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Title
The structure and dynamical evolution of the stellar disc of a simulated Milky Way-mass
galaxy
Permalink
https://escholarship.org/uc/item/9sw9r8gc
Journal
Monthly Notices of the Royal Astronomical Society, 467(2)
ISSN
0035-8711
Authors
Ma, X
Hopkins, PF
Wetzel, AR
et al.
Publication Date
2017-05-11
DOI
10.1093/mnras/stx273
Peer reviewed
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University of California
Mon. Not. R. Astron. Soc. 000, 1–14 (0000) Printed 16 August 2016 (MN L
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X style file v2.2)
The Structure and Dynamical Evolution of the Stellar Disk of a
Simulated Milky Way-Mass Galaxy
Xiangcheng Ma,
1
∗ Philip F. Hopkins,
1
Andrew R. Wetzel,
1,2,3
Evan N. Kirby,
4
Daniel Anglés-Alcázar,
5
Claude-André Faucher-Giguère,
5
Dušan Kereš
6
and Eliot Quataert
7
1
TAPIR, MC 350-17, California Institute of Technology, Pasadena, CA 91125, USA
2
Carnegie Observatories, 813 Santa Barbara Street, Pasadena CA 91101, USA
3
Department of Physics, University of California, Davis, CA 95616, USA
4
Department of Astrophysics, MC 249-17, California Institute of Technology, Pasadena, CA 91125, USA
5
Department of Physics and Astronomy and CIERA, Northwestern University, 2145 Sheridan Road, Evanston, IL 60208, USA
6
Department of Physics, Center for Astrophysics and Space Sciences, University of California at San Diego, 9500 Gilman Drive, La Jolla, CA 92093, USA
7
Department of Astronomy and Theoretical Astrophysics Center, University of California Berkeley, Berkeley, CA 94720, USA
Draft version 16 August 2016
ABSTRACT
We study the structure, age and metallicity gradients, and dynamical evolution using a cosmo-
logical zoom-in simulation of a Milky Way-mass galaxy from the Feedback in Realistic En-
vironments project. In the simulation, stars older than 6 Gyr were formed in a chaotic, bursty
mode and have the largest vertical scale heights (1.5–2.5 kpc) by z = 0, while stars younger
than 6 Gyr were formed in a relatively calm, stable disk. The vertical scale height increases
with stellar age at all radii, because (1) stars that formed earlier were thicker ‘at birth’, and
(2) stars were kinematically heated to an even thicker distribution after formation. Stars of the
same age are thicker in the outer disk than in the inner disk (flaring). These lead to positive
vertical age gradients and negative radial age gradients. The radial metallicity gradient is neg-
ative at the mid-plane, flattens at larger disk height |Z|, and turns positive above |Z| ∼ 1.5kpc.
The vertical metallicity gradient is negative at all radii, but is steeper at smaller radii. These
trends broadly agree with observations in the Milky Way and can be naturally understood
from the age gradients. The vertical stellar density profile can be well-described by two com-
ponents, with scale heights 200–500 pc and 1–1.5 kpc, respectively. The thick component is
a mix of stars older than 4 Gyr which formed through a combination of several mechanisms.
Our results also demonstrate that it is possible to form a thin disk in cosmological simulations
even with strong stellar feedback.
Key words: galaxies: abundances – galaxies: evolution – galaxies: formation – cosmology:
theory
1 INTRODUCTION
Gilmore & Reid (1983) first discovered that the vertical stellar den-
sity profile in the solar neighborhood in the Milky Way (MW) can
be described by two exponential components with scale heights
∼ 300pc and ∼ 1450pc, respectively, and identified them as the
thin disk and the thick disk. Such a two-component profile is also
seen in external edge-on disk galaxies (e.g. Yoachim & Dalcan-
ton 2006
; Comerón et al. 2011, 2012). However, it remains unclear
whether the thin and thick disks are two distinct components or one
single structure that varies continuously above the disk plane.
Several mechanisms have been proposed to explain the for-
∗ E-mail:
xchma@caltech.edu
mation of the thick disk, despite the ambiguity of whether it is a
discrete component or not. Some popular scenarios, all motivated
by theory or observations, include: (1) kinematic heating from a
pre-existing thin disk during minor mergers (e.g.
Quinn et al. 1993;
Kazantzidis et al. 2008; Hopkins et al. 2008; Villalobos & Helmi
2008; Purcell et al. 2009; Qu et al. 2011), (2) star formation at high
redshift from chaotic gas accretion during hierarchical assembly
(Brook et al. 2004) or in a turbulent, gas-rich disk (Bournaud et al.
2009; Haywood et al. 2013), (3) radial migration of stars from the
inner disk to the outer disk (Schönrich & Binney 2009b; Loebman
et al. 2011
), and (4) accretion of stars from SMC-like satellites
(Abadi et al. 2003). Nonetheless, it is still unclear which mecha-
nism (or combination of mechanisms) is responsible for the forma-
tion of thick disks in the MW and other galaxies.
c
0000 RAS
arXiv:1608.04133v1 [astro-ph.GA] 14 Aug 2016
2 X. Ma et al.
Thanks to spectroscopic surveys of stars in the MW, such
as RAVE (
Steinmetz et al. 2006), SEGUE (Yanny et al. 2009),
APOGEE (
Allende Prieto et al. 2008), and Gaia-ESO (Gilmore
et al. 2012), one can now combine three-dimensional position, ve-
locity, and chemical abundance information for large samples (for
a recent review, see Rix & Bovy 2013). Many groups have claimed
that there are two distinct sub-populations, named α-rich and α-
poor stars, as revealed by the gap in the [α/Fe]–[M/H] plane
([M/H] represent total stellar metallicity relative to solar abun-
dance) or the bimodality of the [α/ Fe] distribution at fixed [M/H].
These two populations are attributed to the thick and thin disks
(e.g. Adibekyan et al. 2013; Bensby et al. 2014; Anders et al. 2014;
Nidever et al. 2014; Mikolaitis et al. 2014; Kordopatis et al. 2015).
However, some samples show a much less significant gap in the
[α/Fe]–[M/H] plane than others (e.g. Mikolaitis et al. 2014; Kor-
dopatis et al. 2015), or no gap at all (e.g. Boeche et al. 2014). Also,
in some cases, the bimodality appears in certain α elements but dis-
appears in others (e.g. Bensby et al. 2014; Mikolaitis et al. 2014).
The bimodality, if real, implies that the MW may have a special
formation history (e.g. Nidever et al. 2014). Also, it is not clear
whether such feature is common in other galaxies.
Many groups have confirmed a negative radial metallicity gra-
dient with a slope d[M/H]/dR ∼ −0.06dexkpc
−1
in MW stars
near the disk plane (height |Z| < 0.5kpc), with d[M/H]/dR grad-
ually flattening above the mid-plane and turning positive at and
above |Z| > 1.5kpc (e.g.
Cheng et al. 2012; Boeche et al. 2013,
2014; Anders et al. 2014; Hayden et al. 2014; Mikolaitis et al.
2014). A negative vertical metallicity gradient is also found in the
MW disk from the mid-plane to |Z| ∼ 3kpc, but the slope varies
dramatically in the literature (e.g. Carrell et al. 2012; Boeche et al.
2014
; Hayden et al. 2014). Hayden et al. (2014) found that the verti-
cal metallicity gradient is steeper at inner Galactocentric radii than
at outer radii.
Nevertheless, using the data at a single epoch alone is not suf-
ficient to identify the mechanism for MW thick disk formation.
Cosmological simulations are useful for this problem as they al-
low one to trace the evolution of the galaxy as well as understand
the underlying implications in the observational data. For example,
Stinson et al. (2013) presented a cosmological simulation that pro-
duces a disk galaxy with similar mass and structure to the MW; they
found that older stars tend to have larger scale heights but shorter
scale lengths than younger stars and supported the observationally
motivated conjecture in Bovy et al. (2012) that mono-abundance
populations (stars with certain [Fe/H] and [α / Fe]) are good prox-
ies for single age populations. They found that the thick disk was
formed kinematically hot in their simulated galaxy. However, Mi-
randa et al. (2016) pointed out that the metallicity gradients in the
disk strongly rely on the treatment of (simplified) feedback in these
simulations and only certain recipes produced similar behavior to
the MW in their simulations. Therefore, it is important to include
realistic models of the interstellar medium (ISM) and stellar feed-
back to understand the formation of galactic disks.
In this paper, we study a simulation from the Feedback in Re-
alistic Environments project (FIRE;
Hopkins et al. 2014)
1
, which
produces a disk galaxy with stellar mass similar to the MW at z = 0,
to study the structure and abundance pattern of stars in the galactic
disk. We present the structure and dynamical evolution of the stel-
lar disk, compare the metallicity gradients and their variation with
recent observations, and show how the metallicity gradients can
1
http://fire.northwestern.edu
Table 1. A list of symbols used in this paper.
Symbol Description
z Redshift
t
lookback
Lookback time
age Stellar age at z = 0
X, Y, Z Cartesian coordinates
R Galactocentric radius
|Z| Height from the mid-plane
[M/H] Total metallicity (relative to solar)
[Fe/H] Fe abundance (relative to solar)
[Mg/Fe] Mg to Fe abundance ratio (relative to solar)
be understood from the disk structure. The FIRE project is a suite
of cosmological zoom-in simulations with detailed models of the
multi-phase ISM, star formation, and stellar feedback taken directly
from stellar evolution models and it produces reasonable galaxy
properties broadly consistent with observations from z = 0–6, such
as the stellar mass–halo mass relation (
Hopkins et al. 2014; Feld-
mann et al. 2016), the Kennicutt–Schmidt law (M. Orr, in prepara-
tion), neutral hydrogen covering fractions around galaxies at both
low and high redshift (Faucher-Giguère et al. 2015, 2016; Hafen
et al. 2016), the stellar mass–metallicity relation (Ma et al. 2016),
mass-loading factors of galactic winds (Muratov et al. 2015), metal
budgets and CGM metal content (Muratov et al. 2016), galaxy
sizes (El-Badry et al. 2016), and the population of satellite galaxies
around MW-mass galaxies (Wetzel et al. 2016). We briefly summa-
rize the simulation in Section 2, present our main results in Section
3, discuss our findings in Section 4, and conclude in Section 5.
We adopt a standard flat ΛCDM cosmology with cosmological
parameters H
0
= 70.2km s
−1
Mpc
−1
, Ω
Λ
= 0.728, Ω
m
= 1− Ω
Λ
=
0.272, Ω
b
= 0.0455, σ
8
= 0.807 and n = 0.961, broadly consistent
with observations (e.g. Hinshaw et al. 2013; Planck Collaboration
et al. 2014).
2 SIMULATION AND METHODS
In this work, we perform a case study using galaxy m12i, a disk
galaxy with mass comparable to the Milky Way at z = 0, from
the FIRE project. We pick this simulation because it has been
well-studied in previous work (e.g.
Hopkins et al. 2014; Mura-
tov et al. 2015, 2016; El-Badry et al. 2016) and has a morphol-
ogy that is closest to the MW in our suite. A detailed descrip-
tion of the simulations, numerical recipes, and physics included
is presented in
Hopkins et al. (2014, and references therein). We
briefly summarize their main features here. The simulation is run
using GIZMO (Hopkins 2015), in P-SPH mode, which adopts a La-
grangian pressure-entropy formulation of the smoothed particle hy-
drodynamics (SPH) equations that improves the treatment of fluid-
mixing instabilities (
Hopkins 2013).
The cosmological ‘zoom-in’ initial conditions for m12i are
adopted from the AGORA project (Kim et al. 2014). The zoom-
in region is about one Mpc in radius at z = 0. The initial particle
masses for baryons and dark matter are m
b
= 5.7 × 10
4
M
⊙
and
m
dm
= 2.8 × 10
5
M
⊙
, respectively. The minimum force softening
lengths for gas and star particles are ǫ
gas
= 14pc and ǫ
star
= 50pc
(Plummer-equivalent). The force softening lengths for the gas par-
ticles are fully adaptive (
Price & Monaghan 2007). The most mas-
sive halo in the zoom-in region has a halo mass of M
halo
= 1.4 ×
10
12
M
⊙
and a stellar mass around M
∗
= 6 × 10
10
M
⊙
at z = 0.
In our simulation, gas follows a molecular-atomic-ionized
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The Stellar Disk of a Simulated MW-Mass Galaxy 3
Table 2. Lookback time vs redshift.
Lookback Time [t
lookback
, in Gyr] 0 1 2 3 4 5 6 7 8 10
Redshift [z] 0 0.076 0.162 0.258 0.369 0.497 0.649 0.834 1.068 1.812
cooling curve from 10–10
10
K, including metallicity-dependent
fine-structure and molecular cooling at low temperatures and high-
temperature metal-line cooling followed species-by-species for 11
separately tracked species (H, He, C, N, O, Ne, Mg, Si, S, Ca,
and Fe; see Wiersma et al. 2009a). At each timestep, the ioniza-
tion states and cooling rates are determined from a compilation of
CLOUDY runs, including a uniform but redshift-dependent photo-
ionizing background tabulated in Faucher-Giguère et al. (2009),
and approximate models of photo-ionizing and photo-electric heat-
ing from local sources. Gas self-shielding is accounted for with a
local Jeans-length approximation, which is consistent with the ra-
diative transfer calculations in
Faucher-Giguère et al. (2010).
We follow the star formation criteria in Hopkins et al. (2013)
and allow star formation to take place only in locally self-
gravitating, self-shielding/molecular gas which also exceeds a hy-
drogen number density threshold n
th
= 5cm
−3
. Stars form on the
local free-fall time when the gas meets these criteria and there is no
star formation elsewhere. Once a star forms, it inherits the metallic-
ity of each tracked species from its parent gas particle. Every star
particle is treated as a single stellar population with known mass,
age, and metallicity, assuming a
Kroupa (2002) initial mass func-
tion (IMF) from 0.1–100M
⊙
. All the feedback quantities, includ-
ing ionizing photon budgets, luminosities, supernovae (SNe) rates,
mechanical luminosities of stellar winds, etc., are then directly tab-
ulated from the stellar population models in STARBURST99 (
Lei-
therer et al. 1999). We account for several different stellar feedback
mechanisms, including (1) local and long-range momentum flux
from radiative pressure, (2) energy, momentum, mass and metal in-
jection from SNe and stellar winds, and (3) photo-ionization and
photo-electric heating. We follow
Wiersma et al. (2009b) and ac-
count for metal production from Type-II SNe, Type-Ia SNe, and
stellar winds using the metal yields in Woosley & Weaver (1995),
Iwamoto et al. (1999), and Izzard et al. (2004), respectively. The
rates of Type-II and Type-Ia SN are separtately computed from
STARBURST99 and following Mannucci et al. (2006), respectively.
We note that the Mg yield from Type II SN in
Woosley &
Weaver (1995) is ∼ 0.4 dex lower than typical values in more re-
cent models (e.g. Nomoto et al. 2006). Therefore, we manually add
0.4 dex to all Mg abundances in our simulation to compare with
observations more accurately. This will have little effect on global
galaxy properties, since Mg is not an important coolant (it is simply
a “tracer species”). Also, the total number of Type Ia SNe calcu-
lated from
Mannucci et al. (2006) is lower than that derived from
Maoz et al. (2010) by a factor of a few for a stellar population older
than 1 Gyr; this may lead to predictions of lower Fe, but we cannot
simply renormalize the Fe abundances in the simulation. We do not
include a sub-resolution metal diffusion model in the simulation;
all mixing above the resolution scale is explicitly resolved.
We use the Amiga Halo Finder (AHF;
Knollmann & Knebe
2009) to identify halos in the simulated box, where we adopt the
time-dependent virial overdensity from Bryan & Norman (1998).
In this work, we only study the most massive (hence best-resolved)
halo in the zoom-in region, which hosts a disk galaxy of very sim-
ilar properties to the MW at z = 0. At each epoch, we define the
galactic center at the density peak of most stars and find the stellar
half-mass radius as the radius within which the stellar mass equals
to a half of the stellar mass within 0.1 virial radius. Then the Z-axis
is defined to be aligned with the total angular momentum of the
gas within 5 stellar half-mass radii. In this paper, we will primarily
focus on the stellar component. We do not perform a kinematic de-
composition for the stellar content, but take all star particles in the
analysis to form an unbiased sample.
A list of symbols used in this paper and their descriptions are
presented in Table
1. In the rest of this paper, we always mean the
z = 0 age when we quote stellar ages and will predominantly use
lookback time (t
lookback
) when referring to an epoch in the simula-
tion. In Table 2, we list the conversion between lookback time and
redshift at selected epochs for reference.
3 RESULTS
3.1 General Picture
At high redshifts, the galaxy accretes gas rapidly and undergones
multiple mergers, producing violent, bursty star formation, until a
final minor merger finished at z ∼ 0.7 (corresponding to a look-back
time of t
lookback
∼ 6Gyr). Since then, a calm, stable gas disk was
formed and maintained, with stars forming in the disk at a nearly
constant rate (∼ 7M
⊙
yr
−1
) regulated by stellar feedback.
The top panel in Fig. 1 illustrates the stellar morphologies at
z = 0 for stars in the galaxy in six different z = 0 age intervals. The
top and bottom panels show the stellar surface density viewed face-
on and edge-on, respectively. The thickness increases with stellar
age, from a thin disk-like structure to more spheroidal morphol-
ogy, broadly consistent with the MW (
Bovy et al. 2012) and other
simulations (e.g. Stinson et al. 2013). On the other hand, the radial
morphology first shrinks with increasing age, but then becomes less
concentrated for ages greater than 8 Gyr, leaving intermediate-age
stars (age ∼ 6Gyr) the most radially concentrated. This is in con-
trast with the systems studied in Bovy et al. (2012) and Stinson
et al. (2013) where the oldest stars have the smallest scale lengths.
This directly owes to a minor merger in the simulation around look-
back time t
lookback
∼ 6Gyr (z ∼ 0.7), which drove a concentrated
nuclear starburst.
The middle panel in Fig.
1 shows the stellar morphologies for
the same stars shown in the top panel (divided into the same z = 0
age intervals), but viewed at the epoch when they just formed (la-
beled by look-back time). In other words, we trace the galaxy back
to these epochs, and show the young stars in the main progeni-
tor galaxy at that time. Stars older than 8 Gyr were born to be a
chaotic, non-disk-like structure. For illustrative purposes, we also
show gas morphologies at the same epochs in the bottom panel in
Fig.
1. During the early stage of galaxy assembly when the stellar
mass was sufficiently low, this galaxy experienced bursty, chaotic
star formation (Sparre et al. 2015). Starbursts drive bursts of gas
outflows with high efficiency (Muratov et al. 2015), and the bursty
outflows in turn modify the potential and cause radial migration
of stars, resulting in radial expansion and quasi-spherical morphol-
ogy for stars older than 8 Gyr (El-Badry et al. 2016). A gas disk is
formed by t
lookback
∼ 6 Gyr (z ∼ 0.7). Below t
lookback
. 6 Gyr, star
formation takes place in a relatively calm mode, with stars forming
in a relatively stable disk at a rate self-regulated by feedback, and
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0000 RAS, MNRAS 000,
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4 X. Ma et al.
Figure 1. Top: Morphology of stars in different age intervals at z = 0. The thickness increases with stellar age, but the scale length first decreases with stellar
age in 0 < age < 6Gyr and then increases in age > 8Gyr, leaving stars of age ∼ 6Gyr the most radially concentrated (owing to a merger-driven nuclear
starburst about this time). Middle: Morphology of the same stars from each z = 0 age interval in the top panel, but viewed at the epoch when they just formed
(labeled by lookback time) in the galaxy progenitor. Stars younger than 6 Gyr at z = 0 were formed in a relatively calm disk. Stars older than 8 Gyr at z = 0
were formed in a violent, bursty mode and relax by z = 0. Bottom: Morphology of gas, viewed at the same epochs as in the middle panel. At early time, the
gas is highly irregular and chaotic. By t
lookback
∼ 6Gyr (z ∼ 0.7), the gas eventually formed a disk.
there are no longer large scale outflows (
Muratov et al. 2015). Hay-
ward & Hopkins (2015) proposed an analytic model and argued
that such bursty-to-calm transition is expected in massive galaxies
at late times, due to the change of ISM structure at low gas frac-
tions.
We estimate the fraction of stars that comes from mergers or
tidally disrupted satellites, i.e. stars formed outside the main pro-
genitor galaxy, using the particle tracking technique developed by
and presented in D. Anglés-Alcázar et al. (in preparation). We find
that only . 10% of the stellar mass in the z = 0 galaxy was formed
ex situ and this contribution is only significant far above the galac-
tic plane (|Z| & 5kpc). For example, during the last minor merger
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