Universal properties of the high- and low-α disk: small intrinsic abundance scatter and migrating stars
DDraft version February 25, 2021
Typeset using L A TEX twocolumn style in AASTeX63
Universal properties of the high- and low − α disk: small intrinsic abundance scatter and migratingstars Yuxi(Lucy) Lu ,
1, 2
Melissa Ness, Tobias Buck, and Joel Zinn ∗ Department of Astronomy, Columbia University, 550 West 120 th Street, New York, NY, USA American Museum of Natural History, Central Park West, Manhattan, NY, USA Leibniz Institute for Astrophysics Potsdam, An der Sternwarte 16, 14482 Potsdam, Germany
Submitted to
The Astronomical Journal
ABSTRACTThe detailed age-chemical abundance relations of stars measures time-dependent chemical evolution.These trends offer strong empirical constraints on nucleosynthetic processes, as well as the homogeneityof star-forming gas. Characterizing chemical abundances of stars across the Milky Way over time hasbeen made possible very recently, thanks to surveys like Gaia, APOGEE and Kepler. Studies of thelow- α disk have shown that individual elements have unique age-abundance trends and the intrinsicdispersion around these relations is small. In this study, we examine and compare the age distributionof stars across both the high and low- α disk and quantify the intrinsic dispersion of 16 elementsaround their age-abundance relations at [Fe/H] = 0 using APOGEE DR16. We find the high- α disk has shallower age-abundance relations compared to the low- α disk, but similar median intrinsicdispersions of ≈ α disks, despite differences in formation history. We visualize the temporal and spatial distribution of diskstars in small chemical cells, revealing signatures of upside-down and inside-out formation. Further,the metallicity skew and the [Fe/H]-age relations across radius indicates different initial metallicitygradients and evidence for radial migration. Our study is accompanied by an age catalogue for 64,317stars in APOGEE derived using The Cannon with ≈ Keywords:
Giant stars; Stellar nucleosynthesis; Milky Way Galaxy; Stellar abundances; Stellar ages;Galactic archaeology INTRODUCTIONLarge spectroscopic surveys such as Apache Point Ob-servatory Galactic Evolution Experiment (APOGEE)(Majewski et al. 2017), Large Sky Area Multi-ObjectFibre Spectroscopic Telescope (LAMOST) (Cui et al.2012), GALactic Archaeology with HERMES (GALAH)(De Silva et al. 2015; Buder et al. 2019) and time-domainsurveys such as Kepler (Borucki et al. 2010) and TESS(Ricker et al. 2015) are observing hundreds of thousandsof stars. These surveys provide the data that gives usinsight as to the formation and evolution of the Galaxy
Corresponding author: Yuxi (Lucy) [email protected] ∗ NSF Astronomy and Astrophysics Postdoctoral Fellow as well as the nucleosynthetic channels of chemical en-richment.The APOGEE survey (Majewski et al. 2017) is anIR survey at R=22,500 that primarily targets the disk,where the majority of the baryonic matter of the MilkyWay resides (e.g. Bland-Hawthorn & Gerhard 2016).From the APOGEE R=22,500 spectra, more than 20precision element abundances [X/Fe] (Garc´ıa P´erez et al.2016a; Ahumada et al. 2020), imprecise spectroscopicages ( e.g.
Leung & Bovy 2019; Ness et al. 2016; Mar-tig et al. 2015), and precision distances (e.g. Leung &Bovy 2019; Hogg et al. 2019) can be determined. Time-domain missions, most notably to date the Kepler survey(Borucki et al. 2010), are enabling precision ages to bedetermined via asteroseismology by examining internaloscillation frequencies of stars. A population of Kepler a r X i v : . [ a s t r o - ph . GA ] F e b Lu et al. red giants with both asteroseismic data and APOGEEspectra are collated in the APOKASC catalogue (Pin-sonneault et al. 2018). This provides 2,616 precise as-teroseismic ages. This catalogue has proven to be a use-ful benchmark for building larger catalogues of stellarages using machine learning (e.g., Ness et al. 2016, 2019;Mackereth et al. 2019).Using both 1) small local benchmark samples of starswith high precision abundances and ages from stellarspectra and astroseismology and 2) large samples ofstars with high precision abundances and imprecise agesacross the Galactic disk allows for testing the chemicalenrichment of the disk over wide ranges in time and spa-tial position. With these data, we can examine globalage distributions of stars across the Milky Way as wellas the temporal and spatial properties of stars with dif-ferent chemical compositions. Globally, this can link thestar formation history to the galaxy formation historyand reveal evolutionary processes at work like radial mi-gration (e.g. Roˇskar et al. 2008).The spectroscopic age distributions built using largesurveys have shown the detailed mapping from the oldpopulations in the inner Galaxy, to the young popula-tions in the outer disk (e.g. Ness et al. 2016; Martiget al. 2016; Bovy et al. 2019; Bensby et al. 2017). Fur-ther, younger stars are clearly concentrated to the planeof the disk and old stars at larger heights with flaringacross radius (e.g. Mackereth et al. 2019; Martig et al.2016). The age gradient indicates an inside-out forma-tion for the Galaxy. Although stars also evolve fromtheir birth sites over time, stellar ages have been usedto model the so called radial migration across part of thedisk, which has been determined to be strong (Frankelet al. 2018, 2019). To connect the star formation en-vironment and history to formation and evolutionaryprocesses like radial migration, we need to explore age-individual chemical abundance relations at different lo-cations of the disk.Age-individual chemical abundance trends at fixedmetallicity find utility as chemical clocks, via which wecan understand: • Nucleosynthesis processes: Different elements arebelieved to be produced in different processes ondifferent timescales. For example, light elementssuch as C and N are produced in large part dur-ing the phase of asymptotic giant branch (AGB)stars; iron-peak elements (e.g. V, Cr, Mn, Ni, Co)are produced mostly by type Ia supernovae; α -elements (e.g. O, Mg, Si, S, and Ca) derive fromcore-collapse supernovae. Many elements are pro-duced by multiple channels are have both bothmass and metallicity dependent yields (more de- tailed description and references see Kobayashiet al. 2020). These complicated nucleosynthesisprocesses and stellar yields are in detail based onmany approximations and estimates. By studyingthe age-chemical abundance trends, one can learnthe chemical yields as informed by the data, andconstrain the theoretical models (Rybizki et al.2017). • Formation processes in the Milky Way: By com-bining the insights from chemical clocks with spa-tial and kinematic properties of stars across theGalaxy, we can study how the disk has formedand evolved subsequently through radial migra-tion (e.g. Frankel et al. 2018, 2019). Ultimatelywe can use this information in combination withsimulations to link the current day properties ofstars to their birth location and environments.Chemically, the disk is broadly characterised by thepresence of a high and low- α sequence of stars. The[ α /Fe]-[Fe/H] bi-modality was discovered by Fuhrmann(1998). The stars in the high- α disk are predominantlyold and those in the low alpha disk are predominantlyyoung (e.g. Bensby et al. 2014). This bi-modality hasbeen linked to the structural “thin” and “thick” diskGilmore & Reid (1983), and certainly, the [ α -Fe] ver-sus [Fe/H] plane changes dramatically with spatial posi-tion over the Galaxy (Nidever et al. 2014; Hayden et al.2015). However, as pointed out in Bland-Hawthornet al. (2019), a star’s kinematic changes throughout itslifetime but not its chemistry. As a result, if it is advan-tageous to break up the disk into constituents to studyit, it is often desirable to divide it in the chemical ratherthan the dynamical plane. The high and low- α diskshave different element abundance ratios in a multitudeof elements, indicative of their different star formationhistories ( e.g. Bensby et al. 2014; Masseron & Gilmore2015). Recent work leveraging large data shows that thehigh and low- α sequence appear to have different dy-namical properties, at all ages (Mackereth et al. 2019;Gandhi & Ness 2019).Different hypothesis have been proposed for the for-mation of the α -bimodality. Vertical disk heating drivenby an encounter between the Milky Way and satellitegalaxies Quinn et al. (1993) and the accretion of satellitestars Abadi et al. (2003) has been invoked as potentialculprits. More recent simulations demonstrate other sce-narios such as clumpy formation to form the high- α disk( e.g. Clarke et al. 2019; Debattista et al. 2019) or gas ac-cretion to form the low- α sequence (Agertz et al. 2020;Buck 2020). Regardless of the mechanisms via whichthe high and low- α disk were respectively formed, and niversal properties of the high- and low- α disk α disk for part of our analysis. However,we go beyond this dichotomy and explore the character-istics of the disk across a grid of chemical cells in the[Fe/H]-[ α/F e ] plane (see section 3). This is perhaps arefar more powerful approach to study the disk. Indeed itis now readily enabled with large samples of stars fromsurveys like APOGEE. A similar line of analysis wasalready suggested by (Bovy et al. 2011). Under this de-composition approach they reported a a continuous andmonotonic distribution of disk thicknesses rather than abi-modal disk. Nevertheless, the visual appearance of anhigh- α /low- α bimodality in [Fe/H]-[ α /Fe] space is a pre-diction of several models. In this sense, the bimodalityis broadly indicative of different formation mechanismsof the two populations, even if an exact, simple divisionbetween the apparent populations in chemical space maybe undesirable for a number of analyses.We first examine the global properties of the high-and low- α disk. We investigate how their mean agedistributions change spatially and chemically (how themean age distribution changes at different location inthe [ α /Fe]-[Fe/H] plane). We then investigate the over-all age-metallicity relation (where by metallicity we re-fer to [Fe/H]), which can place broad constraints ongalactic and chemical evolution of the Galaxy ( e.g. Ed-vardsson et al. 1993; Casagrande et al. 2011). Stud-ies have revealed a large range of stellar ages at anyfixed metallicity throughout the disk ( e.g.
Feuillet et al.2019; J¨onsson et al. 2020), showcasing that [Fe/H] it-self is not a chemical clock. Finally, we quantify therelationship between ages and individual chemical ele-ment abundances using red clump stars. We identify thered clump stars in the APOGEE catalogue from theirspectra, using data-driven modeling of the correlationbetween flux variability and evoluionary state (Hawkinset al. 2018). Red clump stars provide a narrow region inevolutionary state, thus mitigating systematic imprintsof abundance variation in the data (Jofr´e et al. 2019).Furthermore, they enable precision distance estimatesacross a large radial extent.Specifically, we examine the age-abundance propertiesfor 16 elements for stars of the low- compared to thehigh − α disk. Studies of detailed age-individual chemi-cal abundance relations - at fixed metallicity - have pre-viously found low intrinsic dispersion for stars aroundthese relations ( e.g. Ness et al. 2019; Bedell et al. 2018;Sharma et al. 2020; Hayden et al. 2020). However, these studies have focused on all the stars in the disk or onlystars in the low- α disk. The small intrinsic dispersionaround the individual age-abundance relations ( ≈ − α disk) implies we can usethese element abundance trends to age-date stars.The age-individual chemical abundance results set outstrong constraints on nucleosynthetic channels and theinitial composition of the star-forming gas. Examiningthese separately for the high and low- α disk gives us in-sight as to which properties are shared and which aredistinct across this chemical plane. This gets towardunderstanding the relationship between these sequencesand if the high- α disk could be an ancestor of the low,or if its formation channel must be entirely distinct. Indetail, we compare and contrast the age-abundance re-lations and the intrinsic dispersions around these rela-tions. We highlight which elements are most similarbetween the two disks and which are least similar. Weexamine the mean age distributions, both spatially andin the chemical-plane, and showcase the signatures ofradial migration. Using the age variable in concert withmetallicity directly demonstrates how the formation andevolutionary signatures of the disk are imprinted in thedata. We also provide reader an age catalog for 64,317stars from APOGEE DR16 (Ahumada et al. 2020) withan mean age error of 0.25 dex (APO-CAN stars) as wellas a red clump catalog with 22,031 stars with a contam-ination rate of 2.7%.Section 2.1 describes the data used in this project.Section 2.2 details how we determined ages and redclump membership, and how we separated the high- andlow- α disk. In Section 3.1, we look at the overall age dis-tribution of the APO-CAN stars from APOGEE DR16across the Galaxy. In Section 3.2, we investigate the agedistribution of the stars in the chemical plane at differentlocations in the Galaxy. Then, we examine the tempo-ral and spatial distributions of the high- and low- α diskin a grid of chemical cells across [ α /Fe]-[Fe/H]. In Sec-tion 3.4, we explore the detailed age-element abundancetrends for 16 different elements and the age-metallicityrelation for the high- and low- α disk. Finally, in Section4, we compare our results to simulations. DATA & METHODSWe used two data sets for this work – the APOGEEsurvey DR16 spectra and abundances data (Ahumadaet al. 2020), and the APOKASC catalogue that containsages and asteroseismic parameters (Pinsonneault et al.2018). The APOGEE spectrograph has a resolution of R = 22 ,
500 and is mounted on the 2.5-m telescope ofthe Sloan Digital Sky Survey (Wilson et al. 2019; Gunnet al. 2006). For details on the data reduction process,
Lu et al. see Nidever et al. (2015). APOGEE spectroscopic anal-ysis is performed using the APOGEE Stellar Parameterand Chemical Abundance Pipeline (ASPCAP; Garc´ıaP´erez et al. 2016b), with temperatures calibrated tothe infrared flux method scale of Gonz´alez Hern´andez& Bonifacio (2009) (Holtzman et al. 2015).
Figure 1.
Histograms of the parameters in our training setof 2,616 stars for
The Cannon . We combined both data sets to examine theabundance-age relations. The APOKASC catalogueserves not only as a benchmark data set of stars withprecision ages, but also as a training set for the datadriven approach of
The Cannon to estimate ages for therest of the red giant stars in APOGEE from their spectraand to identify red clump stars.We worked in a narrow region of T eff -log g for our anal-ysis to circumvent systematics ( e.g. Jofr´e et al. 2019) and we selected the red clump stars for our endeavouras we can determine precise distances for them to usein our follow on dynamical analyses of these stars andtheir age-abundance relations.In order to create the age and the red clump catalog,we used
The Cannon (Ness et al. 2015) . The Cannon isa data driven approach to derive stellar parameters fromstellar spectra. Here we use a quadratic combination ofthe labels to predict each pixel of the spectrum, as isconsisent with previous implementations ( e.g.
Ness et al.2015; Ho et al. 2017; Casey et al. 2017; Wheeler et al.2020). 2.1.
Data
In order to use
The Cannon to determine stellar agesand identify the red clump stars, we needed a high fi-delity set of reference objects for training the model.
The Cannon is a tool that determines the relationshipbetween flux and labels that describe the variability ofthe flux. Therefore, it is important to include the labelsthat describe most of the variability in the flux, hencewe included the set of labels of metallicity, T eff , log g ,and [Mg/Fe] in addition to the asteroseismic parameterand ages that we wished to infer for APOGEE DR16spectra.We used measurements of frequency spacing between p -modes, ∆ ν , and period spacing of the mixed g and p modes, ∆P, from Vrard et al. (2016) for 6,111 Ke-pler stars. We obtained estimates of ages from thesecond APOKASC catalog (Pinsonneault et al. 2018)and parameters of T eff , log g , [Fe/H], and [Mg/Fe] fromAPOGEE’s DR16 data release (J¨onsson et al. 2020). Weincluded ∆ ν and ∆P since these astroseismic parameterscan be used to better separate the red clump stars withthe red giant branch stars (Bedding et al. 2011; Tinget al. 2018). After cross-matching these two catalogs,we were able to find 2,616 common stars to constructthe training set. Figure 1 shows the parameter spaceoccupied by the training set.The distances that we use in our analysis are from StarHorse (Queiroz et al. 2018), which is a bayesiantool for determining stellar masses, ages, distances, andextinctions for field stars. To study the detailed age-element abundance relations, we also included 16 in-dividual element abundances, C, N, O, Mg, Al, Si,S,K, Ca, Ti, V, Mn, Ni, P, Cr, Co from the APOGEEDR16 catalog, inferred using ASPCAP . We removedNa as this showed anomalous behaviour and indeed in Available at https://annayqho.github.io/TheCannon/intro.html niversal properties of the high- and low- α disk .2.2. Methods
Creating the age/red clump catalog with
The Cannon
For our implementation of
The Cannon we use asecond-order polynomial to fit the spectra flux ( F ) foreach star, n , with labels at each wavelength, λ . Thelabels for each star used in this project, in vector form,is l n = [ T eff , log g , [Mg/Fe], [Fe/H], ∆P, ∆ ν , and Log (age)]. As a result, the model can be describedas: F nλ = θ λ + θ T eff λ T eff + ... + θ log ( age ) λ log ( age )+ θ T eff λ T + ... + θ log ( age ) λ log ( age ) + θ T eff log gλ T eff log g + ... + θ log ( age )∆ νλ log ( age )∆ ν + error In order to infer the stellar parameters, we have totrain
The Cannon on a set of reference stars in order tofit for the coefficients, θ λ . To train The Cannon , we firstexcluded stars that were flagged as “bad” (stars with
ASPCAPFLAG flag 23), and/or had signal-to-noise ra-tio less than 100. This left us with 2,480 stars with7 labels in our training set of stars (parameter rangeshown in Figure 1).To test the performance of
The Cannon , we performeda 10-fold cross-validation test, in which we left 10% ofthe data untouched and trained the model on the restof the 90% and predicted the labels for stars in the restof that 10%. We then repeated the same test 10 timeswith a different 10% of the data left out (hence called10-fold). The cross-validation result for stellar age isshown in Figure 2. We added the cross-validation rootmean squared (rms) scatter to the error estimated from
The Cannon to obtain the final systematic age uncer-tainty, which yield a median uncertainty of around 1.9Gyr across all ages. The rms scatter for other labels is —0.017 dex for [Fe/H], 26.8 K for T eff , 0.056 dex for log g ,0.028 dex for [Mg/Fe], 40.1 s for ∆P, and 0.6 µ Hz for∆ ν . After training The Cannon , we applied the trainedmodel to the rest of the APOGEE DR16 spectra. Onecaveat of using data-driven method is that we were notable to (reliably) infer stellar parameters for stars out-side of the range of those values of the training set since Avaliable at https://data.sdss.org/sas/
Figure 2.
The Cannon for all 2,480 stars. The ages are inunit of Myr. the
The Cannon extrapolates beyond the training sam-ple regime. Therefore, we first discarded stars outsideof the training parameter range. We only included starswith T eff between 4,400 K - 5,200 K, log g between 2.2dex - 3.5 dex, and [Fe/H] between -0.8 dex - 0.5 dex. Wealso excluded stars with abnormal element abundances(absolute abundance values > >
230 s as red clump stars. Figure 3 shows our results.The black dots show all the stars in ∆P-∆ ν space andthe red clump stars are shown in red. It is clear that ∆Pseparates the two types of stars. We calculate the con- Figure 3. ∆P vs ∆ ν for the APO-CAN stars (black). Thered dots show the 22,031 red clump stars (∆P >
230 s) inthis parameter space. It is clear that the ∆P separates thered clump stars and the red giant branch stars.
Lu et al. tamination rate following their method, where we mea-sured the false positive rate by taking the ratio of starsthat have predicted ∆P >
230 s but true ∆P < Separation of the high- and low- α disk For the purpose of examining the different propertiesof the high and low − α stars, we separated the high- andlow- α disk with an ad-hoc line, (0.1 × [Fe/H]+0.063) Wealso explored separating the two disks with a cluster-ing algorithm described in Ratcliffe et al. (2020) in theAppendix. Figure 4 shows the APO-CAN stars in the[ α /Fe]-[Fe/H] plane. The left plot shows the stars col-ored by age and the right plot shows the high- (red)and the low- α (blue) disk. This color code will be usedthroughout the paper to distinguish between these twodisks. It is clear that the stars in the high- α disk areon average older than those in the low- α disk, which iswhat we expected. Within the low- α disk, stellar agesincrease with [ α /Fe]. RESULTSIn this section, we first examine the global age andmetallicity trends across the disk. We then explorethe age distribution in the chemical plane; first, acrossthe disk spatially, and then across small cells in [ α /Fe]-[Fe/H] (section 3.2). In section 3.4, we report the age-chemical abundance trends for 16 elements and calculatethe intrinsic dispersions around these relations. We ex-amine the high- and low- α disk separately, comparingand contrasting the relations and their intrinsic disper-sions.3.1. The global age/metallicity skew distribution acrossthe Milky Way: two episodes of star formation
In Figure 5, the top left plot shows the age distribu-tion of the APO-CAN stars with inferred ages from
TheCannon across the APOGEE footprint (mean age: 6.3Gyr; standard deviation: 3.3 Gyr). These stars rangefrom R = 0 ∼
18 kpc in radius and | z | < α disk stars (45,983 stars; mean age: 5.4 Gyr; standard deviation: 2.9 Gyr); and thebottom left plot shows the mean age distribution of thehigh- α disk (16,416 stars; mean age: 8.8 Gyr; standarddeviation: 3.1 Gyr). We found that 7% of the α -enrichedstars are younger than 5 Gyr, which are also observedby Martig et al. (2015); Chiappini et al. (2015); Feuilletet al. (2018). Within the low- α disk stars, 15% are olderthan 8 Gyr.Looking first at the age distribution of the low- α disk:Young stars are concentrated to the mid-plane and starswith larger ages are seen higher above the mid-plane, asexpected (see also Ness et al. 2016; Mackereth et al.2017). Looking at the middle left figure, the low- α diskshows flaring in the young population (Mackereth et al.2018; Bovy et al. 2016) and at a given height from theplane, | z | , the mean age decreases with radius, R. Theconcentration of old stars in the inner region and youngin the outer is indicative of inside-out formation of theMilky Way disk. Looking, second, at the age distribu-tion of the high- α disk: There are no age gradients acrosseither R or | z | . The high- α disk stars are old even alongthe mid-plane and extend to larger heights compared tothe low- α stars.There are a range of ages in the high- α disk. Yet,the absence of any age gradient suggests a rapid forma-tion history for the high- α disk where all the stars wereformed early, before the stars of the low- α disk.Next, we examine the spatial distribution of the metal-licity skew across the disk, where the skewness is usedas a measure of how far the distribution deviates froma Gaussian. A positive age skew means there is an ofstars with ages older than the average stellar age in thatbin, and visa-versa. The top panel shows the skew in allstars, the middle in the low- α disk and the bottom forthe high- α disk.Hayden et al. (2015) and also Loebman et al. (2016)highlighted the change in the direction of the metallicityskewness across radius in the disk as a possible signatureof radial migration. In the presence of migration andan initial disk metallicity gradient, the distribution canskew in opposite ways in the inner and outer region,respectively, as stars migrate in and out, across the disk.We calculated the skewness of the metallicity distribu-tion in spatial bins with a bin size of (R, z) = (0.4 kpc,0.4 kpc) using the Python package scipy.stats.skew ,excluding any bins with fewer than 20 stars.From the middle right plot, we can see that there is aclear trend from negative skewness to positive skewnessas we move from the inner Galactic disk to the outerdisk in the low- α disk (see also Kochukhov 2021). Thissupports the idea that the disk formed with a negative niversal properties of the high- and low- α disk Figure 4. α /Fe]-[Fe/H] space. The black dotted line separates the high- (red) and low- α (blue) disk. The bi-modal distribution of these two disks and the positive α -age gradient are clearly visible. metallicity gradient, and radial migration has been sig-nificant in the low- α disk.We note there is a strong negative skewness for thegroup of stars around R = 17.5 kpc ( ∼
140 stars). Wefurther investigated these stars and we did not find anyspecific APOGEE programs associated with these stars.This group of (on average) young stars has an excessnumber of metal poor stars. We note that the meanmetallicity of these stars is on average higher than thatof stars around R= 12 kpc and is in fact similar to thatof stars that are around R= 5 kpc.For the high- α disk (bottom right plot), there is aweak positive metallicity skew across (R,z), but no gra-dient in the skew across R as seen for the low- α diskabove it. However, this does not indicate that radialmigration is not significant. Rather, this is consistentwith the high- α disk having no initial metallicity gradi-ent, at formation; subsequently any migration would notaffect the metallicity skewness across radius, in each spa-tial bin. The lack of metallicity gradient in the high- α disk is also seen in cosmological simulations (e.g. Agertzet al. 2020). In the high- α disk there is an overall pos-itive skewness on the order of 0.19 dex in metallicity.Presumably this places constraints on the enrichmentrate and formation history of the high- α disk.3.2. The age distribution of the chemical plane acrossthe Galaxy: signatures of radial migration andtwo modes of star formation
We dissect the APO-CAN stars into spatial (figure 6)and chemical (figure 7) bins in order to piece-wise ex-amine the structure of these two disks. Figure 6 shows the age distribution of stars in [ α /Fe]-[Fe/H] plane at different locations of the Galaxy’s disk.From left to right, the Galactic radius increases, from R = 0 to 13 kpc, and from bottom to top, the absolutevertical height increases, from | z | = 0 to 2 kpc, similar tothe figure in Nidever et al. (2014); Hayden et al. (2015)but coloured here by age. Moving away from the galacticplane, the mean stellar age clearly increases, and in theinner disk at small Galactic radius, the (older) high- α disk stars dominate. On the other hand, the (younger)low- α disk dominates nearer to the mid- plane and inthe outer Galactic disk, where low- α stars with largegalactic heights in the outer disk indicate signatures offlaring. It is clear that a significant mean age gradientis imputed across (R,z) merely by the changing ratio ofthe number of (younger) low- α and (older) high- α stars,respectively.We qualitatively compare this result to the expecta-tion from simulations (Figure A1 and B1 top two plots)from Buck (2020). These simulations suggest that the α -bimodality is a generic consequence of a low- α diskforming gas-rich merger after the high- α disk is in place.The simulations presented in Buck (2020) reveal a simi-lar age gradient along the [ α /Fe] axis in the low- α disk atany spatial bin whilst almost no age gradient is foundfor the high- α disk. Overall, in both simulation anddata, there is a strong age gradient with [ α /Fe] (at fixed[Fe/H]) and a weak gradient with [Fe/H] (at fixed [ α /Fe].The shape of the distribution of stars with similar agesin each spatial bin in Figure 6 is inclined with respect tothe [Fe/H] axis. Interestingly, the inclination in the agedistribution of the low- α disk as shown across (R,z) in Lu et al.
Figure 5.
The top plots show the overall age distribution/metallcity skewness, the middle plots shows the age distribu-tion/metallcity skewness of the low- α disk, and the bottom plots shows the age distribution/metallcity skewness of the high- α disk. The overall age distribution of the stars and flaring of the low- α disk stars suggests an inside-out formation history andthe negative skew in metallicity suggests radial migration (for more explanation, see section 3.1). The lack of any age gradientacross the Galaxy in the high- α disk places constraints on the enrichment rate and formation history of the high- α disk. this figure is only seen in the simulation with a strongbar (Fig. A1 in Buck 2020).The simulations further show a similar trend of in-creasing [Fe/H] with decreasing radius. Note, this com-parison is only of qualitative nature since no APOGEEselection function nor age uncertainties were taken intoaccount in their work.From Figure 6, we see that there is no age gradientfor the high- α disk along either [Fe/H] or [ α /Fe], at anygiven location that has been observed. The absence ofany age gradient in the high- α disk across [Fe/H] or[ α /Fe] is consistent with the results from Agertz et al.(2020), in which, similarly to Buck (2020) they connectthe last gas rich merger as a low- α disk formation mech- anism around the in-place high- α disk (Renaud et al.2020)We have examined the mean spatial trends of ageacross the overall chemical, [ α /Fe]-[Fe/H], plane. Wenow look deeper into the conditions of the star-forminggas by examining the age distribution across small cellsin [ α /Fe]-[Fe/H] across the disk. This is related to theanalysis route of Bovy et al. (2011), who examined thescale height and lengths of mono-abundance popula-tions.Figure 7 shows the age distribution of the same APO-CAN stars as shown in Figure 6, in a grid of [ α /Fe]-[Fe/H] bins. We call these chemical cells (they arenot strictly ‘mono’ abundance populations; the cells are niversal properties of the high- and low- α disk Figure 6.
The age distribution of the APO-CAN stars in APOGEE DR16 in mono spatial bins inspired by Figure 4 in Haydenet al. (2015). The radius increases moving to the right, and the Galactic height increases moving towards the top. The high- α disk dominates as the Galactic height increases, and the low- α disk dominates at larger Galactic radius. The low- α stars atlarge Galactic height in the outer disk is the signature of the flaring young disk. larger than the errors on the [Fe/H] and [ α /Fe]). Themetallicity, [Fe/H] increases toward the right and [ α /Fe]increases upwards. The bin sizes are 0.04 dex in [ α /Fe]and 0.14 dex in [Fe/H]. Each individual cell shows thespatial distribution of stars in the R - z plane. The bluedashed lines show the z =0 plane and the radius locationof the sun.Across the matrix of chemical cells, we see differentportions of the stellar disk, that together, comprise thefull disk stellar distribution. Globally, the chemical cellprojection shows a chemical population of spatially andtemporally distinct disks, that looks to be consistentwith an inside-out and upside-down formation process(Bird et al. 2013). Note, we do not take into accountthe selection function. Nonetheless, the age gradient ofolder to younger stars from the inner to outer region andspatial flattening across cells of mean decreasing age isindicative of these processes.Figure 7 shows that the transition from the young toold stars is marked and rapid across the chemical plane,in that the transformation happens within a small rangeof [Fe/H]-[ α /Fe], across chemical cells. Outside of theseclear and most dramatic changes across chemical cells,there are subtle spatial and temporal variations alongboth rows of [Fe/H] and columns of [ α /Fe]. We see usingthe chemical cells, that away from where there are strongage gradients across cells, most cells do not show agegradients within them.Along fixed rows in ([Fe/H]) the disks are far moresimilar than across columns of [ α /Fe]. Most notably,moving along rows reveals subtle age gradients and shift-ing radial distribution of the stars. Along fixed columnsin [ α /Fe], there are strong changes in the mean age ofpopulations and more dramatic spatial changes. Look- ing along say the forth column from left, the bottomrow shows young stars concentrated to the outer diskand distributed around the mid-plane, and old stars con-centrated to the inner Galaxy and diffusely distributedaround the plane at top.The matrix of the chemical cells reveals an inversionof the age gradient along [Fe/H] moving from highestto lowest [ α /Fe]. Looking along the top five rows, forthe chemical cells with highest α -enhancement, there isa mean decrease in age as [Fe/H] increases. Correspond-ingly, along these rows, the stars are less diffusely dis-tributed around the plane spatially, and as metallicityincreases the mean radius of the stars increases. Notethat in chemical cell projection, along the bottom rows,the age gradient inverts; the stars become older movingto increasing [Fe/H]. However, they also are on averagenearer to the Galactic center, which is the reverse spatialtrend to high [ α /Fe] stars. This is indicative of the ini-tial negative [Fe/H] gradient in the low-alpha disk. Theflattening distribution of stars around the mid-plane asthey become younger across the chemical cells, and atfixed [ α /Fe], is indicative of an upside-down formationof an ensemble of disks represented within the chemicalcells. The oldest stars in the disk at the high [Fe/H]and low [ α /Fe] have presumably migrated from the in-ner disk, which would explain this age gradient inversionand change in spatial trend compared to the high- α rowsof stars.We repeated this analysis using the ages included inthe APOGEE DR16 release, derived using a neural net-work (Mackereth et al. 2019). We found a small butimportant difference in doing this: the most metal-poorhigh- α stars are younger than the more metal-rich high- α stars using the ages provided in Mackereth et al.0 Lu et al. (2019). This is the opposite to what we find using ourage catalogue and this instead suggests a outside-in for-mation of the high- α disk. The differences in the re-sults from our inference using The Cannon and the neu-ral network approach are likely a consequence of sparsetraining data in this chemical realm. This small dis-crepancy has significant implications for the formationhistory inferred under the different catalogues for thehigh- α stars.We also investigated the skew and standard devia-tion of ages in this plane and found the high- α disk hasthe strongest negative age skew, and the low- α disk hasthe strongest positive age skew (see Figure C.1 in Ap-pendix). The largest age dispersion is seen for the low α and metal rich stars (see Figure C.2 in Appendix).This large dispersion could support the two in-fall ana-lytic model described in Spitoni et al. (2021). Overall,Figure 7 suggests the disk can be well considered as acontinuum of populations, rather than two distinct pop-ulations. The nature of the changing age distribution inchemical cells resonates with the scale height and scalelength analysis of Bovy et al. (2012).Now that we have examined the age and spatial dis-tribution of our stars in chemical cells, we turn to theage-metallicity relations of stars and their detailed age-abundance trends for 16 individual elements. In doingso we seek to quantify the star formation environmentin chemical enrichment over time across the disk.3.3. Age-metallicity trends in the high- and low- α disk We now explore the age-metallicity relations for oursample across its spatial extent (R, z). This is similar tothe analysis of Feuillet et al. (2019), who examined theage-metallicty relation for stars in their sample at differ-ent Galactic radius and heights (Figure 3 in their paper).They subsequently argued the trends to be signature ofradial migration (see Minchev et al. 2013; Buck 2020).We employ this same analysis but we separate the starsinto high and low- α populations. Since high and low- α stars have different initial conditions, spatial and tem-poral distributions, it is a natural next step to examinethe age-[Fe/H] relations conditioned on narrower regionsof chemical space (including beyond our bi-modal popu-lation model here). This should place stronger empiricalconstraints on the formation and evolution mechanismsof the disk - and here reveals interesting differences be-tween the high and low- α sequences.Figure 8 shows the age-metallicity relation in (four)different spatial bins, separated by the high- (red) andlow- α (blue) disk for all the 64,339 stars. This figurespans a radial range from R = 5 kpc to R = 13 kpc, and3 different Galactic height bins, from | z | = 0 kpc to | z | = 2 kpc. In each spatial bin, we calculated the mean agein each small metallicity bin. These 50 metallicity binsrange from -0.8 to 0.5 dex so that each bin spans 0.027dex. We then calculated the standard error on the meanby σ age / √ N −
1, in which σ age is the standard deviationof the ages in each bin, and N is the number of stars inthat bin, to be the uncertainty on the mean stellar ages.The lines connecting the mean age bins vertically aregenerated by running a 1D Gaussian filter with a kernelsize of 3 using the scipy.ndimage.gaussian filter function from scipy (Virtanen et al. 2020).The black dots and dashed line show the overall trendsfor the entire sample. The average age for stars in eachspatial bin is shown in the legend.Compared to Figure 3 from Feuillet et al. (2019),in which they measured the age-metallicity trends forstars in the APOGEE DR14, our overall trends showvery similar results throughout the Galaxy. One of themain features in these relations is the primary turnoverpoint in the age-metallicity trends, which is a presumedmarker of radial migration (see Frankel et al. 2018,2019). These turnover points locate the oldest/youngeststars in the trends where the age-metallicity relationschange. For stars with | z | < ∼ < R <
7. The location of thispoint gradually moves towards lower metallicity as theradius increases ( ∼ < R < ∼ -0.2 dexfor 9 < R <
11, and ∼ -0.4 dex for 11 < R < α stars.To aide interpretation of this figure consider thefollowing: The age-[Fe/H] relationship in the solarneighbourhood is fairly flat (Nordstr¨om et al. 2004;Ibukiyama & Arimoto 2002, e.g.). Thus, [Fe/H] is not anage indicator, and presumably stars in the solar neigh-bourhood have a large range of initial birth radii. Anygiven spatial location will comprise stars born acrossthe disk and at different times. Nucleosynthetic enrich-ment processes increase overall metallicity over time.Assuming an initial radial metallicity gradient in theGalaxy and self-enriching disk, this means that the firstborn, oldest stars would have the lowest metallicitiescompared to the younger stars at a fixed birth radius(assuming the [Fe/H] is a birth property and stays rel-atively constant throughout the stars’ lifetime). As aresult, without stars migrating throughout the Galaxy,the metallicity should monotonically decrease with in-creasing stellar age, which is expected from temporalgas enrichment.However, we see turning points where the age-metallicity relation has changed, away from a presumed niversal properties of the high- and low- α disk Figure 7.
Spatial age distribution for all APO-CAN stars in mono [ α /Fe]-[Fe/H] bins. The mean values of [ α /Fe] and metallcityfor each subplot are displayed along the axis, and the bin sizes are 0.039 dex and 0.14 for [ α /Fe] and metallcity, respectively.The metallicity increases towards the right, and stars are more α enhanced towards the top. The blue dashed line mark the z =0 and solar radius. Every column is at a fixed [Fe/H], and every row is at a fixed [ α /Fe]. The transition from low- to high- α disk as the α element increases is gradual in the chemical cells, which means in order to understand the formation of these twodisks in the chemical plane, one should consider a smooth transition function instead of separating them into two disks. Theskew and dispersion of ages in each bin are shown in Figure C.1 and Figure C.2. fiducial monotonic decrease. Under this scenario, themost metal rich old stars in the sample that are presentacross all radii must have migrated from the inner regionwhere the gas was more enriched than the stars formedat the same time at larger radii in the disk.The most striking result in this figure is the differ-ences in the low- and high- α age-metallicity relations.The high- α and low- α disk have different mean ages, but also show different locations of the age-[Fe/H] turn-ing points across the galactic disk. The difference inthe turning point location between the low- and high- α disk suggests that the high- α disk has had differentmean migration directions and/or initial age-metallicitygradient in the star-forming gas, compared to the low- α disk. Unlike the low- α disk where the turning pointsare at lower metallicity moving away from the Galactic2 Lu et al.
Figure 8.
Age-metallicity relations from all APO-CAN stars (black), high- α disk stars (red), and low- α disk stars (blue) indifferent spatial bins. Each point is the mean age in that metallicity bin (width of 0.027 dex), and the errorbars are calculatedas σ age / √ N −
1, where σ age is the standard deviation of the ages in each bin, and N is the number of stars in that bin. Thedashed lines are calculated using a 1D Gaussian filter ( scipy.ndimage.gaussian filter , 2020SciPy) with a kernel size of 3.There are significant differences between the age-metallicity relations for the high- and low- α disks. center, suggesting an initial negative metallicity gradi-ent in the gas, the high- α disk has age-[Fe/H] turningpoints roughly at the same metallicity at all locationsacross the Galaxy. This suggests the absence of anyinitial metallicity gradient in this population.The age-[Fe/H] turning point in the high- α disk doessuggest that radial migration is a relevant evolutionaryprocess in the high- α disk too. The empirical role anddetails of radial migration have been characterised todate only for the low- α disk (e.g. Frankel et al. 2018,2019). However, the role of radial migration in the high- α disk has been recognised really only within simulations(eg Roˇskar et al. 2008; Minchev et al. 2012; Buck 2020;Khoperskov et al. 2020).One peculiar feature of Figure 8 is the reversal of theturning point in the high- α disk for 7 kpc < R < | z | < α disk at large | z | . One explanation is thatthe method of using a line to distinguish the high- andlow- α disk is inappropriate. Ratcliffe et al. (2020) sug-gested a clustering algorithm to separate the high- andlow- α disk which resulted in a very different separation compared to that of a line. We will discuss evidencethat this formalised method of assigning stars to groupsusing their chemical similarity may be preferable than aby-eye division in the Appendix.3.4. The intrinsic dispersion of elements around theirage-abundance trends
In previous sections, we looked at the overall age dis-tribution for different spatial and chemical bins as well asthe age-metallicity relation separated by the two disks.We now examine the enrichment channels for the high- α and low- α disk. Specifically we look to see if they aresimilar or show marked differences.Since the metallicity of a star can significantly im-pact the element abundances (see Jofr´e et al. 2019), weconstrain our analysis to a narrow range in [Fe/H]. Welook into detailed age-element abundance relations at asingle reference solar metallicity, [Fe/H] = 0. We ex-amine these relations for 16 elements (C, N, O, Mg, Al,Si, S,K, Ca, Ti, V, Mn, Ni, P, Cr, Co) observed byAPOGEE. They mostly belong to the following nucle-osynthetic families — Iron-peak: V, Mn, Cr, Ni, Co, niversal properties of the high- and low- α disk Figure 9.
The age-abundance distributions and best-fit second-order polynomial relations for 16 elements as well as metallicityand [C/N] for the 1,651 low- α and 224 high- α disk red clump stars, with ages determined from The Cannon . The shaded areashows the 1- σ dispersion of the trends, and the typical error bars are shown in the bottom right corner. Note that the y -axisscales are different to show the details in the age-abundance relations. It is clear that the high- and low- α disks have differentage-abundance trends for most elements besides [C/N], [N/Fe], [V/Fe], and [Cr/Fe] ([Na/Fe] is excluded due to high systematicuncertainty). The age-metallicity relations are similar between the two disks ensure the differences in their relations are notcaused by the metallicity. Sc; α -element: O, Mg, Si, Ti, Ca; Odd-z: Al, K, P andlight: C, NWe measure the age-abundance trends for each ele-ment at solar metallicity and calculate the intrinsic dis-persions ( σ int ) around these relations (Ness et al. 2019).That is, the scatter around the age-individual abun-dance trends not accounted for by the measurement er-rors.Previous work has done this for the low- α disk (eg Be-dell et al. 2018; Ness et al. 2019) and a small σ int hasbeen found for almost all the elements. Recent work us-ing GALAH has found small σ int combining both high-and low- α populations together (Hayden et al. 2020; Sharma et al. 2020) In this section, we will investigateand compare the trends in the age-individual elementrelations and σ int for the low- and high- α disk.We use two sets of stars for this (i) the benchmarkset of asteroseismic stars identified as red clump starswith 1,261 high- α and 3,173 low- α stars, with typical ageerrors of 0.88 Gyr and (ii) the red clump stars identifiedas per section 2, with 5,290 high- α and 16,784 low alphastars respectively, with typical age errors of 3.4 Gyr.To do so, we selected stars with asteroseismic agesfrom Pinsonneault et al. (2018) as well as red clump starswith solar metallicity ( | [Fe/H] | < < Lu et al. excluded 11 high- α and 12 low- α stars from the astero-seismic sample and 46 high- α and 114 low- α red clumpstars with age >
10 Gyr. The relations for stars > χ > ,
000 (with¯ χ > .
17) between the spectra model by
The Cannon and the real spectra. This leaves us with 642 low- α diskstars, 53 high- α disk stars with asteroseismic ages and1,650 low- α disk stars, 224 high- α disks stars with agesdetermined from The Cannon .To make sure there are no systematic temperature de-pendencies for the abundances, we examined the abun-dances of these stars versus stellar age, as a functionof temperature. We see no temperature gradients alongthe abundance axis, with the exception of the element V.This could indicate bias in the measurement of V, as aresult, we excluded this element in analyzing the intrin-sic dispersion and the slope of the age-abundance rela-tions. For each element we determine the age-abundancerelations, using both samples of stars.The results for the solar metallicity red clump starsare shown in Figure 9. We show lines fit using a secondorder polynomial, to quantify these age-abundance rela-tions. The blue and red lines show the fit to the low- andhigh- α stars, respectively. The shaded region representthe total dispersion around the relations, and the typ-ical error bar for each element is shown in the bottomright corner. In general, the average abundances for thehigh- α disk are higher than those of the low- α disk andthe relations between the two disks are different apartfrom [C/N], [N/Fe], [V/Fe] and [Cr/Fe]. The differencesin the age-[Mg/Fe] trends for the high- and low- α disk isalso observed in Kochukhov (2021). The [Fe/H]-age re-lations are similar between the two disks ensure the dif-ferences in the other abundance relations are not causedby the difference in metallicity.We also calculated the slopes of these trends by fittingstraight lines through the age-abundance relations forthe red clump stars. However, the relations in Figure 9suggests the linear relation is in log(age)-abundancespace ([X/Fe]=a log(age)+b), but we calculated theslope in linear age space to compare our results withliterature values from Bedell et al. (2018); Ness et al.(2019).The results are shown in Figure 10, in which the reddots represent the slopes for the trends in the high- α disk, the blue dots represent those for the low- α disk, theblack circles show the results from Bedell et al. (2018),and the black squares show the results from Ness et al.(2019). The elements are arranged so that the average absolute slope of the two sequence decreases towardsthe right of the x -axis. We excluded Na and V from ourcalculation as we suspect systematic bias in the mea-surements as previously discussed.The uncertainties (shown as the shaded area) weremeasured by perturbing each point within its uncertain-ties both in age and abundance, fitting a new line eachtime. We recalculated the slope 500 times weighting inthe uncertainties of the data, and the uncertainty wasthen determined by the standard deviation of all these500 measurements.We also tested how the slope varies across Galacticradius by calculating the age-abundance relation slopein bins of 1 kpc width, between R = 8 kpc to 13 kpc.In doing this, we found no significant spatial varia-tion of the age-abundance slopes. Thus, we concludethe age-individual abundance relations are global acrossthe disk, conditioned on [Fe/H]; note that they changeacross [Fe/H] so would presumably change spatially ifnot examined at this fixed metallicity (see Ness et al.2019).The slopes between the high- and low- α disk stars aresimilar for some elements (e.g. N, V, Cr, Mn) and quitedifferent for others (e.g. Al, Mg, O, C). We expectedthe slopes for the low- α disk to be slightly dissimilarfrom the results shown in Bedell et al. (2018) since theyused dwarf stars around solar temperature as opposedto giant stars in this work. Differences may hint at thecontribution of stellar versus galactic chemical evolution.Similarly, the slopes are very similar to those reportedin Ness et al. (2019), comparing the low- α disk results.We then calculated the σ int using the method de-scribed in Ness et al. (2019), σ int = σ tot − σ measure , (1)where σ tot is the total dispersion, measured by calculat-ing the dispersion around the best-fit 2 nd order polyno-mial, and σ measure is the measurement dispersion. Themeasurement dispersion is estimated by perturbing theabundance and age of each point within their uncertain-ties and then measure the dispersion around the originaldetermined 2 nd order polynomial. We perform this 100times and σ measure was then taken to be the standarddeviation of the 100 dispersion measurements.Figure 11 shows the intrinsic dispersion for thestars with asteroseismic ages from Pinsonneault et al.(2018) (circles) and ages determined from The Cannon (squares), separated by the high- (red) and low- α (blue)disk. The dashed lines show the median dispersion forthe high- (red) and low- α (blue) disk and the bars arethe mean abundance error for the high- (red) and low- α (blue) red clump stars. Our intrinsic dispersion mea- niversal properties of the high- and low- α disk Figure 10.
Slopes of the detailed age-element abundance relations for solar metallicity stars [Fe/H] = 0 ± α disk (from largest to smallest). The shaded area represents the 1 − σ confidenceof the measurement of the slope, determined by calculating the 1 − σ dispersion in the best-fit slope from 500 re-draws of themeasurements from their age and individual abundance errors, for each element. The slope is calculated using a straight line.Results from the main sequence study of Bedell et al. (2018) and Ness et al. (2019) are included for comparison. Note these twostudies are for the low- α stars only. surements are very similar to those of Bedell et al. (2018)(and Ness et al. (2019) who also found consistent re-sults), with the exception of V, Na, and Co. The slopesof the age-abundance relations for the high- and low- α disk are very similar, and are not correlated with theintrinsic dispersion.We found very similar intrinsic dispersion between thehigh- and the low- α disk, with a median of 0.039 dex and0.035 dex, respectively. Note Vincenzo et al. (2021) alsocalculated the intrinsic dispersion for [Mg/Fe] and founda value of ∼ α se-quence. The slightly higher dispersion in the high- α diskmight simply indicate a faster rate of enrichment whichleads to more variability in the range of each element’sabundance at any given age, at fixed metallicity [Fe/H].The low intrinsic dispersion that we report here sug-gests we should be able to determine ages using thedetailed age-element abundance relations for both thelow- and the high- α disk (see also Hayden et al. 2020;Sharma et al. 2020). Further, our result hints at univer-sal chemical enrichment processes that have given rise tothe abundance distributions of the high- and low- α disk.The small variation in the intrinsic dispersions indicatesubtle differences in the nucleosynthesis processes thatare taking place.Figure 12 shows the absolute difference of σ int betweenthe high- and low- α disk for the red clump stars. Ele-ments with small ∆ σ int are mostly iron-peak elements,and those with large ∆ σ int are mostly odd-z elements. DISCUSSION & FUTURE WORKLarge spectroscopic surveys such as Apache Point Ob-servatory Galactic Evolution Experiment (APOGEE)(Majewski et al. 2017), Large Sky Area Multi-ObjectFibre Spectroscopic Telescope (LAMOST) (Cui et al.2012), GALactic Archaeology with HERMES (GALAH)(De Silva et al. 2015; Buder et al. 2019) and time-domainsurveys such as Kepler (Borucki et al. 2010) and TESS(Ricker et al. 2015) are observing hundreds of thousandsof stars. These surveys enable us to test galaxy forma-tion and evolution mechanisms as well as channels ofelement production.By using the APOGEE DR16 spectra, measurementsof frequency spacing between p -modes, ∆ ν , and periodspacing of the mixed g and p modes, ∆P, from Vrardet al. (2016), as well as estimation of ages from thesecond APOKASC catalog (Pinsonneault et al. 2018)and T eff , log g , metallicity [Fe/H], and [Mg/Fe] fromAPOGEE’s DR16, we constructed an age catalogue for64,317 stars in APOGEE derived using The Cannonwith ∼ α disk:1. Similarities:6 Lu et al.
Figure 11.
Intrinsic dispersion at solar metallicity, [Fe/H] = 0 ± α (blue)disk for both stars with asteroseismic ages from Pinsonneault et al. (2018) (circles) and ages determined from The Cannon (squares). The black dots are results from Bedell et al. (2018); the bars show the mean abundance error for the high- (red)and low- α (blue) red clump stars; and the dashed lines show the median intrinsic dispersion of the elements, which is 0.039 and0.035 for the high- and low- α sequence respectively. These indicate that there is no obvious correlation between measurementerror on the elements and the calculated intrinsic dispersion. Elements are ordered by the average dispersion of the asterosismiclow- α stars and the red clump low- α stars. Figure 12.
Absolute difference of the intrinsic dispersion around the age-abundance relations σ int between the high- andlow- α disk for the red clump stars at solar [Fe/H] = 0 ± • Both disks show evidence for radial migrationand upside-down formation (Figures 5 & 8). • Intrinsic dispersions around the age-abundance relations are small, highlightingthe universality of temporal chemical enrich-ment pathways (Figure 11). • Given large numbers of stars as in our study,the high and low- α disk can be describedwithin a single framework as an ensembleof temporal and spatial populations acrosschemical space that underlie a global disk dis-tribution. Presumably the gradients in themean age, dynamics and spatial extent (andhigher order moments of these distributions) niversal properties of the high- and low- α disk • Our analysis suggests that the high- α diskhad no initial metallicity gradient, where asthe low- α disk formed with a gradient in place(Figure 5). • The high- α disk is old and has a larger ver-tical reach and narrower radial expanse thanthe young low- α disk, which has a shortervertical reach and extends over a larger ra-dial range (Figure 6, 7). • There are differences in the age-[Fe/H] rela-tions for the high- and low- α sequences across(R,z). These suggest distinct rates and/or di-rections of radial migration and/or differentinitial metallicity gradients with Galactic ra-dius (Figure 8). • Most of the age-individual abundance rela-tions for the high- and the low- α disk (Fig-ure 9) show differences, with some excep-tions. Some elements, such as N, show near-identical relations. Other elements, like Mgand Al, have quite different slopes (see Figure10). • Although some elements have identical in-trinsic dispersions around the age-individualabundance relations for the high and low- α disk, on average this is abour 10% larger inthe high- α disk. This hints at either differentstar formation efficiencies/rates or the levelof mixing of chemical elements in the star-forming gas (Figure 11, 12).4.1. Comparing with simulations/analytic models
In this paper, we provide a population study of thesimilarities and differences between the high- and low- α disks using APOGEE DR16 and Gaia data. In thissection, we will briefly summarise our results in the con-text of formation mechanisms seen in simulations and inanalytic models.Figure 5 examines the global age distribution and themetallicity skewness of the two disks. The skewness gra-dient for all stars is seen in the simulations of Agertzet al. (2020), suggesting radial migration.Figure 6 revealed the age distribution of stars in smallspatial bins. The lack of age gradient in the high- α diskis seen in the simulations of Agertz et al. (2020), andthe strong age gradient in the low- α disk resembles thatof the simulations in Buck (2020). Furthermore, the flat age gradient in the high- α disk points towards a fastformation mechanism which is in line with the recentfindings of Di Matteo et al. (2020).Figure 7 showcased the age distribution of stars indifferent chemical cells together with their spatial dis-tribution across the disk. In general, older stars haveshorter scale length and extend to larger heights abovethe plane compared to younger stars. This is in line withearly star formation happening in a compact turbulentgas disk (e.g. Buck et al. 2020) while the low- α diskforms later (e.g. Lian et al. 2020). We found the largestage dispersion appears at the most metal rich and α poorregion (see Figure C.2), supporting the analytic two in-fall model described in Spitoni et al. (2021). Further-more, the different age-abundance relations for low- andhigh- α stars shown in Fig. 9 might hint towards differ-ent formation mechanisms/time scales or star formationefficiencies and/or the level of mixing of chemical ele-ments in the star-forming gas. Similar conclusions havealso been made by Nissen et al. (2020) using HARPSdata.Figure 8 shows the age-metallicity relations at differ-ent locations in the disk in (R, z). These results suggestthat radial migration has been significant in both disks.This result is supported by Buck (2020); Khoperskovet al. (2020) but are in tension with recent formationscenarios without strong radial migration (Khoperskovet al. 2021). 4.2. Limitations
We did not take into account the selection function,this means we are not able to calculate the scale heightor scale length of the two disks. However, we arguethat the major results will not change because of thesimplicity of the APOGEE selection function.We only examined stars with solar metallicity, [Fe/H]= 0 for the detailed age-abundance trends. However, bytesting the intrinsic dispersion for stars with metallic-ity centered around -0.3 dex, we concluded the intrin-sic dispersion does not vary much, although the age-abundance relations are different for stars with differentoverall metallicity, [Fe/H]. CONCLUSIONSWith such a large and detailed benchmark compari-son of the age-abundance relations across the chemicallydefined high- and low- α disk, these results can poten-tially constrain nucleosynthesis channels across broadlydifferent chemical regimes. While the similarity acrosschemical space in the intrinsic dispersions in the age-abundance relation indicates the universality of chemi-cal enrichment, the small element-dependent differences8 Lu et al.
Feature name Description sourceN FE [N/Fe] APOGEEC FE [C/Fe] APOGEEMG FE [Mg/Fe] APOGEETI FE [Ti/Fe] APOGEEAL FE [Al/Fe] APOGEEALPHA M [ α /Fe] APOGEETEFF SPEC spectroscopictemperature APOGEERV CCFWHM radial velocity APOGEEradius val radius value Gaiapmdec proper motionin dec Gaiapmra proper motionin ra Gaiaparallax parallax Gaiab Galacticlatitude Gaial Galacticlongtitude GaiaLog(g) log g The Cannon r est estimateddistances Bailer-Joneset al. (2018)
Table A.1.
Stellar parameters used to train
Astraea to get stellar ages. we see are relevant in informing metallicity dependentyields, and the impact of different star formation ratesand environment (Buck et al. in prep.).Using the distributions of ages of stars across chemicaland spatial cells, we hope to provide the empirical datato distinguish between different formation scenarios forthe Galaxy, by e.g., comparing to cosmological simula-tions. Moving forward, we expect a powerful analysistool to constrain the origin of the bi-modality in thedisk will be to examine the age, dynamical and spatialproperties of stars as a function of their chemical dis-tributions. To first order, simulations that reproduce abi-modality in the [ α /Fe] plane must also reproduce the results we see in Figure 7, given equivalent sampling, toreflect the formation channel(s) that underlie the MilkyWay’s current set of observed properties. To second or-der, Figure 8 is demonstrative of the strength of evolu-tionary processes like radial migration across differentchemical (and correspondingly, initial spatial) spaces.Next generation surveys (e.g. Kollmeier et al. 2017) willenable this analysis to be taken to the next level bycompleting this exploration over a vast expanse of thedisk into the bulge and to sample the disk finely acrossits temporal and spatial variables, within true mono-abundance chemical populations.APPENDIXA. Predicting stellar ages with
Astraea
We also tried to predict stellar ages estimated using
The Cannon with
Astraea (Lu et al. 2020) . Astraea usesRandom Forest, a machine learning algorithm, to predict label from features.We performed a simple cross-match between APOGEE and the GaiaKepler cross-match catalog and found 3,417stars with the measurements we needed. The features we trained on are all the 17 element abundances from APOGEE,metallicity, and all the Gaia parameters. The important features are listed in table A.1. Avaliable at https://astraea.readthedocs.io/en/latest/. Avaliable at https://gaia-kepler.fun. niversal properties of the high- and low- α disk The Cannon with a median relative error of 15%. Figure A.1 shows the “ gini ” importance (ranges from 0to 1, where 1 being the most important) of the 18 most important feature in predicting these ages. This importancecan be determined by calculating the mean decrease in impurity (MDI), which indicates whether a single feature alonecan predict the outcome. For example, if one can predict the stellar ages of a star just by the effective temperature,then the gini importance for the effective temperature will be 1.
Figure A.1.
The “ gini ” importance of the features used to predict stellar ages using
Astraea . This indicates that we are ableto predict stellar ages with only a few stellar parameters.
It is not surprising [N/Fe] is the most important feature in determining the stellar ages, as age-[N/Fe] relation hasone of the steepest slopes (see Figure 10) and smallest intrinsic dispersion (see Figure 11). The fact that [Na/Fe]is not important in determining the ages despite the fact that it has the steepest slope further indicates that thereis anomaly in this abundance measurement. The importance of [ α /Fe] is relatively low, suggesting the two disksexperience similar enrichment process. The distribution of importance is relatively spread-out (in that several featuresare relatively important to predict ages) suggesting determining stellar ages is complicated. It also suggests stellarages are indeed related to a sum of complicated stellar processes such as nucleosynthesis, gravity, kinematics.Even with a spread in importance, it is still striking that we were able to predict stellar ages within 20% uncertaintywith only a handful of stellar parameters. This means we should be able to estimate stellar ages for a large number offield stars fairly straightforwardly with large spectroscopic survey such as LAMOST and GALAH.B. Separating the high- and low- α disk with a clustering algorithm In this paper, we separated the high- and low- α disk with an ad-hoc straight line. However, it is not clear whetherthis is the most appropriate way to separate the two disks. Particularly since the [ α /Fe] and metallicity, [Fe/H] onlyrepresent two of the chemical dimensions of a larger chemical space. Ratcliffe et al. (2020) suggested a clusteringalgorithm approach to deconstruct stars of the disk, using the 19 dimensions of available APOGEE abundances. Intheir work, they reported that a small group of the high- α stars was more stronly associated to the low- α disk thanthe high. We performed the same ward hierarchical clustering as per Ratcliffe et al. (2020), using sklearn (Pedregosaet al. 2011) with the same 17 elements and [Fe/H] and found the same two-cluster projection in the [ α /Fe]-[Fe/H] asin that work. The clustering result is shown in Figure B.1. The green points are stars that are considered high- α starswith the line separation used in this paper, but are classified as low- α stars in Ratcliffe et al. (2020).One line of independent evidence that these nominallly high- α disk stars could be associated with the low- α diskmore than the high, is from the age-metallicity relations. As pointed out in the section 3.3, we were not able to explainsome of the features in the age-metallicity relations for the high- α disks. For example, the reversal of the turning pointin age for the spatial bin of 7 < R < | z | < α disks defined by hierarchical clustering,0 Lu et al.
Figure B.1.
The high- (red) and low- α (blue) disk separated using ward hierarchical clustering. We were able to reproducethe result in Ratcliffe et al. (2020). The green points are stars that were considered high- α disk stars with our separation butclassified as low- α disk stars with the clustering algorithm. The separation of the two disk in the age-[ α /Fe] plain (right) favorsthe clustering algorithm. we are able to extract what look to be clearer and more distinctly different relations for the high- α disk stars acrossthe galaxy. Figure B.2.
Same as figure 8 but the high- and low- α disks are determined by the clustering algorithm. niversal properties of the high- and low- α disk α disk.However, note that clustering algorithms, similarly to by-eye designations, do not offer a “best” solution. They aresubject to algorithmic choices. These results should be interpreted with caution and used to inform what varies underdifferent analysis choices. C. Additional graphs
Figure C.1 and C.2 show the skew and standard deviation of the ages in each bin using the matplotlib.axes.Axes.hexbin function.
Figure C.1.
Same as Figure 7 but plotting the skew in age. Only included bins with >
10 stars. Lu et al.
Figure C.2.
Same as Figure 7 but plotting the standard deviation in age. Only included bins with >
10 stars.
ACKNOWLEDGMENTSWe thank Adrian Price-Whelan and Kate Daniel for helpful discussions.JCZ is supported by an NSF Astronomy and Astrophysics Postdoctoral Fellowship under award AST-2001869.Melissa Ness is supported in part by a Sloan Fellowship.This work made use of the gaia-kepler.fun crossmatch database created by Megan Bedell.This paper includes data collected by the
Kepler mission. Funding for the
Kepler mission is provided by the NASAScience Mission directorate.This work has made use of data from the European Space Agency (ESA) mission
Gaia
Gaia
Gaia
Multilateral Agreement. niversal properties of the high- and low- α disk a community-developed core Python package for Astronomy (Astropy Collab-oration et al. 2013; Price-Whelan et al. 2018). Facilities:
Gaia, Kepler, APOGEE
Software:
Astropy (Astropy Collaboration et al. 2013; Price-Whelan et al. 2018), Numpy (Oliphant 2006), sklearn(Pedregosa et al. 2011), The Cannon (Ness et al. 2015), Astraea (Lu et al. 2020)REFERENCES
Abadi, M. G., Navarro, J. F., Steinmetz, M., & Eke, V. R.2003, ApJ, 591, 499, doi: 10.1086/375512Agertz, O., Renaud, F., Feltzing, S., et al. 2020, arXive-prints, arXiv:2006.06008.https://arxiv.org/abs/2006.06008Ahumada, R., Allende Prieto, C., Almeida, A., et al. 2020,ApJS, 249, 3, doi: 10.3847/1538-4365/ab929eAstropy Collaboration, Robitaille, T. P., Tollerud, E. J.,et al. 2013, A&A, 558, A33,doi: 10.1051/0004-6361/201322068Bailer-Jones, C. A. L., Rybizki, J., Fouesneau, M.,Mantelet, G., & Andrae, R. 2018, AJ, 156, 58,doi: 10.3847/1538-3881/aacb21Bedding, T. R., Mosser, B., Huber, D., et al. 2011, Nature,471, 608, doi: 10.1038/nature09935Bedell, M., Bean, J. L., Mel´endez, J., et al. 2018, ApJ, 865,68, doi: 10.3847/1538-4357/aad908 Bensby, T., Feltzing, S., & Oey, M. S. 2014, A&A, 562,A71, doi: 10.1051/0004-6361/201322631Bensby, T., Feltzing, S., Gould, A., et al. 2017, A&A, 605,A89, doi: 10.1051/0004-6361/201730560Bird, J. C., Kazantzidis, S., Weinberg, D. H., et al. 2013,ApJ, 773, 43, doi: 10.1088/0004-637X/773/1/43Bland-Hawthorn, J., & Gerhard, O. 2016, ARA&A, 54,529, doi: 10.1146/annurev-astro-081915-023441Bland-Hawthorn, J., Sharma, S., Tepper-Garcia, T., et al.2019, MNRAS, 486, 1167, doi: 10.1093/mnras/stz217Borucki, W. J., Koch, D., Basri, G., et al. 2010, Science,327, 977, doi: 10.1126/science.1185402Bovy, J., Hogg, D. W., & Roweis, S. T. 2011, Annals ofApplied Statistics, 5, 1657, doi: 10.1214/10-AOAS439Bovy, J., Leung, H. W., Hunt, J. A. S., et al. 2019,MNRAS, 490, 4740, doi: 10.1093/mnras/stz2891Bovy, J., Rix, H.-W., Liu, C., et al. 2012, ApJ, 753, 148,doi: 10.1088/0004-637X/753/2/148Bovy, J., Rix, H.-W., Schlafly, E. F., et al. 2016, ApJ, 823,30, doi: 10.3847/0004-637X/823/1/30 Lu et al.
Buck, T. 2020, MNRAS, 491, 5435,doi: 10.1093/mnras/stz3289Buck, T., Obreja, A., Macci`o, A. V., et al. 2020, MNRAS,491, 3461, doi: 10.1093/mnras/stz3241Buder, S., Lind, K., Ness, M. K., et al. 2019, A&A, 624,A19, doi: 10.1051/0004-6361/201833218Casagrande, L., Sch¨onrich, R., Asplund, M., et al. 2011,A&A, 530, A138, doi: 10.1051/0004-6361/201016276Casey, A. R., Hawkins, K., Hogg, D. W., et al. 2017, ApJ,840, 59, doi: 10.3847/1538-4357/aa69c2Chiappini, C., Anders, F., Rodrigues, T. S., et al. 2015,A&A, 576, L12, doi: 10.1051/0004-6361/201525865Clarke, A. J., Debattista, V. P., Nidever, D. L., et al. 2019,MNRAS, 484, 3476, doi: 10.1093/mnras/stz104Cui, X.-Q., Zhao, Y.-H., Chu, Y.-Q., et al. 2012, Researchin Astronomy and Astrophysics, 12, 1197,doi: 10.1088/1674-4527/12/9/003De Silva, G. M., Freeman, K. C., Bland-Hawthorn, J., et al.2015, MNRAS, 449, 2604, doi: 10.1093/mnras/stv327Debattista, V. P., Gonzalez, O. A., Sanderson, R. E., et al.2019, MNRAS, 485, 5073, doi: 10.1093/mnras/stz746Di Matteo, P., Spite, M., Haywood, M., et al. 2020, A&A,636, A115, doi: 10.1051/0004-6361/201937016Edvardsson, B., Andersen, J., Gustafsson, B., et al. 1993,A&A, 500, 391Feuillet, D. K., Frankel, N., Lind, K., et al. 2019, MNRAS,489, 1742, doi: 10.1093/mnras/stz2221Feuillet, D. K., Bovy, J., Holtzman, J., et al. 2018,MNRAS, 477, 2326, doi: 10.1093/mnras/sty779Frankel, N., Rix, H.-W., Ting, Y.-S., Ness, M., & Hogg,D. W. 2018, ApJ, 865, 96,doi: 10.3847/1538-4357/aadba5Frankel, N., Sanders, J., Rix, H.-W., Ting, Y.-S., & Ness,M. 2019, ApJ, 884, 99, doi: 10.3847/1538-4357/ab4254Fuhrmann, K. 1998, A&A, 338, 161Gandhi, S. S., & Ness, M. K. 2019, ApJ, 880, 134,doi: 10.3847/1538-4357/ab2981Garc´ıa P´erez, A. E., Allende Prieto, C., Holtzman, J. A.,et al. 2016a, AJ, 151, 144,doi: 10.3847/0004-6256/151/6/144—. 2016b, AJ, 151, 144, doi: 10.3847/0004-6256/151/6/144Gilmore, G., & Reid, N. 1983, MNRAS, 202, 1025,doi: 10.1093/mnras/202.4.1025Gonz´alez Hern´andez, J. I., & Bonifacio, P. 2009, A&A, 497,497, doi: 10.1051/0004-6361/200810904Gunn, J. E., Siegmund, W. A., Mannery, E. J., et al. 2006,AJ, 131, 2332Hawkins, K., Ting, Y.-S., & Walter-Rix, H. 2018, ApJ, 853,20, doi: 10.3847/1538-4357/aaa08a Hayden, M. R., Bovy, J., Holtzman, J. A., et al. 2015, ApJ,808, 132, doi: 10.1088/0004-637X/808/2/132Hayden, M. R., Bland-Hawthorn, J., Sharma, S., et al.2020, MNRAS, 493, 2952, doi: 10.1093/mnras/staa335Ho, A. Y. Q., Ness, M. K., Hogg, D. W., et al. 2017, ApJ,836, 5, doi: 10.3847/1538-4357/836/1/5Hogg, D. W., Eilers, A.-C., & Rix, H.-W. 2019, AJ, 158,147, doi: 10.3847/1538-3881/ab398cHoltzman, J. A., Shetrone, M., Johnson, J. A., et al. 2015,AJ, 150, 148Ibukiyama, A., & Arimoto, N. 2002, A&A, 394, 927,doi: 10.1051/0004-6361:20021157Jofr´e, P., Heiter, U., & Soubiran, C. 2019, ARA&A, 57,571, doi: 10.1146/annurev-astro-091918-104509J¨onsson, H., Holtzman, J. A., Allende Prieto, C., et al.2020, AJ, 160, 120, doi: 10.3847/1538-3881/aba592Khoperskov, S., Haywood, M., Snaith, O., et al. 2020,arXiv e-prints, arXiv:2006.10195.https://arxiv.org/abs/2006.10195—. 2021, MNRAS, 501, 5176, doi: 10.1093/mnras/staa3996Kobayashi, C., Karakas, A. I., & Lugaro, M. 2020, ApJ,900, 179, doi: 10.3847/1538-4357/abae65Kochukhov, O. 2021, A&A Rv, 29, 1,doi: 10.1007/s00159-020-00130-3Kollmeier, J. A., Zasowski, G., Rix, H.-W., et al. 2017,arXiv e-prints, arXiv:1711.03234.https://arxiv.org/abs/1711.03234Leung, H. W., & Bovy, J. 2019, MNRAS, 483, 3255,doi: 10.1093/mnras/sty3217Lian, J., Thomas, D., Maraston, C., et al. 2020, MNRAS,497, 2371, doi: 10.1093/mnras/staa2078Loebman, S. R., Debattista, V. P., Nidever, D. L., et al.2016, ApJL, 818, L6, doi: 10.3847/2041-8205/818/1/L6Lu, Y. L., Angus, R., Ag¨ueros, M. A., et al. 2020, AJ, 160,168, doi: 10.3847/1538-3881/abada4Mackereth, J. T., Bovy, J., Schiavon, R. P., &SDSS-IV/APOGEE Collaboration. 2018, inRediscovering Our Galaxy, ed. C. Chiappini, I. Minchev,E. Starkenburg, & M. Valentini, Vol. 334, 265–268,doi: 10.1017/S1743921317006627Mackereth, J. T., Bovy, J., Schiavon, R. P., et al. 2017,MNRAS, 471, 3057, doi: 10.1093/mnras/stx1774Mackereth, J. T., Bovy, J., Leung, H. W., et al. 2019,MNRAS, 489, 176, doi: 10.1093/mnras/stz1521Majewski, S. R., Schiavon, R. P., Frinchaboy, P. M., et al.2017, AJ, 154, 94, doi: 10.3847/1538-3881/aa784dMartig, M., Minchev, I., Ness, M., Fouesneau, M., & Rix,H.-W. 2016, ApJ, 831, 139,doi: 10.3847/0004-637X/831/2/139 niversal properties of the high- and low- α disk25