Chemical Cartography with APOGEE: Metallicity Distribution Functions and the Chemical Structure of the Milky Way Disk

TL;DR: In this paper, the authors measured the distribution of stars in the [$α$/Fe] vs [Fe/H] plane and the metallicity distribution functions (MDF) across an unprecedented volume of the Milky Way disk, with radius $3 11$ kpc.

Abstract: Using a sample of 69,919 red giants from the SDSS-III/APOGEE Data Release 12, we measure the distribution of stars in the [$\alpha$/Fe] vs [Fe/H] plane and the metallicity distribution functions (MDF) across an unprecedented volume of the Milky Way disk, with radius $3 11$ kpc The peak of the midplane MDF shifts to lower metallicity at larger $R$, reflecting the Galactic metallicity gradient Most strikingly, the shape of the midplane MDF changes systematically with radius, with a negatively skewed distribution at $3 1$ kpc or [$\alpha$/Fe]$>018$, the MDF shows little dependence on $R$ The positive skewness of the outer disk MDF may be a signature of radial migration; we show that blurring of stellar populations by orbital eccentricities is not enough to explain the reversal of MDF shape but a simple model of radial migration can do so

Summary

1. INTRODUCTION

• The Milky Way is an excellent testing ground of their understanding of Galaxy evolution, owing to the ability to resolve individual stars and study stellar populations in greater detail than in other galaxies.
• The distribution of stars in the [α/Fe] versus [Fe/H] plane shows two distinct stellar populations in the solar neighborhood (e.g., Fuhrmann 1998; Prochaska et al.
• The radial mixing of gas and stars from their original birth radii has also been proposed as an important process in the evolution of the Milky Way disk (e.g., Wielen et al.
• The main survey goals were to obtain a uniform sample of giant stars across the disk with moderately high resolution spectroscopy to study the chemical and kinematical structure of the Galaxy, in particular the inner Galaxy,where optical surveys cannot observe efficiently owing to high extinction.

2. DATA AND SAMPLE SELECTION

• Data are taken from DR12, which contains stellar spectra and derived stellar parameters for stars observed during the 3 yrof APOGEE.
• Because of this, the authors do not correct for the non-uniform age sampling of giants, and their MDFs are slightly biased against the oldest (and potentially more metal-poor) stars of the disk.

2.1. Distances

• Distances for each star are determined from the derived stellar parameters and PARSEC isochrones from the Padova-Trieste group (Bressan et al. 2012 ) based on Bayesian statistics, following methods described by Burnett & Binney (2010) , Burnett et al. (2011), and Binney et al. (2014) ; see also Santiago et al. (2015) .
• "Data"refers to the observed spectroscopic and photometric parameters for the star.
• Additional terms can be added if density priors are included, but the authors did not include density priors for the distances used in this paper; their effective prior is flat in distance modulus.
• The distance modulus most likely to be correct given the observed parameters and the stellar models is determined by creating a probability distribution function (PDF) of all distance moduli.
• To generate the PDF, the equation above is integrated over all possible distance moduli, although in practice the authors use a range of distance moduli between the minimum and maximum magnitudes from the isochrone grid matches to reduce the required computing time.

3.1. [α/Fe] versus [Fe/H]

• The lower envelope of the distribution has a concave-upward, bowl shape.
• These observations are similar to previous studies of the solar neighborhood (e.g., Adibekyan et al.
• The red clump offers more precise distance and abundance determinations compared to the entire DR12 sample, but it covers a more restricted distance and metallicity range.
• There appears to be a slight shift toward lower-[α/Fe] for the same metallicities by 0.05 dex compared to the high-[α/Fe] sequence observed in the rest of the disk.
• To summarize their results for the distribution of stars in the [α/Fe] versus [Fe/H] plane: 1. There are two distinct sequences in the solar neighborhood, one at high[α/Fe], and one at solar[α/Fe], which appear to merge at [Fe/H] 0.2 ~+ .

3.2. Metallicity Distribution Functions

• With 3 yrof observations, there are sufficient numbers of stars in each Galactic zone to measure MDFs in a number of radial bins and at different heights above the plane.
• In the inner disk, at large heights above the plane the high-[α/Fe] sequence dominates the number density of stars.
• At these larger heights above the plane, the MDFs are leptokurtic as well, but the trend with radius is reversed compared to the distributions close to the plane.
• Simple chemical evolution models often use instantaneous recycling approximations where metals are immediately returned to the gas reservoir after star formation occurs.
• The shape and skewness of the MDF in the midplane are strongly dependent on location in the Galaxy: the inner disk has a large negative skewness, the solar neighborhood MDF is roughly Gaussian, and the outer disk has a positive skewness.

4.1. Comparison to Chemical Evolution Models

• MDFs are useful observational tools in constraining the chemical history of the Milky Way.
• Additions such as gas inflow and outflow to chemical evolution models have been able to better reproduce observations of the solar neighborhood, in particular the MDF and stellar distribution [α/Fe] versus [Fe/H] plane.
• Additionally, this model reproduces general trends found in the distribution of stars in the [α/Fe] versus [Fe/H] plane, in particular with the dilution of the metallicity of the existing gas reservoir with pristine gas to form the low-[α/Fe] sequence.
• Kubryk et al. (2013) do not find significant shifts in the peak or skewness with radius in their simulations, contrary to what is observed in the APOGEE observations.
• The metal-rich components of the MDFs from the simulation are in the wings of the distributions, leading to positively skewed MDFs in the inner Galaxyand roughly Gaussian shapes in the outer disk.

4.2. Radial Mixing

• Simple chemical evolution models (closed or leaky box) are unable to produce the positively skewed MDFs that the authors observe in the outer disk.
• Models that include radial mixing (e.g., Schönrich & Binney 2009) are able to at least produce a more Gaussian-shaped MDF across the disk.
• The fraction of stars that undergo radial migration is difficult to predict from first principles because it depends in detail on spiral structure, bar perturbations, and perturbations by and mergers with satellites (e.g., Roškar et al.
• To test the effects of blurring and churning on their observed MDFs, the authors create a simple model of the MDF across the disk.
• These distribution function parameters adequately fit the kinematics of the main APOGEE sample (Bovy et al. 2012d ).

4.2.1. Blurring

• In Figure 9 the authors compare the initial MDF and the MDF with the effects of blurring included.
• While blurring does reduce the observed skewness of the MDFs, the MDFs are still negatively skewed at all radii.
• This model is simplistic, and it is possible that their underlying assumption regarding the intrinsic shape of the MDF may not be correct.
• Because the intrinsic MDF is unlikely to have positive skewness anywhere in the Galaxy, it appears that blurring alone is unable to reproduce the.

4.2.2. Radial Migration

• The authors expand their simple model to include churning to determine whether radial migration is better able to reproduce the observations.
• These tests demonstrate that blurring alone, as suggested by Snaith et al. (2014) , is unable to reproduce their observations, and that the addition of churning to their model yields significantly better agreement with the observed MDF, in particular the change in skewness with radius.
• It is likely that a combination of both gas and stellar migration is required to reproduce their observations in chemo-dynamical models for the Milky Way.
• In their model, the outer disk has a wide range of metallicities at any age owing to radial migration, in agreement with models from Minchev et al. (2014) .
• Heating of stellar populations by encounters with molecular clouds, spiral arms, or other perturbations will naturally increase the fraction of older stars at greater heights above the plane simply because they have more time to experience heating.

5. CONCLUSIONS

• The solar neighborhood MDF has proven itself a linchpin of Galactic astronomy, enabling major advances in their understanding of chemical evolution (e.g., van den Bergh 1962) in conjunction with stellar dynamics (Schönrich & Binney 2009) .
• Galaxy formation models must ultimately reproduce the empirical MDF as well (Larson 1998) .
• The authors simple dynamical model reveals the exciting prospect that the detailed shape of the MDF is likely a function of the dynamical history of the Galaxy.

Figures

Figure 1. Spectroscopic H-R diagram for the full calibrated APOGEE sample, where the mean metallicity in each g Tlog , eff bin is shown. The gray box denotes the selected sample of 69,919 stars presented in this paper.

Figure 8. Top: change in skewness as a function of galactocentric radius for stars close to the plane ( z 0.5<∣ ∣ kpc). There is a negative skewness for R 7< kpc, which increases toward positive skewness at larger radii. The change in skewness with location is similar for both the MDF and ADF. Bottom: change in the average metallicity or α-abundance of the distributions as a function of R for stars close to the plane ( z 0.5<∣ ∣ kpc). The fit was done for R 6> kpc, and the slopes are nearly identical for both. The slope is similar in magnitude to other measurements of the radial gradient.

Figure 11. MDF as a function of R with the inclusion of blurring and churning. The dashed lines show the initial MDF, and the solid lines display the MDF including the effects of churning and blurring. The redistribution of guiding radii due to churning is able to significantly change the skewness compared to the initial MDFs and can explain the changes in skewness and its sign observed in the APOGEE sample.

Table 2 Metallicity Distribution Functions in the Milky Way

Figure 10. Age–metallicity relation at different radii for our simple model. The blue line shows the metallicity of the ISM as a function of age at different radii, while the solid black lines denote 1σ, 2σ, and 3σ of the distribution of stars in the age–metallicity plane, respectively; the solid red line gives the mean metallicity as a function of age. The solar neighborhood and the outer disk both display a wide range of metallicities for all but the oldest stars.

Figure 16. Similar to above, but with the surface gravity restrictions removed. The [α/Fe] abundance trends with temperature are clear with the inclusion of the lower surface gravity stars. Cooler stars have lower [α/Fe] abundances by ∼0.1 dex.

Figure 17. Similar to above, but with the [α/Fe] measured by averaging the abundances for the individual α-elements. We find similar trends as in Figure 16 above, with the cooler stars having lower-[α/Fe] abundances than the warmer stars at the same metallicities.

Figure 14. Mock targeted MDF (black) vs. the mock observed MDF after applying distance errors to the TRILEGAL simulation (red). The difference between the two is negligible except for the very outer disk (R 13> kpc).

Figure 15. Distribution of stars in the [α/Fe] vs. [Fe/H] plane color coded by Teff for stars with z 0.5<∣ ∣ kpc. There is evidence for temperature trends in the [α/Fe] abundance in the inner Galaxy ( R3 5< < kpc). This figure is down-sampled and shows only 15% of the data points for R 5> kpc.

Figure 9. MDF as a function of R for our simple blurring model. The dashed lines show the initial MDFs (which the stars on circular orbits would have), and the solid lines represent the MDFs including the effect of blurring. The skewness of the blurred MDFs is indicated. The magnitude of the skewness diminishes with radius, but it does not change sign.

Figure 4. Stellar distribution of stars in the [α/Fe] vs. [Fe/H] plane as a function of R and z∣ ∣. The typical uncertainty in the abundances is shown as a function of metallicity across the bottom of each panel. The size of individual points is inversely related to the density at that location, to avoid saturation. Top: observed [α/Fe] vs. [Fe/H] distribution for stars with z1.0 2.0< <∣ ∣ kpc. Middle: observed [α/Fe] vs. [Fe/H] distribution for stars with z0.5 1.0< <∣ ∣ kpc. Bottom: observed [α/Fe] vs. [Fe/H] distribution for stars with z0.0 0.5< <∣ ∣ kpc. The gray line on each panel is the same, showing the similarity of the shape of the high-[α/Fe] sequence with R. The extended solar-[α/Fe] sequence observed in the solar neighborhood is not present in the inner disk (R < 5 kpc), where a single sequence starting at high[α/Fe] and low metallicity and ending at solar[α/Fe] and high metallicity fits our observations. In the outer disk (R > 11 kpc), there are very few high-[α/Fe] stars.

Figure 3. Observed [α/Fe] vs. [Fe/H] distribution for the solar neighborhood ( R7 9< < kpc, z0 0.5< <∣ ∣ kpc). The left panel is down-sampled and shows only 20% of the observed data points in the solar circle. The right panel shows the entire sample in the solar neighborhood, with contours denoting 1, 2, 3s of the overall densities. The typical uncertainty in the abundances is shown as a function of metallicity across the bottom of both panels. There are two sequences in the distribution of stars in the [α/Fe] vs. [Fe/H] plane, one at solar-[α/Fe] abundances, and one at high-[α/Fe] abundances that eventually merges with the solar-[α/Fe] sequence at [Fe/ H] ∼ 0.2.

Figure 12. Observed mock MDF of giants (red) compared to the intrinsic MDF of giants (black) as a function of R. (A)Only targeting criteria (field placement, color cuts, magnitude limits) applied to the input simulations. (B)Observed MDF with the temperature restrictions imposed by the ASPCAP grid edge. (C)Observed MDF with a restricted surface gravity range. (D)Observed MDF with both the temperature and surface gravity restrictions. There is little difference between panels (C) and (D);the effects of the temperature grid edge on the observed MDF havelargely been mitigated owing to the restriction in surface gravity, leading to a significantly less biased MDF.

Figure 13. Intrinsic age distribution of giants in the TRILEGAL simulation (black) compared to the mock observed age distribution (red). The sample selection criteria donot induce a large bias in the observed sample, although the targeted sample is slightly older in general than the underlying age distribution of giants in the simulation.

Table 3 α Distribution Functions in the Milky Way

Figure 5. Observed MDF for the entire sample as a function of galactocentric radius over a range of distances from the plane. The shape and skewness are a function of radius and height. Close to the plane, the inner Galaxy ( R3 5< < kpc) is a negatively skewed distribution and a peak metallicity at ∼0.25 dex, while the outer disk (R > 11 kpc) has a positively skewed distribution with peak metallicity of 0.4~ - dex . For z 1>∣ ∣ kpc, the MDF is fairly uniform across all radii.

Table 1 Sample Selection

Full text

Hayden, MR, Holtzman, JA, Bovy, J, Nidever, DL, Bird, JC, Weinberg, DH,
Johnson, JA, Andrews, BH, Majewski, SR, García Pé Rez, AE, Hearty, FR,
O'Connell, R, Skrutskie, M, Wilson, JC, Prieto, CA, García-Herńandez, DA,
Zamora, O, Anders, F, Chiappini, C, Minchev, I, Steinmetz, M, Beers, TC,
Bizyaev, D, Pan, K, Girardi, L, Cunha, K, Smith, V, Frinchaboy, P, Harding, P,
Schneider, DP, Mészáros, S, Robin, AC, Schiavon, RP, Schultheis, M, Shetrone,
M and Zasowski, G
CHEMICAL CARTOGRAPHY with APOGEE: METALLICITY DISTRIBUTION
FUNCTIONS and the CHEMICAL STRUCTURE of the MILKY WAY DISK
http://researchonline.ljmu.ac.uk/id/eprint/2564/
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Hayden, MR, Holtzman, JA, Bovy, J, Nidever, DL, Bird, JC, Weinberg, DH,
Johnson, JA, Andrews, BH, Majewski, SR, García Pé Rez, AE, Hearty, FR,
O'Connell, R, Skrutskie, M, Wilson, JC, Prieto, CA, García-Herńandez, DA,
Zamora, O, Anders, F, Chiappini, C, Minchev, I, Steinmetz, M, Beers, TC,
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CHEMICAL CARTOGRAPHY WITH APOGEE: METALLICITY DISTRIBUTION FUNCTIONS AND THE
CHEMICAL STRUCTURE OF THE MILKY WAY DISK
Michael R. Hayden
1
,JoBovy
2,27
, Jon A. Holtzman
1
, David L. Nidever
3
, Jonathan C. Bird
4
, David H. Weinberg
5
,
Brett H. Andrews
6
, Steven R. Majewski
7
, Carlos Allende Prieto
8,9
, Friedrich Anders
9
, Timothy C. Beers
11
,
Dmitry Bizyaev
12
, Cristina Chiappini
10,13
, Katia Cunha
14,15
, Peter Frinchaboy
16
, D. A. García-Herńandez
8,9
,
Ana E. García Pérez
7,8,9
, Léo Girardi
13,17
, Paul Harding
18
, Fred R. Hearty
7,19
, Jennifer A. Johnson
5
,
Szabolcs Mészáros
20
, Ivan Minchev
10
, Robert O’Connell
7
, Kaike Pan
12
, Annie C. Robin
21
, Ricardo P. Schiavon
22
,
Donald P. Schneider
19,23
, Mathias Schultheis
24
, Matthew Shetrone
25
, Michael Skrutskie
7
, Matthias Steinmetz
10
,
Verne Smith
14
, John C. Wilson
7
, Olga Zamora
8,9
, and Gail Zasowski
26
1
New Mexico State University, Las Cruces, NM 88003, USA; mrhayden@nmsu.edu, holtz@nmsu.edu
2
Institute for Advanced Study, Einstein Drive, Princeton, NJ 08540, USA; bovy@ias.edu
3
Department of Astronomy, University of Michigan, Ann Arbor, MI48109, USA; dnidever@umich.edu
4
Department of Physics and Astronomy, Vanderbilt University, 6301 Stevenson Center, VU Station B #351807, Nashville, TN 37235, USA;
jonathan.bird@vanderbilt.edu
5
Department of Astronomy and CCAPP, The Ohio State University, Columbus, OH 43210, USA; dhw@astronomy.ohio-state.edu, jaj@astronomy.ohio-state.edu
6
PITT PACC, Department of Physics and Astronomy, University of Pittsburgh, 3941 O’Hara Street, Pittsburgh, PA 15260, USA; andrewsb@pitt.edu
7
Departmentof Astronomy, University of Virginia, Charlottesville, VA 22904-4325, USA; srm4n@virginia.edu, aeg4x@virginia.edu, rwo@virginia.edu,
mfs4n@virginia.edu, jcw6z@virginia.edu
8
Instituto de Astrofísica de Canarias (IAC), E-38200 La Laguna, Tenerife, Spain
9
Departamento de Astrofísica, Universidad de La Laguna (ULL), E-38205 La Laguna, Tenerife, Spain
10
Leibniz-Institut für Astrophysik Potsdam (AIP), An der Sternwarte 16, D-14482, Potsdam, Germany; fanders@aip.de, cristina.chiappini@aip.de,
msteinmetz@aip.de, iminchev1@gmail.com
11
Departmentof Physics and JINA-CEE: Joint Institute for Nuclear Astrophysics-Center for the Evolution of the Elements, University of Notre Dame, Notre Dame,
IN 46556, USA; tbeers@nd.edu
12
Apache Point Observatory and New Mexico State University, P.O. Box 59, Sunspot, NM88349-0059, USA; dmbiz@apo.nmsu.edu, kpan@apo.nmsu.edu
13
Laboratório Interinstitucional de e-Astronomia—LIneA, Rua Gal. José Cristino 77, Rio de Janeiro, RJ—20921-400, Brazil
14
National Optical Astronomy Observatories, Tucson, AZ 85719, USA; cunha@email.noao.edu, vsmith@email.noao.edu
15
Observatório Nacional, São Cristóvão, Rio de Janeiro, Brazil
16
Department of Physics and Astronomy, Texas Christian University, Fort Worth, TX 76129, USA; p.frinchaboy@tcu.edu
17
Osservatorio Astronomico di Padova—INAF, Vicolo dell’Osservatorio 5, I-35122 Padova, Italy; leo.girardi@aopd.inaf.it
18
Department of Astronomy, Case Western Reserve University, 10900 Euclid Ave, Cleveland, OH 44106, USA; paul.harding@case.edu
19
Department of Astronomy and Astrophysics, The Pennsylvania State University, University Park, PA 16802, USA; frh10@psu.edu, dps7@psu.edu
20
ELTE Gothard Astrophysical Observatory, H-9704 Szombathely, Szent Imre Herceg st. 112, Hungary; meszi@gothard.hu
21
Institute Utinam, CNRS UMR6213, Université de Franche-Comté, OSU THETA de Franche-Comté-Bourgogne, Besancon, France; annie@obs-besancon.fr
22
Astrophysics Research Institute, IC2, Liverpool Science Park, Liverpool John Moores University, 146 Brownlow Hill, Liverpool, L3 5RF, UK;
rpschiavon@gmail.com
23
Institute for Gravitation and the Cosmos, The Pennsylvania State University, University Park, PA 16802, USA
24
Laboratoire Lagrange (UMR7293), Université de Nice Sophia Antipolis, CNRS, Observatoire de la Côte d’Azur, BP 4229, F-06304 Nice Cedex 4, France;
mathias.schultheis@oca.edu
25
The University of Texas at Austin, McDonald Observatory, TX 79734, USA; shetrone@astro.as.utexas.edu
26
Department of Physics and Astronomy, Johns Hopkins University, Baltimore, MD 21218, USA; gail.zasowski@gmail.com
Received 2015 March 6; accepted 2015 May 22; published 2015 July 28
ABSTRACT
Using a sample of 69,919 red gia nts from th e SDSS-I II/APOGEE Data Release 12, we measure the distribution
of stars in the [α/Fe] versus [Fe/H] plane and the metallicity distribution functions (MDFs) across an
unprecedented volume of the Milky Way disk, with radius 3 < R < 15 kpc and height
z 2<
∣
∣
kpc. Stars in the
inner disk (R <5kpc) liealongasingletrackin[α/Fe] versus [Fe/H], starting with α-enhanced, metal-p oor
stars and en ding at [α/Fe] ∼ 0and[Fe/H] ∼ +0.4. At larger radii we find two distinct sequences in [α/Fe] versus
[Fe/H] space, wit h a roughly s olar- α sequence that spans a decade in metallicity and a high-α sequence that
merges with the low-α sequence at s uper-so lar [Fe/H]. The location o f the high-α sequence is nearly constant
across the disk;however, there are very few high- α stars at R > 11 kpc. The peak of the midplane MDF shifts to
lower metallicity at larger R,reflecting the Galactic metallicity gradient . Most st rikingl y, the shape of the
midplane MDF changes systematically with radius, from a negatively skewed distribution at 3 < R <7kpc,toa
roughly Gaussian distrib ution at the solar annulus, to a posi tively skewed shape in the outer Galaxy. For s tars
with
z 1>
∣
∣
kpc or [α/Fe] > 0.18, the MDF shows little dependence on R. The positive skewness of the outer-
disk MDF may be a signature of radial migration; we show that blurring of stellar populations by orbital
eccentricities is not enough to explain the reversal of MDF shape, but a simple model of radial migration can
do so.
Key words: Galaxy: abundances – Galaxy: disk – Galaxy: evolution – Galaxy: stellar content – Galaxy: structure
The Astrophysical Journal, 808:132 (18pp), 2015 August 1 doi:10.1088/0004-637X/808/2/132
© 2015. The American Astronomical Society. All rights reserved.
27
Bahcall Fellow.
1

1. INTRODUCTION
The Milky Way is an excellent testing ground of our
understanding of Galaxy evolution, owing to the ability to
resolve individual stars and study stellar populations in greater
detail than in other galaxies. However, understanding the
composition, structure, and origin of the Milky Way disk is still
one of the outstanding questions facing astronomy, and there is
great debate about this topic (e.g., Rix & Bovy 2013). The
ability to resolve individual stars allows one to trace the fossil
record of the Milky Way across the disk, as the stars contain the
chemical footprint of the gas from which they formed.
Observations of stars in the Milky Way have led to the
discovery of several chemical and kinematic properties of the
disk of the Galaxy, such as the thick disk (e.g., Yoshii 1982;
Gilmore & Reid 1983), chemical abundance gradients (e.g.,
Hartkopf & Yoss 1982; Cheng et al. 2012b; Anders et al. 2014;
Hayden et al. 2014; Schlesinger et al. 2014), and the G-dwarf
problem (van den Bergh 1962; Pagel & Patchett 1975), from
the study of the metallicity distribution function (MDF) of the
solar neighborhood (van den Bergh 1962; Casagrande
et al. 2011; Lee et al. 2011; Schlesinger et al. 2012). Much
of the previous work on the Milky Way disk has focused on the
solar neighborhood, or tracer populations (e.g., Cepheid
variables, H
II regions) that span a narrow range in age and
number only a few hundred objects even in the most thorough
studies. Large-scale surveys such as SEGUE (Yanny et al.
2009), RAVE (Steinmetz et al. 2006), APOGEE (Majewski S.
R. 2015, in preparation), GAIA-ESO (Gilmore et al. 2012),
and HERMES-GALAH (Freeman et al. 2012) aim to expand
observations across the Milky Way and will greatly increase
the spatial coverage of the Galaxy with large numbers of stars.
In this paper we use observations from the Twelfth Data
Release of SDSS-III/APOGEE (Alam et al. 2015) to measure
the distribution of stars in the [α/Fe] versus [Fe/H] plane and
the MDF across the Milky Way galaxy with large numbers of
stars over the whole radial range of the disk.
Different stellar populations can be identified in chemical
abundance space, with the α abundance of stars separating
differing populations. The distribution of stars in the [α/Fe]
versus [Fe/H] plane shows two distinct stellar populations in the
solar neighborhood (e.g., Fuhrmann 1998; Prochaska et al.
2000; Reddy et al. 2006; Adibekyan et al. 2012; Haywood
et al. 2013; Anders et al. 2014; Bensby et al. 2014; Nidever
et al. 2014; Snaith et al. 2014), with one track having roughly
solar-[α/Fe] ratios across a large range of metallicities, and the
other track having a high-[α/Fe] ratio at low metallicity that is
constant with [
Fe/H] until [Fe/H] ∼ −0.5, at which point there is
a knee and the [α/Fe] ratio decreases at a constant rate as a
function of [Fe/H] , eventually merging with the solar-[α/Fe]
track at [Fe/H] ∼ 0.2 dex. The knee in the high-[α/Fe] sequence
is likely caused by the delay time for the onset of Type Ia
supernovae (SNe Ia): prior to formation of the knee, core-
collapse supernovae (SNe II) are the primary source of metals
in the interstellar medium (ISM), while after the knee SNe Ia
begin to contribute metals, enriching the ISM primarily in iron-
peak elements and lowering the [α/Fe] ratio.
Stars on the [α/Fe]-enhanced track have much larger vertical
scale heights than solar-[α/Fe] stars (e.g., Lee et al. 2011; Bovy
et al. 2012a, 2012b, 2012c) and make up the stellar populations
belonging to the thick disk. Nidever et al. (2014) used the
APOGEE Red Clump Catalog (Bovy et al. 2014) to analyze
the stellar distribution in the [α/Fe] versus [Fe/H] plane across
the Galactic diskand found that the high-[ α/Fe](thick disk)
sequence was similar over the radial range covered in their
analysis (5<R < 11 kpc). The thick-disk stellar populations are
in general observed to be more metal-poor andα-enhanced
andhave shorter radial scalelengths, larger vertical scale
heights, and hotter kinematics than most stars in the solar
neighborhood (e.g., Bensby et al. 2003, 2011; Allende Prieto
et al. 2006; Bovy et al. 2012c; Cheng et al. 2012a; Anders et al.
2014), although there do exist thick-disk stars with solar-[α/Fe]
abundances and supersolar metallicities (Bensby
et al. 2003, 2005, 2014; Adibekyan et al. 2011; Nidever
et al. 2014; Snaith et al. 2014). However, the exact structure of
the disk is still unknown, and it is unclear whether the disk is
the superposition of multiple components (i.e., a thick and thin
disk),the disk is a continuous sequence of stellar populations
(e.g., Ivezic et al. 2008; Bovy et al. 2012a, 2012b, 2012c),or
the structure varies with location in the Galaxy.
Meanwhile, Nidever et al. (2014) found that the position of
the locus of low-[α/Fe](thin-disk) stars depends on location
within the Galaxy
(see also Edvardsson et al. 1993), and it is
possible that in the inner Galaxy the high- and low-[α/Fe]
populations are connected, rather than distinct. Most previous
observations were confined to the solar neighborhoodand use
height above the plane or kinematics to separate between thick-
and thin-disk populations. However, kinematical selections
often misidentify stars (Bensby et al. 2014)and can remove
intermediate or transitional populations,which may bias results
(Bovy et al. 2012c).
Observations of the MDF at different locations in the Galaxy
can provide information about the evolutionary history across
the disk. The MDF has generally only been well characterized
in the solar neighborhood (e.g., van den Bergh 1962;
Nordström et al. 2004; Ak et al. 2007; Casagrande
et al. 2011; Siebert et al. 2011; Schlesinger et al. 2012) and
in the Galactic bulge (Zoccali et al. 2008; Gonzalez et al. 2013;
Ness et al. 2013). The first observations of the MDF outside of
the solar neighborhood were made using APOGEE observa-
tionsand found differences in the MDF as a function of
galactocentric radius (Anders et al. 2014). MDFs have long
been used to constrain models of chemical evolution. Early
chemical evolution models (e.g., Schmidt 1963; Pagel &
Patchett 1975) that attempted to explain the observed metal
distribution in local Gdwarfs were simple, closed-box systems
(no gas inflow or outflow) that overpredicted the number of
metal-poor stars relative to observations. This result is
commonly known as the “G-dwarf problem” (
e.g., Pagel &
Patchett 1975; Rocha-Pinto & Maciel 1996; Schlesinger et al.
2012). Solutions to the G-dwarf problem include gas inflow
and outflow (e.g., Pagel 1997); observations of the MDF led to
the realization that gas dynamics play an important role in the
chemical evolution of galaxies. However, it is not clear whether
the G-dwarf problem exists at all locations in the Galaxy, as
there have been limited observations outside of the solar circle.
Simulations and models of the chemical and kinematical
evolution of the Milky Way have become increasingly
sophisticated (e.g., Hou et al. 2000; Chiappini et al. 2001;
Schönrich & Binney 2009; Kubryk et al. 2013; Minchev et al.
2013) and attempt to explain both the chemical and dynamical
history of the Galaxy. Recent chemical evolution models (e.g.,
Hou et al. 2000; Chiappini et al. 2001) treat the chemistry of
gas and stars in multiple elements across the entire disk, rather
than just the solar neighborhood. Several simulations and
2
The Astrophysical Journal, 808:132 (18pp), 2015 August 1 Hayden et al.

models find that “inside-out” (e.g., Larson 1976; Kobayashi &
Nakasato 2011) and “upside-down” (e.g., Bournaud
et al. 2009; Bird et al. 2013) formation of the Galactic disk
reproduces observed trends in the Galaxy, such as the radial
gradient and the lower vertical scale heights of progressively
younger populations. Centrally concentrated hot old disks, as
seen in cosmological simulations, would result in a decrease in
scaleheight with radius, which is not observed. In order to
explain the presence of stars at high altitudes in the outer disk,
in an inside-out formation scenario, Minchev et al. (2015)
suggested that disk flaring of mono-age populations is
responsible. Such a view also explains the inversion of
metallicity and [α/Fe] gradients when the vertical distance
from the disk midplane is increased (e.g., Boeche et al. 2013;
Anders et al. 2014; Hayden et al. 2014). Alternatively, the
larger scale heights of older populations could be a conse-
quence of satellite mergers.
The radial mixing of gas and stars from their original birth
radii has also been proposed as an important process in the
evolution of the Milky Way disk (e.g., Wielen et al. 1996;
Sellwood & Binney 2002;Roškar et al. 2008; Schönrich &
Binney 2009; Loebman et al. 2011; Solway et al. 2012; Halle
et al. 2015). Radial mixing occurs through blurring, in which
stars have increasingly more eccentric orbits and therefore
variable orbital radii, and churning, where stars experience a
change in guiding radius or angular momentum and migrate to
new locations. However, there is much debate on the relative
strength of mixing processes throughout the disk. Recent
observations and modeling of the solar neighborhood have
suggested that the local chemical structure of the disk can be
explained by blurring alone (Snaith et al. 2014)and that
churning is not required, but see Minchev et al. (2014).
To disentangle these multiple processes and characterize the
history of the Milky Way disk, it is crucial to map the
distribution of elements throughout the disk, beyond the solar
neighborhood. This is one of the primary goals of the SDSS-III/
APOGEE survey, which observed 146,000 stars across the
Milky Way during 3 yrof operation. APOGEE is a moderately
high resolution (R ∼ 22,500) spectrograph (Wilson et al. 2012)
operating in the Hband, where extinction is 1/6 that of the V
band. This allows observations of stars lying directly in the
plane of the Galaxy, giving an unprecedented coverage of the
Milky Way disk. The main survey goals were to obtain a
uniform sample of giant stars across the disk with moderately
high resolution spectroscopy to study the chemical and
kinematical structure of the Galaxy, in particular the inner
Galaxy,where optical surveys cannot observe efficiently owing
to high extinction. The APOGEE survey provides aradial
velocity precision of ∼100 m s
−1
(Nidever et al. 2015)and
chemical abundances to within 0.1–0.2 dex for 15 different
chemical elements (Garcia-Perez A.E. 2015, in preparation),in
addition to excellent spatial coverage of the Milky Way from
the bulge to the edge of the disk.
In this paper we present results from the Twelfth Data
Release (DR12; Alam et al. 2015) of SDSS-III/APOGEE on
the distribution of stars in the [α/Fe] versus [Fe/H] plane and
their MDFs, across the Milky Way and at a range of heights
above the plane. In Section 2 we discuss the APOGEE
observations, data processing, and sample selection criteria. In
Section 3 we discuss our findings in the context of chemical
evolution models. In Section4 we present our observed results
for the distribution of stars in the [α/Fe] versus [Fe/H] plane and
MDFs.In the appendix we discuss corrections for biases due to
survey targeting, sample selection, population effects, and
errors in the [α/Fe] determination.
2. DATA AND SAMPLE SELECTION
Data are taken from DR12, which contains stellar spectra
and derived stellar parameters for stars observed during the 3
yrof APOGEE. APOGEE is one of the main SDSS-III surveys
(Eisenstein et al. 2011), which uses the Sloan Digital Sky
Survey (SDSS) 2.5 m telescope (Gunn et al. 2006) to obtain
spectra for hundreds of stars per exposure. These stars cover a
wide spatial extent of the Galaxyand span a range of
magnitudes between
H8 13.8<<
for primary science targets.
Target selection is described in detail in the APOGEE targeting
paper (Zasowski et al. 2013) and the APOGEE DR10 paper
(Ahn et al. 2014). Extinction and dereddening for each
individual star are determined using the Rayleigh–Jeans Color
Excess method (RJCE;Majewski et al. 2011), which uses Two
Micron All Sky Surveyphotometry (Skrutskie et al. 2006) in
conjunction with near-IR photometry from the Spitzer/IRAC
(Fazio & Team 2004) GLIMPSE surveys (Benjamin
et al. 2003; Churchwell et al. 2009) where available, or from
WISE (Wright et al. 2010). In-depth discussion of observing
and reduction procedures is described in Hayden et al. (2014),
the DR10 paper (Ahn et al. 2014), the APOGEE reduction
pipeline paper (Nidever et al. 2015), the DR12 calibration
paper (Holtzman et al. 2015), the APOGEE linelist paper
(Shetrone et al. 2015), the APOGEE spectral libraries paper
(Zamora et al. 2015), and the APOGEE Stellar Parameters and
Chemical Abundances Pipeline (ASPCAP;Garcia-Perez A.E.
2015, in preparation) paper.
For this paper, we select cool (T
5500
eff
<
K) main survey
(e.g., no ancillary program or Kepler field) giant stars
(
g1.0 log 3.8<<
) with signal-to-noise ratio (S/N) > 80, as
described in Table 1. Additionally, stars flagged as “Bad” as a
result of being near the spectral library grid edge(s) or having
poor spectral fits are removed. The cuts applied to the H-R
diagram for DR12 are shown in Figure 1. ASPCAP currently
has a cutoff temperature of 3500 K on the cool side of the
spectral grid (see Garcia-Perez A.E. 2015, in preparation;
Zamora et al. 2015), which could potentially bias our results
Table 1
Sample Selection
Parameter Range Notes
g
log g
1
.0 log 3.
8
<<
Select giants only
T
e
ff
T
3
500 5500
eff
<<
K Reliable temperature range
S/N S/N
80>
Required for accurate stellar parameters
ASPCAPFLAG Bits
2
3
Ï
Remove all stars flagged as bad
APOGEE_TARGET1 Bits
11, 12,Î
or 13 Select main survey targets only
3
The Astrophysical Journal, 808:132 (18pp), 2015 August 1 Hayden et al.

Frequently asked questions

Q1. What contributions have the authors mentioned in the paper "Chemical cartography with apogee: metallicity distribution functions and the chemical structure of the milky way disk" ?

The positive skewness of the outerdisk MDF may be a signature of radial migration ; the authors show that blurring of stellar populations by orbital eccentricities is not enough to explain the reversal of MDF shape, but a simple model of radial migration can do so. 

Q2. What were the first chemical evolution models?

The first chemical evolution models were simple closed-box systems, with no gas inflow or outflow, and often employed approximations such as instantaneous recycling. 

Q3. How many kpc of the outer disk do stars need to migrate to produce the observed?

Stars need to migrate at least 6 kpc to the outer disk and at least 3 kpc around the solar neighborhood to produce the observed change in skewness. 

Q4. How do the authors reproduce the change in skewness observed in the MDFs?

With the addition of churning, the authors are able to reproduce the change in skewness observed in the MDFs across the plane of the disk and in particular the change in sign around R = 9 kpc. 

Q5. What is the effect of splitting the sample into bins?

Splitting the sample into vertical and radial bins allows us to analyze the changes in the MDF across the Galaxy, but also minimizes selection effects due to the volume sampling of the APOGEE lines of sight and their target selection. 

Q6. What is the ability to trace the fossil record of the Milky Way across the disk?

The ability to resolve individual stars allows one to trace the fossil record of the Milky Way across the disk, as the stars contain the chemical footprint of the gas from which they formed. 

Q7. What is the effect of the change in the /Fe distributions with height?

The change of [α/Fe] distributions with height could be a consequence of heating of the older stellar populations or of forming stars in progressively thinner, “cooler” populations as turbulence of the early starforming disk decreases. 

Q8. What is the skew-normal distribution of the MDF in the inner Galaxy?

The authors model the initial MDF as a skew-normal distribution with a peak at 0.4+ dex in the inner Galaxy, a dispersion of 0.1 dex, and a skewness of −4; the authors assume a radial gradient of −0.1 dex kpc−1 to shift the peak of the MDFs as a function of radius, keeping the dispersion and skewness fixed. 

Q9. What is the striking feature of the stellar distribution in the solar neighborhood?

The most striking feature of the stellar distribution in the [α/Fe] versus [Fe/H] plane in the inner disk ( R3 5< < kpc) is that the separate low-[α/Fe] sequence evident in the solar neighborhood is absent—there appears to be a single sequence starting at low metallicities and high-[α/Fe] abundances, which ends at approximately solar[α/Fe] and high metallicity ([Fe/H] 0.5~ + ). 

Q10. What are the uncertainties in the spectroscopic parameters from Holtzman et?

The typical uncertainties in the spectroscopic parameters from Holtzman et al. (2015) are0.11 dex in glog , 92 K in Teff , and 0.05 dex in [Fe/H] and [α/Fe] for a star with T 4500eff = K and solar metallicity. 

Q11. What is the spread in metallicity for the very outer disk?

The spread in metallicity for the very outer disk (R 13> kpc) is small: most stars are within [Fe/H] 0.4 0.2~ - dex at all heights about the plane. 

Q12. What is the skewness of the MDFs in the outer disk?

The inner disk has a large negative skewness (−1.68± 0.12 for R3 5< < kpc;see Table 2), with a tail toward low metallicities, while the solar neighborhood is more Gaussian in shape with a slight negative skewness (−0.53± 0.04), and the outer disk is positively skewed with a tail toward high metallicities (+0.47± 0.13 for13 < R < 15 kpc). 

Q13. How close is the gradient in /H to the plane of the disk?

The observed gradient in [α/H] is extremely close to the observed gradient in [Fe/H] close to the plane of the disk ( z 0.5<∣ ∣ kpc;bottom panel of Figure 8). 

Q14. What is the trend of [/Fe] with z?

The trend of [α/Fe] with z∣ ∣ is particularly striking in the 3–5 kpc annulus, where the stars lie along the sequence expected for a single evolutionary track, but the dominant locus of stars shifts from low-[Fe/H], high-[α/Fe] at z1 2< <∣ ∣ kpc to high-[Fe/H], low-[α/Fe] at z0 0.5< <∣ ∣ kpc. 

Q15. What is the MDF distribution at z 1> kpc?

For z 1>∣ ∣ kpc (top panel of Figure 5), the MDF is uniform with a roughly Gaussian shape across all radii, although it is more strongly peaked for the very outer disk (R 13> kpc). 

Q16. How do the authors calculate the distance modulus?

The distance modulus most likely to be correct given the observed parameters and the stellar models is determined by creating a probability distribution function (PDF) of all distance moduli.