The Global Dynamical Atlas of the Milky Way Mergers: Constraints from Gaia EDR3–
based Orbits of Globular Clusters, Stellar Streams, and Satellite Galaxies
Khyati Malhan1,9
, Rodrigo A. Ibata2
, Sanjib Sharma3,4
, Benoit Famaey2
, Michele Bellazzini5
,
Raymond G. Carlberg6
, Richard D’Souza7
, Zhen Yuan2
, Nicolas F. Martin1,2
, and Guillaume F. Thomas8
1 Max-Planck-Institut für Astronomie, Königstuhl 17, D-69117, Heidelberg, Germany; kmalhan07@gmail.com
2 Université de Strasbourg, CNRS, Observatoire astronomique de Strasbourg, UMR 7550, F-67000 Strasbourg, France
3 Sydney Institute for Astronomy, School of Physics, The University of Sydney, NSW 2006, Australia
4 ARC Centre of Excellence for All Sky Astrophysics in Three Dimensions (ASTRO-3D), Australia
5 INAF—Osservatorio di Astrofisica e Scienza dello Spazio, via Gobetti 93/3, I-40129 Bologna, Italy
6 Department of Astronomy & Astrophysics, University of Toronto, Toronto, ON M5S 3H4, Canada
7 Vatican Observatory, Specola Vaticana, V-00120, Vatican City State, Italy
8 Universidad de La Laguna, Dpto. Astrofísica E-38206 La Laguna, Tenerife, Spain
Received 2021 December 11; revised 2022 January 14; accepted 2022 January 18; published 2022 February 17
Abstract
The Milky Way halo was predominantly formed by the merging of numerous progenitor galaxies. However,
our knowledge of this process is still incomplete, especially in regard to the total number of mergers, their
global dynamical properties and their contribution to the stellar population of the Galactic halo. Here, we
uncover the Milky Way mergers by detecting groupings of globular clusters, stellar streams, and satellite
galaxies in action (J) space. While actions fully characterize the orbits, we additionally use the redundant
information on their energy (E) to enhance the contrast between the groupings. For this endeavor, we use Gaia
EDR3–based measurements of 170 globular clusters, 41 streams, and 46 satellites to derive their J and E. To
detect groups, we use the ENLINK software, coupled with a statistical procedure that accounts for the observed
phase-space uncertainties of these objects. We detect a total of N = 6 groups, including the previously known
mergers Sagittarius, Cetus, Gaia–Sausage/Enceladus, LMS-1/Wukong, Arjuna/Sequoia/I’itoi, and one new
merger that we call Pontus. All of these mergers, together, comprise 62 objects (≈25% of our sample). We
discuss their members, orbital properties, and metallicity distributions. We find that the three most-metal-
poor streams of our galaxy—“C-19” ([Fe/H] = −3.4 dex), “Sylgr” ([Fe/H] = −2.9 dex), and “Phoenix”
([Fe/H] = −2.7 dex)—are associated with LMS-1/Wukong, showing it to be the most-metal-poor merger. The
global dynamical atlas of Milky Way mergers that we present here provides a present-day reference for galaxy
formation models.
Unified Astronomy Thesaurus concepts: Globular star clusters (656); Milky Way formation (1053); Milky Way
stellar halo (1060); Dwarf galaxies (416); Stellar streams (2166); Galaxy formation (595); Galaxy structure (622)
1. Introduction
The stellar halo of the Milky Way was predominantly
formed by the merging of numerous progenitor galaxies (Ibata
et al. 1994; Helmi et al. 1999; Chiba & Beers 2000; Majewski
et al. 2003; Bell et al. 2008; Newberg et al. 2009; Nissen &
Schuster 2010; Belokurov et al. 2018; Helmi et al. 2018;
Koppelman et al. 2019a; Matsuno et al. 2019; Myeong et al.
2019; Naidu et al. 2020; Yuan et al. 2020b), and this
observation appears consistent with the ΛCDM-based models
of galaxy formation (e.g., Bullock & Johnston 2005; Pillepich
et al. 2018). However, challenging questions remain, for
instance: How many progenitor galaxies actually merged with
our galaxy? What were the initial physical properties of these
merging galaxies, including their stellar and dark matter
masses, their stellar population, and their chemical composi-
tion (e.g., their [Fe/H] distribution function)? Which objects
among the observed population of globular clusters, stellar
streams, and satellite galaxies in the Galactic halo were
accreted inside these mergers? Answering these questions is
important to understand the hierarchical buildup of our galaxy
and thereby to inform galaxy formation models.
It was recently proposed that a significant fraction of the
Milky Way’s stellar halo (∼95% of the stellar population)
resulted from the merging of ≈9–10 progenitor galaxies. This
scenario is suggested by Naidu et al. (2020), who identified
these mergers by selecting “overdensities” in the chemody-
namical space of ∼5700 giant stars (these giants lie within
50 kpc from the Galactic center). Many of their selections
were based on the knowledge of the previously known
mergers. Here, our motivation is also to find the mergers of
our galaxy but using a different approach from theirs. First,
our objective is to be able to detect these mergers using the
data (and not select them) while being agnostic about the
previously claimed mergers of our galaxy. Second, we aim
for a procedure that is possibly reproducible in cosmological
simulations. Finally, we use a very different sample of halo
objects, comprising only of globular clusters, stellar streams,
and satellite galaxies.
The Milky Way halo harbors a large population of globular
clusters (Harris 2010; Vasiliev & Baumgardt 2021), stellar
streams (Ibata et al. 2021; Li et al. 2021a), and satellite galaxies
(McConnachie & Venn 2020; Battaglia et al. 2022), and these
The Astrophysical Journal, 926:107 (30pp), 2022 February 20
https://doi.org/10.3847/1538-4357/ac4d2a
© 2022. The Author(s). Published by the American Astronomical Society.
9 Humboldt Fellow and IAU Gruber Fellow.
Original content from this work may be used under the terms
of the Creative Commons Attribution 4.0 licence. Any further
distribution of this work must maintain attribution to the author(s) and the title
of the work, journal citation and DOI.
1
objects represent the most ancient and metal-poor structures of
our galaxy (e.g., Harris 2010; Kirby et al. 2013; Helmi 2020).10
A majority of halo streams are the tidal remnants of either
globular clusters or very low-mass satellites (Ibata et al. 2021; Li
et al. 2021a, see Section 2.1). For all of these halo objects, a
significant fraction of their population is expected to have been
brought into the Galactic halo inside massive progenitor galaxies
(e.g., Deason et al. 2015; Kruijssen et al. 2019; Carlberg 2020).
This implies that these objects, which today form part of our
Galactic halo, can be used to trace their progenitor galaxies (e.g.,
Malhan et al. 2019b; Massari et al. 2019; Bonaca et al. 2021).
Consequently, this knowledge also has direct implications on the
long-standing question—which of the globular clusters (or
streams) were initially formed within the stellar halo (and
represent an in situ population) and which were initially formed
in different progenitors that only later merged into the Milky Way
(and represent an ex situ population). Therefore, using these halo
objects as tracers of mergers is also important to understand their
own origin and birth sites.
In this regard, using these halo objects also provides a
powerful means to detect even the most-metal-poor mergers of
the Milky Way. This is important, for instance, to understand
the origin of the metal-poor population of the stellar halo (e.g.,
Komiya et al. 2010; Sestito et al. 2021) and also to constrain
the formation scenarios of the metal-deficient globular clusters
inside high-redshift galaxies (e.g., Forbes et al. 2018b). In the
context of stellar halos, we currently lack knowledge of the
origin of the “metallicity floor” for globular clusters; this has
recently been pushed down from [Fe/H] =−2.5 dex (Harris
2010) to [Fe/H] = −3.4 dex (Martin et al. 2022a). In fact, the
stellar halo harbors several very metal-poor globular clusters
(e.g., Simpson 2018) and also streams (e.g., Roederer &
Gnedin 2019; Wan et al. 2020; Martin et al. 2022a). These
observations raise the question: Did these metal-poor objects
originally form in the Milky Way itself or were they accreted
inside the merging galaxies? Moreover, such globular-cluster–
merger associations also allow us to understand the cluster
formation processes inside those protogalaxies that had formed
in the early universe (e.g., Freeman & Bland-Hawthorn 2002;
Frebel & Norris 2015).
Our underlying strategy to identify the Milky Way’s mergers
is as follows. For each halo object we compute their three
actions J and then detect those “groups” that clump together
tightly in J space.11 However, to enhance the contrast between
groups, we additionally use the redundant information on their
energy E as this allows us to separate the groups even more
confidently.
The motivation behind this strategy can be explained as
follows. First, imagine a progenitor galaxy (that is yet to be
merged with the Milky Way) containing its own population of
globular clusters, satellite galaxies, and streams,12 along with
its population of stars. Upon merging with the Milky Way, the
progenitor galaxy will get tidally disrupted and deposit its
contents into the Galactic halo. If the tidal disruption occurs
slowly, the stars of the merging galaxy will themselves form a
vast stellar stream in the Galactic halo (e.g., this is the case for
the Sagittarius merger;
Ibata et al. 2020; Vasiliev &
Belokurov 2020). However, if the disruption occurs rapidly,
then the stars will quickly get phase-mixed and no clear clear
signature of the stream will be visible (e.g., this is expected for
the Gaia-Sausage/Enceladus merger; Belokurov et al. 2018;
Helmi et al. 2018). In either case, the member objects of the
progenitor galaxy (i.e., its member globular clusters, satellites,
and streams), which are now inside the Galactic halo, will
possess very similar values of actions J. This is because the
dynamical quantities J are conserved for a very long time, if the
potential of the primary galaxy changes adiabatically. The
Milky Way’s potential
likely evolved adiabatically (e.g.,
Cardone & Sereno 2005) and, therefore, those objects that
merge inside the same progenitor galaxy are expected to remain
tightly clumped in the J space of the Milky Way, even long
after they have been tidally removed from their progenitor.
While E is not by itself an adiabatic invariant, objects that
merge together are expected to occupy a small subset of the
energy space. Hence, even though actions fully characterize the
orbits, E is useful as a redundant “weight” to enhance the
contrast between different groups. Moreover, because the mass
of the merging galaxies (Mhalo  109−11Me; e.g., Robertson
et al. 2005; D’Souza & Bell 2018) are typically much smaller
than that of our galaxy (Mhalo ∼ 10
12Me; e.g., Karukes et al.
2020), the merged objects are expected to occupy only a small
volume of the (J, E) space. Therefore, detecting tightly
clumped groups of halo objects in J and E space potentially
provides a powerful means to detect the past mergers that
contributed to the Milky Way’s halo.
This strategy for detecting mergers has now become feasible
in the era of the ESA/Gaia mission (Gaia Collaboration et al.
2016) because the precision of this astrometric data set allows
one to compute reasonably accurate (J, E) values for a very
large population of halo objects. In particular, the excellent
Gaia EDR3 data set (Gaia Collaboration et al. 2021; Lindegren
et al. 2021) has provided the means to obtain very precise
phase-space measurements for an enormously large number of
globular clusters (e.g., Vasiliev & Baumgardt 2021), stellar
streams (e.g., Ibata et al. 2021; Li et al. 2021a), and satellite
galaxies (e.g., McConnachie & Venn 2020), and we use these
measurements in the present study.
Before proceeding further, we note that some recent studies
have also analyzed energies and angular momenta of globular
clusters (e.g., Massari et al. 2019) and streams (e.g., Bonaca
et al. 2021). However, the objective of those studies was
largely to associate these objects with the previously known
mergers of
the Milky Way.13 Here, our objective
is
fundamentally different, namely—to detect the Milky Way’s
mergers by being completely agnostic about the previously
hypothesized groupings of mergers and accretions.
This paper is arranged as follows. In Section 2, we describe
the data used for the halo objects and explain our method to
compute their actions and energy values. In Section 3, we
present our procedure for detecting the mergers by finding
“groups of objects” in (J, E) space. In Section 4, we analyze the
detected mergers for their member objects, their dynamical
10 While globular clusters and satellite galaxies represent two very different
categories of stellar systems, streams do not represent a third category as they
are produced from either globular clusters or satellite galaxies. Streams differ
from the other two objects only in terms of their dynamical evolution, in the
sense that streams are much more dynamically evolved.
11 Conceptually, J represents the amplitude of an object’s orbit along different
directions. For instance, in cylindrical coordinates, J ≡ (JR, Jf, Jz), where Jf
represents the z component of angular momentum (≡Lz), and JR and Jz describe
the extent of oscillations in cylindrical radius and z directions, respectively.
12 The population of streams can originate from the tidal stripping of the
member globular clusters and/or satellites inside the progenitor galaxy (e.g.,
Carlberg 2018).
13 An exception is the study by Myeong et al. (2019), who used the Gaia DR2
measurements of globular clusters and hypothesized the “Sequoia” merger.
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The Astrophysical Journal, 926:107 (30pp), 2022 February 20
Malhan et al.
properties, and their [Fe/H] distribution function. In Section 5,
we discuss the properties of a specific candidate merger.
Additionally, in Section 6, we find several physical connections
between streams and other objects (based on the similarity of
their orbits and [Fe/H]). Finally, we discuss our findings and
conclude in Section 7.
2. Computing Actions and Energy of Globular Clusters,
Stellar Streams, and Satellite Galaxies
To compute the (J, E) of an object, we require (1) data of the
complete 6D phase-space measurements of that object, i.e., its
2D sky position (α, δ), heliocentric distance (De) or parallax
(ϖ), 2D proper motion (
cos ,
m
m
d m
º
a
a
d
*
), and line-of-sight
velocity (vlos), and (2) a Galactic potential model that suitably
represents the Milky Way. Below, Section 2.1 describes the
phase-space measurements of n= 257 objects and Section 2.2
details the adopted Galactic potential model and our procedure
for computing the (J, E) quantities.
2.1. Data
For globular clusters, we obtain their phase-space measure-
ments from the Vasiliev & Baumgardt (2021) catalog. This
catalog provides, for 170 globular clusters, their phase-space
measurements, and we use the observed heliocentric coordi-
nates (i.e., α, δ, De, ma*, μδ, vlos) along with the associated
uncertainties. Vasiliev & Baumgardt (2021) derive the 4D
astrometric measurement (α, δ, ma* , μδ) of globular clusters
using the Gaia EDR3 data set, while the parameters De and vlos
are based on a combination of Gaia EDR3 and other surveys.
For satellite galaxies, we obtain their phase-space measure-
ments from the McConnachie & Venn (2020) catalog. This
catalog provides data in heliocentric coordinates format similar
to that described above but for the satellite galaxies. From this
catalog, we use only those objects that lie within a distance of
De < 250 kpc (equivalent to the virial radius of the Milky Way;
Correa Magnus & Vasiliev 2021), yielding a sample of 44
objects. In McConnachie & Venn (2020), the uncertainties on
each component of the proper motion are only the observational
uncertainties, and therefore, we add in quadrature a systematic
uncertainty of 0.033 mas yr−1 to each component of proper
motion
(A. McConnachie, private communication). While
inspecting this catalog, we found that it lacks the proper motion
measurements of two other satellites of the Milky Way, namely
Bootes III (Grillmair 2009) and the Sagittarius dSph (Ibata et al.
1994). For Bootes III, we obtain its Gaia DR2−based proper
motion from Carlin & Sand (2018). For Sagittarius, we use the
Vasiliev & Belokurov (2020) catalog that provides Gaia DR2
−based proper motions for this dwarf. From this, we compute
the median and uncertainty for the Sagittarius dSph as (ma*,
μδ)= (−2.67± 0.45,−1.40± 0.40)mas yr
−1. Our final sample
comprises 46 satellite galaxies.
For stellar streams, we acquire their phase-space measurements
primarily from the Ibata et al. (2021) catalog, but we also use
some other public stream catalogs (as described below). We first
use the Ibata et al. (2021) catalog that contains those streams
detected in the Gaia DR2 and EDR3 data sets using the
STREAMFINDER algorithm (Malhan & Ibata 2018; Malhan et al.
2018; Ibata et al. 2019b). In this catalog, all the stream stars
possess the 5D astrometric measurements on (α, δ, ϖ, ma*, μδ),
along with their observational uncertainties, as listed in the EDR3
catalog. However, most of these stream stars lack spectroscopic
vlos measurements; this is because (to date) Gaia has provided vlos
for only very bright stars with G 12 mag. Therefore, to obtain
the missing vlos measurements, we use various available
spectroscopic surveys and also rely on the data from our own
follow-up spectroscopic campaigns. These spectroscopic mea-
surements are already presented in Ibata et al. (2021) for the
streams “Pal 5” (originally discovered by Odenkirchen et al.
2001), “GD-1” (Grillmair & Dionatos 2006), “Orphan” (Grill-
mair 2006; Belokurov et al. 2007), “Atlas” (Shipp et al. 2018),
“Gaia-1” (Malhan et al. 2018), “Phlegethon” (Ibata et al. 2018),
“Slidr” (Ibata et al. 2019b), “Ylgr” (Ibata et al. 2019b), “Leiptr”
(Ibata et al. 2019b), “Svöl” (Ibata et al. 2019b), “Gjöll” (Ibata
et al. 2019b, the stream of NGC 3201; Hansen et al. 2020; Palau
& Miralda-Escude 2021), “Fjörm” (Ibata et al. 2019b, the stream
of NGC 4590/M68; Palau & Miralda-Escude 2019), “Sylgr”
(Ibata et al. 2019b, the low-metallicity stream with [Fe/H]=
−2.92 dex; Roederer & Gnedin 2019), “Fimbulthul” (stream of
the ω Centauri cluster, Ibata et al. 2019a), “Kshir” (Malhan et al.
2019a), “M92” (Thomas et al. 2020; Sollima 2020), “Hríd,” “C-
7,” “C-3,” “Gunnthrà,” and “NGC 6397.” This spectroscopic
campaign suggests that 85% of the Ibata et al. (2021) sample
stars are bona fide stream members.
Ibata et al. (2021) also detected other streams, namely “Indus”
(Shipp et al. 2018), “Jhelum” (Shipp et al. 2018), “NGC 5466”
(Belokurov et al. 2006; Grillmair & Johnson 2006), “M5”
(Grillmair 2019), “Phoenix” (Balbinot et al. 2016, the low-
metallicity globular cluster stream with [Fe/H]=−2.7 dex;
Wan et al. 2020), “Gaia-6,” “Gaia-9,” “Gaia-10,” “Gaia-12,”
“NGC 7089.” For these streams, we obtain their vlos measure-
ments in this study by cross-matching their stars with various
public spectroscopic catalogs, namely SDSS/Segue (Yanny
et al. 2009), LAMOST DR7 (Zhao et al. 2012), APOGEE DR16
(Majewski et al. 2017), S5 DR1 (Li et al. 2019), and our own
spectroscopic data (that we have collected from our follow-up
campaigns; Ibata et al. 2021).
Finally, we include additional streams into our analysis from
some of the public stream catalogs. From Malhan et al. (2021)
we take the data for the “LMS-1” stream (a recently discovered
dwarf galaxy stream, Yuan et al. 2020a). We use the Yuan et al.
(2021) catalog for the streams “Palca” (Shipp et al. 2018), “C-
20” (Ibata et al. 2021), and “Cetus” (Newberg et al. 2009). For
“Ophiuchus” (Bernard et al. 2014), we use those stars provided
in the Caldwell et al. (2020) catalog that possess membership
probabilities >0.8. We also include those streams provided in
the S5 DR1 survey (Li et al. 2019) but were not detected by
Ibata et al. (2021). These include “Elqui,” “AliqaUma,” and
“Chenab.” Lastly, we also include into our analysis the “C-19”
stream (the most-metal-poor globular cluster stream known to
date with [Fe/H] ≈ −3.4 dex; Martin et al. 2022a). For all
these streams, we use the Gaia EDR3 astrometry.
In summary, we use a total of 41 stellar streams for this
study. This stream sample comprises n= 9192 Gaia EDR3
stars, of which 1485 possess spectroscopic vlos measurements.
The parallaxes of all the stream stars are corrected for the
global parallax zero point in Gaia EDR3 using the Lindegren
et al. (2021) value.
Figure 1 shows phase-space measurements of all
the
n= 257 objects considered in our study. In this plot, the
distance of a given stream corresponds to the inverse of the
uncertainty-weighted average mean parallax value of its
member stars.
3
The Astrophysical Journal, 926:107 (30pp), 2022 February 20
Malhan et al.
2.2. Computing Actions and Energy of the Halo Objects
To compute the orbits of the objects in our sample, we adopt
the Galactic potential model of McMillan (2017). This is a
static and axisymmetric model comprising a bulge, disk
components, and an NFW (Navarro–Frenk–White) halo. For
this potential model,
the total galactic mass within the
galactocentric distance rgal < 20 kpc is 2.2 × 10
11Me, rgal <
50 kpc is 4.9× 1011Me, and rgal < 100 kpc is 8.1 × 10
11Me.
Another model that is often used to represent the Galactic
potential is MWPotential2014 of Bovy (2015), and this
model (on average) is ∼1.5 times lighter than the McMillan
(2017) model. For our study, we prefer the McMillan (2017)
model because (1) the predicted velocity curve of this model is
more consistent with the measurements of the Milky Way (e.g.,
Bovy 2020; Nitschai et al. 2021), and (2) we find that all halo
objects in this mass model possess E < 0 (i.e., their orbits are
bound); however, in the case of MWPotential2014 we infer
that 34 clusters and all the satellite galaxies possess E… 0 (i.e.,
their orbits are unbound). To set the McMillan (2017) potential
model and to compute (J, E) and other orbital parameters, we
make use of the galpy module (Bovy 2015). Moreover, to
transform the heliocentric phase-space measurements of the
objects into the Galactocentric frame (which is required for
computing orbits), we adopt the Sun’s Galactocentric distance
from Gravity Collaboration et al. (2018) and the Sun’s galactic
velocity from Reid et al. (2014) and Schonrich et al. (2010).
To compute the (J, E) values of globular clusters, we do the
following. For a given globular cluster, we sample 1000 orbits
using the mean and the uncertainty on its phase-space
measurement. For that particular cluster, this provides an (J,
E) distribution of 1000 data points, and this distribution
represents the uncertainty in the derived (J, E) value for that
cluster. Note that this (J, E) uncertainty, for a given cluster,
reflects its uncertainty on the phase-space measurement. This
orbit-sampling procedure is repeated for all globular clusters,
and for each cluster we retain their
respective
(J, E)
distribution. This (J, E) distribution is a vital information,
and we subsequently use this while detecting the mergers (as
shown in Section 3). The resulting (J, E) distribution of all the
globular clusters is shown in Figure 2, where each object is
effectively represented by a distribution of 1000 points.
We analyze actions in cylindrical coordinates, i.e., in the J≡
(JR, Jf, Jz) system, where Jf corresponds to the z component of
angular momentum (i.e., Jf ≡ Lz) and negative Jf represents
prograde motion (i.e., rotational motion in the direction of the
Galactic disk). Similarly, components JR and Jz describe the
extent of oscillations in cylindrical radius and z directions,
respectively. Figure 2 shows these globular clusters in (1) the
“projected action space,” represented by a diagram of Jf/Jtotal
Figure 1. The Galactic maps showing phase-space measurements of n = 257 halo objects used in our study, namely 170 globular clusters (denoted by “star”
markers), 41 stellar streams (denoted by “dot” markers), and 46 satellite galaxies (denoted by “square” markers). From panel (a) to (d), these objects are colored by
their heliocentric distances (De), line-of-sight velocities (vlos), proper motion in the Galactic longitude direction ( ℓm*), and proper motion in the Galactic latitude
direction direction (μb), respectively. In panel (d), we only show streams with their names and do not plot other objects to avoid crowding.
4
The Astrophysical Journal, 926:107 (30pp), 2022 February 20
Malhan et al.
Figure 2. Action–energy (J, E) space of the Milky Way showing the globular clusters (top panels), stellar streams (middle panels), and satellite galaxies (bottom
panels). Each object can be seen as a “cloud” of 1000 Monte Carlo representations of its orbit (see Section 2.2). In each row, the left panel corresponds to the projected
action-space map, where the horizontal axis is Jf/Jtot and the vertical axis is (Jz – JR)/Jtot with Jtot = JR + Jz + |Jf|. In these panels, the points are colored by the total
energy of their orbits (E). The right panels show the z component of the angular momentum (Jf ≡ Lz) vs. E, and the points are colored by the orthogonal component of
their angular momenta (L
L
L
x
y
2
2
=
+
^
).
5
The Astrophysical Journal, 926:107 (30pp), 2022 February 20
Malhan et al.
versus (Jz − JR)/Jtotal, where Jtotal = JR + Jz + |Jf|, and (2) the
Jf versus E space. The reason for using the projected action
space is that this plot is effective in separating objects that lie
along circular, radial, and in-plane orbits, and it is considered to
be superior to other commonly used kinematic spaces (e.g.,
Lane et al. 2022). We also use the orthogonal component of the
angular momentum L
L
L
x
y
2
2
=
+
^
for representation. Note
that even though L⊥ is not fully conserved in an axisymmetric
potential,
it still serves as a useful quantity for orbital
characterization
(e.g., Bonaca et al. 2021). Along with
retrieving the (J, E) values, we also retrieve other orbital
parameters (e.g., rapo, rperi, eccentricity—these values are used
at a later stage for the analysis of the detected mergers).
To compute the (J, E) values of satellite galaxies, we use
exactly the same orbit-sampling procedure as described above
for globular clusters. The corresponding (J, E) distribution is
shown in Figure 2.
To compute the (J, E) values of stellar streams, we follow
the orbit-fitting procedure; this approach is more sophisticated
than the above-described orbit-sampling procedure and more
suitable for stellar streams. That is, we obtain (J, E) solutions
of a given stream by fitting orbits
to the phase-space
measurements of all its member stars (e.g., Koposov et al.
2010). This procedure ensures that the resulting orbit solution
provides a reasonable representation of the entire stream
structure and also that the resulting (J, E) values are precise.14
We use this method only for narrow and dynamically cold
streams (that make up most of our stream sample), but for the
other broad and dynamically hot streams we rely on the orbit-
sampling procedure (see further below). To carry out the orbit
fitting of streams, we follow the same procedure as described in
Malhan et al. (2021). Briefly, we survey the parameter space
using our own Metropolis–Hastings-based Markov Chain
Monte Carlo (MCMC) algorithm, where the log-likelihood of
each member star i is defined as
((
)
)
( )

N
D
ln
ln 2
ln
ln
,
1
i
v
5 2
sky
los
p
s s s s s
= -
+
-
v m m
a
d
where
(
)
(
)
(
)
(
)
(
)
( )
N
e
D
R
R
R
R
R
R
v
v
1
,
,
,
,
,
,
.
2
j
R
j
j
v
1
5
2
1
5
2
1
2
sky
2
sky
2
2
2
d
o 2
2
3
2
d
o 2
2
4
2
d
o 2
2
5
2
los
d
los
o 2
2
j
2
los


q
s
v
v
s
m
m
s
m
m
s
s
=
-
=
=
=
-
=
-
=
-
=
-
v
a
a
m
d
d
m
=
-
=
a
d
Here, θsky is the on-sky angular difference between the orbit
and the data point,
,
,
d
d
d
v m m
a
d and vlos
d are the measured data
parallax, proper motion, and line-of-sight velocity, with the
corresponding orbital model values marked with “o.” The
Gaussian dispersions
,
,
,
,
v
sky
los
s
s s s s
v m
m
a
d
are the sum in
quadrature of the intrinsic dispersion of the model and the
observational uncertainty of each data point. The particular
reason for adopting this “conservative formulation” of the log-
likelihood function (Sivia 1996) is to lower the contribution
from outliers that could be contaminating the stream data.
Furthermore, in a given stream, we set all those stars that
lack spectroscopic measurements to vlos = 0 km s
−1 with a
104 km s−1 Gaussian uncertainty. While undertaking this orbit-
fitting procedure for a given stream, we chose to anchor the
orbit solutions at a fixed R.A. value (which was approximately
halfway along the stream), while
leaving all
the other
parameters to be varied. We do this because without setting
an anchor, the solution would have wandered over the full
length of the stream. The success of such a procedure in fitting
streams has been demonstrated before (Malhan & Ibata 2019;
Malhan et al. 2021). This procedure works well for most of the
streams, as the final MCMC chains are converged and the
resulting best-fit orbits provide good representations to the
phase-space structures of all these streams.
The above orbit-fitting procedure was carried out for the
majority of streams; however, for a subset of them we
considered it better
to instead adopt
the orbit-sampling
procedure. This subset includes LMS-1, Orphan, Fimbulthul,
Cetus, Svol, NGC 6397, Ophiuchus, C-3, Gaia-6, and Chenab.
The orbit-sampling procedure means that we no longer use
Equation (1) (this ensures that the resulting orbit provides a
reasonable fit to the entire stream structure), but instead, we
simply sample orbits using directly the phase-space measure-
ments of the individual member stars (this does not guarantee
an orbit-fit to the entire stream structure). The reason for
adopting this scheme for LMS-1, Cetus (which are dwarf
galaxy streams), and Fimbulthul (which is the stream of the
massive ω Cen cluster) is that these are dynamically hot and
physically broad streams, and the aforementioned orbit-fitting
procedure would have underestimated their dispersions in the
derived (J, E) quantities. Similarly, Ophiuchus also appears to
possess a broader dispersion in vlos space (∼10–15 km s
−1; see
Figure 10 of Caldwell et al. 2020). For Orphan, which is a
stream with a “twisted” shape (due to perturbation by the LMC;
Erkal et al. 2019), we deemed it better to sample its orbits (Li
et al. 2021a also adopt a similar procedure to compute the orbit
of Orphan). For the remaining streams, although they did
appear narrow and linear in the (α, δ) and (ma*, μδ) spaces, it was
difficult to visualize this linearity in vlos space. This was
primarily because these streams lack enough spectroscopic
measurements so that a clear stream signal can be visible in vlos
space. Therefore, it was difficult to apply the orbit-fitting
procedure for them, and we resort to the orbit-sampling
procedure. For all of these streams, the sampling in α, δ, ma*, μδ,
and vlos was performed directly using the measurements and the
associated uncertainties. However, to sample over the distance
parameter in a given stream, we computed the average distance
(and the uncertainty) using the uncertainty-weighted average
mean parallax of the member stars.
The above orbit-fitting and orbit-sampling schemes generate
the MCMC chains for the orbital parameters of all 41 streams,
and for each stream, we randomly sample 1000 steps (this we
do after rejecting the burn-in phase). These sampled values are
shown in Figure 2. Note that for most of the streams, their (J,
E) dispersions are much smaller than those of globular clusters
and satellite galaxies. This is because the orbits of streams are
much more precisely constrained (because we employ the
above orbit-fitting procedure). The derived orbital properties of
our streams are provided in Tables 1 and 2.
14 By employing the orbit-fitting procedure, we are assuming that the entire
phase-space structure of a stream can be well represented by an orbit. Although
streams do not strictly delineate orbits (Sanders & Binney 2013), our
assumption is still reasonable as far as the scope of this study is concerned.
6
The Astrophysical Journal, 926:107 (30pp), 2022 February 20
Malhan et al.
2.3. A Qualitative Analysis of the Orbits
As a passing analysis, we qualitatively examine some basic
orbital properties of globular clusters, satellite galaxies, and
stellar streams. The knowledge gained from this analysis allows
us to put our final results in some context.
For globular clusters, we find that ∼70% of them move
along prograde orbits (i.e., their Jf < 0), 18% move along polar
orbits (i.e., their orbital planes are inclined almost perpendi-
cularly to the Galactic disk plane, with f … 75°), ∼12% have
their orbits nearly confined to the Galactic plane (i.e., their
f „ 20°), 11% have disk-like orbits (i.e., both prograde and in
plane), 1% have in-plane and retrograde orbits, and 10% have
highly eccentric orbits
(with ecc > 0.8). This excess of
prograde globular clusters could be indicating that the Galactic
halo itself initially had an excess of prograde clusters or it may
owe to the possible spinning of the dark matter halo (e.g.,
Obreja et al. 2022).
For satellites, we find that ∼60% of them move along
prograde orbits, 10% have highly eccentric orbits, and ∼45%
move along polar orbits (most of these “polar” satellites belong
to the “Vast Plane of Satellites” structure; see Pawlowski et al.
2021). None of the satellites move in the disk plane; this could
be because satellites on coplanar orbits are expected to be
destroyed quickly compared to those on polar orbits (e.g.,
Penarrubia et al. 2002). The satellites possess quite high
energies and angular momenta compared to the globular
clusters (and also stellar streams, as we note below). The high E
values of satellites suggest that many of them are not ancient
inhabitants of the Milky Way but have only recently arrived
into our galaxy (perhaps 4 Gyr ago; e.g., Hammer et al.
2021).
For stellar streams, we find that 55% of them move along
prograde orbits, 22% move along polar orbits, and 5% possess
highly eccentric orbits. Some of these polar streams are LMS-1,
C-19, Sylgr, Jhelum, Elqui, Gaia-10, Ophiuchus, and Hrìd.
None of the streams orbit in the disk plane. Our inference on
the prograde distribution of streams is somewhat consistent
with the study of Panithanpaisal et al. (2021), who analyzed
FIRE 2 cosmological simulations and found that Milky Way–
mass galaxies should have an even distribution of streams on
prograde and retrograde orbits.
Table 1
Constrained Heliocentric Parameters of Stellar Streams. For Each Stream, the Following Values Represent the Posterior Distribution at the Stream’s “Anchor” Point
(i.e., at a Fixed R.A. Value)
Stream
No. of Gaia
No. of
R.A.
Decl.
De
ma*
μδ
vlos
Sources
vlos sources
(deg)
(deg)
(kpc)
(mas yr−1)
(mas yr−1)
(km s−1)
Gjoll
102
35
82.1
13.95 0.36
0.35
-
-
+
3.26 0.03
0.03
-
+
23.58 0.09
0.08
-
+
23.7 0.05
0.06
-
-
+
78.73 1.84
2.36
-
+
Leiptr
237
67
89.11
28.37 0.27
0.2
-
-
+
7.39 0.07
0.07
-
+
10.59 0.04
0.03
-
+
9.9 0.04
0.03
- -
+
194.22 1.86
2.23
-
+
Hrid
233
24
280.51
33.3 0.6
0.75
-
+
2.75 0.07
0.1
-
+
5.88 0.08
0.11
-
-
+
20.08 0.19
0.21
-
+
238.77 5.52
3.3
-
-
+
Pal5
48
29
229.65
0.26 0.13
0.1
-
+
20.16 0.33
0.24
-
+
2.75 0.02
0.03
-
-
+
2.68 0.02
0.02
-
-
+
57.03 1.04
1.08
-
-
+
Gaia-1
106
8
190.96
9.16 0.1
0.15
-
-
+
5.57 0.1
0.16
-
+
14.39 0.04
0.04
-
-
+
19.72 0.04
0.03
-
-
+
214.91 2.16
3.5
-
+
Ylgr
699
32
173.82
22.31 0.3
0.22
-
-
+
9.72 0.14
0.16
-
+
0.44 0.03
0.04
-
-
+
7.65 0.04
0.05
-
-
+
317.86 3.05
2.83
-
+
Fjorm
182
28
251.89
65.38 0.22
0.24
-
+
6.42 0.14
0.16
-
+
3.92 0.08
0.07
-
+
3.1 0.06
0.06
-
+
25.37 2.19
1.89
-
-
+
Kshir
55
16
205.88
67.25 0.17
0.13
-
+
9.57 0.08
0.08
-
+
7.67 0.04
0.04
-
-
+
3.92 0.05
0.04
-
-
+
249.88 2.92
2.62
-
-
+
Gunnthra
61
8
284.22
73.49 0.14
0.23
-
-
+
2.83 0.13
0.12
-
+
15.83 0.13
0.11
-
-
+
24.04 0.17
0.15
-
-
+
132.26 4.97
6.23
-
+
Slidr
181
29
160.05
10.22 0.41
0.43
-
+
2.99 0.09
0.11
-
+
24.6 0.08
0.08
-
-
+
6.65 0.06
0.06
-
-
+
87.98 3.17
3.44
-
-
+
M92
84
9
259.89
43.08 0.2
0.2
-
+
8.94 0.18
0.2
-
+
5.15 0.05
0.05
-
-
+
0.63 0.04
0.06
-
-
+
140.66 7.53
6.28
-
-
+
NGC 3201
388
4
152.46
46.32 0.08
0.11
-
-
+
4.99 0.02
0.01
-
+
8.87 0.02
0.02
-
+
2.22 0.02
0.02
-
-
+
489.63 3.82
3.36
-
+
Atlas
46
10
25.04
29.81 0.1
0.1
-
-
+
19.93 0.75
0.76
-
+
0.04 0.02
0.02
-
+
0.89 0.02
0.02
-
-
+
85.65 1.58
1.48
-
-
+
C-7
120
10
287.15
50.17 0.14
0.16
-
-
+
6.77 0.21
0.28
-
+
13.79 0.06
0.07
-
-
+
12.38 0.07
0.06
-
-
+
55.05 2.51
1.5
-
+
Palca
24
24
36.57
36.15 0.31
0.33
-
-
+
12.31 1.44
1.68
-
+
0.9 0.02
0.02
-
+
0.23 0.04
0.04
-
-
+
106.32 2.54
2.62
-
+
Sylgr
165
19
179.68
2.44 0.4
0.27
-
-
+
3.77 0.11
0.07
-
+
13.98 0.14
0.12
-
-
+
12.9 0.1
0.09
-
-
+
184.8 8.15
15.48
-
-
+
Gaia-9
286
15
233.27
60.42 0.11
0.04
-
+
4.68 0.09
0.08
-
+
12.49 0.12
0.11
-
-
+
6.37 0.08
0.14
-
+
359.86 4.11
4.65
-
-
+
Gaia-10
90
9
161.47
15.17 0.14
0.14
-
+
13.32 0.28
0.34
-
+
4.14 0.05
0.05
-
-
+
3.15 0.04
0.04
-
-
+
289.64 3.32
2.75
-
+
Gaia-12
38
1
41.05
16.45 0.13
0.13
-
+
15.71 1.03
1.29
-
+
5.84 0.05
0.05
-
+
5.66 0.06
0.07
-
-
+
303.83 15.07
22.55
-
-
+
Indus
454
45
340.12
60.58 0.1
0.1
-
-
+
14.96 0.16
0.19
-
+
3.59 0.03
0.03
-
+
4.89 0.03
0.02
-
-
+
49.15 3.68
2.45
-
-
+
Jhelum
972
246
351.95
51.74 0.08
0.08
-
-
+
11.39 0.15
0.13
-
+
7.23 0.04
0.04
-
+
4.37 0.03
0.04
-
-
+
1.29 3.11
2.6
-
-
+
Phoenix
35
19
23.96
50.01 0.24
0.24
-
-
+
16.8 0.36
0.33
-
+
2.72 0.03
0.03
-
+
0.07 0.03
0.03
-
-
+
45.92 1.58
1.63
-
+
NGC5466
62
4
214.41
26.84 0.11
0.12
-
+
14.09 0.25
0.27
-
+
5.64 0.03
0.03
-
-
+
0.72 0.02
0.03
-
-
+
95.04 5.91
7.4
-
+
M5
139
5
206.96
13.5 0.14
0.15
-
+
7.44 0.11
0.12
-
+
3.5 0.04
0.03
-
+
8.76 0.04
0.04
-
-
+
42.97 3.83
3.33
-
-
+
C-20
34
9
359.81
8.63 0.16
0.16
-
+
18.11 1.39
1.45
-
+
0.58 0.03
0.03
-
-
+
1.44 0.02
0.02
-
+
116.87 1.44
1.46
-
-
+
C-19
34
8
355.28
28.82 1.17
0.63
-
+
18.04 0.53
0.55
-
+
1.25 0.03
0.03
-
+
2.74 0.05
0.03
-
-
+
193.48 2.52
2.61
-
-
+
Elqui
4
4
19.77
42.36 0.29
0.3
-
-
+
51.41 7.04
4.64
-
+
0.33 0.03
0.02
-
+
0.49 0.02
0.02
-
-
+
15.86 20.38
8.82
-
+
AliqaUma
5
5
34.08
33.97 0.34
0.31
-
-
+
21.48 1.2
2.32
-
+
0.24 0.03
0.02
-
+
0.79 0.03
0.03
-
-
+
42.33 2.23
2.29
-
-
+
Phlegethon
365
41
319.89
32.07 0.37
0.43
-
-
+
3.29 0.05
0.05
-
+
3.97 0.09
0.09
-
-
+
37.66 0.09
0.08
-
-
+
15.9 6.12
4.97
-
+
GD-1
811
216
160.02
45.9 0.19
0.25
-
+
8.06 0.07
0.07
-
+
6.75 0.03
0.04
-
-
+
10.88 0.05
0.04
-
-
+
101.83 2.47
2.05
-
-
+
Note. This anchor is defined during the orbit-fitting procedure. From left to right, the columns provide the stream’s name, number of Gaia EDR3 sources in the stream,
number of sources with spectroscopic line-of-sight velocities (vlos), R.A. (which acts as the anchor point in our orbit-fitting procedure), decl., heliocentric distance
(De), proper motions (
,
m m
a
d
*
), and vlos. The quoted values are medians of the sampled posterior distributions and the corresponding uncertainties represent their 16th
and 84th percentiles. Only those streams for which the orbit-fitting procedure was employed are listed (see Section 2.2).
7
The Astrophysical Journal, 926:107 (30pp), 2022 February 20
Malhan et al.
As a final passing analysis, and not to deviate too much from
the prime objective of the paper, we quickly compare the
distribution of the orbital phase and eccentricity of all the halo
objects (as shown in Figure 13 of Appendix A). First, we
observe a pileup of objects at the pericenter and at the
apocenter, and this is more prevalent for globular clusters and
stellar streams and not so much for satellite galaxies.
Particularly, in the case of streams, we note that more objects
are piled-up at the pericenter than at the apocenter. This effect
points toward our inefficiency in detecting those streams
that, at the present day, could be close to their apocenters
(at distances De  30 kpc). This inefficiency, in part, is also
Table 2
Actions, Energies, Orbital Parameters, and Metallicities of the Stellar Streams
Stream
(JR, Jf, Jz)
Energy
rperi
rapo
zmax
ecc.
[Fe/H]
(kpc km s−1)
(×102 km2 s−2)
(kpc)
(kpc)
(kpc)
(dex)
LMS-1
(
)
255
,
627
, 2514
149
239
232
183
263
383
-
-
+
-
+
-
+
1227 39
65
-
-
+
10.8 1.8
2.5
-
+
20.6 1.9
3.7
-
+
20.2 2.0
3.6
-
+
0.32 0.12
0.11
-
+
−2.1 ± 0.4
Gjoll
(
)
783
, 2782
, 274
65
73
60
60
6
7
-
+
-
+
-
+
1152 18
19
-
-
+
8.5 0.1
0.1
-
+
27.4 1.2
1.4
-
+
10.8 0.5
0.5
-
+
0.52 0.01
0.01
-
+
−1.78
Leiptr
(
)
1455
, 4128
, 378
119
133
73
77
10
11
-
+
-
+
-
+
933 18
19
- -
+
12.3 0.1
0.1
-
+
45.1 2.1
2.3
-
+
17.6 0.9
0.9
-
+
0.57 0.01
0.01
-
+
L
Hrid
(
)
1642
, 78
, 83
79
110
47
54
5
6
-
+
-
+
-
+
1319 22
30
-
-
+
1.1 0.0
0.0
-
+
22.0 1.0
1.4
-
+
7.0 0.5
0.9
-
+
0.9 0.0
0.0
-
+
−1.1
Pal5
(
)
282
,
744
, 1357
17
19
44
61
51
42
-
-
+
-
+
-
+
1385 15
11
-
-
+
6.9 0.4
0.3
-
+
15.8 0.3
0.2
-
+
14.7 0.3
0.2
-
+
0.39 0.02
0.02
-
+
−1.35 ± 0.06
Orphan
(
)
959
,
3885
, 1199
271
978
1017
405
213
484
-
-
+
-
+
-
+
949 64
175
- -
+
15.6 2.1
3.8
-
+
41.2 6.2
23.6
-
+
26.4 4.8
16.9
-
+
0.48 0.06
0.09
-
+
−1.85 ± 0.53
Gaia-1
(
)
3638
, 2678
, 997
632
1307
57
89
58
93
-
+
-
+
-
+
794 55
90
- -
+
8.2 0.0
0.1
-
+
67.6 8.9
18.3
-
+
45.7 6.5
13.6
-
+
0.78 0.03
0.04
-
+
−1.36
Fimbulthul
(
)
202
, 427
, 95
78
109
588
244
44
197
-
+
-
+
-
+
1847 16
73
-
-
+
2.4 0.7
0.8
-
+
7.2 0.3
0.4
-
+
2.4 0.7
3.5
-
+
0.51 0.13
0.12
-
+
−1.36 to −1.8
Ylgr
(
)
205
, 2766
, 556
35
40
66
68
25
30
-
+
-
+
-
+
1219 19
20
-
-
+
11.5 0.1
0.1
-
+
20.7 1.1
1.2
-
+
11.2 0.7
0.8
-
+
0.29 0.02
0.02
-
+
−1.87
Fjorm
(
)
831
,
2332
, 877
62
60
24
24
40
43
-
-
+
-
+
-
+
1123 15
15
-
-
+
9.1 0.1
0.1
-
+
29.1 1.1
1.1
-
+
19.7 1.0
1.0
-
+
0.52 0.01
0.01
-
+
−2.2
Kshir
(
)
18
, 2755
, 491
4
6
53
60
13
14
-
+
-
+
-
+
1268 11
12
-
-
+
13.4 0.2
0.2
-
+
16.0 0.5
0.6
-
+
8.2 0.3
0.3
-
+
0.09 0.01
0.01
-
+
−1.78
Cetus
(
)
815
,
2416
, 2287
317
513
1064
841
954
1282
-
-
+
-
+
-
+
1000 64
124
-
-
+
14.7 4.5
7.2
-
+
35.9 3.7
9.9
-
+
30.2 4.9
10.9
-
+
0.45 0.1
0.14
-
+
−2.0
Svol
(
)
97
,
1501
, 224
32
94
248
384
54
107
-
-
+
-
+
-
+
1566 61
89
-
-
+
5.9 0.6
0.6
-
+
10.0 1.0
2.8
-
+
5.0 0.8
0.9
-
+
0.28 0.05
0.07
-
+
−1.98 ± 0.10
Gunnthra
(
)
69
, 852
, 218
7
14
77
67
34
30
-
+
-
+
-
+
1765 28
31
-
-
+
4.2 0.4
0.3
-
+
7.2 0.2
0.3
-
+
3.8 0.4
0.4
-
+
0.27 0.02
0.03
-
+
L
Slidr
(
)
1076
,
1358
, 1831
149
217
23
23
102
126
-
-
+
-
+
-
+
1086 32
41
-
-
+
8.7 0.1
0.1
-
+
32.3 2.5
3.5
-
+
29.1 2.4
3.4
-
+
0.58 0.02
0.03
-
+
−1.8
M92
(
)
361
, 181
, 544
9
9
41
39
70
83
-
+
-
+
-
+
1639 10
12
-
-
+
3.0 0.1
0.2
-
+
10.7 0.2
0.2
-
+
9.9 0.6
0.5
-
+
0.56 0.01
0.01
-
+
−2.16 ± 0.05
NGC 6397
(
)
75
,
586
, 222
5
5
29
15
14
23
-
-
+
-
+
-
+
1851 6
11
-
-
+
3.4 0.1
0.1
-
+
6.4 0.1
0.1
-
+
3.7 0.1
0.2
-
+
0.3 0.01
0.01
-
+
L
NGC 3201
(
)
975
, 2860
, 296
48
48
33
32
5
5
-
+
-
+
-
+
1110 10
10
-
-
+
8.5 0.0
0.0
-
+
30.5 0.8
0.8
-
+
12.3 0.3
0.3
-
+
0.56 0.01
0.01
-
+
L
Ophiuchus
(
)
507
,
160
, 1192
202
387
41
34
98
91
-
-
+
-
+
-
+
1490 84
130
-
-
+
3.9 0.4
0.3
-
+
14.2 2.7
4.9
-
+
14.1 2.6
4.9
-
+
0.58 0.1
0.11
-
+
−1.80 ± 0.09
Atlas
(
)
757
,
1817
, 2093
35
39
33
34
86
100
-
-
+
-
+
-
+
1061 11
12
-
-
+
11.7 0.3
0.3
-
+
32.4 0.9
1.0
-
+
28.6 1.0
1.1
-
+
0.47 0.01
0.01
-
+
−2.22 ± 0.03
C-7
(
)
1059
, 706
, 728
215
397
25
17
69
107
-
+
-
+
-
+
1319 65
100
-
-
+
3.5 0.0
0.0
-
+
21.0 2.8
5.2
-
+
18.1 2.8
5.1
-
+
0.72 0.04
0.05
-
+
L
C-3
(
)
142
, 468
, 872
64
538
1185
1110
510
910
-
+
-
+
-
+
1571 111
338
-
-
+
5.7 1.2
2.0
-
+
10.0 1.4
13.2
-
+
8.7 1.3
12.5
-
+
0.35 0.1
0.18
-
+
L
Palca
(
)
91
,
1830
, 1076
24
37
29
28
128
138
-
-
+
-
+
-
+
1300 28
30
-
-
+
10.8 0.3
0.4
-
+
16.5 1.3
1.5
-
+
12.7 1.4
1.5
-
+
0.21 0.03
0.03
-
+
−2.02 ± 0.23
Sylgr
(
)
602
,
702
, 2220
202
141
24
28
153
94
-
-
+
-
+
-
+
1192 61
36
-
-
+
8.7 0.0
0.0
-
+
24.6 3.7
2.4
-
+
23.8 3.7
2.4
-
+
0.48 0.06
0.03
-
+
−2.92 ± 0.06
Gaia-6
(
)
125
, 907
, 557
71
51
229
342
204
288
-
+
-
+
-
+
1593 70
129
-
-
+
6.0 1.8
1.4
-
+
9.5 0.3
3.1
-
+
6.9 0.9
3.6
-
+
0.3 0.1
0.08
-
+
−1.16
Gaia-9
(
)
393
, 1928
, 852
38
37
61
47
20
22
-
+
-
+
-
+
1255 18
15
-
-
+
8.7 0.1
0.1
-
+
20.8 0.9
0.8
-
+
14.7 0.6
0.6
-
+
0.41 0.01
0.01
-
+
−1.94
Gaia-10
(
)
2189
, 287
, 1542
64
66
43
43
140
155
-
+
-
+
-
+
1051 18
20
-
-
+
4.3 0.3
0.4
-
+
37.7 1.4
1.6
-
+
37.2 1.5
1.6
-
+
0.8 0.01
0.01
-
+
−1.4
Gaia-12
(
)
9834
, 7340
, 794
4378
5378
801
608
107
80
-
+
-
+
-
+
433 142
98
- -
+
18.5 1.2
0.9
-
+
194.3 75.0
96.8
-
+
83.0 32.5
42.9
-
+
0.83 0.08
0.05
-
+
−2.6
Indus
(
)
99
,
1121
, 2211
19
25
36
35
49
61
-
-
+
-
+
-
+
1232 15
17
-
-
+
12.6 0.1
0.2
-
+
18.9 0.9
1.0
-
+
17.8 0.8
0.9
-
+
0.2 0.02
0.02
-
+
−1.96 ± 0.41
Jhelum
(
)
594
,
356
, 2557
56
49
17
19
72
62
-
-
+
-
+
-
+
1193 22
17
-
-
+
8.7 0.2
0.2
-
+
24.5 1.3
1.1
-
+
24.3 1.3
1.1
-
+
0.48 0.01
0.01
-
+
−1.83 ± 0.34
Phoenix
(
)
107
,
1563
, 1578
10
11
32
35
62
56
-
-
+
-
+
-
+
1259 12
10
-
-
+
11.7 0.5
0.4
-
+
18.1 0.3
0.3
-
+
15.6 0.3
0.3
-
+
0.22 0.01
0.01
-
+
−2.70 ± 0.06
NGC5466
(
)
1769
, 619
, 1373
114
144
35
38
80
93
-
+
-
+
-
+
1098 24
29
-
-
+
4.8 0.2
0.3
-
+
33.7 1.8
2.3
-
+
31.8 1.7
2.2
-
+
0.75 0.01
0.01
-
+
L
M5
(
)
1366
,
353
, 931
57
69
18
20
40
46
-
-
+
-
+
-
+
1246 14
17
-
-
+
3.4 0.1
0.1
-
+
24.8 0.8
1.0
-
+
23.6 0.9
1.1
-
+
0.76 0.01
0.01
-
+
−1.34 ± 0.05
C-20
(
)
1329
,
3042
, 3823
350
526
167
131
484
503
-
-
+
-
+
-
+
800 59
65
- -
+
20.8 1.3
1.3
-
+
58.5 8.8
12.0
-
+
52.4 8.5
11.3
-
+
0.47 0.04
0.05
-
+
−2.44
NGC7089
(
)
800
,
638
, 359
270
713
555
414
123
99
-
-
+
-
+
-
+
1504 104
307
-
-
+
2.9 0.7
1.2
-
+
14.7 3.0
12.7
-
+
10.9 3.8
7.5
-
+
0.71 0.06
0.06
-
+
L
C-19
(
)
383
,
210
, 2712
47
53
46
48
253
258
-
-
+
-
+
-
+
1232 21
21
-
-
+
9.3 1.0
1.0
-
+
21.6 0.5
0.5
-
+
21.6 0.6
0.5
-
+
0.4 0.03
0.04
-
+
−3.38 ± 0.06
Elqui
(
)
2072
,
273
, 4324
602
543
191
166
352
321
-
-
+
-
+
-
+
868 35
27
- -
+
12.1 2.0
1.8
-
+
54.0 6.2
4.6
-
+
53.9 6.3
4.6
-
+
0.64 0.08
0.07
-
+
−2.22 ± 0.37
Chenab
(
)
2469
,
4062
, 3735
286
463
509
601
338
341
-
-
+
-
+
-
+
690 53
52
- -
+
22.0 2.7
2.2
-
+
81.0 10.4
12.8
-
+
69.1 8.2
10.6
-
+
0.58 0.01
0.01
-
+
−1.78 ± 0.34
AliqaUma
(
)
738
,
1838
, 2025
71
138
64
96
126
223
-
-
+
-
+
-
+
1067 18
30
-
-
+
11.6 0.3
0.4
-
+
31.9 1.5
2.6
-
+
27.9 1.6
3.0
-
+
0.47 0.02
0.03
-
+
−2.30 ± 0.06
Phlegethon
(
)
815
, 1882
, 231
93
120
37
39
10
11
-
+
-
+
-
+
1272 28
32
-
-
+
5.5 0.0
0.0
-
+
22.1 1.4
1.8
-
+
9.4 0.7
0.9
-
+
0.6 0.02
0.02
-
+
−1.96 ± 0.05
GD-1
(
)
164
, 2952
, 938
28
35
61
66
22
23
-
+
-
+
-
+
1153 14
15
-
-
+
14.1 0.1
0.1
-
+
23.0 1.0
1.1
-
+
14.8 0.7
0.7
-
+
0.24 0.02
0.02
-
+
−2.24 ± 0.21
Note. From left to right, the columns provide the stream’s name, action components (J), energy (E), pericentric distance (rperi), apocentric distance (rapo), maximum
height of the orbit from the Galactic plane (zmax), eccentricity (ecc), and [Fe/H] measurements (most of these are spectroscopic and a few are photometric). The (J, E)
and other orbital parameters are derived in this study. The quoted orbital parameter values are the medians of the sampled posterior distributions and the corresponding
uncertainties reflect their 16th and 84th percentiles. The [Fe/H] values of Gaia-6, Gaia-9, Gaia-10, and Gaia-12 correspond to the median of the spectroscopic sample
that we obtained in this study. The other streams with spectroscopic [Fe/H] include LMS-1 (its value is taken from Malhan et al. 2021), Gjöll, Ylgr, Slidr, Fjörm (Ibata
et al. 2019b), Jhelum, Chenab, Elqui, Ophiuchus, Orphan, Palca, Indus (Li et al. 2021a), Fimbulthul (Ibata et al. 2019a), Gaia-1, C-2 and Hríd (Malhan et al. 2020),
Cetus (Yam et al. 2013), Sylgr (Roederer & Gnedin 2019), GD-1 (Malhan & Ibata 2019), Kshir (Malhan et al. 2019a), C-20 (Yuan et al. 2021), Pal 5 (Ishigaki et al.
2016), Atlas, and AliqaUma (Li et al. 2021b). Streams with photometric [Fe/H] include Phlegethon, Svöl, M92, and M5 (their values are taken from Martin et al.
2022b).
8
The Astrophysical Journal, 926:107 (30pp), 2022 February 20
Malhan et al.
because of Gaia’s limiting magnitude at G ∼ 21. Our result is
different from that of Li et al. (2021a), who find that more
streams (in their sample of 12 streams) are piled-up at the
apocenter. Second, we find that most of the objects (be it
clusters, streams, or satellites) have eccentricities e ≈ 0.5, and it
is rare for the objects to possess very radial orbits (e ≈ 1) or
very circular orbits (e ≈ 0). This last inference, with regard to
streams, is consistent with that of Li et al. (2021a).
In summary, we now possess (J, E) information for a total of
n= 257 halo objects of the Milky Way (as shown in Figure 2).
In the next section, we process the entire (J, E) data to detect
groups of objects (i.e., mergers). Therefore, at this stage, it is
important to clarify that some of the objects are being counted
twice in our data set. These objects include those systems that
have counterparts both in the globular cluster catalog and the
stream catalog. For instance, a subset of these objects include
Pal 5, NGC 3201, ω Centauri and M5. One possible way to
proceed would be to remove their counterparts from either of
the catalogs. However, there could be many other streams in
our catalog that could be physically associated to other globular
clusters (e.g., see Section 6) or even to other streams (e.g.,
Orphan–Chenab, Koposov et al. 2019; Palca–Cetus, Chang
et al. 2020; AliqaUma–Atlas, Li et al. 2021b), and it is a
difficult task to separate these plausible associations. We
therefore consider it to be less biased to proceed with all of the
detected structures. Prior associations will be discussed in our
final grouping analysis.
3. Detecting Groups of Objects in (J, E) Space
To search for the Milky Way mergers, we essentially process
the data shown in Figure 2 and detect groups of objects that
tightly clump together in the (J, E) space. To detect these
groups, we employ the ENLINK software
(Sharma &
Johnston 2009) and couple it with a statistical procedure that
accounts for the uncertainties in the (J, E) values of every
object. Below, we first briefly describe the working of ENLINK
and then our procedure to detect groups.
3.1. Description of ENLINK
ENLINK
is a density-based hierarchical group-finding
algorithm that detects groups of any shape and density in a
multidimensional data set. This software employs nonpara-
metric methods to find groups, i.e., it makes no assumptions
about the number of groups being identified or their form.
These functionalities of ENLINK are particularly useful for our
study because a priori we neither know the number of groups
(i.e., number of mergers) that are present in the (J, E) data set,
nor the shapes of these groups (because objects that accrete
inside the same merging galaxy can realize extended/irregular
ellipsoidal shapes in (J, E) space; e.g., Wu et al. 2022).
To detect groups in the data set, ENLINK does not use the
typical Euclidean metric, but builds a locally adaptive Mahala-
nobis (LAM) metric. The importance of this metric can be
explained as follows. Generally speaking, the task of finding
groups in a given data set ultimately boils down to computing
“distances” between different data points. Then, those data points
that lie at smaller distances from each other form part of the same
group. In a scenario where the correlation between different
dimensions of the data set are zero or negligible, one can simply
adopt the Euclidean metric to compute these distances. In this
case, the distance between two data points xi and xj is given by
(
)
(
) (
)
x x
x
x
x
x
s
,
.
,
i
j
i
j
T
i
j
2
= -
-
where x is a 1D matrix whose
length equals the dimension of the data set. However, in real data
sets, correlations between different dimensions are nonzero.
Particularly in our case, one expects significant correlation in
the space constructed with J and E dimensions. Therefore, to find
groups in such a correlated data set, one effectively requires a
multivariate equivalent of the Euclidean distance. This is the
importance of LAM that ENLINK employs, because the
Mahalonobis distance is the distance between a point and a
distribution (and not between two data points). At its heart,
ENLINK uses the LAM metric, where the distance between the
two data points (under discrete approximation) is defined as
(
)
∣
(
)∣
(
)
(
) (
)
( )
x x
x x
x
x
x x
x
x
s
,
,
.
.
,
.
,
3
i
j
i
j
i
j
i
j
i
j
d
T
2
1
1
= S
-
S
-
-
where d is the dimension of the data, Σ is the covariance
matrix, Σ(xi, xj) = 0.5[Σ(xi) + Σ(xj)] and Σ
−1(xi, xj) =
0.5[Σ−1(xi) + Σ
−1(xj)].
The above formula can be intuitively understood as follows.
Consider the term (
)
x
x
.
i
j
T
1
-
S- . Here, (xi − xj) is the distance
between two data points. This is then multiplied by the inverse
of the covariance matrix Σ (or divided by the covariance
matrix). So, this is essentially a multivariate equivalent of the
regular standardization y = (x − μ)/σ. The effect of dividing
by covariance is that if the x values in the data set are strongly
correlated, then the covariance will be high and dividing by this
large covariance will reduce the distance. On the other hand, if
the x are not correlated, then the covariance is small and the
distance is not reduced by much. The overall workings and
implementation of ENLINK are detailed in Sharma & Johnston
(2009), and this software has also been previously applied to
various data sets (e.g., Sharma et al. 2010; Wu et al. 2022).
3.2. Applying ENLINK
To detect groups, we work in the four-dimensional space of
xi ≡ (JR,i, Jf,i, Jz,i, Ei), where i represents a given halo object
and the units of J and E are kpc km s−1 and km2 s−2,
respectively. The reason for working with both J and E
quantities is that their combined information allowed us to
detect several groups (as we show below).
Initially, we
operated ENLINK only in the three-dimensional space of J.
However, this resulted in the detection of the Sagittarius group
(Ibata et al. 1994; Bellazzini et al. 2020) (although with
unusual membership of objects), the Arjuna/Sequoia/I’itoi
group (Naidu et al. 2020; Bonaca et al. 2021), and one to two
other very low-significance groups. At first, this may seem odd
that ENLINK requires the additional (redundant) E information
to find high-significance groups because J fully characterized
the orbits and the parameter E brings no additional dynamical
information. However, this oddity relates to the uncertainties
on J and E. For instance, the relative uncertainties on (JR,i, Jf,i,
Jz,i) for all the objects in our sample (on average) are (12%,
17%, 9%), while the relative uncertainty on E is only 2%.
Therefore, ENLINK prefers these precise values of E
in
addition to J as this helps it to easily distinguish between
different groups.
The ENLINK parameters that we use are neighbors,
min_cluster_size, min_peak_height, cluster_
separation_method, density_method, and gme-
tric. neighbors
is
the “smoothing”
that is used to
compute a local density for each data point because ENLINK
9
The Astrophysical Journal, 926:107 (30pp), 2022 February 20
Malhan et al.
first estimates the density and then finds groups in the density
field. To search for groups in a d-dimensional data set,
ENLINK requires neighbors … (d+ 1). In our case, d= 4 (3
components of J and E) and therefore we set neighbors = 5.
Second, we set min_cluster_size = 5. This is because it
is difficult to find groups smaller than the smoothing length
(i.e., we satisfy the min_cluster_size … neighbors
condition of ENLINK). min_peak_height can be thought
of as the signal-to-noise ratio of the detected groups, and we set
min_peak_height = 3.0. For the parameters cluster_
separation_method and gmetric, we adopt the default
values (i.e., 0). Further, we set density_method = sbr as
this uses an adaptive metric to detect groups. We also tried
different metric definitions, but these gave very similar results
to those we obtained from the above parameter setting.15 Our
experimentation with various parameter settings makes us
confident that we are detecting robust groups.
Before unleashing ENLINK onto the (J, E) data set, we
couple it with a statistical procedure that accounts for the
dispersion in the (J, E) values of the objects (these dispersions
are visible in Figure 2). This is important because ENLINK
itself does not account for the dispersion associated with each
data point. This statistical procedure can be explained as
follows. Fundamentally, we want
to compute a “group
probability” (PGroup) for each halo object, such that this
probability is higher for those objects that belong to the groups
detected by ENLINK. To compute this PGroup value, we
undertake an iterative procedure.
In the first iteration, each halo object is represented by a
single (J, E) value that is sampled from its MCMC chain (we
obtained these MCMC chains in Section 2.2). At this stage, the
total number of (J, E) data points equals the total number of
objects (i.e., 257). After this, we process this (J, E) data using
ENLINK. An attribute that ENLINK returns is a 1D array
labels. labels has the same length as the number of input
data points, and it stores the grouping information. That is, all
the elements in labels possess integer values in the range 1
to n, where n is the total number of groups detected by
ENLINK, and elements that form part of the same group
receive the same values. Furthermore, elements for which
labels = 1 correspond to those objects that form part of the
largest group. For all the objects with labels … 2, we
explicitly set their probability of group membership at iteration
i to be PGroup,i = 1. Among objects with labels = 1, we
accept only those objects
that possess density > 99th
percentile and set their PGroup,i = 1, while the remaining low
density objects are set as PGroup,i = 0.
16 In the next iteration,
a new set of (J, E) values is sampled and the above procedure is
repeated. Note that in this new iteration, the input (J, E) data
has changed, and therefore, the same object can now belong to
a different group and thus receive a different labels value
and a different PGroup,i value. We iterate this procedure 1000
times. This produces, for each halo object, a one-dimensional
array (of length 1000) that contains a combination of 0 s or 1 s.
For each halo object, we take the average of this array and this
we interpret as the group probability PGroup of that object. The
PGroup parameter can be defined as the probability of an object
belonging to a group in (J, E) space. Indeed, those halo objects
that lie in denser regions of (J, E) space—i.e., objects whose (J,
E) distributions overlap significantly—will possess higher
PGroup values.
Figure 3 shows the (J, E) distribution of the halo objects as a
function of the computed PGroup values. In this figure, each
object is represented by the median of its (J, E) distribution. It
can be seen that different objects possess different PGroup
values. We also note that objects with high PGroup values lie in
denser regions of (J, E) space, suggesting that our procedure of
detecting groups has worked as desired. In Figure 3, one can
already visually identify many possible groupings—comprising
those objects that possess high PGroup values and that appear
well separated from other groups.
3.3. Detecting High-significance Groups
Due to the relatively large (J, E) uncertainties, the ENLINK
algorithm’s output of proposed groupings varies considerably
over the 1000 random iterations described above. This means
that the proposed groups cannot be immediately used to
identify the Milky Way’s mergers.
Therefore, we proceed by first defining a threshold value
PThreshold, such that objects with PGroup … PThreshold belong to
high-significance groups, and this corresponds to a likely
detection. To find a suitable PThreshold value, we follow a
pragmatic approach. We repeat the above analysis of comput-
ing the PGroup values of all the halo objects, except this time
we use a “randomized” version of our real (J, E) data. This
randomized data is artificially created, where each object is first
assigned a random orbital pole and then its new (J, E) values
are computed. These randomized (J, E) data are shown in
Figure 14 in Appendix B. Such a randomization procedure
erases any plausible correlations between the objects in (J, E)
space. For the resulting PDF of the new PGroup values (that is
shown in Figure 16), its 90 percentile limit motivates setting a
threshold at PThreshold = 0.3 for a 2σ detection. This procedure
may seem convoluted, but it is required by the astrometric
uncertainties which project in a complicated, nonlinear way
into (J, E) space (hence the usual
techniques of error
propagation would not have been appropriate). This method
of finding the PThreshold value is detailed in Appendix B.
Consequently, for the real PGroup values (shown in Figure 4),
all those objects that possess PGroup … PThreshold are considered
as high-significance groups.
The selection PGroup … PThreshold yields 108 objects (42% of
the total n= 257 objects), and these are shown in Figure 5.
These objects include 81 globular clusters, 25 stellar streams,
and 2 satellite galaxies. This figure also shows different objects
being linked by straight lines. This “link,” between two given
objects, represents the frequency with which these objects were
classified as members of the same group (as per the procedure
described
in Section 3.2). Thicker
links
imply higher
frequency. In Figure 5, these links are pruned by removing
those cases where two objects resulted in the same group in less
than (approximately) one third (300/1000) of the realizations.
Due to this pruning, a couple of objects can be seen without
15 For example, instead of using the adaptive metric, we defined a constant
metric using the uncertainties on (J, E) by setting gmetric = 2 and using the
custom_metric parameter. We made this test because as we are dealing
with a very low number of data points (only 257 points), we wanted to ensure
that the detected groups are robust and are not noise driven. However, in this
case we found similar results to those with the original ENLINK setting.
16 The reason that we make such a distinction for the objects in the
labels = 1 group is that a majority of objects in this largest group are those
that that could not be associated with any “well-defined group” by ENLINK
(these represent the background objects). However, even in this group, some of
the high-density objects may still represent a real merger. Therefore, in order to
consider these potential objects of interest, we accept only those objects that
satisfy the threshold density criteria.
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Malhan et al.
any links, even though they satisfy the condition PGroup …
PThreshold, and it is therefore difficult to associate them with one
unique group. The power of Figure 5 is
that such a
representation automatically reveals the detection of several
independent groups.
Figure 5 shows that we have detected nine high-significance
groups and the properties of these groups are discussed below.
4. Analyzing the Detected Groups
We detect a total of nine distinct groups at …2σ significance.
Among these, we interpret N = 6 groups as the mergers of the
Milky Way because the remaining three actually contain the
in situ population of the Milky Way (see below). The merger
groups comprise 62 halo objects ( 25% of the total 257 objects
considered in our study), including 35 globular clusters, 25
streams, and 2 satellite galaxies. For each of the merger groups,
we analyze
the objects’ memberships
(which are also
summarized in Table 3), their (J, E) properties (which result
from Figure 5), orbital parameters as a function of [Fe/H] (see
Figure 6), [Fe/H] distribution function (MDF; see Figure 7),
other orbital parameters (see Figure 8), and also estimate the
masses of the corresponding progenitor galaxies.
For each group discussed below, we also make a comparison
between our object membership and those proposed in previous
studies. Therefore, to also facilitate this comparison visually,
Figure 3. (J, E) distribution of the halo objects as a function of their group probability PGroup (see Section 3). In this plot, each object is represented by the median of
its (J, E) distribution (which is shown in Figure 2). The globular clusters are denoted by “stars,” streams by “circles,” and satellite galaxies by “squares.” Note that
objects with higher PGroup values lie in the denser regions of this (J, E) space. Such objects with high PGroup values, which also clump together in (J, E) space, form
part of the same group. In panel (b), we label all the high-significance groups.
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Malhan et al.
we provide Figure 17 in Appendix C. This figure is constructed
by adopting the object–merger associations from other studies
(specifically from Massari et al. 2019; Myeong et al. 2019;
Kruijssen et al. 2020; Bonaca et al. 2021). We explicitly note
that our results are not based on Figure 17, and we use it purely
for comparison with our Figure 5.
4.1. Group 1: The Sagittarius Merger
The first group we detect is a high-energy and prograde
overdensity in (J, E) space. Its member objects possess
dynamical properties in the range E ∼ [−0.91, −0.79] ×
105 km2 s−2, JR ∼ [1205, 2090] km s
−1 kpc, Jf ∼ [−2115,
−265] km s−1 kpc, Jz ∼ [3285, 5350] km s
−1 kpc, L⊥ ∼ [4565,
6835] km s−1 kpc, eccentricity ∼[0.5, 0.6], rperi ∼ [11, 22] kpc,
rapo ∼ [45, 60] kpc, and f∼ [66°, 86°], where f defines how
“polar” the merger group is. This highly polar group represents
the previously known Sagittarius merger (Ibata et al. 1994;
Majewski et al. 2003; Bellazzini et al. 2020).
We find that eight objects belong to this group: six globular
clusters (namely, Pal 12, Whiting 1, Terzan 7, Terzan 8, Arp 2,
NGC 6715/M54), one stream (namely, Elqui), and one satellite
(namely, the Sagittarius dSph itself). Our globular cluster
member list is similar to those previously reported by other
studies (e.g., Massari et al. 2019; Bellazzini et al. 2020;
Forbes 2020). We note that our Sagittarius group lacks
NGC 2419 as its member, but previous studies have advocated
for this association based on the fact that this cluster also lies
within the phase-space distribution of the Sagittarius stream
(e.g., Sohn et al. 2018; Bellazzini et al. 2020). A possible
reason why our analysis does not identify a strong association
between NGC 2419 and Sagittarius could be due to this
cluster’s large (J, E) uncertainties that arise due to its large
observational uncertainties (because it is a very distant cluster,
De ≈ 83 kpc). On the other hand, our stream–Sagittarius
association is completely different from that of Bonaca et al.
(2021). Bonaca et al. (2021) found five stream–Sagittarius
associations by comparing the (Jf, E) values of their stream
sample to the (Jf, E) distribution of the mergers previously
found by Naidu et al. (2021), but their stream member list does
not include Elqui.17 In fact, we find that most of their
Sagittarius stream members actually belong to the Cetus group
(see below). Moreover, given that the Elqui stream is produced
from a low-mass dwarf galaxy (Li et al. 2021a), this further
suggests that Elqui was likely the satellite dwarf galaxy of
the progenitor Sagittarius galaxy (i.e., of the Sagittarius
dSph galaxy itself).
We use the above-listed member objects of Sagittarius and
analyze their [Fe/H]. The [Fe/H] measurements of streams are
taken from Table 2 and for globular clusters we rely on the
Harris (2010) catalog. Figure 6 shows the orbital properties of
the objects as a function of their [Fe/H]. One can notice that
the member objects of Sagittarius possess varied metallicities,
and this is consistent with previous studies (e.g., Massari et al.
2019; Bellazzini et al. 2020). To quantify this
[Fe/H]
distribution, we also construct the MDF shown in Figure 7.
This MDF has a median [Fe/H] = −0.85 dex and spans a wide
range from −2.22 dex to −0.32 dex.
For the progenitor Sagittarius galaxy, we determine its halo
mass (Mhalo) and stellar mass (M*) as follows. We first
determine Mhalo using the globular-cluster-to-halo-mass rela-
tion (Hudson et al. 2014) and then convert this Mhalo to M*
using the stellar-to-halo-mass relation (Read et al. 2017). To
this end, we use the masses of the individual globular clusters
from Baumgardt et al. (2019). The combined masses of the
clusters provide Mhalo ∼ 4.5 × 10
10Me, and this further implies
M*∼ 13 × 10
7Me. These mass values are similar to those
found by previous studies (e.g., Gibbons et al. 2017; Niederste-
Ostholt et al. 2012).
Note that such a method provides a very rough estimate of
the mass values and is not very accurate. This is because (1)
both the Hudson et al. (2014) and Read et al. (2017) relations
have some scatter that we do not account for. (2) Such a
method makes a strong assumption that the present-day
observations of the globular-cluster-to-halo-mass relation and
stellar-to-halo-mass relation do not evolve with redshift.
Because our estimates are not corrected for redshift, they
provide an overestimate of the actual progenitor mass (at
merging time). (3) On the other hand, such a mass estimation
technique uses knowledge of only member globular clusters
and not member stellar streams (some of which could be
produced from globular cluster themselves). Therefore, this
may underestimate the actual progenitor mass. (4) Such a
method does not account for other objects that in principle
could belong to the merger groups but were actually not
identified by our study. For instance, the globular cluster AM 4
has also been previously linked to the Sagittarius group
(Forbes 2020), but we do not identify it here. In view of these
limitations, we note that this method provides an approximate
value on the mass of the progenitor galaxy (at the time of
merging).
4.2. Group 2: The Cetus Merger
This group is the most prograde among all the detected groups
and possesses dynamical properties in the range E∼ [−1.09,
−0.93]× 105 km2 s−2,
JR ∼ [605,
1075] km s−1 kpc,
Jf ∼
[−2700, −1360] km s−1 kpc, Jz ∼ [1835, 2820] km s
−1 kpc,
Figure 4. PDF of the group probability PGroup of all the halo objects (see
Section 3.3). The vertical line represents the PThreshold value and all the objects
with PGroup … PThreshold belong to high-significance groups. The value quoted
in the top-right corner is the median of the distribution and the corresponding
uncertainties reflect the 16th and 84th percentiles.
17 Our stream sample contains all the streams that Bonaca et al. (2021)
associated with Sagittarius, except for “Turranburra.”
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Malhan et al.
L⊥ ∼ [2905, 4635] km s
−1 kpc, eccentricity∼ [0.4, 0.6], rperi ∼ [8,
16] kpc, rapo ∼ [31, 43] kpc, and f∼ [50°, 65°]. It corresponds to
the previously known Cetus merger (Newberg et al. 2009; Yuan
et al. 2019). Inspecting Figure 5, it can be seen that Cetus is
situated in the vicinity of the Sagittarius group. However, these
two groups overall possess quite different JR and Jf components
and different orbital properties, and they can also be distinguished
on the basis of their [Fe/H] properties (the Cetus members are
overall more metal poor than the Sagittarius members).
We find that six objects belong to this group: four streams
(namely, Cetus itself, Slidr, Atlas, AliqaUma), one cluster
(namely, NGC 5824), and one satellite galaxy (Willman 1).
Among the stream member list, AliqaUma and Atlas were
recently associated with the Cetus stream by Li et al. (2021a).
On the other hand, Bonaca et al. (2021) associated most of
these streams with the Sagittarius group. Bonaca et al. (2021)
found three other streams to be associated with Cetus, but these
streams are not present in our data sample.18 Furthermore, we
could not find the streams C-20 and Palca as members of
this group, but their associations have been suggested by
previous studies (e.g., Chang et al. 2020; Li et al. 2021a; Yuan
et al. 2021). As for the globular-cluster–Cetus association,
NGC 5824 has been previously linked with the Cetus stream by
various studies on the basis that this cluster lies within the
phase-space distribution of the Cetus stream (e.g., Newberg
et al. 2009; Yuan et al. 2019; Chang et al. 2020). However,
other studies indicate that NGC 5824 is associated with the
Sagittarius group (Massari et al. 2019; Forbes 2020).
Surprisingly, some of the previous studies do not mention the
Cetus group in their analysis. For instance, Massari et al. (2019)
made a selection in Lz−L⊥ space to identify the Sagittarius
globular clusters and found that this integral-of-motion space also
contains NGC 5824, so they assigned it to the Sagittarius
group. On the other hand, Forbes (2020) identify their merger
groups by combining the orbit information of globular clusters
from Massari et al. (2019) and the ages and [Fe/H] from
Kruijssen et al. (2019). Also, they guide their analysis with the
previously known cluster−merger memberships from Massari
et al. (2019). A possible reason that these studies could not
identify Cetus is because they were analyzing only globular
clusters, and the Cetus group (likely) contains only one such
object—NGC 5824 itself. However, we are able to detect Cetus
because we have combined the globular cluster information
with that of streams and satellites, and the Cetus group clearly
contains many streams. As for the satellite−Cetus association,
this is the first time that Willman 1 has been associated with
this group (to the best of our knowledge). It could be that
Willman 1, which is an ultrafaint dwarf galaxy (Willman et al.
2005), is actually the remnant of the progenitor Cetus galaxy
(in other words, the remnant of the Cetus stream). This scenario
is also supported by the fact that the [Fe/H] of Willman
1 (≈–2.1 dex; McConnachie & Venn 2020) is very similar to
that of the Cetus stream (see Table 2).
In Figure 5, one can see two additional objects that lie close
to the Cetus group, namely the globular cluster NGC 4590/
M68 and the stream Fjörm (which is the stream produced from
NGC 4590/M68). These two objects have very similar (JR, Jf,
E) values to those of the Cetus group but possess lower Jz
values, rendering this association rather tentative. We note that
NGC 4590 was previously associated with the Helmi sub-
structure by Massari et al. (2019), Forbes (2020), and Kruijssen
et al. (2020) and with the Canis Major progenitor galaxy
(Martin et al. 2004) by Kruijssen et al. (2019). On the other
hand, Fjörm was previously linked with Sagittarius by Bonaca
et al. (2021).
Figure 5. (J, E) distribution of the groups detected in our study. The plot shows several independent groups that comprise those objects with high probabilities
(i.e., PGroup … PThreshold; see Section 3.3). The left panel shows Jf vs. JR, and the objects are colored by their Jz values. The right panel shows Jf vs. E, colored by L⊥.
The gray points are all the remaining objects with PGroup < PThreshold. The straight lines between any two objects indicate the frequency of these objects being
members of the same group—the thicker the line, the higher is this frequency. These lines are colored using the same scheme described above. Such a representation
automatically reveals several independent groups.
18 These streams are Willka Yaku, Triangulum, and Turbio.
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From Figure 6, it can be seen that all the Cetus member
objects possess similar [Fe/H] values. We find that the MDF of
this group has a median at [Fe/H]= −2.05 dex and spans a
very narrow range from −2.3 dex to −1.8 dex. Using the mass
of NGC 5824, we estimate the mass of the progenitor Cetus
galaxy as Mhalo ∼ 2× 10
10Me, and this in turn provides
Table 3
Various Groups Detected in Our Study along with Their Member Globular Clusters, Stellar Streams, and Satellite Galaxies
Merger/
No. of
Member
Member
Member
In Situ Group
Members
Globular Clusters
Stellar Streams
Satellite Galaxies
Sagittarius
8
Pal 12, Whiting 1, Terzan 7, Terzan 8,
Elqui
Sagittarius dSph
(Section 4.1)
NGC 6715/M54, Arp 2
Cetus
6–8
NGC 5824
Cetus [stream of Cetus],
Willman 1
(Section 4.2)
Slidr, Atlas, AliqaUma
tentative:
NGC 4590/M68 [stream:Fjörm]
Fjörm [stream of NGC 4590/M68]
Gaia-Sausage/Enceladus
16–18
NGC 7492, NGC 6229, NGC 6584,
C-7, Hrìd,
(Section 4.3)
NGC 5634, IC 1257, NGC 1851,
M 5 [stream of NGC 5904/M5]
NGC 2298, NGC 4147, NGC 1261,
NGC 6981/M72, NGC 1904/M79,
NGC 7089/M2 [stream:NGC 7089],
NGC 5904/M5 [stream: M5]
tentative:
NGC 6864/M75
NGC 7089 [stream of NGC 7089/M2]
Arjuna/Sequoia/I’itoi
9
NGC 6101,
GD-1, Phlegethon, Gaia-9, Kshir,
(Section 4.4)
NGC 3201 [streams: NGC 3201, Gjöll]
NGC 3201 [stream of NGC 3201],
Gjöll [stream of NGC 3201], Ylgr
LMS-1/Wukong
11
NGC 5272/M3, NGC 5053,
LMS-1 [stream of LMS-1/Wukong],
(Section 4.5)
NGC 5024/M53,
C-19, Sylgr, Phoenix, Indus,
Pal 5 [stream: Pal 5]
Jhelum, Pal 5 [stream of Pal 5]
Pontus
8–10
NGC 288, NGC 5286, NGC 7099/M30
M92 [stream of NGC 6341/M92]
(Section 4.6)
NGC 6205/M13, NGC 6779/M56,
NGC 6341/M92 [stream: M92], NGC 362
tentative:
NGC 6864/M75
NGC 7089 [stream of NGC 7089/M2]
Candidate merger
5
NGC 5466 [stream: NGC 5466],
Gaia-10,
Tucana III
(not detected, but
NGC 7492
NGC 5466 [stream of NGC 5466]
selected, Section 5)
Galactic disk
6-7
Pal 10, NGC 6838/M71, NGC 6356,
(Section 4.7)
IC 1276/Pal 7, Pal 11, NGC 104/47 Tuc
tentative:
NGC 7078/M15
Galactic Bulge
28
Terzan 2/HP 3, 1636-283/ESO452, Gran 1,
(Section 4.7)
Djorg 2/ESO 456, NGC 6453, NGC 6401,
NGC 6304, NGC 6256, NGC 6325, Pal 6,
Terzan 6/HP 5, Terzan 1/HP 2, NGC 6528,
NGC 6522, NGC 6626/M28, Terzan 9,
Terzan 5 11, NGC 6355, NGC 6638 ,
NGC 6624, NGC 6266/M62, NGC 6642,
NGC 6380/Ton1, NGC 6717/Pal9, NGC 6558,
NGC 6342, HP 1/BH 229, NGC 6637/M69
Galactic Bulge/
11
Terzan 3, NGC 6569, NGC 6366, NGC 6139,
disk/low energy
BH 261/AL 3, NGC 6171/M107, Pal 8,
(Section 4.7)
Lynga 7/BH 184, NGC 6316, FSR 1716,
NGC 6441
Note. This table is based on the associations that are visible in Figure 5. The detailed properties of these groups are described in Section 4. From left to right the
columns provide the name of the group, total number of halo objects that are members of this group, names of the member globular clusters, names of the member
streams, and names of the member satellite galaxies. In case of globular clusters, we provide in brackets the names of their streams (if any present in our sample).
Likewise, in the case of stellar streams, we provide in brackets the names of their parent globular clusters (in case the parent globular cluster of the stream is known).
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Malhan et al.
M*∼ 3× 10
7Me. Note that these mass values likely represent
a severe underestimation of the true (infall) mass of the
progenitor Cetus galaxy, because this group contains many
streams whose masses we have not accounted for (because we
do not possess that information).
4.3. Group 3: The Gaia−Sausage/Enceladus Merger
This group represents the largest of all the mergers that we
detect here. The member objects of this group possess relatively
low values in |Jf| and L⊥, implying that they lie along radial
orbits. This group possesses dynamical properties in the range
E∼ [−1.44, −1.16]× 105 km2 s−2, JR ∼ [935, 2075] km s
−1 kpc,
Jf ∼ [−715, 705] km s
−1 kpc, Jz ∼ [85, 1505] km s
−1 kpc, L⊥ ∼
[85, 1520] km s−1 kpc, eccentricity∼ [0.7, 0.9], rperi ∼ [1, 4] kpc,
rapo ∼ [16, 30] kpc, and f∼ [27°, 85°]. This group represents the
Gaia−Sausage/Enceladus merger (Belokurov et al. 2018; Helmi
et al. 2018; Myeong et al. 2018; Massari et al. 2019).
We find that 16 objects belong to this group: 3 streams
(namely, C-7, M5, Hrìd) and 13 globular clusters (namely,
NGC 7492, NGC 6229, NGC 6584, NGC 5634, NGC 5904/
M5, NGC 2298, NGC 4147, NGC 1261, NGC 6981/M72,
NGC 7089/M2, IC 1257, NGC 1904/M79, NGC 1851). There
exist two additional objects close to this group, namely the
globular cluster NGC 6864/M75 and the stream NGC 7089,
but their association is not very strong (because of their slightly
lower JR values).
These streams−Gaia−Sausage/Enceladus associations are
reported here for the first time. Unlike Bonaca et al. (2021),
we do not find the streams Ophiuchus and Fimbulthul to be
members of this group. As for the globular-cluster–Gaia
−Sausage/Enceladus associations, our list contains half of those
10 clusters that were previously associated with this group by
Myeong et al. (2018). However, more recent studies have
attributed a large number of globular clusters to the Gaia
−Sausage/Enceladus merger. For instance, Massari et al. (2019)
associated≈32 globular clusters to this merger, although some
of their associations were tentative. They found these association
by making hard cuts in the (Jf, E, L⊥) space that were previously
used by Helmi et al. (2018)
to select the Gaia-Sausage/
Enceladus stellar debris. Massari et al. (2019) further supported
their associations by arguing that the resulting globular clusters
show a tight age–metallicity relation (AMR). We show the AMR
of our Gaia−Sausage/Enceladus globular clusters in Figure 9
that (visually) appears to be tighter than Figure 4 of Massari
et al. (2019). The study of Forbes (2020), which is based on the
analysis of Massari et al. (2019), found 28 globular-cluster
−Gaia−Sausage/Enceladus associations. We find that some of
these additional globular clusters, which have recently been
linked with Gaia−Sausage/Enceladus by other studies, likely
belong to a different merger group (see Section 4.6).
The halo objects associated with the Gaia−Sausage/Enceladus
merger span a very wide range in [Fe/H] from −2.4 dex to
−1.1 dex, with the median of the MDF located at [Fe/H] = −1.6.
This large spread in MDF supports the scenario that Gaia
−Sausage/Enceladus was a massive galaxy. We estimate the
mass of the progenitor galaxy to be Mhalo ∼ 10× 10
10Me and
M*∼ 50× 10
7Me. This mass estimate is consistent with those
found by previous studies from chemical evolution models (e.g.,
Fernández-Alvar et al. 2018; Helmi et al. 2018), counts of metal-
poor and highly eccentric stars (e.g., Mackereth & Bovy 2020),
and the mass–metallicity relation (e.g., Naidu et al. 2020).
4.4. Group 4: The Arjuna/Sequoia/I’itoi Merger
This group is highly retrograde and its member objects
possess dynamical properties
in
the range E ∼ [−1.27,
−1.02] × 105 km2 s−2,
JR ∼ [20,
1190] km s−1 kpc,
Jf ∼
[1880, 2955] km s−1 kpc, Jz ∼ [230, 940] km s
−1 kpc, L⊥ ∼
[980, 2530] km s−1 kpc, eccentricity ∼ [0.1, 0.6], rperi ∼ [5,
14] kpc, rapo ∼ [15, 37] kpc, and f ∼ [25°, 46°]. We refer to
this group as the Arjuna/Sequoia/I’itoi group, because it
likely comprises objects that actually resulted from three
independent mergers: Sequoia (Myeong et al. 2019), Arjuna,
Figure 6. The orbital parameters of the halo objects as a function of their [Fe/H] values. We consider the [Fe/H] of only those objects that possess
PGroup … PThreshold, and the remaining objects are shown as gray points. The left plot shows Jf vs. E, and the right plot shows rperi vs. rapo. The LMS-1/
Wukong group has a minimum of [Fe/H] = −3.4 dex.
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Malhan et al.
and I’itoi (Naidu et al. 2020). This understanding comes from
Naidu et al. (2020), who performed a chemodynamical
analysis of stars and proposed that at this (E, Jf) location,
there exist three different (but somewhat overlapping) stellar
populations: a metal-rich population whose MDF peaks at
[Fe/H] ≈ −1.2 dex (namely Arjuna), another one whose
MDF peaks at [Fe/H] ≈ −1.6 dex (namely Sequoia), and the
most metal-poor among these whose MDF peaks at [Fe/H] ≈
−2 dex (namely I’itoi). Here, we analyze this detected group
as a single merger because our detected grouping contains
only a handful of objects and therefore it is difficult to detect
any plausible subgroups within this Arjuna/Sequoia/I’itoi
group.
We find that nine objects belong to this group: seven streams
(namely, Phlegethon, Gaia-9, NGC 3201, Gjöll, GD-1, Kshir,
and Ylgr) and two globular clusters (namely, NGC 6101 and
NGC 3201). These two globular clusters were previously
associated with Sequoia by Myeong et al. (2019), although
they associated five additional clusters with this group that we
do not identify here. To discover the Sequoia group, Myeong
et al. (2019) applied a “Friends-of-Friends” grouping algorithm
to the projected action space containing only globular clusters
(essentially, they applied their algorithm to the Gaia DR2
version of the top-left panel shown in Figure 2). With this, they
found a group of globular clusters (which they named Sequoia)
whose combined dynamical properties ranged from E = [−2.2,
−0.97]× 105 km2 s−2, JR ∼ [54, 1400] km s
−1 kpc, Jf = [250,
3210] km s−1 kpc, and Jz = [66, 800] km s
−1 kpc (they used the
same Galactic potential model as ours). This dynamical range is
larger than the range we infer for the Arjuna/Sequoia/I’itoi
group, especially in Jf and E. Moreover, it could be due to their
wide E selection that even the low-energy cluster NGC 6401
ends up in their Sequoia group; we note that NGC 6401
possesses such a low energy (Massari et al. 2019) that it likely
belongs to the Galactic bulge (see below). On the other hand,
our two Arjuna/Sequoia/I’itoi globular clusters were pre-
viously associated with both Sequoia and Gaia–Sausage/
Enceladus by Massari et al. (2019); we note that their (Jf, E)
selection is motivated by the results of Myeong et al. (2019).
But Massari et al. (2019) also found five additional member
clusters for Sequoia, and many of these are not present in the
Myeong et al. (2019) selection. The Sequoia group found by
Forbes (2020) is very similar to that of Massari et al. (2019),
likely because the selection of the former study is based on the
latter. As for the stream−Arjuna/Sequoia/I’itoi associations,
Myeong et al. (2019) analyzed the (J, E) of only GD-1 and
argued against its association. However, Bonaca et al. (2021)
favored an association of GD-1 with Arjuna/Sequoia/I’itoi,
along with those of Phlegethon, Gjöll, and Ylgr.
The MDF of this group spans a wide range from −2.24 dex
to −1.56 dex, with
the median of
[Fe/H]∼ −1.78 dex.
Interestingly, this [Fe/H] median is similar to the [Fe/H] of
the Kshir stream (Malhan et al. 2019a). Kshir is a broad stream
that moves in the Milky Way along a very similar orbit to that
of GD-1, and this observation encouraged Malhan et al.
(2019a) to propose that Kshir is likely the stellar stream
produced from the tidal stripping of the merging galaxy that
brought in GD-1. If true, this indicates that Kshir is likely the
stream of the progenitor Arjuna/Sequoia/I’itoi galaxy, perhaps
that of the Sequoia galaxy (given the similarity in their [Fe/H]).
Using only the member globular clusters of Arjuna/
Sequoia/I’itoi and not the streams, we estimate the mass of
the progenitor galaxy
to be Mhalo ∼ 1.2 × 10
10Me and
M*∼ 1.5 × 10
7Me. Note that the actual masses should be
higher than these computed masses because this group contains
several streams (as compared to globular clusters) whose
masses we could not account for. Interestingly, these mass
values are similar to those derived by Myeong et al. (2019) for
the Sequoia merger, using similar techniques, even though we
could not identify many of their globular clusters as members
of our Arjuna/Sequoia/I’itoi group.
Figure 7. The metallicity distribution function (MDF) of different groups
detected in our study. This MDF is constructed using the [Fe/H] measurements
of globular clusters and streams that belong to different groups. The LMS-1/
Wukong group has a minimum of [Fe/H] = −3.4 dex.
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Malhan et al.
4.5. Group 5: The LMS-1/Wukong Merger
This group has a slight prograde motion and its member
objects are very tightly clumped in (J, E) space. It possesses
dynamical properties in the range E∼ [−1.41, −1.19] ×
105 km2 s−2, JR ∼ [100, 605] km s
−1 kpc, Jf ∼ [−1560, − 210]
km s−1 kpc,
Jz ∼ [875,
2710] km s−1 kpc,
L⊥ ∼ [1400,
3085] km s−1 kpc, eccentricity ∼ [0.2, 0.5], rperi ∼ [5, 13] kpc,
rapo ∼ [15, 25] kpc, and f ∼ [58°, 85°]. This polar group corr-
esponds to the low-mass-stream-1 (LMS-1)/Wukong merger
(Yuan et al. 2020a; Naidu et al. 2020; Malhan et al. 2021).
We find that 11 objects belong to this group: 7 streams (LMS-
1 itself, Phoenix, Pal 5, C-19, Indus, Sylgr, and Jhelum) and 4
globular clusters (namely NGC 5272/M3, NGC 5053, Pal 5,
and NGC 5024/M53). With regard to the stream−LMS-1/
Wukong associations, Phoenix, Indus, Jhelum, and Sylgr were
tentatively associated with this merger by Bonaca et al. (2021).
The association of Indus was also favored by Malhan et al.
(2021); however,
this study had argued against Jhelum’s
association. Our result here could be different from Malhan
et al. (2021) because here we are using different data for streams;
that consequentially results
in different
(J, E) solutions.
Furthermore, because Indus and Jhelum are tidal debris
of dwarf galaxies (Li et al. 2021a), this indicates that they
were likely the satellite dwarf galaxies of the progenitor
LMS-1/Wukong galaxy (also see Malhan et al. 2021). As for
the globular cluster−LMS-1/Wukong associations, Koppelman
et al. (2019b) and Massari et al. (2019) associated NGC 5024,
NGC 5053, and NGC 5272 with the Helmi substructure (Helmi
et al. 1999). Koppelman et al. (2019b), in particular, supported
the association of four additional clusters with the Helmi
substructure, but we find many of these clusters as part of the
Gaia−Sausage/Enceladus group. As for Massari et al. (2019),
they could only associate the clusters with those merger groups
that were known at that time, but LMS-1/Wukongwas detected
after their study by Yuan et al. (2020a) and Naidu et al. (2020).
On the other hand, recent studies have shown that there indeed
exists a strong association of NGC 5024 and NGC 5053 with the
LMS-1/Wukong group (Yuan et al. 2020a; Naidu et al. 2020;
Malhan et al. 2021), based on the fact that these clusters
lie within the phase-space distribution of the LMS-1 stream
(e.g., Yuan et al. 2020a; Malhan et al. 2021). Another recent
study by Wan et al. (2020) advocates for a dynamical connection
between Phoenix, Pal 5, and NGC 5053. In summary, our
analysis supports these recent studies and makes a stronger case
that all of these objects are associated with the LMS-1/
Wukongmerger.
We find that LMS-1/Wukong is the most metal-poor merger
of the Milky Way because this group contains the three most
metal-poor streams of our galaxy, namely C-19, Sylgr, and
Phoenix (see their [Fe/H] values in Table 2). Overall, this
group has a wide MDF ranging from −3.38 dex to −1.41 dex
with the median of [Fe/H] ∼−2 dex. We note that this median
is similar to the metallicity of the LMS-1 stream (Malhan et al.
2021). Using the masses of the globular clusters, we estimate
the progenitor galaxy’s mass to be Mhalo ∼ 2.7 × 10
10Me and
M*∼ 5.5 × 10
7Me. These mass values are higher than those
reported in Malhan et al. (2021) because here we find a higher
number of globular-cluster−LMS-1/Wukong associations.
4.6. Group 6: Discovery of the Pontus Merger
We detect a new group that possesses low energy and is
slightly retrograde. Its dynamical properties are in the range
E∼ [−1.72, −1.56]× 105 km2 s−2, JR ∼ [245, 725] km s
−1 kpc,
Jf ∼ [−5, 470] km s
−1 kpc, Jz ∼ [115, 545] km s
−1 kpc, L⊥ ∼
[390, 865] km s−1 kpc, eccentricity∼ [0.5, 0.8], rperi ∼ [1, 3] kpc,
rapo ∼ [8, 13] kpc, and f∼ [54°, 89°]. We refer to this group as
Pontus.19 We find that eight objects belong in this group: one
stream (namely, M92) and seven clusters (namely, NGC 288,
NGC 5286, NGC 7099/M30, NGC 6205/M13, NGC 6341/
M92, NGC 6779/M56, and NGC 362). There exist two add-
itional objects close to this group, namely the globular cluster
NGC 6864/M75 and the stream NGC 7089, but their associa-
tion was not very strong (because of their slightly higher JR and
slightly lower Jf values).
Pontus lies close to Gaia–Sausage/Enceladus in (Jf, E)
space (although the two groups possess very different JR
values) and essentially all of Pontus’s globular clusters (which
we mentioned above) have been previously associated with
Figure 8. Comparing the orbital properties of those objects that belong to different groups. The left panel shows rperi vs. eccentricity, and the right panel shows rperi vs.
rapo. We use the same color for all those objects that belong to the same group. The gray points represent all the objects in our sample. The objects that form part of the
same group are clumped in this space (in addition to being clumped in (J, E) space; see Figure 5).
19 In Greek mythology, “Pontus” (meaning “the Sea”) is the name of one of
the first children of the deity Gaia .
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Malhan et al.
Gaia–Sausage/Enceladus(Massari et al. 2019). Given this
potential overlapping between the two groups, it is natural to
ask: Do these groups in fact represent different merging events,
or is it that our procedure has fragmented the large Gaia–
Sausage/Enceladus group into two pieces? We argue that
fragmentation cannot be the reason, otherwise the neighboring
Sagittarius and Cetus groups should also be regarded as a
single group, as these latter groups are much closer to each
other in (J, E) space compared to the former groups. Similarly,
even the neighboring LMS-1/Wukong and Gaia–Sausage/
Enceladus groups could be distinguished by our detection
procedure. To understand the nature of Pontus and Gaia–
Sausage/Enceladus groups, we use their member objects and
analyze their dynamical properties and the AMR.
First, we find that the objects belonging to these two groups
possess different dynamical properties. The average eccentri-
city of Pontus objects is smaller than that of the Gaia-Sausage/
Enceladus objects (see Figure 8), while we note that the
eccentricity range of our Gaia–Sausage/Enceladus group is
similar to that of Myeong et al. (2018). This implies that the
orbits of Gaia–Sausage/Enceladus objects are more radial than
those of the Pontus objects (this can also be discerned by
comparing their JR values). Also, the average rapo of Pontus
objects is smaller than that of the Gaia–Sausage/Enceladus
objects. Furthermore, we also compare the velocity behavior of
their member objects in spherical polar coordinates, namely
radial Vr and azimuthal Vf (see Figure 9). The motivation for
adopting
this particular coordinate system comes from
Belokurov et al. (2018), who used a similar system to
originally identify the “sausage” structure. From Figure 9, we
note
that both the Pontus and Gaia–Sausage/Enceladus
distributions are stretched along the Vr direction (implying
radial orbits), although their Vf components (on average) differ
by ≈60 km s−1. This implies, as noted above, that Pontus
objects are more retrograde than the Gaia–Sausage/Enceladus
objects. Also, Gaia–Sausage/Enceladus objects possess a
larger dispersion in Vf compared to Pontus objects.
Moreover, in Figure 9, the AMR for the globular clusters
belonging to these two groups also appear quite different,
especially the age difference of their metal-poor clusters
(−1.5 dex) is 1 Gyr. In view of this investigation, we
conclude that Pontus and Gaia–Sausage/Enceladus represent
two distinct and independent merging events: Gaia–Sausage/
Enceladus comprising slightly younger globular clusters than
those present in Pontus and Gaia–Sausage/Enceladus’s objects
possessing overall different dynamical properties compared to
Pontus’s objects.
Similarly, we argue that the Pontus group is also different than
the Thamnos substructures identified by Koppelman et al. (2019a).
Koppelman et al. (2019a) suggested that at the location (E,
Jf)∼ (–1.65× 10
5 km2 s−2,
1500 km s−1 kpc)
and∼(–1.75×
105 km2 s−2, 900 km s−1 kpc), there lie two substructures, namely
Thamnos 1 and Thamnos 2 (see their Figure 2). Motivated by their
selection, Naidu et al. (2020) selected Thamnos stars around a
small region of (E, Jf)∼ (–1.75× 10
5 km2 s−2, 500 km s−1 kpc)
(see their Figure 23). Given that these (E, Jf) locations for
Thamnos are different from those of Pontus, we argue that
Pontus is independent of Thamnos. Moreover, the metallicity of
Thamnos 2 members is different from that of Pontus members.
This we argue by inspecting Figure 2 of Koppelman et al. (2019a),
which shows that the metallicity of Thamnos 2 stars range from
[Fe/H]∼−1.4 dex to −1.1 dex, and this is different from the
metallicity range of Pontus (see below). We also note that a few of
the Pontus member clusters were previously tentatively associated
with the Canis Major progenitor galaxy (Kruijssen et al. 2019).
The MDF of Pontus spans a range from −2.3 dex to
−1.3 dex with a median of [Fe/H] = −1.7 dex. We estimate
the mass of the progenitor Pontus galaxy to be Mhalo ∼ 5×
1010Me and M*∼ 15 × 10
7Me.
4.7. The in Situ Groups 7, 8, and 9
We detect three additional groups; however, their locations
in (E, Jf) space indicates that they do not represent any merger
Figure 9. Comparing properties of those objects that belong to the groups Gaia-Sausage/Enceladus and Pontus. The left panel shows the age–metallicity relationship
of the globular clusters belonging to these groups; the [Fe/H] and age values are taken from Kruijssen et al. (2019). The right panel shows the velocity behavior of
these objects in spherical polar coordinates, namely radial Vr and azimuthal Vθ. The filled ellipses represent the 1.5σ confidence contour and the Gaussians represent
the mean and the standard deviation in the Vf components of the member objects of these groups.
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Malhan et al.
but actually belong to the in situ population of the Milky Way
—the population of the Galactic disk and the Galactic bulge.
This we infer based on the fact that the member objects of these
groups possess low E, low rapo, and high [Fe/H]—as expected
from the in situ globular cluster population (see Figure 6).
The first of these groups possess dynamical properties
in the range E ∼ [−1.77, −1.66] × 105 km2 s−2, JR ∼ [15,
135] km s−1 kpc, Jf ∼ [−1315, −960] km s
−1 kpc, Jz ∼ [5,
235] km s−1 kpc, L⊥ ∼ [115, 730] km s
−1 kpc, eccentricity
∼[0.1, 0.4], rperi ∼ [3, 6] kpc, rapo ∼ [7, 9] kpc, and f ∼ [5°,
36°]. Given these dynamical properties, especially low
eccentricity (implying circular orbits), low f value (implying
that the objects orbit close to the Galactic plane), and the values
of rperi and rapo being similar to stars in the Galactic disk, we
interpret this as the disk group. This group contains six globular
clusters (their names are provided in Table 3). There exists one
additional cluster, NGC 7078/M15, that lies close to this group
in (J, E) space but we do not identify it as a strong associate. The
member globular clusters are metal rich and the corresponding
MDF ranges from −0.8 dex to −0.1 dex with a median of
[Fe/H]∼−0.65 dex (see Figure 7). It is interesting to note that
this MDF minimum is consistent with the results of Zinn (1985),
who found [Fe/H]… −0.8 as the threshold between the disk and
halo clusters (they inferred this simply on the basis of the
bimodality of the [Fe/H] distribution of the globular clusters). All
of our globular clusters,
including
the very metal-poor
NGC 7078/M15, were previously associated with the disk by
Massari et al. (2019); although they associated a total of 26
clusters to the disk, we could not identify all of these objects.
The second group possesses the lowest energy among all the
detected groups, implying that its member objects orbit deep in
the potential of the Milky Way—close to the Galactic center.
The members of this group possess the dynamical properties
in
the
range E∼ [−2.55, −2.22]× 105 km2 s−2, JR ∼ [5,
140] km s−1 kpc, Jf ∼ [−380, 150] km s
−1 kpc, Jz ∼ [0, 275]
km s−1 kpc, L⊥ ∼ [10, 405] km s
−1 kpc, eccentricity∼ [0.1,
0.8], rperi ∼ [0, 2] kpc, rapo ∼ [1, 4] kpc, and f∼ [1°, 89°]. This
group comprises 28 globular clusters (their names are provided in
Table 3). Given these dynamical properties, especially very low
values of E, rperi, and rapo, and that the objects are spherically
distributed (as we note from the range of the f parameter), we
interpret this as the Galactic bulge group. The member objects
span a wide range in [Fe/H], ranging from −1.5 dex to −0.1 dex
with a median at [Fe/H]∼−1.0 dex. We confirm that several of
these objects have been associated with the Galactic bulge by
Massari et al. (2019), although they associated a total of 36
globular clusters to the bulge. A few of our member objects were
interpreted by Massari et al. (2019) as “unassociated objects with
low energy,” but Forbes (2020) interpreted these objects as those
accreted inside the Koala progenitor galaxy. We further note that
some of our clusters have also been interpreted as the bulge
objects by Horta et al. (2020) on the basis of their high alpha-
element abundances and high [Fe/H] values.
We detect a third group that is slightly prograde and possesses
E values between that of the bulge and disk groups (see
Figure 5). Its dynamical properties lie in the range E∼ [−2.17,
−1.92]× 105 km2 s−2, JR ∼ [10, 110] km s
−1 kpc, Jf ∼ [−630,
−250] km s−1 kpc, Jz ∼ [55, 190] km s
−1 kpc, L⊥ ∼ [215, 485]
km s−1 kpc, eccentricity∼ [0.2, 0.4], rperi ∼ [1, 3] kpc, rapo ∼ [3,
6] kpc, and f∼ [18°, 56°]. This group contains 11 globular
clusters (these are listed in Table 3). The metallicity of these
objects range from [Fe/H]∼−1.65 dex to −0.4 dex with a
median of [Fe/H]=−0.7 dex. For this group, while its dyna-
mical properties appear consistent with those of the disk (e.g.,
low eccentricity, the rapo range, and low f values), its relatively
lower [Fe/H] value appears more consistent with that of the
bulge. This makes it challenging to associate these objects with
either disk or bulge. Perhaps Massari et al. (2019) were also in a
similar conundrum that they interpreted some of these objects as
the bulge clusters, some as disk clusters, and others simply as
“low-energy objects.” Among our member objects, NGC 6441
was tentatively associated with the Kraken merger by Kruijssen
et al. (2020). We argue that our objects likely do not belong to
Kraken because our objects possess slightly negative Jf values
(on average), while Kraken objects have an average Jf ∼ 0 (that
we observed from Figure 17 in Appendix C). Also, a few of our
objects have been interpreted as either bulge or simply low-
energy clusters by Horta et al. (2020) on the basis of their
chemical compositions.
5. A Candidate Merger
All the above-mentioned groups were detected at …2σ
significance following the ENLINK procedure described in
Section 3. However, during our multiple ENLINK runs (while
we were initially experimenting with different parameters), we
noticed a particular group that comprised five objects whose
PGroup values were fluctuating close to the detection threshold.
This is likely due to the ENLINK parameter min_cluster_size
that we set to 5 (see Section 3.2), thus making it difficult for
ENLINK to detect groups containing „ 5 objects. Motivated by
the possibility that this group may represent an actual merger,
we discuss its properties below.
This group possesses a slight retrograde motion and relatively
high energy (as shown in Figure 10). The dynamical properties of
this group lie in the range E∼ [−1.2, −0.94]× 105 km2 s−2,
JR ∼ [1385,
2525] km s−1 kpc,
Jf ∼ [130,
915] km s−1 kpc,
Jz ∼ [1125, 2095] km s
−1 kpc, L⊥ ∼ [1435, 2795] km s
−1 kpc,
eccentricity∼ [0.7, 0.8], rperi ∼ [3, 7] kpc, rapo ∼ [27, 47] kpc,
and f∼ [69°, 85°]. The group comprises two globular clusters
(namely, NGC 5466 and NGC 7492),
two stellar streams
(NGC 5466 and Gaia-10), and one dwarf galaxy (Tucana III).
The f parameter indicates that the member objects have very
“polar” orbits. Particularly for Tucana III, Gaia-10, and NGC
5466, we note that their orbital planes are very similar; this
further lends credence to their possible association. The MDF of
this group ranges from [Fe/H] = −2.4 dex to −1.4 dex. These
minima and maxima are set by Tucana III (Simon et al. 2017) and
Gaia-10, respectively. NGC 5466 has
[Fe/H]∼−1.98 dex
(Lamb et al. 2015) and NGC 7492 has [Fe/H]∼−1.8 dex
(Cohen & Melendez 2005). We further compare the stellar
population of these objects in terms of their color–magnitude
distributions (CMDs), and this is shown in Figure 11. These
objects possess strikingly similar CMDs, despite their differences
in [Fe/H].20 In summary,
the similarities
in the stellar
population of these objects, together with their coincidence in
(J, E) space, indicate that these objects were perhaps born at the
same time inside the same progenitor galaxy.
Previous studies have associated NGC 5466 and NGC 7492
with
the Sequoia and Gaia–Sausage/Enceladus groups,
respectively (Massari et al. 2019; Forbes 2020). On the other
20 The reason that Tucana III’s CMD appears scattered is because we construct
the CMD using the photometry from Gaia EDR3, and Gaia has a limiting
magnitude at G ∼ 21.
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