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Year:2011
TheGenesisoftheMilkyWay’sthickdiskviastellarmigration
Loebman,SR;Roškar,R;Debattista,VP;Ivezić,Ž;Quinn,TR;Wadsley,J
Abstract:Wecomparethespatial,kinematic,andmetallicitydistributionsofstarsintheMilkyWay
disk,asobservedbytheSloanDigitalSkySurveyandGeneva-CopenhagenSurvey,topredictionsmade
byN-bodysimulationsthatnaturallyincluderadialmigrationasproposedbySellwoodBinney.Inthese
simulations,starsthatmigrateradiallyoutwardfeeladecreasedrestoringforce,consequentiallytheyreach
largerheightsabovethemid-plane.Wendthatthismodelisinqualitativeagreementwithobservational
dataandcanexplainthedisk’sdouble-exponentialverticalstructureandothercharacteristicsasdueto
internalevolution.Inparticular, themodelreproducesobservationsofstarsinthetransitionregion
betweenexponentialcomponents,whichdonotshowastrongcorrelationbetweenrotationalvelocityand
metallicity.Althoughsuchacorrelationispresentinyoungstarsbecauseofepicyclicmotions,radial
migrationecientlymixesolderstarsandweakensthecorrelation. Classifyingstarsasmembersofthe
thinorthickdiskbyeithervelocityormetallicityleadstoanapparentseparationintheotherproperty,
asobserved.Wendamuchstrongerseparationwhenusing[/Fe],whichisagoodproxyforstellarage.
ThemodelsuccessisremarkablebecausethesimulationwasnottunedtoreproducetheGalaxy,hinting
thatthethickdiskmaybeaubiquitousGalacticfeaturegeneratedbystellarmigration.Nonetheless,we
cannotexcludethepossibilitythatsomefractionofthethickdiskisafossilofamoreviolenthistory,nor
canradialmigrationexplainthickdisksinallgalaxies,moststrikinglythosewhichcounterrotatewith
respecttothethindisk.
DOI:https://doi.org/10.1088/0004-637X/737/1/8
PostedattheZurichOpenRepositoryandArchive,UniversityofZurich
ZORAURL:https://doi.org/10.5167/uzh-60049
JournalArticle
AcceptedVersion
Originallypublishedat:
Loebman,SR;Roškar,R;Debattista,VP;Ivezić,Ž;Quinn,TR;Wadsley,J(2011).TheGenesisof
theMilkyWay’sthickdiskviastellarmigration.AstrophysicalJournal,737(1):8.
DOI:https://doi.org/10.1088/0004-637X/737/1/8
arXiv:1009.5997v1 [astro-ph.GA] 29 Sep 2010
Draft version October 1, 2010
Preprint typeset using L
A
T
E
X style emulateapj v. 11/10/09
THE GENESIS OF THE MILKY WAY’S THICK DISK VIA STELLAR MIGRATION
Sarah R. Loebman
1
, Rok Ro
ˇ
skar
1
, Victor P. Debattista
2,3
,
ˇ
Zeljko Ivezi
´
c
1,4
, Thomas R. Quinn
1
, and James
Wadsley
5
Draft version October 1, 2010
ABSTRACT
The separation of the Milky Way disk into a thin and thick component is supported by differences
in the spatial, kinematic and metallicity distributions of their stars. These differences have lead to
the predominant view that the thick disk formed early via a cataclysmic event and constitutes fossil
evidence of the hierarchical growth of the Milky Way. We show here , using N -bo dy simulations, how a
double-exponential vertical structure, with stellar populations displaying similar dichotomies can arise
purely through internal evolution. In this picture, stars migr ate radially, while retaining nea rly circular
orbits, as described by Sellwood & B inney (2002). As stars move outwards their vertical motions carry
them to larger heights above the mid- plane, populating a thickened component. Such stars found at
the present time in the so lar neig hborhood formed early in the disk’s history at smaller radii whe re
stars are mor e metal-poor and α-enhanced, leading to exactly the properties observed for thick disk
stars. Cla ssifying stars as memb ers of the thin or thick disk by either velocity or metallicity leads to
an apparent separation in the other property as observed. This sc enario is supported by the SDSS
observatio n that stars in the transition r egion do not s how any correlation between rotational velocity
and metallicity. Although such a correlation is present in young stars because of epicyclic motions,
the radial migration mixes stars, washing out the correlation. Using the Geneva Copenhagen Survey,
we indeed find a velocity-metallicity correlation in the younger stars and none in the older stars. We
predict a similar result when separating stars by [α/Fe]. The good qualitative agreement between our
simulation and observations in the Milky Way are especially remarkable because the simulation was
not tuned to reproduce the Milky Way, hinting that the thick disk may be a ubiquitous galaxy feature
generated by stellar migration. Nonetheless, we cannot exclude that some fraction of the thick disk
is a fo ssil of a past more violent history, nor can this scenario explain thick disks in a ll galaxies, most
strikingly those which counter-rotate with respect to the thin disk.
Subject headings: galaxies: evolution — galax ie s: spiral — galaxies: stellar content – Galaxy: solar
neighborhood – Galaxy: stellar content — stellar dynamics
1. INTRODUCTION
In the years since Gilmore & Reid (1983) first proposed
a two component s tructure to the Milky Way disk , a
large body of observational work has provided supporting
evidence for contrasting thin and thick disk attributes.
Structurally, the thin dis k scale height is shorter than
thick disk scale height (for reviews see Majewski 1993;
Buser et al. 1999; Norris 1999, a nd references therein),
and the thick disk may have a longer scale length than
the thin disk (Robin et al. 1996; Ojha 2001; Chen et al.
2001; L arsen & Humphreys 2003). K ine matically, thick
disk stars have la rger velocity dispersions and lag the net
rotation of the disk (Nissen 1995; Chiba & Beers 2000;
Gilmore et al. 2002; Soubiran et al. 2003; Parker et al.
2004; Wyse et al. 2006). Additionally, thick disk
stars are older and meta l poor relative to their thin
disk counterparts (e.g. Majewski 1993; Chiba & Beers
2000; Bochanski et al. 2007) and at a given iron a bun-
dance thick disk stars are α-enhanced (Fuhrmann
1
Astronomy Department, University of Washing-
ton, Box 351580, Seattle, WA 98195-1580, USA;
sloebman@astro.washington.edu
2
Jeremiah Horrocks Institute, U niversity of Central Lan-
cashire, Preston, PR1 2HE, UK; vpdebattista@uclan.ac.uk
3
RCUK Fellow
4
University of Zagreb, Croatia
5
Department of Physics and Astronomy, McMaster Univer-
sity, Hamilton, Ontario, L8S 4M1, Canada
1998; Prochaska et al. 2000; Tautvaiˇsien˙e et al. 2001;
Bensby et al. 2003; Feltzing et al. 2003; Mishenina et al.
2004; Brewer 2004; Bensby et al. 2005). Moreoever, thin
and thick disk attributes are no t unique to the Milky
Way but a ubiquitous featur e for late type galaxie s
(Burstein 197 9; van der Kruit & Searle 1981; Abe et al.
1999; Neeser et al. 2002; Yoachim & Dalcanton 2005,
2006; Yoa chim 2007).
Recently, several SDSS–based studies have pr ovided
further strong observational cons traints on the struc-
tural, kinematic and chemical properties of stars in the
solar cylinder. Juri´c et al. (2008, her eafter J08) used
a photometric parallax method on SDSS data to esti-
mate distances to ∼48 million stars and studied their
spatial distribution. Because SDSS provides accurate
photometry, which enables rea sonably robust distance s
(10–15%, Sesar et al. 20 08), as well as faint ma gnitude
limits (r < 22) and a large sky cover age (6500 deg
2
), J08
were able to robustly constrain the parameters o f a model
for the global spatial dis tribution of stars in the Milk y
Way. The J08 model is qualitatively similar to previ-
ous work (e.g. Bahcall & Soneir a 198 0) which identifies a
clear change of slope in the counts of disk s tars as a func-
tion of distance from the Galactic plane; this change in
slope is usually interpreted as the transition from the thin
to thick disk (Gilmore & Reid 1983; Sie gel et al. 2002).
Ivezi´c et al. (2008, hereafter I08) further extended this
2 Loebman et al.
global analysis o f SDSS data by developing a photomet-
ric metallicity estimator a nd by utilizing a large proper
motion catalog based on SDSS and Palomar Observa-
tory Sky Survey data (Munn et al. 2004). I08 studied
the dependence of the metallicity, [Fe/H] and rotational
velocity, V
φ
, of disk stars on the distance from the Galac-
tic plane and detected gradients o f both quantities over
the distance ranging from several hundred parsecs to sev-
eral kiloparsecs. Such gradients would be expected in a
thin/thick disk decomposition where the thick disk stars
are a separate populatio n defined by a bulk rotational
velocity lag and a lower metallicity compared to thos e of
the thin disk . However, such a model would also predict
a co rrelation between the metallicity and the velocity
lag, which is strongly excluded (∼7σ level) by the I08
analysis (see Figure 17, I08). In this work we turn to a
more sophisticated Galactic description — an N –body
model — to characterize stars within the SDSS volume
and solve this puzzle.
Over the pas t few decades, N –body simulations have
been use d to provide supporting evidence for three
distinct theories of thick disk formation: violent re-
laxation (Jones & Wyse 1983), substructure disruption
(Statler 1988), and heating by satellites (Quinn et al.
1993). Several works have recently redressed these ideas.
Brook et al. (2004) and Bournaud et al. (2009) formed a
thick disk in situ at hig h redshift during gas-rich mergers,
where star formation is triggered by the rapid accretion
of gas; this re sult is consistent with the thick disk for ming
through violent relaxation of the galactic potential. In
contrast, Kazantzidis et al. (2008), Villalobos & Helmi
(2008), a nd Villalobos et al. (2010) investigated sub-
structure disruption by using a cosmologically derived
satellite accr etion histo ry to perturb a Milky Way-like
disk; subhalo-disk encounters increased the scale height
of this disk at all radii effectively forming a thick disk.
Finally, Abadi et al. (2003) showed that by tidally strip-
ping/accr eting satellites, the majority of the oldest stars
in the thick disk could have formed externally r ather than
in situ.
In this work, we study a new method of forma-
tion: radial migration. Radial migra tion due to scat-
tering from transient spirals was first described by
Sellwood & Binney (2002). In this model energy and
angular momentum changes occur from interactions with
transient spiral arms, which move stars at the corotation
resonance inward or outward in radius while preserv-
ing their nearly-circula r orbits. Roˇskar et al. (2008a,b,
R08ab herea fter) studied this phenomenon in N-body
+ Smooth Particle Hydrodynamic (SPH) simulations of
disk formation, and showed that migrations are possible
on short timescales. They explored the implications of
radial mixing for stella r populations for a variety of stel-
lar systems, including the solar neighborhood. Here we
extend their work by highlighting the vertical evolution
that occurs a s a result of migration.
We note that in this paper, we are not testing the va-
lidity of the other models of formation. However, re-
cently, Sa le s et a l. (2009) proposed using the eccentr icity
of orbits of stars in the thick disk to constrain the thick
disk’s formation mechanism; they presented the eccen-
tricity distributions that result from four N-body simu-
lations: Abadi et al. (20 03), Villalobos & Helmi (2008),
R08b, and Brook et al. (2004). They found that the
distributions that result from heating, radial migration
and mergers all had a strong peak at low eccentric-
ity (ǫ ∼ 0.2 − 0.3), while the distribution that results
from accretion is centered at higher orbital e c centries
(<ǫ>∼ 0.5). Building on this, Wilson et al. (2010) stud-
ied the eccentricity of orbits of stars in the thick disk
observed in the Radial Velocity Experiment (RAVE)
(Steinmetz et al. 2006) and fo und thes e results to be in-
consistent with expecta tions for the pure accretion sim-
ulation. Ruchti et al. (2 010) also leveraged α measure-
ments from RAVE to co nc lude that the α enhancement
of the metal-poor thick disk implies that direct accretio n
of stars from dwarf galaxies did not play a major role
in the formation of the thick disk. Using SDSS DR7,
Dierickx et al. (2010) showed that the eccentricity of or-
bits of stars in the thick disk implies the thick disk is
unlikely to be fully populated by radially migrated stars.
We note that we cannot exclude that some fractio n of
the thick disk is a foss il of a pas t more violent histor y,
nor can this scenario explain thick disks in all galax ies.
However, in what follows, we show that a lar ge fraction
of the stars in the thick disk could have formed in situ
and arr ived a t their present location v ia radial migr ation.
The outline of this paper is as follows: in §2, we present
two simulations, one with substantial migration and the
other with relatively little migration. When we compa re
these two simulations we can show tha t migration can
build a thick disk as first conceived by Gilmore & Reid
(1983): a component with a scale-height larger than that
of the thin disk. In §3 we qualitatively compare the Milky
Way-like simulation (with migratio n) with the SDSS ob-
servations to show that they match each other sufficiently
well to pursue further comparison. In §4 we present a
detailed comparison between the simulation and the lo-
cal SDSS volume focusing on the reason for the lack of
correlation between V
φ
and [Fe/H]; in Appendix A we re-
consider recent observational claims concerning the lack
of correlation be tween V
φ
and [Fe/H]. In §5 we use the
simulation as a proxy for the Milky Way to show that
classifying stars as members of the thin or thick disk by
either velocity or metallicity leads to an appare nt se p-
aration in the other property as observed. In §6 we
compare our results to recent theoretical work that used
semi-analytics to investigate how the solar neighborhood
could have been shaped by radial mig ration and chem-
ical evolution effects. In §7 we explore the correlation
between [α/Fe] and age to show the diagnostic power of
[α/Fe] as a stand-in for age. Finally, in §8 we summarize
our results and c onclusions.
2. NU MERICAL SIMULATIONS
We analy ze the results of an N –body + SPH simu-
lation designed to mimic the q uie scent formation and
evolution of a Milky Way–mass galaxy following the
last major merger. The system is initialized as in
Kaufmann et al. (2007) and R08 ab and consists of a
rotating, pre ssure–supported gas halo embedded in an
NFW (Navarro et al. 1997) dark matter halo. This sim-
ulation was evolved for 10 Gyr using the parallel N –
body+SPH code , GASOLINE (Wadsley et al. 2004). As
the s imulation proceeds, the gas cools and collapses to
the center of the halo, forming a thin disk from the
inside–out. Gas is continually infa lling from the hot halo
onto the disk for the duration of the simulation. Star
Genesis of the Milky Way’s Thick Disk 3
formation and stellar feedback are modeled with sub-
grid recip es as described in Stinson et al. (2006). Impor-
tantly, the stellar feedback prescriptions include SN II,
SN Ia and AGB metal production, as well as injection
of supernova energy which impa c ts the thermodynamic
properties of the disk interstellar medium (ISM). Meta l
diffusion is calculated from a subgrid model of eddy tur-
bulence based on the loca l smoothing length and velocity
gradients (Smagorinsky 1963; Wadsley et al. 2008). The
simulation we utilize is nearly identical to R08ab (see
R08ab for further details), but with the addition of metal
diffusion (Shen et al. 2009).
No a priori assumptions about the disk’s structure
are made — its growth and the subsequent evolu-
tion o f its stellar populations are completely sponta-
neous and governed only by hydrodynamics/stellar feed-
back and gravity. Although we do not acco unt for
the full cosmological context, merging in the ΛCDM
paradigm is a higher order effect at the epochs in ques-
tion (Brook et al. 2005). Thus, o ur model galaxy lacks
some s tructural components such as a stellar halo, which
in ΛCDM is built up primarily during the merg ing pro-
cess (e.g. Bullock & Johnston 2005; Zolotov et al. 2009).
Our focus here, however, is disk evolution; by simplifying
our assumptions, we are able to use much higher resolu-
tion and more easily study the impa c t of key dyna mical
effects on observational properties of stellar populations
within the disk.
Based on such simulations, R08ab pre sented the im-
plications of stellar radial migration resulting from
the interactions of stars with transient spiral arms
(Sellwood & Binney 2 002) on the observable properties
of disk stella r populations. Radial migration efficiently
mixes stars througho ut the disk into the solar neigh-
borhood, resulting in a flattened age-metallicity rela-
tion (R08ab). Figures 1, 2, & 3 illustr ate the basic
premise of this paper — stars migrate radially and in
the process rise out of the plane over time, so many star s
are pres ently not near their birth place. Previous stud-
ies have shown (Loebman e t al. 2008; Sales et al. 2009;
Caruana 2009; Sch¨onrich & Binney 2009) that the verti-
cal evolution that re sults from radial migration ca n in-
fluence the characterization of the thick disk.
In orde r to further illustrate the importance of radial
migration within our adopted Milky Way (MW) simula-
tion, we have repeated much of our analysis on a control
case. The control simulation is a s ystem with the same
initial co nditions as the MW simulation e xcept for having
a higher angular momentum content with a dimension-
less spin parameter λ = 0.1 (Bullock et al. 2001). This
results in a more extended disk (final disk scale-length
= 5.04 kpc, versus 3.23 kpc for the MW simulation),
possibly similar to a low surface brightness galaxy; we
therefore refer to this s imulation as the LSB simulation.
Due to its lower surface density, the disk forms weaker
spirals and as a result the stellar populations at all radii
are less affected by radial mixing . When we compare mi-
gration as a function of scale-lengths, we find that there
is significantly less migra tion in the LSB galaxy than in
the MW galaxy.
The distribution of stellar mass away from the mid-
plane is strongly affected by r adial migration; this can
be seen in Figure 4, which contrasts the MW simulation
against the LSB case. Here the normalized mass den-
0.6 1.2 1.9 2.5 3.1 3.7 4.3
R
form
[scale length]
0.00
0.02
0.04
0.06
0.08
0.10
0.12
f
0.0 ≤ |z| ≤ 0.3
0.5 ≤ |z| ≤ 1.0
1.0 ≤ |z| ≤ 1.5
1.5 ≤ |z| ≤ 2.0
Figure 1. Star particles that fall within the solar cylinder at the
end of the simulation are considered here. These stars ar e broken
into four volumes by distance away fr om the mid-plane, |z|, with
low to medium to high given by black to blue to red. For compari-
son, four similar volumes from the LSB simulation with little radial
migration are over-plotted (dotted lines). For each volume, the for-
mation radius of stars is shown; in the MW simulation, away from
the mid-plane, a large fraction of the stars formed significantly in-
terior to their final location. For reference, the solar cylinder is
indicated in the shaded gray region: galactocentric radius = 2.2–
2.8 scale lengths. In the MW simulation this corresponds to 7 kpc
≤ R ≤ 9 kpc while i n the LSB simulation it corresponds to 11 kpc
≤ R ≤ 14 kpc.
0 2 4 6 8 10
Age [Gyr]
0
2
4
6
8
10
12
R
form
[kpc]
0.0 < |z| [kpc] < 0.3
0 2 4 6 8 10
Age [Gyr]
0
2
4
6
8
10
12
R
form
[kpc]
0.5 < |z| [kpc] < 1.0
0 2 4 6 8 10
Age [Gyr]
0
2
4
6
8
10
12
R
form
[kpc]
1.0 < |z| [kpc] < 1.5
0 2 4 6 8 10
Age [Gyr]
0
2
4
6
8
10
12
R
form
[kpc]
1.5 < |z| [kpc] < 2.0
Figure 2. Contour plots of the MW simulation showing the dis-
tribution of R
f orm
vs. Age for the four volumes considered in
Figure 1 with solar cylinder shaded in gray. For al l z, older stars
formed significantly interior to their final location; this net outward
movement of s tars over time is due to radial migration. Volumes
sampling the thick disk (|z| ≥ 1 kpc) are dominated by older stars
that have migrated to the solar radius from interior radii.
4 Loebman et al.
0 2 4 6 8 10
Age [Gyr]
6
8
10
12
14
16
18
R
form
[kpc]
0.0 < |z| [kpc] < 0.3
0 2 4 6 8 10
Age [Gyr]
6
8
10
12
14
16
18
R
form
[kpc]
0.5 < |z| [kpc] < 1.0
0 2 4 6 8 10
Age [Gyr]
6
8
10
12
14
16
18
R
form
[kpc]
1.0 < |z| [kpc] < 1.5
0 2 4 6 8 10
Age [Gyr]
6
8
10
12
14
16
18
R
form
[kpc]
1.5 < |z| [kpc] < 2.0
Figure 3. Same as Figure 2 but for the LSB simulation which
has little radial migration. Regardless of distance away from the
midplane, all stars originate from a roughly symmetric distribution
centered at the midpoint of the cylindr ical volume. While volumes
sampling the thick disk (|z| ≥ 1 kpc) are dominated by older stars,
these s tars are largely uninfluenced by radial migration.
0.6 ≤ R/R
d
≤ 1.2
0 1 2 3
|z| [kpc]
0.0001
0.0010
0.0100
0.1000
1.0000
ρ / ρ
0
MW
LSB
1.2 ≤ R/R
d
≤ 1.9
0 1 2 3
|z| [kpc]
0.0001
0.0010
0.0100
0.1000
1.0000
ρ / ρ
0
MW
LSB
2.2 ≤ R/R
d
≤ 2.8
0 1 2 3
|z| [kpc]
0.001
0.010
0.100
1.000
ρ / ρ
0
MW
LSB
2.8 ≤ R/R
d
≤ 3.7
0 1 2 3
|z| [kpc]
0.01
0.10
1.00
ρ / ρ
0
MW
LSB
Figure 4. Density profiles drawn from analogous regions within
the MW and LSB simulations. At larger radii, the LSB simula-
tion has a fairly flat (pure exponential) profile whereas the MW
simulation has a transition between a steep and shallow profile.
2 ≤ R [kpc] ≤ 4
0 1 2 3
|z| [kpc]
0.0001
0.0010
0.0100
0.1000
1.0000
ρ [ M
O
•
/ pc
3
]
Total
In situ
Migrated
4 ≤ R [kpc] ≤ 6
0 1 2 3
|z| [kpc]
0.0001
0.0010
0.0100
0.1000
1.0000
ρ [ M
O
•
/ pc
3
]
Total
In situ
Migrated
7 ≤ R [kpc] ≤ 9
0 1 2 3
|z| [kpc]
0.0001
0.0010
0.0100
0.1000
1.0000
ρ [ M
O
•
/ pc
3
]
Total
In situ
Migrated
9 ≤ R [kpc] ≤ 12
0 1 2 3
|z| [kpc]
0.0001
0.0010
0.0100
0.1000
1.0000
ρ [ M
O
•
/ pc
3
]
Total
In situ
Migrated
Figure 5. Simultaneous fits to the vertical density profile in the
MW simulation for radial bins: R = 2 − 4 kpc, R = 4 − 6 kpc,
R = 7 − 9 kpc, R = 9 − 12 kpc. While the radial bin sampling the
smallest radii is best fit by a double exponential function, all other
bins are better fit by a double sech
2
function. Best fit parameters
are given in Table 1. Thin, thick, and total curves shown in purple,
orange and green repectively; the vertical dotted line marks the
intersection between thin and thick disk components. Red and
cyan points represent stellar mass density that has migrated more
than 2 kpc or less than 2 kpc respectivel y from radius of formation.
sity distribution within four analogo us cylindric al vol-
umes drawn from a variety of radii are presented. At
larger radii, the steepness of the profiles are q uite dif-
ferent; the LSB simulation has a constant slope while
the MW simulation shows a transition from a steep to
a shallow density distribution. Thus the MW simula-
tion cannot be characterized by a single exponential or
sech
2
component in the vertical dir ection, as we show ex-
plicity in the following Section and Figure 5. It is this
double-component nature which first led to the identifi-
cation of the thick disk (Gilmore & Reid 19 83); we have
thus shown that this feature need re present nothing more
than internal evolution of the Milky Way.
3. COMPARISON OF SIMULATIONS WITH SDSS
In the following section, we compare SDSS observa-
tions with the MW simulation to demonstrate its use ful-
ness as a model for understanding the Milky Way thick
disk. Here we study the stellar mass distribution, rota-
tional velocity and metallic ity as functions of distance
from the Galactic plane, |z|, and galactocentric cylindri-
cal radius, R. We draw qualitative comparisons betwe en
the data sets by examining their ma ss weighted metallic-
ity and kinematic distributions in this R–|z| space.
The observed Milky Way disk is best fit by a 2-
component model that is exp onential both in the R and
z directions (see Table 10, bias-corrected results, J08).
The top panel of Figure 6 shows the mass weighted den-
sity distribution of the entire MW simulation at its final
timestep. This distribution is in qualita tive agreement in
both the R and z directions with J08 for up to ∼2.5 kpc
![Figure 11. Results of a simple kinematic cut on the local sample: R = 7−9 kpc, |z| = 0.0−0.3 kpc. Top left: Distribution of [α/Fe] for the entire local sample. The distribution is continuous, not bimodal. The mean [α/Fe] for [Fe/H] bins, shown in yellow, qualitatively matches observational data (Bensby et al. 2005). When the sample is decomposed by age, the weighted mean value of old stars is clearly α-enhanced relative to the younger populations. Top right: Toomre diagram. Stars with VLSR ≥ −70 km/s are assigned thin disk membership, while stars with −150 ≤ VLSR < −70 km/s are considered thick disk. All other stars are assigned halo membership in agreement with Nissen & Schuster (2009). Bottom left: the resulting weighted mean distributions for the thin and thick disk populations. The thick disk is α-enhanced relative to the thin disk at low [Fe/H]. Bottom right: stars from just the shaded [Fe/H] cut in the bottom left plot. Stars falling within the “thick” disk zone have a higher fraction of old stars relative to the overall population. These old stars are α-enhanced. Thus kinematically dividing the stars locally biases the sample to an older, α-enhanced population.](/figures/figure-11-results-of-a-simple-kinematic-cut-on-the-local-5bma5y6k.webp)
![Figure 12. Thin and thick disk membership assigned based on [α/Fe]; the sample includes star particles within R = 7 − 11 kpc, |z| = 0.3− 2.0 kpc. Top left: mass weighted contour plot of [α/Fe] vs. Age in logrithmically spaced bins (low to medium to high: black to green to orange). Overplotted for reference is the dividing line [α/Fe] = −0.1; stars with [α/Fe] ≥ −0.1 are considered αenhanced and are assigned thick disk membership. Clearly the majority of these stars are quite old. Stars with [α/Fe] < −0.1 are considered thin disk members and sample a wide range of ages. Counterclockwise from top right to bottom left: resulting thin and thick disk trends. Notably, the thick disk stars are metal poor with no gradient in R and lag the rotation of the thin disk stars. Despite the appearance of these trends here, there is no distinct thick disk population in the MW simulation.](/figures/figure-12-thin-and-thick-disk-membership-assigned-based-on-a-u36xdjri.webp)
![Figure 15. Left panel: ∼ 16, 000 stars selected from SDSS DR7 spectroscopic sample with g − r = 0.2 − 0.6 from z = 1.0 − 1.5 kpc. The stellar number density is shown as the color-coded map (low to high: blue to red) and by the contours. Triangles are the median Vφ for bins of [Fe/H], and squares are the median [Fe/H] for bins of Vφ. Spagna et al. (2010) results are overplotted with a dashed blue line for reference. Right panel: Analogous to plot in right panel but for full photometric sample: ∼ 124, 000 stars with g − r = 0.2 − 0.6 and z = 1.0− 1.5 kpc, selected from the meridional plane defined by l ∼ 0 ◦ or l ∼ 180 ◦ (See Section 3.2 in Bond et al. 2010).](/figures/figure-15-left-panel-16-000-stars-selected-from-sdss-dr7-116u25mk.webp)
![Figure 6. Top: Mass density distribution in galactocentric coordinates of the entire MW simulation. The colors scale logrithmically with density in each bin. Overplotted is the SDSS field of view (|b| > 30◦). Middle & Bottom: Mass-weighted mean [Fe/H] and Vφ values as mapped onto the R–|z| plane. For a color box to be plotted we required a minimum of 50 star particles.](/figures/figure-6-top-mass-density-distribution-in-galactocentric-1zropppb.webp)
![Figure 10. Vφ vs. [Fe/H] for stars from the Geneva Copenhagen Survey (GCS), which samples stars within 100 pc of the Sun. We have repeated the analysis we presented in Figure 9 for all GCS stars flagged as non-binary. Top panel: when the sample is considered as a whole, there is no discernable trend. Middle row: the sample split into two broad age bins: Age = 0-4 Gyr and Age = 4-15 Gyr. Left middle panel, the young stars show a trend, while in the right middle panel, the old stars are not correlated. This result agrees with the prediction from the MW simulation and strongly motivates a history of radial mixing in the solar neighborhood. Bottom panels: histogram of overall age distribution, with shaded region corresponding to the data sampled in the panel above it.](/figures/figure-10-vph-vs-fe-h-for-stars-from-the-geneva-copenhagen-2py3a1z3.webp)