High- and Low- α Disk Stars Separate Dynamically at all Ages
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High- and Low- α Disk Stars Separate Dynamically at all Ages
Suroor S Gandhi and Melissa K Ness
2, 3 Department of Physics, New York University, 726 Broadway, New York, NY, 10003, USA Center for Computational Astrophysics, Flatiron Institute, 162 5th Ave., New York, NY 10010, USA Department of Astronomy, Columbia University, 550 W 120th St, New York, NY 10027, USA
ABSTRACTThere is a dichotomy in the Milky Way in the [ α/ Fe]-[Fe/H] plane, in which stars fall into high- α , andlow- α sequences. The high- α sequence comprises mostly old stars, and the low- α sequence comprisesprimarily young stars. The origin of this dichotomy is uncertain. To better understand how the high-and low- α -stars are affiliated, we examine if the high- and low- α sequences have distinct orbits atall ages, or if age sets the orbital properties of stars irrespective of their α -enhancement. Orbitalactions J R , J z , and J φ (or L z ) are our labels of stellar dynamics. We use ages for 58,278 LAMOSTstars (measured to a precision of 40%) within ≤ at all ages , the high- and low- α sequences are dynamically distinct. This implies separate formation and evolutionary histories for thetwo sequences; a star’s membership in the high- or low- α sequence indicates its dynamical propertiesat a given time. We use action space to make an efficient selection of halo stars and subsequentlyreport a group of old, low- α stars in the halo, which may be a discrete population from an infall event. Keywords: stars, Galaxy, Galaxy formation, chemical abundance INTRODUCTIONA growing number of extensive stellar surveys includ-ing GALAH (De Silva et al. 2015), LAMOST (Cui et al.2012; Luo et al. 2016), APOGEE (Majewski et al. 2017),RAVE (Kunder et al. 2017; Casey et al. 2017), and Gaia(Gilmore et al. 2012; Gaia Collaboration et al. 2018) arecataloging larger regions of our Galaxy. Subsequently,understanding the structure and formation of the MilkyWay is within our reach more than it has ever beenbefore. Each part of the Milky Way (the bulge, disk,and halo) has stars which have different chemical anddynamical properties, as well as possibly different birthproperties. Deducing the formation histories of variousparts of the Milky Way by studying the chemistry, dy-namics and ages of stars in different regions can lead usto understand epochs in the life of the Galaxy itself (e.g.Silva Aguirre et al. 2018). The disk of the Milky Wayis the most expansive stellar component, where most ofthe stellar mass resides, and potentially holds immense
Corresponding author: Suroor S [email protected] information, which can shed light on how the universeevolves on galactic and cosmological scales.Disk stars in the Milky Way appear to fall intotwo broad categories of chemical composition: (1) α -enhanced or high- α stars, and (2) α -poor or low- α stars(Fuhrmann 1998; Gratton et al. 2000; Prochaska et al.2000; Bensby et al. 2003; Venn et al. 2004; Bensby et al.2005; Adibekyan et al. 2011; Bensby et al. 2014; An-ders et al. 2014; Nidever et al. 2014; Hayden et al.2015). The α -abundance measurement is typically de-rived from some ratio of elements fused in Helium cap-ture (i.e. Mg, Si, Ti, Ca). The bimodality seen in the[Fe/H]-[ α -Fe] plane has been inferred to be the signa-ture of two distinct populations (e.g. Mackereth et al.2018a; Clarke et al. 2019), and chemical enrichmentmodels suggest this requires a mix of populations withdistinct enrichment histories (e.g. Nidever et al. 2015).Spectroscopic surveys have established correlations be-tween α -enhancement and properties such as age (Wyse& Gilmore 1988; Haywood et al. 2013; Bensby et al.2014; Bergemann et al. 2014): high- α stars are mostlyold, and low- α stars are typically young. Quite possibly,the distinct formation timescales and velocity dispersionof the “thin” and “thick” components of the Milky Waydisk could translate into α -abundance signatures. How- a r X i v : . [ a s t r o - ph . GA ] M a r Gandhi et al. ever, the α -enhancement of stars does not directly mapto their assignment to the thin or thick disk (Feltzing& Bensby 2008; Sch¨onrich & Binney 2009; Adibekyanet al. 2011; Loebman et al. 2011; Bensby et al. 2014;Silva Aguirre et al. 2018; Bland-Hawthorn et al. 2018).Chemistry is our parameter of Galactic inquisition andwe wish to understand how the high- and low- α se-quences are distributed dynamically at a given age. Wehave the expectation that this will enable us to betterunderstand the origin of the dichotomy that is seen inthe [ α /Fe]-[Fe/H] plane. That is, if the birth and evo-lution tracks of the high- and low- α sequences might bediscrete or related.To make any sort of generalizable, empirical statementabout how the two α -sequences separate along otheraxes, we need access to accurately measured propertiesfor a large sample of stars. Gaia DR2 (Gaia Collab-oration et al. 2018) measured positions, distances, andproper motions for ∼ ∼ − ∼ ,
000 red gi-ants.
The Cannon , developed by Ness et al. (2015), pro-vides a data-driven method to infer information abouta large number of stars by channeling and combiningdata from across various astronomical surveys. It hasbeen a challenge to accurately and precisely measureages for large samples of bright red giant stars that canbe observed to vast distances across the Galaxy. Thisis because there is little discriminating power in stellarmodels in this regime. However, using
The Cannon , Hoet al. (2017) created the largest catalog of age estimatesfor ∼ ,
000 red giants by inferring the masses from[C/M] and [N/M] abundances. Data-driven modelingusing the correlations between [C/M], [N/M], [Fe/H],and age (from asteroseismic determinations) has givenus access to a far larger sample of stars for which wecan determine ages (Martig et al. 2016; Masseron et al.2016; Ness et al. 2016).Actions provide a powerful description of stellar dy-namics because they can encapsulate information touniquely define an orbit (Trick et al. 2018). We usecylindrical coordinates ( r, φ, z ) for positions of stars andcalculate actions using: J i ≡ (cid:73) orbit p i dx i where i = r, φ, z , and p i is the conjugate momentum (fora detailed introduction to actions see Sellwood 2014; Binney & Tremaine 2008). If we approximate the MilkyWay’s potential to be axisymmetric and its evolutionover time to be slow enough, actions are constants ofmotion for timescales of the order of several orbits (e.g.Bland-Hawthorn et al. 2018). The three actions, J R , J z ,and J φ (or angular momentum, L z ) separately providephysical interpretations of a star’s orbit. (We will use L z instead of J φ in our discussion hereafter.) J R indicatesthe eccentricity of an orbit, or an orbit’s deviation froma circle. L z is a direct indicator of the radius of theorbit, and J z indicates the maximum vertical distanceof an orbit from the Galactic plane.This paper is organized as follows: in §
2, we describethe main properties of our data sample, and explainour process of analysis. In §
3, we present our main re-sults, and further analysis of the dynamics of the two α -sequences as a function of [Fe/H] ( § | z | ( § § § α stars in the halo which might bepart of the Gaia Enceladus ( § § DATAWe investigate ∼ ,
000 red giant stars in the disk( ≤ α /Fe]-[Fe/H] plane. We see that, asexpected, there are two collections of stars that emergeclearly in this plane (separated roughly by the black line,which we set to differentiate high- and low- α stars). Wedenote the high- α stars as those that fall above the blackline, and the low- α stars are those that fall below theblack line. There are 7,334 high- α stars and 50 ,
944 low- α stars in our sample. On average, for our sample, thehigh- α sequence has an overall lower metallicity ([Fe/H])compared to the low- α sequence. At a metallicity of[Fe/H] ∼ − α -elementsand iron-peak elements goes down, and the high- α andlow- α sequences appear to converge (e.g. Hayden et al.2015).Figure 1b shows the distribution of our sample of(disk) stars once again in the [ α /Fe]-[Fe/H] plane, butcolored by age. It becomes apparent that the meanages of the two sequences are different, in the sense thathigh- α stars are typically older than the low- α popula-tion. However, there is overlap in the age distribution igh- and Low- α Disk Stars Separate Dynamically at all Ages Figure 1.
Main properties of our data sample of the LAMOST disk red giants. (a) The number density distribution of 58 , α /Fe]-[Fe/H] plane. We use the black line to differentiate between high- and low- α stars. There are 7,334high- α stars and 50,944 low- α stars (as indicated in the plot). (b) The same plot as (a), but colored by age. We can see thathigh- α stars (above the black line) are mostly old, whereas the low- α stars (below the line) are typically much younger. (c) Thespatial spread of the ∼ ,
000 strong sample is shown in a density plot of z vs. Galactic radius ( R GAL ). The Galactic plane at z = 0 is shown by the horizontal red line. Our analyses are restricted to stars within ≤ x - y distribution of stars, again showing our restriction on distance, within the dashed circle ofradius ≤ R GAL = 8 kpc. and both α -sequences span stars across a broad rangeof ages.Figures 1c,d show the spatial extent of the ∼ , ∼ ∼ ∼ ≤ R GAL , for the high- and low- α sequences, and the lower panel showsthe spread of the distance from the Galactic plane, z ,for three different metallicity ranges, (i) [Fe/H] < − . − . < [Fe/H] < > α -sequence is recorded inthe bottom subplots in the respective color of the [Fe/H]range. We see a weak gradient in the radii of low- α stars with respect to metallicity; mean [Fe/H] decreasesat higher R GAL as expected from prior literature whichhas proposed that the radial metallicity gradient in theMilky Way comes about largely from low- α stars (e.g.Duong et al. 2018). Gandhi et al.
Figure 2.
Normalized histograms for R GAL (top panel) and z (lower panel) for the two α -sequences (high- α to the left,low- α to the right) in three different metallicity ranges: (i)[Fe/H] < − . − . < [Fe/H] < > α -sequenceis indicated in the lower panels, in the respective color ofthe [Fe/H] range. We see in the top panel that the two α -sequences have different mean radii for all metallicity ranges.The low- α stars are preferentially located at larger Galac-tic radii, compared to the low- α stars. In the lower panel,the dispersion of stars around the mid-plane is clearly muchsmaller for stars in the low- α sequence compared to the high- α sequence. However, within the high- α sequence, the mostmetal-rich stars show the narrowest span in z. We have stellar ages precise to 0.2 dex from the carbonand nitrogen abundances catalogued in Ho et al. (2017).Additionally, in order to determine precise actions, weneed precise and accurate distance measurements (e.g.Coronado et al. 2018; Trick et al. 2018; Beane et al.2018). We use the inverse of parallax ( ω − ) as a proxyfor distance and restrict our sample to stars which havea parallax error ( δω/ω ) of less than 20%.We calculate actions using the same method as Tricket al. (2018): by first converting the observable po-sitions and velocities into cartesian ( X, Y, Z ) and he-liocentric ( U HC , V HC , W HC ) coordinates, and finally togalactocentric ( R, φ, z, v R , v T , v z ) coordinates using the galpy package (Bovy 2015). U is the velocity compo-nent towards the Galactic center, V is the componentin the direction of rotation of the Galaxy, and W is thecomponent towards the Galactic north pole. The co-ordinate conversion from cartesian and heliocentric togalactocentric is necessary to calculate the actions J R , J z , and L z in galpy and is done using ( U (cid:12) , V (cid:12) , W (cid:12) ) =(11 . , . , . s − as the Sun’s velocity in the Lo-cal Standard of Rest (LSR) (Sch¨onrich et al. 2010) and( R (cid:12) , φ (cid:12) , z (cid:12) ) = (8 , , . R (cid:12) , z (cid:12) in kpc) as theSun’s position within the Galaxy (Juri´c et al. 2008). RESULTS3.1.
Dynamical Actions as a Function of Age
We examine the actions J R , J z , and L z for for 7,334high- α stars and 50,944 low- α stars as a function of stel-lar age, and find that the high- and low- α stars have verydistinct mean dynamical properties. Figure 3 shows therunning mean of each of the actions as a function ofage for the two α -sequences (high- α in blue and verti-cally hatched, low- α in red and diagonally hatched). Inthis Figure, each α -sequence displays distinct dynami-cal behavior in all three orbital parameters: eccentricity( J R ), height above the Galactic plane ( J z ), and radius( L z ). Moreover, the distinction in dynamical trends ofthe high- and low- α stars is present consistently at allages.The running means of actions and age were calcu-lated using a bin size of N = 600 stars for both the α -sequences. The 1- σ standard deviation ( σ ) is used toestimate the dispersion in the running means, and thestandard errors are calculated as σ/ ( √ N − J R and J z for the high- α and low- α stars, withlow- α stars having lower orbital eccentricities and lowervertical excursions. The low- α stars on average have ∼ .
25 times larger angular momentum ( L z ) than thehigh- α stars. There are slight gradients in the runningmeans with respect to age, which might be affected bythe selection function of the LAMOST survey. Sincewe have not taken the selection function into account,we make no quantitative measure or claims regardingthe trend of the dynamics with respect to age for oursample. The dispersion around the running mean is sig-nificant and overlapping between the two α -sequences.In Table 1 we report the ratio of average dispersion( σ ( J i )) to average action ( ¯ J i ) for each of the three ac-tions of the two α -sequences. These numbers reportedonly the average values, and they do not take into ac-count the change in variance over time that is seen in J R and J z of low- α sequence. However, they do givean adequate idea of the relative dispersion in actions forthe high- and the low- α stars in our sample.3.2. Dynamical Actions for the High- and Low- α Sequence as a Function of [Fe/H]
We now analyze the two α -sequences as a functionof [Fe/H] to examine if they also separate dynami- igh- and Low- α Disk Stars Separate Dynamically at all Ages Figure 3.
Key results of our work. They show that high- and low- α sequences display distinct dynamical trends at all ages,with significant scatter about the mean. The running means (with bin size of N = 600 stars) and standard deviations ( σ ) ofeach of the three actions for 7,334 high- α stars and 50,944 low- α stars are plotted as a function of age. The running meansof high- and the low- α sequences are represented by the solid blue curve and the solid red curve respectively. The runningmeans have been smoothed using a Gaussian kernel with σ s = 100kpc km s − . The thickness of the solid curves represents thestandard error ( σ/ √ N − σ standard deviation in actions (vertically hatched forhigh- α and diagonally hatched for low- α ).Action σ ( J i ) / ¯ J i high- α low- αJ R J z L z Table 1.
A table showing the mean 1- σ dispersion ( σ ( J i ))divided by the mean of each action ( ¯ J i ), for the two α -sequences. The dispersions and running means used in thistable are those which are shown in Figure 3. cally when conditioned on metallicity. Figure 4 showssmoothed running means of J R , J z , and L z versus agefor high- α stars in the left panel, and the low- α stars inthe right panel, for three different metallicity ranges of(i) [Fe/H] < − .
5, (ii) − . < [Fe/H] <
0, and (iii) [Fe/H] >
0. The different [Fe/H] ranges are shown with differ-ent colors and line styles, as used in Figure 2 and indi-cated in the legend. The standard errors on these curvesare shown by the shaded regions. From these plots, itis quite clear that the mean eccentricity, vertical excur-sion from the Galactic plane, and angular momentum ofthe two α -sequences are distinct even if they have thesame metallicity. This Figure also shows the richnessof the information linking orbits to stellar chemistry.The high- α stars separate out significantly in J R com-pared to the low- α stars as a function of [Fe/H], withthe lowest metallicity stars showing the highest radialactions. Similarly the high- α stars separate out moremarkedly, particularly at high metallicity, in J z com-pared to the low- α stars, as a function of [Fe/H], withthe lowest metallicity stars showing the highest verticalactions. The two sequences are similarly dispersed inangular momentum ( L z ) as a function of [Fe/H]. This examination demonstrates that there is clearlya relationship between stellar orbits and [Fe/H] that isdetermined by a star’s membership in either the lowand high- α sequences. While the stars separate dynam-ically for these two sequences, the metallicity of a staris additionally indicative of its dynamics at a given age,particularly for the high- α sequence.3.3. Dynamical Actions of the High- and Low- α Sequences as a Function of Spatial Selection, | z | The measured actions are a function of spatial po-sition of the stars; stars at higher distances from theplane in the disk have higher J z values and the high- α sequence is preferentially distributed at larger | z | , at theSun. We therefore wish to examine in more detail thedifferences in the action distributions of the high- andlow- α sequences conditioned on height from the plane( | z | ). We examine this by testing the respective actionsof the high- and low- α sequences in three narrow slicesin | z | : (i) 0 < | z | ≤ . . < | z | ≤ < | z | ≤ . α -sequences have meanactions that are different from each other at all ages, asshown in Figure 5. The standard errors on all curves(not shown in the Figure) are on the order of the thick-ness of the lines.It can be seen that the high- α stars have significantlyhigher eccentricity ( J R ) at all ages compared to thelow- α stars even when the stars have the same | z | -distances. Angular momentum ( L z ) as a function ofage is much lower for high- α stars compared to the low- α stars (at a given | z | -distance), with stellar angularmomenta decreasing with increasing distance from theGalactic plane. Note that there are small differences in J z as a function of age (middle panel of Figure 5) forthe two α -sequences; this indicates that within our bins Gandhi et al.
Figure 4.
Smoothed running means of J R , J z , and L z (with bin size N = 300) for the high- α (left panel) and low- α stars(right panel) as a function of age in three different metallicity ranges. Each [Fe/H] bin is represented by the same color schemeand line style as in Figure 2. The legend for all plots is once again shown in the bottom left subplot, and the number of starsin each [Fe/H] range and α -sequence is recorded in the bottom panel in the respective color of the [Fe/H] range. We used agaussian kernel with σ s = 100kpc km s − for smoothing the data. The standard errors ( σ/ √ N −
1) are shown by the shadedregions around each curve, which we can see are on the order of the thickness of the lines. These plots make it clear that thetwo α -sequences have quite distinct dynamical properties (associated with each of the three actions) at a given metallicity. of height | z | , the low- α sequence stars are preferentiallynearer to the Galactic plane.These plots demonstrate that the orbital properties ofthe stars in each α -sequence are sensitive to the spatialselection of the stars in height above the plane, whichreflects the correlation between structure and chemistryin the Galaxy and also the selection function of the sur-vey. However, it is clear that at a given spatial selectionin height above the plane there is the clear separationin the mean of the dynamical action between the two α -sequences.3.4. Comparison with Ages Derived from BayesianInference
We also used ages and actions from a catalog devel-oped by Sanders & Das (2018) to test whether or notwe get similar results with their data. In their analysis,Sanders & Das employed Bayesian neural networks todate stars, and the Gaia DR2 data to find the actions us- ing the Stackel fudge method. Figure 6 shows the plotsobtained using the data from Sanders & Das (2018),made in the same way as Figure 3. These plots have30,579 high- α stars, and 122,668 low- α stars restrictedto within ≤ < α -sequences is quite encouraging. DISCUSSION4.1.
Orbital properties of the High- and Low- α Sequences
Studying the actions J R , J z , and L z as a function ofage for the two α -sequences makes it clear that diskstars in the solar neighborhood that fall into different α -enrichment groups have very different mean orbitalproperties at all ages. The fact that this dichotomy inthe action plane is present throughout all ages, for all igh- and Low- α Disk Stars Separate Dynamically at all Ages Figure 5.
Smoothed running means of J R , J z , and L z versus age for the high- (left panel) and low- α (right panel) sequencesseparated into three ranges of height above the Galactic plane, | z | : (i) 0 < | z | ≤ . . < | z | ≤ < | z | ≤ . | z | range and α -sequence are recorded in the bottom panel in the respective color of each | z | range. Agaussian kernel with σ s = 100kpc km s − was used for smoothing the running means. Division into | z | ranges helps decouplethe | z | -positions of the stars from their chemistry and dynamics. We can see that even at the same height from the plane, thetwo α -sequences have different J R , J z , and L z , i.e., different dynamical properties, at all ages. Standard errors have been leftout in these plots because they are on the order of the thickness of the curves. actions, is a strong indication that high- and low- α se-quences form distinct populations which have differentevolution and birth properties. We also find that withina given α -sequence, a star’s [Fe/H] is additionally infor-mative as to its orbital properties, particularly for J z and J R for the high- α sequence. Figure 3 shows ourmain results, from which we can understand what thenature of the orbits of stars in the high- or low- α se-quence is, at least with respect to each other. Orbits ofhigh- α stars are on average more eccentric (have greater J R ) than the low- α stars, almost consistently by a fac-tor of two. We see a similar relationship between thetwo sequences in how much their orbits diverge fromthe Galactic plane (or J z ): the high- α sequence has or-bits which go almost up to twice the height from theplane compared to low- α stars. The angular momentum( L z ) of low- α stars is ∼ .
25 times that of the high- α stars, which indicates that low- α stars on average have larger radii than high- α stars (e.g. Beane et al. 2018;Hayden et al. 2015). Our results are consistent withMackereth et al. (2019), who find similar relationshipsbetween α -abundance and velocity dispersions ( σ z , σ R )of high- and low- α stars. Our findings are also alignedwith the analysis of Nidever et al. (2015), who determinesingle population chemical evolution models to be insuf-ficient to explain the α -bimodality seen in the APOGEEdata. These empirical findings can be explained in a cos-mological context if the high- α sequence has a distinct,early and rapid star formation origin, in “clumps” (e.g.Clarke et al. 2019). Such clumps are also observed athigh redshift in young spiral Galaxies that are presum-ably typical Milky Way progenitors (Guo et al. 2015).It is interesting to note that we find a valley betweentwo slight peaks (in Figure 3) in J R and J z for the high- α sequence between age ∼ L z for high- α stars in the same age Gandhi et al.
Figure 6.
The same plots as in Figure 3 but using Sanders & Das (2018) ages and actions. The running means (with binsize N = 2000 stars) and standard deviations ( σ ) of each of the three actions for 30,579 high- α stars and 122,668 low- α starsare plotted as a function of age. The high- and the low- α sequences are represented by the solid blue curve and the solid redcurve respectively. The running means have been smoothed with a gaussian kernel using σ s = 200kpc km s − . The thicknessof the solid curves represents the standard error ( σ/ √ N − σ standarddeviations in actions. These plots quite closely match Figure 3. window. We see similar signatures in analyzing LAM-OST stars from Sanders & Das (2018), as can be seenin Figure 6. The presence of a perturbation in J z wasalso suggested by Beane et al. (2018) ( § α -enrichment).Such a perturbation could be a signature of an infallevent in the Milky Way, which altered the dynamicalproperties of stars at ∼ α -enrichment as well as metallicity, which means thatany infalling gas cloud would have a consistent aver-age chemical composition. As can be seen in Figure 4,they appear only in the high- α sequence in the rangeof − . < [Fe/H] <
0, within the same age range ( ∼ α stars in the Galaxy of this age.4.2. Discovery of Old and α -Poor Halo Stars in theLAMOST Sample Numerous works (e.g. Silva Aguirre et al. 2018; Nesset al. 2016; Bensby et al. 2014; Bergemann et al. 2014;Haywood et al. 2013; Adibekyan et al. 2011) have es-tablished that high- α stars of the disk are old and low- α stars of the disk are typically young. Furthermore,Milky Way halo stars ( ∼ α , metal poor ([Fe/H] < − . α -sequences for the halo stars in LAM-OST including stars within ≤ J R ) and low angular mo-menta ( L z ). Figure 7a shows how the LAMOST starsare distributed across the L z -log ( J R ) plane; the diskflares out and appears joined to the halo which is dis-tributed around an L z ∼ J z , as indicatedin the box drawn around this region. Such a selectionin actions discriminates halo stars from the disk popu-lation. This discrete cut is not intended as an absolutemarker of halo membership but these stars have orbitalproperties which align with halo membership and arequite distinct from the disk (e.g. Helmi et al. 2018).We now show the distribution of our selected halostars in Figures 7b,c coloured by age and angular mo-mentum, respectively. We use the same line as previ-ously to differentiate high- and low- α stars. Surpris-ingly, we find low- α stars in the halo in our sample.There are 292 high- α stars and 58 low- α stars whichmake the halo cut. Respectively, the age distribution ofthe high- and low- α sequences is similar, with a meanage and 1- σ standard deviation of (7.8,2.3)Gyr for thehigh- α halo stars and (7.2,2.5)Gyr for the low- α stars.These ages may be badly measured, but we found noindication of this in examining the χ ( χ ∼ .
5) andage uncertainties (∆ age ∼ . α halo stars, 21 exhibit retro-grade motion with L z <
0. The metallicity distribu-tion of mean [Fe/H] and the standard error of the mean( σ err = σ/ √ N −
1) is different for the retrograde com-pared to the prograde low- α stars. The retrograde starshave ([ F e/H ] ± σ err ) = ( − . ± . − . ± .
04) for the prograde stars. The retrogradestars are also younger (than the prograde stars) with( age ± σ err ) = (6 . ± . . ± . igh- and Low- α Disk Stars Separate Dynamically at all Ages (a) (b) (c) Figure 7. (a) The distribution of 144 ,
231 high- and low- α stars within ≤ L z -log ( J R ) plane, coloredby age. The L z -log ( J R ) plane visually separates the disk and the halo; stellar orbits with a variety of angular momenta( L z ) and eccentricity ( J R ) values represent the disk, resulting in the triangular shape of the distribution, whereas the taperingbottom end of the distribution with low L z and high J R characterizes the halo orbits. In the adjacent plots, we examine the α -enhancement, age, and orbital motion of halo stars (within the dashed box) with log ( J R ) > . L z < s − .(b) The distribution of 350 stars within 5kpc of the Sun with L z < s − and log ( J R ) > . α /Fe]-[Fe/H] plane, colored by age. The numbers of high- and low- α stars are indicated above and below the black separationline respectively. We find that the 58 low- α stars that make this cut have a mean age of ∼ σ standard deviationof ∼ α stars which make this cut have a mean age of ∼ σ standard deviation of ∼ L z ). Of the 58 low- α stars, 21 exhibit retrograde motion,i.e., have L z < This anomalous low- α halo population may be asso-ciated with the coherent population of infall discoveredin the Gaia data by a number of groups (Myeong et al.2018; Koppelman et al. 2018; Helmi et al. 2018). In par-ticular, Helmi et al. (2018) find a retrograde populationin the halo within 5kpc of the Sun which they call the“Gaia Enceladus” and show that it might have mergedwith the Milky Way ∼
10 Gyr ago. At [Fe/H] ∼ − . ∼ α stars as demon-strated using the APOGEE data in Helmi et al. (2018),however has not been previously spectroscopically agedated.If the stars in the LAMOST data that we have iden-tified as potential Gaia Enceladus members are ex-situto the Milky Way, they will have experienced a differ-ent star formation rate and therefore have different birthand evolution history from the typical stars in the MilkyWay. So we expect multiple abundances to show anoma-lous trends in other elements, which can be tested usingindividual abundance derivations from LAMOST data(Belokurov et al. 2018; Ting et al. 2017). Additional di-mensions of information along these lines will enable usto determine if these stars are from a single or multipleset of infall events. CONCLUSIONWe calculated actions ( J R , J z , and L z ) using dynami-cal information from Gaia DR2, and used ages for LAM- OST red giants (in the disk near the Sun) from Hoet al. (2017). We have found clear indications that α -enrichment is correlated with dynamical properties ofstellar orbits. Our main conclusions are summarizedbelow:1. Consistently and at all ages, the high- and low- α sequences exhibit distinct mean trends in eccen-tricity ( J R ), divergence from Galactic plane ( J z ),and angular momentum ( L z )—the three dynami-cal properties which (simplistically, but uniquely)characterize a stellar orbit. This result can beseen clearly in Figure 3. This implies that the two α -sequences are distinct populations in the MilkyWay, with different birth and evolution properties.This conclusion is also supported by studies whichuse models to simulate Milky Way-like galaxiesand find that the two α -sequences emerge via dis-tinct birth and evolutionary tracks (e.g. Mackerethet al. 2018b; Grand et al. 2018).2. The conclusion that chemistry is strongly linkedto orbital properties of stars at all ages has beenshown to be consistent at a given metallicity (Fig-ure 4) as well as at a narrow slice in height fromthe plane (Figure 5).3. The L z -log ( J R ) plane is an effective space to se-lect for halo stars. We find a population of low- α stars which are atypically older and live predom-inantly in the halo, which may be remnants of0 Gandhi et al. merger events in the Milky Way, e.g. Gaia Ence-ladus (Helmi et al. 2018; Belokurov et al. 2018).Our findings of high- and low- α sequences being dynami-cally distinct at all ages, including at a given ([Fe/H], | z | )is strong evidence for the discrete origin of these popula-tions in building the disk. These findings are consistentat different spatial locations and for different stellar sur-veys with different selection functions (e.g. APOGEE(Mackereth et al. 2019; Nidever et al. 2014)). ACKNOWLEDGEMENTSWe would like to thank the Flatiron Institute andColumbia University for providing the infrastructureand support for this research. We also thank GlennysFarrar, Angus Beane, and David Hogg for helpful con-versations.REFERENCES
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