>0.007</td><td>−0.003</td><td>0.0048</td><td>0</td><td>10.534</td><td>1.03</td><td>8.066</td><td>0.023</td><td>7.233</td><td>0.017</td><td>0.833</td><td>0.029</td></tr><tr><td>211623551</td><td>−0.0557</td><td>0.0058</td><td>−0.056</td><td>0.0067</td><td>−0.0197</td><td>0.0056</td><td>0</td><td>9.99</td><td>0.804</td><td>8.451</td><td>0.026</td><td>7.925</td><td>0.018</td><td>0.526</td><td>0.032</td></tr><tr><td>251566284</td><td>−0.0918</td><td>0.0059</td><td>−0.0934</td><td>0.0069</td><td>0.0327</td><td>0.0057</td><td>0</td><td>9.797</td><td>0.869</td><td>8.056</td><td>0.019</td><td>7.452</td><td>0.026</td><td>0.604</td><td>0.032</td></tr><tr><td>248856910</td><td>−0.001</td><td>0.0058</td><td>−0.0074</td><td>0.007</td><td>0.0142</td><td>0.0052</td><td>0</td><td>10.136</td><td>1.076</td><td>8.205</td><td>0.026</td><td>7.534</td><td>0.026</td><td>0.671</td><td>0.037</td></tr><tr><td>212328705</td><td>−0.3587</td><td>0.0068</td><td>−0.3615</td><td>0.0077</td><td>0.0777</td><td>0.0067</td><td>0</td><td>9.872</td><td>1.046</td><td>7.947</td><td>0.029</td><td>7.278</td><td>0.023</td><td>0.669</td><td>0.037</td></tr><tr><td>228902151</td><td>−0.4721</td><td>0.0069</td><td>−0.4822</td><td>0.0077</td><td>0.1096</td><td>0.0074</td><td>0</td><td>9.75</td><td>1.171</td><td>7.993</td><td>0.035</td><td>7.383</td><td>0.027</td><td>0.61</td><td>0.044</td></tr><tr><td>212342710</td><td>0.0617</td><td>0.0058</td><td>0.0549</td><td>0.007</td><td>−0.0082</td><td>0.0049</td><td>0</td><td>10.328</td><td>1.074</td><td>8.349</td><td>0.024</td><td>7.662</td><td>0.026</td><td>0.687</td><td>0.035</td></tr><tr><td>211342712</td><td>−0.148</td><td>0.0064</td><td>−0.1552</td><td>0.0076</td><td>0.0319</td><td>0.0056</td><td>0</td><td>9.994</td><td>0.923</td><td>7.935</td><td>0.026</td><td>7.222</td><td>0.017</td><td>0.713</td><td>0.031</td></tr><tr><td>248833327</td><td>−0.2773</td><td>0.0068</td><td>−0.2961</td><td>0.008</td><td>0.1988</td><td>0.006</td><td>1</td><td>10.46</td><td>1.337</td><td>8.454</td><td>0.023</td><td>7.758</td><td>0.036</td><td>0.696</td><td>0.043</td></tr><tr><td>211418744</td><td>−0.1674</td><td>0.0063</td><td>−0.1749</td><td>0.0074</td><td>0.0238</td><td>0.0058</td><td>0</td><td>9.997</td><td>0.878</td><td>8.087</td><td>0.02</td><td>7.423</td><td>0.023</td><td>0.664</td><td>0.03</td></tr><tr><td>248828012</td><td>−0.0359</td><td>0.006</td><td>−0.0436</td><td>0.0072</td><td>0.0343</td><td>0.0052</td><td>0</td><td>10.552</td><td>0.939</td><td>8.665</td><td>0.021</td><td>8.009</td><td>0.023</td><td>0.656</td><td>0.031</td></tr><tr><td>247487137</td><td>−0.1926</td><td>0.0063</td><td>−0.1987</td><td>0.0073</td><td>0.0349</td><td>0.006</td><td>0</td><td>10.637</td><td>0.898</td><td>8.369</td><td>0.021</td><td>7.592</td><td>0.016</td><td>0.777</td><td>0.026</td></tr><tr><td>211380313</td><td>−0.0124</td><td>0.0062</td><td>−0.019</td><td>0.0077</td><td>0.0052</td><td>0.0048</td><td>0</td><td>10.072</td><td>0.92</td><td>7.875</td><td>0.023</td><td>7.119</td><td>0.018</td><td>0.756</td><td>0.029</td></tr><tr><td>228973349</td><td>−0.286</td><td>0.0065</td><td>−0.3033</td><td>0.0074</td><td>0.0633</td><td>0.0064</td><td>0</td><td>9.88</td><td>0.903</td><td>8.114</td><td>0.023</td><td>7.501</td><td>0.024</td><td>0.613</td><td>0.033</td></tr><tr><td>212357017</td><td>0.1313</td><td>0.0056</td><td>0.1253</td><td>0.0068</td><td>0.0039</td><td>0.0046</td><td>0</td><td>10.482</td><td>0.812</td><td>8.746</td><td>0.024</td><td>8.144</td><td>0.016</td><td>0.602</td><td>0.029</td></tr><tr><td>204964919</td><td>0.3467</td><td>0.0074</td><td>0.3219</td><td>0.0096</td><td>0.0244</td><td>0.0054</td><td>0</td><td>13.724</td><td>1.579</td><td>11.196</td><td>0.021</td><td>10.347</td><td>0.025</td><td>0.849</td><td>0.033</td></tr><tr><td>251541831</td><td>−0.1212</td><td>0.006</td><td>−0.1322</td><td>0.007</td><td>0.0202</td><td>0.0058</td><td>0</td><td>10.04</td><td>0.874</td><td>8.366</td><td>0.023</td><td>7.787</td><td>0.023</td><td>0.579</td><td>0.033</td></tr><tr><td>247418635</td><td>0.0323</td><td>0.0061</td><td>0.0167</td><td>0.0076</td><td>−0.0133</td><td>0.0047</td><td>0</td><td>10.706</td><td>1.23</td><td>7.76</td><td>0.023</td><td>6.809</td><td>0.017</td><td>0.951</td><td>0.029</td></tr><tr><td>248404489</td><td>0.1938</td><td>0.0059</td><td>0.1833</td><td>0.0075</td><td>0.0631</td><td>0.0041</td><td>1</td><td>11.041</td><td>1.185</td><td>8.532</td><td>0.019</td><td>7.688</td><td>0.024</td><td>0.844</td><td>0.031</td></tr><tr><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td></tr></tbody></table>

**Notes.** Metallicity is presented in the form of both [M/H] [dex] and iron abundance [Fe/H] [dex], taken from APOGEE, with their corresponding errors. The α abundance [α/M] [dex] was also taken from APOGEE. An α flag is provided, and an explanation is given in Section 3.2. The V<sub>mag</sub> [mag] was calculated from Equation (5) with the error calculated using the standard propagation of uncertainty. Also included are the J- and K<sub>s</sub>-band magnitudes [mag] from EPIC along with the J − K<sub>s</sub> color, with their associated errors. Note that the full data set shown in Tables 1–4 is available in machine-readable format. These versions only show an example for the reader.

(This table is available in machine-readable form.)
<table><caption>Table 4
Kinematic Data for the Catalog</caption><thead><tr><th>EPIC ID</th><th>ω (mas)</th><th>σω (mas)</th><th>e</th><th>σe</th><th>|Z<sub>max</sub>| (kpc)</th><th>σ|Z<sub>max</sub>| (kpc)</th><th>L<sub>Z</sub> (10<sup>3</sup> kpc km s<sup>-1</sup>)</th><th>σL<sub>Z</sub> (10<sup>3</sup> kpc km s<sup>-1</sup>)</th><th>E<sub>TOT</sub> (10<sup>5</sup> km<sup>2</sup> s<sup>-2</sup>)</th><th>σE<sub>TOT</sub> (10<sup>5</sup> km<sup>2</sup> s<sup>-2</sup>)</th><th>U (km s<sup>-1</sup>)</th><th>σU (km s<sup>-1</sup>)</th><th>V (km s<sup>-1</sup>)</th><th>σV (km s<sup>-1</sup>)</th><th>W (km s<sup>-1</sup>)</th><th>σW (km s<sup>-1</sup>)</th><th>DR3 Flag</th></tr></thead><tbody><tr><td>211705076</td><td>3.461</td><td>0.02</td><td>0.1815</td><td>0.0003</td><td>0.3807</td><td>0.0027</td><td>-1.761</td><td>0.0021</td><td>-1.3107</td><td>0.0005</td><td>42.95</td><td>0.19</td><td>-20.3</td><td>0.11</td><td>-23.85</td><td>0.13</td><td>1</td></tr><tr><td>212873074</td><td>6.812</td><td>0.033</td><td>0.1669</td><td>0.0002</td><td>0.171</td><td>0.0005</td><td>-2.1553</td><td>0.0006</td><td>-1.2094</td><td>0.0002</td><td>-14.14</td><td>0.05</td><td>35.11</td><td>0.04</td><td>1.52</td><td>0.11</td><td>0</td></tr><tr><td>204651310</td><td>4.492</td><td>0.018</td><td>0.0468</td><td>0.0005</td><td>0.1447</td><td>0.0006</td><td>-1.8019</td><td>0.0008</td><td>-1.3169</td><td>0.0002</td><td>-18.09</td><td>0.19</td><td>-4.28</td><td>0.02</td><td>8.23</td><td>0.05</td><td>0</td></tr><tr><td>212386819</td><td>1.911</td><td>0.022</td><td>0.1568</td><td>0.0003</td><td>0.4823</td><td>0.0006</td><td>-2.0743</td><td>0.0006</td><td>-1.2282</td><td>0.0003</td><td>0.11</td><td>0.08</td><td>32.22</td><td>0.08</td><td>7.26</td><td>0.11</td><td>0</td></tr><tr><td>228774437</td><td>2.298</td><td>0.019</td><td>0.0701</td><td>0.0003</td><td>0.3881</td><td>0.0002</td><td>-1.9035</td><td>0.0012</td><td>-1.2837</td><td>0.0003</td><td>-30.32</td><td>0.06</td><td>5.12</td><td>0.09</td><td>0.95</td><td>0.12</td><td>0</td></tr><tr><td>212349887</td><td>1.818</td><td>0.022</td><td>0.204</td><td>0.0006</td><td>0.4503</td><td>0.0009</td><td>-1.9458</td><td>0.0026</td><td>-1.2532</td><td>0.0005</td><td>-71.84</td><td>0.14</td><td>14.23</td><td>0.11</td><td>-3.16</td><td>0.18</td><td>0</td></tr><tr><td>204970434</td><td>0.407</td><td>0.02</td><td>0.3159</td><td>0.002</td><td>1.2523</td><td>0.0081</td><td>-0.983</td><td>0.0434</td><td>-1.5328</td><td>0.0156</td><td>-89.72</td><td>1.05</td><td>-59.57</td><td>0.18</td><td>-66.23</td><td>0.36</td><td>0</td></tr><tr><td>228909546</td><td>1.737</td><td>0.024</td><td>0.0537</td><td>0.0003</td><td>0.6553</td><td>0.0011</td><td>-1.9355</td><td>0.0006</td><td>-1.2723</td><td>0.0001</td><td>-13.68</td><td>0.06</td><td>8.85</td><td>0.08</td><td>18.0</td><td>0.12</td><td>0</td></tr><tr><td>201698245</td><td>0.406</td><td>0.019</td><td>0.3177</td><td>0.0028</td><td>3.592</td><td>0.019</td><td>-1.091</td><td>0.0456</td><td>-1.3769</td><td>0.0012</td><td>-47.89</td><td>0.2</td><td>-107.95</td><td>0.39</td><td>-95.19</td><td>0.63</td><td>0</td></tr><tr><td>201495451</td><td>1.803</td><td>0.02</td><td>0.1917</td><td>0.0005</td><td>0.4131</td><td>0.0003</td><td>-1.6493</td><td>0.0016</td><td>-1.3427</td><td>0.0002</td><td>-54.83</td><td>0.05</td><td>-33.83</td><td>0.11</td><td>-0.31</td><td>0.14</td><td>0</td></tr><tr><td>206384822</td><td>0.688</td><td>0.02</td><td>0.2196</td><td>0.0007</td><td>0.9477</td><td>0.0004</td><td>-1.3928</td><td>0.0124</td><td>-1.4106</td><td>0.0024</td><td>-2.96</td><td>0.13</td><td>-50.11</td><td>0.13</td><td>2.36</td><td>0.17</td><td>0</td></tr><tr><td>247512035</td><td>1.75</td><td>0.02</td><td>0.0379</td><td>0.0004</td><td>0.2467</td><td>0.001</td><td>-1.9701</td><td>0.0007</td><td>-1.2688</td><td>0.0002</td><td>6.43</td><td>0.15</td><td>-5.3</td><td>0.05</td><td>13.29</td><td>0.06</td><td>0</td></tr><tr><td>211623551</td><td>1.478</td><td>0.022</td><td>0.0454</td><td>0.0003</td><td>0.3824</td><td>0.0004</td><td>-1.9677</td><td>0.0008</td><td>-1.2677</td><td>0.0002</td><td>1.83</td><td>0.12</td><td>-3.63</td><td>0.09</td><td>3.84</td><td>0.11</td><td>0</td></tr><tr><td>251566284</td><td>2.683</td><td>0.023</td><td>0.2038</td><td>0.0001</td><td>0.3831</td><td>0.0001</td><td>-2.0522</td><td>0.0005</td><td>-1.2264</td><td>0.0004</td><td>43.47</td><td>0.06</td><td>25.91</td><td>0.05</td><td>-1.25</td><td>0.12</td><td>0</td></tr><tr><td>248856910</td><td>1.078</td><td>0.027</td><td>0.1301</td><td>0.0004</td><td>0.8584</td><td>0.0008</td><td>-1.9635</td><td>0.0024</td><td>-1.255</td><td>0.0003</td><td>23.9</td><td>0.11</td><td>3.72</td><td>0.11</td><td>-9.88</td><td>0.13</td><td>0</td></tr><tr><td>212328705</td><td>2.121</td><td>0.027</td><td>-999.0</td><td>-999.0</td><td>...</td><td>-999.0</td><td>-999.0</td><td>-999.0</td><td>-999.0</td><td>-999.0</td><td>-999.0</td><td>-999.0</td><td>-999.0</td><td>-999.0</td><td>-999.0</td><td>-999.0</td><td>0</td></tr><tr><td>228902151</td><td>1.673</td><td>0.019</td><td>0.148</td><td>0.0002</td><td>0.8763</td><td>0.0024</td><td>-1.6687</td><td>0.0017</td><td>-1.3348</td><td>0.0003</td><td>27.45</td><td>0.06</td><td>-22.71</td><td>0.08</td><td>33.56</td><td>0.13</td><td>0</td></tr><tr><td>212342710</td><td>1.464</td><td>0.021</td><td>0.1279</td><td>0.0003</td><td>0.5987</td><td>0.0009</td><td>-1.9301</td><td>0.0018</td><td>-1.2679</td><td>0.0003</td><td>15.41</td><td>0.1</td><td>17.27</td><td>0.09</td><td>-16.21</td><td>0.12</td><td>0</td></tr><tr><td>211342712</td><td>1.054</td><td>0.024</td><td>0.1276</td><td>0.0003</td><td>1.1991</td><td>0.0027</td><td>-1.8917</td><td>0.0009</td><td>-1.2682</td><td>0.0008</td><td>23.27</td><td>0.1</td><td>-14.79</td><td>0.08</td><td>42.69</td><td>0.09</td><td>0</td></tr><tr><td>248833327</td><td>1.664</td><td>0.025</td><td>0.3462</td><td>0.0004</td><td>0.729</td><td>0.0022</td><td>-1.3208</td><td>0.0057</td><td>-1.4041</td><td>0.0008</td><td>-55.83</td><td>0.07</td><td>-74.35</td><td>0.09</td><td>33.33</td><td>0.16</td><td>0</td></tr><tr><td>211418744</td><td>1.329</td><td>0.018</td><td>-999.0</td><td>-999.0</td><td>...</td><td>-999.0</td><td>-999.0</td><td>-999.0</td><td>-999.0</td><td>-999.0</td><td>-999.0</td><td>-999.0</td><td>-999.0</td><td>-999.0</td><td>-999.0</td><td>-999.0</td><td>0</td></tr><tr><td>248828012</td><td>1.209</td><td>0.018</td><td>0.1809</td><td>0.0004</td><td>0.7986</td><td>0.0008</td><td>-2.0093</td><td>0.0014</td><td>-1.2365</td><td>0.0003</td><td>38.54</td><td>0.09</td><td>10.4</td><td>0.1</td><td>-13.17</td><td>0.15</td><td>0</td></tr><tr><td>247487137</td><td>1.502</td><td>0.024</td><td>0.1907</td><td>0.0004</td><td>0.2011</td><td>0.001</td><td>-1.9287</td><td>0.0017</td><td>-1.263</td><td>0.0003</td><td>-62.87</td><td>0.16</td><td>-12.34</td><td>0.06</td><td>8.11</td><td>0.07</td><td>0</td></tr><tr><td>211380313</td><td>1.214</td><td>0.018</td><td>-999.0</td><td>-999.0</td><td>...</td><td>-999.0</td><td>-999.0</td><td>-999.0</td><td>-999.0</td><td>-999.0</td><td>-999.0</td><td>-999.0</td><td>-999.0</td><td>-999.0</td><td>-999.0</td><td>-999.0</td><td>0</td></tr><tr><td>228973349</td><td>1.517</td><td>0.025</td><td>0.0738</td><td>0.0004</td><td>0.6323</td><td>0.0002</td><td>-1.9701</td><td>0.0009</td><td>-1.2622</td><td>0.0002</td><td>-12.52</td><td>0.07</td><td>13.7</td><td>0.08</td><td>0.3</td><td>0.14</td><td>0</td></tr><tr><td>212357017</td><td>1.994</td><td>0.024</td><td>0.195</td><td>0.0002</td><td>0.4134</td><td>0.0002</td><td>-1.9521</td><td>0.0007</td><td>-1.2537</td><td>0.0003</td><td>44.67</td><td>0.1</td><td>17.71</td><td>0.08</td><td>0.35</td><td>0.12</td><td>0</td></tr><tr><td>204964919</td><td>0.598</td><td>0.02</td><td>0.2003</td><td>0.0023</td><td>0.4867</td><td>0.0008</td><td>-1.4372</td><td>0.0164</td><td>-1.412</td><td>0.0054</td><td>-67.91</td><td>0.8</td><td>-11.55</td><td>0.12</td><td>10.09</td><td>0.26</td><td>0</td></tr><tr><td>251541831</td><td>1.323</td><td>0.027</td><td>0.2332</td><td>0.0004</td><td>0.7839</td><td>0.0003</td><td>-2.0732</td><td>0.0009</td><td>-1.2101</td><td>0.0009</td><td>-66.81</td><td>0.11</td><td>30.46</td><td>0.1</td><td>3.68</td><td>0.16</td><td>0</td></tr><tr><td>247418635</td><td>1.219</td><td>0.027</td><td>0.1665</td><td>0.0005</td><td>0.2178</td><td>0.0012</td><td>-2.1155</td><td>0.0027</td><td>-1.2188</td><td>0.0007</td><td>-55.65</td><td>0.14</td><td>4.74</td><td>0.1</td><td>6.81</td><td>0.11</td><td>0</td></tr><tr><td>248404489</td><td>1.071</td><td>0.022</td><td>0.1185</td><td>0.0006</td><td>0.8223</td><td>0.0004</td><td>-2.1213</td><td>0.0032</td><td>-1.2178</td><td>0.0011</td><td>-21.57</td><td>0.11</td><td>21.76</td><td>0.15</td><td>2.28</td><td>0.15</td><td>0</td></tr><tr><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td></tr></tbody></table>

Notes. Includes the EPIC ID that links all the tables. We then provide, in the next columns, the Gaia DR3 parallaxes corrected according to the Gaia zero-point, evaluated using the *Python* implementation of the Lindegren et al. (2021) correction, and their uncertainties [mas] (according to El-Badry et al. 2021). In the succeeding columns we give the *Gala*-defined parameters: the Galactic eccentricity, the maximum excursion of the orbit from the Galactic plane (|Z<sub>max</sub>|) [kpc], the orbital angular momentum (L<sub>Z</sub>) [10<sup>3</sup> kpc km s<sup>-1</sup>], the total orbital energy (E<sub>TOT</sub>) [10<sup>5</sup> km<sup>2</sup> s<sup>-2</sup>], and the U, V, and W velocities [km s<sup>-1</sup>]. All these parameters' values are provided with their associated errors. Finally, we provide a DR3 binary flag, an explanation of which can be found in Section 3.2. Note that the full data set shown in Tables 1–4 is available in machine-readable format. These versions only show an example for the reader.

(This table is available in machine-readable form.)
<figure><img src="image_7.png" /><figcaption>**Figure 5.** Each histogram shows the APOGEE [M/H] distribution for the K2 campaigns. The bottom right-hand plot, with hatched markings, is the metallicity distribution of the Kepler field taken from APOKASC-2. Color indicates the mean metallicity, with a darker blue corresponding to a higher mean metallicity. The title of each plot gives the campaign number, the number of stars in the campaign, the average metallicity, and the average Galactic latitude of the campaign field.</figcaption></figure>

Section 3.3. We did not include C9 or C19 (see Section 2.2). Throughout this work we investigate, in particular, the low-metallicity stars below −1.0 [dex], which have not been available in large asteroseismic catalogs until now. For comparison, there are ~288 stars in this catalog with [Fe/H] ≤ −1.0, and only ~35 in the APOKASC-2 catalog.

### 3.5. Identifying Stellar Subpopulations

We separated the APO-K2 sample into two subsamples (RGB and RC) using their evolutionary states (as described in

Section 2.3). The H-R diagram shown in Figure 7 illustrates that combining asteroseismology and spectroscopy enables us to decipher areas that contain interesting details like the RGB bump and secondary RC stars (Tayar et al. 2019). The left plot presents the RC stars prominently, with the RGB stars indicated by gray crosses in the background, and the right-hand side presents the RGB stars prominently, with the RC stars indicated by gray crosses. By separating these two groups of stars, we hope to make the different samples clear to the reader. Figure 8 also displays these stars but in log(g)–T<sub>eff</sub>
<figure><img src="image_8.png" /><figcaption>**Figure 6.** Footprint of each of the K2 campaigns in this sample, on a backdrop of the Milky Way, with axes representing the coordinates [deg]. Each point represents a star in our catalog and color indicates its metallicity. The position of the Kepler mission field (also colored by metallicity [Fe/H]) as taken from APOKASC-2 is shown for reference. Gaps seen in the telescope's field of view correspond to CCD modules 3 and 7, which failed prior to the K2 mission. Each campaign is labeled with the campaign number in the format "C-[number]." The metallicity color bar has been scaled between -1.0 and 0.5 to show the resulting metallicity distribution within each campaign. C9 and C19 are not used and therefore not shown. The background image was modified from ESA/Gaia/DPAC, and applied using the mw plot Python module and the MWSkyProjection map "equirectangular."</figcaption></figure>

space, also known as a Kiel diagram. The size of the points indicates the asteroseismically derived mass for Figure 7 and the left-hand plot of Figure 8. The right-hand side of Figure 8 has the asteroseismically derived radius represented by the point size.

These figures show a rich array of features that are qualitatively in agreement with the physics of the RGB and RC phases of stellar evolution (Cox & Giuli 1968; Kippenhahn et al. 2013; Girardi 2016). We mention some of these patterns here, and ongoing investigation will explore to what extent the RC observations are consistent with models as a function of mass and metallicity. These plots indicate the importance of precisely derived evolutionary states (see Section 2.3), as there is substantial overlap between RGB stars and RC stars.

The combination of spectroscopic temperatures with well-constrained asteroseismic radii (used to calculate luminosity) allow for the investigation of small subsamples of secondary RGB and RC bump stars. The RGB bump stars are clearly shown by the overdensity of gray crosses on the left-hand side of Figure 7, at a temperature of ~4650 K and 30 $L_\odot$.

When considering these plots as one sample, the RC stars are generally at higher temperatures than their RGB counterparts. The RC stars show an increase in mass with temperature and luminosity. Using mass as a proxy for age, this gradient implies youth at higher temperature and luminosity. A clear metallicity gradient can be seen with temperature, with lower metallicities corresponding to hotter stars. The existence of a secondary RC is seen on the left-hand side of Figure 8, with a collection of stars at log(g) ~ 2.75 dex and T<sub>eff</sub> ~ 5000 K. We explore possible secondary RC stars further in Figure 9, as they are not seen clearly in the left-hand plot of Figure 7.

The RGB stars also show a gradient in metallicity toward higher temperature and luminosity, most clearly in Figure 8, where metallicity decreases toward the left of the branch. This gradient also corresponds to increased radii (see marker size in Figure 8). These relationships and the slight dispersion of points at higher luminosities (representing a wider range of temperatures for the more luminous stars) may be

representative of asymptotic giant branch (AGB) stars, although it is difficult to fully determine stars belonging to the AGB. Using MIST models (Choi et al. 2016; Dotter 2016) we were able to rule out AGB stars at log(g) > 2.0 with reasonable certainty for low-metallicity stars ([Fe/H] < -1.5), and with relative confidence at solar metallicities. However, we found a log(g) cut alone does not rule out all AGB stars.

Using this sample we attempted to make a distinction between secondary RC stars in different stages of evolution. In Figure 9 we further investigate possible members of the secondary RC, outlined by eye in the pink box in the left-hand plot of Figure 8. This plot shows the RC stars using four different parameters as a function of temperature. Each of these plots uses gray circles to show the RC sample as a whole, purple triangles to indicate stars with a luminosity > 100 $L_\odot$, and green diamonds to indicate stars with a mass > 1.8 $M_\odot$ and a luminosity < 100 $L_\odot$. The 1.8 $M_\odot$ cut was used to select for secondary clump stars, which do not undergo a helium flash and therefore show a range of luminosities due to their range of core masses (Girardi 2016). In T<sub>eff</sub> versus luminosity we see a number of high-luminosity stars above the RC, while massive stars are hidden within the RC. We see in the mass versus temperature space that the luminous stars are generally at least as massive as the less luminous high-mass stars. The high-luminosity clump stars are therefore likely secondary RC stars due to their high mass, but may be later in their evolution compared to the other high-mass clump stars. Indeed, we would expect their radii to expand with evolution as the core of them having radii > 12.5 $R_\odot$ and lower surface gravities. Still some of the luminous stars have masses larger than 2.5 $M_\odot$, and so would be expected to begin their RC phase with luminosities that are already higher than those of the less massive secondary clump stars at the beginning of their RC phase (Girardi 2016).

To test whether the calculated uncertainties in mass and radius may be scattering the high-luminosity stars above the high-mass stars we calculated their mean errors in mass and
<figure><img src="image_9.png" /><figcaption>**Figure 7.** Two H-R diagrams showing the APO-K2 sample. Left: RC stars. Right: RGB stars. The title of each plot includes the number of stars in the plot. Only one observation of each star is plotted for stars that were observed in multiple campaigns. Stars with $R > 30 R_⊙$ are removed. The marker size, for the filled circles, corresponds to the asteroseismic stellar mass [$M_⊙$] (see Section 2.2) and the color scale corresponds to the [M/H] [dex] from APOGEE, and has been restricted within $-2.0 < [M/H] < 0.5$ to show any relation in metallicity. A representative error bar is given in the lower right corner of each plot for the stars shown as filled circles. The points are plotted by metallicity in descending order so that low-metallicity stars are plotted at the top of the scatter. Luminosity was calculated using the asteroseismic radius and APOGEE temperature.</figcaption></figure>

radius. For the high-luminosity stars, the mean error in mass is 0.46 $M_⊙$ and the mean error in radius is 1.07 $R_⊙$. For the high-mass stars these values are 0.25 $M_⊙$ and 0.43 $R_⊙$, respectively. Although the mean error in radius for the high-luminosity (purple) stars is roughly double that of the high-mass stars (green) it is unlikely to account for the entire difference that we see between these groups, given that the mean radius for the high-luminosity stars is 16.9 $R_⊙$ and the mean radius for the high-mass stars is 10.8 $R_⊙$.

### 3.6. Comparison to APOKASC-2

Pinsonneault et al. (2014) presented the initial combination of asteroseismic (Kepler) and spectroscopic (APOGEE) data for 1916 evolved stars in the first APOKASC catalog. They used the asteroseismic data to calibrate the relationships between parameters such as mass and age with spectroscopic observables. The second APOKASC release (hereafter APOKASC-2; Pinsonneault et al. 2018) looked at an additional 4760 evolved stars (6676 in total) with an empirical approach, combining asteroseismic measurements across different methodologies to calculate average values and reduce systematic errors. APOKASC used the SDSS DR10 (Mészáros et al. 2013) parameters, and APOKASC-2 used SDSS DR14 (Holtzman et al. 2015).

The K2-GAP asteroseismic parameters used here follow a similar averaging approach (Zinn et al. 2022) to APOKASC-2. The main difference between the approaches is in the target selection. The K2 stars were chosen as a function of magnitude and color with the intention of creating a clean and easy-to-reproduce sample, unlike the Kepler stars. Indeed, Wolniewicz et al. (2021) found a strong selection bias against cool, low-luminosity red giant stars in Kepler, where the observed red giants decrease from ≈80% at $K_p = 14$ mag to ≈50% at $K_p = 15$ mag, with only 40% of red giants at $K_p = 15$ being observed for more than eight quarters. They noted that the scarcity of observed red giants could be due to the fact that the goal of Kepler was to observe solar-type stars; therefore, many

identified red giants were removed from the target list after one quarter.

K2 is better suited to Galactic archaeology compared to Kepler not just because of its well-understood and largely complete giant selection function. Due to its multiple Galactic lines of sight, it allows wider coverage of the Galaxy, observing multiple stellar populations at greater distances both radially and above and below the Galactic plane, and thus broadening our understanding of the Galaxy’s stellar composition as a whole. However, the downside to K2’s wide coverage is the shorter length of lightcurves in comparison to Kepler’s, resulting in lower S/N, meaning that oscillation spectra are harder to analyze.

APO-K2 also differs from APOKASC in the addition of stars in the low-metallicity regime (see Figure 5). These broader parameter spaces subsequently extend our understanding of related parameters, i.e., the low-mass/low-metallicity space (see Section 4.1) and the [α/Fe] bimodality (see Section 4.2).

## 4. Discussion: Example Applications of the APO-K2 Catalog

### 4.1. Asteroseismic Mass versus Metallicity

Epstein et al. (2014) showed that the asteroseismic masses determined through scaling relations in a handful of halo and thick disk APOKASC red giant stars were too large, under the assumption that such stars should be old and therefore of low mass. Sharma et al. (2016) subsequently reanalyzed these stars using different temperature and $v_{max}$ scales, which largely removed the discrepancy reported by Epstein et al. (2014). Following these observational findings, a theoretical motivation then emerged for a metallicity-dependent error in asteroseismic masses due to the $v_{max}$ scaling relation not including a molecular weight term (Viani et al. 2017).

Other authors have investigated low-metallicity asteroseismic masses and compared them against Gaia-derived masses
<figure><img src="image_10.png" /><figcaption>**Figure 8.** Two Kiel diagrams showing the APO-K2 sample. All cuts, colors, and placement are the same as those in Figure 7 with the exception of the circle size for the RGB plot (right), which is indicative of the asteroseismic stellar radius, as opposed to the stellar mass. The pink box outlines stars falling below the RC, within the secondary RC, and is explored in more detail in Figure 9.</figcaption></figure>

(Zinn et al. 2019), M4 cluster masses (Miglio et al. 2016; Howell et al. 2022; Tailo et al. 2022), and field stars (Valentini et al. 2019; Matsuno et al. 2021). These studies find mixed evidence for mass inflation at low metallicities. With our relatively large sample of low-metallicity stars, we therefore revisit the issue of seismic-scaling-based mass for the low-metallicity regime.

We made a number of cuts to the data sample in order to investigate the asteroseismic mass versus metallicity relation in an unbiased way. In Figure 10 we show how we select halo stars ($V \ge 220$ km s⁻¹). To ensure that stars with masses higher than expected were not the result of explainable factors we also made the following cuts: All stars with evolutionary type “RC” were removed as it was likely that the evolutionary states in this regime were wrong, because hot RC stars would not show oscillations. All stars with a mass > 1.6 $M_\odot$ were removed to reduce the likelihood of merger products. There was also the recognition that there were asteroseismic biases in the highly luminous stars, so we removed stars with $R > 30 R_\odot$ (Mosser et al. 2013; Stello et al. 2014; Kallinger et al. 2018; Zinn et al. 2019, 2023). Finally, we removed stars with a fractional mass error ($\delta M/M$) > 0.15.

Initially, we plotted our stars using the calibrated temperatures from APOGEE (top plot in Figure 11). These temperatures were calibrated to González Hernández & Bonifacio (2009). Full details are available in Holtzman et al. (2018). In order to evaluate the asteroseismic mass scale, we compared to masses inferred from Dartmouth isochrones (Dotter et al. 2008) with an $\alpha$ enhancement of $[\alpha/\text{Fe}] = 0.4$, which is an upper bound of the $\alpha$ enhancement at low metallicities; adopting a lower bound of $[\alpha/\text{Fe}] = 0.2$ would lower the isochronal mass scale by less than 2%.<fnref n="40" />

The APOGEE-adopted IRFM scale (González Hernández & Bonifacio 2009) was anchored on a small sample of metal-poor stars, and so it is plausible that there are systematics in the temperature calibration at low metallicity. We therefore considered

the effect of using the uncalibrated, ionization-balanced temperatures from APOGEE. Plotting the stars using the uncalibrated temperatures (bottom plot in Figure 11) we found much better agreement with the older isochrones (10 and 14 Gyr); this indicates that temperature calibration may be a key factor in the resulting mass values at low metallicities, with much of the mass shift resulting indirectly from the temperature dependence of $f_{\Delta\nu}$.

Figure 12 shows the weighted median masses plotted with the Dartmouth isochrones, without the data points. This plot clearly shows the improved agreement for the asteroseismic masses derived using the uncalibrated APOGEE temperatures (red curve).

We compared the asteroseismic masses to the isochrone masses for each data point by subtracting the 10 Gyr isochrone mass from the uncalibrated and calibrated mass values and then finding the weighted mean. The weighted average mass difference is $12.4\% \pm 4.5\%$ (stat.) + 6\% (syst.) for the calibrated masses and $2.9\% \pm 2.8\%$ (stat.) + 6\% (syst.) for the uncalibrated masses, indicating that the asteroseismic masses are larger than the isochronal masses. The 6\% systematic errors added to these values are due to the 2\% uncertainty on the $\nu_{\text{max}}$ scale. Performing the same calculations with the 14 Gyr isochrone values gave results of $20.6\% \pm 4.5\%$ (stat.) + 6\% (syst.) and $11.1\% \pm 2.8\%$ (stat.) + 6\% (syst.). If we consider the 14 Gyr isochrone as the true age, the masses could be 8.2\% more inflated (for both the calibrated and uncalibrated temperature scales). Running these masses again with a weighted median, which is less sensitive to outliers, did not significantly change the result.

Two mass limits on this plot are of particular interest considering the precision of our asteroseismic masses. The first is the few RGB stars at $M < 0.8 M_\odot$, which corresponds to the approximate minimum mass of an RGB star at the current age of the Galaxy (see mass for 14 Gyr isochrone with Dartmouth). These stars may have undergone mass loss throughout their evolution and represent interesting objects of future study. Conversely, 1.6 $M_\odot$ corresponds to the maximum possible mass (the maximum merger mass of two 0.8 $M_\odot$ stars). The

<footnote n="40">⁴⁰ In Section 3.5 we use the MIST models instead of the Dartmouth isochrones used here. The use of Dartmouth at this point was to allow for an $\alpha$ enhancement factor that was not necessary for the AGB cut.</footnote>
<figure><img src="image_11.png" /><figcaption>**Figure 9.** Four scatter plots showing the RC stars, in various parameter spaces. Each plot has $T_{\text{eff}}$ on the x-axis and the y-axis depicting stellar luminosity [$L_{\odot}$] (top left), log(g) [dex] (top right), radius [$R_{\odot}$] (bottom left), or mass [$M_{\odot}$] (bottom right), with their associated errors. The entire sample of RC stars is shown by gray circles. Stars with $L > 100 L_{\odot}$ are represented by purple triangles and stars with $L < 100 L_{\odot}$ and $M > 1.8 M_{\odot}$ are shown by green diamonds.</figcaption></figure>

<figure><img src="image_12.png" /><figcaption>**Figure 10.** A Toomre diagram of our sample, showing stellar velocity relative to the local standard of rest. The color bar in this plot represents [Fe/H] from APOGEE and the dashed black line represents a velocity of 220 [km s⁻¹]. This line is used to delineate the boundary between halo stars and the rest of the sample, for use in Figure 11.</figcaption></figure>

RGB stars above this limit, although removed in Figure 11, warrant follow-up as they could represent interaction products.

## 4.2. [α/Fe] Bimodality

An important abundance relation for exploring chemical enrichment in the Milky Way is the [α/Fe] bimodality. This association compares α process elements (e.g., O, Mg, Ca, and Si) to Fe abundance in stellar populations, which results in two groups, clearly separable on a plot of [Fe/H] versus [α/Fe], called high- and low-[α/Fe] stars.

There are multiple theories about the origin of this double sequence. It has been suggested that stars with larger α abundance form under different circumstances than low-[α/Fe] stars (Mackereth et al. 2018). An enhanced α with high Fe suggests that the majority of the heavy elements come from core-collapse SNe,

while a low-[α/Fe] mixture arises from a combination of SNe Ia and core-collapse SNe. Low-[α/Fe] stars tend to be young, reside in the thin disk, and form their own sequence. One possibility is that they result from decreased star formation efficiency as the Galaxy ages (Nidever et al. 2014). They also show different birth radii and an anticorrelation between angular momentum and [Fe/H], which suggests the existence of radial migration could be needed to form the sequence (Sharma et al. 2021); the effects of radial migration on the bimodality are also seen with the inward migration of super solar-metallicity stars in the solar-vicinity thin disk $R_{\text{Gal}} = 7-9$ kpc (Anders et al. 2017). Old, high-[α/Fe] stars generally reside in the thick disk; they display enhanced α abundance, and sometimes low metal abundance, and are relatively kinematically hot (e.g., Haywood et al. 2013). These stars are thought to form from intense episodes of star formation, wherein the interstellar medium is dominated by the ejecta of core-collapse SNe. The [α/Fe] bimodality has been seen both in the solar neighborhood and beyond (Hayden et al. 2017); recent studies using asteroseismic ages have found the age distributions for high- and low-[α/Fe] stars converge with increasing distance from the Galactic plane (Warfield et al. 2021).

Our K2 data allows investigation of the [α/Fe] bimodality. Figure 13 shows the α bimodality plot for our sample. Asteroseismic masses are defined as in Section 2.2 and the abundance information is taken from APOGEE. The eccentricity is defined in Section 4.3.

Our data extends the abundance ranges to lower metallicities, higher α abundances, and farther distances than those of Kepler. The APO-K2 sample offers a sample with asteroseismic masses including a known selection function to build on existing asteroseismic catalogs (e.g., Mackereth et al. 2019b; Rendle et al. 2019; Imig et al. 2022).

Using the asteroseismic mass as a proxy for age, we can see a clump of higher-mass stars in the low-[α/Fe] regime, suggesting these stars are generally younger. Using the size of the marker
<figure><img src="image_13.png" /></figure>

**Figure 11.** Weighted median asteroseismic mass [$M_\odot$] as a function of APOGEE [Fe/H] [dex], calculated using asteroseismic scaling relations and mass and radius coefficients (as discussed in Section 2.2). The Dartmouth isochrones are shown by gray lines and labeled with their ages to the right of the plots (8, 10, and 14 Gyr). The black points in the top plot represent masses derived using the calibrated temperatures from APOGEE and the existence of so many black points above the isochrone lines demonstrates the existence of potential overestimates in asteroseismic mass for the low-metallicity regime. The red triangles in the bottom plot represent masses calculated using the uncalibrated temperatures from APOGEE. The title shows the cuts made to this plot (e.g., halo and RGB stars only). Binned medians of both samples have been added using a black (red) line in the top (bottom) plot with the $1\sigma$ errors shown by the shaded regions.

<figure><img src="image_14.png" /></figure>

**Figure 12.** Asteroseismic mass [$M_\odot$] as a function of APOGEE [Fe/H] [dex]. Same as Figure 11 but excluding the scatter plot. Gray lines correspond to Dartmouth isochrones at 8 Gyr (dashed), 10 Gyr (dashed-dotted), and 14 Gyr (dotted).

(scaled for ease to the reader) to represent eccentricity, we see that the highest-eccentricity stars generally have high [α/Fe] abundance and low metallicity.

Our sample adds over 1000 stars to the [α/Fe] bimodality plot as compared to the APOKASC-2 sample (~6000 stars), extending to lower metallicities and higher [α/Fe] abundance, which allowed us to more clearly separate the high- and low-[α/Fe] samples. Figure 14 shows both the APOKASC-2 and APO-K2 catalogs overplotted in metallicity–[α/Fe], illustrating the extent to which the APO-K2 catalog has expanded on the Kepler field, and confirming the convergence of the bimodality into a single distribution at higher metallicities.

Warfield et al. (2021) explored this space in K2 C4, C6, and C7, and discovered an overlap between high- and low-α populations with stars of similar ages. This discussion will continue in the companion paper on ages for this sample (J. T. Warfield et al. 2024, in preparation).

### 4.3. Kinematics

The GES structure is thought to represent the remnants of a dwarf galaxy that merged with the Milky Way in its early history (Belokurov et al. 2018; Helmi et al. 2018; Montalbán et al. 2021). Though initially identified by kinematics, the GES
<figure><img src="image_15.png" /><figcaption>Figure 13. The [α/Fe] bimodality plot with the metallicity [Fe/H] ([α/Fe]) on the x-axis (y-axis). The color scale represents the asteroseismic mass [M⊙], which has been truncated for clarity, with the full range of masses shown in the title. Gray points correspond to stars with an alpha flag of −1. The darker blue colors correspond to lower masses, with the data sorted by mass so that higher-mass stars appear at the top. The size of each marker represents the Galactic eccentricity from Gala, which has been scaled for clarity to the reader. A dividing line is drawn to separate the low- and high-[α/Fe] stars, and this separation results in the flag included in the APO-K2 catalog. Representative error bars are shown for both the relatively high and relatively low metallicity stars, where the separation occurs at [Fe/H] = −1.0.</figcaption></figure>

can also be identified by its combination of low metallicity and a particular abundance pattern (Haywood et al. 2018; Mackereth et al. 2019b).

To define the dynamical information for our sample we used Gala (Bovy 2015; Price-Whelan et al. 2017), an Astropy-affiliated (Astropy Collaboration et al. 2013, 2018) Python package. Gala uses the Astropy Galactocentric frame parameters adopted in Astropy v4.0. These are defined with a solar position of R⊙ = 8.122 kpc and z⊙ = 20.8 pc. The velocity of the Sun in the Galactocentric frame is (U, V, W)⊙ = (12.9, 245.6, 7.78) km s⁻¹, as measured from Sgr A*. For our analysis we adopted the Milky Way potential (MilkyWayPotential) available with Gala, using the default parameters of Milky Way mass, virial radius, etc. The circular velocity at the Sun’s position for the adopted potential is 231.5 km s⁻¹. Gala employs proper motions, parallaxes (distances), and radial velocities, with their associated errors, in its calculations of stellar orbital parameters. In Table 4 we provide the kinematic information for our stars including the Gaia DR3 parallaxes corrected according to the Gaia zero-point,<fnref n="41" /> evaluated using the Python implementation of the Lindegren et al. (2021) correction, and the uncertainties [mas] according to El-Badry et al. (2021). We also include a DR3 binary flag, which is nonzero if either of the following is true: the star is flagged in the non_single_star column of DR3 or the fidelity_v2 value from Rybizki et al. (2022) is ≤0.5 or unavailable. All other parameters included in Table 4 are described in Section 3.2.

In Section 4.2 we use eccentricities (e) from Gala defined as

$$e = \frac{r_{\text{apo}} - r_{\text{peri}}}{r_{\text{apo}} + r_{\text{peri}}}, \qquad (9)$$

where $r_{apo}$ is the orbital apocenter and $r_{peri}$ is the orbital pericenter.

<figure><img src="image_16.png" /><figcaption>Figure 14. The α bimodality plot with both APOKASC-2 (black) and APO-K2 (blue) overplotted to highlight the increase of sample size in this parameter space.</figcaption></figure>

To derive the orbital parameters of eccentricity and |Zmax| we created 100 instances of each star, and used Pyia<fnref n="42" /> and Gala to integrate their orbits over 5000 steps with a time step of 0.8 Myr. The values for each star were then determined using the mean value from the 100 iterations, and errors were calculated using the standard deviation of the measurements. We note that the uncertainty of |Zmax| increases with the Galactic radius of the star, so for those stars with large |Zmax| values, these orbital parameters may not be accurate. The velocities, total energy, and angular momentum for each star were computed in much the same way.

Figure 15 shows the orbital angular momentum (Lz) [10³ kpc km s⁻¹] as a function of total energy (E_TOT) [10⁵ km² s⁻²]. This space is most often used to identify merger debris from past accretion events. Colors correspond to the relative α abundance with high [α/Fe] (gold) and low [α/Fe]

<footnote n="41">⁴¹ https://gitlab.com/icc-ub/public/gaiadr3_zeropoint/-/tree/master</footnote>

<footnote n="42">⁴² https://pyia.readthedocs.io/en/latest/#</footnote>
<figure><img src="image_17.png" /><figcaption>**Figure 15.** Kinematic plots for the APO-K2 sample. The plot on the left (right) corresponds to RC stars (RGB stars). Only stars with positive Gaia parallaxes are plotted. The gray areas of the plots correspond to the areas likely to host GES stars, and are defined by the lines drawn (and described in the text). In both of these plots, the gold (green) stars correspond to the high-[α/Fe] (low-[α/Fe]) stars, as defined by Figure 13, and the stars shown in gray are uncategorized (i.e., have an alpha flag of −1).</figcaption></figure>

(green), based on the alpha flag provided in the catalog. We also show the stars with an alpha flag of −1 as gray circles. We display the sample broken down by evolutionary state (RGB and RC), with boundaries for the GES overlaid. The vertical lines denote the GES limits in angular momentum from Helmi et al. (2018), $-150 < L_Z$ [kpc km s⁻¹] < 1500. The GES distinction in total energy was taken from Koppelman et al. (2019) and placed between $-1.1 \times 10^5$ km² s⁻² and $-1.5 \times 10^5$ km² s⁻². Inside the gray box lie a few dozen GES substructure candidates.

Figure 15 shows the low-[α/Fe] stars mainly occupy the disk, and hence are in fairly circular orbits that sit close to the curve that defines the minimum energy given the Milky Way potential. By contrast, the high-[α/Fe] stars, residing mainly in the thick disk and halo, are expected to be kinematically hot (possessing eccentric orbits) and occupy more diffusely the region above the minimum energy curve.

Koppelman et al. (2019) discussed the necessity of a chemical tagging analysis to determine whether substructures are related to accretion events. They studied the distribution of nearby thick disk and halo stars using 6D phase-space data from Gaia DR2 and found that not all substructures are due to accretion, nor are they all due to the settling of the gravitational potential after major activity (Haywood et al. 2018). The range of kinematic parameter space probed in this sample may prove useful for future analysis, in combination with the selection functions presented in S22.

## 5. Conclusions

In this paper we summarize the APO-K2 evolved star sample, with corresponding spectroscopic (APOGEE DR17), asteroseismic (K2-GAP), and astrometric (Gaia DR3) parameters. Our sample of 7672 unique stars contains RGB, RC, secondary RC, and RGB bump evolutionary states, from

various areas of the Galaxy. Our work provides precise asteroseismic radii and masses as well as evolutionary states and metallicities, explored in multiple parameter spaces.

Throughout this work, we give an overview of many parameter spaces that our catalog extends, some for the first time. We investigate the completeness of our sample by comparing it to the S22 selection function, in the mass-radius, mass-metallicity, color-magnitude, and magnitude-ν<sub>max</sub> regimes. The large sample of red giants presented here results in a significant number of intrinsically rare objects, like secondary clump stars, which are promising for stellar physics tests. We examine our asteroseismic masses in the low-metallicity regime, resulting in higher masses than expected for the low-metallicity stars, even when taking corrections to the Δν scaling relation into account. We find that using raw APOGEE temperatures to derive stellar masses results in better agreement with astrophysical estimates for very metal-poor stars. We also show that these low-metallicity stars dramatically increase the number of stars available in the high-α population as compared to Kepler asteroseismic samples. Finally, we look at our sample in kinematic space, with Gaia DR3, and identify potential GES stars. The chemical properties of potential GES members are an interesting topic—we have identified potential GES members in order to advertise the importance of this catalog for Galactic evolution studies, and we leave the detailed abundance patterns of the kinematics-selected GES candidate members to future work.

The overview presented in our paper only scratches the surface of the rich data sample; some of the spaces explored in this paper will be further investigated in follow-up papers. Further work will be undertaken to explore the multiplicity and the abundance space provided by APOGEE (J. Schonhut-Stasik et al. 2024, in preparation), for example, to investigate the carbon-enhanced stars known to exist at low metallicity (e.g., Beers & Christlieb 2005; Suda et al. 2008), and the young
high-α population (Chiappini et al. 2015). A companion paper will release age information for the APO-K2 catalog (J. T. Warfield et al. 2024, in submission).

The number of stars accessible to Galactic archaeology using
asteroseismology will only grow with future missions. For
example, the NASA planet-finding mission TESS (Ricker et al.
2014; Hon et al. 2022) and the Nancy Grace Roman Telescope
(Gould et al. 2015; Spergel et al. 2015), as well as the ESA
missions Euclid (Laureijs et al. 2011; Gould et al. 2016) and
PLATO (Rauer et al. 2014; Miglio et al. 2017), will yield
enormous harvests of asteroseismic detections. In terms of
spectroscopic measurements, the upcoming projects WEAVE
(Dalton et al. 2020), MOONS (Cirasuolo et al. 2014), and
4MOST (de Jong et al. 2012) will increase chemical abundance
yields. Finally with future releases from Gaia, our astrometric
and kinematic data will only increase in precision.

Acknowledgments

We would like to thank the community that supports APO-K2. J.S.-S. is supported by a Neurodiversity Inspired Science and Engineering (NISE) Fellowship. J.C.Z. was supported by an NSF Astronomy and Astrophysics Postdoctoral Fellowship under award AST-2001869. D.M. gratefully acknowledges support from the ANID BASAL projects ACE210002 and FB210003 and from Fondecyt Project No. 1220724. S.M. acknowledges support from the Spanish Ministry of Science and Innovation (MICINN) with the Ramón y Cajal Fellowship No. ~RYC-2015-17697, grant No. PID2019-107187GB-I00 and PID2019-107061GB-C66 for PLATO, and through AEI under the Severo Ochoa Centres of Excellence Programme 2020-2023 (CEX2019-000920-S). D.S. acknowledges support from the Australian Research Council Discover Project DP190100666. R.A.G. and B.M. acknowledge support from a PLATO Centre National D'Études Spatiales grant. D.M. also acknowledges support from CNPq/Brazil through project 350104/2022-0.

This paper includes data collected by the Kepler mission and
the K2 mission. Funding for the Kepler mission and K2
mission is provided by the NASA Science Mission Directorate.

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 participat-
ing in the Gaia Multilateral Agreement. This research has made
use of the VizieR catalog access tool, CDS, Strasbourg, France
(DOI:10.26093/cds/vizier). The original description of the
VizieR service was published in Ochsenbein et al. (2000).

Funding for SDSS-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 acknowl-
edges 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 Con-
sortium for the Participating Institutions of the SDSS Collaboration
including the Brazilian Participation Group, the Carnegie Institu-
tion for Science, Carnegie Mellon University, the Chilean
Participation Group, the French Participation Group, the Har-
vard-Smithsonian Center for Astrophysics, Instituto de Astrofísica
de Canarias, the Johns Hopkins University, the Kavli Institute for
the Physics and Mathematics of the Universe (IPMU)/University

of Tokyo, Lawrence Berkeley National Laboratory, Leibniz
Institut für Astrophysik Potsdam (AIP), Max-Planck-Institut für
Astronomie (MPIA Heidelberg), Max-Planck-Institut für Astro-
physik (MPA Garching), Max-Planck-Institut für Extraterrestrische
Physik (MPE), the 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, the United Kingdom Participation Group, Universi-
dad 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. This paper includes data collected
by the Kepler mission and obtained from the MAST data archive
at the Space Telescope Science Institute (STScI). Funding for the
Kepler mission is provided by the NASA Science Mission
Directorate. STScI is operated by the Association of Universities
for Research in Astronomy, Inc., under NASA contract NAS
5-26555.

This majority of this paper was written on the Big Island of
Hawai'i. We would like to begin by acknowledging that the
'aina on which this paper was written, is part of the larger
territory recognized by Indigenous Hawaiians as their ancestral
grandmother, Papahānaumoku. We further recognize that
generations of Indigenous Hawaiians and their knowledge
systems shaped Hawai'i in sustainable ways that allow me to
enjoy these gifts today. Additionally, work on this paper took
place in Nashville, Tennessee, which occupies the ancestral
hunting and traditional Lands of the Cherokee, Shawnee,
Choctaw, Chickasaw, and Creek peoples.

Facilities: Du Pont (APOGEE), Sloan (APOGEE), CTIO:2-MASS, FLWO:2MASS, Kepler.

Software: Python 3 (Van Rossum & Drake 2009), numpy (Harris et al. 2020), matplotlib (Hunter 2007), pandas (McKinney 2010), Astropy (Astropy Collaboration et al. 2013, 2018), mw_plot (https://milkyway-plot.readthedocs.io/en/latest/).

ORCID iDs

Jessica Schonhut-Stasik https://orcid.org/0000-0002-1043-8853

Joel C. Zinn https://orcid.org/0000-0002-7550-7151

Keivan G. Stassun https://orcid.org/0000-0002-3481-9052

Marc Pinsonneault https://orcid.org/0000-0002-7549-7766

Jennifer A. Johnson https://orcid.org/0000-0001-7258-1834

Jack T. Warfield https://orcid.org/0000-0003-1634-4644

Dennis Stello https://orcid.org/0000-0002-4879-3519

Rafael A. García https://orcid.org/0000-0002-8854-3776

Savita Mathur https://orcid.org/0000-0002-0129-0316

Benoit Mosser https://orcid.org/0000-0002-7547-1208

Marc Hon https://orcid.org/0000-0003-2400-6960

Jamie Tayar https://orcid.org/0000-0002-4818-7885

Guy S. Stringfellow https://orcid.org/0000-0003-1479-3059

Rachael L. Beaton https://orcid.org/0000-0002-1691-8217

Henrik Jönsson https://orcid.org/0000-0002-4912-8609

Dante Minniti https://orcid.org/0000-0002-7064-099X

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