# Stellar Mergers or Truly Young?
Intermediate-Age Stars on Highly-Radial Orbits in the Milky Way’s Stellar Halo

Danny Horta Center for Computational Astrophysics, Flatiron Institute, 162 5th
Ave., New York, NY 10010, USA
Yuxi (Lucy) Lu Astrophysics Department, American Museum of Natural History,
200 Central Park West, New York, 10024, NY, USA  Department of Astronomy,
Columbia University, 550 West 120th Street, New York, NY 10027, USA  Melissa
K. Ness Department of Astronomy, Columbia University, 550 West 120th Street,
New York, NY 10027, USA  Research School of Astronomy $\&$ Astrophysics,
Australian National University, Canberra ACT 2611, Australia  Mariangela
Lisanti Center for Computational Astrophysics, Flatiron Institute, 162 5th
Ave., New York, NY 10010, USA
Department of Physics, Princeton University, Princeton, NJ 08544, USA
Adrian M. Price-Whelan Center for Computational Astrophysics, Flatiron
Institute, 162 5th Ave., New York, NY 10010, USA
Danny Horta<EMAIL_ADDRESS>
###### Abstract

Reconstructing the mass assembly history of the Milky Way relies on obtaining
detailed measurements of the properties of many stars in the Galaxy,
especially in the stellar halo. One of the most constraining quantities is
stellar age, as it can shed light on the accretion time and quenching of star
formation in merging satellites. However, obtaining reliable age estimates for
large samples of halo stars is difficult. We report published ages of 120
subgiant halo stars with highly-radial orbits that likely belong to the debris
of the Gaia-Enceladus/Sausage (GES) galaxy. The majority of these halo stars
are old, with an age distribution characterized by a median of 11.6 Gyr and
16th(84th) percentile of 10.5 (12.7) Gyr. However, the distribution is skewed,
with a tail of younger stars that span ages down to $\sim 6$–$9$ Gyr. All
highly-radial halo stars have chemical and kinematic/orbital quantities that
associate them with the GES debris. Initial results suggest that these
intermediate-age stars are not a product of mass transfer and/or stellar
mergers, which can bias their age determination low. If this conclusion is
upheld by upcoming spectro-photometric studies, then the presence of these
stars will pose an important challenge for constraining the properties of the
GES merger and the accretion history of the Galaxy.

Milky Way — Stellar halo — Stellar ages

††software:  matplotlib (Hunter, 2007), numpy (Harris et al., 2020), Gala
(Price-Whelan, 2017), AGAMA (Vasiliev, 2019)

##  1 Introduction

In addition to a star’s chemical and kinematic/orbital properties, its age
also serves as a useful quantity for inferring its origin. For large samples,
stellar ages are crucial for understanding stellar and galactic evolution
(Edvardsson et al., 1993; Lachaume et al., 1999; Nordström et al., 2004;
Martig et al., 2016; Ness et al., 2016; Sanders et al., 2023, e.g.,). However,
obtaining stellar age measurements is a non-trivial task.

Traditional recipes typically rely on using colour-magnitude diagrams (CMD)
and fitting theoretical stellar evolutionary sequences (i.e., stellar
isochrones) to stars to infer their age (Soderblom, 2010). This technique is
robust for main-sequence turn off (MSTO) and subgiant stars that extend to the
oldest possible ages ($\sim 14$ Gyr, Xiang et al., 2017, e.g.,). This is
because there is substantial discriminating power of ischrones for measuring
stellar age at this evolutionary state. Moreover, the chemical compositions of
stellar atmospheres determined from spectra of subgiant stars reflect the
birth gas from which they formed (Freeman & Bland-Hawthorn, 2002). This makes
subgiants some of the best chemical-chronological-dynamical tracers (Xiang &
Rix, 2022).

Figure 1: Dynamical selection of the GES sample. Left: The GES sample (pink)
and parent sample (black) in the orbital energy versus azimuthal angular
momentum plane. Shown as blue are the intermediate-age GES stars (see Section
3). GES stars sit on high-energy and low-$L_{z}$ orbits. Here, prograde
populations have negative $L_{z}$. Right: Same as the left panel, but for the
radial action versus $L_{z}$ plane, which we use to select the GES sample.

For the Milky Way, the time at which a star is born is particularly useful for
retelling the mass assembly history of the Galaxy because different Galactic
populations have different stellar age distributions (Gallart et al., 2019;
Spitoni et al., 2019; Xiang & Rix, 2022, e.g.,). For example, old stars (i.e.,
Age $\gtrsim 10$ Gyr) tend to be associated with the Galactic stellar halo
and/or thick (high-$\alpha$) disc. Conversely, younger stars (Age $\lesssim 6$
Gyr) are typically associated with the thin (low-$\alpha$) disc and are
predominantly formed in situ. Moreover, the ages of stars born ex situ help
constrain the time in which accretion events occurred in the Galaxy (Montalbán
et al., 2021). They also help constrain the time in which these accreted
systems quenched star formation (Bonaca et al., 2020), as the youngest star
should be the latest one formed. Thus, stellar ages are crucial for unveiling
the accretion history of the Milky Way and for inferring the properties of
accreted satellites.

Until recently, obtaining large samples of subgiant stars across the Galaxy
has been difficult due to the short lifetime of their evolutionary phase, as
compared to their red giant star counterparts. However, the advent of large-
scale stellar surveys (e.g., APOGEE: Majewski et al., 2017, LAMOST: Zhao et
al., 2012, GALAH: Freeman, 2012) and the Gaia mission (Gaia Collaboration et
al., 2016, 2022) has supplied a wealth of data for millions of Milky Way
stars, making it possible to determine reliable ages, element abundances, and
orbits for large samples of subgiants.

In this paper, we use the publicly available catalogue of stellar ages for
subgiant stars compiled by Xiang & Rix (2022) (hereafter, XR22) using the
LAMOST DR7 and Gaia DR3 data to examine the age distribution of stars in the
Galaxy on highly-radial orbits that likely belong to the remnant of the Gaia-
Enceladus/Sausage (GES) accretion event (Belokurov et al., 2018; Haywood et
al., 2018; Helmi et al., 2018; Mackereth et al., 2019). We seek to investigate
$i$) what is the overall distribution of ages in the GES debris, and $ii$) how
old are the youngest stars in GES, with the aim of constraining the properties
of the GES system and its accretion episode within the Milky Way.

This paper is organized as follows. In Section 2, we present the data and
define our sample. In Section 3, we present the results on the element
abundance, age, and kinematic/orbital properties. We then discuss the
implications of our findings in Section 4 before concluding in Section 5.

##  2 Data

We use the public catalogue of stellar ages for subgiant stars computed by
XR22 using the LAMOST DR7 and Gaia DR3 surveys. This catalogue also has the
element abundances from LAMOST and the required 6D phase-space information to
determine kinematics/orbits from Gaia/LAMOST. In total, this sample contains
247,104 subgiant stars.

As we are focusing on examining the ages of stars in the GES, which is
primarily a metal-poor population in the Galactic stellar halo, we follow the
advice from XR22 to obtain reliable age measurements for metal-poor stars and
enforce the following selection criteria:

High signal-to-noise spectra

LAMOST spectral S/N $>80$,

Subgiant stars

LAMOST-determined atmospheric parameters, effective temperature and surface
gravity $4000<T_{\mathrm{eff}}<7000$ K and $2<\log(g)<5$,

Precise age measurements

$\sigma_{\mathrm{age}}/\mathrm{age}<0.1$,

High-quality astrometry and stars not in wide binaries

RUWE $<1.2$,

No low-$\alpha$ disc stars

$\mathrm{[Fe/H]}<-0.5$.

These quality cuts yield a sample of 11,336 stars.

###  2.1 Sample of Gaia-Enceladus/Sausage stars

Figure 2: The GES sample (colour) and parent sample (black) in the Kiel
diagram, where the GES sample is colour-coded by stellar age (left) and [Fe/H]
abundance (right). As blue markers we also show the intermediate-age GES stars
(see Section 3). There is a subset of hot young stars ($T_{\mathrm{eff}}>6500$
K), which we remove from the analysis (see text for details).

To pick out stars on highly-radial orbits that are likely part of a pure
sample of the GES debris, we perform a dynamical cut following a similar
criteria to Feuillet et al. (2021). We select stars with $|L_{z}|<700$ kpc km
s-1 and $\sqrt{J_{R}}>30$ kpc km s-1. This selection yields 124 stars with
highly-radial orbits.111The $J_{r}$-$L_{z}$ method has been pointed out by
Carrillo et al. (2024) to be the most robust method of picking out a pure
sample of GES stars. We integrate orbits using the Gala package (Price-Whelan,
2017) assuming the MilkyWayPotential2022 potential (Price-Whelan et al.,
2022), which is a four-component Milky Way mass model consisting of spherical
Hernquist nucleus and bulge components, an (approximate) exponential disk
component, and a spherical NFW halo component. This potential model is fitted
to the Eilers et al. (2019) rotation curve and a compilation of Milky Way mass
enclosed measurements (see Section 2 of Hunt et al. 2022). This is done by
converting the 6D phase-space information222Sky positions and proper motions
are obtained from Gaia DR3 astrometry, the distances are taken from Xiang &
Rix (2022), and the radial velocities are taken from LAMOST DR7. into
Cartesian and cylindrical coordinates assuming a position of the Sun of
$R_{\odot}=8.275$ kpc (GRAVITY Collaboration et al., 2022) and
$z_{\odot}=20.8$ pc (Bennett & Bovy, 2019), and a local standard of rest of
($U_{\odot}$, $V_{\odot}$, $W_{\odot}$) = $(8.4,251.8,8.4)$ km s-1. Orbital
actions, $J=(J_{R},J_{\phi},J_{z})$, are then computed using the AGAMA package
(Vasiliev, 2019) using the “Staeckel Fudge” approximation (Binney, 2012).

The GES sample is shown in pink/blue in the orbital energy, $E$, and radial
action, $J_{R}$, as a function of azimuthal angular momentum, $L_{z}$, planes
in Fig. 1. Here, the parent sample is shown as a black 2D histogram. The GES
sample occupies a locus of high-energy and radial orbits (by definition),
typical of the GES debris (e.g., Belokurov et al., 2018; Helmi et al., 2018;
Koppelman et al., 2019; Mackereth et al., 2019; Horta et al., 2023a).

In Fig. 2, we also show the same data in the Kiel diagram. In the left panel,
the highly-radial stars are coloured by their stellar age and in the right
panel, by their [Fe/H] abundance. Overall, the highly-radial stars sit at a
higher surface gravity for a given effective temperature when compared to the
parent sample, as expected for more metal-poor populations. However, there is
a tail of young hot stars in the GES sample. To ensure trustworthy age
measurements, we remove these four young hot-star outliers333It is possible
that these hotter and younger stars could be blue stragglers. by enforcing
$T_{\mathrm{eff}}<6500$ K. This additional cut leads to a final working sample
comprised of 120 (candidate) GES stars.

Lastly, we also examined the extinctions provided by Gaia ($A_{G}$,
$A_{\mathrm{BP}}$, $A_{\mathrm{RP}}$) and compared the GES stars to the parent
sample. The GES stars do not present anomalous extinction values. We also
checked if the MK,geo and MK,spec for all stars agreed to ensure no unresolved
binaries were infiltrating our GES sample, and found this to be the case
($|$M${}_{K\mathrm{,geo}}-$ M${}_{K\mathrm{,spec}}|<0.5$).

##  3 Results

###  3.1 Ages and Element Abundances

Figure 3: Element abundances and ages for GES stars (pink) and the younger GES
stars with $\mathrm{Age<8.6}$ Gyr (blue). Left: The [$\alpha$/Fe]-[Fe/H]
diagram. Middle: The [Fe/H]-age plane. Right: The age histogram. The GES stars
(pink and blue) are distinguishable from the dominant in situ disc population
(black) in element abundance-age space. The median age of the GES debris is
$=11.6^{+1.14}_{-1.15}$ Gyr, with the range indicating the $16^{\rm th}$ and
$84^{\rm th}$ percentiles. The age distribution of GES stars is skewed towards
younger ages, reaching $\sim 6$–$9$ Gyrs.

Fig. 3 shows the sample of GES stars (pink) in the [$\alpha$/Fe]-[Fe/H] plane
(left) and the [Fe/H]-age plane (middle), as well as a histogram of their age
distribution (right). In all these panels, we also show the parent sample as
black. The $\alpha$-Fe compositions of the highly-radial star sample occupy a
similar locus to that of the GES, as seen in previous work (Nissen & Schuster,
2010; Hayes et al., 2018; Mackereth et al., 2019; Monty et al., 2020; Horta et
al., 2021, 2023a, e.g.,). The GES stars are metal-poor ([Fe/H] $<-0.9$) and
trace an $\alpha$-Fe trajectory that sits below the metal-poor tail of the
high-$\alpha$ disc. The age-metallicity distribtion shows how the majority of
the GES stars are old (Age $\gtrsim 10$ Gyr) and metal-poor, sitting below the
main body of the parent sample that is primarily more metal-rich and younger,
as expected for disc populations. However, there is a tail of stars in the GES
sample that reach younger ages ($6\lesssim\mathrm{Age}\lesssim 9$ Gyr, shown
in blue), which are also more metal-poor than stars in the parent sample for
the same age. The tail of intermediate-age stars in the GES sample is also
clearly seen in the right panel of Fig. 3. Here, the median is
$11.6^{+1.14}_{-1.15}$ Gyr, with the range indicating the [$16^{\mathrm{th}}$,
$84^{\mathrm{th}}$] percentiles of the distribution. However, the distribution
is skewed to younger ages. In total, there are seven GES outlier stars with
ages below the $5^{\mathrm{th}}$ percentile ($<8.6$ Gyr) of the distribution.

To ensure that these outliers are statistically significant, we perform two
exercises. First, we randomly sample the age of each star from a normal
distribution $10^{4}$ times, centered on the XR22 reported age measurement,
with a standard deviation equal to the corresponding age error. For each of
these $10^{4}$ trials, we compute the $5^{\mathrm{th}}$ percentile of the
distribution of the resampled 120 ages, and count the number of stars that
fall below this value. For $86\%$ of the trials, we often recover the same
seven intermediate-age stars; $11\%$ of the time we recover six stars, and
$3\%$ of the time we recover eight stars. Thus, when sampling within the age
uncertainties, we still recover the intermediate-age stars. In the second
test, we randomly sample with replacement 120 stars from the GES age
distribution and calculate the number of times we are able to identify these
intermediate-age GES outlier stars. When running this random sampling $10^{4}$
times, the average number of stars that fall below the $5^{\mathrm{th}}$
percentile value of the _original_ distribution is $\sim 6$–$8$. However,
$\sim 3\%$ of the time, we only recover $\sim 1$–$3$. This result confirms
that this tail of younger GES stars is statistically significant.

In the following subsection, we set out to examine the kinematics and orbits
of the GES sample and seek to ensure if the younger GES stars follow the same
orbital pattern as the main body of the debris.

###  3.2 Velocities and Orbits

The GES remnant was initially discovered due to the highly-radial orbits of
its debris. One of the kinematic diagrams used to illustrate this point is the
$v_{r}$ vs. $v_{\phi}$ plane (Belokurov et al., 2018), which relates the
radial and azimuthal velocities of stars in a cylindrical Galactocentric
coordinate system. The GES stars are shown in this diagram, as well as the
$v_{R}$ vs. $v_{z}$ and $v_{z}$ vs. $v_{\phi}$ planes, in Fig. 4. Here, the
full GES sample is shown as pink, and the intermediate-aged stars (i.e., Age
$<8.6$ Gyr) are shown in blue. All the GES-selected stars occupy a position in
this diagram at either end of the $v_{R}$ distribution, where one would expect
highly-radial orbits. This is to be expected, as the initial selection of the
GES sample is tailored to pick out highly-radial orbits, and thus these stars
will not present a high signature of rotation (i.e., low-$v_{\phi}$).
Additionally, the sample presents low vertical velocities, $v_{z}$, implying
that the majority of the kinetic energy of these stars is in the radial
direction.

Figure 4: GES stars (pink) in different Galactocentric cylindrical velocity
projections. Highlighted as blue points are stars in the GES sample with ${\rm
Age}<8.6$ Gyr. This cutoff corresponds to the $5^{\mathrm{th}}$ percentile of
the age distribution, as shown in the right panel of Fig. 3. The intermediate-
age stars occupy the same locus as the main body of the GES debris in all
velocity planes.

Highly-radial orbits can be found in the plane of the Galaxy due to
interactions with the Galactic bar and resonances in the disc. To ensure that
the GES sample is comprised of stars on halo-like orbits and thus not confined
to the plane, we examine the maximum orbital vertical height,
$z_{\mathrm{max}}$, of its stars as a function of eccentricity in the left
panel of Fig. 5. All the stars in the sample have $z_{\mathrm{max}}\gtrsim 1$
kpc and are thus not likely part of the Milky Way disc. They also present high
eccentricity ($e>0.8$), by definition. Moreover, their apocentric distances
are large ($R_{\mathrm{apo}}>10$ kpc, see right panel of Fig. 5), whilst their
pericentric distances are small ($R_{\mathrm{peri}}<2$ kpc), indicating that
these are likely halo stars on eccentric orbits, consistent with the
expectation for the GES debris.

Figure 5: Same as Fig. 4, but now showing orbital properties of stars. In
detail, left shows the maximum orbital height, $z_{\mathrm{max}}$, as a
function of orbital eccentricity, $e$; right shows apocenter versus pericenter
distance. Both the main body of the GES debris, as well as the intermediate-
age stars, present orbits that are not confined to the Galactic plane (i.e.,
$z_{\mathrm{max}}\gtrsim 1$ kpc) and reach large apocenter radii
($R_{\mathrm{apo}}\sim 10$–$30$ kpc).

Lastly, in addition to the kinematics and orbits, we inspected the present-day
position of these stars and their distance with respect to the position of the
Sun. All the GES stars, including the intermediate-age ones, are distributed
uniformly within a (present-day) radius of 3 kpc from the Sun.

##  4 Discussion

This work demonstrates that the age distribution of the GES stars has a median
of $\sim 11.6$ Gyr, with $16^{\rm th}$ and $84^{\rm th}$ percentiles of $\sim
10.5$ and 12.7 Gyr, respectively (Fig. 3). This corroborates the findings from
previous work attempting to age date the GES debris either using CMD fitting
(Helmi et al., 2018; Gallart et al., 2019; Bonaca et al., 2020; Feuillet et
al., 2021, e.g.,) or asteroseismology (e.g., Montalbán et al., 2021), which
suggests an age for the GES debris that is ancient ($\gtrsim 9$–$10$ Gyr ago).
However, we have also identified a tail of intermediate-age stars (${\rm
Age}\sim 6$–$9$ Gyr) that sit within the first $5^{\mathrm{th}}$ percentile of
the distribution.

In a recent study (Bonaca et al., 2020), the age distribution of an “accreted
halo” sample (that is largely similar to the GES sample) was examined using
MSTO stars. The authors found a similar profile to the one presented here,
whereby the peak of the distribution is old (${\rm Age}>10$–$11$ Gyr), but
skewed to younger ages. This was also seen in Feuillet et al. (2021) and
Grunblatt et al. (2021) using red giants. The raw distribution of ages between
the MSTO/red giant stars from these studies and the subgiants from this work
are in qualitative agreement and suggest a tail of younger ages in the GES
debris.

Here, we discuss the implications of the sample of intermediate-age stars in
GES and attempt to contextualise the results by discussing a number of
possible scenarios that could explain the data.

###  4.1 Robustness of the age estimates

We begin by performing a series of tests to answer two questions: 1) how
robust are the age determinations for the intermediate-age GES stars?; 2) what
observable is the culprit for a younger age determination when performing
XR22’s isochrone fitting procedure?

We set out to compare all the observable properties that are used in XR22’s
isochrone fitting (namely, $T_{\mathrm{eff}}$, MK, [Fe/H], [$\alpha$/Fe],
$G,G_{\mathrm{BP}},G_{\mathrm{RP}},J,H,K$) of the intermediate-age stars with
the main body of the GES sample. In Fig 2, we show how the effective
temperature, $T_{\mathrm{eff}}$, for the intermediate-age stars overlaps with
the main body of the GES debris. This is also the case when examining the
[Fe/H] and [$\alpha$/Fe] abundances (Fig 3) and the Gaia and 2MASS magnitudes
(right panel of Fig 6; figures for $J,H,K$ not shown).

In the left panel of Fig 6, we also show the absolute $K$-band magnitude, MK,
as a function of Teff for the GES stars (in a similar fashion to Fig. 1 from
XR22). Here, we also overlay two Yonsei-Yale isochrone tracks (Demarque et
al., 2004), corresponding to stars with [Fe/H] $=-1.5$ and [$\alpha$/Fe]
$=0.3$ (approximately the mean of the GES sample). The two tracks correspond
to either an age of 8 or 12 Gyr. The intermediate-age GES stars appear
brighter, at fixed effective temperature, than the main body of the GES
debris, as would be expected for younger populations. Thus, MK is likely the
observable that is swaying the age inference for these stars to younger ages
when compared to the main body of the GES debris. Conversely, all the other
observable properties used to estimate the stellar ages are the same for the
intermediate-age GES and the main body of the debris.

Figure 6: Left: $K$-band absolute magnitude, MK (computed as in equation 2
from XR22), as a function of effective temperature, $T_{\mathrm{eff}}$, for
the main sample (black), the GES sample (pink), and the intermediate-age GES
stars (blue). Also shown on this plot are the 8 and 12 Gyr Yonsei-Yale
(Demarque et al., 2004) isochrone tracks for a star of [Fe/H] $=-1.5$ and
[$\alpha$/Fe] $=0.3$. The average uncertainties in MK and $T_{\mathrm{eff}}$
are $\sim 0.04$ mag and $\sim 12$ K, respectively. Moreover, the uncertainty
in the parallax for all these stars is below $\sim 0.04$ arc seconds. Right:
Gaia color-magnitude diagram (with apparent magnitude, $G$). These figures
show how the MK value is higher for the intermediate-age GES stars when
compared to the main body of the debris, leading to a younger age
determination when performing the isochrone fitting. On the contrary, the Gaia
magnitudes and colors appear all similar for both the intermediate-age stars
and the main body of the GES debris.

###  4.2 Binaries and mass transfer leading to incorrect isochrone ages?

Inaccurate age inferences due to mass transfer from, or coalescence with, a
binary stellar companion could explain the intermediate-age stars found in the
GES sample. In such a scenario, the resulting primary star would appear
brighter than its initial conditions and by default, have a younger inferred
age from isochrone fitting. Peculiar element abundances serve as a key
diagnostic to determine if a star has gone through mass transfer and/or has
merged with an Asymptotic Giant Branch (ABG) star companion. To check for this
possibility, we use the LAMOST spectra for the seven intermediate-age GES
stars, as well as 35 nearest-neighbour stars in stellar parameters444A nearest
neighbour is defined as a star with near-identical $T_{\mathrm{eff}}$,
$\log(g)$, [Fe/H], [$\alpha$/Fe], but which is old (${\rm Age}>9$ Gyr)—see
Appendix A for more details. (five for each intermediate-age star) and compare
particular Barium (Ba) lines (Guo et al., 2023). If a low-mass AGB companion
enriches the primary with Barium (e.g., Boffin & Jorissen, 1988; Han et al.,
1995) via mass transfer, then the intermediate-age star should show
anomalously strong Ba lines compared to the nearest-neighbour reference
spectra.

Fig. 7 shows the LAMOST spectra for one of the seven intermediate-age GES
stars, around the wavelength of the Ba lines
($\lambda=[4554,4934,6495]~{}\AA$), compared to the five nearest-neighbours.
Similar results for the other six intermediate-age GES stars are provided in
Appendix A. None of the seven intermediate-age GES stars have a Ba absorption
line that is stronger than its nearest neighbours. Therefore, they likely do
not have higher Ba abundances than the rest of the population and are likely
not a product of a mass transfer with a low-mass AGB companion. Moreover, for
two of these seven stars, there are [Ba/Fe] abundances determined in LAMOST;
the abundances of these two stars are not enhanced and are similar to their
nearest-neighbour counterparts.

While we find no evidence for mass transfer from a low-mass AGB companion, it
could still be that the intermediate-age GES stars experienced mass transfer
from a higher-mass AGB or Red Giant Branch (RGB) and are masquerading as
younger stars (for the same reasons stated above), that cannot be spotted with
peculiar element abundances. Follow-up investigation of the apparent young
alpha-rich population that comprises around $\sim 5$–$10\%$ of the high-alpha
disk (Chiappini et al., 2015; Martig et al., 2015) has demonstrated that a
subset of these stars are likely merger or mass-transfer products (Jofré et
al., 2016; Hekker & Johnson, 2019, e.g.,). This young alpha-rich fraction is
aligned with the numbers of intermediate-mass stars in the GES sample.

In addition to peculiar element abundances, one can also test for binarity
looking at line-of-sight-velocity measurements for the same star from
different surveys/epocs. If a star is in a binary, its line-of-sight-velocity
measurement may show possible shifts in value depending on when the star is
observed. To test this, we obtained line-of-sight-velocity measurements from
Gaia DR2, APOGEE DR17, and GALAH DR3 for overlapping stars with the LAMOST DR7
subgiants and compared their measurements. For all 28,863 stars in common (and
27 GES stars), the line-of-sight-velocity measurements are in good agreement
and there are no discrepancies/outliers. While this is a very restricted test
of binarity, without intra-survey time-domain data, it is a simple approach
available to exclude any stars that do have line-of-sight-velocity
differences.

Testing for a white-dwarf companion with the current data is extremely limited
and a wider parameter space of binary architectures may be explored with high-
resolution time-domain spectroscopy to obtain very precise line-of-sight-
velocity measurements. Such data will help establish whether the intermediate-
age GES stars are a population that has experienced mass transfer from a
companion and are intrinsically old.

Figure 7: Spectra of one of the seven intermediate-age GES stars (black)
around the wavelength region for barium (Ba) lines (red) in the LAMOST
spectrum. For comparison, we also show the spectra of five nearest-neighbour
stars in the catalogue as gray lines (see Appendix A for details). The seven
intermediate-age GES stars do not present any strong Ba absorption lines.
Thus, these stars are likely not the result of mass transfers from a (low-
mass) AGB companion.

###  4.3 Intermediate-aged stars in the GES progenitor?

If the intermediate-age stars in the GES sample are not due to incorrect
isochrone ages, then it is worth considering the implications for the GES
progenitor and the MW’s merger history more broadly.

One plausible scenario given our results is that the GES system contains stars
that are younger than the time in which it accreted onto the Milky Way. This
scenario would naturally result in the chemical-dynamical properties of the
younger GES stars matching the distribution of the main body of the GES
debris. Indeed, the intermediate-age stars identified here are [Fe/H]-poor and
present [$\alpha$/Fe] abundances that follow the distribution of the main body
of GES stars (left panel of Fig. 3; Nissen & Schuster, 2010; Mackereth et al.,
2019; Monty et al., 2020; Horta et al., 2023a, e.g.,). They also trace a
trajectory in the [Fe/H]-age plane that is distinct from in situ populations
(see middle panel of Fig. 3). Given our selection criteria, the GES stars
present high radial velocities and low azimuthal ones (Fig. 4), typical of the
GES debris (Belokurov et al., 2018; Helmi et al., 2018). All these results
suggest that the $6$–$9$ Gyr stars are in fact part of the GES debris.

If the intermediate-age stars are part of the GES system, they were likely
formed prior to when the progenitor galaxy quenched star formation. Recent
theoretical work has shown that large pericentric passages of satellites
during their first infall onto larger-mass hosts can induce star formation in
the infalling satellite (Pasetto et al., 2011; Rocha et al., 2012; Di Cintio
et al., 2021, e.g.,). This is expected to be the case for the Sagittarius
dwarf spheroidal (Sgr dSph) and the LMC (Nidever et al., 2020; Hasselquist et
al., 2021). Thus, one feasible explanation for the presence of these younger
GES stars is a burst of star formation during infall of the GES progenitor
galaxy onto the Milky Way. However, this scenario would also imply that the
GES merger event was not short-lived, but instead occurred over a longer
timescale. It also likely implies that the GES merger was an accretion episode
that endured more than one pericentric passage. While different types of
accreted satellites can yield highly-radial orbit debris (Amorisco, 2017;
Khoperskov et al., 2023; Horta et al., 2023b), radialization is most effective
for satellites with high initial eccentricity (Vasiliev et al., 2022) that
typically are more short-lived. Interestingly, in a recent study, Naidu et al.
(2021) ran a high number of tailored $N$-body simulations and found that the
GES debris are most closely matched to a satellite that was accreted on a
retrograde orbit and underwent three (close) pericentric passages, which then
rapidly radialized. While these results should be taken with caution as these
simulations were run in an idealised set-up (i.e., no other mergers and no
Milky Way galaxy growth), they highlight that the GES debris could be
explained by a merger event with multiple pericentric passages.

Furthermore, it is also plausible that, instead of a star formation burst in
the GES being induced by first infall onto the Milky Way, that a burst in star
formation could have been provoked by the interaction of the GES progenitor
and a separate infalling satellite that accreted at a similar time onto the
Galaxy. There have been additional debris/mergers proposed in the literature
that present radial orbits, conjectured to have possibly fallen in with the
GES (e.g., Sequoia: Barbá et al., 2019; Myeong et al., 2019) that could
satisfy this scenario.

Another possible scenario could be that the GES merger event is not as ancient
as once thought (namely, $\gtrsim 10$ Gyr ago) and in fact accreted onto the
MW at a later time, approximately $6$–$9$ Gyr ago. If the gas pertaining to
the GES galaxy was stripped during accretion onto the Milky Way, the GES
system would have ceased star formation, and thus would not have formed any
intermediate-age stars after the merger event. Naturally, the presence of
stars with ages below the infall time (suggested to be $\gtrsim 10$ Gyr) would
rule out this scenario. Moreover, recent dynamical work has suggested that the
GES debris can be explained from a younger merger event (Donlon et al., 2022,
2023, e.g.,). Thus, a scenario where the GES progenitor(s) merged with the
Milky Way approximately $\sim 6$–$9$ Gyr ago could explain the observed
intermediate-age stars we see in this work, assuming that no stars were formed
during infall onto the Milky Way and that the majority of the stars in the GES
formed well before infall onto the Milky Way. Furthermore, if the mass ratios
estimated for the GES are consistent with it being a major accretion event, a
younger merger scenario would also imply that the mass of the GES system is
greater than current estimates (Mackereth & Bovy, 2020; Lane et al., 2023,
e.g.,). Conversely, if the GES merger happened more recently than previously
thought and the current mass estimates are correct, it would imply that the
mass ratio of this merger was smaller.

Lastly, we note that to describe the younger stars in their “accreted halo”
sample, Bonaca et al. (2020) used a simple one-parameter model with constant
star formation rate that shuts off at some end time, $t_{\rm end}$. Fitting to
the data, they found that $t_{\rm end}\gtrsim 10$ Gyr ago. While a one-
parameter model is a good starting point to understand the star formation
history of the GES system, we argue that it may be worthwhile to examine this
data with more complex Galactic chemical evolution models as well (see for
example Hasselquist et al., 2021; Johnson et al., 2023).

###  4.4 Another sausage in the GES debris?

Intermediate-age stars with GES-like orbits could be explained by additional
younger debris from a separate merger event. Expectations from cosmological
simulations suggest that accreted satellites of different mass and infall time
can manifest radial orbits (Amorisco, 2017; Fattahi et al., 2020; Horta et
al., 2023b; Khoperskov et al., 2023; Orkney et al., 2023; Rey et al., 2023,
e.g.,). However, radialization is most efficient in cases of high satellite
mass, not very steep host density profiles, and high initial eccentricity
(Vasiliev et al., 2022). While it is entirely plausible that additional debris
could be infiltrating the GES sample and could help explain the intermediate-
age stars we observe (Donlon et al., 2022, 2023, e.g.,), the sequence in the
[$\alpha$/Fe]-[Fe/H] plane and the [Fe/H]-age relation would suggest that the
additional merger would have had a similar star formation history to the GES
and thus would be of similar mass (e.g., Cunningham et al., 2022; Horta et
al., 2023b; Khoperskov et al., 2023). If this is the case, it would also imply
that a considerable fraction of the old stars in the GES are also part of this
additional debris, bringing the overall mass of the GES down (Lane et al.
2023).

###  4.5 Stripped stars from the Sagittarius dSph galaxy?

Another possible scenario is that the intermediate-age stars on highly-radial
orbits are the result of stars that were stripped from the infalling Sgr dSph
galaxy, which have somehow dynamically evolved to have the same radial orbits
as the GES debris. This scenario would (qualitatively) satisfy the element
abundances observed (Hasselquist et al., 2021; Horta et al., 2023a, e.g.,).
However, we rule out this possibility based on the fact that the stars in the
GES sample, including the the intermediate-age stars, all show present-day
positions within $\sim 3$ kpc from the Sun.

###  4.6 Heated disc stars?

Intermediate-age stars on highly-radial orbits could be the result of heated
disc populations due to interactions with satellite galaxies. This has been
shown to be the case in the Milky Way for the high-$\alpha$ (Bonaca et al.,
2017; Belokurov et al., 2020) and low-$\alpha$ discs (Laporte et al., 2020,
2022; Das et al., 2024) and could be the result of the GES merger or the Sgr
dSph one. This scenario is less likely as the intermediate-age and highly-
radial stars occupy a sequence in the [$\alpha$/Fe]-[Fe/H] and [Fe/H]-age
planes that does not overlap with either of the high/low-$\alpha$ discs, but
does overlap with the main body of the GES debris. The abundance and age
properties of these stars suggest they are (accreted) stellar halo
populations.

##  5 Conclusions

In summary, using the subgiant catalogue of ages and element abundances
provided by XR22 and orbits determined in this work, we explored the age
distribution of stars in the Galactic stellar halo on highly-radial orbits. We
selected stars in this sample that are likely to form part of the debris from
the GES accretion event and found that the majority are old, with median age
of $11.6^{+1.14}_{-1.15}$ Gyr, where the range indicates the
$16^{\mathrm{th}}$ and $84^{\mathrm{th}}$ percentiles. We also identified a
tail of younger outlier stars, with ages down to $\sim 6$–$9$ Gyr, below the
$5^{\mathrm{th}}$ percentile of the distribution. The [$\alpha$/Fe]-[Fe/H]
element abundances, [Fe/H]-age relation, and orbital properties of these $\sim
6$–$9$ Gyr stars overlap with the main body of the GES debris.

One potential explanation for these intermediate-age stars is that they are
the product of mass transfer and/or stellar mergers, masquerading as young
stars when they are intrinsically old. While initial tests do not find
evidence for this, we cannot rule out this scenario completely with current
data. If the ages of these outliers are indeed well-measured and these stars
were formed in, and belong to, the debris of the GES accretion event, it could
imply that either: $i$) the GES event is either not as ancient as previously
conjectured; $ii$) the GES merger formed stars during infall onto the Milky
Way and/or due to interactions with a satellite of its own. The last possible
scenario we conjecture is that the local stellar halo is comprised by the
debris of two satellites (the GES and a companion debris with younger stars).

While our results corroborate previous stellar halo age studies (e.g., Bonaca
et al., 2020; Feuillet et al., 2021; Grunblatt et al., 2021), we emphasize
that we have only identified seven intermediate-age GES stars. Thus, these
findings should be revisited with larger sample statistics and ideally with
subgiant and/or MSTO stars, from which more reliable ages can be determined.
Moreover, calibrations of [C/N]-based ages for RGB stars in the metal-poor
regime will aid in discerning the age distribution of stellar halo
populations. It would be interesting to follow up this study with data from
the WEAVE (Dalton et al., 2014) and Milky Way Mapper/SDSS-V (Kollmeier et al.,
2017) programmes that deliver the required spectro-photometric information to
obtain stellar ages for GES stars. With these data, it will likely be possible
to constrain the origin of these intriguing intermediate-age, metal-poor, and
highly-radial stars in the Milky Way’s stellar halo.

## Acknowledgements

DH thanks Sue, Alex, and Debra. He also thanks Carrie Fillion, Conny Aerts,
Ricardo P. Schiavon, and the Nearby Universe group at the Flatiron Instittue
for helpful discussions. The Flatiron Institute is funded by the Simons
Foundation. ML is supported by the Department of Energy (DOE) under Award
Number DE-SC0007968 as well as the Simons Investigator in Physics Award.

## Data Availability

All data used in this work was compiled by Xiang & Rix (2022) and is publicly
available at https://keeper.mpdl.mpg.de/d/019ec71212934847bfed/. The orbital
quantities used in this work for the parent sample of 11,336 stars can be
found at https://www.dropbox.com/scl/fi/t9z8nhtur9591mvfjo91k/subgiant-paper-
orbits-gala22.fits?rlkey=m2ppam8iyn67tc4au6c2f65uz&dl=0.

## References

  * Amorisco (2017) Amorisco, N. C. 2017, MNRAS, 464, 2882, doi: 10.1093/mnras/stw2229
  * Barbá et al. (2019) Barbá, R. H., Minniti, D., Geisler, D., et al. 2019, ApJ, 870, L24, doi: 10.3847/2041-8213/aaf811
  * 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
  * Belokurov et al. (2020) Belokurov, V., Sanders, J. L., Fattahi, A., et al. 2020, MNRAS, 494, 3880, doi: 10.1093/mnras/staa876
  * Bennett & Bovy (2019) Bennett, M., & Bovy, J. 2019, MNRAS, 482, 1417, doi: 10.1093/mnras/sty2813
  * Binney (2012) Binney, J. 2012, MNRAS, 426, 1324, doi: 10.1111/j.1365-2966.2012.21757.x
  * Boffin & Jorissen (1988) Boffin, H. M. J., & Jorissen, A. 1988, A&A, 205, 155
  * Bonaca et al. (2017) Bonaca, A., Conroy, C., Wetzel, A., Hopkins, P. F., & Kereš, D. 2017, ApJ, 845, 101, doi: 10.3847/1538-4357/aa7d0c
  * Bonaca et al. (2020) Bonaca, A., Conroy, C., Cargile, P. A., et al. 2020, ApJ, 897, L18, doi: 10.3847/2041-8213/ab9caa
  * Carrillo et al. (2024) Carrillo, A., Deason, A. J., Fattahi, A., Callingham, T. M., & Grand, R. J. J. 2024, MNRAS, 527, 2165, doi: 10.1093/mnras/stad3274
  * Chiappini et al. (2015) Chiappini, C., Anders, F., Rodrigues, T. S., et al. 2015, A&A, 576, L12, doi: 10.1051/0004-6361/201525865
  * Cunningham et al. (2022) Cunningham, E. C., Sanderson, R. E., Johnston, K. V., et al. 2022, ApJ, 934, 172, doi: 10.3847/1538-4357/ac78ea
  * Dalton et al. (2014) Dalton, G., Trager, S., Abrams, D. C., et al. 2014, in Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series, Vol. 9147, Ground-based and Airborne Instrumentation for Astronomy V, ed. S. K. Ramsay, I. S. McLean, & H. Takami, 91470L, doi: 10.1117/12.2055132
  * Das et al. (2024) Das, P., Huang, Y., Ciucă, I., & Fragkoudi, F. 2024, MNRAS, 527, 4505, doi: 10.1093/mnras/stad3344
  * Demarque et al. (2004) Demarque, P., Woo, J.-H., Kim, Y.-C., & Yi, S. K. 2004, ApJS, 155, 667, doi: 10.1086/424966
  * Di Cintio et al. (2021) Di Cintio, A., Mostoghiu, R., Knebe, A., & Navarro, J. F. 2021, MNRAS, 506, 531, doi: 10.1093/mnras/stab1682
  * Donlon et al. (2022) Donlon, Thomas, I., Newberg, H. J., Kim, B., & Lépine, S. 2022, ApJ, 932, L16, doi: 10.3847/2041-8213/ac7531
  * Donlon et al. (2023) Donlon, Thomas, I., Newberg, H. J., Sanderson, R., et al. 2023, arXiv e-prints, arXiv:2310.09376, doi: 10.48550/arXiv.2310.09376
  * Edvardsson et al. (1993) Edvardsson, B., Andersen, J., Gustafsson, B., et al. 1993, A&A, 275, 101
  * Eilers et al. (2019) Eilers, A.-C., Hogg, D. W., Rix, H.-W., & Ness, M. K. 2019, ApJ, 871, 120, doi: 10.3847/1538-4357/aaf648
  * Fattahi et al. (2020) Fattahi, A., Deason, A. J., Frenk, C. S., et al. 2020, MNRAS, 497, 4459, doi: 10.1093/mnras/staa2221
  * Feuillet et al. (2021) Feuillet, D. K., Sahlholdt, C. L., Feltzing, S., & Casagrande, L. 2021, MNRAS, 508, 1489, doi: 10.1093/mnras/stab2614
  * Freeman & Bland-Hawthorn (2002) Freeman, K., & Bland-Hawthorn, J. 2002, ARA&A, 40, 487, doi: 10.1146/annurev.astro.40.060401.093840
  * Freeman (2012) Freeman, K. C. 2012, in Astronomical Society of the Pacific Conference Series, Vol. 458, Galactic Archaeology: Near-Field Cosmology and the Formation of the Milky Way, ed. W. Aoki, M. Ishigaki, T. Suda, T. Tsujimoto, & N. Arimoto, 393
  * 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
  * Gaia Collaboration et al. (2022) Gaia Collaboration, Vallenari, A., Brown, A. G. A., et al. 2022, arXiv e-prints, arXiv:2208.00211, doi: 10.48550/arXiv.2208.00211
  * Gallart et al. (2019) Gallart, C., Bernard, E. J., Brook, C. B., et al. 2019, Nature Astronomy, 3, 932, doi: 10.1038/s41550-019-0829-5
  * GRAVITY Collaboration et al. (2022) GRAVITY Collaboration, Abuter, R., Aimar, N., et al. 2022, A&A, 657, L12, doi: 10.1051/0004-6361/202142465
  * Grunblatt et al. (2021) Grunblatt, S. K., Zinn, J. C., Price-Whelan, A. M., et al. 2021, ApJ, 916, 88, doi: 10.3847/1538-4357/ac0532
  * Guo et al. (2023) Guo, F., Cheng, Z., Kong, X., et al. 2023, AJ, 165, 40, doi: 10.3847/1538-3881/aca323
  * Han et al. (1995) Han, Z., Eggleton, P. P., Podsiadlowski, P., & Tout, C. A. 1995, MNRAS, 277, 1443, doi: 10.1093/mnras/277.4.1443
  * Harris et al. (2020) Harris, C. R., Millman, K. J., van der Walt, S. J., et al. 2020, Nature, 585, 357, doi: 10.1038/s41586-020-2649-2
  * Hasselquist et al. (2021) Hasselquist, S., Hayes, C. R., Lian, J., et al. 2021, ApJ, 923, 172, doi: 10.3847/1538-4357/ac25f9
  * Hayes et al. (2018) Hayes, C. R., Majewski, S. R., Shetrone, M., et al. 2018, ApJ, 852, 49, doi: 10.3847/1538-4357/aa9cec
  * Haywood et al. (2018) Haywood, M., Di Matteo, P., Lehnert, M. D., et al. 2018, ApJ, 863, 113, doi: 10.3847/1538-4357/aad235
  * Hekker & Johnson (2019) Hekker, S., & Johnson, J. A. 2019, MNRAS, 487, 4343, doi: 10.1093/mnras/stz1554
  * Helmi et al. (2018) Helmi, A., Babusiaux, C., Koppelman, H. H., et al. 2018, Nature, 563, 85, doi: 10.1038/s41586-018-0625-x
  * Horta et al. (2021) Horta, D., Schiavon, R. P., Mackereth, J. T., et al. 2021, MNRAS, 500, 1385, doi: 10.1093/mnras/staa2987
  * Horta et al. (2023a) —. 2023a, MNRAS, 520, 5671, doi: 10.1093/mnras/stac3179
  * Horta et al. (2023b) Horta, D., Cunningham, E. C., Sanderson, R. E., et al. 2023b, ApJ, 943, 158, doi: 10.3847/1538-4357/acae87
  * Hunt et al. (2022) Hunt, J. A. S., Price-Whelan, A. M., Johnston, K. V., & Darragh-Ford, E. 2022, MNRAS, 516, L7, doi: 10.1093/mnrasl/slac082
  * Hunter (2007) Hunter, J. D. 2007, Computing in Science & Engineering, 9, 90, doi: 10.1109/MCSE.2007.55
  * Jofré et al. (2016) Jofré, P., Jorissen, A., Van Eck, S., et al. 2016, A&A, 595, A60, doi: 10.1051/0004-6361/201629356
  * Johnson et al. (2023) Johnson, J. W., Conroy, C., Johnson, B. D., et al. 2023, MNRAS, 526, 5084, doi: 10.1093/mnras/stad2985
  * Khoperskov et al. (2023) Khoperskov, S., Minchev, I., Libeskind, N., et al. 2023, A&A, 677, A91, doi: 10.1051/0004-6361/202244234
  * Kollmeier et al. (2017) Kollmeier, J. A., Zasowski, G., Rix, H.-W., et al. 2017, arXiv e-prints, arXiv:1711.03234, doi: 10.48550/arXiv.1711.03234
  * Koppelman et al. (2019) Koppelman, H. H., Helmi, A., Massari, D., Price-Whelan, A. M., & Starkenburg, T. K. 2019, A&A, 631, L9, doi: 10.1051/0004-6361/201936738
  * Lachaume et al. (1999) Lachaume, R., Dominik, C., Lanz, T., & Habing, H. J. 1999, A&A, 348, 897
  * Lane et al. (2023) Lane, J. M. M., Bovy, J., & Mackereth, J. T. 2023, MNRAS, 526, 1209, doi: 10.1093/mnras/stad2834
  * Laporte et al. (2020) Laporte, C. F. P., Belokurov, V., Koposov, S. E., Smith, M. C., & Hill, V. 2020, MNRAS, 492, L61, doi: 10.1093/mnrasl/slz167
  * Laporte et al. (2022) Laporte, C. F. P., Koposov, S. E., & Belokurov, V. 2022, MNRAS, 510, L13, doi: 10.1093/mnrasl/slab109
  * Mackereth & Bovy (2020) Mackereth, J. T., & Bovy, J. 2020, MNRAS, 492, 3631, doi: 10.1093/mnras/staa047
  * Mackereth et al. (2019) Mackereth, J. T., Schiavon, R. P., Pfeffer, J., et al. 2019, MNRAS, 482, 3426, doi: 10.1093/mnras/sty2955
  * Majewski et al. (2017) Majewski, S. R., Schiavon, R. P., Frinchaboy, P. M., et al. 2017, AJ, 154, 94, doi: 10.3847/1538-3881/aa784d
  * Martig et al. (2015) Martig, M., Rix, H.-W., Silva Aguirre, V., et al. 2015, MNRAS, 451, 2230, doi: 10.1093/mnras/stv1071
  * Martig et al. (2016) Martig, M., Fouesneau, M., Rix, H.-W., et al. 2016, MNRAS, 456, 3655, doi: 10.1093/mnras/stv2830
  * Montalbán et al. (2021) Montalbán, J., Mackereth, J. T., Miglio, A., et al. 2021, Nature Astronomy, 5, 640, doi: 10.1038/s41550-021-01347-7
  * Monty et al. (2020) Monty, S., Venn, K. A., Lane, J. M. M., Lokhorst, D., & Yong, D. 2020, MNRAS, 497, 1236, doi: 10.1093/mnras/staa1995
  * Myeong et al. (2019) Myeong, G. C., Vasiliev, E., Iorio, G., Evans, N. W., & Belokurov, V. 2019, MNRAS, 488, 1235, doi: 10.1093/mnras/stz1770
  * Naidu et al. (2021) Naidu, R. P., Conroy, C., Bonaca, A., et al. 2021, ApJ, 923, 92, doi: 10.3847/1538-4357/ac2d2d
  * Ness et al. (2016) Ness, M., Hogg, D. W., Rix, H. W., et al. 2016, ApJ, 823, 114, doi: 10.3847/0004-637X/823/2/114
  * Nidever et al. (2020) Nidever, D. L., Hasselquist, S., Hayes, C. R., et al. 2020, ApJ, 895, 88, doi: 10.3847/1538-4357/ab7305
  * Nissen & Schuster (2010) Nissen, P. E., & Schuster, W. J. 2010, A&A, 511, L10, doi: 10.1051/0004-6361/200913877
  * Nordström et al. (2004) Nordström, B., Mayor, M., Andersen, J., et al. 2004, A&A, 418, 989, doi: 10.1051/0004-6361:20035959
  * Orkney et al. (2023) Orkney, M. D. A., Laporte, C. F. P., Grand, R. J. J., et al. 2023, MNRAS, 525, 683, doi: 10.1093/mnras/stad2361
  * Pasetto et al. (2011) Pasetto, S., Grebel, E. K., Berczik, P., Chiosi, C., & Spurzem, R. 2011, A&A, 525, A99, doi: 10.1051/0004-6361/200913415
  * Price-Whelan et al. (2022) Price-Whelan, A., Sipőcz, B., Wagg, T., et al. 2022, adrn/gala: v1.6.1, v1.6.1, Zenodo, doi: 10.5281/zenodo.7299506
  * Price-Whelan (2017) Price-Whelan, A. M. 2017, The Journal of Open Source Software, 2, 388, doi: 10.21105/joss.00388
  * Rey et al. (2023) Rey, M. P., Agertz, O., Starkenburg, T. K., et al. 2023, MNRAS, 521, 995, doi: 10.1093/mnras/stad513
  * Rocha et al. (2012) Rocha, M., Peter, A. H. G., & Bullock, J. 2012, MNRAS, 425, 231, doi: 10.1111/j.1365-2966.2012.21432.x
  * Sanders et al. (2023) Sanders, J. L., Kawata, D., Matsunaga, N., et al. 2023, arXiv e-prints, arXiv:2311.00035, doi: 10.48550/arXiv.2311.00035
  * Soderblom (2010) Soderblom, D. R. 2010, ARA&A, 48, 581, doi: 10.1146/annurev-astro-081309-130806
  * Spitoni et al. (2019) Spitoni, E., Silva Aguirre, V., Matteucci, F., Calura, F., & Grisoni, V. 2019, A&A, 623, A60, doi: 10.1051/0004-6361/201834188
  * Vasiliev (2019) Vasiliev, E. 2019, MNRAS, 482, 1525, doi: 10.1093/mnras/sty2672
  * Vasiliev et al. (2022) Vasiliev, E., Belokurov, V., & Evans, N. W. 2022, ApJ, 926, 203, doi: 10.3847/1538-4357/ac4fbc
  * Xiang & Rix (2022) Xiang, M., & Rix, H.-W. 2022, Nature, 603, 599, doi: 10.1038/s41586-022-04496-5
  * Xiang et al. (2017) Xiang, M., Liu, X., Shi, J., et al. 2017, ApJS, 232, 2, doi: 10.3847/1538-4365/aa80e4
  * Zhao et al. (2012) Zhao, G., Zhao, Y.-H., Chu, Y.-Q., Jing, Y.-P., & Deng, L.-C. 2012, Research in Astronomy and Astrophysics, 12, 723, doi: 10.1088/1674-4527/12/7/002

##  Appendix A Testing for Evidence of Mass Transfer from AGB Stars

Figs. A1–A6 are the same as Fig. 7, but for the remaining six intermediate-age
GES stars (black) and their associated nearest neighbors (gray). The nearest
neighbors (nn) are selected using the following criteria:
$|\mathrm{[Fe/H]_{star}}-\mathrm{[Fe/H]_{nn}}|<0.05$ dex;
$|\mathrm{[\alpha/Fe]_{star}}-\mathrm{[\alpha/Fe]_{nn}}|<0.05$ dex;
$|T\mathrm{{}_{eff,star}}-T\mathrm{{}_{eff,nn}}|<50$ K; $|\log(g_{\rm
star})-\log(g_{\rm nn})|<0.05$ dex; SNR$>50$. To obtain enough nearest
neighbors, the selection criteria are loosened for two stars. These two stars
and the different selection criteria for their nearest neighbors are: 1) for
Gaia DR3 source ID 3920760165733793152, we select stars with
$\mathrm{[Fe/H]}$, $\mathrm{[\alpha/Fe]}$, $\log(g)$ within 0.1 dex of the
targeted stars, $T\mathrm{{}_{eff}}$ within 100 K, and SNR $>$10;555This still
yields only four nearest neighbors stars with a median age of 7.5 Gyr. and 2)
for Gaia DR3 source ID 751738058415860992 and Gaia DR3 source ID
1884664845289850368, we select stars with SNR $>30$.

Figure A1: Fig. 7 continued. Figure A2: Fig. 7 continued. Figure A3: Fig. 7
continued. Figure A4: Fig. 7 continued. Figure A5: Fig. 7 continued. Figure
A6: Fig. 7 continued.

##  Appendix B Supplementary material: catalogue of orbits

Table A1-A2 shows the information contained in the table of orbits compiled in
this work for the 11,336 stars in our parent sample, which is publicly
available at https://www.dropbox.com/scl/fi/t9z8nhtur9591mvfjo91k/subgiant-
paper-orbits-gala22.fits?rlkey=m2ppam8iyn67tc4au6c2f65uz&dl=0.

Table A1: From left to right, Gaia DR3 ID, LAMOST DR7 ID, orbital actions, angular momentum, orbital energy, pericenter radius, apocenter radius, maximum height, eccentricity, and a boolean mask to select GES stars (options are either “PARENT” or “GES”). Here we show the value for the first three stars. The full table can be downloaded using the link in the main text. Gaia DR3 ID |  LAMOST DR7 ID | ($J_{R},J_{\phi},J_{z}$) | ($L_{x},L_{y},L_{z}$)
---|---|---|---
|  | [kpc km s-1] | [kpc km s-1]
303792868026997248 | 20151001-HD014422N323057V01-02-183 | (52.59, -1969.25, 9.79) | (0.115, 16.22, -1969.25)
303857739213031296 | 20151001-HD014422N323057B01-05-250 | (54.18, -2205.91, 14.22) | (-17.84, 19.98, -2205.91)
303909240165205632 | 20151001-HD014422N323057V01-04-179 | (89.76, -2392.29, 11.78) | (-24.60, 12.85, -2392.29)
Table A2: Table A1 continued. Energy | $R_{\mathrm{peri}}$ | $R_{\mathrm{apo}}$ | $z_{\mathrm{max}}$ | $e$ | “IN-GES”
---|---|---|---|---|---
[$\times 10^{5}$ km2 s-2] | [kpc] | [kpc] | [kpc] |  |
-1.23 | 7.26 | 10.74 | 0.62 | 0.19 | PARENT
-1.18 | 8.28 | 12.07 | 0.86 | 0.18 | PARENT
-1.13 | 8.68 | 13.85 | 0.85 | 0.23 | PARENT


\par\pardf = pd.read_csv(’employee.csv’)

\par\par# In[ ]:

\par\par# Schema of Dataframes:

# Columns in df with example values:

# name (Peter), gender (m), DOB (1992/01/17)

\par\par# In[ ]:

\par\par# Problem: How many male and female employees are born in 1992?

\par\par# In[ ]:

\par\par# Solution:

df[’DOB’] = pd.to_datetime(df[’DOB’])

num_male_students = len(df[(df[’DOB’].dt.year == 1992) & (df[’gender’] ==
’m’)])

num_female_students = len(df[(df[’DOB’].dt.year == 1992) & (df[’gender’] ==
’f’)])

\par\par# In[ ]:

\par\par# # Exercise 2

\par\par# In[ ]:

\par\pardf = pd.read_csv(’scores.csv’)

\par\par# In[ ]:

\par\par# Schema of Dataframes:

# Columns in df with example values:

# Stu_Name (Mike), Engineering (90), English (89), Math (92)

\par\par# In[ ]:

\par\par# Problem: Get the students with an averaged score above 90 for
science subjects.

\par\par# In[ ]:

\par\par# Solution:

df[’Science_Avg’] = (df[’Engineering’] + df[’Math’]) / 2

df[df[’Science_Avg’] > 90][[’Stu_Name’, ’Science_Avg’]]

\par\par# In[ ]:

\par\par# # Exercise 3

\par\par# In[ ]:

\par\pardf = pd.read_csv(’geo.csv’)

\par\par# In[ ]:

\par\par# Schema of Dataframes:

# Columns in df with example values:

# state (WA), capital (Seattle), population (1.4 millon)

\par\par# In[ ]:

\par\par# Problem: What is the population of California?

\par\par# In[ ]:

\par\par# Solution:

result = df[df[’state’] == ’CA’][’population’]

\par\par# In[ ]:

\par\par# # Exercise 4

\par\par# In[ ]:

\par\pardf = pd.read_csv(’phones.csv’)

\par\par# In[ ]:

\par\par# Schema of Dataframes:

# Columns in df with example values:

# model (Pixel 6), brand (Google), price (387), release (2022)

\par\par# In[ ]:

\par\par# Problem: What is the most expensive phone in each brand.

\par\par# In[ ]:

\par\par# Solution:

df.loc[df.groupby(’brand’)[’price’].idxmax()][[’brand’, ’model’, ’price’]]

\par\par# In[ ]:

\par\par# # Exercise 5

$\mathrm{Vanilla~{}Code}$ Prompt Prefix (Setup 2)

⬇

# In[ ]:

\par\parimport pandas as pd

import matplotlib.pyplot as plt

\par\par# In[ ]:

\par\par# You are a professional data scientist. Answer the following
questions using pandas and matplotlib.

\par\par# In[ ]:

\par\par# # Exercise 1

\par\par# In[ ]:

\par\pardf = pd.read_csv(’employee.csv’)

\par\par# In[ ]:

\par\par# Schema of Dataframes:

# Columns in df with example values:

# name (Peter), gender (m), DOB (1992/01/17)

\par\par# In[ ]:

\par\par# Problem: How many male and female employees are born in 1992?

\par\par# In[ ]:

\par\par# Solution:

df[’DOB’] = pd.to_datetime(df[’DOB’])

num_male_students = len(df[(df[’DOB’].dt.year == 1992) & (df[’gender’] ==
’m’)])

num_female_students = len(df[(df[’DOB’].dt.year == 1992) & (df[’gender’] ==
’f’)])

\par\par# In[ ]:

\par\par# # Exercise 2

\par\par# In[ ]:

\par\pardf = pd.read_csv(’scores.csv’)

\par\par# In[ ]:

\par\par# Schema of Dataframes:

# Columns in df with example values:

# Stu_Name (Mike), Engineering (90), English (89), Math (92)

\par\par# In[ ]:

\par\par# Problem: Get the students with an averaged score above 90 for
science subjects.

\par\par# In[ ]:

\par\par# Solution:

df[’Science_Avg’] = (df[’Engineering’] + df[’Math’]) / 2

df[df[’Science_Avg’] > 90][[’Stu_Name’, ’Science_Avg’]]

\par\par# In[ ]:

\par\par# # Exercise 3

\par\par# In[ ]:

\par\pardf = pd.read_csv(’geo.csv’)

\par\par# In[ ]:

\par\par# Schema of Dataframes:

# Columns in df with example values:

# state (WA), capital (Seattle), population (1.4 millon)

\par\par# In[ ]:

\par\par# Problem: What is the population of California?

\par\par# In[ ]:

\par\par# Solution:

result = df[df[’state’] == ’CA’][’population’]

\par\par# In[ ]:

\par\par# # Exercise 4

\par\par# In[ ]:

\par\pardf = pd.read_csv(’phones.csv’)

\par\par# In[ ]:

\par\par# Schema of Dataframes:

# Columns in df with example values:

# model (Pixel 6), brand (Google), price (387), release (2022)

\par\par# In[ ]:

\par\par# Problem: What is the most expensive phone in each brand.

\par\par# In[ ]:

\par\par# Solution:

df.loc[df.groupby(’brand’)[’price’].idxmax()][[’brand’, ’model’, ’price’]]

\par\par# In[ ]:

\par\par# # Exercise 5

$\mathrm{Vanilla~{}Code}$ Prompt Prefix (Setup 3)

⬇

# In[ ]:

\par\parimport pandas as pd

import matplotlib.pyplot as plt

\par\par# In[ ]:

\par\par# You are a professional data scientist. Answer the following
questions using pandas and matplotlib.

\par\par# In[ ]:

\par\par# # Exercise 1

\par\par# In[ ]:

\par\pardf = pd.read_csv(’olympics.csv’)

\par\par# In[ ]:

\par\par# Schema of Dataframes:

# Columns in df with example values:

# Year (1896), City (Athens), Country (Greece), Nations (14)

\par\par# In[ ]:

\par\par# Problem: Which countries host at least two olympic games?

\par\par# In[ ]:

\par\par# Solution:

count_df = df[’Country’].value_counts()

count_df[count_df >= 2].index.tolist()

\par\par# In[ ]:

\par\par# # Exercise 2

\par\par# In[ ]:

\par\pardf = pd.read_csv(’employee.csv’)

\par\par# In[ ]:

\par\par# Schema of Dataframes:

# Columns in df with example values:

# name (Peter), gender (m), DOB (1992/01/17)

\par\par# In[ ]:

\par\par# Problem: How many male and female employees are born in 1992?

\par\par# In[ ]:

\par\par# Solution:

df[’DOB’] = pd.to_datetime(df[’DOB’])

num_male_students = len(df[(df[’DOB’].dt.year == 1992) & (df[’gender’] ==
’m’)])

num_female_students = len(df[(df[’DOB’].dt.year == 1992) & (df[’gender’] ==
’f’)])

\par\par# In[ ]:

\par\par# # Exercise 3

\par\par# In[ ]:

\par\pardf = pd.read_csv(’score.csv’)

\par\par# In[ ]:

\par\par# Schema of Dataframes:

# Columns in df with example values:

# name (John), score (97)

\par\par# In[ ]:

\par\par# Problem: Make a new column "grade" for letter grades (A: 90+, B:
70-90, C: <70) and plot the number of students in each grade.

\par\par# In[ ]:

\par\par# Solution:

df[’grade’] = df.score.apply(lambda x: ’A’ if x >= 90 else (’B’ if 70 <= x <
90 else ’C’))

df.grade.value_counts().plot(kind=’bar’)

\par\par# In[ ]:

\par\par# # Exercise 4

\par\par# In[ ]:

\par\pardf = pd.read_csv(’phones.csv’)

\par\par# In[ ]:

\par\par# Schema of Dataframes:

# Columns in df with example values:

# model (Pixel 6), brand (Google), price (387), release (2022)

\par\par# In[ ]:

\par\par# Problem: What is the most expensive phone in each brand.

\par\par# In[ ]:

\par\par# Solution:

df.loc[df.groupby(’brand’)[’price’].idxmax()][[’brand’, ’model’, ’price’]]

\par\par# In[ ]:

\par\par# # Exercise 5

The notebook context part of the prompt for $\bm{u}_{2}$ in Fig. 1

⬇

# In[ ]:

\par\parimport pandas as pd

\pardf=pd.read_csv(’dataset/Gamepass_Games_v1.csv’)

\par\par# In[ ]:

\par\par# Schema of Dataframes:

# Columns in df with example values:

# GAME (Mass Effect Legendary Edition), RATIO (1.87), GAMERS (84,143), COMP
\par\par# In[ ]:

\par\par# Extract min and max (if applicable) hours as two columns

\par\par# In[ ]:

\par\pardef get_avg(x):

try:

return float(x[0]) , float(x[1])

except:

return 0,0

df[’min’],df[’max’]=zip(*df[’TIME’].str.replace("
hours",”).str.strip(’+’).str.split("-").apply(get_avg))

\par\par# In[ ]:

\par\pardf[’ADDED’]=pd.to_datetime(df[’ADDED’],format="\par\par# In[ ]:

\par\par# In which year was the most played game added?

\par\par# In[ ]:

|$\triangleright$ \textcolor{red}{\textrm{Model starts prediction}}|


* [61] Teresa Twaroch and Franz Hlawatsch, _Modulation and warping operators in joint signal analysis_ , Proceedings of the IEEE-SP International Symposium on Time-Frequency and Time-Scale Analysis, 1998. (Pittsburgh, PA, USA), oct 1998, pp. 9–12 (english).