# Evidence of a dwarf galaxy stream populating the inner Milky Way Halo

Khyati Malhan11affiliation: The Oskar Klein Centre, Department of Physics,
Stockholm University, AlbaNova, SE-10691 Stockholm, Sweden , Zhen
Yuan22affiliation: Université de Strasbourg, CNRS, Observatoire Astronomique
de Strasbourg, UMR 7550, F-67000 Strasbourg, France , Rodrigo A.
Ibata22affiliation: Université de Strasbourg, CNRS, Observatoire Astronomique
de Strasbourg, UMR 7550, F-67000 Strasbourg, France , Anke
Arentsen22affiliation: Université de Strasbourg, CNRS, Observatoire
Astronomique de Strasbourg, UMR 7550, F-67000 Strasbourg, France , Michele
Bellazzini33affiliation: INAF - Osservatorio di Astrofisica e Scienza dello
Spazio,via Gobetti 93/3, 40129 Bologna, Italy , Nicolas F.
Martin22affiliation: Université de Strasbourg, CNRS, Observatoire Astronomique
de Strasbourg, UMR 7550, F-67000 Strasbourg, France 44affiliation: Max-Planck-
Institut für Astronomie, Königstuhl 17, D-69117, Heidelberg, Germany

###### Abstract

Stellar streams produced from dwarf galaxies provide direct evidence of the
hierarchical formation of the Milky Way. Here, we present the first
comprehensive study of the “LMS-1” stellar stream, that we detect by searching
for wide streams in the Gaia EDR3 dataset using the STREAMFINDER algorithm.
This stream was recently discovered by Yuan et al. (2020). We detect LMS-1 as
a $60^{\circ}$ long stream to the north of the Galactic bulge, at a distance
of $\sim 20$ kpc from the Sun, together with additional components that
suggest that the overall stream is completely wrapped around the inner Galaxy.
Using spectroscopic measurements from LAMOST, SDSS and APOGEE, we infer that
the stream is very metal poor (${\rm\langle[Fe/H]\rangle=-2.1}$) with a
significant metallicity dispersion ($\sigma_{\rm[Fe/H]}=0.4$), and it
possesses a large radial velocity dispersion (${\rm\sigma_{v}=20\pm
4\,km\,s^{-1}}$). These estimates together imply that LMS-1 is a dwarf galaxy
stream. The orbit of LMS-1 is close to polar, with an inclination of
$75^{\circ}$ to the Galactic plane. Both the orbit and metallicity of LMS-1
are remarkably similar to the globular clusters NGC 5053, NGC 5024 and the
stellar stream “Indus”. These findings make LMS-1 an important contributor to
the stellar population of the inner Milky Way halo.

###### Subject headings:

Galaxy: halo – Galaxy: stellar content – surveys – galaxies: formation –
Galaxy: structure – Milky Way formation – Stellar streams

††slugcomment: Accepted in The Astrophysical Journal

##  1\. Introduction

The standard $\Lambda$ cold dark matter ($\Lambda$CDM) cosmological model
predicts that the Milky Way halo formed hierarchically by the accretion of
numerous progenitor galaxies (e.g., Bullock & Johnston 2005; Pillepich et al.
2018; Kruijssen et al. 2019). These progenitor galaxies initially brought in
their own stellar populations (in the form of stars and globular clusters).
Over time, the progenitor galaxies were disrupted by the tidal forces of the
Galactic potential, eventually leading to the dispersal of their stars. Today,
these accreted stellar populations can be observed as a part of our Galactic
halo. Since these accretion events are expected to have contributed
significantly to the Milky Way’s stellar halo (cf. Chiba & Beers 2000; Bell et
al. 2008; Nissen & Schuster 2010; Belokurov et al. 2018; Helmi et al. 2018;
Myeong et al. 2019; Matsuno et al. 2019; Koppelman et al. 2019; Yuan et al.
2020b; Naidu et al. 2020), it is important to identify and study these events
in order to understand the formation history of our Galaxy. For instance, the
number of dwarf galaxy streams observed in the Milky Way can effectively place
a lower limit on the number of accretions that have taken place into our
Galaxy.

Low mass satellites that are not on extremely radial orbits can give rise to
stellar streams as they disrupt. These structures trace approximately the
orbit of the progenitor in the Galactic potential. Therefore, mapping the
positions and velocities of stream stars provides a first estimate of the
orbital path along which the accretion took place and along which the
progenitor deposited its stellar contents. This orbital property of streams
also makes them extremely powerful probes of the dark matter distribution of
the Milky Way (Law & Majewski, 2010). In this regard, particularly interesting
are the ‘polar’ streams111By ‘polar streams’, we refer to those streams whose
orbital planes are inclined almost perpendicularly to the Galactic plane.
since they are very useful for gauging the flattening of the dark matter halo
(Erkal et al., 2016). These important goals of studying the dark matter and
the assembly history of our Galaxy has motivated much of the work in detecting
and analysing dwarf galaxy streams.

Most of the dwarf galaxy streams (e.g., Sagittarius, Majewski et al. 2003,
Orphan, Grillmair 2006; Belokurov et al. 2007, Cetus , Newberg et al. 2009,
Tucana III, Li et al. 2018b) appear to be dynamically-young systems. That is,
these systems were perhaps only recently accreted into the Milky Way ($\lower
2.15277pt\hbox{$\;\buildrel<\over{\sim}\;$}3-6{\rm\,Gyr}$ ago), long after our
Galaxy reached its current size and mass. Such recent accretion times are
suggested by the studies that have attempted to construct dynamical models of
these streams (e.g., see Erkal et al. 2018 for Tucana III, Erkal et al. 2019
for Orphan). For Sagittarius, this time frame is based on the starburst
episode in the disk $\sim 6{\rm\,Gyr}$ ago, that has been linked with the
first pericentric passage of this massive dwarf galaxy (Ruiz-Lara et al.,
2020; Lian et al., 2020). Furthermore, many of these streams are highly
coherent in phase-space, implying that they have not yet had enough time to
phase mix in the halo — again favouring a recent accretion scenario. However,
the hierarchical paradigm of galaxy formation suggests that several dwarf
galaxies must have accreted into the Milky Way at earlier times (e.g., $\lower
2.15277pt\hbox{$\;\buildrel>\over{\sim}\;$}8-10{\rm\,Gyr}$ ago) when our
Galaxy was smaller in size and still rapidly forming (e.g., Zhao et al. 2009).
If this scenario is true, then it raises the question: at the present day,
does the Milky Way contain signatures of dynamically-old dwarf galaxy streams,
or are they completely phase-mixed and impossible to detect?

If the Galaxy grew “inside-out”, these dynamically-old streams are likely to
be discovered in the inner regions of the halo ($\lower
2.15277pt\hbox{$\;\buildrel<\over{\sim}\;$}20-30{\rm\,kpc}$), where the
progenitor galaxy would have originally been accreted and disrupted. We expect
it to be challenging to detect these ancient dwarf galaxy fragments amidst the
other populations of the stellar halo, primarily because of their low contrast
after undergoing significant phase-mixing. However, the excellent astrometric
dataset from the ESA/Gaia mission (Gaia Collaboration et al., 2016) may
provide the key to their detection.

Here, we study the properties of the so-called “LMS-1” stream. This stream was
discovered by Yuan et al. (2020a) using RR Lyrae and blue horizontal-branch
stars in Gaia DR2 (Gaia Collaboration et al., 2018; Lindegren et al., 2018).
Yuan et al. (2020a) designated this structure as the “low-mass stream” (LMS-1
for short) to be consistent with their inference that the progenitor of this
stream was likely a low-mass dwarf galaxy; given its low mean metallicity
($\langle{\rm[Fe/H]}\rangle\sim-2$) and broad physical width. LMS-1 is the
same halo structure referred to as “Wukong” in Naidu et al. (2020), who
independently discovered it using the combination of Gaia and H3 Spectroscopic
Survey (Conroy et al., 2019). No progenitor of LMS-1 has so far been detected,
likely because it has completely disrupted. Yuan et al. (2020a) originally
discovered LMS-1 as a stream located towards the north of the Galactic bulge,
and a rough orbital analysis indicated that it possesses a very small
apocentre of $\sim 20{\rm\,kpc}$ and a pericentre of $\sim 10{\rm\,kpc}$. As
far as we are aware, no other dwarf galaxy stream, or even an intact dwarf
galaxy, is known to orbit the Milky Way at such small orbital radius222Indeed,
among the $46$ dwarf galaxies analysed by Li et al. (2021), the smallest
orbital radius is that of Tuc III with apocentre $\sim 46{\rm\,kpc}$ and a
pericentre $\sim 3{\rm\,kpc}$.. This makes LMS-1 an extremely interesting
system, and the motivation of our current study is to answer the following
questions. What is the nature of LMS-1? How are LMS-1 stars distributed in the
Milky Way? Which other objects of the Milky Way (e.g., globular clusters,
other streams) were accreted inside the LMS-1’s parent galaxy? How do the
overall properties of LMS-1 compare with other dwarf galaxy streams of the
Milky Way?

To answer these questions about the LMS-1 stream, we re-analyse this system
using the superb new astrometric data from Gaia EDR3 (Gaia Collaboration et
al., 2020). This paper is arranged as follows. Section 2 describes the data
used and briefly summarises the detection algorithm and adopted parameters.
Section 3 explains the method for constraining the LMS-1’s orbit. In Section 4
we estimate the velocity dispersion of the LMS-1 stream. Section 5 details the
procedure of selecting the RR Lyrae candidates of LMS-1. In Section 6 we
construct and study dynamical models of LMS-1. In Section 7 we search for
companion globular clusters and other streams that move on similar orbits as
that of LMS-1 and were possibly accreted into the Milky Way along with LMS-1.
Finally, we discuss our findings and conclude in Section 8.

Figure 1.— The LMS-1 stream detected in Gaia EDR3 using the STREAMFINDER
algorithm. The Galactic sky maps show stars that are identified as stream-like
with $>10\sigma$ confidence upon using a stream template of Gaussian width
$0.5{\rm\,kpc}$ and searching for streams in the distance interval
$10<d_{\odot}<30{\rm\,kpc}$ (assuming a metal-poor stellar population model
with Age=$12.5{\rm\,Gyr}$ and [Fe/H]=$−2.2$). Also, only those stars are shown
that possess proper motions in the range as highlighted by the color bars. The
top and bottom panels show the distribution of proper motion in
$\mu^{*}_{\ell}$ and $\mu_{b}$, respectively. In addition to detecting the
LMS-1 stream, some of the previously known broad stellar streams are also
detected (e.g., “Orphan”, “Galactic Anticenter stellar structure(s)” and parts
of “Sagittarius”). We also discover some of the off-stream sub-structures that
are likely associated with LMS-1 (labelled as sub-1, sub-2 and sub-3).
Finally, the agglomeration of stars at $(\ell,b)\sim(-40^{\circ},-60^{\circ})$
is probably the continuation of LMS-1 in the southern galactic sky. In the
bottom panel, the gray curve highlights the orbit of LMS-1 derived in Section
3.

##  2\. Data and LMS-1 detection

To detect LMS-1, we process the Gaia EDR3 catalogue using the STREAMFINDER
algorithm (Malhan & Ibata, 2018; Malhan et al., 2018a). The application of
STREAMFINDER on Gaia DR2 and EDR3 has been previously detailed in Malhan et
al. (2018b); Ibata et al. (2019); Malhan et al. (2019) and Ibata et al.
(2020c, hereafter I20). In brief, STREAMFINDER is effectively a friend-finding
algorithm that considers each star in a dataset in turn, and searches for
similar stars along all possible orbits of the star under consideration. To
search for streams this way, STREAMFINDER analyses the following Gaia
measurements of stars: positions ($\alpha,\delta$), parallaxes
($\overline{\mathbb{\omega}}$), proper motions
($\mu^{*}_{\alpha},\mu_{\delta}$) and photometry (in the $G,G_{\rm BP},G_{\rm
RP}$ pass-bands). For this, we first correct the Gaia magnitudes for dust
extinction using the Schlegel et al. (1998) maps, adopting the re-calibration
by Schlafly & Finkbeiner (2011), assuming the extinction ratios $A_{\rm
G}/A_{\rm V}=0.86117,A_{\rm BP}/A_{\rm V}=1.06126,A_{\rm RP}/A_{\rm
V}=0.64753$ (as listed on the web interface of the PARSEC isochrones, Bressan
et al. 2012). Henceforth, all magnitudes and colors refer to these extinction-
corrected values. We only consider stars down to a limiting magnitude of
$G_{0}=20$ and discard the fainter sources to minimise the spatial
inhomogeneities in the maps. Moreover, STREAMFINDER integrates orbits to find
streams, and for this we adopt the Galactic potential model 1 of Dehnen &
Binney (1998). Furthermore, we adopt the Sun’s Galactocentric distance from
Gravity Collaboration et al. (2018) and the Sun’s galactic velocity from Reid
et al. (2014); Schönrich et al. (2010). These parameters are required to
transform the measured Heliocentric positions and velocities of stars in the
Galactocentric coordinates to integrate orbits, and also to transform the
orbits back in the Heliocentric frame for the comparison with the
measurements.

Our overall procedure for detecting streams is identical to the one employed
in I20. However, we made changes in some of the parameters so as to
specifically find broad and metal-poor streams (as expected from dwarf
galaxies). In particular, we adopt a stream width of (Gaussian) dispersion
$0.5{\rm\,kpc}$, and allowed the algorithm to search for “friends” along
$20^{\circ}$-long orbits. Also, we ran the algorithm using a specific stellar
population template from the PARSEC library of age and metallicity (Age,
[Fe/H])=($12.5{\rm\,Gyr},-2.2$). Moreover, the algorithm was only allowed to
search for distance solutions in the Heliocentric distance range
$d_{\odot}=[10,30]{\rm\,kpc}$, and analyse only those sources with Galactic
latitudes $|b|>20^{\circ}$. We note that LMS-1 was originally detected in our
regular STREAMFINDER run on Gaia EDR3 (using an identical procedure described
in I20). However, after this, we conducted a tailored run to better map out
this stream (using the parameters described above)333For instance, the prime
reason for adopting the [Fe/H]=$-2.2$ model was that when we cross-matched the
initially found LMS-1 members with the spectroscopic surveys, we inferred a
metallicity of $\sim-2.2$ dex..

Figure 1 shows the all-sky map of Gaia EDR3 stars that exhibit stream-like
behavior with significance $>10\sigma$ (as per the STREAMFINDER analysis). The
sample shown corresponds to the selection in proper motion as
$-3.0{\rm\,mas\,yr^{-1}}<\mu^{*}_{\ell}<-0.3{\rm\,mas\,yr^{-1}}$ and
$-4.0{\rm\,mas\,yr^{-1}}<\mu_{b}<1.0{\rm\,mas\,yr^{-1}}$, as this selection
was appropriate to highlight the structures of interest. This map shows
several structures, including some of the previously known streams such as
“Orphan” (Koposov et al., 2019), “Galactic Anticenter stellar structure(s)”
(Newberg et al., 2002a; Ibata et al., 2003; Slater et al., 2014) and parts of
Sagittarius (Ramos et al., 2020; Ibata et al., 2020a). The structure at
$(\ell,b)\sim(-80^{\circ},-70^{\circ})$ is possibly the southern part of the
Cetus stream, but it is hard to conclude on its true nature at this stage.
Among these objects, the LMS-1 stream stands out as one of the most striking
structures. LMS-1 lies towards the north of the Galactic bulge between
$\ell=[-50^{\circ},50^{\circ}],b=[40^{\circ},80^{\circ}]$, and is located at a
heliocentric distance of $d_{\odot}\sim 20{\rm\,kpc}$ (as inferred from the
uncertainty-weighted average mean parallax), and at a galactocentric distance
of $\sim 15{\rm\,kpc}$. The heliocentric distance and the angular dispersion
of the stream imply that LMS-1 has a physical width of (Gaussian) dispersion
of $\sim 700{\rm\,pc}$.

Figure 2.— Comparing the color-magnitude distribution of LMS-1 with sub-1,
sub-2, sub-3 and the southern sub-structure visible in Figure 1. The data are
corrected for dust extinction in Gaia ’s $G$ vs $G_{\rm BP}-G_{\rm RP}$
photometry.

In Figure 1, we also observe some other sub-structures that are likely
associated with LMS-1. For instance, we note three newly-found off-stream
features that are located adjacent to LMS-1 on sky, labelled as sub-1, sub-2
and sub-3. Using the uncertainty-weighted average mean parallax, we infer the
distance of sub-2 and sub-3 as $d_{\odot}\sim 21{\rm\,kpc}$ and $8{\rm\,kpc}$,
respectively. For sub-3, the STREAMFINDER finds a distance solution of $\sim
16{\rm\,kpc}$. These two very different distance estimates for sub-3 may be
due an intrinsically large distance range along the line of sight, but it may
also simply reflect the difficulty of measuring distances for such low surface
brightness structures. Sub-1 contains very few stars to provide any useful
distance estimate. Color magnitude distributions (CMDs) of these features are
compared with LMS-1 in Figure 2, and they show some similarities in their
stellar population. Moreover, we also detect an agglomeration of stars in the
southern Galactic sky around $(\ell,b)\sim(-40^{\circ},-60^{\circ})$. The
uncertainty-weighted average mean parallax of these stars provides a distance
estimate of $d_{\odot}\sim 19{\rm\,kpc}$, similar to that of LMS-1. The CMD of
this southern sub-structure is compared with LMS-1 in Figure 2b (the sub-giant
branch of this candidate feature seems cut-off by the limiting magnitude at
$G_{0}=20$). The fact that many of these sub-structures have similar CMDs and
distances as that of LMS-1, and that they also possess similar on-sky
curvature as LMS-1, may be indicating that they originated from the same
parent galaxy. To examine this scenario further, we examine the kinematic
information of these sub-structures in Section 6.

The detected LMS-1 stream does not necessarily represent the entire underlying
structure. This is because just like any other stream finding algoirthm, even
STREAMFINDER does not guarantee the recovery of all the relics of the
progenitor (e.g., all the wraps of the accreted dwarf and all the associated
components). Assessing this completeness in the LMS-1 detection by
STREAMFINDER is beyond the scope of this paper. Secondly, in order to
investigate the possible bias due to the choice of the stellar population
model, we re-processed the Gaia data with STREAMFINDER using a slightly metal
rich template of [Fe/H]$=-1.5$ (rest of the parameters were kept fixed to
their original values). We infer that our final results do not vary with this
change, and conclude that the metallicity selection-bias is not very
significant.

Figure 3.— The metallicity distribution of the LMS-1 stream. The top panel
focuses around the northern region of Figure 1, where the Gaia  stars are
shown in gray. Among these stars, those possessing spectroscopic [Fe/H]
measurements are color coded as per their [Fe/H] values. The globular clusters
NGC 5053 and NGC 5024 are also shown (with “star” markers). The bottom panel
shows the 1D distribution corresponding to all of these [Fe/H] measurements.
The panel also shows the [Fe/H] values of those objects that are dynamically
associated with LMS-1 (see text).

###  2.1. Metallicity of LMS-1

To measure the metallicity ([Fe/H]) of LMS-1 stars, we made the selection of
the northern part of the structure as shown in the top panel of Figure 3 and
cross-matched these sources with public spectroscopic surveys. We found $N=41$
matches in LAMOST DR6 (Zhao et al., 2012), $N=18$ in SDSS/SEGUE DR10 (Yanny et
al., 2009) and $N=2$ in APOGEE DR14 (Majewski et al., 2017). Furthermore, we
discovered that there are a significant number of spectra for LMS-1 stars in
LAMOST DR6 that do not have stellar parameters in their catalogue.
Additionally, the DR6 parameters saturate at [Fe/H]$=-2.5$ due to limitations
in their pipeline. We therefore re-analysed all LMS-1 LAMOST spectra to gain
additional member stars and to derive more accurate metallicities. The spectra
were analysed in the spectral range of $3800-5500$ Å using the full-spectrum
fitting package ULySS (Koleva et al., 2009), with the latest version of the
MILES library model interpolator (Prugniel et al., 2011; Sharma et al., 2016).
The effective temperature, surface gravity, metallicity and radial velocity
are determined simultaneously in the fit. For giant stars, metallicities can
be derived reliably down to [Fe/H]$=-3.0$. We tested our method on the very
metal-poor LAMOST sample by Li et al. (2018a) and find metallicities
consistent with theirs (see Appendix A). We derive stellar parameters for
$N=57$ stars, of which $N=22$ do not have parameters in LAMOST DR6. Most of
the missing stars have [Fe/H]$<-2.5$. The internal fitting uncertainties on
[Fe/H] are $0.1-0.25$ dex and $5-15{\rm\,km\,s^{-1}}$ on the radial
velocities, depending on the signal-to-noise ratio. The $rms$ between our
metallicities and radial velocities and those from the LAMOST DR6 catalogue is
$0.15$ dex and $7{\rm\,km\,s^{-1}}$, respectively. Assuming both
determinations contribute equally to the $rms$, we add $rms/\sqrt{2}$ in
quadrature to our uncertainties to include an estimate of the external
uncertainties. Henceforth, all the LAMOST parameters refer to our derived
values.

As shown in Figure 3, LMS-1 is a very metal poor stream with mean
[Fe/H]$=-2.09\pm 0.05$, and a (Gaussian) intrinsic dispersion of
$\sigma_{\rm[Fe/H]}=0.42\pm 0.04$. These values were computed following our
own Metropolis–Hastings based MCMC algorithm, where the log-likelihood
function is taken to be:

$\ln\mathcal{L}=\sum_{\rm
data}\Big{[}-\ln\sigma_{\rm[Fe/H]_{obs}}-0.5\Big{(}\dfrac{\rm[Fe/H]_{0}-[Fe/H]_{\rm
d}}{\sigma_{\rm[Fe/H]_{obs}}}\Big{)}^{2}\Big{]}\,.$ (1)

Here, ${\rm[Fe/H]_{d}}$ is the measured metallicity, and the Gaussian
dispersion $\sigma_{\rm[Fe/H]_{obs}}$ is the sum in quadrature of the
intrinsic dispersion of the model together with the observational uncertainty
of each data point
($\sigma^{2}_{\rm[Fe/H]_{obs}}=\sigma^{2}_{\rm[Fe/H]}+\sigma^{2}_{\rm[Fe/H]_{d}}$).
For this inference, we impose a very conservative metallicity cut, selecting
only those stars with [Fe/H]$<-1$ so as to retain a maximal population of
LMS-1. Moreover, we note that the median of this [Fe/H] distribution is
$-1.96$ dex. Our [Fe/H] measurement of LMS-1 is consistent with the value
reported in Yuan et al. (2020a). A non-zero and large value of
$\sigma_{\rm[Fe/H]}$ implies that LMS-1 is produced from a dwarf galaxy. For
the stars in sub-1, sub-2 and sub-3, we found either zero or very few cross-
matches, and therefore it is difficult to infer whether their [Fe/H] is
similar to that of LMS-1.

Figure 3 also shows the [Fe/H] measurements of the globular clusters NGC 5053
(Boberg et al., 2015), NGC 5024 (Boberg et al., 2016) and Pal 5 (Koch & Côté,
2017), and the “Indus” stellar stream (Shipp et al., 2018; Ji et al., 2020).
Note that all of these objects fall within the [Fe/H] range of LMS-1. An
additional reason for highlighting these particular objects is that they are
also strongly linked with LMS-1 in the dynamical action-energy space (as we
show in Section 7).

Next, we investigate the alpha abundances for LMS-1 stars. The one star in
APOGEE has $[\rm{\alpha/M}]=0.38\pm 0.06$ and [Mg/Fe]$=0.31\pm 0.07$ (this
star has [Fe/H]=$-2.09\pm 0.09$). We also cross-matched the above dataset with
the Xiang et al. (2019) catalogue of LAMOST DR5. With $N=51$ positive cross-
matches we infer $\rm{[\alpha/Fe]}\sim 0.25$ (similar to the one obtained by
Naidu et al. 2020 for the Wukong structure). However, we are skeptical about
this value because (1) Xiang et al. (2019) analysis of LAMOST DR5 has not been
carefuly tested for very metal-poor stars, especially for the stars with
[Fe/H]$<-1.5$, and (2) we found that for very metal-poor stars from Li et al.
(2018a), the [Fe/H] values in the Xiang et al. (2019) catalogue are $\sim 0.4$
dex higher than the literature values (see Appendix A). Therefore, we conclude
that the alpha abundances (and even metallicities) from the Xiang et al.
(2019) catalogue should likely not be used for very metal-poor stars, such as
those in LMS-1.

It is important to note that our estimate of ${\rm\langle[Fe/H]\rangle}$ for
LMS-1, and also the median, is $\sim 0.4$ dex lower than the median of [Fe/H]
distribution reported for Wukong by Naidu et al. (2020). This is strange given
that these two objects likely represent the same structure, since they possess
very similar dynamical properties (we show this for LMS-1 below). A possible
reason for this [Fe/H] discrepancy could be systematic differences in the
metallicity scales of our analysis and that of the H3 survey (which Naidu et
al. 2020 used); we briefly discuss this in Appendix A. Another reason could be
the difference in the procedures to select the LMS-1 member stars. The
spectroscopic sample selected from STREAMFINDER is purely based on the
information of phase space and stellar population. However, the Wukong sample
is first selected from a box in the ($L_{z},E$) space, and a further cut is
made based on the break in [Fe/H] distribution function, which possibly have
more contamination by (more metal-rich) halo stars, leading to a higher
average metallicity.

Figure 4.— Orbit-fit to the LMS-1 stream. From (a) to (d) the panels compare
the best orbit-fit model to the data in position, parallax, proper motion and
line-of-sight velocity space. These panels also show the phase-space positions
and orbits of the globular clusters NGC 5024 and NGC 5053.

##  3\. Orbit of LMS-1

The orbit of a stellar stream informs about the path along which the parent
galaxy was accreted, got tidally stripped, and thereby contributed to
populating the stellar halo. To constrain the orbit of LMS-1, we fit orbits to
the stars shown in Figure 4. These sources correspond to a $10^{\circ}$ wide
selection made around the stream path in the northern galactic sky, that also
allows us to isolate LMS-1 stars of interest from the neighbouring sub-
structures. This selection results in a sample of $N=877$ stars, and all of
these stars possess the 5D astrometric measurements of positions, parallaxes
and proper motions. To obtain the line-of-sight (los) velocities $(v_{\rm
los})$ we resort to the aforementioned cross-matches with spectroscopic
surveys. We find that only $N=63$ of these stars possess $v_{\rm los}$
measurements. To deal with the missing $v_{\rm los}$ information for the
remaining stars, we set them all to $v_{\rm los}=0{\rm\,km\,s^{-1}}$ with a
$10^{4}{\rm\,km\,s^{-1}}$ Gaussian uncertainty444The results are almost
identical if instead an uncertainty of $10^{3}{\rm\,km\,s^{-1}}$ is assumed.
The choice of adopting such a large uncertainty is effectively imposing a
prior that the stars must be located in the local universe. See Malhan & Ibata
(2019).. The LMS-1 stars that possess spectroscopic $v_{\rm los}$ measurements
are listed in Table 1.

To compute orbits, we adopted the Galactic potential model of McMillan (2017).
This is an axisymmetric model comprising a bulge, disk components and an NFW
halo. To set this Galactic potential model, and to compute orbits, we make use
of the galpy module (Bovy, 2015). Moreover, to transform the orbits from the
Galactocentric frame into the Heliocentric frame (required to implement
equation 2) we adopt the same values of the Sun’s Galactocentric distance and
the Sun’s galactic velocity as described in Section 2. Finally, to obtain the
best orbit model for LMS-1, we survey the parameter space using our own
Metropolis-Hastings based MCMC algorithm, where the log-likelihood of each
data point $i$ is defined as

$\ln\mathcal{L}_{i}=-\ln((2\pi)^{5/2}\sigma_{\rm
sky}\sigma_{\overline{\omega}}\sigma_{\mu_{\alpha}}\sigma_{\mu_{\delta}}\sigma_{v_{\rm
los}})+\ln N-\ln D,$ (2)

where

$\displaystyle N$ $\displaystyle=\prod_{j=1}^{5}(1-e^{-R^{2}_{j}/2})\,,$ (3)
$\displaystyle D$ $\displaystyle=\prod_{j=1}^{5}R^{2}_{j}\,,$ $\displaystyle
R_{1}^{2}$ $\displaystyle=\dfrac{\theta^{2}_{\rm sky}}{\sigma^{2}_{\rm
sky}}\,,$ $\displaystyle R_{2}^{2}$
$\displaystyle=\dfrac{(\overline{\omega}^{\rm d}-\overline{\omega}^{\rm
o})^{2}}{\sigma^{2}_{\overline{\omega}}}\,,$ $\displaystyle R_{3}^{2}$
$\displaystyle=\dfrac{(\mu^{\rm d}_{\rm\alpha}-\mu^{\rm
o}_{\rm\alpha})^{2}}{\sigma^{2}_{\mu_{\alpha}}}\,,$ $\displaystyle R_{4}^{2}$
$\displaystyle=\dfrac{(\mu^{\rm d}_{\rm\delta}-\mu^{\rm
o}_{\rm\delta})^{2}}{\sigma^{2}_{\mu_{\delta}}}\,,$ $\displaystyle R_{5}^{2}$
$\displaystyle=\dfrac{(v^{\rm d}_{\rm los}-v^{\rm o}_{\rm
los})^{2}}{\sigma^{2}_{v_{\rm los}}}\,.$

Here, $\theta_{\rm sky}$ is the on-sky angular difference between the orbit
and the data point, $\overline{\omega}^{\rm d},\mu^{\rm
d}_{\rm\alpha},\mu^{\rm d}_{\rm\delta}$ and $v^{\rm d}_{\rm los}$ are the
measured data parallax, proper motion and los velocity, with the corresponding
orbital model values marked with “$o$”. The Gaussian dispersions $\sigma_{\rm
sky},\sigma_{\overline{\omega}},\sigma_{\mu_{\alpha}},\sigma_{\mu_{\delta}},\sigma_{v_{\rm
los}}$ are the sum in quadrature of the intrinsic dispersion of the model and
the observational uncertainty of each data point. The reason for avoiding the
standard log-likelihood function, and adopting this “conservative formulation”
of Sivia (1996), is to lower the contribution from outliers that could be
contaminating our data. The success of this modified log-likelihood equation
in fitting streams has been demonstrated in Malhan & Ibata (2019).

The best-fit orbit for LMS-1 is shown in Figure 4. We find this orbit to be
very circular (eccentricity$\sim 0.20$), slightly prograde (z-component of
angular momentum is $L_{z}\sim-700{\rm\,km\,s^{-1}}{\rm\,kpc}$) and quite
polar (with an inclination of $\sim 75^{\circ}$ to the Galactic plane). Note
that our inferred value of LMS-1’s inclination is slightly lower than the
previous estimate of $80^{\circ}$ by Yuan et al. (2020a). This new estimate of
the LMS-1’s inclination is similar to that of the Sagittarius stream ($\sim
76^{\circ}$, Yuan et al. 2020a), and significantly higher than that of the
Cetus stream ($60^{\circ}$, Chang et al. 2020). Furthermore, LMS-1’s orbit has
a small apocentre of $r_{\rm apo}\sim 16{\rm\,kpc}$, a pericentre of $r_{\rm
peri}\sim 10{\rm\,kpc}$ and a maximum height above the Galactic plane of
$z_{\rm max}\sim 16{\rm\,kpc}$. Some of these orbital parameters were
previously computed by Yuan et al. (2020a) and here we find slightly different
values. Furthermore, the best-fit orbit also indicates that the heliocentric
distance of LMS-1 is $d_{\odot}\sim 16{\rm\,kpc}$ ($\sim 20\%$ smaller from
the one we obtained above using parallaxes). The orbit of LMS-1 is also shown
in Figure 5 in the Galactocentric Cartesian system.

Figure 5.— The orbit of the LMS-1 stream in Galactocentric coordinates. (a)
The orbit is presented in the Galactic y−z plane, and is color coded by
integration time (where Time=0 represents the present day). For perspective
the present day location of LMS-1 is shown in red. (b) Same as (a) but in the
Galactic R−z plane. The arrows represent the direction of motion of LMS-1.

Figure 4 also shows the remarkable coincidence of the LMS-1’s orbit with the
positions, proper motions and velocities of the globular clusters NGC 5053 and
NGC 5024 (values for the globular cluster taken from Baumgardt et al. 2019).
This coincidence was also previously noted by Yuan et al. (2020a); Naidu et
al. (2020). Moreover, the heliocentric distance of these two clusters ($\sim
17-18{\rm\,kpc}$) is also very similar to that of LMS-1. To facilitate visual
comparison, we also show the orbits of these clusters in Figure 4. Admittedly,
the coincidence of NGC 5024 with LMS-1 is not so obvious in $v_{\rm los}$, as
one can note a large offset of $\sim 100{\rm\,km\,s^{-1}}$ between their
orbits. However, given the large velocity spread of LMS-1 that is apparent in
Figure 4, it is possible that these two systems are indeed dynamically
associated. This phase-space overlap strongly indicates that NGC 5053 and NGC
5024 were possibly accreted within the LMS-1’s parent galaxy, and now all of
these objects are orbiting in the Milky Way along very similar trajectories.
We explore this scenario further in Section 7.

Table 1Stars of LMS-1 with spectroscopic observations (details of only first $10$ stars are shown). Survey |  R.A. | Dec. | $v_{\rm los}$ | [Fe/H]
---|---|---|---|---
| [deg] | [deg] | [${\rm\,km\,s^{-1}}$] | [dex]
2 | 195.3385 | 13.22992 | 109.51 $\pm$ 8.03 | -2.32 $\pm$ 0.13
2 | 197.53424 | 17.42584 | -14.22 $\pm$ 17.59 | -2.79 $\pm$ 0.17
1 | 198.938 | 16.12697 | 59.64 $\pm$ 0.11 | -2.09 $\pm$ 0.09
2 | 200.9852 | 17.4919 | 40.47 $\pm$ 11.07 | -1.68 $\pm$ 0.13
2 | 203.35826 | 18.0979 | -35.01 $\pm$ 21.85 | -2.78 $\pm$ 0.2
2 | 204.44497 | 22.74855 | -73.71 $\pm$ 11.49 | -2.12 $\pm$ 0.16
2 | 204.48571 | 21.20221 | -1.6 $\pm$ 15.05 | -2.82 $\pm$ 0.16
2 | 204.71231 | 22.77687 | -48.22 $\pm$ 21.85 | -1.85 $\pm$ 0.27
2 | 204.93202 | 23.05065 | -51.28 $\pm$ 25.93 | -2.74 $\pm$ 0.2
2 | 205.48435 | 18.43294 | 46.62 $\pm$ 14.54 | -2.97 $\pm$ 0.15
3 | 205.72079 | 20.09672 | 71.51 $\pm$ 12.22 | -

##  4\. Velocity dispersion of LMS-1

The velocity dispersion of stellar streams informs us on the nature of their
progenitors (for instance, whether the system in question was of high or low
mass), and it also serves as an observational constraint to construct
dynamical models. Moreover, the estimate of a stream’s velocity dispersion
provides an approximate extent to which the stream stars could be spread out
in phase-space.

We estimate the velocity dispersion of LMS-1 using the best-fit orbit model
obtained in Section 3. Our method is similar to that adopted in Malhan & Ibata
(2019). We decompose the internal (3-dimensional) velocity dispersion
($\sigma_{\rm v,int}$) as the sum

$\sigma^{2}_{\rm v,int}=\sigma^{2}_{\rm v_{T},int}+\sigma^{2}_{\rm
vlos,int}\,,$ (4)

where $\sigma_{\rm v_{T},int}$ and $\sigma_{\rm vlos,int}$ are the tangential
and the line-of-sight components of the velocity dispersion, respectively.
Therefore, to compute $\sigma_{\rm v,int}$, we first independently estimate
these two components of velocity dispersion.

To measure $\sigma_{\rm v_{T},int}$, we take advantage of Gaia ’s precise
proper motion measurements and assume that $\sigma^{2}_{\rm
v_{T},int}=2\sigma^{2}_{\rm v_{\alpha},int}=2\sigma^{2}_{\rm v_{\delta},int}$.
Here, the $\alpha$ and $\delta$ correspond to components along the directions
of Right Ascension and Declination, respectively. With this, the log-
likelihood function to compute $\sigma_{\rm v_{T},int}$ is taken to be:

$\ln\mathcal{L}_{1}=\sum_{\rm data}\Big{[}-\ln(2\pi\sigma^{\rm obs}_{\rm
v_{\alpha}}\sigma^{\rm obs}_{\rm v_{\delta}}\sqrt{1-\rho^{2}})+\ln N-\ln
D\Big{]}\,,$ (5)

where

$\displaystyle N$
$\displaystyle=\prod_{j=1}^{3}(1-e^{-\frac{R^{2}_{j}}{2(1-\rho^{2})}})\,,$ (6)
$\displaystyle D$ $\displaystyle=\prod_{j=1}^{3}R^{2}_{j}\,,$ $\displaystyle
R_{1}^{2}$ $\displaystyle=\Big{(}\dfrac{v^{\rm o}_{\alpha}-v^{\rm
d}_{\alpha}}{\sigma^{\rm obs}_{\rm v_{\alpha}}}\Big{)}^{2}\,,$ $\displaystyle
R_{2}^{2}$ $\displaystyle=\Big{(}\dfrac{v^{\rm o}_{\delta}-v^{\rm
d}_{\delta}}{\sigma^{\rm obs}_{\rm v_{\delta}}}\Big{)}^{2}\,,$ $\displaystyle
R_{3}^{2}$ $\displaystyle=-2\rho\Big{(}\dfrac{v^{\rm o}_{\alpha}-v^{\rm
d}_{\alpha}}{\sigma^{\rm obs}_{\rm v_{\alpha}}}\Big{)}\Big{(}\dfrac{v^{\rm
o}_{\delta}-v^{\rm d}_{\delta}}{\sigma^{\rm obs}_{\rm v_{\delta}}}\Big{)}\,.$

Here, $v^{\rm d}_{\alpha},v^{\rm d}_{\delta}$ are the observed tangential
velocity components (calculated by multiplying the proper motion measurement
with the orbit model distance), and the corresponding orbital model values are
marked with “o”. The Gaussian dispersions $\sigma_{\rm
v_{\alpha,obs}},\sigma_{\rm v_{\delta,obs}}$ are the sum in quadrature of the
observational uncertainty of each data point together with the intrinsic
dispersion (i.e., $\sigma^{2}_{\rm obs}=\sigma^{2}_{\rm d}+\sigma^{2}_{\rm
int}$, and the quantity of interest is $\sigma_{\rm int}$). The parameter
$\rho$ takes into account the measured correlation in proper motions
$C(=$pmra_pmdec_corr in the Gaia dataset) such that

$\rho=\frac{C\sigma^{\rm d}_{\mu_{\alpha}}\sigma^{\rm
d}_{\mu_{\delta}}}{\sqrt{(\sigma^{\rm d}_{\mu_{\alpha}})^{2}+(\sigma^{\rm
int}_{\mu_{\alpha}})^{2}}\sqrt{(\sigma^{\rm
d}_{\mu_{\delta}})^{2}+(\sigma^{\rm int}_{\mu_{\delta}})^{2}}}\,.$ (7)

To estimate $\sigma_{\rm vlos,int}$, we use the spectroscopic $v_{\rm los}$
measurements, and the log-likelihood function is taken to be:

$\ln\mathcal{L}_{2}=\sum_{\rm data}\Big{[}-\ln(\sqrt{2\pi}\sigma_{\rm
v_{los,obs}})+\ln N-\ln D\Big{]}\,,$ (8)

where

$\displaystyle D$ $\displaystyle=\Big{(}\dfrac{v^{\rm o}_{\rm los}-v^{\rm
d}_{\rm los}}{\sigma_{\rm v_{los,obs}}}\Big{)}^{2}\,,$ (9) $\displaystyle N$
$\displaystyle=(1-e^{-\frac{D}{2}})\,.$

Here, $v^{\rm d}_{\rm los}$ is the observed los velocity and the corresponding
orbital model values are marked with “o”. The Gaussian dispersion $\sigma_{\rm
v_{los,obs}}$ are the sum in quadrature of the intrinsic dispersion of the
model together with the observational uncertainty of each data point
($\sigma^{2}_{\rm obs}=\sigma^{2}_{\rm int}+\sigma^{2}_{\rm d}$).

Figure 6.— Velocity dispersion of the LMS-1 stream along the tangential (left)
and line-of-sight (right) directions. The dashed lines correspond to quantiles
(0.16,0.50,0.84).

The resulting velocity dispersion distribution is shown in Figure 6. We infer
$\sigma_{\rm v_{T},int}=35.4^{+0.8}_{-0.7}{\rm\,km\,s^{-1}}$ and $\sigma_{\rm
vlos,int}=20\pm 4{\rm\,km\,s^{-1}}$. These values together imply that the
total 3-dimensional velocity dispersion of LMS-1 is $\sigma_{\rm
v,int}=40.9\pm 2.1{\rm\,km\,s^{-1}}$. Such a large velocity dispersion has not
been previously measured for any stellar stream in the Milky Way. Even the
massive Sagittarius stream has a line of sight velocity dispersion of only
$\sim 13{\rm\,km\,s^{-1}}$ (Gibbons et al., 2017), which is slightly smaller
than $\sigma_{\rm vlos,int}$ of LMS-1. It is important to note that if the
detected LMS-1 is dynamically colder than the actual underlying substructure,
then this velocity dispersion value only provides a lower limit. We discuss
the possible sources of such a large velocity dispersion of LMS-1 in Section
8.

Figure 7.— Comparing phase-space distribution of simulation particles with the
data of LMS-1, other sub-structures, globular clusters NGC 5024, NGC 5053 and
Pal 5, and the Indus stream. Panel (a) and (b) show Galactocentric Y-Z
coordinate and Galactic sky coordinates, respectively. From (c) to (f) the
panels show proper motion along Right Ascension, proper motion along
Declination, heliocentric distance and line-of-sight velocity as functions of
Right Ascension. Panels (a) and (e) also show the RR Lyrae stars found along
the LMS-1’s orbit. The simulation is also able to reproduce the southern
agglomeration of stars, at least in the position and the proper motion space
(the rectangle highlights the simulated particles that overlap with the
southern stars).

##  5\. Tracing LMS-1 in Gaia’s RR Lyrae catalogue

RR Lyrae provide a means to determine very accurate distances of stellar
structures, which can otherwise be hard to estimate even from Gaia  parallaxes
(at least for distant halo objects). Especially for streams, finding their
associated RR Lyrae can provide distance anchors to the stream in the 3D
spatial volume of the halo, and this assists in improving dynamical models.
Here we use the best-fit orbit of LMS-1 as the reference to create a catalog
of LMS-1 RR Lyrae stars.

The RR Lyrae data that we use is the same described in Ibata et al. (2020b),
that is based on the sources identified in the gaiadr2.vari_rrlyrae catalog of
Gaia DR2 (Clementini et al., 2019). To select the LMS-1 RR Lyrae candidates
from this dataset, we use the best-fit orbit model integrated from Time=$-2$
to $+2$ Gyr (with Time=0 representing the present day location of LMS-1). We
use the orbit’s positional and proper motion information, and perform sigma-
clipping to select only those RR Lyrae stars that lie within $2\sigma$ of the
model (we do not use the orbit’s distance or line-of-sight velocity
information). For this selection, we also use the inferred values of LMS-1’s
physical width and its tangential velocity dispersion. Moreover, we select
only those stars that lie more than $3{\rm\,kpc}$ above or below the Galactic
plane (to avoid the contamination from the stellar disk), range in distance
from $d_{\odot}=7-22{\rm\,kpc}$ (comparable to the range between
perigalacticon and apogalacticon of LMS-1), and for which [Fe/H]$<-1$ (if
metallicity is available). Furthermore, we also avoid all those RR Lyrae
sources that lie in the regions containing NGC 5024, NGC 5053, Pal 5, NGC
5272, IC 4499, LMC, SMC and also the Sagittarius stream.

Following these selection criteria, we obtain a sample of $N=134$ RR Lyrae
stars lying along the LMS-1’s orbit. These RR Lyraes are also shown in Figure
7, where we compare their distances with the simulation of LMS-1. Note that
some of these RR Lyrae could be field contaminants. However, it is hard to
numerically gauge the level of contamination. Therefore, in order to ascertain
the statistical significance of the RR Lyrae sample found along the LMS-1’s
orbit, we follow a pragmatic approach. To this end, we follow exactly the same
RR Lyrae selection procedure as above, except this time inverting the orbit
model in the velocity space (i.e., setting $\mathbf{v}\to\mathbf{-v}$). In
this case fewer RR Lyrae are selected, $N=91$, implying that the original
detection along LMS-1’s orbit has a statistical significance of $2.9\sigma$.

We conclude that, in spite of the spatially variable incompleteness of the
available RR Lyrae sample, a marginally significant overdensity is detected,
suggesting that LMS-1 does contain RR Lyrae. However, this conclusion should
be confirmed with the new RR Lyrae catalogs that will be available in future
Gaia DRs.

##  6\. Dynamical model of LMS-1

Dynamical modelling of a stellar stream allows us to understand the process of
tidal stripping of its progenitor, the overall formation and evolution of the
stream itself, and the extent to which the member stars could be spread out in
phase-space of the Galaxy.

We try $6$ dynamical models of LMS-1 as follows. We use the best-fit orbit
model of LMS-1 and integrate it backward in time for $T\sim 8{\rm\,Gyr}$ and
$T\sim 3{\rm\,Gyr}$, and the final values of these orbits provide the starting
phase-space positions to launch the progenitors forward in time. The reason
for trying these two values is to examine how the resulting stream models
differ if the accretion was early or recent. At each of these two starting
phase-space locations, we further try three progenitor models using Plummer
spheres of masses $M_{\rm halo}=[1\times 10^{8},10\times 10^{8},100\times
10^{8}]{\rm\,M_{\odot}}$ with the corresponding scale radii
$r_{s}=[1.0,2.0,2.5]{\rm\,kpc}$, respectively. These three mass values are
motivated by the [Fe/H] value of LMS-1 (see Section 8), and they allow us to
examine the differences in a low-mass and a high-mass stream model. Note that
there is no additional stellar component in these models, so the particles
should be interpreted as dark matter. We also account for the self-gravity of
the progenitor as stream particles are released. To initialise the progenitor
model and to run the simulation, we use the gala package (Price-Whelan, 2017).
This system is evolved in the MilkyWayPotential Galactic mass model (Price-
Whelan, 2017), which is a static, axisymmetric model of the Milky Way. This
model is similar to the one used above, and also has a very similar mass
profile (at least out to the Galactocentric distance of $50{\rm\,kpc}$).

After running these $6$ simulations, we visually compared the resulting stream
models with the observed phase-space data of LMS-1. The model $[M_{\rm
halo},T]=[1\times 10^{8}{\rm\,M_{\odot}},3{\rm\,Gyr}]$ was least probable as
it possessed very low phase-space dispersion and failed to reproduce the
measured $\sigma_{\rm v_{T}\,int}$ and $\sigma_{\rm vlos,int}$ of LMS-1. The
model $[M_{\rm halo},T]=[1\times 10^{8}{\rm\,M_{\odot}},8{\rm\,Gyr}]$
possessed higher phase-space dispersion, that was at least qualitatively
consistent with that of LMS-1. This model implies that the observed segment of
LMS-1 is comprised of multiple wrappings of this stream. However, this model
was not spread out enough in phase-space so as to be able to reproduce the
phase-space location of NGC 5024. The model $[M_{\rm halo},T]=[10\times
10^{8}{\rm\,M_{\odot}},3{\rm\,Gyr}]$ also failed to reproduce the phase-space
location of NGC 5024. As for the high mass models corresponding to $M_{\rm
halo}=100\times 10^{8}{\rm\,M_{\odot}}$, they failed to reproduce the densest
(north) part of LMS-1 with a high contrast, and the overall phase-space
structure of the simulated stream did not match very well with the observed
data. Finally, we found that the model $[M_{\rm halo},T]=[10\times
10^{8}{\rm\,M_{\odot}},8{\rm\,Gyr}]$ was the best of the set as it matched
quite well with the LMS-1 stars in position, proper motions, and line-of-sight
velocities, and was able to reproduce the phase-space locations of NGC 5024
and NGC 5053 (as shown in Figure 7). This model comprises multiple wrappings,
and it further suggests that the detected LMS-1 is the trailing arm of the
overall stream. However, this inference depends on the present-day phase-space
location of the (completely dissolved) LMS-1 progenitor, that we assumed to be
the mid-point of the LMS-1 stream.

Figure 7 also compares the phase-space measurements of the sub-structures
sub-1, sub-2, sub-3, and the southern agglomeration of stars with the best
model described above. The qualitative match between the positions and proper
motions of the southern stars with the simulations suggests that LMS-1 is
likely completely wrapped around the inner Milky Way halo. If LMS-1 and the
southern stars are truly connected, then using the model we predict for the
southern stars that their $v_{\rm los}$ should lie in the range $\sim-50$ to
$150{\rm\,km\,s^{-1}}$. The features sub-1, sub-2 and sub-3 overlap with the
simulation in position and proper motion space. The model further suggests
that sub-3 is part of the leading arm of the overall stream. However, at this
stage, it is hard to analyze further their true nature and their possible
association with LMS-1. Either these features are simply the over-densities of
stars along the LMS-1 stream (that STREAMFINDER detects as independent stream-
like features), or they are portions of LMS-1 that are wrapped by $\sim
360^{\circ}$ (or multiples thereof). This model is also able to reproduce the
distances of the RR Lyraes in the southern sky, that also implies that most of
the detected RR Lyrae lie in the leading arm of the stream.

Figure 7 also shows some additional objects that overlap with LMS-1’s
simulation in phase-space. These objects include NGC 5024, NGC 5053 and Pal 5
(data taken from Baumgardt et al. 2019) and the Indus stream (data taken from
I20 and Ji et al. 2020). Pal 5 overlaps with the leading arm of the
simulation. The phase-space measurements of Indus matches with the southern
segment in the position and the proper motion space, and also with RR Lyrae in
the distance space. The reason for particularly highlighting Pal 5 and Indus
is that we found these objects to strongly overlap with LMS-1 in the dynamical
action-energy space (see Section 7).

Table 2Action, energy, other orbital properties and metallicity of the LMS-1 stream and of the possibly associated objects. Name | ($J_{R},J_{\phi},J_{z}$) | Energy | $r_{\rm peri}$ | $r_{\rm apo}$ | $z_{\rm max}$ | eccentricity | [Fe/H]
---|---|---|---|---|---|---|---
| [${\rm\,kpc}{\rm\,km\,s^{-1}}$] | [${\rm\,km^{2}\,s^{-2}}$] | [${\rm\,kpc}$] | [${\rm\,kpc}$] | [${\rm\,kpc}$] |  | [dex]
LMS-1 (simulation) | $(107^{+153}_{-66},-635^{+273}_{-390},1907^{+1433}_{-852})$ | $-130836^{+19187}_{-27298}$ | $9.2^{+6.1}_{-3.3}$ | $16.5^{+8.2}_{-6.7}$ | $15.8^{+8.3}_{-6.5}$ | $0.24^{+0.11}_{-0.09}$ | $-2.1\pm 0.4$
NGC 5024 | $(473^{+10}_{-10},-688^{+10}_{-9},2048^{+23}_{-21})$ | $-124015^{+280}_{-299}$ | $8.4^{+0.1}_{-0.1}$ | $21.9^{+0.1}_{-0.1}$ | $21.1^{+0.1}_{-0.1}$ | $0.44^{+0.01}_{-0.01}$ | $-2.07\pm 0.07$
NGC 5053 | $(192^{+9}_{-9},-625^{+9}_{-9},2103^{+22}_{-22})$ | $-130167^{+261}_{-264}$ | $9.5^{+0.2}_{-0.2}$ | $17.6^{+0.0}_{-0.0}$ | $17.1^{+0.0}_{-0.0}$ | $0.3^{+0.01}_{-0.01}$ | $-2.45\pm 0.04$
Pal 5 | $(193^{+17}_{-17},-1052^{+24}_{-26},1634^{+37}_{-33})$ | $-130902^{+590}_{-537}$ | $9.3^{+0.3}_{-0.3}$ | $17.4^{+0.0}_{-0.0}$ | $15.9^{+0.0}_{-0.0}$ | $0.3^{+0.02}_{-0.01}$ | $-1.56\pm 0.1$
Indus | $(58^{+58}_{-36},-996^{+144}_{-123},2095^{+171}_{-178})$ | $-127649^{+5352}_{-5778}$ | $12.1^{+0.5}_{-0.6}$ | $16.7^{+2.8}_{-2.6}$ | $15.8^{+2.6}_{-2.3}$ | $0.16^{+0.05}_{-0.06}$ | $-2$
Figure 8.— Comparing the action ($\mathbf{J}$) and energy ($E$) of LMS-1 with
the globular clusters and streams of the Milky Way. (a) The projected action-
space map. The horizontal axis is $J_{\phi}/J_{\rm total}$ and the vertical
axis is $(J_{z}-J_{R})/J_{\rm total}$, where $J_{\rm
total}=J_{R}+J_{z}+|J_{\phi}|$. The blue points represent the LMS-1
simulation, the golden ‘star’ markers represent the globular clusters that
have similar actions and energy as that of LMS-1, the gray ‘star’ markers
represent globular clusters of the Milky Way, and the pink ‘square’ marker
represents the Indus stream that is also strongly co-incident with LMS-1 in
action-energy space. The unfilled ‘square’ and ‘star’ markers correspond to
the “Jhelum” stream and ESO280-SC06 cluster, respectively (see text). The
panel also highlights the approximate locations of the Sagittarius stream and
the Cetus stream. (b) The z-component of angular momentum ($J_{\phi}$) vs. the
orbital energy. The gap in the LMS-1 simulation points marks the location of
the progenitor, and the two tidal arms are located on opposite sides of the
gap. (c) $J_{\phi}$ vs. $J_{z}$. (d) $J_{R}$ vs. $J_{\phi}$.

##  7\. Objects associated with LMS-1 in action-energy space

In Sections 2 and 3 we showed that both the [Fe/H] and the orbital properties
of globular clusters NGC 5053 and NGC 5024 are very similar to that of the
LMS-1 stream. This already provides strong evidence that these objects were
accreted inside the parent LMS-1 galaxy. These associations also motivated us
to examine whether there exist other Galactic globular clusters and streams
that might also be associated with LMS-1.

To search for all the objects that possibly accreted within LMS-1’s parent
galaxy, a strategy is to find those objects that cluster close to LMS-1 in
energy-action ($E,\mathbf{J}$) space. This is because orbital parameters $E$
and $\mathbf{J}$ are preserved for adiabatic systems. This implies that
objects that accrete inside the same parent galaxy, that naturally have very
similar orbits, should remain tightly clustered in ($E,\mathbf{J}$); even long
after they have been tidally removed from the progenitor. Conceptually,
actions represent the amplitude of the orbit along different directions in a
given coordinate system. We analyse the actions in cylindrical coordinates,
i.e., in the $\mathbf{J}\equiv(J_{R},J_{\phi},J_{z})$ system, where $J_{\phi}$
corresponds to the z-component of angular momentum.

Figure 8 shows the derived $E$ and $\mathbf{J}$ values for the LMS-1 stream,
the Indus stream and all the globular clusters of the Milky Way. For LMS-1,
these values are computed using the phase-space positions of the simulated
particles that gives an ellipsoidal distribution for LMS-1 in ($E,\mathbf{J}$)
space. For the globular clusters, we compute these values using their phase-
space measurements from Baumgardt et al. (2019). Moreover, for every globular
cluster, we sample $N=1000$ orbits using the observational uncertainties.
Here, the ($E,\mathbf{J}$) value corresponds to their mean values. To compute
these values for Indus, we fit an orbit to this stream following a similar
procedure as described in Section 3. The positions, parallaxes and proper
motions of the Indus stars, along with the observational uncertainties, are
taken from I20 and the line-of-sight velocities are taken from Ji et al.
(2020). Here, the ($E,\mathbf{J}$) value corresponds to the best fit orbit
model of Indus. We tried a few other prograde streams as well (e.g., Sylgr,
Jhelum) but found that they do not strongly overlap with LMS-1 in this
dynamical space. As an example we show Jhelum in Figure 8 that lies beyond the
LMS-1 distribution. Note that since Jhelum is unrelated to LMS-1, it
effectively implies that it is also unrelated to Indus. This result is
different from a recent analysis that indicates a common origin of the Indus
and Jhelum streams (Bonaca et al., 2021). This conclusion is also different
from the common assumption in the literature that Indus and Jhelum have very
similar orbital properties, and thus represent different orbital wraps of the
very same stream (e.g., see Shipp et al. 2018; Bonaca et al. 2019; although
their assumption is based on analyses that included either zero or only
partial velocity information on these streams).

As is evident in Figure 8, NGC 5024, NGC 5053, Pal 5 and Indus are remarkably
co-incident with LMS-1 in the ($E,\mathbf{J}$) space (also see Table 2). From
this strong dynamical clustering, it is tempting to instantly conclude that
all of these objects were accreted inside the LMS-1’s progenitor galaxy.
However, despite Pal 5’s striking similarity with LMS-1 in ($E,\mathbf{J}$),
their association is not clear. This is because 1) Pal 5 has a slightly higher
metallicity than LMS-1 (see Figure 3), and 2) the orbital pole of Pal 5 is
almost opposite to that of LMS-1, $\theta\sim 143^{\circ}$ apart. This
difference in their orbital poles is evaluated as
$\rm{\theta=cos^{-1}(\hat{L_{1}}.\hat{L_{2}})}$; where
$\rm{\hat{L_{1}},\hat{L_{2}}}$ refers to the present day unit vector angular
momenta of LMS-1 and Pal 5, respectively. In other words, at the present day,
Pal 5 orbits in the opposite direction in the Y-Z plane compared to the orbit
of LMS-1 (i.e., the x-component of angular momentum has an opposite sign).
These differences render the association of Pal 5 with LMS-1 a bit doubtful,
albeit worthy of further investigation. Moreover, unlike Naidu et al. (2020),
we find that the globular cluster ESO 280-SC06 lies beyond the dynamical
region of LMS-1 (as shown in Figure 8), and is not associated with this dwarf
galaxy stream. Also, the orbital pole of ESO 280-SC06 is $\theta\sim
84^{\circ}$ apart from the orbital pole of LMS-1. In conclusion, the
similarity of NGC 5024, NGC 5053 and Indus with LMS-1 in ($E,\mathbf{J}$)
space, and also in [Fe/H], strongly indicates that these objects were accreted
inside the LMS-1’s parent galaxy.

The above result is based on the simulation where the progenitor accretes
along the best-fit orbit of LMS-1 (obtained in Section 3). Instead, if we
assume NGC 5053 (or NGC 5024) as the nuclear star cluster, and run the LMS-1
simulation using its orbit, we obtain a slightly different result.
Particularly, in this new scenario, Pal 5 does not strongly overlap with LMS-1
in ($E,\mathbf{J}$) space. However, another globular cluster can now be
associated with LMS-1, namely NGC 6715 (a.k.a. M 54, the nuclear star cluster
of the Sagittarius dwarf). This examination makes us confident that atleast
NGC 5053, NGC 5024 and Indus are associated with LMS-1. However, the fact that
we find M 54 to overlap with LMS-1 in ($E,\mathbf{J}$) space indicates that
the association of different objects purely based on the dynamical parameters
can be misleading, and therefore one should be extremely cautious during such
analyses. This is the reason that along with comparing the dynamical
properties of LMS-1 and its associated objects, we also compare their [Fe/H]
(see Section 2.1) and stellar population (see Section 8).

##  8\. Discussion and Conclusion

We have presented the first comprehensive study of the LMS-1 stellar stream,
based on the astrometric dataset of Gaia  EDR3 and spectroscopic datasets of
LAMOST, SDSS/SEGUE and APOGEE. This stream was detected by the STREAMFINDER
algorithm during our hunt for wide streams in the Gaia  EDR3 dataset. We found
that LMS-1 has a broad physical width ($\sim 700{\rm\,pc}$), a very low
metallicity ($\rm{\langle[Fe/H]\rangle}\sim-2.1$) with significant metallicity
dispersion ($\sigma_{\rm[Fe/H]}\sim 0.4$), and these inferences together imply
that this stream was produced from a dwarf galaxy. However, we do note that no
progenitor of LMS-1 has so far been detected, likely because it has been
completely disrupted. Below, we briefly discuss some of the properties of
LMS-1 that make it a very interesting dwarf galaxy stream.

LMS-1’s orbit is very circular (eccentricity$\sim 0.2$) and possesses a
strikingly small apocentre ($\sim 16{\rm\,kpc}$). These orbital properties
make LMS-1 a very intriguing structure because dwarf galaxy streams, and even
‘intact’ dwarf galaxies, generally lie on highly eccentric orbits (since
accretions occur radially to the host galaxy) and they also possess quite
large apocentres. For instance, the Orphan stream has an eccentricity of $\sim
0.7$ (Newberg et al., 2010). Also, most of the dwarf galaxy streams have
apocentres $\lower 2.15277pt\hbox{$\;\buildrel>\over{\sim}\;$}35{\rm\,kpc}$
(this lower limit of the apogalacticon value is set by the Cetus stream, Yam
et al. 2013). One scenario that explains these surprising orbital properties
of LMS-1 is if its parent galaxy was very massive and was accreted at a
sufficiently early time to have experienced dynamical friction that eventually
circularised its orbit (Chandrasekhar, 1943). LMS-1’s orbit around the Milky
Way is also quite polar, with an inclination of $\sim 75^{\circ}$ to the
Galactic plane (similar to that of the Sagittarius stream) which may make it a
powerful probe of the flattening of the dark matter halo in the inner regions
of our Galaxy.

LMS-1 can be observed in Figure 1 as a simple $60^{\circ}$-long broad stream
located towards the north of the Galactic bulge, at a distance of $\sim
20{\rm\,kpc}$ from the Sun. However, this stream is probably a much more
complex system, completely wrapping around the inner Milky Way halo, as
suggested by two main evidences: (1) the presence of multiple off-stream sub-
structures adjacent to LMS-1 (namely sub-1, sub-2 and sub-3) and the
agglomeration of stars in the southern galactic sky, and (2) the very large
velocity dispersion of LMS-1, as measured along both the line-of-sight
direction ($\sigma_{\rm v_{los}}\sim 20{\rm\,km\,s^{-1}}$) and the tangential
direction ($\sigma_{\rm v_{T}}\sim 35{\rm\,km\,s^{-1}}$). Also, the CMDs of
these sub-structures are plausibly similar to that of LMS-1 (see Figure 2),
indicating similarity in their stellar population (although we note that it
would be useful to obtain deeper CMDs of the sub-structures to better compare
their populations). Furthermore, the positions and proper motions of these
sub-structures were (qualitatively) reproducible in our N-body model (see
Figure 7). The N-body model also predicts that if the southern component is a
part of LMS-1, then its line-of-sight velocity should range between $v_{\rm
los}\sim-50$ to $150{\rm\,km\,s^{-1}}$. Note that we lacked the measurements
of [Fe/H] and line-of-sight velocities of these sub-structures that would have
been very useful to elucidate their origin and possible link with LMS-1.

Figure 9.— Comparing the color-magnitude distribution of LMS-1 with that of
NGC 5024, NGC 5053 and Indus. All panels show photometry corrected only for
extinction. The stellar population model (blue line) has been shifted to
account for the heliocentric distance of LMS-1.

Therefore, in light of these limited observations, we consider three scenarios
and deem that their combined effect could explain both the presence of the
sub-structures (proximal to LMS-1’s orbit) and LMS-1’s large velocity
dispersion. (A) LMS-1 is highly phase-mixed: Given that LMS-1 orbits the inner
regions of the Milky Way halo, it is possible that this system accreted early
($\lower 2.15277pt\hbox{$\;\buildrel>\over{\sim}\;$}8-10{\rm\,Gyr}$ ago), was
severely damaged by the large tidal forces of the inner Galactic potential,
and the eventual phase-mixing increased the velocity dispersion of the stream.
(B) LMS-1 and the observed sub-structures are orbital wraps of the same
stream: A dwarf galaxy on a similar orbit as that of LMS-1 would completely
wrap around the inner halo in $\sim 0.5{\rm\,Gyr}$ (as suggested by our
controlled simulations). Therefore, it is possible that the observed segment
of LMS-1 is actually a projection of multiple wrappings of the stream along
the line-of-sight direction, and we have ended up measuring their cumulative
velocity dispersion. The same scenario also suggests that the observed sub-
structures correspond to highly-dense segments of LMS-1 that are wrapped by
$\sim 360^{\circ}$ (or multiples thereof). (C) Precession of LMS-1: The
orbital planes continuously evolve in flattened potentials (Erkal et al.,
2016). If the Milky Way’s dark matter halo is flattened in the inner regions
(which most likely is the case due to the presence of the Galactic disk), then
the angular momentum vector of LMS-1 has been continuously evolving during its
lifetime, and this precession effect could be the source of its large velocity
dispersion. Moreover, due to precession, streams lying along nearly polar
orbits are expected to quickly spread in phase-space (Erkal et al., 2016).
This effect may also explain the estimated broad physical width and large
velocity dispersion of LMS-1.

Future observational and modeling studies will be required to examine the
association of these sub-structures with LMS-1, and to test whether LMS-1
completely wraps around the inner Milky Way halo. For this, the prime
requirement will be to obtain measurements of [Fe/H] and line-of-sight
velocities of these sub-structures. A similarity in [Fe/H] (and element
abundances) between these sub-structures and LMS-1 would strengthen the case
for their association. Velocity measurements will also be useful to infer
whether these sub-structures can be reproduced in detailed N-body simulations,
alongside LMS-1 itself. For this, it will be important to model both the
parent LMS-1 galaxy and the Galactic potential more realistically to properly
consider both the precession effect and the dynamical friction effect in the
inner regions of the Milky Way.

We also found that in action-energy ($E,\mathbf{J}$), and other orbital
properties, LMS-1 is remarkably similar to the globular clusters NGC 5024, NGC
5053, Pal 5 and the stellar stream “Indus”. The dynamical association of these
objects is shown in Figure 8 (also see Table 2). The co-incidence of LMS-1’s
orbit with that of NGC 5024 and NGC 5053 was also proposed in Yuan et al.
(2019); Naidu et al. (2020), and here we have confirmed this through proper
orbital analysis. Among these objects, NGC 5024, NGC 5053 and Indus also have
very similar orbital poles (at the present day), as well as [Fe/H], as that of
LMS-1. On the other hand, Pal 5’s orbital pole is $\sim 140^{\circ}$ different
from LMS-1, and it is also slightly more metal rich than LMS-1 (see Figure 3),
casting doubt on an association. Furthermore, the CMDs of NGC 5053, NGC 5024
and Indus match well with that of LMS-1 (see Figure 9), implying similarity
also in their stellar populations. In summary, the remarkable similarity of
LMS-1, NGC 5053, NGC 5024 and Indus in their dynamics, [Fe/H] and stellar
population indicates that all of these objects were accreted inside the same
parent galaxy.

Given that Indus is produced from a dwarf galaxy555Indus has recently been
interpreted as a low-mass dwarf galaxy stream, and not a globular cluster
stream, based on chemical signatures of its stars (Ji et al., 2020)., this
further implies that Indus’s progenitor was a satellite dwarf galaxy of the
parent LMS-1 dwarf. Another possibility is that Indus is not an independent
object, but simply a subpart of the southern wrap of LMS-1 (see Figure 7a).
However, this scenario holds less merit because Indus is a narrow and highly-
coherent stream that is clearly distinguishable from the broad and diffuse
southern wrap of LMS-1 (see Figure 7f). This indicates that the progenitor of
Indus must have been an independent object that was smaller in size, and much
denser, than the parent LMS-1 dwarf. This scenario is also supported by
cosmological simulations that have shown that smaller galaxies formed at
higher redshifts (like Indus), that eventually ended up being satellites of
larger galaxies (like LMS-1), possess higher densities (Bullock et al., 2001).

Figure 10.— Comparing the spatial distributions of stellar stream models of
LMS-1, Cetus and Sagittarius in the Galactocentric coordinate system. Figure
11.— The age-metallicity distribution of the Milky Way globular clusters.
Typical uncertainties on the parameters are mentioned on the plot. Globular
clusters associated with LMS-1, Cetus and Sagittarius are shown for
comparison.

We also found that the orbit of NGC 5053 is strikingly similar to that of
LMS-1 (see Figure 4). At some level, this indicates that NGC 5053 probably
originated from the very central regions of LMS-1’s parent galaxy; reminiscent
of the M 54 star cluster that currently resides inside the very nucleus of the
Sagittarius dwarf galaxy (e.g., Bellazzini et al. 2008). This particular
inference is different from that of Yuan et al. (2020a) who otherwise proposed
that it is NGC 5024 that originated from the nucleus of LMS-1’s progenitor
(based only on the fact that NGC 5024 is more massive than NGC 5053). However,
we note that neither NGC 5024 nor NGC 5053 make good candidates for nuclear
star clusters because neither of them are Type II clusters666Type II clusters
are those that exhibit complex/multiple stellar population, and where first
and second generations of stars are distinguishable. Examples of Type II
clusters include M 54, $\omega$-Centauri, that have been confirmed to have
formed in the central regions of their parent dwarfs (e.g., Pfeffer et al.
2021). On the other hand, Type I clusters correspond to those that exhibit
simpler stellar population, and where first and second generations of stars
are not easily distinguishable (likely because they host only one generation
of stars). (Milone et al., 2017) and they also do not show any [Fe/H] spread
(Boberg et al., 2015, 2016). Nonetheless, given that the difference in the
orbital energies of NGC 5053 and LMS-1 is smaller than that between NGC 5024
and LMS-1 suggests that NGC 5053 must have formed closer to the LMS-1 dwarf’s
centre.

We now predict LMS-1 parent galaxy’s mass given that LMS-1’s mean metallicity
is ${\rm\langle[Fe/H]\rangle}\sim-2.1$ and it brought in no less than two
globular clusters. The [Fe/H] measurement of LMS-1 implies that the stellar
mass of its parent dwarf galaxy was $M_{*}\sim 10^{5}{\rm\,M_{\odot}}$ (from
the present-day Stellar Mass-Stellar Metallicity Relation of dwarf galaxies,
Kirby et al. 2013), and this further indicates that the dark matter halo mass
of the progenitor was $M_{\rm halo}\sim 10^{9}{\rm\,M_{\odot}}$ (from the
stellar-to-halo-mass relation from Read et al. 2017). These estimates suggest
that the parent LMS-1 dwarf was probably similar to the Draco dwarf galaxy
that has ${\rm\langle[Fe/H]\rangle}=-1.93$ (Kirby et al., 2011) and $M_{*}\sim
3\times 10^{5}{\rm\,M_{\odot}}$ (McConnachie, 2012). However, this estimate
implies that the stellar mass of the parent LMS-1 galaxy was lower than the
combined mass of the two clusters: NGC 5024 ($M\sim 5\times
10^{5}{\rm\,M_{\odot}}$) and NGC 5053 ($M\sim 0.5\times
10^{5}{\rm\,M_{\odot}}$). This in stark contrast with the observations of the
present day dwarfs, where the ratio between the total mass of their member
clusters and the stellar mass of the host dwarf is measured to be much smaller
than unity. For instance, in Fornax dwarf, this mass fraction is $\sim 0.2$ at
[Fe/H]$\lower 2.15277pt\hbox{$\;\buildrel<\over{\sim}\;$}-2.1$ (de Boer &
Fraser, 2016). We argue that $M_{*}$-[Fe/H] relation can only provide a lower
limit on the $M_{*}$ value of LMS-1-like dwarfs that accreted very early in
time, since this relation possesses a redshift dependence (Torrey et al.,
2019) and, in general, also possesses a significant scatter.

An alternate way to estimate $M_{*}$ is to first constrain the value of
$M_{\rm halo}$. $M_{\rm halo}$ of a parent galaxy can be constrained from the
total mass of the member globular clusters (Hudson et al., 2014). Adopting the
masses of NGC 5053, NGC 5024 from Baumgardt et al. (2019), we obtain $M_{\rm
halo}\sim 10^{9-10}{\rm\,M_{\odot}}$. This halo mass implies a stellar mass of
$M_{*}\sim 10^{6-7}{\rm\,M_{\odot}}$. Note that in this case, the stellar mass
is larger than the combined masses of globular clusters. Overall, these
properties suggest that the parent LMS-1 dwarf was similar to the Fornax dwarf
galaxy (that hosts a population of at least $5$ globular clusters and has
$M_{*}\sim 2\times 10^{7}{\rm\,M_{\odot}}$, McConnachie 2012). These mass
estimates of LMS-1’s parent galaxy justify the assumptions we made for our
N-body models.

To put LMS-1 into some perspective, we now briefly examine how this stream
compares with two other dwarf galaxy streams of the Milky Way: the Sagittarius
stream and the Cetus stream. The prime reason for comparing these particular
streams is that all of them lie along prograde orbits, and possess quite polar
structures (inclined at angles $\lower
2.15277pt\hbox{$\;\buildrel>\over{\sim}\;$}60^{\circ}$ to the Galactic plane).
The dynamical models of these streams are shown in Figure 10, where the
Sagittarius model is adopted from Law & Majewski (2010), the Cetus model is
taken from Chang et al. (2020) and the LMS-1 model corresponds to the one that
we found most suitable in Section 6. Among these streams, the colossal
Sagittarius spans a large range in Galactocentric distance from $15{\rm\,kpc}$
to $100{\rm\,kpc}$ (Belokurov et al., 2013), and is a major contributor to the
stellar populations of the outer Galactic halo (Newberg et al., 2002b;
Belokurov et al., 2006). This stream has also contributed $6-8$ globular
clusters to the Milky Way (Massari et al., 2019; Bellazzini et al., 2020),
with M 54 being the nuclear star cluster of the parent Sagittarius galaxy.
Moreover, this massive stream has a large spread in metallicity from
[Fe/H]$\sim-0.5$ to $-2.5$ (Hayes et al., 2020). Recent dynamical models of
Sagittarius indicate that it is a dynamically young system that recently
accreted into our Galaxy, $\sim 6{\rm\,Gyr}$ ago (Ruiz-Lara et al., 2020; Lian
et al., 2020). The next stream that we consider is Cetus that orbits
intermediate Galactocentric distances from $24{\rm\,kpc}$ and $36{\rm\,kpc}$
on a nearly circular trajectory (Yam et al., 2013). Furthermore, the
metallicity of Cetus is [Fe/H]$\sim-2$, implying that its progenitor was
probably a low-mass dwarf galaxy (similar to that of LMS-1). Cetus has been
dynamically linked with the globular cluster NGC 5824, that was probably the
nuclear star cluster of its parent dwarf galaxy (Yuan et al., 2019).

Figure 11 shows age-metallicity distribution of $96$ globular clusters of the
Milky Way, taken from compilation by Kruijssen et al. (2019). This plot shows
two well-known branches: (1) a branch corresponding to nearly uniform old age
group and higher metallicities, and (2) a branch corresponding to younger ages
and lower metallicities (cf. Forbes & Bridges 2010). The former branch is
associated with in-situ GCs, and the latter is assumed to have emerged via
accretion of clusters from ex-situ dwarf galaxies. We particularly highlight
the globular clusters associated with Sagittarius, Cetus and LMS-1. The
location of NGC 5024, NGC 5053 and Pal 5 on this map provides supporting
evidence of their accreted origin.

Our analysis suggests that LMS-1 with its very small apocenter is a very
interesting fossil remnant of the early formation of our Galaxy. Streams such
as LMS-1 also provide a novel opportunity to study the formation and evolution
of globular clusters in ancient dwarf galaxies. Future detection and analysis
of other dwarf galaxy streams will allow us to build a reliable understanding
of the Milky Way’s assembly history, that could ultimately be compared with
the predictions from the cosmological models of galaxy formation.

## ACKNOWLEDGEMENTS

We thank the referee for helpful comments and suggestions. It is a pleasure to
thank Raphaël Errani for insightful conversations. KM acknowledges support
from the $\rm{Vetenskapsr\mathring{a}de}$t (Swedish Research Council) through
contract No. 638-2013-8993 and the Oskar Klein Centre for Cosmoparticle
Physics. RI, NM and ZY acknowledge funding from the Agence Nationale de la
Recherche (ANR project ANR-18-CE31-0006, ANR-18-CE31-0017 and
ANR-19-CE31-0017), from CNRS/INSU through the Programme National Galaxies et
Cosmologie. RI, NM and AA acknowledge funding from the European Research
Council (ERC) under the European Unions Horizon 2020 research and innovation
programme (grant agreement No. 834148). MB acknowledges the financial support
to this research by INAF, through the Mainstream Grant 1.05.01.86.22 assigned
to the project “Chemo-dynamics of globular clusters: the Gaia revolution”
(P.I. E. Pancino).

This work has made use of data from the European Space Agency (ESA) mission
Gaia (https://www.cosmos.esa.int/gaia), processed by the Gaia Data Processing
and Analysis Consortium (DPAC,
https://www.cosmos.esa.int/web/gaia/dpac/consortium). Funding for the DPAC has
been provided by national institutions, in particular the institutions
participating in the Gaia Multilateral Agreement.

Funding for SDSS-III has been provided by the Alfred P. Sloan Foundation, the
Participating Institutions, the National Science Foundation, and the U.S.
Department of Energy Office of Science. The SDSS-III web site is
http://www.sdss3.org/.

SDSS-III is managed by the Astrophysical Research Consortium for the
Participating Institutions of the SDSS-III Collaboration including the
University of Arizona, the Brazilian Participation Group, Brookhaven National
Laboratory, Carnegie Mellon University, University of Florida, the French
Participation Group, the German Participation Group, Harvard University, the
Instituto de Astrofisica de Canarias, the Michigan State/Notre Dame/JINA
Participation Group, Johns Hopkins University, Lawrence Berkeley National
Laboratory, Max Planck Institute for Astrophysics, Max Planck Institute for
Extraterrestrial Physics, New Mexico State University, New York University,
Ohio State University, Pennsylvania State University, University of
Portsmouth, Princeton University, the Spanish Participation Group, University
of Tokyo, University of Utah, Vanderbilt University, University of Virginia,
University of Washington, and Yale University.

Guoshoujing Telescope (the Large Sky Area Multi-Object Fiber Spectroscopic
Telescope LAMOST) is a National Major Scientific Project built by the Chinese
Academy of Sciences. Funding for the project has been provided by the National
Development and Reform Commission. LAMOST is operated and managed by the
National Astronomical Observatories, Chinese Academy of Sciences.

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##  Appendix A Comparing [Fe/H] measurements for very metal-poor stars from
different datasets

Figure 12.— Comparing [Fe/H] from our method (ULySS) with [Fe/H] from
different literature sources for a sample of very metal-poor LAMOST giants
from Li et al. (2018a). The literature values come from Li et al. (2018a),
Yuan et al. (2020b) and Xiang et al. (2019) shown in the left-hand, middle and
right-hand panel, respectively. The one-to-one relation is represented by the
grey-dashed line, and the text in each panel presents the mean difference
($\mu$, ULySS minus literature) and dispersion ($\sigma$) between the samples,
for stars with [Fe/H]${}_{\mathrm{Li+18}}>-2.5$ (red) and $<-2.5$ (blue).

###  A.1. Testing our spectroscopic metallicities

The metallicities for LAMOST stars in this work were determined with the ULySS
(Koleva et al., 2009) pipeline, making use of the empirical MILES library
interpolator model (Prugniel et al., 2011; Sharma et al., 2016). This method
has been tested extensively for stars of widely varying stellar types and
metallicities, and was also used on the X-shooter Spectral Library (Arentsen
et al., 2019). Here we show that this method works well for estimating [Fe/H]
of very metal-poor (VMP, $-3.0<$ [Fe/H] $<-2.0$) giant stars. We analyse a few
hundred stars from the LAMOST VMP catalogue of Li et al. (2018a) in the same
way as we analysed the LMS-1 stars, and present the comparison in the left-
most panel of Figure 12. The agreement is excellent for $-2.5<$[Fe/H]$<-2.0$
with an average difference of $\mu\sim-0.04$ dex and a standard deviation of
$\sigma\sim 0.17$ dex. For [Fe/H]$<-2.5$, the ULySS metallicities are on
average $0.15$ dex higher, and there is a larger scatter of $0.28$ dex. The
middle panel of Figure 12 shows a comparison between our [Fe/H] estimates and
those from Yuan et al. (2020b) who re-analysed the LAMOST spectra for the Li
et al. (2018a) VMP sample with the Segue Stellar Parameter Pipeline for LAMOST
(L-SSPP, Lee et al. 2015). There is a small offset that is similar in both
metallicity ranges ($0.08/0.11$ dex), and the scatter is of the same order as
before.

We also compare our [Fe/H] with those from Xiang et al. (2019), who analysed
the LAMOST DR5 spectra using the “data-driven Payne” method, that they train
on the parameters from APOGEE DR14 (Holtzman et al., 2018) and GALAH DR2
(Buder et al., 2018). However, since the latter two surveys do not contain
many metal-poor stars, the authors of Xiang et al. (2019) themselves caution
about their results for stars with [Fe/H] $<-1.5$. We confirm that this
caution is necessary, as we find a large difference in metallicity
($\mu\sim-0.40$ dex) between our results and those from Xiang et al. (2019)
for a sample of VMP stars from the Li et al. (2018a) catalogue (see the right-
most panel of Figure 12). We note that the dispersion is lower than in the
previous two comparisons, even for [Fe/H]$<-2.5$. The reason for this low
dispersion may owe to the fact that both the ULySS and the Xiang et al. (2019)
analysis are data-driven, and such techniques are known to provide more
precise results (Jofré et al., 2019), although not necessarily more accurate.
In sum, the overall comparison of our ULySS metallicities with Li et al.
(2018a) and Yuan et al. (2020b) makes a strong case that our [Fe/H]
measurements for the metal-poor stars are more accurate than those from Xiang
et al. (2019).

###  A.2. Investigating differences in the metallicity scale of our method and
the H3 survey

LMS-1 and Wukong appear to be the same structure (especially in the dynamical
space), but we find that our [Fe/H] measurement for LMS-1 is $\sim 0.4$ dex
lower as compared to that of Naidu et al. (2020) for Wukong. This discrepancy
may partly owe to the differences in the metallicity scales of the two
analysis, and this discrepancy can be particularly strong for VMP stars. Naidu
et al. (2020) derive the median metallicity for Wukong using the H3
spectroscopic survey. Cargile et al. (2020) test the H3 pipeline on metal-poor
globular clusters ([Fe/H] $\leq-1.5$) and find slightly higher metallicities
than the literature (by $\sim 0.1-0.15$ dex), although they do find a good
agreement with the literature specifically for the metal-poor “Sextans” dwarf
galaxy (that has [Fe/H] $=-1.9$). We also note that small scale differences of
$\sim 0.1-0.2$ dex generally exist across different surveys, and is a common
issue since different spectroscopic surveys analyse different
resolutions/wavelengths to derive chemical composition of stars. Additionally,
Conroy et al. (2019) compare the metallicities from H3 with the literature,
which for metal-poor stars comes from SEGUE DR14 (analysed with the SSPP, Lee
et al. 2008) and from the Xiang et al. (2019) analysis of LAMOST DR5. For
stars with [Fe/H] $>-1.5$, the H3 metallicities typically agree with the
literature, but for more metal-poor stars they are higher than the SEGUE
metallicities by $\sim 0.2$ dex and lower than the Xiang et al. (2019) values
by $\sim 0.1$ dex. Given that we found that the Xiang et al. (2019)
metallicities are possibly too high by $\sim 0.4$ dex (see Figure 12), both
comparisons point to H3 having a slightly more metal-rich metallicity scale
for very metal-poor stars. This can contribute to the discrepancy in the
metallicity that we note for LMS-1 and Wukong.