# The Atari Disk, a Metal-Poor Stellar Population in the Disk System of the
Milky Way

Mohammad K. Mardini Kavli IPMU (WPI), UTIAS, The University of Tokyo, Kashiwa,
Chiba 277-8583, Japan  Institute for AI and Beyond, The University of Tokyo
7-3-1 Hongo, Bunkyo-ku, Tokyo 113-8655, Japan  Anna Frebel Department of
Physics and Kavli Institute for Astrophysics and Space Research, Massachusetts
Institute of Technology, Cambridge, MA 02139, USA  Anirudh Chiti Department of
Astronomy $\&$ Astrophysics, University of Chicago, 5640 S Ellis Avenue,
Chicago, IL 60637, USA  Kavli Institute for Cosmological Physics, University
of Chicago, Chicago, IL 60637, USA  Yohai Meiron SciNet High Performance
Computing Consortium, University of Toronto, 661 University Ave., Toronto, ON
M5G 1M1, Canada  Kaley V. Brauer Department of Physics and Kavli Institute for
Astrophysics and Space Research, Massachusetts Institute of Technology,
Cambridge, MA 02139, USA  Xiaowei Ou Department of Physics and Kavli Institute
for Astrophysics and Space Research, Massachusetts Institute of Technology,
Cambridge, MA 02139, USA Mohammad K. Mardini<EMAIL_ADDRESS>
###### Abstract

We have developed a chemo-dynamical approach to assign 36,010 metal-poor
SkyMapper stars to various Galactic stellar populations. Using two independent
techniques (velocity and action space behavior), $Gaia$ EDR3 astrometry, and
photometric metallicities, we selected stars with the characteristics of the
”metal-weak” thick disk population by minimizing contamination by the
canonical thick disk or other Galactic structures. This sample comprises 7,127
stars, spans a metallicity range of $-3.50<$$[\mathrm{Fe}/\mathrm{H}]$
$<-0.8$, and has a systematic rotational velocity of $\langle
V_{\phi}\rangle=154$ km s-1 that lags that of the thick disk. Orbital
eccentricities have intermediate values between typical thick disk and halo
values. The scale length is $h_{R}=2.48^{+0.05}_{-0.05}$ kpc and the scale
height is $h_{Z}=1.68^{+0.19}_{-0.15}$ kpc. The metallicity distribution
function is well fit by an exponential with a slope of $\Delta\log{\rm
N}/\Delta[\mathrm{Fe}/\mathrm{H}]=1.13\pm 0.06$. Overall, we find a
significant metal-poor component consisting of 261 SkyMapper stars with
$[\mathrm{Fe}/\mathrm{H}]$$<-2.0$. While our sample contains only eleven stars
with $[\mathrm{Fe}/\mathrm{H}]$ $\lesssim-3.0$, investigating the JINAbase
compilation of metal-poor stars reveals another 18 such stars (five have
$[\mathrm{Fe}/\mathrm{H}]$$<-4.0$) that kinematically belong to our sample.
These distinct spatial, kinematic and chemical characteristics strongly
suggest this metal-poor, phase-mixed kinematic sample to represent an
independent disk component with an accretion origin in which a massive dwarf
galaxy radially plunged into the early Galactic disk. Going forward, we
propose to call the metal-weak thick disk population as the Atari disk, given
its likely accretion origin, and in reference to it sharing space with the
Galactic thin and thick disks.

Galaxy: formation – Galaxy: structure – Galaxy: disk – Galaxy: kinematics and
dynamics – Galaxy: abundances

††journal: ApJ

##  1 Introduction

The existence of chemo-dynamically distinguishable components of the Galactic
disk was first proposed several decades ago, in which the “thick disk” was
introduced as a distinct component of the Milky Way disk (e.g., Gilmore &
Reid, 1983). Many studies have investigated in detail the nature of this
component, which is considered the “canonical thick disk” by determining its
age (older than 8 Gyr; Kilic et al., 2017), velocity dispersion
($\sigma_{z}\approx 35\,$km s-1 Norris, 1993), metallicity distribution
(peaking at $[\mathrm{Fe}/\mathrm{H}]$
$\approx-0.5$111$[\mathrm{Fe}/\mathrm{H}]$=
$\log_{10}(N_{\text{Fe}}/N_{\text{H}})_{\star}-\log_{10}(N_{\text{Fe}}/N_{\text{H}})_{\sun}$;
Kordopatis et al. 2011), and relative abundance ([X/Fe]) trends (see; Bensby
et al., 2005). In addition, a seemingly more metal-poor
($[\mathrm{Fe}/\mathrm{H}]$ $<-0.8$) stellar population within this canonical
thick disk was identified (Norris et al., 1985; Morrison, 1990), and termed
the “metal-weak thick disk” (MWTD) (e.g., Chiba & Beers, 2000).

While various properties of the canonical thick disk could be conclusively
determined, the metal-weak thick disk remained insufficiently studied, likely
due to its somewhat elusive nature. For example, several open questions remain
regarding its nature – what are the upper and lower $[\mathrm{Fe}/\mathrm{H}]$
bounds characterizing the metal-weak thick disk? How did it form and evolve?
Is it mainly the metal-poor tail of, and hence associated with, the canonical
thick disk, or actually a separate component of the Milky Way’s disk? Several
clues from recent chemo-dynamical analyses Carollo et al. (2019); An & Beers
(2020) suggested the metal-weak thick disk as being independent from the the
canonical thick disk, with plausibly distinct spatial, kinematic, chemical,
and age distributions.

Moreover, recent reports of very and extremely metal-poor stars being part of
the Milky Way disk system has provided further insights into, and questions
about, the formation of the Galactic disk system and the Milky Way itself
(Sestito et al., 2019; Carter et al., 2020; Cordoni et al., 2020; Di Matteo et
al., 2020; Venn et al., 2020). The existence of these low-metallicity stars in
the disk could be a signature of an early component of this disk system,
assembled from a massive building block(s) entering the proto-Milky Way.
Alternatively, these stars might have formed in the early disk system, which
was later dynamically heated.

More generally, investigating thick disk origin scenarios through metal-poor
stellar samples of the disk may shed light on the nature and origin of the
metal-weak thick disk; for instance, in gauging whether metal-weak thick disk
stars have consistent behavior(s) or an implied origin that aligns with stars
belonging to the canonical thick disk. In this paper, we implement several
approaches using kinematics derived from the Gaia mission (Gaia Collaboration
et al., 2016, 2020) and photometric metallicities (Chiti et al., 2020, 2021a)
obtained from using public SkyMapper DR2 data (Onken et al., 2020) to select a
clean and representative sample of metal-poor stars of the metal-weak thick
disk.

While addressing to what extent the metal-weak thick disk could be viewed as a
component distinct from the canonical thick disk to learn about its early
formation and evolution, we found that it is indeed characterizable as a
distinct spatial, kinematic and chemical stellar component. While it appears
independent of the thick disk, this disk component remains described by its
low-metallicity stellar content, as originally envisioned with the description
of “metal-weak thick disk”. To account for the different nature of this
component, we propose to call it the Atari disk (with Atari 辺り meaning “in the
neighborhood” or “nearby” in Japanese), in reference to it sharing close space
with the Galactic thin and thick disks. This paper explores a full
characterization of the nature of the Atari disk which appears to have an
accretion origin in which a massive dwarf galaxy plunged into the early
Galactic disk.

##  2 Sample Selection and Quality Assessment

To build a representative sample of Atari disk/MWTD stars, we applied the
following procedure. We used the photometric metallicity catalog presented in
Chiti et al. (2021a), which provides metallicities
($[\mathrm{Fe}/\mathrm{H}]$) for $\sim 280,000$ relatively bright (g
$\leqslant 17$) and cool (0.35 $<$ $g-i$ $<$ 1.20) giants using metallicity-
sensitive photometry from SkyMapper DR2 (Onken et al., 2020). We then limited
the sample to $g-i>0.65$ and random metallicity uncertainties $<0.5$ dex,
following Chiti et al. (2021b), to ensure a high-quality sample of photometric
metallicities. We cross-matched this sample with the early third data release
of the Gaia mission (Gaia EDR3, Gaia Collaboration et al., 2020; Lindegren et
al., 2020a) to collect five-parameter astrometric solutions (sky positions:
$\alpha$, $\delta$, proper motions: $\mu_{\alpha}\cos\delta$, $\mu_{\delta}$,
and parallaxes: $\varpi$). For sources typical in our sample (e.g., brighter
than G = 17 mag), Gaia EDR3 provides meaningfully more accurate astrometric
measurements relative to Gaia DR2. For instance, the parallax errors
($\Delta\varpi$) in our sample improve by $20\%$ and proper motion
uncertainties improve by a factor of two.

In addition to these improvements, Lindegren et al. (2020a) introduced several
quality cuts for the selection of reliable astrometric solutions. We thus
apply the following restrictions based on the Gaia EDR3 quality flags which
reduces our sample to 169,530 stars:

  * •

astrometric_excess_noise ($<$ 1 $\mu$as): Higher values might indicate that
the astrometric solution for the target has failed and/or that the star is in
a multiple-system for which the single object solution is not
reliable222Without filtering on the astrometric excess noise, artefacts might
present (see Appendix C of Lindegren et al., 2018).. This also accounts for
the fact that our metallicity technique may fail for binaries.

  * •

Parallax$\\_$over$\\_$error ($\geqslant$ 5): Ensures reliable distance
measurements (i.e., 20% uncertainty or better).

For reference, typical uncertainties in the parallaxes and proper motions of
the resulting sample of stars are 0.01 $\mu$as and 0.02 $\mu$as yr-1,
respectively.

To calculate the full space motions of our sample, line-of-sight radial
velocities (RV) are required. About $\sim$7 million stars have RV measurements
in the $Gaia$ DR2 catalog which is similar to what is available in Gaia EDR3.
Yet only $\sim 19\,\%$ of our sample have any of these RV measurements. We
apply an additional quality cut (dr2_radial_velocity_error $<3.0$ km s-1) to
conservatively select stars with reliable RV values. This results in a sample
of 28,714 stars. To further increase the size of our sample, we collected
additional high-quality RV data from other surveys. We acquired 311, 1581,
771, and 4905 unique measurements from the APOGEE DR16, LAMOST DR6, RAVE DR5,
and GALAH DR3 surveys, respectively (Majewski et al., 2017; Cui et al., 2012;
Kunder et al., 2017; Buder et al., 2021). In case of stars having multiple
spectroscopic RV measurements, we choose to keep the ones with the highest
S/N. The final sample of our stars with available RV measurements increases to
36,010 stars after including these datasets.

We followed Lindegren et al. (2020b) by assuming that additional parallax zero
point ($\varpi_{zp}$) corrections are required for each star. These
corrections utilize the magnitude, color, and ecliptic latitude of each source
to compute an individual $\varpi_{zp}$ correction for each star in our sample.
For our sample, $\varpi_{zp}$ ranges from $-0.047$ to $0.004$ $\mu$as, as
shown in the upper panel of Figure 1. We obtained corrected parallaxes
($\varpi_{corr}$) by subtracting the estimated $\varpi_{zp}$ from the $Gaia$
EDR3 parallaxes ($\varpi_{corr}=\varpi-\varpi_{zp}$).

Figure 1: Top panel: Distribution of our calculated parallax zero points for
our final sample of 36,010 stars with available RV measurements. Bottom panel:
Calculated parallax distances with the zero-point correction (black dots),
without the zero-point correction (gray dots), and the Bailer-Jones et al.
(2021) values (blue dots) as a function of the mean value distances calculated
using a space density prior. The blue solid line represents the one-to-one
relation.

Stellar distances derived from directly inverting these corrected parallaxes
($d=1/\varpi$) should principally be reliable and not introduce additional
biases (e.g., Mardini et al., 2019a, b). However, as an additional check, we
calculated the distance of each star in our sample by implementing a Monte
Carlo simulation with an exponentially decreasing space density prior as
presented in Bailer-Jones et al. (2018), which we label “SDP” distances333At
the time we started this project, the catalog in Bailer-Jones et al. (2021)
was not public.. For this, we generated 10,000 realizations for each star
assuming a normal distribution with $\varpi$ as the central value and the
dispersion given by $\Delta\varpi$. We adopt the mean value as our final
distance estimate. The lower panel of Figure 1 shows a direct comparison
between distances calculated by inverting the parallax, our SDP approach, and
the distances in Bailer-Jones et al. (2021). For the parallax distances, we
show two versions, one obtained without the zero-point correction, and one
after the zero-point correction was applied.

Out to 3 kpc, all three distance measurements agree reasonably well. Beyond
that, the un-corrected parallax distances are overestimated (the effect is
prominent from 1-8 kpc) compared to SDP distances, with the effect becoming
worse at the largest distances. However, the corrected parallax distances show
excellent agreement with the SDP distances. We adopt the SDP distances for our
entire sample, since they are more statistically vetted, though we note that
the differences between those distances and the corrected parallax distances
are minor. Table 1 then lists $Gaia$ source ID, velocities, SDP distances, and
orbital actions for each star of our final sample.

Table 1: Stellar Parameters and $Gaia$ Astrometric Solutions

source_id | parallax |  $\mu_{\alpha}$ $cos(\delta)$ | $\mu_{\delta}$ | RV | l | b | dSDP | $[\mathrm{Fe}/\mathrm{H}]$ | Lz | Jr | Jz
---|---|---|---|---|---|---|---|---|---|---|---
| (mas) | (mas yr-1) | (mas yr-1) | (km s-1) | (deg) | (deg) | (kpc) | (dex) | (kpc km s-1) | (kpc km s-1) | (kpc km s-1)
2334983060942097664 | 0.671 | 2.330 |  $-$28.582 | 70.27 | 37.245 |  $-$78.457 | 1.49 |  $-$0.86 | 542.99 | 389.25 | 192.81
4918304837496677248 | 0.304 | 4.711 |  $-$0.954 | 53.08 | 314.997 |  $-$56.947 | 3.31 |  $-$0.79 | 1305.19 | 26.08 | 163.45
4901413310941027072 | 1.125 | 32.894 |  $-$1.159 | 119.69 | 312.286 |  $-$52.664 | 0.89 |  $-$1.12 | 1015.84 | 158.48 | 198.71
2421111311440455168 | 0.198 |  $-$2.679 |  $-$9.637 |  $-$104.37 | 80.127 |  $-$71.531 | 5.09 |  $-$3.20 | 607.15 | 696.21 | 236.33
2422492847800684416 | 0.300 |  $-$0.500 |  $-$23.563 |  $-$110.44 | 83.613 |  $-$70.002 | 3.36 |  $-$2.42 |  $-$607.64 | 753.16 | 219.27
2339756040919188480 | 0.257 | 5.320 |  $-$7.972 | 69.20 | 47.902 |  $-$77.903 | 3.93 |  $-$1.25 | 605.90 | 238.43 | 356.76
4991401092065999360 | 0.376 | 0.444 | 3.777 | 20.18 | 328.375 |  $-$68.950 | 2.67 |  $-$0.81 | 2081.24 | 131.16 | 145.21
2340071806914929920 | 0.517 |  $-$4.974 |  $-$34.741 |  $-$97.15 | 50.676 |  $-$77.698 | 1.96 |  $-$1.97 |  $-$215.55 | 884.75 | 90.11
4995919432020493440 | 0.475 |  $-$2.472 |  $-$1.622 |  $-$34.00 | 333.978 |  $-$71.668 | 2.11 |  $-$0.89 | 1867.50 | 54.88 | 102.31
2341853840385868288 | 0.320 | 5.335 |  $-$19.603 |  $-$110.72 | 62.991 |  $-$76.206 | 3.15 |  $-$1.74 |  $-$508.89 | 376.26 | 137.58
2314830593353777280 | 0.727 | 30.731 |  $-$7.730 |  $-$18.87 | 13.964 |  $-$78.469 | 1.38 |  $-$0.92 | 852.38 | 467.33 | 36.53
4994799132751744128 | 0.354 | 0.902 |  $-$4.096 |  $-$4.87 | 331.310 |  $-$70.548 | 2.84 |  $-$0.88 | 1411.96 | 37.25 | 127.50
4688252950170144640 | 0.437 | 22.078 |  $-$2.191 |  $-$28.16 | 307.226 |  $-$41.562 | 2.29 |  $-$1.06 | 1303.86 | 427.46 | 60.41
2320839596198507648 | 0.604 | 5.558 |  $-$11.909 | 9.12 | 14.965 |  $-$78.575 | 1.66 |  $-$1.05 | 1118.50 | 145.25 | 49.47
2340104929702744192 | 0.185 |  $-$1.568 |  $-$12.358 |  $-$59.60 | 51.845 |  $-$77.765 | 5.44 |  $-$1.34 |  $-$49.71 | 827.14 | 429.74
4901401907804117632 | 0.693 | 43.595 |  $-$24.514 | 7.91 | 312.082 |  $-$52.667 | 1.44 |  $-$1.39 |  $-$19.81 | 874.88 | 94.39
2340079091179498496 | 0.732 |  $-$12.163 |  $-$11.067 | 27.42 | 50.690 |  $-$77.917 | 1.38 |  $-$0.93 | 1792.91 | 178.37 | 47.83

Note. — Parallax is the corrected parallax based on Lindegren et al. (2020b).
$d_{\text{SDP}}$ is the mean value of the 10,000 realizations and
$[\mathrm{Fe}/\mathrm{H}]$ adopted from Chiti et al. (2021a). The complete
version of Table 1 is available online only. A short version is shown here to
illustrate its form and content. Distance and actions are rounded to two
digits, but are given at full numerical precision in the online table.

##  3 Derivation of Kinematic Parameters

###  3.1 Position and Velocity Transformation

We transform Galactic longitude ($l$), Galactic latitude ($b$), and distance
to the Sun ($d$) to rectangular Galactocentric coordinates ($X,Y,Z$) using the
following coordinate transformations:

$\displaystyle X=R_{\odot}-d\,\cos(l)\,\cos(b)$ $\displaystyle
Y=-d\,\sin(l)\,\cos(b)$ (1) $\displaystyle Z=d\,\sin(b),$

where the Sun is located at R${}_{\odot}=8.178\pm 0.013$ kpc from the Galactic
center (Gravity Collaboration et al., 2019); $X$ is taken to be oriented
toward $l$=0∘, $Y$ toward $l$=90∘, and $Z$ toward the north Galactic pole.

We transform $\mu_{\alpha}\cos\delta$, $\mu_{\delta}$, and RV measurements to
rectangular Galactic ($U,V,W$) velocities with respect to the Local Standard
of Rest (LSR). $U$ is oriented toward the Galactic center, $V$ in the
direction of Galactic rotation, and $W$ toward the North Galactic pole. We
adopt the peculiar motion of the Sun ($U_{\odot}=11.1\pm 0.72$ km s-1,
$V_{\odot}=12.24\pm 0.47$ km s-1, and $W_{\odot}=7.25\pm 0.36$ km s-1) from
Schönrich et al. (2010), and a maximum height of $z_{\odot}=20.8\pm 0.3$ pc of
the Sun (Bennett & Bovy, 2019) above the plane. We take VLSR = $220$ km s-1
from Kerr & Lynden-Bell (1986)444Using more recent values (e.g., 232.8 $\pm$
3.0 km s-1; McMillan 2017) did not produce large discrepancies in the Galactic
component classifications/membership. However, using such higher LSR value
would shift the $<V_{\phi}>$ by 10 km s-1, which might create some confusion
for the reader once we compare our calculated $<V_{\phi}>$ with literature
values calculated using LSR = 220 km s-1.

We transform $U,V,W$ to velocities in cylindrical Galactocentric coordinates
($V_{R},V_{\phi},V_{z}$) using the following coordinate transformations:

$\displaystyle V_{R}=U\cos(\phi)+(V+V_{rot})\sin(\phi)$ $\displaystyle
V_{\phi}=(V+V_{rot})\cos(\phi)-U\sin(\phi)$ (2) $\displaystyle V_{z}=W$

Where $\cos$ ($\phi$) = $X/\sqrt{X{{}^{2}}+Y{{}^{2}}}$, $V_{rot}$ is the
circular velocity of the LSR, $\sin$ ($\phi$) =
$Y/\sqrt{X{{}^{2}}+Y{{}^{2}}}$, and objects with V${}_{\phi}>0$ km s-1 are
retrograde.

###  3.2 Orbital Parameters

We used galpy and a scaled version of MWPotential2014 potential (Bovy, 2015)
to derive orbital parameters (rperi, rapo, and Zmax) for each star. The
modified MWPotential2014 contains (i) a potential based on a virial mass of
$M_{200}=1.4\times 10^{12}\,M_{\odot}$ instead of a canonical, shallower NFW
profile, and (ii) a concentration parameter ($c=8.25$) that matches the
rotation curve of the Milky Way. This modification helps overcome an issue of
erroneously identifying unbound stars, a known issue of the original
MWPotential2014 potential.

We define the total orbital energy as
$E=(1/2)\mbox{\boldmath$v$}^{2}+\Phi(\mbox{\boldmath$x$})$ and set $E=0$ at a
very large distance from the Galactic center. We define the eccentricity as
$e=(r_{\mathrm{apo}}-r_{\mathrm{peri}})/(r_{\mathrm{apo}}+r_{\mathrm{peri}})$
and the vertical angular momentum component as $L_{z}=R\times V_{\phi}$ (see
Mackereth & Bovy, 2018, for more details). The distance from the Galactic
center (cylindrical radius) is set by $R=\sqrt{X^{2}+Y^{2}}$. We calculate
these orbital parameters based on the starting point obtained from the
observations via a Markov Chain Monte Carlo sampling method, assuming normally
distributed input parameters around their observed values. We generate 10,000
realizations based on the observed input for each star to obtain medians and
standard deviations of all kinematic parameters and to infer their values and
associated uncertainties. We note that we use these orbital properties in all
of the remaining Sections in the paper except in Section 4.1, where we follow
a separate approach to assign stars to their Galactic components.

##  4 Identification of the Metal-Weak Thick Disk/Atari Disk and other
Galactic Components

The Galactic thick disk has been extensively studied as part of learning about
the formation and evolution of the Milky Way system. Previous studies
(beginning with Gilmore & Reid 1983 and the many others over the last several
decades) all selected member stars assuming the thick disk to be a one-
component, single population. However, it has long been suspected (e.g.,
Norris et al. 1985) that a small portion of this canonical thick disk might
actually be a separate, more metal-poor component that was eventually termed
the “metal-weak thick disk” (Chiba & Beers, 2000). It was found that it has a
mean rotational velocity $\langle V_{\phi}\rangle\,\sim 150$ km s-1 (e.g.,
Carollo et al., 2019). This presents a notable lag compared to the rotational
velocity of the canonical thick disk with $\langle V_{\phi}\rangle\,\sim 180$
km s-1 (e.g., Carollo et al., 2019). Yet, more details remained outstanding to
fully characterize this elusive body of metal-poor disk stars.

Beers et al. (2014) suggested specific criteria to select MWTD stars, i.e.
$Z_{max}\leqslant 3$ kpc and $-1.8\leqslant$
$[\mathrm{Fe}/\mathrm{H}]$$\leqslant-0.8$. More recently Naidu et al. (2020)
also suggested a MWTD selection criteria, namely $-2.5\leqslant$
$[\mathrm{Fe}/\mathrm{H}]$$\leqslant-0.8\land(0.25<\rm{[\alpha/Fe]}<0.45)\land\
(J_{\phi}/\sqrt{J_{\rm{\phi}}^{2}+J_{\rm{z}}^{2}+J_{\rm{R}}^{2}}<-0.5)$. The
chosen lower metallicity bounds aim to avoid possible contamination with the
metal-poor halo. This prevents exploration of the potential existence of
extremely low-metallicity stars typically associated with the halo within the
MWTD (hereafter Atari). If the Atari disk has an accretion origin, it is
principally expected that at least some extremely metal-poor stars should have
been brought in from the early evolution of the progenitor.

Another selection has also been suggested by Carollo et al. (2019), based on
enhanced $\alpha$-abundances and an angular momentum of L${{}_{z}}\sim 1200$
${\rm kpc}$ km s-1 (the less-prograde group in their Figure 1(a)) to
characterize the Atari disk. However, using angular momentum as sole
discriminator can only select stars within a given radial bracket as Lz varies
as a function of Galactic radius $R$ (due to a roughly constant rotational
velocity throughout the outer Galactic parts). For instance, for a sample
restricted to the solar vicinity around R$\sim$8 kpc, and using the suggested
circular angular velocity of V${}_{\phi}=150$ km s-1, the resulting angular
momentum is Lz = $1200$ ${\rm kpc}$ km s-1. But for a more distant sample,
e.g. at $3<$R$<5$ kpc, then Lz peaks at between $462$ and $770$ ${\rm kpc}$ km
s-1 (see Figure 2).

Figure 2: Distribution of the angular momenta of our final SMSS Atari disk
sample for different Galactic radii (R) cuts. The distributions have the same
x-axis range to allow visual comparisons of the shift of the peak of the Lz
distributions between different R bins. The selection procedure for this
sample is explained in Section 4.1 and 4.2.

These different selection approaches show that it remains difficult to cleanly
select Atari disk samples given that candidate stars have very similar
chemical and kinematic properties to those of the canonical thick disk. In the
following, we thus explore a different identification process to characterize
the Atari disk, based on two different techniques (space velocities and
behavior in action space) with the aim of selecting a representative, clean
sample. We start by identifying stars in the thick disk using both of these
methods, and then apply metallicity cut to isolate the Atari disk sample. This
approach returns a sample of stars with kinematic properties in line with what
was previously identified as the MWTD and thus allows us to more firmly
establish the properties of this elusive Galactic component, including its
low-metallicity member stars.

###  4.1 Galactic Space Velocities Approach

In order to select the traditional thin disk, thick disk and halo components,
we adopt the kinematic analysis method presented in Bensby et al. (2003) that
assumes the Galactic space velocities to have Gaussian distributions defined
as follows:

$\displaystyle f(U,V,W)=k\cdot\textrm{exp}($
$\displaystyle-\frac{(V_{\textrm{LSR}}-V_{\textrm{asym}})^{2}}{2\sigma_{V}^{2}}$
$\displaystyle-\frac{W_{\textrm{LSR}}^{2}}{2\sigma_{W}^{2}}-\frac{U_{\textrm{LSR}}^{2}}{2\sigma_{U}^{2}})$
(3)

where

$\displaystyle k=\frac{1}{(2\pi)^{3/2}\sigma_{U}\sigma_{V}\sigma_{W}}$

The expressions $\sigma_{U}$, $\sigma_{V}$, and $\sigma_{W}$ denote the
characteristic dispersions of each Galactic velocity component. The
$V_{\textrm{asym}}$ denotes the asymmetric drift. We adopt these values from
Table 1 in Bensby et al. (2003).

To calculate the relative likelihood for a given star of being a member of a
specific Galactic population, we take into account the observed number
densities (thin disk $X_{D}=0.8649$, thick disk $X_{TD}=0.13$, and halo
$X_{H}=0.0051$) in the solar neighborhood vicinity (which we assume to be $\pm
3$ kpc from the Sun) as reported in Jurić et al. (2008). Therefore, the
relative probabilities for the thick disk-to-thin disk (TD/D) and thick disk-
to-halo (TD/H) ratios are defined as follows:

$\displaystyle\textrm{TD/D}=\frac{X_{\textrm{TD}}\cdot
f_{\textrm{TD}}}{X_{\textrm{D}}\cdot f_{\textrm{D}}}$
$\displaystyle\textrm{TD/H}=\frac{X_{\textrm{TD}}\cdot
f_{\textrm{TD}}}{X_{\textrm{H}}\cdot f_{\textrm{H}}}$

Following Eqs. 4.1 and 4.1, we assign every star that has a membership
probability of TD/D $>2.0$ to the Galactic thick disk, while stars with TD/D
$<0.5$ are assigned to the Galactic thin disk. Furthermore, we exclude all
stars with TD/H $<10.0$ from the thick disk sample to minimize any possible
contamination with halo stars. Our selection results in 10,588 thick disk
stars, 2,571 thin disk stars, and 15,096 halo stars. Figure 3 shows a Toomre
diagram of all these Galactic components, with typical halo stars having
$v_{{\rm tot}}>180\,{\rm km\,s^{-1}}$, and thick disk stars having $70\,{\rm
km\,s^{-1}}<v_{{\rm tot}}<180\,{\rm km\,s^{-1}}$. We note that discarding
these low TD/H stars produces the small gap between the distributions of the
thick disk (red) and halo (yellow) samples in Figure 3.

Figure 3: Toomre diagram for our halo, thick disk, and thin disk stars in
yellow, red, and gray points, respectively. Blue dashed curves denote $v_{{\rm
tot}}=\sqrt{U_{{\rm LSR}}+V_{{\rm LSR}}+W_{{\rm LSR}}}=70$ and $180\,{\rm
km\,s^{-1}}$.

###  4.2 Orbital Properties Approach

In the previous subsection, we have identified thick disk stars by selecting
its highly likely members (high relative probabilities) according to stellar
velocities. Here, we develop another method to identify the traditional
Galactic components based on the probability distribution functions of the
action integrals of our sample, following the procedures presented in Piffl et
al. (2014) and Posti et al. (2018).

The mass-normalized distribution function (DF) of the stellar halo is assumed
to have the following form:

$\displaystyle
f_{\mathrm{halo}}(J_{r},J_{z},L_{z})=f_{0}\left[1+\frac{J_{r}+J_{z}+|L_{z}|}{J_{0}}\right]^{\beta_{*}}$
(5)

where $f_{0}\approx
0.09\,\mathrm{M}_{\odot}\mathrm{Gyr}^{3}\,\mathrm{kpc}^{-6}$ denotes a
normalization constant that results in a total stellar halo mass555We note
that adopting different total mass estimates (e.g., $1.3\times 10^{9}$ M⊙;
Mackereth & Bovy, 2020) would not change our halo membership assignment. of
$M_{\mathrm{halo}}=5\times 10^{8}\,\mathrm{M}_{\odot}$. The constant
$J_{0}=511\,\mathrm{kpc}^{2}\,\mathrm{Gyr}^{-1}$ controls the core in the
center of the stellar halo, and the power law index $\beta_{*}=-4$ is chosen
to set a reasonable density profile in the solar neighbourhood.

Most of the stellar mass is assumed to lie within the thin and thick disk
components, and follows quasi-isothermal DFs (Binney, 2010) with the basic
form

$\begin{split}f_{\mathrm{disk}}(J_{r},J_{z},L_{z})=\frac{\Omega\Sigma\nu}{2\pi^{2}\sigma_{r}^{2}\sigma_{z}^{2}\kappa}\,[1+\tanh(L_{z}/L_{0})]\,\times\\\
\exp(-\kappa J_{r}/\sigma_{r}^{2}-\nu J_{z}/\sigma_{z}^{2})\end{split}$ (6)

$\Omega$ is the circular frequency, $\kappa$ and $\nu$ are the radial and
vertical epicycle frequencies, respectively, of a planar circular orbit with
angular momentum $L_{z}$ (these quantities are related to the potential
through its spatial derivatives, see Chapter 3.2.3 of Binney & Tremaine 2008).
The surface density $\Sigma$ and the velocity dispersions ($\sigma_{r}$ and
$\sigma_{z}$) are similarly functions of $L_{z}$, as they depend on the radius
of a planar circular orbit in the potential. We adopt
L${}_{0}=10\,\mathrm{kpc\,km\,s^{-1}}$ assuming that L0 should not be bigger
than the typical angular momentum of a star in the bulge/bar. We then derive
separate forms of DFs for each the thin and thick disk component through
different adopted forms of the parameters (e.g., in $\sigma_{r}$,
$\sigma_{z}$), exactly following Piffl et al. (2014).

These DFs are calculated using the parameters given in Binney & Sanders
(2016)666It is worth noting that adopting different literature parameters can
meaningfully change the relative fraction of Galactic thin disk vs. thick disk
stars. These are the best fitting parameters given the assumed forms of the
DFs, and other assumptions related to the kinematics of RAVE DR1 stars
(Steinmetz et al., 2006) and the resulting mass distribution. The mass
distribution has five components: thin and thick stellar disks, a gas disk, a
flattened stellar bulge, and a spherical dark matter halo (the stellar halo is
neglected due to its relatively low mass), exactly following the form in Piffl
et al. (2014). We calculated the potential by numerically solving the Poisson
equation given the mass distribution, and we then were able to evaluate the
DFs for every J. In the case of the thin disk, $\sigma_{r}$ and $\sigma_{z}$
are assumed to additionally depend on time (the velocity-dispersion functions
increase with stellar age), and the DF is evaluated through a weighted time
integration (again, following Piffl et al. 2014).

Note also that an additional order-unity multiplicative term in the quasi-
isothermal DF is found by Binney (2010). It is not used here as that term is
needed to control the asymmetry of probabilities with respect to the direction
of rotation (sign of $L_{z}$) that is not constrained by Piffl et al. (2014).
Instead, Piffl et al. (2015) use a refined way to calculate the quasi-
isothermal DFs by iteratively inputting a newly calculated potential from the
DF back into Equation (6) until convergence is achieved.

In order to evaluate each of the three DFs for each star in our sample, the
actions have to be calculated. For internal consistency of this method, we use
the same potential that was used to derive the disk DFs. Accordingly, we use a
spherically symmetric ad-hoc approximation:

$\displaystyle\Phi_{\mathrm{approx}}(r)=-\Phi_{0,\mathrm{fit}}\frac{r_{\mathrm{fit}}}{r}\left[1-\frac{1}{\left(1+r/r_{\mathrm{fit}}\right)^{\beta_{\mathrm{fit}}-3}}\right]$
(7)

This corresponds to the analytical potential of a $\beta$-model presented in
Zhao (1996), where $\Phi_{0,\mathrm{fit}}=2.08\times
10^{6}\,\mathrm{kpc}^{2}\>\mathrm{Gyr}^{-2}$,
$r_{\mathrm{fit}}=6.63\,\mathrm{kpc}$, and $\beta_{\mathrm{fit}}=3.148$. The
approximate potential is accurate to within 6% everywhere inside the virial
radius. The actions are calculated using the formulae in Binney & Tremaine
(2008, chapter 3.5.2)

Finally, the probability to find a star in a phase space volume
$\mathrm{d}^{3}\bm{J}$ around $\bm{J}_{i}$ is proportional to the value of the
DF at this point divided by the total mass of the component. Therefore,
relative probabilities are:

$\displaystyle\mathrm{TD/D}=\frac{f_{\mathrm{thick}}(\bm{J}_{i})/M_{\mathrm{thick}}}{f_{\mathrm{thin}}(\bm{J}_{i})/M_{\mathrm{thin}}}$
(8)

and

$\displaystyle\mathrm{TD/H}=\frac{f_{\mathrm{\mathrm{thick}}}(\bm{J}_{i})/M_{\mathrm{thick}}}{f_{\mathrm{\mathrm{halo}}}(\bm{J}_{i})/M_{\mathrm{halo}}}$
(9)

where $M_{\mathrm{thin}}=2.86\times 10^{10}\>\mathrm{M}_{\odot}$,
$M_{\mathrm{thick}}=1.17\times 10^{10}\>\mathrm{M}_{\odot}$, and
$M_{\mathrm{halo}}=5\times 10^{8}\,\mathrm{M}_{\odot}$.

Using this approach and the same probability thresholds as in the previous
section results in the selection of 15,521 thick disk stars, 3,278 thin disk
stars, and 15,289 halo stars. These results are in good agreement; for
example, the two methods select the main bulk (more than $\sim 87\%$) of each
Galactic component obtained by the other selection technique in Section 4.1.
To construct a clean Atari disk sample, we then adopt an inclusion method by
first selecting all thick disk stars that are common to both selection
methods. Then, we only include stars with photometric
$[\mathrm{Fe}/\mathrm{H}]$$<-0.8$, following the upper limit of the
metallicity criteria in Beers et al. (2014) and Naidu et al. (2020) to isolate
the Atari disk. This results in a sample of 7,127 stars, which we hereby refer
to as the Atari sample. We find that 261 stars in our Atari disk sample have
$[\mathrm{Fe}/\mathrm{H}]$ $\leq-2.0$.

We decided to further assess the quality of our Atari disk sample via an
independent check of our selection procedure, based on the spatial
distribution of our Atari disk sample. We first considered the Zmax
distribution of the sample to identify any outliers (stars with high Zmax)
that can plausibly be associated with the halo. The halo becomes more
pronounced at Z${}_{max}>3$ kpc, while the thin disk is confined to
Z${}_{max}<0.8$ kpc. The vast majority of our Atari disk sample lies in the
range of $0.8\leq$ Z${}_{max}\leq 3$ kpc which suggests that this sample
predominantly includes objects not belonging to the halo or thin disk but
rather in between, and thus more consistent with the thick disk.

As a second check, we then computed orbital histories for the past 10 Gyr for
all stars following Mardini et al. (2020) to further validate their stellar
membership to the Atari disk. Again, the vast majority of stars have orbital
properties similar to that of the canonical thick disk. This agrees with what
was suggested by the Zmax values, that contamination from the metal-poor halo
or thin disk is low.

We do find that 439 stars in our sample of 7,127 Atari disk stars lie outside
of the 0.8 kpc $\leq$ $Z_{max}\leq 3.0$ kpc range. We find that the long-term
orbits of these stars largely reflect thick disk characteristics, i.e., their
orbital energies of E $<-0.9$ km2 s-2, eccentricity of $0.3<$ e $<$ 0.5, and
distances of $r_{\mathrm{apo}}<5$ kpc very much align with thick disk
kinematics. Only 137 stars of these 439 outlier stars have orbital histories
not consistent with the thick disk. We do, however, find that all these stars
have putative thick disk membership via evidenced by their TD/D ratios, as
derived in Sections 4.1 and 4.2, ranging from $10$ to $10^{5}$ and from $10$
to $10^{8}$, respectively.

We thus conclude that our Atari disk sample is clean at the 98% level, given
the 137/7127 stars that do not have orbital histories consistent with thick
disk-like motions. Accordingly, at most relatively few stars with halo-like or
thin disk-like kinematics are coincidentally selected by our technique.
Considering this a representative sample of the Atari disk, we now assess
various characteristics to describe this elusive Galactic component.

###  4.3 Simple Atari disk star selection recipe

The bulk of our Atari disk sample has unique kinematic parameters unassociated
with the general properties of the canonical thick disk. For example, the
canonical thick disk is known to have a rotational velocity $V_{\phi}\approx
180$ km s-1, which lags the VLSR by $\sim 40$ km s-1. But our Atari disk
sample has rotational velocity $V_{\phi}=154$ km s-1. Also, $\sim 20\%$ of our
Atari disk sample have orbital eccentricities above the typical range of
orbital eccentricities reported in the literature for the canonical thick disk
(see Table 2).

Given the complex and involved nature of our selection procedures in Sections
4.1 and 4.2, we also attempted to develop a simplified procedure that would
allow the selection of Atari disk stars from other existing and future stellar
samples with more ease. We suggest the following. Stars that fulfil the
criteria

$[\mathrm{Fe}/\mathrm{H}]$$\ <-0.8\ \land\ Z_{max}<3.0\ \land\
(J_{\phi}/\sqrt{J_{\rm{\phi}}^{2}+J_{\rm{z}}^{2}+J_{\rm{R}}^{2}}<-0.98)\
\land\ (0.3<e<0.6)\ \land\ (140<V_{\phi}<160)$

will be Atari disk stars with high likelihood, albeit not yield an all-
encompassing sample of Atari disk stars. Applying these criteria to our
initial SMSS sample (36,010 stars), we find that 84% of the stars recovered
from our simple selection are also in the Atari disk sample. We investigated
the nature of the remaining 16% of stars found with the simple selection
recipe. Our calculated membership probabilities suggest equal probability of
thin and halo of these contaminants.

##  5 Properties of the Atari disk

In this Section, we aim to establish the kinematic properties of the Atari
disk using our representative sample as selected in the previous section.
Specifically, we investigate the scale length, scale height, and correlations
between several variables (e.g., metallicity, eccentricity, rotational
velocity) to characterize the nature of this component. Table 2 lists our
derived properties of the Atari disk, along with those of other galactic
populations for comparison.

Table 2: Orbital properties of the Galactic thin disk, thick disk, and inner
halo

Parameter | unit | Thin disk | Thick disk | Inner halo | Atari disk
---|---|---|---|---|---
$h_{R}$ | (kpc) | 2.6aaStars that have too large uncertainties in their Gaia EDR3 astrometric data to be useful.  \- 3.0bbfootnotemark:  | 2.0bbfootnotemark:  \- 3.0ccfootnotemark:  |  $\cdots$ | 2.48 $\pm$ 0.05
$h_{Z}$ | (kpc) | 0.14ddfootnotemark:  \- 0.36eefootnotemark:  | 0.5eefootnotemark:  \- 1.1eefootnotemark:  |  $\cdots$ | 1.68${}^{+0.19}_{-0.15}$
$<V_{\phi}>$ | (km s-1) | 208eefootnotemark:  | 182ggfootnotemark:  | 0fffootnotemark:  | 154 $\pm$ 1
Zmax | (kpc) |  $<0.8$hhfootnotemark:  |  $0.8$ \- $3.0$ggfootnotemark:  |  $>3.0$ggfootnotemark:  |  $<$ 3.0
e |  $\cdots$ |  $<0.14$ggfootnotemark:  | 0.3 - 0.5ggfootnotemark:  |  $>$ 0.7ggfootnotemark:  | 0.30 - 0.7

††footnotetext: References are as follows: (a): Jurić et al. 2008; (b): Li &
Zhao 2017; (c): Li et al. 2018; (d): Sanders & Binney 2015; (e): Recio-Blanco
et al. 2014; (f): Carollo et al. 2010; (g): Lee et al. 2011; (h): Anders et
al. 2014.

###  5.1 Scale Length

Measurements of the scale length ($h_{R}$) and scale height ($h_{Z}$) are
important to trace the structure, size, mass distribution, and radial
luminosity profile of the Galactic disk components (e.g., Dehnen & Binney,
1998). In order to calculate $h_{R}$ and $h_{Z}$ of our Atari disk sample, we
solve the fundamental collisionless Boltzmann equation of axisymmetric
systems, which is expressed as the following (see equation 4.12; Binney &
Tremaine, 2008):

$\displaystyle\frac{\partial f}{\partial t}$
$\displaystyle+v_{R}\frac{\partial f}{\partial
R}+\frac{v_{\phi}}{R^{2}}\frac{\partial f}{\partial\phi}+v_{z}\frac{\partial
f}{\partial z}-\left(\frac{\partial\Phi}{\partial
R}-\frac{v_{\phi}^{2}}{R^{3}}\right)\frac{\partial f}{\partial v_{R}}$
$\displaystyle-\frac{\partial\Phi}{\partial\phi}\frac{\partial f}{\partial
v_{\phi}}-\frac{\partial\Phi}{\partial z}\frac{\partial f}{\partial v_{z}}=0,$
(10)

where $f$ is the number of objects in a small volume, and $\Phi$ is the
gravitational potential. It is then convenient to derive the Jeans equation
from the Boltzmann equation in the radial and Z-component directions as the
following (see equation 9; Gilmore et al., 1989):

$\displaystyle\rho
K_{R}=\frac{1}{R}\frac{\partial(R\rho\sigma^{2}_{V_{R}})}{\partial
R}+\frac{\partial(\rho\sigma^{2}_{V_{R,Z}})}{\partial
Z}-\frac{\rho\sigma^{2}_{V_{\phi}}}{R}-\frac{\rho}{R}\bar{V_{\phi}}^{2}$ (11)

$\displaystyle\rho K_{Z}=\frac{\partial(\rho\sigma^{2}_{V_{Z}})}{\partial
Z}+\frac{1}{R}\frac{\partial(R\rho\sigma^{2}_{V_{R,Z}})}{\partial R}$ (12)

where $\rho(R,Z)$ is the space density of the stars in the thick disk, and
$K_{R}$= $\frac{\partial\phi}{\partial R}$, and $K_{Z}$=
$\frac{\partial\phi}{\partial Z}$ are the derivatives of the potential.
Assuming an exponential density profile, the radial Jeans equation can be
rewritten as follows (Li et al., 2018):

$\displaystyle\frac{\sigma^{2}_{V_{\phi}}}{\sigma^{2}_{V_{R}}}-2+\frac{2R}{h_{R}}-\frac{V_{c}^{2}-\bar{V_{\phi}}^{2}}{\sigma^{2}_{V_{R}}}+\frac{\sigma^{2}_{V_{Z}}}{\sigma^{2}_{V_{R}}}=0$
(13)

where $h_{R}$ is the scale length. By substituting our calculated velocity
dispersions from the Atari disk sample, within $\approx$ 3 kpc of the Sun in
the cynlindrical $R$ coordinate and $\approx$ 2 kpc above or below the
Galactic plane, (6,347 stars) into Equation 13, we obtain a radial scale
length of $h_{R}=2.48$ kpc. Calculating the scale length using different
metallicity bins shows a small increase from 2.38 kpc among the higher
metallicity stars up to 2.91 kpc for the low-metallicity stars. The results
are detailed in Table 3. In general, these results point to the Atari disk
being comparable in size in the radial direction to the thick and thin disk.
For reference, the scale length of the canonical thick disk has been measured
as 2.0 kpc (Bensby et al., 2011), 2.2 kpc (Carollo et al., 2010), and 2.31 kpc
(Sanders & Binney, 2015), although larger values have also been reported
previously (Chiba & Beers, 2000; de Jong et al., 2010). Thin disk values refer
to an overall similar spatial distribution although it is likely somewhat more
extended ($h_{R}>3.0$ kpc; e.g., Bensby et al. 2011; Sanders & Binney 2015).
See Table 2 for further details.

###  5.2 Scale Height

Assuming an exponential density distribution and constant surface density
($\sigma^{2}_{V_{R,Z}}\approx 0$)777$\sigma^{2}_{V_{R,Z}}$ is negligible small
compared to the remaining term in Eq.(14), as described in Gilmore et al.
(1989), Equation 12 can be rewritten as follows:

$\displaystyle\frac{\partial\ln{\sigma^{2}_{V_{Z}}}}{\partial
Z}-\frac{1}{h_{Z}}+\frac{K_{Z}}{\sigma^{2}_{V_{Z}}}=0$ (14)

where $h_{Z}$ is the scale height. By substituting $K_{Z}=2\pi G\times
71M_{\odot}$ pc-2 at $|$z$|$ = 1.1 kpc (see equation 4 in Kuijken & Gilmore
1991), relevant velocity dispersions, and gradients into Equation 14, the
scale height can be obtained.

We applied this technique to derive scale heights for both the original
velocity-selected sample of 7,451 stars (see Section 4.1) as well as the
action-selected sample of 10,351 stars, using the same spatial selection as in
Section 5.1. By design, the velocity selection method employed in our study
sets out to select stars roughly within the spatial distribution of the thick
disk (in the z-direction by using $\sigma_{\text{W}}=35$ km s-1; see Section
4.1). This might lead to a bias when attempting to use the velocity-selected
sample to determine the scale height. Table 3 shows the results. Using the
action-selection sample, we then derive 1.68 kpc for the scale height of the
Atari disk. Restricting the sample to stars with
$-1.2<[\mathrm{Fe}/\mathrm{H}]<-0.8$, we find $h_{Z}=$1.92 kpc. However, stars
with $-1.5<[\mathrm{Fe}/\mathrm{H}]<-1.2$ suggest a lower value of $\sim 1.37$
kpc. Stars with even lower metallicity once again follow a wider distributions
with larger scale heights. However, the larger uncertainty associated with the
calculated $h_{Z}$ in this metallicity bin comes from the low number of stars
to calculate the slope of the velocity dispersion (see term 1 of Equation 14)
accurately. We also investigated the idea that these different $h_{Z}$ values
might be due to possible contamination from other accreted substructures. To
address this question, we investigated the E-Lz space of each of the used
different $[\mathrm{Fe}/\mathrm{H}]$ bins. Overplotting these E-Lz
distributions on our Figure 9 suggests no significant overlap with any of the
other accreted substructures. Also, we performed a 2D Gaussian mixture model
fitting in E-Lz space for each of these $[\mathrm{Fe}/\mathrm{H}]$ bins and
found that the E-Lz distribution in each $[\mathrm{Fe}/\mathrm{H}]$ bin could
be reasonably fit by one Gaussian. This suggests no obvious substructure
contaminating our sample at various $[\mathrm{Fe}/\mathrm{H}]$ bins.

At face value, the $h_{Z}$ values calculated for the action-selected sample
are about 0.2 to 0.5 kpc larger than what we find for the velocity-selected
sample, as can be seen in Table 3. While there is a small change in $h_{Z}$
for the highest metallicity bin ($-1.2<[\mathrm{Fe}/\mathrm{H}]<-0.8$)
compared to the whole Atari disk sample, the low number of stars in the other
metallicity bins (i.e., large uncertainties) refrain us from determining any
scale height gradient with metallicity. For comparison, using a chemo-
dynamical selection, (Carollo et al., 2010) find a scale height of
$h_{Z}=1.36$ kpc. Their sample had $[\mathrm{Fe}/\mathrm{H}]$$<-1.0$ and
ranging down to below $[\mathrm{Fe}/\mathrm{H}]$$=-1.5$. Such low value
corresponds to what we obtain for our metallicity bin of
$-1.5<[\mathrm{Fe}/\mathrm{H}]<-1.2$. Based on our comprehensive analysis,
this value may well depend on the metallicity of the chosen sample.

To further quantify the bias introduced by the velocity method, we reran our
analysis with an increased $\sigma{{}_{z}}=45$ km s-1 and $\sigma{{}_{z}}=55$
km s-1. Our intention was to learn whether increasing the initial spatial
distribution would impact the scale height to the extent of matching that of
the action method. While choosing $\sigma{{}_{z}}=55$ km s-1 did indeed result
in scale height increases, the values of the action-selected sample were not
entirely reached. At the same time, however, the halo contamination rate
drastically increased, suggesting that loosening the velocity selection
criterion was detrimental to our overall science goal of accurately selecting
a high-confidence sample of Atari disk stars. To avoid this bias, we thus
chose to use the scale height value obtained from the action-selection sample
only. For the remainder of the analysis, we then kept the common sample as
originally selected with $\sigma{{}_{z}}=35$ km s-1.

Interestingly, a scale height of $h_{Z}\sim 1.7$ kpc derived for the whole
metallicity range is significantly more extended than what is measured for the
canonical thick disk having $h_{Z}\sim 0.5$ to 1 kpc. More recent papers have
reported progressively shorter scale heights (see Table 2) which suggests that
the scale height of the Atari disk is could be up to three times that of the
thick disk. Considering a more matching metallicity range of these two
populations, the Atari disk scale height for stars with
$-1.2<[\mathrm{Fe}/\mathrm{H}]<-0.8$ is $\sim$1.9 kpc which is about two to
four times that of the thick disk. But even the lowest value derived for stars
with $-1.5<[\mathrm{Fe}/\mathrm{H}]<-1.2$ of $\sim 1.4$ kpc is still more than
the scale height of the thick disk. Values for other metallicity bins can also
be found in Table 3, for additional comparisons. Overall, this robustly
suggests the Atari disk to be generally significantly more extended than the
thick disk in the the z-direction.

Table 3: Scale Lengths and Scale Heights for Different Metallicity Bins

Sample | Metallicity bin | $N_{\rm stars}$ | scale length | scale height
---|---|---|---|---
|  |  | (kpc) | (kpc)
Common | $-1.2\leq{\rm[Fe/H]}<-0.8$ | 4,868 | $2.38^{+0.05}_{-0.05}$ | $1.75^{+0.17}_{-0.14}$
| $-1.5\leq{\rm[Fe/H]}<-1.2$ | 835 | $2.62^{+0.09}_{-0.09}$ | $1.36^{+0.31}_{-0.23}$
| $-1.8\leq{\rm[Fe/H]}<-1.5$ | 314 | $2.98^{+0.15}_{-0.15}$ | $1.41^{+1.37}_{-0.52}$
| $-3.5\leq{\rm[Fe/H]}<-1.8$ | 268 | $2.91^{+0.16}_{-0.16}$ | $2.03^{+2.82}_{-0.95}$
| $-3.5\leq{\rm[Fe/H]}<-0.8$ | 6,347 | $2.48^{+0.05}_{-0.05}$ | $1.67^{+0.20}_{-0.16}$
Velocity | $-1.2\leq{\rm[Fe/H]}<-0.8$ | 5,570 | $2.64^{+0.04}_{-0.04}$ | $1.43^{+0.18}_{-0.15}$
| $-1.5\leq{\rm[Fe/H]}<-1.2$ | 993 | $3.30^{+0.10}_{-0.10}$ | $1.15^{+0.19}_{-0.16}$
| $-1.8\leq{\rm[Fe/H]}<-1.5$ | 414 | $4.00^{+0.11}_{-0.12}$ | $1.33^{+1.14}_{-0.48}$
| $-3.5\leq{\rm[Fe/H]}<-1.8$ | 394 | $4.14^{+0.09}_{-0.09}$ | $1.68^{+1.32}_{-0.56}$
| $-3.5\leq{\rm[Fe/H]}<-0.8$ | 7,451 | $3.00^{+0.05}_{-0.05}$ | $1.39^{+0.19}_{-0.16}$
Action | $-1.2\leq{\rm[Fe/H]}<-0.8$ | 7,694 | $2.51^{+0.04}_{-0.04}$ | $1.92^{+0.17}_{-0.15}$
| $-1.5\leq{\rm[Fe/H]}<-1.2$ | 1,497 | $2.95^{+0.08}_{-0.08}$ | $1.37^{+0.32}_{-0.22}$
| $-1.8\leq{\rm[Fe/H]}<-1.5$ | 707 | $3.30^{+0.12}_{-0.12}$ | $1.63^{+1.19}_{-0.49}$
| $-3.5\leq{\rm[Fe/H]}<-1.8$ | 639 | $3.38^{+0.12}_{-0.12}$ | $2.08^{+3.15}_{-1.10}$
| $-3.5\leq{\rm[Fe/H]}<-0.8$ | 10,351 | $2.70^{+0.04}_{-0.04}$ | $1.68^{+0.19}_{-0.15}$
Additional metallicity bins |
Common | $-0.9\leq{\rm[Fe/H]}<-0.8$ | 1,960 | $2.32^{+0.06}_{-0.06}$ | $1.64^{+0.47}_{-0.30}$
| $-1.1\leq{\rm[Fe/H]}<-0.9$ | 2,161 | $2.41^{+0.06}_{-0.06}$ | $2.03^{+0.87}_{-0.48}$
| $-1.3\leq{\rm[Fe/H]}<-0.8$ | 5,264 | $2.40^{+0.04}_{-0.05}$ | $1.73^{+0.18}_{-0.15}$
| $-3.5\leq{\rm[Fe/H]}<-1.1$ | 1,964 | $2.73^{+0.07}_{-0.07}$ | $1.59^{+0.56}_{-0.34}$
| $-3.5\leq{\rm[Fe/H]}<-1.3$ | 1,046 | $2.85^{+0.09}_{-0.08}$ | $1.52^{+0.59}_{-0.35}$
| $-3.5\leq{\rm[Fe/H]}<-1.4$ | 786 | $2.92^{+0.10}_{-0.10}$ | $1.84^{+1.59}_{-0.60}$
Velocity | $-0.9\leq{\rm[Fe/H]}<-0.8$ | 2,231 | $2.51^{+0.07}_{-0.07}$ | $1.40^{+0.25}_{-0.20}$
| $-1.1\leq{\rm[Fe/H]}<-0.9$ | 2,486 | $2.71^{+0.06}_{-0.06}$ | $1.64^{+0.58}_{-0.34}$
| $-1.3\leq{\rm[Fe/H]}<-0.8$ | 6,040 | $2.70^{+0.05}_{-0.05}$ | $1.40^{+0.18}_{-0.15}$
| $-3.5\leq{\rm[Fe/H]}<-1.1$ | 2,433 | $3.61^{+0.07}_{-0.07}$ | $1.30^{+0.36}_{-0.24}$
| $-3.5\leq{\rm[Fe/H]}<-1.3$ | 1,369 | $3.96^{+0.09}_{-0.09}$ | $1.37^{+0.48}_{-0.30}$
| $-3.5\leq{\rm[Fe/H]}<-1.4$ | 1,064 | $4.06^{+0.08}_{-0.08}$ | $1.61^{+0.97}_{-0.46}$
Action | $-0.9\leq{\rm[Fe/H]}<-0.8$ | 3,065 | $2.43^{+0.05}_{-0.05}$ | $1.65^{+0.28}_{-0.21}$
| $-1.1\leq{\rm[Fe/H]}<-0.9$ | 3,422 | $2.53^{+0.06}_{-0.06}$ | $2.37^{+0.47}_{-0.35}$
| $-1.3\leq{\rm[Fe/H]}<-0.8$ | 8,353 | $2.55^{+0.05}_{-0.05}$ | $1.80^{+0.17}_{-0.15}$
| $-3.5\leq{\rm[Fe/H]}<-1.1$ | 3,760 | $3.09^{+0.06}_{-0.06}$ | $1.74^{+0.64}_{-0.37}$
| $-3.5\leq{\rm[Fe/H]}<-1.3$ | 2,223 | $3.22^{+0.07}_{-0.07}$ | $1.83^{+0.77}_{-0.42}$
| $-3.5\leq{\rm[Fe/H]}<-1.4$ | 1,740 | $3.27^{+0.08}_{-0.08}$ | $2.14^{+2.25}_{-0.79}$
Velocity (45) | $-1.2\leq{\rm[Fe/H]}<-0.8$ | 5,794 | $2.68^{+0.05}_{-0.04}$ | $1.49^{+0.24}_{-0.19}$
| $-1.5\leq{\rm[Fe/H]}<-1.2$ | 1,108 | $3.44^{+0.09}_{-0.10}$ | $1.44^{+0.36}_{-0.24}$
| $-1.8\leq{\rm[Fe/H]}<-1.5$ | 467 | $4.11^{+0.12}_{-0.12}$ | $1.26^{+1.43}_{-0.48}$
| $-3.5\leq{\rm[Fe/H]}<-1.8$ | 447 | $4.25^{+0.09}_{-0.10}$ | $2.82^{+4.61}_{-1.61}$
| $-0.9\leq{\rm[Fe/H]}<-0.8$ | 2,288 | $2.55^{+0.06}_{-0.06}$ | $1.39^{+0.20}_{-0.16}$
| $-1.1\leq{\rm[Fe/H]}<-0.9$ | 2,617 | $2.74^{+0.06}_{-0.06}$ | $1.71^{+0.54}_{-0.33}$
| $-3.5\leq{\rm[Fe/H]}<-1.1$ | 2,688 | $3.71^{+0.06}_{-0.07}$ | $1.65^{+0.58}_{-0.33}$
Velocity (55) | $-1.2\leq{\rm[Fe/H]}<-0.8$ | 5,794 | $2.73^{+0.05}_{-0.05}$ | $1.79^{+0.44}_{-0.29}$
| $-1.5\leq{\rm[Fe/H]}<-1.2$ | 1,108 | $3.56^{+0.10}_{-0.09}$ | $1.48^{+0.30}_{-0.22}$
| $-1.8\leq{\rm[Fe/H]}<-1.5$ | 467 | $4.34^{+0.10}_{-0.10}$ | $1.53^{+1.84}_{-0.61}$
| $-3.5\leq{\rm[Fe/H]}<-1.8$ | 447 | $4.42^{+0.10}_{-0.10}$ | $4.56^{+8.32}_{-4.56}$
| $-0.9\leq{\rm[Fe/H]}<-0.8$ | 2,386 | $2.59^{+0.06}_{-0.06}$ | $1.45^{+0.21}_{-0.17}$
| $-1.1\leq{\rm[Fe/H]}<-0.9$ | 2,647 | $2.79^{+0.06}_{-0.07}$ | $2.26^{+1.49}_{-0.63}$
| $-3.5\leq{\rm[Fe/H]}<-1.1$ | 2,821 | $3.88^{+0.07}_{-0.07}$ | $2.09^{+0.57}_{-0.36}$

Note. — We list results for various [Fe/H] bins for comparisons with other
studies and sample sizes.

###  5.3 Correlation between the radial and vertical distances and metallicity

The spatial-metallicity correlation of metal-poor stars in the Galactic disk
places observational constraints on our understanding of the formation and
evolution of the Milky Way system. The mean metallicity
($\langle[\mathrm{Fe}/\mathrm{H}]\rangle$) of stars at a particular region in
the disk primarily depends on the gas accretion rate, the chemical composition
of the early interstellar gas, and subsequent evolution of stars at that
region. To investigate the presence of any correlation between metallicity and
radial distance from the Galactic center ($R$), we apply a simple linear fit
to the individual measurements of R vs. $[\mathrm{Fe}/\mathrm{H}]$ in our
Atari disk sample. The top panel of Figure 4 presents a 2d histogram of the
$R$ distribution of the Atari disk sample as a function of
$[\mathrm{Fe}/\mathrm{H}]$. The points and error bars represent the mean value
and standard error of $R$ of bins of 0.20 dex for visualization purposes. The
slope of the dashed line represents a positive radial metallicity gradient
(${\rm\partial R/\partial}[\mathrm{Fe}/\mathrm{H}]=0.73\pm 0.05$ kpc ${\rm
dex^{-1}}$). This result is different from what has been found for the
canonical thick disk which is essentially flat. Recio-Blanco et al. (2014)
used 1,016 stars from the Gaia-ESO DR1 to chemically separate the disk
components and found ${\rm\partial[\mathrm{Fe}/\mathrm{H}]/\partial
R}=+0.006\pm 0.008$ for the thick disk. Peng et al. (2018) used a kinematic
approach to separate 10,520 stars taken from South Galactic Cap u-band Sky
Survey and SDSS/SEGUE data and found
${\rm\partial[\mathrm{Fe}/\mathrm{H}]/\partial R}=-0.001\pm 0.020$. We note
that the above studies have a higher metallicity range
($[\mathrm{Fe}/\mathrm{H}]$$\gtrsim-1.2$), caveating a direct comparison to
our results. Indeed,

Figure 4: Top: Radial metallicity gradient as a function of Galactocentric
radial distance of the Atari disk sample. Bottom: Vertical metallicity
gradient of the Atari disk as a function of $[\mathrm{Fe}/\mathrm{H}]$. Error
bars denote the standard deviation in each bin and show the statistical
uncertainty only.

We also test for the presence of a $[\mathrm{Fe}/\mathrm{H}]$ trend with
absolute vertical distance from the Galactic plane ($|Z|$), using the same
technique as for deriving the radial gradient, including using bin sizes of
0.2 dex for visualization purposes. The bottom panel of Figure 4 shows the
correlation between $[\mathrm{Fe}/\mathrm{H}]$ and $|Z|$ and the best fit
line, which represents a positive vertical metallicity gradient
(${\rm\partial|Z|/\partial}[\mathrm{Fe}/\mathrm{H}]=-0.45\pm 0.03$ kpc ${\rm
dex^{-1}}$). On average, the more metal-poor stars of the Atari disk are
preferentially found at high $|Z|$ values. The relatively more metal-rich
stars are on average located at $|Z|\lesssim 2$. Note that only stars within 5
kpc were included in both of these analyses following Chiti et al. (2021b), to
avoid selection effects toward more metal-poor stars at larger distances.

Following the last point, we investigated a few further avenues to assess to
what extent selection effects affect our observed spatial-metallicity
correlations. There are two primary ways in which selection effects could bias
our gradients: (1) metal-poor stars are brighter than more metal-rich stars in
the SkyMapper $v$ filter, making the most distant stars preferentially metal-
poor; and (2) based on our exclusion of regions of high reddening in the
initial sample (see Chiti et al., 2021a, b, for more details), there is an
exclusion of low $Z$ stars at $R$ close to the galactic center; this could
lead to an artificial $R$-$[\mathrm{Fe}/\mathrm{H}]$ gradient given that lower
metallicity stars are at high $Z$. The effect of (1) is generally accounted
for by only considering stars within 5 kpc from the Sun, which is the distance
within which the SkyMapper filter should not significantly preferentially
select metal-poor stars at large distances. To more stringently test this
effect, we restrict our sample to stars within 4 kpc and still find a positive
$R$-$[\mathrm{Fe}/\mathrm{H}]$ gradient. Restricting the sample to $<$2 kpc
results in no statistically significant gradient, but this is not necessarily
surprising because we lose sensitivity to any gradient by restricting our
sample to only nearby stars. We investigate the effect of (2) by searching for
a gradient in $R$-$[\mathrm{Fe}/\mathrm{H}]$ at various $Z$ bins ($0.1<Z<1.1$
with 0.2 kpc bins and $1.1<Z<3.0$ with 0.4 kpc bins). In general, this
analysis still leads to positive gradients at a given Z range, suggesting that
(2) is not a significant effect. We note that the
$R$-$[\mathrm{Fe}/\mathrm{H}]$ gradient appears to not be significant at the
lowest metallicities (below [Fe/H] $<-1.4$).

###  5.4 Gradients with Rotational Velocity

We investigate the variation of rotational velocity $V_{\phi}$ versus
$[\mathrm{Fe}/\mathrm{H}]$, $R$, and $|Z|$. The top panel of Figure 5 shows a
density plot of the rotational velocity versus the metallicity of stars in our
Atari disk sample. The mean values and standard errors of $V_{\phi}$ in
metallicity bins of 0.2 dex are overplotted. There is an overall positive
rotational velocity gradient as a function of $[\mathrm{Fe}/\mathrm{H}]$ of
${\rm\partial V_{\phi}/\partial}[\mathrm{Fe}/\mathrm{H}]=13.22\pm 1.57$ km s-1
${\rm dex^{-1}}$. The lower left panel of Figure 5 shows the rotational
velocity gradient in the radial direction, ${\rm\partial
V_{\phi}/\partial}R=-2.6\pm 0.4$ km s-1 ${\rm kpc^{-1}}$. While the detection
is statistically significant, the value of the gradient ($\sim 2$ km/s per 1
kpc) is small. There is also a negative correlation between $V_{\phi}$ and
$|Z|$ of ${\rm\partial V_{\phi}/\partial}|z|=-8.96\pm 0.75$ km s-1 ${\rm
kpc^{-1}}$.

Previous studies have found negative and positive slopes for the rotational
velocity-metallicity gradient for the thin and thick disk populations,
respectively. For reference, Lee et al. (2011) and Guiglion et al. (2015) used
the chemical abundance approach to assign the stellar population membership
for 17,277 and 7,800 stars, respectively. Using the thick disk samples in
their studies, they reported rotational velocity gradients of ${\rm\partial
V_{\phi}/\partial}[\mathrm{Fe}/\mathrm{H}]=+45.8\pm 2.9$ km s-1 ${\rm
dex^{-1}}$ and ${\rm\partial V_{\phi}/\partial}[\mathrm{Fe}/\mathrm{H}]=+49\pm
10$ km s-1 ${\rm dex^{-1}}$, respectively. While Allende Prieto et al. (2016)
used 3621 APOGEE stars to measure ${\rm\partial
V_{\phi}/\partial}[\mathrm{Fe}/\mathrm{H}]=-18\pm 2$ km s-1 ${\rm dex^{-1}}$.
It is worth mentioning again that in all of these aforementioned studies, the
metallicity range was $[\mathrm{Fe}/\mathrm{H}]$$>-1.0$ and so a direct
comparison of results might not necessarily be accurate.

Figure 5: Top: Rotational velocity as a function of $[\mathrm{Fe}/\mathrm{H}]$
resulting in a gradient of ${\rm\partial
V_{\phi}/\partial}[\mathrm{Fe}/\mathrm{H}]=13.22\pm 1.57$ km s-1 ${\rm
dex^{-1}}$. Bottom left: Rotational velocity as a function of the
Galactocentric radial distance $R$ with a gradient of ${\rm\partial
V_{\phi}/\partial}R=-2.6\pm 0.4$ km s-1 ${\rm kpc^{-1}}$. Bottom right:
Rotational velocity as a function of scale height Z with a gradient of
${\rm\partial V_{\phi}/\partial}|z|=-8.96\pm 0.75$ km s-1 ${\rm kpc^{-1}}$.
Error bars denote the standard deviations throughout.

###  5.5 Orbital Eccentricity

For our Atari disk sample, we investigate the relation between the orbital
eccentricity, and $[\mathrm{Fe}/\mathrm{H}]$, $R$, and $|Z|$. Figure 6 shows
the observed trends of the orbital eccentricity as a function of
$[\mathrm{Fe}/\mathrm{H}]$, $R$, and $|Z|$. The top panel in Figure 6 shows
eccentricity versus $[\mathrm{Fe}/\mathrm{H}]$. Results suggests that the
orbital eccentricity increases as the metallicity decreases, with the most
metal-poor star having fairly eccentric orbits. The best fit yields a slope of
${\rm\partial e/\partial}{[\mathrm{Fe}/\mathrm{H}]}=-0.05\pm 0.01$ dex-1. The
lower left panel presents an overall no significant correlation between the
orbital eccentricity and $R$. The lower right panel identifies that the
orbital eccentricity varies minorly with $|Z|$, with ${\rm\partial
e/\partial}Z=+0.01\pm 0.002$ kpc-1. In general, our Atari disk stars exhibit
different orbital eccentricity with $[\mathrm{Fe}/\mathrm{H}]$, $R$, and $|Z|$
from the ones reported in the literature for the more metal-rich stars in the
canonical thick disk (see Lee et al., 2011, figure 9).

Figure 6: Top: Orbital eccentricities as a function of
$[\mathrm{Fe}/\mathrm{H}]$ with a gradient of ${\rm\partial
e/\partial}[\mathrm{Fe}/\mathrm{H}]=-0.05\pm 0.01$ ${\rm dex^{-1}}$. Bottom
left: $e$ as a function of the Galactocentric radial distance $R$ with a flat
trend of ${\rm\partial e/\partial}R=0.00\pm 0.00$ ${\rm kpc^{-1}}$. Bottom
right: $e$ as a function of scale height $Z$ with a positive gradient of
${\rm\partial e/\partial}|z|=+0.01\pm 0.002$ ${\rm kpc^{-1}}$. Error bars
denote the standard deviation throughout.

##  6 Comparisons with formation models

Compared to the thick and thin disks, the Atari disk has not been extensively
studied or been regarded as a separate component of the Galactic disk until
recently (Carollo et al., 2019; An & Beers, 2020). Accordingly, there are no
detailed theoretical Atari disk formation scenarios discussed in the
literature. In the absence of such, we will compare our observed
characteristics of the Atari disk with predictions from the four main
formation scenarios for a structurally distinct thick disk, as well as models
with predictions regarding eccentricities, to gain insights into how the Atari
disk formed and evolved.

###  6.1 Comparison with predictions of thick disk formation models based on
$[\mathrm{Fe}/\mathrm{H}]$gradients

We use the properties detailed in Section 5 to assess four main formation
scenarios for a structurally distinct thick disk following Li et al. (2018) to
learn about the origin of the Atari disk. We discuss each in detail below.

1\. Disk heating. This scenario posits the dynamical heating of a pre-existing
disk due to minor mergers. The disk will maintain its chemical or kinematic
gradients (Quinn et al., 1993; Kazantzidis et al., 2008) even after the
merger(s). We observe a positive radial metallicity gradient and a negative
vertical metallicity gradient for our Atari disk sample. We note that direct
comparisons of the magnitude of our gradients are not possible to other
studies in the literature due to the upper metallicity limit
($[\mathrm{Fe}/\mathrm{H}]$$<-0.75$) of our SMSS sample. However, our
detection of a correlation between the radial distance and metallicity is not
principally seen in some studies of this formation scenario of the thick disk,
which disfavors this interpretation (e.g., Recio-Blanco et al., 2014; Peng et
al., 2018).

2\. Gas-rich merger. At high redshifts, dwarf galaxies were likely all gas
rich with few stars formed, including those that merged with the early Milky
Way. Any gas-rich deposit into the Milky Way’s highly turbulent early disk
would have expected to have triggered star formation (Brook et al., 2004,
2007). The subsequent stars that formed from this merger should likely show no
obvious clumpy distribution in the integrals of motion space. Also, we would
expect subsequent stars that formed to have formed in a the short timescale
within the disk following a gas-rich merger, suggesting a flat metallicity
behavior (no gradient) (Cheng et al., 2012). However, we do observe a gradient
in our sample (see Figure 4). Thus, it is unlikely that the Atari population
formed in a star formation episode after a gas-rich merger; although, it very
likely could have been associated with the metal-poor stars that formed in an
accreted galaxy before infall.

It is then interesting to consider the existence of significant numbers of
metal-poor stars with $[\mathrm{Fe}/\mathrm{H}]<-2.5$ in this context. These
stars do support accretion as the origin scenario of the Atari disk, as
opposed to star formation following a gas-rich merger, which would lead to a
population of higher metallicity stars with an average of
$[\mathrm{Fe}/\mathrm{H}]\approx-0.6$. It would thus take a merger(s) to
inject gas $\approx 1,000$ times more metal-poor to bring down the
$[\mathrm{Fe}/\mathrm{H}]$ of the disk’s interstellar medium to allow the
formation of such low-metallicity stars post-merger. This seems unlikely from
having occurred. However, such primitive stars may have easily formed in early
low-mass systems which were accreted first by neighboring, more massive
systems and eventually into the massive progenitor of the Atari disk.

3\. Direct accretion. Cosmological simulations have shown that a direct
accretion of dwarf-like galaxies coming in from specific directions can build
up a thick disk by donating their content in a planar configuration (for more
details about such simulations, see Abadi et al., 2003a, b). Either one major
merger with a massive satellite or the accretion of a number of smaller
systems would result in spatially distinct populations as measurable by
differences in $h_{R}$ and $h_{Z}$ (see Gilmore et al., 2002). Correlations
between $[\mathrm{Fe}/\mathrm{H}]$ and values for $h_{R}$ and $h_{Z}$ may
indeed principally indicate multiple populations since such a scenario would
deposit stars (not just gas) into the early Galactic disk that were formed
within the progenitor system before the merger event. For example, an ex-situ
Milky Way population would display a larger scale length compared to that of a
population formed by an in-situ scenario (Amôres et al., 2017). These stars
(now present in the disk) would also still share similar integrals of motion.
Finally, there would also be an expected observable metallicity gradient, both
vertically and radially due to the different origins of the stars (accreted
vs. in-situ formed stars). Eccentricities would also be distributed broadly
and over a wider range (Sales et al., 2009).

As can be seen in Figure 4, our Atari disk sample displays spatial metallicity
gradients in both the vertical and radial direction. It also shows a broad
range of eccentricities, as can be seen in Figure 6. We also find a moderate
correlations of the scale length as a function of $[\mathrm{Fe}/\mathrm{H}]$
for stars in the solar neighborhood vicinity, from $h_{R}\sim 2.4$ to 2.9 (see
Table 3). The existence of this gradient aligns with predictions for an ex-
situ population to have an increased scale length compared to an in-situ one
(Amôres et al., 2017), and supports the Atari disk to have an accretion
origin. Unfortunately, the picture is less obvious regarding the behavior of
the scale height. As our present Atari disk data is not suitable to draw
strong evidence on the existence of a scale height metallicity gradient, we
strongly recommend future studies with larger samples to further quantify this
issue.

The direct accretion explanation is also supported by simulations of Milky
Way-like galaxies in the IllustrisTNG simulation (Nelson et al., 2019). We
analyze 198 simulated Milky Way analogs from Illustris TNG50, defined as disk
galaxies with stellar masses of $M_{*}=10^{10.5-11.2}M\odot$ in relative
isolation at $z=0$ (originally identified by Engler et al., 2021; Pillepich et
al., 2021). Milky Way analogs are also reported in Illustris TNG100 (e.g.,
Mardini et al., 2020). When defining the thick disk of these galaxies, we look
exclusively at star particles vertically located between 0.75 and 3 kpc from
the plane of the galaxy (excluding the area dominated by the thin disk or
halo) and radially located between 3 and 15 kpc from the center of the galaxy
(excluding the area dominated by the bulge). We trace back the origin of the
star particles in the thick disk at $z=0$ and find that the vast majority of
stars were formed ex-situ: $95^{+3}_{-10}\%$ of the thick disk stars in each
Milky Way analog have accretion origins. We also calculated
$[\mathrm{Fe}/\mathrm{H}]$ vs. radial distance gradients for the ex-situ thick
disk populations. Among the 198 “Milky Way thick disks”, 71 of them have a
positive [Fe/H] vs. radial distance gradient for their ex-situ population.
This is 35% of the simulated ex-situ thick disk populations. Several of the
simulated ex situ thick disk populations have gradients that exactly match the
Atari disk observations.

This percentage remains consistently high when we consider lower metallicity
stars; for stars with $[\mathrm{Fe}/\mathrm{H}]$$<-0.8$, $96^{+3}_{-11}\%$ of
the thick disk stars have accretion origins. This trend is supported by the
results of Abadi et al. (2003b).

In summary, the behavior of the stellar spatial distributions, together with
the eccentricity distribution, the scale length, and plausibly also the scale
height lend support to a scenario in which the Atari disk formed by accretion
event(s) similar to those studied in Abadi et al. (2003b) as well as the
IllustrisTNG simulation.

4\. Radial migration. A radial migration scenario suggests that early
dynamical interactions occurred when the metallicity of the interstellar
medium was relatively low and the $\alpha$-abundance ratios of the disk stars
were high. Specifically, interactions of the disk with the spiral arms can
dilute the metallicity gradient by rearranging the orbital motion of stars
(Schönrich & Binney, 2009). This would lead to an exchange of thin and thick
disk stars. Any outward migration places stars on higher orbits above or below
the Galactic plane. By now, these migrated stars would have had enough time to
also experience significant orbital mixing, thus contributing to the
flattening of the gradient.

Accordingly, only a small or even no correlation between the rotational
velocity and the metallicity is expected in this scenario. Our sample does
show a significant correlation, as can be seen in Figure 5, suggesting that
radial migration has not played a major role in the (more recent) evolution of
the Atari disk.

###  6.2 Comparison with predictions of thick disk formation models based on
orbital eccentricities

In addition to metallicity gradients, information can also be gained from the
distribution of the stellar orbital eccentricities (e.g., Sales et al., 2009).
In the following, we consider eccentricity distribution predictions and
compare them with our results in the context of the chemo-dynamic constraints
already discussed in Section 6.1. Sales et al. (2009) predict (their Figure 3)
that
(i) a notable peak at low eccentricity should be present in the radial
migration and gas-rich scenarios ($e\sim$0.2-0.3),
(ii) the accretion scenario has an eccentricity distribution that is broadly
distributed but with a peak shifted towards higher values, and
(iii) the disk heating scenario has two peaks with the primary one being at
$e\sim$ 0.2-0.3 and a secondary one located at $e\sim$ 0.8888This secondary
peak is from the debris of an accreted/merged luminous satellite. If the disk
heating is due to merging of subhalo(s), then this secondary peak might not
likely exist..

Figure 7: Orbital eccentricity distribution for our Atari disk sample, using
the scale length of $h_{R}=2.48\pm 0.15$ kpc and scale height of
$h_{Z}=1.67\pm 0.15$ kpc in the ranges of $1<|Z/h_{Z}|<3$ and $2<|R/h_{R}|<3$,
corresponding to figure 3 in Sales et al. (2009). The solid black line
represents the superposition of the individual Gaussians. Upper panel: best
fit using two Gaussians with peaks at $e$ = 0.30 and 0.49. Lower panel: best
fit using three Gaussians with peaks at $e=$ 0.16, 0.33, and 0.51.

In Figure 7, we show the orbital eccentricity distributions of our Atari disk
sample and best-fitting Gaussians. We can reproduce the observed distribution
with two Gaussians in the upper panel (with peaks at $e=$0.33 and 0.54), and
with three Gaussians in the lower panel (with peaks at $e=$0.24, 0.40, and
0.61). A significant number of stars with $e>0.4$ in our sample principally
argues against the importance of radial migration and these stars having
originated from star-formation after the gas-rich scenario when considering
the formation and evolution of the Atari disk. Instead, the presence of two or
three broad, well separated peaks that fit the observed distribution quite
well supports the prediction of the direct accretion model, in that the
eccentricity distribution is quite broad.

We note that our distribution may qualitatively align with the disk heating
scenario since we note a peak at $e\sim$0.3 and one at higher $e\sim 0.6$.
However, the larger peak is not located quite as high as $e=0.8$ and the
distribution can be well-described by more than two underlying gaussian
distributions. Consequently, the disk heating scenario might play a role in
the formation and evolution of the Atari disk, but the discussion in Section
6.1 and the overall broad eccentricity distribution suggest that an accretion
scenario might be the dominant channel.

##  7 Findings and Conclusions

Our detailed kinematic investigation of metal-poor stars selected from
SkyMapper DR2 that are located in the Galactic disk has allowed us to identify
the Atari disk and learn about its characteristics and speculate on its
origin. In this Section, we synthesize our findings across Sections 5 and 6
and comment on other chemical characteristics of the Atari disk.

###  7.1 Kinematic & Spatial characterization of the Atari disk

We have assessed and characterized the Atari disk with a new sample of 7,127
low-metallicity member stars and have outlined some of its properties in
Section 5. The main findings regarding the spatial distribution of the stars
are as follows.

Our detailed study confirms earlier claims (Carollo et al., 2019) of a notable
velocity lag of the Atari disk compared to the canonical thick disk. The Atari
disk has a well defined mean velocity of V${}_{\phi}\approx 154$ km s-1 and
FWHM = 63.9 km s-1, with individual values ranging from about 80 to 250 km s-1
as can be seen in Figure 5. A Vϕ distribution with a distinct, net rotation
characterizes that of a disk population, rather than a halo population. Our
extensive kinematic selection results also align with previous findings
(Carollo et al., 2019) of a peak in angular momentum of L${}_{z}\sim 1200$
${\rm kpc}$ km s-1 when restricting our sample to stars with $R=7$-$9$ kpc
from the Galactic center (due to Lz increasing with increasing $R$ and
assuming a constant rotational velocity). Correspondingly, other R brackets (R
= 3-5, 5-7, 9-11 kpc) have lower or higher Lz values (see Figure 2).

The eccentricities of our Atari disk sample cover a broad range of values
ranging from $e\sim 0.0$ to 1.0. The bulk of the stars have $e\sim 0.3$ to 0.7
which appears to be a range between that of the canonical thick disk and the
Galactic halo. A notable fraction of our stars have eccentricities different
from typical canonical thick disk values (see Table 2). There is no
significant sub-population of Atari disk stars with $e$ = 0.7-1 (only 61
stars), suggesting, again, that the Atari disk eccentricities range between
typical thick disk and halo eccentricities.

The velocity lag and the range of eccentricities offer strong support to the
origin scenario in which the Atari disk forms as a result of a major accretion
event in which a satellite (or satellites) plunged into the Galactic disk at
early times while coming from a specific direction (Abadi et al., 2003b; Sales
et al., 2009). For comparison, a gas-rich merger is favored as the formation
scenario for the canonical thick disk. This alone highlights distinct
differences between the nature of these two populations.

An accretion scenario for the Atari disk may also principally be supported by
a variable scale length and height with metallicity. However, investigating
this point with Milky Way mass galaxies in the IllustrisTNG simulation (Nelson
et al., 2019) indicates that while accretion history does affect the scale
height, other factors also play a role. Observationally, we do indeed find a
small increase in scale length with decreasing metallicity from around 2.37
kpc at $[\mathrm{Fe}/\mathrm{H}]\sim-1.0$ to nearly 3 kpc at
$[\mathrm{Fe}/\mathrm{H}]\sim-1.6$.

As discussed in Section 5, the behavior of the scale height with decreasing
metallicity is somewhat inconclusive due to significant uncertainties (arising
from small sample sizes and difficulties in measuring the first term in
Equation 14). Therefore, we strongly recommend future studies of larger Atari
disk data attempting to investigate the existence of a $h_{z}$ gradient with
$[\mathrm{Fe}/\mathrm{H}]$.

###  7.2 Very and extremely metal-poor stars in the Atari disk as identified
in our SMSS sample

The $[\mathrm{Fe}/\mathrm{H}]$ behavior of the Atari disk appears to be
significantly different from that of the canonical thick disk, as it stretches
to much lower $[\mathrm{Fe}/\mathrm{H}]$, not unlike what is canonically found
in the (inner and outer) halo populations.

We searched our Atari disk sample for low-metallicity stars and identified 261
stars with $[\mathrm{Fe}/\mathrm{H}]<-2.0$ (4 % of our sample), 55 stars with
$[\mathrm{Fe}/\mathrm{H}]<-2.5$ (1 % of our sample), and 7 stars with
$[\mathrm{Fe}/\mathrm{H}]<-3.0$ (0.1 % of our sample). We list stars with
$[\mathrm{Fe}/\mathrm{H}]<-2.5$ in Table 4, along with any available
literature metallicities. To check again whether these stars could be halo
stars, we inspected the long-term orbital histories ($Z_{max}$ and orbital
eccentricity) of these objects. The bulk of these stars have $Z_{max}<3$ kpc,
suggesting that they are indeed not part of the halo population. Any stars
with a higher $Z_{max}$ stars appear not have eccentricities exceeding e $\sim
0.6$, again confirming no halo membership. This leaves the questions whether
our sample would contain any thick disk stars. However, we find these low-
metallicity stars to generally have either too high an eccentricity or
$Z_{max}$ values to be associated with the thick disk (as shown in Table 2).

Of our 55 Atari disk stars with $[\mathrm{Fe}/\mathrm{H}]<-2.5$, $\sim 60$%
are readily found in the Simbad database (Wenger et al., 2000). Table 4 lists
the literature metallicities and corresponding references. We note that four
stars have also previously been classified to have disk-type kinematics, as is
noted in Table 4. Overall, for these stars with
$[\mathrm{Fe}/\mathrm{H}]<-2.5$ (excluding those with measurements from the
GALAH survey), the photometric $[\mathrm{Fe}/\mathrm{H}]$ estimates from Chiti
et al. (2021a) agree very reasonably with those from the literature, with a
mean difference of $0.11\,\pm\,0.05$.

Several re-discovered stars display interesting chemical abundance patterns.
Five stars are limited-$r$ stars with light neutron-capture element
enhancements (Frebel, 2018; Hansen et al., 2018), two stars are mildly
$r$-process enhanced (Hansen et al., 2018; Ezzeddine et al., 2020) and two are
carbon-enhanced metal-poor (CEMP) stars. Of the seven stars with
$[\mathrm{Fe}/\mathrm{H}]$$<-3.0$, two are already known in the literature.
One was analyzed by the R-Process Alliance (Sakari et al., 2018) and found to
be a CEMP star, and the other was studied by (Schlaufman & Casey, 2014). Of
the remaining five, we have observed one star and chemical abundance results
will be reported in X. Ou et al. (in prep.).

We also decided to search the two original parent samples (the individual
action and velocity-based selection samples) for additional metal-poor stars.
We find eleven and seven more very and extremely metal-poor stars in the
sample, respectively. Of those extra eleven action-selected stars, eight stars
appear to have likely halo kinematics (Z${}_{max}>3.0$ kpc and/or $e>0.7$).
Five have Z${}_{max}<4$ but large eccentricities ($e>0.65$). We add the
remaining three stars to our Atari disk sample. Of the seven velocity-selected
stars, six have likely halo kinematics (Z${}_{max}>3.0$ kpc and/or $e>0.7$).
We add only the remaining one to our sample. The stars are listed in Table 4.

While these four metal-poor stars were not selected into our final common
sample with the highest likelihood for being the most representative of Atari
disk stars, we note that it is highly likely that they do belong to the Atari
disk. They clearly do not belong to another population, as per their kinematic
properties. Hence, when searching for the most metal-poor stars it is critical
to consider these two selection methods individually as well, given the rarity
of such stars.

The existence of large numbers of bona-fide very and extremely metal-poor
stars in the Atari disk significantly supports an accretion scenario. A
massive progenitor system must have undergone at least a limited amount of
(early) chemical evolution that produced an early population of low-
metallicity stars. For comparison, the thick disk is not known for having many
such metal-poor stars, and the gas-rich merger scenario would not support the
existence of a large fraction either. We discuss possible scenarios for the
nature of the potential progenitor further below.

Table 4: Very and extremely metal-poor SMSS stars with Atari disk kinematics

R.A. (J2000) | Decl. (J2000) | Gaia ID |  $[\mathrm{Fe}/\mathrm{H}]$phot |  $[\mathrm{Fe}/\mathrm{H}]$lit |  Zmax [kpc] | e |  References for $[\mathrm{Fe}/\mathrm{H}]$lit
---|---|---|---|---|---|---|---
12 35 57.41 |  $-$34 40 19.70 | 6158268802159564544 |  $-$3.00 |  $\cdots$ | 4.10 | 0.45 |
06 51 52.43 |  $-$25 07 02.22 |  2921777156667244032bbfootnotemark:  |  $-$3.02 |  $\cdots$ | 0.89 | 0.21 |
20 05 28.77 |  $-$54 31 25.97 | 6473118900280458240 |  $-$3.04 |  $-$3.01 | 4.10 | 0.18 | Schlaufman & Casey (2014)
16 23 29.34 |  $-$65 17 53.33 |  5827787046034460672bbfootnotemark:  |  $-$3.04 |  $-$2.31 | 3.99 | 0.31 | Buder et al. (2021)
09 29 49.73 |  $-$29 05 59.03 | 5633365176579363584 |  $-$3.10 |  $-$2.88 | 0.90 | 0.45 | Sakari et al. (2018)
19 25 0.04 |  $-$15 57 43.35 |  4181010754108521472ccfootnotemark:  |  $-$3.14 |  $\cdots$ | 1.49 | 0.28 |
18 11 39.41 |  $-$46 45 43.50 | 6707545022835614464 |  $-$3.24 |  $\cdots$ | 1.90 | 0.42 |
21 48 07.05 |  $-$43 43 23.74 | 6565897654232474240 |  $-$3.24 |  $\cdots$ | 4.80 | 0.57 |
14 59 14.59 |  $-$10 49 42.34 | 6313811313365806208 |  $-$3.31 |  $\cdots$ | 3.70 | 0.41 |
23 30 19.62 |  $-$08 13 15.20 | 2438343952886623744 |  $-$3.48 |  $-$3.20 | 4.20 | 0.56 | X. Ou et al 2022 (in prep)
15 45 12.76 |  $-$31 05 29.22 |  6016676026902257280bbfootnotemark:  |  $-$3.53 |  $\cdots$ | 2.10 | 0.22 |

Note. — A short version is shown here to illustrate the table form and
content, but the full content is accessible in the online table.

Table 5: Very and extremely metal-poor stars with Atari disk kinematics from the literature (collected through JINAbase) R.A. (J2000) | Decl. (J2000) | Simbad identifier |  $[\mathrm{Fe}/\mathrm{H}]$lit | $[\mathrm{C}/\mathrm{Fe}]$ | Zmax [kpc] | e | Ref
---|---|---|---|---|---|---|---
16 28 56.15 |  $-$10 14 57.10 | 2MASS J16285613$-$1014576 |  $-$2.00 | 0.24 | 0.58 | 0.43 | Sakari et al. (2018)
18 28 43.44 |  $-$84 41 34.81 | 2MASS J18284356$-$8441346 |  $-$2.03 |  $-$0.39 | 3.19 | 0.32 | Ezzeddine et al. (2020)
05 52 15.78 |  $-$39 53 18.47 | TYC 7602-1143-1 |  $-$2.05 |  $\cdots$ | 1.33 | 0.69 | Ruchti et al. (2011)
00 25 50.30 |  $-$48 08 27.07 | 2MASS J00255030$-$4808270 |  $-$2.06 | 0.27 | 1.61 | 0.53 | Barklem et al. (2005)
14 10 15.84 |  $-$03 43 55.20 | 2MASS J14101587$-$0343553 |  $-$2.06 |  $-$0.09 | 1.17 | 0.71 | Sakari et al. (2018)
02 21 55.60 |  $-$54 10 14.40 | 2MASS J02215557$-$5410143 |  $-$2.09 | 0.00 | 3.16 | 0.33 | Holmbeck et al. (2020)
23 05 50.54 |  $-$25 57 22.29 | CD $-$26∘ 16470 |  $-$2.13 |  $\cdots$ | 2.75 | 0.34 | Ruchti et al. (2011)
13 43 26.70 |  $+$15 34 31.10 | HD119516 |  $-$2.16 |  $\cdots$ | 1.07 | 0.52 | For & Sneden (2010)
15 54 27.29 |  $+$00 21 36.90 | 2MASS J15542729+0021368 |  $-$2.18 | 0.42 | 0.88 | 0.51 | Sakari et al. (2018)
03 46 45.72 |  $-$30 51 13.32 | HD23798 |  $-$2.22 |  $\cdots$ | 0.83 | 0.54 | Roederer et al. (2010)
15 02 38.50 |  $-$46 02 06.60 | 2MASS J15023852$-$4602066 |  $-$2.23 |  $-$0.16 | 0.97 | 0.30 | Holmbeck et al. (2020)
04 01 49.00 |  $-$37 57 53.40 | 2MASS J04014897$-$3757533 |  $-$2.28 |  $-$0.30 | 2.61 | 0.52 | Holmbeck et al. (2020)
23 02 15.75 |  $-$33 51 11.03 | 2MASS J23021574$-$3351110 |  $-$2.29 | 0.37 | 2.08 | 0.44 | Barklem et al. (2005)
11 41 08.90 |  $-$45 35 28.00 | 2MASS J11410885$-$4535283 |  $-$2.32 |  $\cdots$ | 1.33 | 0.63 | Ruchti et al. (2011)
09 29 49.74 |  $-$29 05 59.20 | 2MASS J09294972$-$2905589 |  $-$2.32 | 0.11 | 0.92 | 0.46 | Sakari et al. (2018)
19 16 18.20 |  $-$55 44 45.40 | 2MASS J19161821$-$5544454 |  $-$2.35 |  $-$0.80 | 2.37 | 0.49 | Hansen et al. (2018)
22 49 23.56 |  $-$21 30 29.50 | TYC 6393-564-1 |  $-$2.38 |  $\cdots$ | 2.96 | 0.54 | Ruchti et al. (2011)
00 31 16.91 |  $-$16 47 40.79 | HD2796 |  $-$2.40 |  $-$0.48 | 1.13 | 0.68 | Mardini et al. (2019b)
11 58 01.28 |  $-$15 22 18.00 | 2MASS J11580127$-$1522179 |  $-$2.41 | 0.62 | 3.62 | 0.38 | Sakari et al. (2018)
15 14 18.90 |  $+$07 27 02.80 | 2MASS J15141890+0727028 |  $-$2.42 | 0.47 | 3.66 | 0.55 | Roederer et al. (2010)
05 10 35.47 |  $-$15 51 38.30 | UCAC4 371-007255 |  $-$2.43 |  $\cdots$ | 0.74 | 0.60 | Cohen et al. (2013)
16 10 31.10 |  $+$10 03 05.60 | 2MASS J16103106+1003055 |  $-$2.43 | 0.53 | 2.49 | 0.23 | Hansen et al. (2018)
05 51 42.14 |  $-$33 27 33.76 | TYC 7062-1120-1 |  $-$2.46 |  $\cdots$ | 1.71 | 0.68 | Holmbeck et al. (2020)
23 16 30.80 |  $-$35 34 35.90 | BPS CS30493$-$0071 |  $-$2.46 |  $-$0.01 | 1.26 | 0.40 | Roederer et al. (2014)
01 07 31.23 |  $-$21 46 06.50 | UCAC4 342-001270 |  $-$2.55 |  $\cdots$ | 3.28 | 0.11 | Cohen et al. (2013)
18 36 23.20 |  $-$64 28 12.50 | 2MASS J18362318$-$6428124 |  $-$2.57 | 0.10 | 1.37 | 0.24 | Hansen et al. (2018)
18 40 59.85 |  $-$48 41 35.30 | 2MASS J18405985$-$4841353 |  $-$2.58 | 0.60 | 1.50 | 0.48 | Ezzeddine et al. (2020)
18 36 12.12 |  $-$73 33 44.17 | 2MASS J18361214$-$7333443 |  $-$2.61 | 0.10 | 2.13 | 0.48 | Ezzeddine et al. (2020)
01 49 07.94 |  $-$49 11 43.16 | CD $-$49∘ 506 |  $-$2.65 |  $\cdots$ | 2.75 | 0.49 | Ruchti et al. (2011)
09 47 19.20 |  $-$41 27 04.00 | 2MASS J09471921$-$4127042 |  $-$2.67 |  $-$0.42 | 2.40 | 0.35 | Holmbeck et al. (2020)
21 51 45.74 |  $-$37 52 30.88 | 2MASS J21514574$-$3752308 |  $-$2.76 | 0.38 | 1.87 | 0.35 | Beers et al. (1992)
22 24 00.14 |  $-$42 35 16.05 | 2MASS J22240014$-$4235160 |  $-$2.77 | 0.14 | 2.45 | 0.49 | Roederer et al. (2014)
15 56 28.74 |  $-$16 55 33.40 | SMSS J155628.74$-$165533.4 |  $-$2.79 | 0.36 | 2.15 | 0.36 | Jacobson et al. (2015)
22 02 16.36 |  $-$05 36 48.40 | 2MASS J22021636$-$0536483 |  $-$2.80 |  $-$0.25 | 3.34 | 0.58 | Hansen et al. (2018)
03 01 00.70 |  $+$06 16 31.87 | BPS CS31079$-$0028 |  $-$2.84 |  $\cdots$ | 1.34 | 0.62 | Roederer et al. (2010)
04 19 45.54 |  $-$36 51 35.92 | 2MASS J04194553$-$3651359 |  $-$2.89 | 0.06 | 3.58 | 0.52 | Roederer et al. (2014)
21 20 28.65 |  $-$20 46 22.90 | BPS CS29506$-$0007 |  $-$2.94 |  $\cdots$ | 1.02 | 0.45 | Roederer et al. (2014)
14 35 58.50 |  $-$07 19 26.50 | 2MASS J14355850$-$0719265 |  $-$2.99 |  $-$0.40 | 3.02 | 0.45 | Ezzeddine et al. (2020)
20 42 48.77 |  $-$20 00 39.37 | BD $-$20∘ 6008 |  $-$3.05 |  $-$0.43 | 1.40 | 0.32 | Roederer et al. (2014)
06 30 55.57 |  $+$25 52 43.81 | SDSS J063055.57+255243.7aaStars that have too large uncertainties in their Gaia EDR3 astrometric data to be useful.  |  $-$3.05 |  $\cdots$ | 0.74 | 0.50 | Aoki et al. (2013)
13 03 29.48 |  $+$33 51 09.14 | 2MASS J12222802+3411318 |  $-$3.05 |  $-$0.18 | 3.93 | 0.61 | Lai et al. (2008)
00 20 16.20 |  $-$43 30 18.00 | UCAC4 233-000355 |  $-$3.07 | 3.02 | 2.70 | 0.52 | Cohen et al. (2013)
13 19 47.00 |  $-$04 23 10.25 | TYC 4961-1053-1aaStars that have too large uncertainties in their Gaia EDR3 astrometric data to be useful.  |  $-$3.10 |  $-$0.52 | 4.50 | 0.30 | Hollek et al. (2011)
12 45 02.68 |  $-$07 38 46.95 | SDSS J124502.68$-$073847.0aaStars that have too large uncertainties in their Gaia EDR3 astrometric data to be useful.  |  $-$3.17 | 2.54 | 4.00 | 0.50 | Aoki et al. (2013)
14 16 04.71 |  $-$20 08 54.08 | 2MASS J14160471$-$208540 |  $-$3.20 | 1.44 | 1.92 | 0.54 | Barklem et al. (2005)
13 22 35.36 |  $+$00 22 32.60 | UCAC4 452-052732 |  $-$3.38 |  $\cdots$ | 2.98 | 0.45 | Cohen et al. (2013)
23 21 21.56 |  $-$16 05 05.65 | HE 2318$-$1621aaStars that have too large uncertainties in their Gaia EDR3 astrometric data to be useful.  |  $-$3.67 | 0.54 | 3.64 | 0.58 | Placco et al. (2020)
11 18 35.88 |  $-$06 50 45.02 | TYC 4928-1438-1aaStars that have too large uncertainties in their Gaia EDR3 astrometric data to be useful.  |  $-$3.73 | 0.08 | 4.71 | 0.31 | Hollek et al. (2011)
13 02 56.24 |  $+$01 41 52.12 | UCAC4 459-050836 |  $-$3.88 | 1.34 | 2.80 | 0.26 | Barklem et al. (2005)
09 47 50.70 |  $-$14 49 07.00 | HE 0945$-$1435aaStars that have too large uncertainties in their Gaia EDR3 astrometric data to be useful.  |  $-$3.90 |  $<$2.03 | 0.76 | 0.57 | Hansen et al. (2015)
10 55 19.28 |  $+$23 22 34.02 | SDSS J105519.28+232234.0aaStars that have too large uncertainties in their Gaia EDR3 astrometric data to be useful.  |  $-$4.00 |  $<$0.70 | 2.20 | 0.45 | Aguado et al. (2017)
14 26 40.33 |  $-$02 54 27.49 | HE 1424$-$0241aaStars that have too large uncertainties in their Gaia EDR3 astrometric data to be useful.  |  $-$4.05 |  $<$0.63 | 3.50 | 0.41 | Cohen et al. (2007)
12 47 19.47 |  $-$03 41 52.50 | SDSS J124719.46$-$034152.4 |  $-$4.11 |  $<$1.61 | 1.71 | 0.24 | Caffau et al. (2013)
12 04 41.39 |  $+$12 01 11.52 | SDSS J120441.38+120111.5aaStars that have too large uncertainties in their Gaia EDR3 astrometric data to be useful.  |  $-$4.34 |  $<$1.45 | 3.35 | 0.39 | Placco et al. (2015)
10 29 15.15 |  $+$17 29 27.88 | SDSS J102915.14+172927.9 |  $-$4.99 |  $<$0.70 | 2.47 | 0.06 | Caffau et al. (2011)

###  7.3 Very and extremely metal-poor stars in the Atari disk as identified
in literature samples

Knowing about the existence of very and extremely metal-poor stars in the
Atari disk, we also applied our selection procedure to known samples of metal-
poor stars to identify additional ones. The SMSS sample used in the analysis
presented here does not cover e.g., Northern hemisphere stars, warm low-
metallicity stars, extremely metal-poor stars with
$[\mathrm{Fe}/\mathrm{H}]<-3.5$, and very faint stars. This leaves room for
more discoveries.

Hence, we chose to investigate the entire data set compiled in the JINAbase
(Abohalima & Frebel, 2018). The latest version is publicly available on
GitHub999https://github.com/Mohammad-Mardini/JINAbase. We cross-matched all
stars with $[\mathrm{Fe}/\mathrm{H}]$$<-2.0$ (2,302 stars) of the JINAbase
catalog with Gaia EDR3 and applied the same quality cuts
(astrometric_excess_noise $<$ 1 $\mu$as and Parallax$\\_$over$\\_$error
$\geqslant$ 5). We then collected radial velocities for these stars if they
were not already listed in JINAbase. This resulted in a sample of 1,098 stars
from which we identified a total of 47 Atari disk stars (5%) with
$[\mathrm{Fe}/\mathrm{H}]<-2.0$. Of those 22 stars have
$[\mathrm{Fe}/\mathrm{H}]<-2.5$, eight have $[\mathrm{Fe}/\mathrm{H}]<-3.0$,
and two have $[\mathrm{Fe}/\mathrm{H}]<-4.0$. A number of stars show
interesting chemical abundance features. Table 5 lists all these Atari disk
stars. These stars have a mean $<V_{\phi}>=152$ km s-1 which is highly
consistent with our full SMSS Atari disk sample’s mean velocity of 154 km s-1
(see Table 2). Eccentricities range from about 0.05 to 0.7, with typical
values around 0.4 to 0.5.

During our investigation of the literature sample as collected from JINAbase,
we noticed a number of e.g. faint stars with low proper motion uncertainties
and high uncertain parallaxes, leading to their exclusion based on the adopted
Gaia astrometry quality cut. In order to prevent the discovery of additional
exremely metal-poor stars due insufficient data quality, we thus opted to do
an additional probability analysis to identify any potential Atari disk
members. We drew 10,000 realizations of each of the 6-d astrometries for these
JINAbase stars with $[\mathrm{Fe}/\mathrm{H}]$$<-3$ assuming a normal
distribution. We then rerun the whole analysis using these possible
combinations to determine the most likely membership for a halo, thin disk and
thick-disk-like kinematic behavior. We only identified nine stars with
$[\mathrm{Fe}/\mathrm{H}]$ $\sim-3.0$. Of those, three stars have
$[\mathrm{Fe}/\mathrm{H}]\lesssim-4.0$. We also identified three stars with
$[\mathrm{Fe}/\mathrm{H}]$ $<-4.0$ with a 50% probability for being be part of
the Atari disk. However, upon further inspection, we find both their Zmax and
eccentricities too high to be bona-fide Atari disk stars. We thus do not
include them in our sample.

###  7.4 The metallicity distribution function of the Atari disk

The upper panel of Figure 8 shows the metallicity distribution function for
our final Atari disk sample (green histogram), and also for the velocity-
selection (red histogram) and action-selection methods (gray histogram). The
distributions look very similar, albeit the overall numbers are different. Our
main sample shows an exponential decrease in stars with decreasing
$[\mathrm{Fe}/\mathrm{H}]$, but with stars reaching down to
$[\mathrm{Fe}/\mathrm{H}]$ $\sim-3.5$, unlike what has been found for the
canonical thick disk. The distribution of the two parent samples support this
overall behavior.

The inset in Figure 8 shows just the metal-poor tail
($[\mathrm{Fe}/\mathrm{H}]$ $<-2.5$) of the MDFs, with a best-fitting
exponential ($\Delta\log{\rm N}/\Delta[\mathrm{Fe}/\mathrm{H}]=1.13\pm 0.06$).
The best-fitting exponential curve (dashed black line) drops to zero at
$[\mathrm{Fe}/\mathrm{H}]\approx-4.0$, supporting the existence of only a
handful of Atari disk stars (as identified in the literature) with
$[\mathrm{Fe}/\mathrm{H}]\approx-4.0$ (see Table 5).

The lower panel of Figure 8 then shows the very metal-poor tail
($[\mathrm{Fe}/\mathrm{H}]$$<-2.5$) of our Atari disk sample (green histogram)
in comparison with the stars from the literature (blue histograms) that we
identified as Atari disk stars (see Section 7.3). Both samples show that Atari
disk contains a number of stars with $[\mathrm{Fe}/\mathrm{H}]$$<-3.0$, with
the literature sample containing stars with $[\mathrm{Fe}/\mathrm{H}]<-4.0$
(in agreement with our best-fitting exponential curve) and even
$[\mathrm{Fe}/\mathrm{H}]\approx-5.0$.

The MDF currently shows no clear peak up to $[\mathrm{Fe}/\mathrm{H}]<-0.8$.
However, there is likely an increasing member contamination by canonical thick
disk stars as [Fe/H] becomes higher than $\sim-1.0$. Assuming the upper bound
of the mean metallicity of the Atari disk is set by [Fe/H] = $-0.8$ (following
from the simple selection recipe presented in and previous Atari disk
selections in Beers et al. 2014 and Naidu et al. 2020), we estimate a
conservative upper limit to the stellar mass of the progenitor system of
$\sim$109 M⊙ from the mass-metallicity relation in Kirby et al. (2013). The
progenitor mass is likely much lower than this value, though, as the Atari
disk ought to be dwarfed by the thick disk (which has a mass of 1.17 $\times
10^{10}$ M⊙) since the Atari disk kinematic signature is only detectable
relative to the thick disk in the low metallicity regime.

Figure 8: Top: Metallicity distribution function (MDF) for stars with
$[\mathrm{Fe}/\mathrm{H}]$$<-0.8$ of the action-selected method (gray
histogram), the velocity-selected method (red histogram), and our Atari disk
sample (green histogram). The inset figure shows the MDFs of stars with
$[\mathrm{Fe}/\mathrm{H}]$$<-2.5$ and the best-fitting exponential
($\Delta\log{\rm N}/\Delta[\mathrm{Fe}/\mathrm{H}]=1.13\pm 0.06$). Bottom: MDF
of the metal-poor tail (with $[\mathrm{Fe}/\mathrm{H}]$$<-2.5$) of our Atari
disk sample (green histogram) compared with the sample of stars that we
identify as Atari disk stars from JINAbase (blue histogram).

###  7.5 Chemical abundance characteristics of the Atari disk

An accretion origin of the Atari disk would imply that distinct chemical
abundance signatures may be identifiable among Atari disk stars, in particular
at the lowest metallicities. We briefly comment on findings as obtained from
the available literature abundances. A more complete discussion will be
presented in X. Ou et al. (2022, in prep.).

Besides the fact that a significant number of stars with
$[\mathrm{Fe}/\mathrm{H}]$$<-3.0$ seem to belong to the Atari disk, we find
several interesting chemical signatures. The 56 (47 + 9 stars with low quality
parallaxes) JINAbase-selected stars with $[\mathrm{Fe}/\mathrm{H}]<-2.0$
display an average [$\alpha$/Fe] $\geqslant 0.3$ dex, which is a feature of
enrichment by core-collapse supernovae and is generally seen in more metal-
poor stars. This enhanced $\alpha$-abundance behavior is unlike that of the
thick disk, which generally shows [$\alpha$/Fe] $\lesssim 0.2$ dex. However,
we note that the lower [$\alpha$/Fe] of the thick disk may be due to its
higher metallicity range than the Atari disk.

Carbon enhancement among metal-poor stars is regarded as a signature of very
early star formation and commonly found among the most metal-poor halo stars
(e.g., Frebel & Norris 2015). Of the 17 stars with $[\mathrm{Fe}/\mathrm{H}]$
$\lesssim-3.0$, three are CEMP stars with $[\mathrm{C}/\mathrm{Fe}]$$>0.7$
(17%). If we were to also count the two additional stars with upper limits
that do not exclude a CEMP-nature, the fraction would increase to 29%.
Interestingly, none of the five stars with $[\mathrm{Fe}/\mathrm{H}]$
$\lesssim-4.0$ appear to be carbon-enhanced at face value, although the two
stars with upper limits on carbon are in this metallicity group. If they were
indeed CEMP stars, the fraction of CEMP stars could be as high as 41%. For
comparison, in the halo, 24% of stars with $[\mathrm{Fe}/\mathrm{H}]$ $<-2.5$
are CEMP stars, 43% at $[\mathrm{Fe}/\mathrm{H}]$ $<-3.0$, 60% at
$[\mathrm{Fe}/\mathrm{H}]$ $<-3.5$, and 81% at $[\mathrm{Fe}/\mathrm{H}]$
$<-4.0$ (Placco et al., 2014). It thus remains to be seen what the CEMP
fraction is among the lowest metallicity stars in the Atari disk but the
existence of at least three CEMP stars with $[\mathrm{Fe}/\mathrm{H}]$
$\lesssim-3.0$ points to Population III inhomogeneous, faint supernova-driven
enrichment (Umeda & Nomoto, 2003) within the earliest star forming systems
which offers additional support for an accretion origin of the Atari disk.

###  7.6 On the origin and history of the Atari disk

Overall, we find that the Atari disk is principally disk-y in nature as it
appears to be confined to a somewhat puffed up, disk-like structure. This is
illustrated by the fact that the long term orbital evolution of Atari disk
stars, including the most metal-poor ones, shows them to remain within
Z${}_{\text{max}}$ = 3 kpc. The Atari disk appears to be distinct from the
canonical thick disk due to its rotational velocity lagging by $\sim 30$ km
s-1 and its distinct peak in angular momentum at a given radius. Moreover,
Atari disk stars exhibit more varied eccentricities than the canonical thick
disk and the Atari disk stellar population exhibits a significant low-
metallicity tail.

Based on our discussion in Section 6, the origin of the Atari disk likely
stems from an early accretion event. However, going forward, it will be
important to compare our findings with results from tailored theoretical
formation models for the Atari disk. In particular, cosmological simulations
focusing on disk formation will be able shed more light on how multiple disk
components (e.g., the Atari disk) may form and evolve and the nature of any
transitory stellar populations between the components. We isolated our sample
to $[\mathrm{Fe}/\mathrm{H}]$$<-0.8$ to preferentially include Atari disk
stars, but future observational investigations may be able to remove this
metallicity criterion if a sufficiently pure dynamical criterion were
established. An improved selection criterion is particularly noteworthy, as an
accretion scenario may support the existence of higher
$[\mathrm{Fe}/\mathrm{H}]$ stars depending on the chemical evolution of the
progenitor system.

To investigate whether any currently known accreted structures could feasibly
be related to the Atari disk, we compared the kinematic properties of the
Atari disk to those of several recently identified structures (see Figure 9).
We list some comparisons below:

Gaia-Sausage-Enceladus: The Gaia-Sausage-Enceladus (GSE) was identified using
varied selection methods (e.g., Belokurov et al., 2018; Helmi, 2020), which
result in differing degrees of contamination with overlapping structures.
However, the GSE stars cover a narrow range in rotational velocity centered at
$\langle V_{\phi}\rangle=0$ km s-1 coupled with a broad $V_{r}$ distribution.
The orbital eccentricities typically are $e>0.8$, and the GSE has a narrow MDF
that peaks at $[\mathrm{Fe}/\mathrm{H}]$$\approx-1.17$ (Feuillet et al.,
2020). A comparison of these properties with kinematics properties of our
Atari disk sample readily shows differences, suggesting no association with
the GSE structure.

Kraken: The Kraken is the largest ($2\times 10^{8}$ M⊙) and oldest ($\approx
11$ Gyr) galactic merger in the Milky Way’s history, as described in Kruijssen
et al. (2020). The spatial boundaries of the Kraken remnants are not well
constrained. However, field stars originating from massive satellites reside
deeper in the gravitational potential of the Milky Way with a clear separation
due to dynamical friction (Amorisco, 2017). This suggests that the Kraken’s
debris would settle in low-energy and more eccentric orbits ($e>0.5$). In
contrast, our Atari disk sample extends to higher Galactocentric distances and
contains a considerable number of stars with near-circular orbits. Hence, the
Kraken appears to be unrelated to the Atari disk.

Heracles: Heracles is a stellar population in the inner Milky Way
(R${}_{GC}<4$ kpc) identified from the SDSS/APOGEE survey DR16 (Horta et al.,
2021) with an accretion origin. Looking at the integrals of motion space of
Heracles (wide range of orbital energies centered around L${}_{z}\approx 0$;
see figure 8 in Horta et al. 2021) and the Atari Disk (narrow range of orbital
energies with wide range Lz), as currently identified, suggests no immediate
association. At face value, the less evolved part of Heracles could occupy
higher orbital energy values, similar to what we found for the Atari disk.
However, it is still unclear how to reconcile the discrepant $L_{z}$
distributions. This makes an association between the two populations seem
unlikely.

Nyx: Nyx is a prograde (V${}_{r}\approx 134$ km s-1, V${}_{\phi}\approx 130$
km s-1, V${}_{\theta}\approx 53$ km s-1) stellar stream spatially located
close to the Galactic disk, originally identified in position-velocity space
(Necib et al., 2020). For a direct comparison with the kinematic properties of
Nyx, we calculated the spherical velocity components (Vr , Vϕ, Vθ) for our
Atari disk sample using Galactocentric spherical coordinates described in
Appendix B of Binney & Tremaine (2008). Interestingly, the mean rotational
velocity for our Atari disk sample (V${}_{\phi}\approx 150$ km s-1), somewhat
overlaps with the Vϕ of Nyx (V${}_{\phi}\approx 130$ km s-1). However, the
mean velocity in the radial direction of our Atari disk sample
($\langle\text{V}_{r}\rangle\sim$ 10 km s-1) is in stark disagreement with
V${}_{r}\approx 134$ km s-1 for Nyx. Nyx also has a mean eccentricity value of
$e=0.68$, somewhat distinct with the eccentricity distribution for the Atari
disk.

Given some similarities in the properties of Nyx and the Atari disk, we
further tested the association of Nyx with the Atari disk by compiling the 6-D
phase space information of the Nyx sample (Necib, priv. comm.) and ran the
sample through our classification algorithm in Section 4. Essentially all of
the Nyx stars are classified as being associated with the Galactic halo, not
the Atari disk. We thus conclude that the Nyx stellar stream is most likely
not associated with the Atari disk.

We also separately investigated the Vr distribution of our Atari disk sample.
If this distribution shows two peaks, both with the same mean value but
opposite sign, it is a sign of a radial merger event that led to the formation
of this structure. At the same time, the two $V_{r}$ peaks should display
near-identical mean rotational velocity and mean azimuthal velocity values.
This has been shown to be the case for e.g. the GSE (Belokurov et al., 2018),
Nyx (Necib et al., 2020) and others.

To test for this scenario, for a well-defined sample of Atari disk stars
within the solar radius ($7<$ kpc R $<9$ kpc), we performed a 3D Gaussian
mixture model fitting over the velocity space (Vr, Vϕ, and Vθ) of our Atari
disk sample (2874 stars). This yielded two Gaussian distributions that peak at
Vr = 42 km s-1 and $-43$ km s-1. These two peaks also have Vϕ= 145 km s-1 and
150 km s-1, Vθ= 0.67 km s-1 and 0.95 km s-1, respectively. The surprisingly
good match of the two peaks’ values of Vr, Vϕ, and Vθ strongly suggest that
the Atari disk was formed through a radial merger.

Finally, we compared the location of our Atari disk sample in $E-L_{z}$ to the
location of other galactic structures, following the right panel of figure 4
in Naidu et al. (2020). For this comparison, we recalculated the orbital
energy of our Atari disk sample and Nyx stream, as described in Naidu et al.
(2020) for consistency. Figure 9 shows a schematic view of the approximate
location in $E-L_{z}$ space of our Atari disk sample (blue ellipsoid) and the
other stellar structures. We also added the approximate location of Nyx (dark
cyan ellipsoid).

Notably, the Atari disk does not overlap with the Kraken, the Helmi stream,
and the GSE. However, it partially overlaps with Wukong, the in-situ halo, and
the rich-$\alpha$-disk (aka. Thick Disk). But the wider spread in the orbital
energy and Lz of our Atari disk sample rules out any close association with
the in-situ halo or the Wukong structures. Also, the rotational velocity lag
of our Atari disk sample with respect to the TD rules out a full association
with the component. Overall, the unique location of the Atari disk in
$E-L_{z}$ space further supports its definition as its own component or
structure within the Milky Way.

Figure 9: Schematic approximate location of various galactic structures in the
$E-L_{z}$ space adopted from Naidu et al. (2020). The approximate location of
our Atari disk sample is highlighted by the blue ellipsoid. Our Atari disk
sample overlaps with the $E-L_{z}$ space of the Wukong, the in-situ halo, and
the $\alpha$-rich disk (canonical thick disk).

We conclude that the Atari disk is a unique, ancient low-metallicity component
that is located within the Galactic disk that is not associated with any other
currently known structure due to its distinct properties (e.g., velocities,
eccentricities, metallicities, and location in $E-L_{z}$). Looking ahead, it
will be important to further study this component. More detailed information
on the chemical abundances of Atari disk stars, especially those with
$[\mathrm{Fe}/\mathrm{H}]<-3.0$ could reveal meaningful insights into the
nature of the progenitor system (mass, star formation history, accretion time)
that may have formed quickly and grown significantly over a short period
before merging by the proto-Milky Way. All massive structures identified in
the Galactic halo, such as the GSE, seems to account for the total mass from
which the early Milky Way grew. However, no mass estimates were considering
any additional structures potentially hiding in the disk (Naidu et al., 2020;
Kruijssen et al., 2020). It thus appears that the Atari disk adds to the
observed tally of galactic structures with massive progenitors that will need
to be taken into consideration when establishing the early accretion history
of the Milky Way.

##  8 Summary

In this extensive chemo-dynamic study, we have comprehensively characterized
the Atari disk as a separate component of the Milky Way’s disk. Below, we
highlight our main conclusions regarding the nature and origin of the Atari
disk:

  * •

We developed a dynamical approach to statistically assign 36,010 low-
metallicity stars selected from SkyMapper DR2 to the Galactic thin disk, thick
disk and halo populations. We utilized two independent probability
distribution function approaches using the action integrals and a velocity-
based method (following Bensby et al. (2003)) to isolate a clean Atari disk
sample while also minimizing the contamination by Galactic halo members, and
thin and thick disk stars. Our clean Atari disk sample comprises 7,127 stars,
all with $-3.5<$ $[\mathrm{Fe}/\mathrm{H}]$$<-0.8$.

  * •

We find the Atari disk to have a scale length of $h_{R}=2.48\,\pm\,0.15$ kpc
and scale height of $h_{Z}=1.67\,\pm\,0.15$ kpc. The metallicity distribution
of the Atari disk has notable correlations with $|Z|$, $V_{\phi}$, $e$, and
$R$. The Atari disk sample shows a mean rotational Velocity of
V${}_{\phi}\approx 154$ km s-1 and a broad eccentricity distribution that
peaks at $e=0.45$. The Atari disk sample has a number of stars with higher
eccentricity orbits than the canonical thick disk. It remains to be seen to
what extent the scale length and scale height are dependent on metallicity.

  * •

Based on our understanding of the nature of the Atari disk and the properties
of our sample, we also developed a simple recipe that could be readily applied
to any sample to single out Atari disk stars.

  * •

Utilizing photometric metallicities adopted from Chiti et al. (2021a) (in
combination with high quality Gaia EDR3 astrometric solutions), in our clean
Atari disk sample of of 7,127 stars, we identify 261 stars with
$[\mathrm{Fe}/\mathrm{H}]$ $<-2.0$, 66 stars with
$[\mathrm{Fe}/\mathrm{H}]\lesssim-2.5$, and 11 stars with
$[\mathrm{Fe}/\mathrm{H}]\lesssim-3.0$. Also, through an additional search, we
find 17 stars with $[\mathrm{Fe}/\mathrm{H}]\lesssim-3.0$ and five stars with
$[\mathrm{Fe}/\mathrm{H}]\lesssim-4.0$ in the literature (collected through
JINAbase) to be associated with the Atari disk. All these metallicities are
below the long-standing metallicity floor of
${[\mathrm{Fe}/\mathrm{H}]}=-2.35$ (Beers et al. 2002) of the thick disk. In
fact, the discovery of these extremely and ultra-metal-poor stars opens a
window to studying the nature and formation history of the proto-disk of our
Galaxy.

  * •

Comparing our results with predictions from the four popular formation
scenarios for the formation and evolution of the thick disk (disk heating,
gas-rich merger, direct accretion, and radial migration), we conclude that the
Atari disk may have been formed through accretion, analogous to what has been
suggested for the canonical thick disk direct accretion scenario. Significant
roles played by other mechanisms in forming the Atari disk are observationally
disfavored. This strongly argues for the need for tailored models to attempt
to explain the observed properties to further reveal the origin and history of
the Atari disk, and its relation to the other disk components.

  * •

We quantified the shape of the MDF for our Atari disk sample. It is well fit
by exponential profile with a slope of $\Delta\log{\rm
N}/\Delta[\mathrm{Fe}/\mathrm{H}]=1.13\pm 0.06$ over the entire metallicity
range of our sample, reaching down to $[\mathrm{Fe}/\mathrm{H}]\sim-4.0$, in
line with several ultra-metal-poor stars being identified as members of the
Atari disk. The MDF currently shows no clear peak, which may be caused by the
likely increasing member contamination by canonical thick disk stars as [Fe/H]
becomes higher than $\sim-1.0$. The mass of the Atari disk is likely lower
than $\sim 10^{9}$ M⊙, both from the fact that it ought to be dwarfed by the
canonical thick disk, and from the mass-metallicity relation assuming an upper
bound of $\langle$[Fe/H]$\rangle$ = $-0.8$.

  * •

We have investigated the existence of any direct association of our Atari disk
component with the following Milky Way structures: Gaia-Sausage-Enceladus,
Kraken, and Nyx, through comparing their space parameters and properties in
the $E-L_{z}$ plane. These comparisons suggest no strong evidence that the
Atari disk is associated with other Galactic structures.

  * •

This study opens a window for the need of more extensive formation modeling(s)
of the Galactic disk system and its history, cosmological simulations of the
early Milky Way, and precise future observations of Atari disk stars. All
these approaches will be required to further investigate in even more detail
the observed chemo-dynamical properties of the Atari disk to comprehensively
reconstruct its origin scenario and subsequent evolution. Quantifying its role
within the early formation of the Galaxy will have important ramifications in
understanding the history of our Milky Way.

We thank John E. Norris, Alexander Ji, Lina Necib, Tilman Hartwig, Miho
Ishigaki, Chengdong Li, and Oudai Oweis for fruitful discussions about stellar
populations. This work is supported by Basic Research Grant (Super AI) of
Institute for AI and Beyond of the University of Tokyo. A.F. acknowledges
support from NSF grant AST-1716251, and thanks the Wissenschaftskolleg zu
Berlin for their wonderful Fellow’s program and generous hospitality. This
work has made use of data from the European Space Agency (ESA) mission Gaia
(https://www.cosmos.esa.int/gaia), processed by the Gaia Data Processing and
Analysis Consortium (DPAC,
https://www.cosmos.esa.int/web/gaia/dpac/consortium). Funding for the DPAC has
been provided by national institutions, in particular the institutions
participating in the Gaia Multilateral Agreement. The national facility
capability for SkyMapper has been funded through ARC LIEF grant LE130100104
from the Australian Research Council, awarded to the University of Sydney, the
Australian National University, Swinburne University of Technology, the
University of Queensland, the University of Western Australia, the University
of Melbourne, Curtin University of Technology, Monash University and the
Australian Astronomical Observatory. SkyMapper is owned and operated by The
Australian National University’s Research School of Astronomy and
Astrophysics. The survey data were processed and provided by the SkyMapper
Team at ANU. The SkyMapper node of the All-Sky Virtual Observatory (ASVO) is
hosted at the National Computational Infrastructure (NCI). Development and
support the SkyMapper node of the ASVO has been funded in part by Astronomy
Australia Limited (AAL) and the Australian Government through the
Commonwealth’s Education Investment Fund (EIF) and National Collaborative
Research Infrastructure Strategy (NCRIS), particularly the National eResearch
Collaboration Tools and Resources (NeCTAR) and the Australian National Data
Service Projects (ANDS). Funding for RAVE has been provided by the Australian
Astronomical Observatory; the Leibniz-Institut fuer Astrophysik Potsdam (AIP);
the Australian National University; the Australian Research Council; the
French National Research Agency; the German Research Foundation (SPP 1177 and
SFB 881); the European Research Council (ERC-StG 240271 Galactica); the
Istituto Nazionale di Astrofisica at Padova; The Johns Hopkins University; the
National Science Foundation of the USA (AST-0908326); the W. M. Keck
foundation; the Macquarie University; the Netherlands Research School for
Astronomy; the Natural Sciences and Engineering Research Council of Canada;
the Slovenian Research Agency; the Swiss National Science Foundation; the
Science $\&$ Technology Facilities Council of the UK; Opticon; Strasbourg
Observatory; and the Universities of Groningen, Heidelberg and Sydney. This
work made use of the Third Data Release of the GALAH Survey (Buder et al.,
2021). The GALAH Survey is based on data acquired through the Australian
Astronomical Observatory, under programs: A/2013B/13 (The GALAH pilot survey);
A/2014A/25, A/2015A/19, A2017A/18 (The GALAH survey phase 1); A2018A/18 (Open
clusters with HER- MES); A2019A/1 (Hierarchical star formation in Ori OB1);
A2019A/15 (The GALAH survey phase 2); A/2015B/19, A/2016A/22, A/2016B/10,
A/2017B/16, A/2018B/15 (The HERMES-TESS program); and A/2015A/3, A/2015B/1,
A/2015B/19, A/2016A/22, A/2016B/12, A/2017A/14 (The HERMES K2-follow-up
program). We acknowledge the traditional owners of the land on which the AAT
stands, the Gamilaraay people, and pay our respects to elders past and
present. This paper includes data that has been provided by AAO Data Central
(datacentral.aao.gov.au). The Guoshoujing Telescope (the Large Sky Area Multi-
Object Fiber Spectroscopic Telescope; LAMOST) is a National Major Scientific
Project built by the Chinese Academy of Sciences. Funding for the project has
been provided by the National Development and Reform Commission. LAMOST is
operated and managed by the National Astronomical Observatories, Chinese
Academy of Sciences. This research has made use of the SIMBAD database,
operated at CDS, Strasbourg, France.

## References

  * Abadi et al. (2003a) Abadi, M. G., Navarro, J. F., Steinmetz, M., & Eke, V. R. 2003a, ApJ, 591, 499, doi: 10.1086/375512
  * Abadi et al. (2003b) —. 2003b, ApJ, 597, 21, doi: 10.1086/378316
  * Abohalima & Frebel (2018) Abohalima, A., & Frebel, A. 2018, ApJS, 238, 36, doi: 10.3847/1538-4365/aadfe9
  * Aguado et al. (2017) Aguado, D. S., González Hernández, J. I., Allende Prieto, C., & Rebolo, R. 2017, A&A, 605, A40, doi: 10.1051/0004-6361/201730654
  * Allende Prieto et al. (2016) Allende Prieto, C., Kawata, D., & Cropper, M. 2016, A&A, 596, A98, doi: 10.1051/0004-6361/201629787
  * Amôres et al. (2017) Amôres, E. B., Robin, A. C., & Reylé, C. 2017, A&A, 602, A67, doi: 10.1051/0004-6361/201628461
  * Amorisco (2017) Amorisco, N. C. 2017, MNRAS, 464, 2882, doi: 10.1093/mnras/stw2229
  * An & Beers (2020) An, D., & Beers, T. C. 2020, ApJ, 897, 39, doi: 10.3847/1538-4357/ab8d39
  * Anders et al. (2014) Anders, F., Chiappini, C., Santiago, B. X., et al. 2014, A&A, 564, A115, doi: 10.1051/0004-6361/201323038
  * Aoki et al. (2013) Aoki, W., Beers, T. C., Lee, Y. S., et al. 2013, AJ, 145, 13, doi: 10.1088/0004-6256/145/1/13
  * Bailer-Jones et al. (2021) Bailer-Jones, C. A. L., Rybizki, J., Fouesneau, M., Demleitner, M., & Andrae, R. 2021, AJ, 161, 147, doi: 10.3847/1538-3881/abd806
  * Bailer-Jones et al. (2018) Bailer-Jones, C. A. L., Rybizki, J., Fouesneau, M., Mantelet, G., & Andrae, R. 2018, AJ, 156, 58, doi: 10.3847/1538-3881/aacb21
  * Barklem et al. (2005) Barklem, P. S., Christlieb, N., Beers, T. C., et al. 2005, A&A, 439, 129, doi: 10.1051/0004-6361:20052967
  * Beers et al. (2002) Beers, T. C., Drilling, J. S., Rossi, S., et al. 2002, AJ, 124, 931, doi: 10.1086/341377
  * Beers et al. (2014) Beers, T. C., Norris, J. E., Placco, V. M., et al. 2014, ApJ, 794, 58, doi: 10.1088/0004-637X/794/1/58
  * Beers et al. (1992) Beers, T. C., Preston, G. W., & Shectman, S. A. 1992, AJ, 103, 1987, doi: 10.1086/116207
  * Belokurov et al. (2018) Belokurov, V., Erkal, D., Evans, N. W., Koposov, S. E., & Deason, A. J. 2018, MNRAS, 478, 611, doi: 10.1093/mnras/sty982
  * Bennett & Bovy (2019) Bennett, M., & Bovy, J. 2019, MNRAS, 482, 1417, doi: 10.1093/mnras/sty2813
  * Bensby et al. (2011) Bensby, T., Alves-Brito, A., Oey, M. S., Yong, D., & Meléndez, J. 2011, ApJ, 735, L46, doi: 10.1088/2041-8205/735/2/L46
  * Bensby et al. (2003) Bensby, T., Feltzing, S., & Lundström, I. 2003, A&A, 410, 527, doi: 10.1051/0004-6361:20031213
  * Bensby et al. (2005) Bensby, T., Feltzing, S., Lundström, I., & Ilyin, I. 2005, A&A, 433, 185, doi: 10.1051/0004-6361:20040332
  * Binney (2010) Binney, J. 2010, MNRAS, 401, 2318, doi: 10.1111/j.1365-2966.2009.15845.x
  * Binney & Sanders (2016) Binney, J., & Sanders, J. L. 2016, Astronomische Nachrichten, 337, 939, doi: 10.1002/asna.201612403
  * Binney & Tremaine (2008) Binney, J., & Tremaine, S. 2008, Galactic Dynamics: Second Edition (Princeton University Press)
  * Bovy (2015) Bovy, J. 2015, ApJS, 216, 29, doi: 10.1088/0067-0049/216/2/29
  * Brook et al. (2007) Brook, C., Richard, S., Kawata, D., Martel, H., & Gibson, B. K. 2007, ApJ, 658, 60, doi: 10.1086/511056
  * Brook et al. (2004) Brook, C. B., Kawata, D., Gibson, B. K., & Freeman, K. C. 2004, ApJ, 612, 894, doi: 10.1086/422709
  * Buder et al. (2021) Buder, S., Sharma, S., Kos, J., et al. 2021, MNRAS, doi: 10.1093/mnras/stab1242
  * Caffau et al. (2011) Caffau, E., Bonifacio, P., François, P., et al. 2011, Nature, 477, 67, doi: 10.1038/nature10377
  * Caffau et al. (2013) Caffau, E., Bonifacio, P., Sbordone, L., et al. 2013, A&A, 560, A71, doi: 10.1051/0004-6361/201322488
  * Carollo et al. (2010) Carollo, D., Beers, T. C., Chiba, M., et al. 2010, ApJ, 712, 692, doi: 10.1088/0004-637X/712/1/692
  * Carollo et al. (2019) Carollo, D., Chiba, M., Ishigaki, M., et al. 2019, ApJ, 887, 22, doi: 10.3847/1538-4357/ab517c
  * Carter et al. (2020) Carter, C., Conroy, C., Zaritsky, D., et al. 2020, arXiv e-prints, arXiv:2012.00036.  https://arxiv.org/abs/2012.00036
  * Cheng et al. (2012) Cheng, J. Y., Rockosi, C. M., Morrison, H. L., et al. 2012, ApJ, 746, 149, doi: 10.1088/0004-637X/746/2/149
  * Chiba & Beers (2000) Chiba, M., & Beers, T. C. 2000, AJ, 119, 2843, doi: 10.1086/301409
  * Chiti et al. (2020) Chiti, A., Frebel, A., Jerjen, H., Kim, D., & Norris, J. E. 2020, ApJ, 891, 8, doi: 10.3847/1538-4357/ab6d72
  * Chiti et al. (2021a) Chiti, A., Frebel, A., Mardini, M. K., et al. 2021a, ApJS, 254, 31, doi: 10.3847/1538-4365/abf73d
  * Chiti et al. (2021b) Chiti, A., Mardini, M. K., Frebel, A., & Daniel, T. 2021b, ApJ, 911, L23, doi: 10.3847/2041-8213/abd629
  * Cohen et al. (2013) Cohen, J. G., Christlieb, N., Thompson, I., et al. 2013, ApJ, 778, 56, doi: 10.1088/0004-637X/778/1/56
  * Cohen et al. (2007) Cohen, J. G., McWilliam, A., Christlieb, N., et al. 2007, ApJ, 659, L161, doi: 10.1086/518031
  * Cordoni et al. (2020) Cordoni, G., Da Costa, G. S., Yong, D., et al. 2020, MNRAS, doi: 10.1093/mnras/staa3417
  * Cui et al. (2012) Cui, X.-Q., Zhao, Y.-H., Chu, Y.-Q., et al. 2012, Research in Astronomy and Astrophysics, 12, 1197, doi: 10.1088/1674-4527/12/9/003
  * de Jong et al. (2010) de Jong, J. T. A., Yanny, B., Rix, H.-W., et al. 2010, ApJ, 714, 663, doi: 10.1088/0004-637X/714/1/663
  * Dehnen & Binney (1998) Dehnen, W., & Binney, J. 1998, MNRAS, 294, 429, doi: 10.1046/j.1365-8711.1998.01282.x
  * Di Matteo et al. (2020) Di Matteo, P., Spite, M., Haywood, M., et al. 2020, A&A, 636, A115, doi: 10.1051/0004-6361/201937016
  * Engler et al. (2021) Engler, C., Pillepich, A., Pasquali, A., et al. 2021, MNRAS, 507, 4211, doi: 10.1093/mnras/stab2437
  * Ezzeddine et al. (2020) Ezzeddine, R., Rasmussen, K., Frebel, A., et al. 2020, ApJ, 898, 150, doi: 10.3847/1538-4357/ab9d1a
  * Feuillet et al. (2020) Feuillet, D. K., Feltzing, S., Sahlholdt, C. L., & Casagrande, L. 2020, MNRAS, 497, 109, doi: 10.1093/mnras/staa1888
  * For & Sneden (2010) For, B.-Q., & Sneden, C. 2010, AJ, 140, 1694, doi: 10.1088/0004-6256/140/6/1694
  * Frebel (2018) Frebel, A. 2018, Annual Review of Nuclear and Particle Science, 68, 237, doi: 10.1146/annurev-nucl-101917-021141
  * Frebel & Norris (2015) Frebel, A., & Norris, J. E. 2015, ARA&A, 53, 631, doi: 10.1146/annurev-astro-082214-122423
  * Gaia Collaboration et al. (2020) Gaia Collaboration, Brown, A. G. A., Vallenari, A., et al. 2020, arXiv e-prints, arXiv:2012.01533.  https://arxiv.org/abs/2012.01533
  * Gaia Collaboration et al. (2016) Gaia Collaboration, Prusti, T., de Bruijne, J. H. J., et al. 2016, A&A, 595, A1, doi: 10.1051/0004-6361/201629272
  * Gilmore & Reid (1983) Gilmore, G., & Reid, N. 1983, MNRAS, 202, 1025, doi: 10.1093/mnras/202.4.1025
  * Gilmore et al. (1989) Gilmore, G., Wyse, R. F. G., & Kuijken, K. 1989, ARA&A, 27, 555, doi: 10.1146/annurev.aa.27.090189.003011
  * Gilmore et al. (2002) Gilmore, G., Wyse, R. F. G., & Norris, J. E. 2002, ApJ, 574, L39, doi: 10.1086/342363
  * Gravity Collaboration et al. (2019) Gravity Collaboration, Abuter, R., Amorim, A., et al. 2019, A&A, 625, L10, doi: 10.1051/0004-6361/201935656
  * Guiglion et al. (2015) Guiglion, G., Recio-Blanco, A., de Laverny, P., et al. 2015, A&A, 583, A91, doi: 10.1051/0004-6361/201525883
  * Hansen et al. (2015) Hansen, T., Hansen, C. J., Christlieb, N., et al. 2015, ApJ, 807, 173, doi: 10.1088/0004-637X/807/2/173
  * Hansen et al. (2018) Hansen, T. T., Holmbeck, E. M., Beers, T. C., et al. 2018, ApJ, 858, 92, doi: 10.3847/1538-4357/aabacc
  * Helmi (2020) Helmi, A. 2020, ARA&A, 58, 205, doi: 10.1146/annurev-astro-032620-021917
  * Hollek et al. (2011) Hollek, J. K., Frebel, A., Roederer, I. U., et al. 2011, ApJ, 742, 54, doi: 10.1088/0004-637X/742/1/54
  * Holmbeck et al. (2020) Holmbeck, E. M., Hansen, T. T., Beers, T. C., et al. 2020, ApJS, 249, 30, doi: 10.3847/1538-4365/ab9c19
  * Horta et al. (2021) Horta, D., Schiavon, R. P., Mackereth, J. T., et al. 2021, MNRAS, 500, 1385, doi: 10.1093/mnras/staa2987
  * Jacobson et al. (2015) Jacobson, H. R., Keller, S., Frebel, A., et al. 2015, ApJ, 807, 171, doi: 10.1088/0004-637X/807/2/171
  * Jurić et al. (2008) Jurić, M., Ivezić, Ž., Brooks, A., et al. 2008, ApJ, 673, 864, doi: 10.1086/523619
  * Kazantzidis et al. (2008) Kazantzidis, S., Bullock, J. S., Zentner, A. R., Kravtsov, A. V., & Moustakas, L. A. 2008, ApJ, 688, 254, doi: 10.1086/591958
  * Kerr & Lynden-Bell (1986) Kerr, F. J., & Lynden-Bell, D. 1986, MNRAS, 221, 1023, doi: 10.1093/mnras/221.4.1023
  * Kilic et al. (2017) Kilic, M., Munn, J. A., Harris, H. C., et al. 2017, ApJ, 837, 162, doi: 10.3847/1538-4357/aa62a5
  * Kirby et al. (2013) Kirby, E. N., Cohen, J. G., Guhathakurta, P., et al. 2013, The Astrophysical Journal, 779, 102, doi: 10.1088/0004-637x/779/2/102
  * Kordopatis et al. (2011) Kordopatis, G., Recio-Blanco, A., de Laverny, P., et al. 2011, A&A, 535, A107, doi: 10.1051/0004-6361/201117373
  * Kruijssen et al. (2020) Kruijssen, J. M. D., Pfeffer, J. L., Chevance, M., et al. 2020, MNRAS, 498, 2472, doi: 10.1093/mnras/staa2452
  * Kuijken & Gilmore (1991) Kuijken, K., & Gilmore, G. 1991, ApJ, 367, L9, doi: 10.1086/185920
  * Kunder et al. (2017) Kunder, A., Kordopatis, G., Steinmetz, M., et al. 2017, AJ, 153, 75, doi: 10.3847/1538-3881/153/2/75
  * Lai et al. (2008) Lai, D. K., Bolte, M., Johnson, J. A., et al. 2008, ApJ, 681, 1524, doi: 10.1086/588811
  * Lee et al. (2011) Lee, Y. S., Beers, T. C., An, D., et al. 2011, ApJ, 738, 187, doi: 10.1088/0004-637X/738/2/187
  * Li & Zhao (2017) Li, C., & Zhao, G. 2017, ApJ, 850, 25, doi: 10.3847/1538-4357/aa93f4
  * Li et al. (2018) Li, C., Zhao, G., Zhai, M., & Jia, Y. 2018, ApJ, 860, 53, doi: 10.3847/1538-4357/aac50f