An Intermediate-age Alpha-rich Galactic Population in K2
Jack T. Warfield, Joel C. Zinn, Marc H. Pinsonneault, Jennifer A. Johnson, Dennis Stello, Yvonne Elsworth, Rafael A. García, Thomas Kallinger, Savita Mathur, Benoît Mosser, Rachael L. Beaton, D. A. García-Hernández
DDraft version February 9, 2021
Typeset using L A TEX twocolumn style in AASTeX63
An Intermediate-age Alpha-Rich Galactic Population in K2 Jack T. Warfield,
1, 2, 3
Joel C. Zinn,
4, 1
Marc H. Pinsonneault, Jennifer A. Johnson,
1, 5
Dennis Stello,
4, 6, 7, 8
Yvonne Elsworth,
9, 7
Rafael A. Garc´ıa,
10, 11
Thomas Kallinger, Savita Mathur,
13, 14, 15
Benoˆıt Mosser, Rachael L. Beaton, ∗ and D. A. Garc´ıa-Hern´andez
14, 15 Department of Astronomy, The Ohio State University, 140 West 18th Avenue, Columbus, OH 43210, USA Department of Physics, The Ohio State University, 191 West Woodruff Avenue, Columbus, OH 43210, USA Department of Astronomy, The University of Virginia, 530 McCormick Road, Charlottesville, VA, 22904, USA School of Physics, University of New South Wales, Barker Street, Sydney, NSW 2052, Australia Center for Cosmology and AstroParticle Physics, The Ohio State University Columbus, OH 43210, USA Sydney Institute for Astronomy (SIfA), School of Physics, University of Sydney, NSW 2006, Australia Stellar Astrophysics Centre, Department of Physics and Astronomy, Aarhus University, Ny Munkegade 120, DK-8000 Aarhus C,Denmark Center of Excellence for Astrophysics in Three Dimensions (ASTRO-3D), Australia School of Physics and Astronomy, University of Birmingham, Edgbaston, Birmingham, B15 2TT, UK IRFU, CEA, Universit´e Paris-Saclay, F-91191 Gif-sur-Yvette, France AIM, CEA, CNRS, Universit´e Paris-Saclay, Universit´e Paris Diderot, Sorbonne Paris Cit´e, F-91191 Gif-sur-Yvette, France Institute of Astrophysics, University of Vienna, T¨urkenschanzstrasse 17, Vienna 1180, Austria Space Science Institute, 4750 Walnut Street Suite Instituto de Astrof´ısica de Canarias (IAC), E-38205 La Laguna, Tenerife, Spain Departamento de Astrof´ısica, Universidad de La Laguna (ULL), E-38206 La Laguna, Tenerife, Spain LESIA, Observatoire de Paris, PSL Research University, CNRS, Sorbonne Universit´e, Universit´e de Paris Diderot, 92195 Meudon,France Department of Astrophysical Sciences, Princeton University, 4 Ivy Lane, Princeton, NJ 08544, USA (Received; Revised; Accepted)
Submitted to AJAbstractWe explore the relationships between the chemistry, ages, and locations of stars in the Galaxyusing asteroseismic data from the K2 mission and spectroscopic data from the Apache Point GalacticEvolution Experiment survey. Previous studies have used giant stars in the Kepler field to map therelationship between the chemical composition and the ages of stars at the solar circle. Consistent withprior work, we find that stars with high [ α /Fe] have distinct, older ages in comparison to stars with low[ α /Fe]. We provide age estimates for red giant branch (RGB) stars in the Kepler field, which supportand build upon previous age estimates by taking into account the effect of α -enrichment on opacity.Including this effect for [ α /Fe]-rich stars results in up to 10% older ages for low-mass stars relativeto corrected solar mixture calculations. This is a significant effect that Galactic archaeology studiesshould take into account. Looking beyond the Kepler field, we estimate ages for 735 red giant branchstars from the K2 mission, mapping age trends as a function of the line of sight. We find that the agedistributions for low- and high-[ α /Fe] stars converge with increasing distance from the Galactic plane,in agreement with suggestions from earlier work. We find that K2 stars with high [ α /Fe] appear tobe younger than their counterparts in the Kepler field, overlapping more significantly with a similarlyaged low-[ α /Fe] population. This observation may suggest that star formation or radial migrationproceeds unevenly in the Galaxy. [email protected] a r X i v : . [ a s t r o - ph . GA ] F e b Warfield et al.
Keywords: surveys — asteroseismology — stars: abundances — Galaxy: abundances — Galaxy:evolution — Galaxy: stellar content INTRODUCTIONThe study of the chemical evolution of the Milky Wayhas a rich history and a vibrant present. Historically, ithas been easier to measure abundances than it has beento measure ages. As a result, most studies have relied onabundance data alone—for example, very low absoluteiron abundance, or characteristic heavy element abun-dance patterns relative to iron—as indicators of mem-bership in old populations. However, we can now mea-sure ages for large samples of evolved stars using stel-lar pulsation—or asteroseismic—data from large timedomain surveys, and we have an unprecedented wealthof abundance data from massive spectroscopic surveys.These new tools allow us to trace out the enrichmenthistory of the Milky Way in a far more detailed fashionthan was possible even a few years ago. In this paper wefocus on ages for evolved red giants with enhanced abun-dances of α -capture elements relative to iron comparedto the Sun, which we will refer to as α -rich stars.The existence of α -rich stars has been known for overhalf a century (Aller & Greenstein 1960; Wallerstein1962). The α -capture elements—such as O, Mg, Si, S,Ca, and Ti—are primarily produced in core-collapse su-pernovae of massive, short-lived stars (SNe II). Fe-peakelements, by contrast, can also be injected into inter-stellar medium by the explosive destruction of a whitedwarf (a Type Ia supernova, SNe Ia). The latter processrequires a longer-lived progenitor. Therefore, in very oldpopulations, such as the Galactic halo, stars are thoughtto be α -rich because they formed before SNe Ia occurredin significant numbers (Tinsley 1979).In a simple chemical evolution model, the [ α /Fe] ra-tio of the gas would decline as the number of SNe Iacontributing Fe-peak elements increases, before reach-ing an equilibrium ratio (e.g., Weinberg et al. 2017).This is not what is observed in the solar neighborhood(Prochaska et al. 2000; Bensby et al. 2003). Rather thana single sequence from high- α to low- α , stars with − < [Fe/H] < α /Fe] values. The ori-gin of this bi-modal α sequence of stars in the Galaxyis still a puzzle. Bensby et al. (2003) showed that thereare distinct trends in [ α /Fe] vs. [Fe/H] space for thegeometrically defined thin and thick discs (Gilmore &Reid 1983). Hayden et al. (2015) investigated how these ∗ Hubble FellowCarnegie-Princeton Fellow trends behave as a function of Galactic radius ( R ) andheight above the Galactic plane ( Z ) using ∼ ,
000 redgiants from the Sloan Digital Sky Survey (SDSS) ApachePoint Galactic Evolution Experiment (APOGEE) DataRelease (DR) 12. These authors found the high- α partof this sequence strongly present only at | Z | > . R <
11 kpc.Because of the origins of the α elements, the α -richand α -poor populations must be somehow tied to thehistory of SNe II and Ia. However, all of the observedpatterns—for instance, the spread in [ α /Fe] at a given[Fe/H]—cannot be explained by the SNe history alone.Therefore, other, more complex mechanisms must alsocontribute to the formation of the observed chemicaland age patterns. Some proposed mechanisms capableof reproducing the observed sequences are the radial mi-gration of stars in the Galaxy (see, e.g., Sellwood & Bin-ney 2002; Sch¨onrich & Binney 2009; Nidever et al. 2014;Weinberg et al. 2017; Sharma et al. 2020); two separatestar formation episodes driven by pristine gas infall intothe Galaxy (e.g. Chiappini et al. 1997; Spitoni et al.2019; Lian et al. 2020); and stars forming throughoutthe Galaxy in clumpy bursts (e.g. Clarke et al. 2019).Though all are able to roughly recreate the observedchemical pattern, each of these mechanisms are respon-sible for different predictions concerning the relative agesof the α -rich and α -poor populations and how homoge-neous these results will be across the Galaxy. Therefore,finding ages for stars as functions of their chemical abun-dances and locations in the Galaxy is an important stepin uncovering the mechanisms that are responsible forthe Galaxy’s formation.Finding ages for large numbers of field red giants up toseveral kpc away from the Sun is now possible throughasteroseismology. Near-surface turbulent convective mo-tions in cool stars generate sound waves, and for dis-tinct resonant frequencies of the stellar interior, stand-ing waves can be induced, forming a frequency patternof overtone modes of different spherical degrees. Thefrequency spacings between the radial modes (∆ ν ) isrelated to the mean density (Ulrich 1986; Kjeldsen &Bedding 1995). The frequency of maximum acousticpower ( ν max ) is related to the acoustic cut-off frequency,and therefore the density scale height and the surfacegravity (Brown et al. 1991; Kjeldsen & Bedding 1995;Chaplin et al. 2008). It is therefore possible to solve formass and radius through scaling relations if ∆ ν , ν max ,and T eff are known. Pinsonneault et al. (2014, 2018) ntermediate Age Population ν max , ∆ ν , asteroseismicmasses & radii, chemical abundance estimates, and ageestimates for targets in the fields observed photometri-cally by NASA’s Kepler mission and spectroscopicallyby APOGEE.Ages for the α -rich and α -poor populations in the Pin-sonneault et al. (2014) data set—including sample selec-tion effect corrections—were calculated by Silva Aguirreet al. (2018) (hereafter SA18). These ages were foundusing different asteroseismic corrections than used forthe ages published by Pinsonneault et al. (2018). Par-tially motivated by finding chemical signatures that canbe used as tracers of the thin and thick disks, SA18used a combination of photometric, spectroscopic, andasteroseismic parameters to estimate the ages of 1590red giant branch and red clump stars located within the Kepler field. They found that the population of giantswith low [ α /Fe] has a distribution peaked at ∼ α /Fe] peaks strongly at ∼
11 Gyr.The ages of these populations were found to have lim-ited overlap, with a transition at ∼ Kepler field. SA18 also found a surprising, small populationof very young, α -rich stars which, though possibly high-mass stars with genuinely young ages, could also indicatean unexpectedly large population of merger products—stars that have gained mass from a companion andtherefore look younger than they actually are (Martiget al. 2015; Chiappini et al. 2015). Investigations ofpopulations along other lines of sight have the potentialto clarify the origin of this unusual cohort. The rela-tionship shown by SA18 between age and α -enrichmentagrees very well with what might be expected if onlyconsidering the contribution of historic SNe rates to theinterstellar medium. However, the sample of stars avail-able from Pinsonneault et al. (2014, 2018), and SA18’ssub-sample, represent a population of stars very localto the Sun, only extending out to a distance of about2 kpc. Therefore, whether these results are true for the α -rich and α -poor populations outside of the solar circleis still relatively uncertain.In an effort to characterize the age distributions withasteroseismology outside of the solar vicinity, Anderset al. (2017) combined asteroseismology from two of the CoRoT fields with APOGEE DR12 to get masses, radii,and ages using the Bayesian parameter estimation codePARAM (da Silva et al. 2006; Rodrigues et al. 2014).These fields, lying very close to the Galactic plane, pro- vide a valuable sampling of the Milky Way’s chemicalhistory at a range of Galactic radii.Building on work from
Kepler and
CoRoT , our papertakes advantage of the multiple Galactic sight-lines thatthe K2 mission (Howell et al. 2014) affords to better un-derstand the age distributions of stars outside of the im-mediate solar neighborhood. Following the failure of the Kepler satellite’s pointing, a new observing strategy wasadopted to use the solar wind for partial stabilization.The re-purposed
Kepler mission, dubbed K2 , could nolonger focus on the original Kepler field. However, byvirtue of its ecliptic orientation, it could now observefields of view along the ecliptic for ∼
80 days at a time(Howell et al. 2014). K2 therefore offers an expandedview of the Galaxy compared to the Kepler prime mis-sion, and thanks to a dedicated program to target red gi-ants, the K2 Galactic Archaeology Program (K2 GAP;Stello et al. 2015), has yielded asteroseismic data be-yond the solar vicinity (Stello et al. 2017). As proof ofthe usefulness of K2 for Galactic archaeology, ages werefound by Rendle et al. (2019) for stars in K2 campaigns3 and 6. This includes a confirmation of the existenceof young, α -rich stars that otherwise are consistent withsharing the kinematic properties of old α -rich stars.In this paper, we look to further investigate the rela-tionship between α abundance and age by combiningasteroseismic data obtained from observations of redgiants observed by K2 with spectroscopic data fromAPOGEE DR16. Giants in the K2 fields, many of whichwere targeted at greater distances compared to the Ke-pler giants, offer the opportunity to discover propertiesof α -rich and α -poor populations well beyond the solarcircle. § § § α -rich and α -poorpopuations in the K2 fields and touch on some possi-ble implications for the Galactic formation mechanismsmentioned above. DATA SELECTIONThe spectroscopic data for this work is from the 16thdata release of the APOGEE survey (Majewski et al.2017; Ahumada et al. 2020). This survey has been col-lecting high resolution IR spectra for hundreds of thou-sand of stars throughout the Milky Way. Access is pro-vided to both the raw spectra and derived estimates forstellar parameters such as effective temperature ( T eff ),surface gravity ( g ), and chemical abundances via an au-tomated pipeline. This includes estimates for metal- Warfield et al. R [kpc] Z [ k p c ] Sun
Campaign 4Campaign 6Campaign 7 Kepler
10 5 0 5 10 X [kpc] Y [ k p c ] R G.C.
Figure 1.
Schematics showing the approximate lines of sight for K2 campaigns 4, 6, and 7. The plot on the left shows thefields in the Galactocentric coordinates Z (height above or below the Galactic plane) and R (radial distance from the Galacticcenter). The plot on the right shows these fields in the Galactocentric X and Y coordinates. The Sun is approximated to be at R = 8 . Z = 0 .
027 kpc, X = − . Y = 0 kpc. Our sample contains 160 stars in C4, 411 stars in C6, and 233stars in C7. T eff [K] l o g ( g ) ( s e i s m i c ) Low-Luminosity RGBLuminous RGB
Figure 2.
Kiel diagram for our sample of stars using ef-fective temperatures from APOGEE and surface gravitiescalculated from the K2 GAP DR2 astereoseismic parame-ters. Low-luminosity giants are defined here as giants withlog ( g ) > . licity ([Fe/H]) and α -enrichment ([ α /M] ). The spec-troscopic data in APOGEE DR16 was collected withthe 2.5-meter Sloan Foundation Telescope (Gunn et al.2006) at the Apache Point Observatory in New Mexicoand the 2.5-meter du Pont Telescope (Bowen & Vaughan1973) at Las Campanas Observatory in Chile as a partof SDSS-IV (Blanton et al. 2017). APOGEE uses twin R ∼ ,
500 H-band spectrographs (Wilson et al. 2019).APOGEE deliberately targeted red giants in the
Kepler and K2 fields to provide spectroscopic data for seismi-cally detected stars. The selection of red giants in the Kepler field is presented in Zasowski et al. (2013, 2017),while the APOGEE program in the K2 fields is pre-sented in Zasowski et al. (2017) and Beaton et al. (inpreparation). Briefly, the K2 program’s stars were se-lected in a priority scheme as follows: (1) known planethosts, (2) confirmed oscillators, (3) red giant targets inthe GAP and not observed with HERMES, (4) red gi-ants targeted in the GAP and observed with HERMES,(5) M-dwarf candidates, and (6) filler giants followingthe APOGEE-2 main red star sample (Zasowski et al.2017). Field centers were chosen to maximize the totalpriority and targets were selected in each field followingthe typical APOGEE fashion (Zasowski et al. 2013).The general scheme for extraction of the spectra,wavelength calibration, latfielding, and radial velocity [ α /Fe] and [ α /M] are conceptually equivalent, with the [ α /M]parameter used by APOGEE measuring the ratio of α elementsto the overall metallicity rather than just to iron. ntermediate Age Population T eff < K2 GAP (Zinn et al. 2020). Over themission lifespan, K2 made observations along 19 differ-ent lines-of-sight across the Galaxy which are referredto as campaigns 0-18. K2 GAP provides the analysisof asteroseismic targets in these fields. Because of theshorter time spent observing each of these fields versusthe
Kepler field ( ∼
80 days versus 4 years), the associ-ated uncertainties with the asteroseismic parameters aresignificantly larger. However, the data from K2 offersa much more diverse positional sampling of stars in theGalaxy. The full K2 GAP project covers K2 campaigns1-18 over a series of three data releases. Data Release1 (Stello et al. 2017) provided analysis for ∼ K2 campaign 1 and worked as a proof of concept forthe project. Data Release 2, used in this work, providesanalysis of ∼ K2 campaigns 4, 6, and 7.These three campaigns were chosen as they probe threelines of sight that are both distinct from each other andfrom the Kepler field (Figure 1). Data Release 3 willprovide the results for the remaining K2 campaigns.Following methods developed for Kepler (Pinson-neault et al. 2018), K2 GAP DR2 improves on K2 GAP DR1 by providing asteroseismic data that havebeen averaged across results from up to six independentpipelines. These pipelines are A2Z+ (based on Mathuret al. 2010), BHM (Elsworth et al. 2020; Hekker et al.2010), CAN (Kallinger et al. 2016), COR (Mosser & Ap-pourchaux 2009), SYD (Huber et al. 2009), and BAM(Zinn et al. 2019b). In this paper, we only considergiants in this catalog for which at least two of thesepipelines returned values for both ν max and ∆ ν , andtake the mean of these results. We include these meanvalues along with all of the associated pipeline values inour catalog.To investigate trends in the age-abundance relation-ship with Galactic position, we adopted Bayesian dis-tance estimates based on Gaia
Data Release 2 (GaiaCollaboration et al. 2016, 2018) parallaxes from Bailer-Jones (2015). Each star’s height above the Galactic plane ( Z ), radial distance from the center of the Galaxy( R ), and Galactocentric X and Y coordinates werecomputed using Astropy (Astropy Collaboration et al.2013; Price-Whelan et al. 2018).We have extensive asteroseismic data sets for bothshell H-burning red giant branch (RGB) stars and coreHe-burning red clump (RC) stars. We restrict ourselvesto RGB stars because the mapping between mass andage for RC stars is complicated by the known existenceof mass-loss between the RGB and RC phases, so thatthe present-day RC asteroseismic mass is systematicallybiased compared to its birth mass (e.g., Casagrandeet al. 2016).The state-of-the-art for RGB vs. RC classifications isto determine a star’s evolutionary state through aster-oseismology (e.g., Bedding et al. 2011). However, thismethod requires very long time domain data. Thoughthese classifications are difficult to do with the short K2 time series, they have been successfully made using the Kepler data by Elsworth et al. (2019).To distinguish between RGB and RC stars in K2 ,we used a spectroscopic evolutionary state classificationsimilar to that of Bovy et al. (2014). A temperature-,surface gravity-, and abundance-dependent cut to sepa-rate RGB and RC stars was found using the evolutionarystates from Elsworth et al. (2019). First, we fit for α , β ,and γ that define a “reference” temperature given by T ref = α + β [Fe / H] RAW + γ (log ( g ) SPEC − .
5) (1)through a non-linear least squares fit for stars classifiedas RGB according to APOKASC-2 asteroseismology.[Fe/H]
RAW and log ( g ) SPEC are the uncorrected valuesfor metallicity and surface gravity, respectively, givenin the APOGEE DR16 catalogue. The fitting resultswere found to have approximate values of α = 4383 . β = − .
136 K/dex, and γ = 532 .
659 K/dex. Aline was then fit through the approximate ridgeline in[C/N]
RAW vs. T SPECeff − T ref space for which 98% ofstars to the right of the line were classified as RGB.This ensures that the contamination from RC stars inour spectroscopic classifications is negligible. The final-ized classification criteria in Table 1 were then used topick out the stars in our K2 sample that are most likelyto be on the RGB. Hereafter in this work, all referencesto “giants” refer specifically to RGB stars unless other-wise stated.From the parameters provided by K2 GAP andAPOGEE, we were able to calculate values for aster-oseismic surface gravity (log ( g ) seis ), for mass, and for Warfield et al.
Table 1.
Grid for if a star is classified as a red giant for different ranges of log ( g ) SPEC and [C/N]
RAW . Stars are classified asred giants if the statement for the given range of conditions is true for that star. ∆ T = T SPECeff − T ref . . > log ( g ) SPEC > .
38 log ( g ) SPEC < . / N] RAW > − . / N] RAW < . − . / H] RAW − . T True[C / N] RAW < − . > . / H] RAW + ∆ T True radius. log ( g ) seis was calculated using ν max and T eff inthe scaling relation (Brown et al. 1991; Kjeldsen & Bed-ding 1995): (cid:18) ν max ν max , (cid:12) (cid:19) ≈ (cid:18) gg (cid:12) (cid:19) (cid:18) T eff T eff , (cid:12) (cid:19) − / , (2)with solar reference values of ν max , (cid:12) = 3076 µ Hz, T eff , (cid:12) = 5772 K, and g (cid:12) = 27400 cm/s . Values for mass andradius can be found by combining Equation 2 with thescaling relation for ∆ ν (Ulrich 1986; Kjeldsen & Bedding1995), ∆ ν ∝ M / R − / . (3)Doing this gives that (cid:18) MM (cid:12) (cid:19) ≈ (cid:18) ν max f ν max ν max , (cid:12) (cid:19) (cid:18) T eff T eff , (cid:12) (cid:19) / (cid:18) ∆ νf ∆ ν ∆ ν (cid:12) (cid:19) − (4)and (cid:18) RR (cid:12) (cid:19) ≈ (cid:18) ν max f ν max ν max , (cid:12) (cid:19) (cid:18) T eff T eff , (cid:12) (cid:19) / (cid:18) ∆ νf ∆ ν ∆ ν (cid:12) (cid:19) − . (5)We adopt ∆ ν (cid:12) = 135.146 µ Hz. We also computetheoretically-motivated corrections to the observed ∆ ν values, f ∆ ν , according to Sharma et al. (2016). Thereis increasing empirical evidence that these and simi-lar corrections from the literature (e.g., White et al.2011; Guggenberger et al. 2017) result in better agree-ment with independent estimates of stellar parameters(e.g., Huber et al. 2017). Evaluating f ∆ ν requires mass,radius, temperature, evolutionary state, and metallic-ity. The bulk metallicities are adjusted for this pur-pose to account for non-solar alpha abundances accord-ing to the Salaris et al. (1993) prescription: [Fe / H] (cid:48) =[Fe / H] + log (0 . × [ α/ M] + 0 . ν max values (i.e., f ν max = 1), pending further empirical con-straints and theoretical understanding of the ν max scal-ing relation (see discussion in, e.g., Pinsonneault et al.2018).The sample was then further limited to stars with[ α /M] values between 0.0 and 0.4 dex, [Fe/H] values be-tween -2.0 and 0.6 dex, and masses between 0.6 and 2.6 This value agrees to within 0 . M (cid:12) in order to ensure meaningful parameter values thatfit within the parameter space defined by the tracks thatwe used for estimating ages ( § / H] < − § g ) seis < . g ) seis > . α -rich and α -poor by approximately drawing a linethrough the ridge-line between the two populations, asseen in Figure 3. AGE DETERMINATIONObtaining reliable ages for RGB stars is primarily de-pendent on having accurate estimates for stellar massand secondarily on harmoniously-calibrated values forchemical compositions. Because the lifetime in the RGBphase is short, the surface gravity has only a minor im-pact on the derived age, especially on the upper RGB.Because of mechanical challenges in incorporating theage dependence tied to surface gravity, which is multi-valued for the RGB, we simply bracket our sample intotwo surface gravity bins and take the age range withinthese bins as a (very small) additional source of uncer-tainty.At fixed surface gravity and composition, age isstrongly sensitive to effective temperature. In grid mod-eling, the derived age combines this information with as-teroseismic properties; for an example see SA18. How-ever, there are large random and systematic uncertain-ties in this age estimate due to effective temperatureoffsets. On the giant branch locus, an error budget of50 K in temperature would produce a random age un-certainty of ∼ ntermediate Age Population [Fe/H] [ / M ] Low-Luminosity RGB [Fe/H] [ / M ] Luminous RGB
Figure 3. [ α /M] vs. [Fe/H] for the low-luminosity and luminous giants in our sample. Our sample is further split into thecategories of α -rich and α -poor, which is defined by the dashed line in the plots. This division was defined by-eye based onthe ridge-line between the groups of points in the data. This cut is similar to that made by e.g. Silva Aguirre et al. (2018)and Weinberg et al. (2019). This line is defined as [ α/ M] = 0 .
15 for [Fe / H] < − .
0, [ α/ M] = 0 .
056 for [Fe / H] > − .
07, and[ α/ M] = − . · [Fe / H] + 0 .
049 for − . ≤ [Fe / H] ≤ − . systematic shifts (Tayar et al. 2017). We therefore adoptthe methodology of Pinsonneault et al. (2018), and donot directly incorporate classical age constraints fromHR diagram position. We note that this choice alsomakes the ages more replicable, and that others can usedifferent choices of stellar models with these data to inferages with a grid modeling approach if they so choose.We used stellar evolutionary tracks, generated withthe Yale Rotating Evolution Code, from Pinsonneaultet al. (1989) with updates from van Saders & Pinson-neault (2012). From these tracks we created three setsof grids for log ( g ) of 3.30, 2.50, and 1.74, with columnsfor log (Mass), [Fe/H], [ α /Fe], and log (age). These val-ues for log ( g ) were chosen to approximately bracket thelow-luminosity giant branch (3.30 and 2.50) and the up-per giant branch (2.50 and 1.74). We made these gridsregular along the log (Mass), [Fe/H], and [ α /Fe] axes bylinearly interpolating to ages at locations where therewere gaps in the tracks. Given a star’s values and as-sociated uncertainties for each of these parameters, aMonte Carlo method was used to calculate 500 age es-timates for each star through 4-point Lagrange interpo-lation within the grid. The reported results for a givenstar is the median of these values along with a lower andan upper 1- σ uncertainty reflecting the 16th and 84thpercentiles of the Monte Carlo results, respectively.Figure 4 shows a comparison between the ages cal-culated for 2407 RGB stars in the Kepler field usingthis method and the ages reported for the same giantsin the APOKASC-2 catalog (Pinsonneault et al. 2018).
Age [Gyr] (This Work) A g e [ G y r ] ( A P O K A S C - ) Figure 4.
A comparison of the ages reported in theAPOKASC-2 catalog vs. the ages calculated for this workfor 2407 RGB stars from Pinsonneault et al. (2018). Errorbars represent the standard deviation of the mean for binsthat are 1 Gyr wide on the x -axis. There are a few main systematic effects, aside from dif-ferences in technique, that lead to the slight disagree-ment in the ages and the age zero-point. First, thoughPinsonneault et al. (2018) used a similar method to es-timate the ages of these stars, the stellar tracks andisochrones used did not take α enhancement into ac-count when generated. Rather, the lookup metallicitywas corrected by adjusting [Fe/H] by +0 .
625 [ α /M]. At Warfield et al. a fixed [Fe/H], an increase in [ α /M] corresponds to anincrease in a star’s opacity. Increasing a star’s opac-ity means also increasing its radius, therefore loweringthe star’s core temperature and extending the amountof time that it takes to burn through core hydrogen onthe main sequence. Therefore, not considering [ α /M]in stellar models has the effect of underestimating theages of stars with [ α /M] >
0, with the biggest effectbeing for the ages of low-mass stars. The correctionon metallicity used by Pinsonneault et al. (2018) is notable to fully account for this effect. On average, thisaffects the ages of stars younger than about 8 Gyr byapproximately +1% and above 8 Gyr by +8%. The sec-ond systematic is that, in order to make the ages in the
Kepler field more concordant with those from the K2 fields, we recalculated f ∆ ν for this sample in the samemanner that it was calculated for K2 GAP. This adjust-ment leads to changes in mass by an average of about+2% to +3%, which corresponds to changes of −
6% to −
9% in age. In order to make masses agree with thosefrom open clusters, Pinsonneault et al. (2018) applied auniform shift in f ν max (and therefore the sample’s aster-oseismic masses). Correcting the zero-point offset fromour reformulation of values for f ∆ ν so that the massesare on the same open cluster scale, therefore, requiredus to scale masses for the Kepler sample down by a fac-tor of 1 . . = 1 .
055 (or about 6%). In addi-tion to these effects, there are also going to be changesassociated with the difference between the abundanceestimates in APOGEE DR14 (which was used for theages by Pinsonneault et al. 2018) and APOGEE DR16(changes between these data releases are discussed inJ¨onsson et al. 2020).Another check we can perform on the data is to seeif our age distributions for
Kepler stars reproduce thefeatures seen by SA18. The ages published by SA18are computed using the Bayesian stellar parameter esti-mation package
BASTA (Silva Aguirre et al. 2015, 2017).The
Kepler age distribution globally reproduces the fea-tures of that from SA18, including the small young, α -rich population. This indicates that adopting a gridmodeling approach does not induce a large change inderived ages. We also note that our Kepler age distri-bution is consistent with recent estimates of the thickdisk age using detailed asteroseismic modeling of
Kepler data (Montalb´an et al. 2020). RESULTS AND DISCUSSIONThe panels in Figure 5 show the age results fromboth the
Kepler and K2 fields. Results are shown forboth the full samples and for the low-luminosity giants in each field. Figure 6 shows these same results foreach K2 campaign individually. Gaussian kernel den-sity functions were drawn over each distribution usingthe kdeplot function from the seaborn Python pack-age (Waskom et al. 2017). We can see that, though theinclusion of the luminous giants does not have a signif-icant impact on the locations of the peaks for the un-derlying kernel density estimates they do contribute anoticeable degree of scatter to the results..Table 2 summarizes these results for the α -rich giantsin each field. Our full K2 data sample, including ageestimates for individual stars, are provided in Table 3.Table 4 contains our ages for stars in the Kepler field.Comparing our results for these K2 fields with the re-sults from the Kepler field brings to light two interestingdifferences. First, though the median age of the α -richpopulation is strongly peaked at a single age in bothof these samples, the populations in the K2 fields arefound to be at an age about 2 Gyr younger than whatwas found in the Kepler field. Secondly, there seemsto be much less of a difference between the ages of the α -rich and α -poor populations in the K2 field.Of course, it is still possible that there are systematicsat play partially driving these discrepancies. The K2 as-teroseismic parameters used in this work yield radii thatmay be up to ∼
2% larger than radii computed based on
Gaia
DR2 parallaxes (Zinn et al. 2020). Assuming thisoffset is due to slightly different ν max scale comparedto APOKASC-2, this implies that the K2 masses maybe too large by ∼ K2 ages to be ∼
15% younger than the
Kepler ages. In thissense, the age gap we find between K2 and Kepler maybe related to the fundamental scale of the K2 astero-seismic data. At this time, we are limited in our abilityto calibrate the K2 asteroseismic scale with Gaia datadue to the
Gaia
DR2 parallax zero-point varying acrossthe sky. The next data release of
Gaia data should beless affected by the zero-point, and will be very usefulin solidifying the K2 asteroseismic scale (see also Khanet al. 2019).There is, however, some reason to believe that an in-termediately aged α -rich population could be physical:Lian et al. (2020) discuss a population of young, α -richstars in the outer disk, suggesting that there should havealso been mechanisms in place to make the intermedi-ate age populations observed in K2 . In addition, theresult from Anders et al. (2017) of a young α -rich pop-ulation with similar ages to the corresponding α -poorpopulation in the CoRoT fields seems to also indicate https://seaborn.pydata.org ntermediate Age Population N o r m a li z e d d i s t r i b u t i o n Full Sample
Kepler Field -poor-rich 0.050.100.150.20 N o r m a li z e d d i s t r i b u t i o n Full Sample
K2 Fields (Gyr) N o r m a li z e d d i s t r i b u t i o n log(g) > 2.5 (Gyr) N o r m a li z e d d i s t r i b u t i o n log(g) > 2.5 Figure 5.
Distributions of the age estimates for the Kepler field (left) and K2 fields (right) for both the α -poor (blue) and α -rich (orange) populations. The top row shows the distributions for the full sample for the respective fields and the bottomrow shows the distributions for the low-luminosity sample (log ( g ) seis > . Kepler field, there are 691 (389) α -rich and1714 (1228) α -poor stars in the full (low-luminosity) sample. In the K2 fields, there are 534 (291) α -rich and 270 (160) α -poorstars in the full (low-luminosity) sample. Table 2.
This table gives information for the kernel density estimation (kde) and the underlying data for the age-distributions of the low-luminosity α -rich populations in each field (shown in Figures 5 and 6). The value for the α -rich age width is calculated as FWHM / . α -rich stars in the indicated field. The possible systematic uncertainties come from the interpolation error (-1%) and from thesystematic uncertainty due to the K2 ν max scale (+15%).Field α -rich Peak Age (Gyr) α -rich Peak Age Width (Gyr) Average Age Uncertainty (Gyr) Possible Sys. Uncertainties (%)Kepler 9.53 1.40 1.46 -1K2 C4 8.08 3.83 2.92 +14K2 C6 7.62 2.16 2.23 +14K2 C7 7.24 2.63 2.40 +14all K2 7.61 2.17 2.32 +14 Warfield et al. N o r m a li z e d d i s t r i b u t i o n Full Sample
Campaign 4 -poor-rich N o r m a li z e d d i s t r i b u t i o n Full Sample
Campaign 6 N o r m a li z e d d i s t r i b u t i o n Full Sample
Campaign 7 (Gyr) N o r m a li z e d d i s t r i b u t i o n log(g) > 2.5 (Gyr) N o r m a li z e d d i s t r i b u t i o n log(g) > 2.5 (Gyr) N o r m a li z e d d i s t r i b u t i o n log(g) > 2.5 Figure 6.
Distributions of the age estimates for both the α -poor (blue) and α -rich (orange) populations for each K2 fieldindividually. The top row shows the distributions for the full sample for the respective fields and the bottom row shows thedistributions for the low-luminosity sample (log ( g ) seis > . α -rich and 128 (62) α -poor stars in thefull (low-luminosity) sample. In C6, there are 335 (208) α -rich and 76 (59) α -poor stars in the full (low-luminosity) sample. InC7, there are 167 (61) α -rich and 66 (39) α -poor stars in the full (low-luminosity) sample. Table 3.
The partial data table for K2 campaigns 4, 6, and 7, including our ages. The complete table is available in machine-readableformat in the online journal, which also includes the asteroseismic values from each of the individual pipelines. K2 EPIC ID K2 Campaign APOGEE ID τ (Gyr) σ − ( τ ) σ + ( τ ) RA (deg.) Dec (deg.) Gaia
Designation210495151.0 4 2M03593912+1519463 9.94 1.81 2.28 59.913042 15.329524 Gaia DR2 40120290241918848210610252.0 4 2M04211626+1706358 9.48 1.71 2.48 65.317758 17.109962 Gaia DR2 3313915749626906752210483090.0 4 2M03585776+1507226 2.98 0.36 0.38 59.740697 15.122972 Gaia DR2 40110463356775296210505442.0 4 2M04003325+1530162 4.41 1.17 1.65 60.138593 15.504482 Gaia DR2 40147159557282560210720697.0 4 2M04220023+1839546 3.62 0.66 0.88 65.500938 18.665140 Gaia DR2 47563498628339072 T eff (K) σ ( T eff ) log ( g ) (cgs) σ (log ( g )) [ α/ M] σ ([ α/ M]) [Fe / H] σ ([Fe / H]) ¯ ν max ( µ Hz) σ (¯ ν max ) ∆¯ ν ( µ Hz)4797.24 106.18 2.87 0.07 0.23 0.01 -0.58 0.01 108.47 0.82 10.364750.61 85.03 2.61 0.06 0.04 0.01 -0.23 0.01 44.15 0.60 5.194958.78 89.15 3.15 0.06 0.04 0.01 -0.01 0.01 183.08 1.38 14.024889.04 91.34 2.84 0.07 0.06 0.01 -0.48 0.01 68.83 0.68 7.104726.70 83.11 2.58 0.06 0.01 0.01 -0.09 0.01 52.67 0.59 5.50 σ (∆¯ ν ) log ( g ) seis (cgs) σ (log ( g ) seis ) M ( M (cid:12) ) σ ( M ) d (kpc) σ ( d ) X (kpc) Y (kpc) Z (kpc) R (kpc)0.10 2.94 0.01 0.96 0.05 1.11 0.05 -9.28 0.07 -0.48 9.280.04 2.55 0.01 1.01 0.06 1.24 0.08 -9.44 0.04 -0.45 9.440.02 3.18 0.01 1.45 0.05 2.35 2.66 -10.37 0.15 -1.07 10.380.14 2.75 0.01 1.19 0.11 1.14 0.05 -9.31 0.07 -0.49 9.310.05 2.63 0.01 1.35 0.08 1.58 0.12 -9.77 0.08 -0.55 9.77 ntermediate Age Population Table 4.
The partial data table for RGB stars in the
Kepler field. The complete table is available in machine-readable format in theonline journal.
KIC APOGEE ID τ (Gyr) σ − ( τ ) σ + ( τ ) APOKASC2 τ (Gyr) T eff (K) σ ( T eff ) log ( g ) (cgs) σ (log ( g )) [ α/ M] σ ([ α/ M])1027337 2M19252021+3647118 5.49 1.09 1.27 6.28 4635.50 78.02 2.76 0.05 0.01 0.011296068 2M19264481+3658152 10.31 1.34 1.68 10.42 4586.52 93.37 2.61 0.05 0.05 0.011429505 2M19225688+3702125 6.42 0.96 1.20 7.36 4682.15 87.07 2.64 0.06 0.02 0.011431059 2M19243068+3701290 7.71 1.22 1.68 6.98 4802.11 106.14 3.07 0.06 0.00 0.011433730 2M19265020+3703054 1.35 0.16 0.21 1.43 4732.06 83.20 2.53 0.06 0.00 0.01[Fe / H] σ ([Fe / H]) ν max ( µ Hz) σ ( ν max ) ∆ ν ( µ Hz) σ (∆ ν ) M ( M (cid:12) ) σ ( M ) X (kpc) Y (kpc) Z (kpc) R (kpc)0.20 0.01 73.97 0.67 7.09 0.09 1.29 0.08 -7.81 1.31 0.26 7.92-0.02 0.01 59.38 0.53 6.32 0.02 1.04 0.04 -7.72 1.57 0.31 7.88-0.11 0.01 55.41 0.61 5.91 0.02 1.15 0.05 -7.88 1.13 0.24 7.960.06 0.01 170.84 1.54 13.86 0.08 1.14 0.05 -7.83 1.26 0.26 7.93-0.08 0.01 40.01 0.36 4.17 0.02 1.79 0.07 -7.91 1.06 0.22 7.98 that an intermediate aged α -rich population is not un-thinkable. At the moment, the comparison of our resultsto Anders et al. 2017’s can only be qualitative. As op-posed to SA18, Pinsonneault et al. (2018), Zinn et al.(2020), and this work, Anders et al. (2017) does not ap-ply theoretically-motivated ∆ ν corrections to their as-teroseismic results, which could results in an offset ofaround 30% in age.It should be noted that, though there is significantlymore spread in the ages around the α -rich peak in the K2 fields, there is no evidence that this spread is due toanything other than the larger uncertainties associatedwith this data.It is also interesting to note that the ages of these twopopulations seem to converge as a function of heightabove the Galactic plane, a trend that is shown inFigure 7. Hayden et al. (2017) finds similar trends,such that coeval populations of α -rich and α -poor starsare found to have the same vertical scale heights.These results potentially coincide with those from Ren-dle et al. (2019), whose K2 Galactic archaeology re-sults seem consistent with the “upside-down” formationmodel (e.g., Bird et al. 2013), wherein stars form in avertically-extended disk, with subsequent formation oc-curring closer and closer to the Galactic plane.We also tentatively recover the young, α -rich starsseen in the Kepler analysis of SA18 and the K2 analysisof Rendle et al. (2019). The origin of these stars has notbeen definitively determined, but part of the populationmay be explained by stellar mergers.To analyse the meaning of these results, it may beuseful to place them within the context of the proposedscenarios in the literature for generating the bi-modal α sequence, each of which comes with their own set ofpredictions concerning the relative ages of α -rich and α -poor populations and the homogeneity of these agesthroughout the Galaxy.One of these possible mechanisms is the radial mi-gration of stars mixing together populations of differentchemical origins. In this scenario, the radial migrationof stars born at different radii in the disk results in thesuperposition of several chemical evolution sequences atany given location in the Galaxy. Stars with high [ α /Fe]at high [Fe/H], for example, could come from inner re-gions where more efficient star formation produced highmetallicity gas relatively quickly. When mixed together,they form the sequence that we are familiar with. There-fore, the primary explanation for the lack of an age-metallicity relation is mostly attributed to stellar neigh-bors not having necessarily been born from the samegas, as stars have moved radially inwards and outwardsin their orbits (see e.g. Sch¨onrich & Binney 2009; Wein-berg et al. 2017; Nidever et al. 2014; Sharma et al. 2020).However, it is not entirely clear whether our results ofsimilar α -rich populations having strongly peaked agesin different parts of the Galaxy is consistent with thistheory.Another possible explanation is that the two loci ofthe bi-modal α sequence are the products of two gas in-fall episodes that both spurred two independent periodsof star formation. In this scenario, the α -rich sequencewas formed during a rapid infall episode that occurredabout 10 billion years ago. This would be followed by adrought of star formation that would itself be followedby a gradual infall episode spurring star formation fromabout 8 billion years ago to present. The pristine gasin this second infall would dilute the disk gas, creat-ing a new starting point at lower [Fe/H] for a second,less α -enriched episode (Chiappini et al. 1997). Eachof these star formation episodes would revive historic2 Warfield et al. N o r m a li z e d d i s t r i b u t i o n Z |<0.5 -poor-rich0.050.100.150.200.25 N o r m a li z e d d i s t r i b u t i o n Z |<1.0 N o r m a li z e d d i s t r i b u t i o n Z |<100.0 Figure 7.
Distributions of the age estimates for both the α -poor and α -rich of the K2 fields as a function of distance fromthe Galactic plane | Z | . While the median age of the α -richpopulation is about constant as a function of vertical height,if not slightly decreasing with | Z | , the α -poor populationseems to increase in age as | Z | increases, with the populationsconverging on an age of about 7 Gyr. rates of SNe II, but have lesser effects on changing therate of SNe Ia. Spitoni et al. (2019), simulating thistwo-infall scenario, were able to successfully replicatethe bi-modal α sequence as well as the age trends foundin SA18 for the high- and low- α sequences. Lian et al.(2020) present a similar model which is able to betterproduce the density ridge-line between the α -rich and α -poor loci while also being able to more accurately re-produce the observed ages of α -poor stars. Adding the K2 data, however, seems to suggest that this two-infallscenario would have to be at least slightly more complexif star formation happened at different times in differ-ent places in the Galaxy during the first, rapid episode.Sharma et al. (2020) points out that the model by Spi-toni et al. (2019) requires a loop in the tracks in the [ α /Fe] vs. [Fe/H] plane which does not agree with ob-servations. Figure 8 shows the K2 sample in the [ α /Fe]vs. [Fe/H] plane with stars colored by their ages, but itis not clear that our results have the resolution nor thevolume needed to fully explore the existence of this ageloop.A third proposed mechanism is that the bi-modal se-quence is the product of star formation happening inclumpy bursts throughout the Galaxy. In this scenario,there is a background of star formation within the α -poor sequence and the rest of the star formation takesplace in gas-rich clumps that naturally arose in the disk.When star formation is spurred in these clumps, thesepopulations of stars are initially enriched with α ele-ments as the number of SNe II is spurred by the forma-tion of new, massive stars. Therefore, in this scenario,the α -rich sequence is formed from a superposition ofthese clumpy star formation episodes (see e.g. Clarkeet al. 2019). If assuming that the populations are notmixed together (by, for example, radial migration), thisallows nearly identical chemical populations observed indifferent regions of the Galaxy to have diverging ages.This mechanism therefore seems promising as a poten-tial explanation for why similar chemical populationsin different parts of the Galaxy would have stronglypeaked, discrepant ages. However, since the ages of the α -rich populations in the three K2 fields seem to agreewith each other but disagree the age of the α -rich pop-ulation in the Kepler field, if this scenario is true, it isstill curious why only the very local Galaxy seems to beunique in its star formation history.Looking forward, the third data release of the K2 Galactic Archaeology Program will provide us with as-teroseismic data for giants along fourteen more lines ofsight in the Galaxy. Additionally, a similar analysis ispossible with data from NASA’s ongoing Transiting Ex-oplanet Survey Satellite mission. This data, along withthe spectroscopy from the final APOGEE data releasesand from other large-scale surveys, can be used to fill ina more complete picture of the age gradients for stellarpopulations throughout the Milky Way.ACKNOWLEDGMENTSThis paper is dedicated to the memory of Nikki Jus-tice.Funding for the Sloan Digital Sky Survey IV has beenprovided by the Alfred P. Sloan Foundation, the U.S.Department of Energy Office of Science, and the Partici-pating Institutions. SDSS-IV acknowledges support andresources from the Center for High-Performance Com- ntermediate Age Population [Fe/H] [ / M ] Low-Luminosity RGB [Fe/H] [ / M ] Luminous RGB ( G y r ) Figure 8. [ α /M] vs. [Fe/H] for the low-luminosity and luminous giants in our sample, colored by age. Ahumada, R., Prieto, C. A., Almeida, A., et al. 2020,ApJS, 249, 3Aller, L. H., & Greenstein, J. L. 1960, ApJS, 5, 139Anders, F., Chiappini, C., Rodrigues, T. S., et al. 2017,A&A, 597, A30Astropy Collaboration, Robitaille, T. P., Tollerud, E. J.,et al. 2013, A&A, 558, A33Bailer-Jones, C. A. L. 2015, PASP, 127, 994Bedding, T. R., Mosser, B., Huber, D., et al. 2011, Nature,471, 608Bensby, T., Feltzing, S., & Lundstr¨om, I. 2003, A&A, 410,527 Bird, J. C., Kazantzidis, S., Weinberg, D. H., et al. 2013,ApJ, 773, 43Blanton, M. R., Bershady, M. A., Abolfathi, B., et al. 2017,AJ, 154, 28Bovy, J., Nidever, D. L., Rix, H.-W., et al. 2014, ApJ, 790,127Bowen, I. S., & Vaughan, A. H. 1973, Appl. Opt., 12, 1430Brown, T. M., Gilliland, R. L., Noyes, R. W., & Ramsey,L. W. 1991, ApJ, 368, 599Casagrande, L., Silva Aguirre, V., Schlesinger, K. J., et al.2016, MNRAS, 455, 987 Warfield et al.
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