# Streams on FIRE:
Populations of Detectable Stellar Streams in the Milky Way and FIRE

Nora Shipp MIT Kavli Institute for Astrophysics and Space Research, 77
Massachusetts Ave., Cambridge, MA 02139, USA  Nondh Panithanpaisal Department
of Physics & Astronomy, University of Pennsylvania, 209 S 33rd St.,
Philadelphia, PA 19104, USA  Lina Necib MIT Kavli Institute for Astrophysics
and Space Research, 77 Massachusetts Ave., Cambridge, MA 02139, USA
Department of Physics, Massachusetts Institute of Technology, Cambridge, MA
02139, USA  Robyn Sanderson Department of Physics & Astronomy, University of
Pennsylvania, 209 S 33rd St., Philadelphia, PA 19104, USA  Center for
Computational Astrophysics, Flatiron Institute, 162 5th Ave., New York, NY
10010, USA  Denis Erkal Department of Physics, University of Surrey, Guildford
GU2 7XH, UK  Ting S. Li Department of Astronomy and Astrophysics, University
of Toronto, 50 St. George Street, Toronto ON, M5S 3H4, Canada  Isaiah B.
Santistevan  Department of Physics and Astronomy, University of California,
Davis, CA 95616, USA  Andrew Wetzel Department of Physics and Astronomy,
University of California, Davis, CA 95616, USA  Lara R. Cullinane Department
of Physics and Astronomy, Johns Hopkins University, 3400 N. Charles St,
Baltimore, MD 21218, USA  Alexander P. Ji Department of Astronomy &
Astrophysics, University of Chicago, 5640 S Ellis Avenue, Chicago, IL 60637,
USA  Kavli Institute for Cosmological Physics, University of Chicago, Chicago,
IL 60637, USA  Sergey E. Koposov Institute for Astronomy, University of
Edinburgh, Royal Observatory, Blackford Hill, Edinburgh EH9 3HJ, UK  Institute
of Astronomy, University of Cambridge, Madingley Road, Cambridge CB3 0HA, UK
Kavli Institute for Cosmology, University of Cambridge, Madingley Road,
Cambridge CB3 0HA, UK  Kyler Kuehn Lowell Observatory, 1400 W Mars Hill Rd,
Flagstaff, AZ 86001, USA  Australian Astronomical Optics, Faculty of Science
and Engineering, Macquarie University, Macquarie Park, NSW 2113, Australia
Geraint F. Lewis Sydney Institute for Astronomy, School of Physics, A28, The
University of Sydney, NSW 2006, Australia  Andrew B. Pace McWilliams Center
for Cosmology, Carnegie Mellon University, 5000 Forbes Ave, Pittsburgh, PA
15213, USA  Daniel B. Zucker School of Mathematical and Physical Sciences,
Macquarie University, Sydney, NSW 2109, Australia  Macquarie University
Research Centre for Astronomy, Astrophysics & Astrophotonics, Sydney, NSW
2109, Australia  Joss Bland-Hawthorn Sydney Institute for Astronomy, School of
Physics, A28, The University of Sydney, NSW 2006, Australia  Centre of
Excellence for All-Sky Astrophysics in Three Dimensions (ASTRO 3D), Australia
Emily C. Cunningham Center for Computational Astrophysics, Flatiron Institute,
162 5th Ave., New York, NY 10010, USA  Stacy Y. Kim Department of Physics,
University of Surrey, Guildford GU2 7XH, UK  Sophia Lilleengen Department of
Physics, University of Surrey, Guildford GU2 7XH, UK  Jorge Moreno Department
of Physics and Astronomy, Pomona College, Claremont, CA 91711, USA  Downing
College, University of Cambridge, Cambridge CB3 OHA, UK  Sanjib Sharma Sydney
Institute for Astronomy, School of Physics, A28, The University of Sydney, NSW
2006, Australia  Centre of Excellence for All-Sky Astrophysics in Three
Dimensions (ASTRO 3D), Australia<EMAIL_ADDRESS>
###### Abstract

We present the first detailed study comparing the populations of stellar
streams in cosmological simulations to observed Milky Way dwarf galaxy
streams. In particular, we compare streams identified around Milky Way analogs
in the FIRE-2 simulations to stellar streams observed by the Southern Stellar
Stream Spectroscopic Survey (${S}^{5}$). For an accurate comparison between
the stream populations, we produce mock Dark Energy Survey (DES) observations
of the FIRE streams and estimate the detectability of their tidal tails and
progenitors. The number and stellar mass distributions of detectable stellar
streams is consistent between observations and simulations. However, there are
discrepancies in the distributions of pericenters and apocenters, with the
detectable FIRE streams, on average, forming at larger pericenters (out to
$>110\mathrm{\,kpc}$) and surviving only at larger apocenters ($\gtrsim
40\mathrm{\,kpc}$) than those observed in the Milky Way. We find that the
population of high-stellar mass dwarf galaxy streams in the Milky Way is
incomplete. Interestingly, a large fraction of the FIRE streams would only be
detected as satellites in DES-like observations, since their tidal tails are
too low-surface brightness to be detectable. We thus predict a population of
yet-undetected tidal tails around Milky Way satellites, as well as a
population of fully undetected low-surface brightness stellar streams, and
estimate their detectability with the Rubin Observatory. Finally, we discuss
the causes and implications of the discrepancies between the stream
populations in FIRE and the Milky Way, and explore future avenues for tests of
satellite disruption in cosmological simulations.

Stars: kinematics and dynamics – Galaxy: structure – Galaxy: halo – Local
Group

##  1 Introduction

The $\Lambda$ Cold Dark Matter ($\rm\Lambda CDM$) cosmological model predicts
that galaxies form via hierarchical merger events and accretion. Within this
framework, galaxies like the Milky Way reside within dark matter halos, which
are built up via the accretion and disruption of lower-mass subhalos.
Surviving subhalos may be traced by observations of the luminous satellite
galaxies that they host; and subhalos undergoing tidal disruption can be
traced by the tidal remnants of these systems – stellar streams.

Observations of surviving satellite galaxies have enabled strong constraints
on near-field cosmology, including unprecedented insight into the intricacies
of galaxy formation at small scales and the properties of dark matter, raising
important challenges to the $\rm\Lambda CDM$ cosmological model (Bullock &
Boylan-Kolchin, 2017), such as the missing satellites (Moore et al., 1999;
Klypin et al., 1999), core-cusp (Navarro et al., 1996), and too-big-to-fail
(Boylan-Kolchin et al., 2011, 2012) problems. These controversies have in
large part been resolved by incorporating the effect of baryonic physics into
cosmological simulations (e.g. Wetzel et al., 2016; Garrison-Kimmel et al.,
2017; Fitts et al., 2017; Simpson et al., 2018; Garrison-Kimmel et al., 2019a;
Buck et al., 2019; Kim et al., 2018; Sales et al., 2022), and by the discovery
of a large number of Milky Way satellites in wide-area optical imaging surveys
(see Drlica-Wagner et al., 2020, and references therein). Despite this
progress, however, many open questions remain. The nature of dark matter is
one of the largest outstanding questions in modern physics, and we have yet to
build a comprehensive understanding of galaxy formation at the smallest
scales.

Stellar streams are strong complementary probes of near-field cosmology and
have the power to provide additional tests of our understanding of galaxy
formation and dark matter in the local universe. Satellite tidal disruption
remains a large source of uncertainty in studies of near-field cosmology (e.g.
Carlsten et al., 2020). Incorporating stellar streams into studies of Milky
Way and simulated satellite populations enables comparisons of not only the
surviving population of satellites, but of their rate of disruption. Since
tidal disruption is sensitive to the density profiles of satellites, which in
turn are highly dependent on properties of the dark matter particle (e.g.
Tulin & Yu, 2018; Du et al., 2018) as well as baryonic physics (e.g. Garrison-
Kimmel et al., 2019a), constraints on disruption rates in the Milky Way may be
be used to test theories of both dark matter and galaxy evolution (e.g.
Peñarrubia et al., 2012; Errani et al., 2015).

Stellar streams also enable precise measurements of the local gravitational
potential (e.g. Johnston et al., 2005; Law & Majewski, 2010; Bovy, 2014;
Gibbons et al., 2014), including the overall mass and shape of the Milky Way
halo and its massive satellites (Erkal et al., 2019; Vasiliev et al., 2021;
Shipp et al., 2021). These measurements place the Milky Way in a cosmological
context, enabling more precise tests of galaxy formation and dark matter
physics with cosmological simulations. In addition, streams are one of a small
number of methods predicted to be able to detect the presence of low-mass
subhalos that host no luminous baryonic component (Johnston et al., 2002;
Ibata et al., 2002; Carlberg, 2009; Koposov et al., 2010; Yoon et al., 2011;
Carlberg, 2012; Erkal & Belokurov, 2015; Sanders et al., 2016; Bovy et al.,
2017; Price-Whelan & Bonaca, 2018; Bonaca et al., 2018).

Streams have traditionally been difficult to incorporate into population-level
comparisons of satellites in simulations and observations. However, with wide-
area surveys, the number and quality of observations of stellar streams have
increased dramatically in recent years. To date, nearly 100 tidal remnants of
dwarf galaxies and globular clusters have been discovered around the Milky Way
(Mateu, 2022). In addition, for the first time, kinematic measurements are
available for a large population of stellar streams, thanks to proper motions
measured by Gaia (Gaia Collaboration et al., 2016, 2018, 2021), as well as
radial velocities obtained by large-scale spectroscopic surveys of stellar
streams (e.g. Li et al., 2019; Zhao et al., 2012; Majewski et al., 2017). At
the same time, zoom-in cosmological simulations (e.g. Wetzel et al., 2016;
Hopkins et al., 2018) are now able to resolve dwarf galaxy streams (down to
$M_{*}\gtrsim 5\times 10^{5}\mathrm{\,M_{\odot}}$) around Milky Way-mass hosts
(Panithanpaisal et al., 2021). Comparing such populations of Milky Way and
simulated stellar streams will enable a broad range of tests of hierarchical
structure formation, tidal disruption, and the nature of dark matter.

Li et al. (2022) presented an overview of a population of one dozen stellar
streams with complete 6D phase space measurements, observed by the Southern
Stellar Stream Spectroscopic Survey (${S}^{5}$; Li et al., 2019). In comparing
these Milky Way streams to those found in the Latte suite of simulations
(Wetzel et al., 2016), based on FIRE-2 physics (Hopkins et al., 2018), they
raised the possibility of a “too-big-to-fail” problem in stellar streams. In
particular, they found an excess of high-stellar mass streams ($M_{*}\gtrsim
5\times 10^{5}\mathrm{\,M_{\odot}}$) in FIRE relative to the population
observed in the Milky Way. While the FIRE Milky Way analogs have a median of 8
stellar streams in this mass range, only ${\sim}\,2$ have been observed around
the Milky Way, perhaps suggesting that a population of high-stellar mass, low-
surface brightness streams remain undetected in the Milky Way. Alternatively,
this discrepancy between simulations and observations may imply that FIRE is
over-disrupting or otherwise over-producing massive streams.

The FIRE simulations have been found to reasonably reproduce the population of
surviving satellites observed around the Milky Way, including the
distributions of stellar masses and velocity dispersions (Wetzel et al., 2016;
Garrison-Kimmel et al., 2019a), as well as the radial distance distribution
(Samuel et al., 2020). Similar comparisons of populations of tidally
disrupting satellites further test the agreement between simulations and
observations, enabling stronger constraints on and new insight into dark
matter and galaxy formation physics in the local universe.

In this paper, we compare detectable stellar streams in the FIRE simulations
to dwarf galaxy streams observed in the Milky Way. We produce mock Dark Energy
Survey (DES; DES Collaboration, 2005; DES Collaboration et al., 2018; Abbott
et al., 2021) observations of the FIRE streams to estimate their
detectability. We then compare the number, stellar mass, and orbital
distributions of these populations. We find that when taking detectability
into account, the number and stellar mass distribution of these streams are
consistent between simulations and observations. However, the orbital
distributions of these populations differ significantly, with FIRE streams
existing at large pericenters and apocenters relative to those in the Milky
Way. We present our observed Milky Way and simulated FIRE stream datasets in
Section 2; in Section 3 we discuss our mock observations and estimate the
detectability of stellar streams and satellites in FIRE. In Section 4 we
compare the populations of stellar streams in the Milky Way and in FIRE; and
in Section 5 we discuss the discrepancies between these two populations, the
implications for satellite galaxy disruption in the Milky Way, and predictions
for future observations.

##  2 Simulations & Data

###  2.1 Stellar Streams in the Milky Way

In this paper, we focus on the dwarf galaxy streams that have been detected
around the Milky Way.111The Latte and ELVIS on FIRE simulations used in this
work do not include globular clusters at $z=0$, thus we only consider dwarf
galaxy streams in this analysis. The population of known streams in the Milky
Way has increased dramatically in recent years, thanks to the advent of large
photometric and astrometric surveys (Grillmair & Carlin, 2016; Shipp et al.,
2018; Malhan et al., 2018; Mateu et al., 2018). The total number of known
streams is approaching 100 (Mateu, 2022), and will continue to grow with
ongoing and upcoming surveys (e.g. Drlica-Wagner et al., 2021; LSST Science
Collaboration, 2009). Recent Gaia data releases (Gaia Collaboration et al.,
2021, 2018) have enabled measurements of the proper motions of stellar streams
out to ${\sim}\,50\mathrm{\,kpc}$ (e.g. Price-Whelan & Bonaca, 2018; Malhan et
al., 2018; Shipp et al., 2019; Koposov et al., 2019; Ramos et al., 2020; Ibata
et al., 2020), providing the first kinematic measurements of a large
population of stellar streams.

In addition, ${S}^{5}$ has obtained spectroscopic measurements of $>20$
stellar streams, using the Two-degree Field fiber positioner (Lewis et al.,
2002) and the AAOmega spetrograph (Sharp et al., 2006) on the 3.9m Anglo-
Australian Telescope. The metallicity and radial velocity measurements
obtained by ${S}^{5}$ enable classification of stream progenitors,
metallicity-based estimates of total stellar mass, and precise orbit modeling.

Li et al. (2022) summarized the orbital and chemical properties of the first
dozen ${S}^{5}$ stellar streams. Of the 12 streams, six are determined to be
disrupted dwarf galaxies (OC, Elqui, Indus, Palca, Turranbura, and Jhelum).
These six streams are classified as dwarf galaxy streams due to their resolved
calcium triplet (CaT) metallicity dispersions and large radial velocity
dispersions ($\sigma_{\rm[Fe/H]}>0.2\ \mathrm{and/or}\ \sigma_{\rm
v}>10\mathrm{\,km}\mathrm{\,s}^{-1}$), relative to the globular cluster
streams. In addition to these six streams, we include in our analysis the
Sagittarius stream (Sgr; Ibata et al., 1994; Majewski et al., 2003), which has
been observed by ${S}^{5}$ as well as by several others (Hasselquist et al.,
2019; Yang et al., 2019; Johnson et al., 2020). These seven streams make up
the population of confirmed dwarf galaxy streams around the Milky
Way.222Although these streams all lie within the DES footprint, they make up
the full current sample of known Milky Way dwarf galaxy streams. Cetus and
LMS-1 are also likely dwarf galaxy streams; however, the former is likely
associated with the Palca stream (Li et al., 2022; Yuan et al., 2022), and the
latter is connected to the Indus stream (Malhan et al., 2021).

In order to compare these stellar streams to those identified in FIRE, we
determine the stellar masses and orbits of each system. As described in Li et
al. (2022), the total luminosities of these streams are calculated from the
measured metallicities, using the empirical relation from Simon (2019). The
luminosities are then converted to stellar mass, assuming $M_{*}/L_{\rm
V}=1.6$ (Kirby et al., 2013). The scatter in this relation is 0.16 dex in
[Fe/H], which corresponds to a factor of 3.5 uncertainty in stellar mass. This
method provides measurements of the total stellar mass, which do not rely on
the detection of the full extent of each stream.

Incorporating the redshift dependence of the mass-metallicity relation, as
discussed, for example, in Naidu et al. (2022) (N22), would increase the
resulting stellar masses of the Milky Way streams, reducing the scale of the
discrepancy between the Milky Way and FIRE. However, we choose not to use the
mass-metallicity relation for disrupting systems derived in N22 for several
reasons. First, the relation is fit primarily to phase-mixed systems, and the
two streams that are considered (Sgr and OC) are outliers from the resulting
fit. Second, the systems considered in N22 have large stellar masses
($M_{*}>10^{6.1}\mathrm{\,M_{\odot}}$), and extrapolating the relation to
smaller masses would overestimate the masses of faint satellites that are
likely to be quenched before infall. In addition, in FIRE, we see that
surviving satellites and streams follow the same mass-metallicity relation
(Panithanpaisal et al., 2021). Using the N22 relation effectively increases
the stellar masses of the Milky Way streams by a factor of ten. This leads to
an excess of low mass streams in the Milky Way relative to those seen in FIRE.
At the higher mass end, the stellar mass distributions of detectable streams
remain consistent within $1\sigma$. We therefore use the $z=0$ relation
throughout this work, and leave a determination of the mass-metallicity
relation for Milky Way dwarf galaxy streams to future work.

The orbit of each ${S}^{5}$ stream is determined by fitting the radial
velocities from ${S}^{5}$, proper motions from Gaia EDR3, and distances of
blue horizontal branch and RR Lyrae member stars in the best-fit static Milky
Way potential from McMillan (2017), as described in Li et al. (2022). The
pericenters and apocenters reported in Li et al. (2022) are compared to the
models of Shipp et al. (2021), which use a modified Lagrange Cloud Stripping
technique (Gibbons et al., 2014) to model stream disruption in the presence of
the Milky Way and Large Magellanic Cloud (LMC). The resulting orbits are found
to be consistent, and therefore the values presented in Table 2 of Li et al.
(2022) are used throughout this paper.

Figure 1: A selection of simulated stellar streams in FIRE. Synthetic stars
are sampled from the simulation star particles, as described in Section 3. The
figure columns are grouped by stellar mass (in units of
$\mathrm{\,M_{\odot}}$) and the rows are grouped by pericenter, to illustrate
a subset of the simulated stream population with a range of parameters and
morphologies. Each panel shows the 2D density of synthetic stars in
coordinates centered on the host galaxy. While all streams do have coherent,
extended structures, some, particularly those with large pericenters, have
very low-surface brightness tidal tails.

###  2.2 Stellar Streams in FIRE

Zoom-in cosmological-baryonic simulations of galaxy formation can now achieve
resolutions that allow for the study of tidal remnants of dwarf galaxies
around Milky Way-like hosts, produced self-consistently via accretion from the
cosmic web. In this work, we focus on one such set of simulated Milky Way
analogs: the FIRE-2 “Latte” and “ELVIS on FIRE” suites (Wetzel et al., 2016;
Hopkins et al., 2018; Garrison-Kimmel et al., 2019a; Samuel et al., 2020). The
FIRE-2 simulations are run with the
Gizmo333https://bitbucket.org/phopkins/gizmo-public code (Hopkins et al.,
2013; Hopkins, 2015), which uses a mesh-free finite-mass Lagrangian Godunov
method for the hydrodynamic solver, and a version of the Tree-PM solver based
on GADGET-3 (Springel, 2005). Star formation and feedback are implemented
using the FIRE-2 prescriptions described in Hopkins et al. (2018).

These simulations produce galaxies with properties that are similar, but not
identical, to those of the Milky Way in many aspects, including the stellar
mass and structure of the central disk (Sanderson et al., 2020) and the
structure of the stellar halo (Sanderson et al., 2018). The population of
satellite galaxies around each host also resembles the Milky Way’s in key
aspects, including their mass function, size-mass relation, and internal
velocity dispersion (Wetzel et al., 2016), radial distribution (Samuel et al.,
2020), star formation histories (Garrison-Kimmel et al., 2019b), and mass-
metallicity trends (Panithanpaisal et al., 2021). The fidelity of the dwarf
satellite population supports our use of these simulations to represent the
population of tidally disrupted dwarfs, which form a different subset of the
same accreted population (Panithanpaisal et al., 2021; Cunningham et al.,
2021).

In this work, we focus on the stellar streams first identified by
Panithanpaisal et al. (2021) in zoom-in simulations of the seven isolated444No
equally massive halo within 10 Mpc. Milky Way-like galaxies from the Latte
suite (Wetzel et al., 2016), and three Milky Way+M31-like pairs from the ELVIS
on FIRE suite (Garrison-Kimmel et al., 2019a), for a total of 13 host
galaxies. These galaxies have halo masses at $z=0$ of $M_{\rm 200}=1\mathchar
45\relax 2.1\times 10^{12}\mathrm{\,M_{\odot}}$ (Sanderson et al., 2018). The
Latte suite has an initial stellar mass resolution of
$7070\mathrm{\,M_{\odot}}$ per star/gas particle, and includes the simulations
m12i, m12f, m12m, m12b, m12c, m12w, and m12r. The ELVIS on FIRE suite includes
the pairs Thelma and Louise, Romeo and Juliet, and Remus and Romulus. The
initial stellar mass resolution of these galaxies is $3500\mathchar 45\relax
4000\mathrm{\,M_{\odot}}$ per particle. Sanderson et al. (2018) discusses the
detailed differences in the stellar halos of each of these galaxies. A table
of the main properties of the central galaxies is available in Santistevan et
al. (2020); Bellardini et al. (2021), and the satellite population is further
discussed in Garrison-Kimmel et al. (2019a) and Samuel et al. (2020).

Panithanpaisal et al. (2021) identified streams around these halos by tracking
luminous substructures that were bound and within the $z=0$ virial radius of
the host (${\sim}\,350\mathrm{\,kpc}$) at any time between 2.7–6.5 Gyr
ago555Systems that become unbound earlier than 6.5 Gyr ago have been
classified as phase-mixed at $z=0$ and are discussed in greater detail in
Horta et al. (in prep.). Systems accreted more recently are predominately on
first infall and have not had sufficient time to disrupt into coherent
streams.. The stream candidates are then selected using the following
criteria: First, they must have between 120 and $10^{5}$ star particles. This
translates to stellar masses between ${\sim}\,5\times
10^{5}\mathrm{\,M_{\odot}}$ and ${\sim}\,10^{9}\mathrm{\,M_{\odot}}$. Second,
the maximum pairwise distance between member star particles must be greater
than $120\mathrm{\,kpc}$, indicating that the stream has stretched at least
partway across the galaxy.666As discussed in Panithanpaisal et al. (2021),
this constraint effectively eliminates dwarf galaxies that are somewhat
tidally deformed but do not have coherent tidal tails. Removing this
constraint increases the sample of coherent streams, as identified by eye, by
one across the 13 simulations. Third, the stream candidates must have a local
velocity dispersion below a stellar mass-dependent threshold (see their
Equation 2), requiring that they remain coherent in phase space. We note that
the accreted debris in FIRE can have complex morphologies (particularly at the
massive end; e.g., Cunningham et al, in prep.), with some portions of the
debris remaining kinematically coherent and other portions fully phase-mixing.
However, for the purposes of this study, and for consistency of the selection,
we limit ourselves to systems that are classified as streams by the selection
criteria of Panithanpaisal et al. (2021).

In order to ensure accurate measurements of the stellar masses and orbits of
the FIRE streams, we update the selection of member stars beyond what has been
done in Panithanpaisal et al. (2021). We require that each stream member star
is associated with the progenitor for at least ten snapshots; this eliminates
contamination from unassociated satellites and from host disk stars that may
be erroneously picked up by the halo finder due to coincidental proximity in
phase space. This updated selection changes the number and the stellar masses
of the streams presented in Panithanpaisal et al. (2021).

We then compute the orbits of the FIRE streams by individually tracing the
orbits of each member star through the saved snapshots, and then integrating
the orbit around each pericenter using the code AGAMA (Vasiliev, 2019). We
integrate each star particle in the corresponding host galaxy potential at the
snapshot closest to the most recent pericentric passage777The time frequency
of the output snapshots (600 snapshots, spaced by ${\sim}\,10\mathrm{\,Myr}$)
is high enough that the integration between snapshots generally has very
little effect on the resulting pericentric distance., using the models from
Arora et al. (2022)888https://web.sas.upenn.edu/dynamics/data/pot_models/.
These models are fit to each snapshot, and consist of multipole expansions (up
to $l=4$), computed using a combination of spherical harmonics and azimuthal
harmonics for the halo and disk respectively. We then fit a Gaussian kernel
density estimate (KDE) to the spatial distribution of stars at $z=0$ to select
the highest density region, corresponding to the portion of the stream around
the surviving or dissolved progenitor. We take the median pericenter and
apocenter of stars in this high-density region as the overall pericenter and
apocenter of the stellar stream. This procedure excludes very diffuse stream
components and produces measurements of the orbital parameters more consistent
with how we measure stream orbits in the Milky Way.

The properties of the updated stream population are summarized in Table A.1 in
Appendix A.

##  3 Mock Observations

Figure 2: Detectability of a sample of simulated stellar streams. Each panel
shows the mock observation of one stream, transformed into stream coordinates
(so that the stream lies along $\phi_{\rm 2}{\sim}\,0$). In order to estimate
detectability, we divide each stream into $15\deg$ segments, and calculate the
average surface brightness within the $1\sigma$ Gaussian width. Blue segments
are detectable ($\mu_{\rm V}<34\ \mathrm{mag/arcsec^{2}}$), and green dashed
segments are undetectable. Surviving progenitors are masked within $4r_{1/2}$.
The underlying image shows the number density of stars along the stream.

In order to compare more directly to observed Milky Way stellar streams, we
produce mock DES observations of the FIRE streams and estimate the
detectability of these systems. The DES data is well-suited to the study of
stellar streams; its precise photometry and depth of observations have enabled
the discovery and detailed study of a large population of stellar streams
(Shipp et al., 2018). The DES streams are generally lower surface brightness
and more distant than other known streams. In addition, the majority of
streams that have been followed up by ${S}^{5}$, which make up the population
of Milky Way stellar streams considered in this work, have been observed with
DES. The DES footprint covers ${\sim}\,5000\deg^{2}$, one eighth of the sky.
Similar photometric surveys, such as the Sloan Digital Sky Survey (SDSS; York
et al., 2000), Pan-STARRS (Chambers et al., 2016), the DESI Legacy Imaging
Surveys (Dey et al., 2018), and the DECam Local Volume Exploration Survey
(DELVE; Drlica-Wagner et al., 2021) span much of the remaining area, albeit to
a shallower magnitude depth. Estimating the detectability of the FIRE streams
in all-sky DES photometry will therefore only overestimate the total
detectable number, and thereby provide a conservative test of whether
considering detectability is sufficient to resolve the too-big-to-fail problem
in stellar streams.

We use the Ananke code (Sanderson et al., 2020) to simulate the mock
observations. We generate a population of synthetic stars from each simulated
star particle. The simulation particles represent the average position,
velocity, age, and metallicity of an ensemble of stars. For the Latte
simulations, the initial mass of each gas particle is
$7070\mathrm{\,M_{\odot}}$; at $z=0$ the average mass of the resulting star
particles is ${\sim}\,5000\mathrm{\,M_{\odot}}$. The ELVIS simulations have
star particles masses of ${\sim}\,3.5\mathchar 45\relax 4\times
10^{3}\mathrm{\,M_{\odot}}$. As in Sanderson et al. (2020); Sharma et al.
(2011), we consider each star particle to represent a population of stars with
a single age and metallicity. We sample individual stellar masses from a
Kroupa initial mass function (IMF) (Kroupa, 2001). We then sample absolute
magnitudes in the DES $grizY$ bands from an isochrone (Bressan et al., 2012)
with the age and metallicity of the parent star particle.

For each host galaxy, we establish a coordinate system centered on a solar
viewpoint and local standard of rest (LSR), with a solar position within the
host disk plane at a Galactocentric distance of $R_{\odot}=8.2\mathrm{\,kpc}$
(Bland-Hawthorn & Gerhard, 2016). We perform a rotation around the z-axis such
that solar position lies in the -$x$ direction. We then transform into the LSR
frame using the solar position and solar velocity from Astropy (Astropy
Collaboration et al., 2013, 2018; The Astropy Collaboration et al., 2022).

We place each synthetic star in position and velocity space, by sampling an
Epanechikov kernel (Epanechnikov, 1969) centered on the parent particle. We
consider position and velocity space independently, and the size of each
kernel is inversely proportional to the cube-root of the local density around
each parent particle. The local density is calculated from the 16 nearest
neighbors, using the density estimator EnBid (Sharma & Steinmetz, 2011). The
kernel shape was selected to be computationally efficient for massive streams,
and the number of nearest neighbors was selected to ensure an accurate local
density estimation for low-mass streams.

We then compute the apparent magnitude of each star, based on the assigned
heliocentric distance, and convolve the apparent magnitude with the DES
photometric uncertainties. We parameterize the $g$-band magnitude error as

$\displaystyle\begin{split}err(g)=0.0006+e^{(g-26.0)/0.88},\end{split}$ (1)

where the coefficients are fit to the DES DR2 (Abbott et al., 2021) weighted-
average magnitudes and magnitude errors (WAVG_MAG_PSF_G, WAVG_MAGERR_PSF_G).
We similarly parameterize the $r$ and $i$ band errors with equation 1, with
coefficients (0.0002, 25.7, 0.87) and (0.0020, 25.1, 0.81), respectively. The
$z$ and $Y$ band magnitudes are not used in this analysis. When calculating
the magnitude uncertainty for each synthetic star, we assume an interstellar
reddening, $E(B-V)$, of 0.04, roughly the average across the DES footprint.

The resulting dataset for each mock-observed stellar stream is available for
download at https://flathub.flatironinstitute.org/sapfire. Figure 1 displays a
selection of these mock-observed streams, binned by stellar mass (columns) and
pericenter (rows) to show a broad sample of FIRE stream morphologies.

###  3.1 Stream Detectability

We determine the detectability of each FIRE stream following a procedure
motivated by matched-filter stream searches in the DES data (Shipp et al.,
2018). The detectability of a stellar stream can be approximated based on the
average surface brightness of observed member stars (i.e. stars falling within
the DES magnitude limits of $16<g<24.7$). Lower luminosity and more diffuse
stellar streams (i.e. fainter surface brightness) are more difficult to
disentangle from contaminating foreground and background stellar populations.
This method also accounts for the fact that more distant streams will have
fewer detectable stars, and will therefore have a fainter observed surface
brightness. Shipp et al. (2018) published the average surface brightness of
the observed portion of each of the DES stellar streams. We correct these
values to include only stars within the DES magnitude limits, and find that
the surface brightness limit for stellar streams detectable within DES is
$\mu_{\rm V}\leq 34\mathrm{\,mag}/\mathrm{\,arcsec}^{2}$.

In order to calculate the average surface brightness of the tidal tails of
each FIRE stream, we first mask all stars within $4r_{1/2}$ of the progenitor,
using the progenitor parameters derived below (Section 3.2). We then convert
to a coordinate system where the stream lies approximately along the
equatorial plane, where $\phi_{1}$ is the coordinate along the stream and
$\phi_{2}$ is the coordinate perpendicular to the stream. In practice, stars
belonging to a long, convoluted stream do not share the exact same orbital
plane, so we estimate the best-fit RA and Dec of the orbital pole
$(\alpha,\delta)$ for each stream by minimizing the quantity
$\mathcal{D}(\alpha,\delta)=\sum_{i}|\frac{\pi}{2}-\mathcal{D}_{i}(\alpha,\delta)|$,
where $\mathcal{D}_{i}(\alpha,\delta)$ is the angular distance from the pole
to each stream member star.

We then divide the stream into equal-length ($15\deg$) segments and
individually calculate the detectability of each segment to account for
variation in surface brightness along the stream. Then, to determine the
$\phi_{2}$ position of each endpoint, we take stars that are within 3 degrees
of $\phi_{1}^{\rm end}$. If there are fewer than 50 stars in this region, we
disregard this endpoint as it is likely an empty space, and automatically mark
its neighboring segments as undetectable. Otherwise, we determine the
corresponding $\phi_{2}^{\rm end}$ to be the peak in the $\phi_{2}$
distribution of the selected stars. We determine the detectability of each of
these segments individually, and consider streams to be detectable if they
have at least one detectable segment. We count all systems with $>1$
detectable segment as one detectable stream (just as we consider associated,
but disconnected, segments of known Milky Way dwarf galaxy streams to be one
single stream).

Within each segment, we perform another coordinate transformation so that the
great circle connecting the two end points lies along the equatorial plane. We
then determine the width in $\phi_{\rm 2}$ of the segment by fitting the peak
interval (i.e. the smallest $\pm 1\sigma$ interval containing the peak of the
distribution). We consider only the inner $\pm 1\sigma$ range in order to
exclude diffuse components at large $\phi_{2}$ that would bias the
detectability estimate. We then select all stars within this range, and
convert their DES $g$ and $r$ band magnitudes to visual magnitudes using the
relation from Bechtol et al. (2015),

$\displaystyle\begin{split}V=g_{\rm DES}-0.487(g_{\rm DES}-r_{\rm
DES})-0.025.\end{split}$ (2)

We then compute the total luminosity ($M_{\rm V}$) and area of each segment,
and calculate the average surface brightness ($\mu_{\rm V}$). Figure 2
illustrates the detectability of segments along 4 of the FIRE streams. The
detectable (blue) and undetectable (green) segments are overplotted on the
number density of stars along the stream.

We find that 32 of the 96 streams with $M_{*}\gtrsim 5\times
10^{5}\mathrm{\,M_{\odot}}$ are detectable across the 13 FIRE halos. This
corresponds to a median of 3 streams per host galaxy. The number of detectable
streams per host is shown in Figure 3, and these results are discussed in
greater detail in Section 4.1.

Figure 3: Total and detectable stream populations around 13 FIRE hosts. The
bottom segment of each bar represents the number of streams with detectable
tidal tails, the middle segment represents the number of streams with only
detectable progenitors (i.e. would be mistaken as intact satellites), and the
top segment indicates the remaining number of streams. The total height of
each bar is the total stream population in each galaxy. The host halos are
sorted in order of host halo mass (low to high). The gray band represents the
$1\sigma$ scatter in the number of streams, within the stellar mass range
considered, that have been detected within the Milky Way (the scatter is due
to uncertainty in stellar mass measurements). The number of detectable streams
in FIRE is consistent with the number detected in the Milky Way. Figure 4:
Estimated satellite detectability, using the analytic approximation from
Drlica-Wagner et al. (2020). Luminosity, half-light radius, and distance at
$z=0$ are derived from the mock observations described in Section 3.2.
Triangles are surviving stream progenitors, and circles are intact satellites.
The majority of satellites in this mass and distance range are detectable
(blue), whereas only a small number of surviving satellites and stream
progenitors are undetectable (green). The curves represent $50\%$
detectability at different distances.

###  3.2 Satellite Detectability

We also estimate the detectability of intact satellites and stream progenitors
in FIRE. Gravitationally-bound dark matter halos and subhalos are identified
in the simulations and assigned dark matter, gas, and star particles using the
ROCKSTAR halo finder (Behroozi et al., 2013), as described in Wetzel et al.
(2016). We select satellites from the halo catalog at $z=0$ with more than
$100$ star particles ($M_{*}\gtrsim 5\times 10^{5}\mathrm{\,M_{\odot}}$),
$d<300\mathrm{\,kpc}$, and bound mass fraction $>0.4$. Across the 13 host
halos, this is a total of 140 satellites, 61 of which are stream progenitors
(a median of $55\%$ and minimum of $40\%$ of streams in this mass range have
surviving progenitors, i.e. have progenitors that are recovered by the halo
finder at $z=0$). Throughout this paper, we refer to satellites included in
this sample as “surviving satellites.” Among the surviving satellites, we
refer to satellites with no evidence of tidal disruption as “intact
satellites” and those with tidal tails as “stream progenitors.”

We simulate the mock DES observations of these satellites, similarly to the
streams, as described in Section 3. We then use a procedure analogous to the
studies of observed satellite galaxies (e.g. Bechtol et al., 2015; Drlica-
Wagner et al., 2015, 2020) to fit an elliptical Plummer (1911) profile to each
mock-observed satellite. We use the code ugali
999https://github.com/DarkEnergySurvey/ugali (Bechtol et al., 2015; Drlica-
Wagner et al., 2015) to measure the half-light radius ($r_{1/2}$), ellipticity
($\epsilon$), position angle ($\theta$), and centroid
($\alpha_{0},\delta_{0}$) of each system. We calculate the total luminosity
($M_{\rm V}$) by converting the mock DES $g$-band magnitudes to visual
magnitudes as in Bechtol et al. (2015), and correcting for the unobserved
luminosity (due to DES magnitude limits) using the synthetic ischrones from
Bressan et al. (2012) implemented in ugali. We take the distance to each
satellite to be the median distance of mock-observed member stars. The derived
properties of each satellite are listed in Table A.2 in Appendix A.

Drlica-Wagner et al. (2020) presented an analytic approximation of the
detectability of satellite galaxies as a function of absolute magnitude, half-
light radius, and distance. We use the derived parameters described above to
estimate satellite detectability (Figure 4). We find that the majority of
satellites in this distance and stellar mass range, including the majority of
surviving stream progenitors, would be detectable with DES, with 72 out of 79
intact satellites and 53 out of 61 stream progenitors detectable. One
important caveat is that this approximation is based on dwarf galaxy search
techniques that are optimized for ultra-faint dwarf galaxies ($M_{\rm
V}\gtrsim-7.7$), and may therefore underestimate the detectability of the
brightest satellites. However, we find on average $<1$ satellite per host
within this luminosity range is undetectable. This assumption therefore has a
negligible effect on our overall conclusions. We combine these results with
the stream detectability estimates in Section 3.1 in order to identify the
number of streams with detectable tidal tails, detectable progenitors only
(i.e. would be mistaken as intact satellites), or no detectable component
(Figure 3). The population of streams mistaken as intact satellites is
discussed in greater detail in Section 5. For clarification of the terms used
throughout this paper, Table B.1 lists the resulting classification of stream
and satellite systems, depending on the detectability of their progenitors and
tidal tails.

##  4 Comparison between Milky Way and FIRE Stellar Streams

###  4.1 Number of Streams

This work was motivated in part by the question of whether there is an excess
of high-stellar mass streams in the FIRE simulations relative to what we
observe in the Milky Way: i.e. is there a too-big-to-fail problem in stellar
streams? In order to address this question, we produced mock observations of
the FIRE streams and estimated their detectability. We can now make a
consistent comparison between the population of Milky Way streams and those in
FIRE.

In Figure 3, we show the number of detectable streams around each FIRE halo in
comparison to the number of streams observed in this stellar mass range in the
Milky Way. The gray line represents the number of Milky Way dwarf galaxy
streams. We find that the Milky Way has $2\pm 1$ of these luminous systems
(Sgr, OC, and Jhelum), where the spread is due to the uncertainties in the
stellar mass measurements (i.e. within uncertainties, both OC and Jhelum could
be below the stellar mass limit considered here). Each bar represents the
number of streams in one of the simulated Milky Way analogs in FIRE. The
bottom segment is the number of streams with detectable tidal tails, the
middle segment is the number with only a detectable progenitor (i.e. they
would be mistaken as an intact satellite galaxy), and the top segment
represents the number of undetectable streams. The full height of the bar is
the total number of streams in this stellar mass range in each halo. Here we
include only streams with $M_{*}\gtrsim 5\times 10^{5}\mathrm{\,M_{\odot}}$
for consistency, although the ELVIS simulations are slightly higher resolution
and have streams down to $M_{*}\gtrsim 3\times 10^{5}\mathrm{\,M_{\odot}}$.
The bars are sorted in order of increasing host halo mass. Within this mass
range, we see no meaningful correlation between host halo mass and number of
streams. Without taking into account detectability, the number of streams in
FIRE would be inconsistent with what we have observed in the Milky Way.
However, we find that many streams, even at this luminosity, remain
undetectable due to their low surface brightness. We also find that many
detectable satellite galaxies have undetectable tidal tails. Therefore, the
observed Milky Way streams are consistent with the detectable FIRE streams and
there is no “too-big-to-fail” problem in stellar streams. In addition, the
FIRE simulations predict a population of yet-undetectable massive streams and
a population of satellites with significant, but still undetected, tidal
tails. We discuss the implications of this unobserved population of streams,
and make predictions for the future detectability of these systems in Section
5.

Figure 5: Cumulative mass distribution of streams and satellites in FIRE and
the Milky Way. The upper row includes only detectable systems, as determined
in Section 3. The lower row includes all systems in FIRE. The left column
includes only streams, the central only intact satellites (no tidal tails/no
detectable tidal tails), and the right includes the combination of these two
populations. The uncertainty on the Milky Way curves (black) comes from
scatter in the stellar mass-metallicity relations used to estimate the total
stellar mass of each system. The shaded bands on the FIRE curves represents
the scatter between systems. When taking into account detectability, the FIRE
stream and satellite mass distributions are largely consistent with those
observed in the Milky Way. The ELVIS halos have a slight excess of streams
with $M_{*}>10^{6}\mathrm{\,M_{\odot}}$ relative to the Milky Way, however the
discrepancy is only $\sim 1\sigma$.

###  4.2 Stellar Mass

In addition to the total number, we consider the stellar mass distribution of
streams and satellites in FIRE and in the Milky Way. In Figure 5 we present
the cumulative stellar mass distribution. The top row includes only detectable
systems, and the bottom row includes all systems in FIRE. The Milky Way
systems are the same between the two rows. In all panels, the black curve
represents the Milky Way systems and the blue curves represent FIRE. We plot
the Latte (light blue) and ELVIS (dark blue) streams independently, because
the simulations have slightly different resolution limits, and to explore
possible differences between stream populations in paired and isolated Milky
Way-like systems. The shaded bands around the blue curves represents the
scatter between systems. The uncertainty on the Milky Way stream stellar
masses corresponds to the scatter in the stellar mass-metallicity relation, as
discussed in Section 2. The Milky Way satellite stellar masses are calculated
from luminosities compiled by Putman et al. (2021); McConnachie (2012), and
stellar mass-to-light ratios from Woo et al. (2008). As uncertainties, we take
the typical 0.17 dex uncertainty on stellar mass reported by Woo et al.
(2008).

In each row, the left panel includes only stellar streams, the middle panel
includes only intact satellites (no tidal tails), and the right panel includes
the combined population of streams and intact satellites. The Milky Way is
largely consistent with the detectable systems in FIRE, with the exception of
the LMC at the high-mass end.101010None of the Latte or ELVIS on FIRE galaxies
have LMC analogs surviving to $z=0$, though some have analogous accretion
events in the past (Samuel et al., 2021). We leave a detailed study of the
effect of the accretion histories of simulated halos on their stream
populations to future work. In addition, the ELVIS pairs have a larger number
of streams with $M_{*}>10^{6}\mathrm{\,M_{\odot}}$, leading to a
${\sim}\,1\sigma$ discrepancy in the stellar mass distribution in this range.
This is consistent with the host halos in the Local Group-like pairs having
formed earlier, as discussed in Garrison-Kimmel et al. (2019a); Santistevan et
al. (2020).

The lower-middle panel includes only intact satellites, with no tidal tails.
The upper-middle panel includes observable satellites with no detectable
tails, including streams that would be mistaken as intact satellites. We find
that many surviving satellites have tidal tails. This suggests that for full
consistency, comparisons between surviving satellites in FIRE and in the Milky
Way should include dwarf galaxy stellar streams with surviving progenitors
(e.g. Sgr).

Figure 6: Most recent pericenters and apocenters of the FIRE and Milky Way
stellar streams. The black crosses indicate the Milky Way dwarf galaxy
streams, where $r_{\rm peri}$ and $r_{\rm apo}$ are taken from Li et al.
(2022). The circles represent the FIRE streams with fully disrupted
progenitors, and the triangles indicate FIRE streams with surviving
progenitors. Among the Milky Way streams, Sgr (largest pericenter and
apocenter) is the only one with a known surviving progenitor. The color
indicates lookback time since accretion. The left panel includes only
detectable streams, and the right panel includes the full population of
streams in FIRE. The dashed line indicates a circular orbit (equal pericenter
and apocenter). Figure 7: Frequency of systems as a function of lookback time
since accretion. Each line indicates the percentage of systems in each time
bin classified as an intact satellite (purple), stream with a surviving
progenitor (dark blue), stream without a surviving progenitor (light blue), or
phase-mixed (green). The plotted values are the means of the percentages
across the 13 halos. Figure 8: Orbital eccentricity of satellites in FIRE. The
blue histogram includes satellites with tidal tails, classified as stellar
streams, and the green histogram includes only satellites with no evidence of
tidal disruption. As expected, tidally disrupting satellites are on slightly
more radial orbits than intact satellites. Figure 9: Distributions of
pericenters (upper) and apocenters (lower) of systems in FIRE and the Milky
Way. The black histograms indicate the Milky Way dwarf galaxy streams. The
solid blue line represents the most recent pericenter and apocenter of the
FIRE streams, which is most analogous to the values measured for the Milky
Way. For comparison, we plot the distributions of the overall minimum
(maximum) pericenter (apocenter) across all passages with the dashed blue
lines. The purple histograms represent surviving satellites in FIRE (with or
without tidal tails), and green represents phase-mixed systems.

###  4.3 Orbits

Finally, we consider the orbits of stellar streams in FIRE and the Milky Way.
Figure 6 shows the pericenters and apocenters of the FIRE streams (with and
without surviving progenitors), in comparison to the Milky Way dwarf galaxy
streams. The left panel shows only the detectable FIRE streams and the right
panel shows the full population of streams. Here, we plot the most recent
pericenter and apocenter, for consistency with the values obtained by fitting
orbits of Milky Way stellar streams. The FIRE streams are colored by lookback
time at accretion. The triangles indicate streams with surviving progenitors,
and circles are streams with fully disrupted progenitors.

We find that the distributions of pericenters and apocenters of streams in the
Milky Way and FIRE are largely inconsistent, even once taking detectability
into account. Many FIRE satellites are disrupting to form streams at large
pericenters (out to $>100\mathrm{\,kpc}$), in contrast to the Milky Way
streams, which have pericenters within $30\mathrm{\,kpc}$. In addition, we
find that the FIRE streams have relatively large apocenters, all
$>40\mathrm{\,kpc}$. The FIRE streams with fully disrupted progenitors
(circles) tend to have smaller pericenters ($r_{\rm peri}\lesssim
60\mathrm{\,kpc}$) than those with surviving progenitors (triangles). This is
more consistent with the Milky Way streams, of which only Sgr has a surviving
progenitor. However, we note that streams with surviving progenitors tend to
have detectable tidal tails only at smaller distances (and correspondingly,
smaller apocenters) due to the relatively small fraction of stellar mass in
their tidal tails.

The method of fitting orbits to the Milky Way streams is discussed in Section
2.1 and to the FIRE streams in Section 2.2. The primary difference between the
two methods is that we calculate the orbits of the FIRE streams by tracing the
positions of stars back through the saved simulation snapshots, thereby
accounting for the full time-dependence of the host galaxy potential. However,
we integrate the orbits of the Milky Way streams in a time-independent
potential. We examine the implications of this assumption in greater detail in
Appendix C. We find that the resulting uncertainties are not sufficient to
account for the qualitative difference observed between the pericenters and
apocenters of streams in FIRE and the Milky Way.

A small number of FIRE streams do overlap with the Milky Way population. The
four streams on the most similar orbits to the Milky Way streams are not
tightly clustered in stellar mass or accretion time, but are all from the m12c
and m12i simulations. These two galaxies have a relatively large number of
streams and, on average, streams with smaller pericenters and apocenters, than
the other simulated systems. However, even these two simulations have a
majority of streams with larger pericenters and apocenters than those seen in
the Milky Way.

In addition, there is some difference between the orbits of streams in the
Latte (isolated Milky Ways) and ELVIS (Local Group pairs) simulations. In
particular, the streams with the largest pericenters are from the ELVIS
simulations. Interestingly, Samuel et al. (2020) found that the population of
intact satellites in the Milky Way is, on average, more concentrated in radial
distance than those in FIRE. Perhaps some feature of the Milky Way, such as
its unusual assembly history (Evans et al., 2020) or its disk size, has led to
a more radially concentrated population of satellites at all stages of
disruption. Additional simulations, as well as observations of stream
populations around external galaxies (e.g. Carlin et al., 2016; Pearson et
al., 2019), will enable studies of the effect of host halo properties and
environment on populations of stellar streams.

We note that the detectable streams, on average, were accreted more recently
than the undetectable streams. Many of the early-accreted, undetectable
streams have relatively small pericenters, but are undetectable due to their
large widths and low surface brightnesses. On the other hand, many of the
undetectable streams with later accretion times have large apocenters, and are
undetectable primarily due to their large distances.

Li et al. (2022) found that more streams are on prograde orbits than
retrograde orbits, relative to the Galactic disk in the Milky Way (only two
out of the 12 studied are on retrograde orbits). Among the FIRE halos, we find
a range of stream orbital orientations. Some have an excess of prograde or
retrograde streams, while some do not. The effect of host properties,
particularly accretion history, on the orbital distributions of stream
populations in cosmological simulations will be explored in greater detail in
future work.

Figure 7 shows the accretion times of systems (detectable and undetectable) at
different stages of disruption in FIRE. The purple line is intact satellites
with no tidal tails, dark blue is streams with a surviving progenitor, light
blue is streams without a surviving progenitor, and green is phase-mixed
systems. As expected, intact satellites dominate the population at recent
accretion times and phase-mixed systems dominate at early accretion times, and
stellar streams lie in between. There is no clear difference between the
accretion times of streams with and without surviving progenitors, suggesting
that orbit, rather than time since accretion, primarily determines the
survival of the stream progenitor. Similarly, we find differences in orbits
between satellites with and without tidal tails. Figure 8 shows the
distributions of orbital eccentricities of intact and disrupting satellites.
Those that are classified as stellar streams have, on average, a larger
orbital eccentricity, suggesting that systems on more radial orbits are more
likely to form tidal tails.

Figure 9 shows a comparison of the distributions of pericenters and apocenters
of these different systems. In black are the Milky Way dwarf galaxy streams.
In solid blue are the FIRE streams, as in Figure 6. The dashed blue lines are
the largest (smallest) among all pericenters (apocenters) of each of the FIRE
streams. Even the overall minimum pericenters are largely inconsistent with
those measured in the Milky Way. In purple are the surviving satellites in
FIRE (with or without tidal tails). The satellite orbits are presented in
Santistevan et al. (in prep.). The pericenters are calculated by searching for
local minima in satellite distance from their Milky Way-mass host in an
adaptive time window, during the time after the satellite has first crossed
the virial radius of the host. The authors then fit a cubic spline within a
large enough time window, and save the minima of the spline-interpolated
distances to ensure that these pericenters are real, and not artificial due to
noise. In green are the orbits of the phase-mixed systems in FIRE. Phase-mixed
systems are classified as systems failing the median velocity dispersion
criterion for stream classification, as described in Section 2.2. These
pericenters and apocenters are calculated in the same way as for the FIRE
streams, described above. However, for these systems, we take the median of
all stars, without first selecting the highest density regions. We find that
the phase-mixed systems in FIRE have pericenters and apocenters that are most
consistent with those measured for the Milky Way dwarf galaxy streams.
Therefore, although the number and mass distribution of streams in the Milky
Way and FIRE are consistent, when taking into consideration detectability, the
orbits are still inconsistent, and may be suggesting that FIRE is disrupting
and phase-mixing satellites at a higher rate than our own Galaxy. We discuss
the implications of this discrepancy and plans for future studies of tidal
disruption in FIRE in Section 5.

##  5 Discussion

We find that, when taking into account detectability, the number and stellar
mass distributions of streams around Milky Way analogs in the FIRE simulations
are consistent with observations. However, we find a discrepancy in the
distributions of orbital parameters. In particular, FIRE streams disrupt at a
larger range of pericenters than observed in the Milky Way, and survive only
at larger apocenters. Despite this disagreement, it is valuable to discuss the
predicted population of undetectable streams. In the future, these predictions
will either highlight further conflict between simulations and observations,
or facilitate the continued discovery of stellar streams. Here, we discuss the
implications of the predicted population of undetectable high-stellar mass
streams, predictions for future stream discovery in the Milky Way, and
possible explanations for the discrepancies between the stream populations in
the Milky Way and FIRE.

###  5.1 Undetected Streams

We find that 64 out of 96 stellar streams, across the 13 halos, would be
undetected. The median number of undetectable streams per halo, in this
stellar mass range, is 5 out of 8. In addition, we find that 42 out of 64
stream progenitors (median 3 out of 5) would be mistaken for intact satellites
given current observations with deep photometric surveys.

Figure 10: Upper: Mean number of satellites with detectable tidal tails (dark
blue), undetectable tidal tails (medium blue), and no tidal tails (light
blue), binned by distance from the host galaxy. Lower: Mean percentage of
satellites with detectable (dark blue) and undetectable (medium blue) tidal
tails. The remaining percentage are the satellites that are fully intact and
have no tidal tails. These values are the mean across the 13 FIRE halos of
each ratio, rather than the ratio of the means plotted above. The error bars
represent the $1\sigma$ scatter between halos in the total number or
percentage of satellites with tidal tails (detectable or undetectable) in each
distance bin.

The FIRE simulations, if accurately reproducing tidal disruption in Milky Way-
like galaxies, therefore suggest that the population of high-stellar mass
Milky Way streams is incomplete, and that an undetected population of high-
stellar mass, yet low-surface brightness, streams may exist in the Milky Way
halo. In addition, they suggest that many systems we have classified as intact
satellites may in fact be undergoing tidal disruption and have yet-undetected
tidal tails.

Figure 10 shows the distribution of satellites that have detectable and
undetectable tidal tails as a function of distance at $z=0$ from the host
galaxy. The upper panel shows the number of satellites with detectable,
undetectable, or no tidal tails, and the bottom panel shows the percentage of
satellites in each distance bin with detectable or undetectable tails. We find
that at distances of $50\mathchar 45\relax 200\mathrm{\,kpc}$, more than
$50\%$ of satellites have tidal tails, many of which remain undetectable.

Several Milky Way satellites do show signs of tidal disruption. Among the
stream sample ($M_{*}\gtrsim 5\times 10^{5}\mathrm{\,M_{\odot}}$) considered
here, Sgr is the only one with a known surviving progenitor. Below this
stellar mass range, the Tucana III stellar stream (Drlica-Wagner et al., 2015;
Shipp et al., 2018) also has a surviving progenitor with two extending tidal
tails. More ambiguous are the Milky Way satellites without clear tidal tails,
but that otherwise show evidence of tidal disruption. For example, Antlia II
has a large size, low density, and a velocity gradient consistent with
predictions of tidal disruption (Torrealba et al., 2019; Ji et al., 2021;
Vivas et al., 2022). With a stellar mass of
${\sim}\,10^{6}\mathrm{\,M_{\odot}}$ and a distance of $\sim
130\mathrm{\,kpc}$ (Ji et al., 2021), Antlia II would fall within the
$50\mathchar 45\relax 100\mathrm{\,kpc}$ bin of Figure 10, where
${\sim}\,50\mathchar 45\relax 90\%$ of satellites are predicted to have
undetected tidal tails. Crater II, a classical satellite just below the mass
range considered here ($M_{*}=10^{5.55}\mathrm{\,M_{\odot}}$) at a distance of
117.5 $\mathrm{\,kpc}$ (Ji et al., 2021), also has strong evidence of tidal
disruption, including a low velocity dispersion and low surface brightness
(Sanders et al., 2018; Fu et al., 2019; Ji et al., 2021; Borukhovetskaya et
al., 2022). Pace et al. (2022) highlight five additional Milky Way dwarf
spheroidals as possibly tidally disrupting. They compare the half-light radius
of each satellite to the Jacobi radius at pericenter and find that Boötes I,
Boötes III, Grus II, Segue 2, and Tucana IV have densities and pericenters
that make them likely candidates for tidal disruption. However, all of these
satellites are below the stellar mass range considered in this work.
Observations have also provided evidence of extended stellar halos around
classical dwarfs, such as Sculptor (Westfall et al., 2006) and Carina (Muñoz
et al., 2006). All of these observations suggest that the Milky Way dwarf
galaxies may be more tidally disrupted than was originally known, and motivate
further searches for evidence of tidal features around known satellites.

###  5.2 Predictions for Future Detectability

Figure 11: Mean number of detectable high-stellar mass streams in LSST as a
function of surface brightness limit. The green curve represents the number of
detectable streams with mock LSST observations. The black point is the current
number of detectable streams in the Milky Way at the DES surface brightness
limit, in this stellar mass range. These results are consistent with previous
predictions (Sharma et al., 2012).

The Vera C. Rubin Observatory Legacy Survey of Space and Time (LSST; LSST
Science Collaboration, 2009; Ivezić et al., 2019) will enable the discovery of
even more low-surface brightness and distant stellar streams throughout the
Milky Way halo. LSST is a photometric survey similar to DES, but covering more
of the sky ($18,000\deg^{2}$) and extending to fainter magnitudes ($r<27.5$).
In order to estimate the near-future detectability of the FIRE streams, we
produce mock LSST observations. We follow the procedure outlined in Section 3,
but sample magnitudes in the LSST $ugrizY$ bands, within the range $17<r<27.5$
and using photometric errors estimated from the LSST DESC DC2 simulated sky
survey (LSST Dark Energy Science Collaboration et al.(2021)LSST Dark Energy
Science Collaboration (LSST DESC), Abolfathi, Alonso, Armstrong, Aubourg,
Awan, Babuji, Bauer, Bean, Beckett, Biswas, Bogart, Boutigny, Chard, Chiang,
Claver, Cohen-Tanugi, Combet, Connolly, Daniel, Digel, Drlica-Wagner, Dubois,
Gangler, Gawiser, Glanzman, Gris, Habib, Hearin, Heitmann, Hernandez, Hložek,
Hollowed, Ishak, Ivezić, Jarvis, Jha, Kahn, Kalmbach, Kelly, Kovacs, Korytov,
Krughoff, Lage, Lanusse, Larsen, Le Guillou, Li, Longley, Lupton, Mandelbaum,
Mao, Marshall, Meyers, Moniez, Morrison, Nomerotski, O’Connor, Park, Park,
Peloton, Perrefort, Perry, Plaszczynski, Pope, Rasmussen, Reil, Roodman,
Rykoff, Sánchez, Schmidt, Scolnic, Stubbs, Tyson, Uram, Villarreal, Walter,
Wiesner, Wood-Vasey, & Zuntz, LSST DESC).

Due to the difficulty in estimating the stream surface brightness limit in
LSST before the availability of real survey data, we estimate the detectable
number as a function of surface brightness limit. In Figure 11, we show the
predicted detectable number of streams as a function of surface brightness
limit with LSST photometry. The green curve represents the mean number of
detectable streams per halo in the LSST mock observations, and the black point
represents the currently detectable number of streams in this stellar mass
range ($M_{*}\gtrsim 5\times 10^{5}\mathrm{\,M_{\odot}}$) in the Milky Way,
given the limit of DES. The surface brightness limit for stream detectability
with LSST remains uncertain, but will be fainter than that of DES due to the
increased survey depth and improved photometric precision. As stream searches
are conducted in real LSST data, we will be able to determine detectability
limits and thereby the number of streams that should be detected in order to
remain consistent with the FIRE simulations.

If these streams are not detected as we approach fainter surface brightness
limits for stream detection, that will indicate an intriguing conflict between
the population of tidal remnants in FIRE and in the Milky Way.

###  5.3 Inconsistencies Between FIRE and the Milky Way

Despite some similarities, important discrepancies remain between the
populations of stellar streams in FIRE and the Milky Way. The pericenters and
apocenters of the detectable FIRE streams are larger than those measured for
Milky Way streams, on average. Furthermore, the consistency of the number and
stellar mass distributions rely on the near-future discovery of a population
of high-stellar mass, low-surface brightness streams in upcoming surveys.

The formation of stellar streams at large pericenters, and the phase-mixing of
systems on orbits similar to the Milky Way stellar streams (Figure 9) may
suggest that the FIRE simulations are over-disrupting satellites. More
precisely, FIRE may be disrupting and phase-mixing systems too quickly and/or
on the wrong orbits. This would have implications for other comparisons
between satellite populations in FIRE and the Milky Way. In order to examine
why systems are disrupting at large distances, we compare the Jacobi radii and
half-light radii of these systems at pericenter. Figure 12 shows the density
within the half-light radius of each satellite (intact satellites and stream
progenitors) relative to two times the average enclosed density of the host
galaxy (gray line). This boundary separates satellites with a Jacobi radius
larger (above the gray line) or smaller (below) than their half-light radius.
We find that many FIRE satellites are disrupting with relatively high
densities. However, while these satellites have relatively small half-light
radii, they also have an extended stellar halo and therefore a large fraction
of their stellar mass (in some cases up to $40\%$) lies outside their Jacobi
radius, even at pericenters of $100\mathrm{\,kpc}$. These are the stars that
make up their tidal tails at $z=0$.

Figure 12: Comparison between the half-light radii and tidal radii of FIRE
intact satellites and stream progenitors. The gray line represents twice the
average enclosed density at pericenter radius (the shaded band represents the
scatter between hosts). Systems with densities below the gray line have tidal
radii (Jacobi radii) smaller than their half-light radii and are expected to
disrupt, and systems above the gray line have tidal radii larger than their
half-light radii and are not expected to disrupt. The points are colored by
fraction of stellar mass in their tidal tails. Systems with lower densities
have a larger fraction of disrupted material, however many systems are
disrupting with large relative densities at pericenter.

The sizes of low-mass galaxies are sensitive to numerical effects in
simulations. Binney & Knebe (2002) found that simulations with two species of
particles with a large relative mass ratio may be affected by two-body
relaxation. This process leads energy to transfer from the more massive
particles (in this case, dark matter) to the less massive particles (stars).
This would lead the dark matter to sink to the bottom of the potential well,
while the distribution of stars is artificially extended. The effect of this
process on galaxy sizes is studied in greater detail in Ludlow et al. (2019).
If the orbital discrepancy were due solely to resolution effects, we may
expect to see a difference between the orbits of the streams from the Latte
and ELVIS simulations, due to the factor of two difference in resolution.
However, we do not find that the ELVIS streams are more consistent with Milky
Way observations. In addition, Samuel et al. (2020) tested the convergence of
the radial profiles of satellites in FIRE and found consistent results across
resolutions. Nevertheless, future studies of stream populations in higher
resolution cosmological simulations will provide valuable insight into the
role of numerical resolution in stream formation. For further discussion of
numerical disruption in FIRE, see Santistevan et al. (in prep.).

Tidal disruption of satellites in simulations may also be affected by the
implementation of baryonic physics models. The FIRE-2 cosmological simulations
of isolated galaxies at $M_{*}{\sim}\,10^{4}\mathchar 45\relax
10^{9}\mathrm{\,M_{\odot}}$ at high baryonic mass resolution ($30\mathchar
45\relax 500\mathrm{\,M_{\odot}}$) generally agree well with observed galaxy
half-stellar-mass radii (Fitts et al., 2017; Wheeler et al., 2019; Richstein
et al., 2022; Shen et al., 2022). That said, at $M_{*}{\sim}\,10^{7}\mathchar
45\relax 10^{10}\mathrm{\,M_{\odot}}$, FIRE-2 galaxies generally experience
bursty star formation, and the stellar feedback during these bursts drives out
significant gas mass, which over time puffs out the galaxy sizes (El-Badry et
al., 2016; Chan et al., 2018). While this leads to good agreement with the
significant population observed to have large stellar radii (such as ultra-
diffuse galaxies), it means that FIRE-2 simulations do not reproduce the most
compact (densest) galaxies observed at these masses (Chan et al., 2018;
Garrison-Kimmel et al., 2019a; Rohr et al., 2022). In other words, at
$M_{*}{\sim}\,10^{7}\mathchar 45\relax 10^{10}\mathrm{\,M_{\odot}}$, the
FIRE-2 simulations produce too many galaxies with large stellar sizes,
regardless of resolution. At lower masses, ($M_{*}{\sim}\,10^{4}\mathchar
45\relax 10^{7}\mathrm{\,M_{\odot}}$), and sufficiently high-resolution
($30\mathchar 45\relax 500\mathrm{\,M_{\odot}}$), the FIRE-2 simulations form
galaxy sizes that agree with observations, but as Shen et al. (2022) noted, at
the necessarily lower resolution of the FIRE Milky Way-mass simulations
($3500\mathchar 45\relax 7100\mathrm{\,M_{\odot}}$), satellite galaxies at
$M_{*}\lesssim 10^{7}\mathrm{\,M_{\odot}}$ are systematically larger than
observed. Indeed, a recent re-simulation of one of the Milky Way-mass galaxies
at 8 times higher mass resolution ($880\mathrm{\,M_{\odot}}$) confirms that,
in the current simulations at $7100\mathrm{\,M_{\odot}}$ resolution, satellite
galaxy sizes are well-converged at $M_{*}\gtrsim 10^{7}\mathrm{\,M_{\odot}}$.
However, below $10^{7}\mathrm{\,M_{\odot}}$, the satellite sizes are too large
because of limited resolution (Wetzel et al. in prep.). In summary, this
combination of physical and numerical effects likely causes the satellite
galaxies in the Milky Way-mass simulations we examine here to be larger (on
average) than observed and thus may contribute to them disrupting into streams
at too-large of Galactocentric distances and/or to phase-mix too quickly once
disrupted (Jiang et al., 2019). In addition, the Milky Way analogs simulated
in FIRE are known to have later disk-settling times than the Milky Way
(Gurvich et al., 2022), perhaps leading to more chaotic inner galaxies than
that of the Milky Way. This in turn may lead satellites with smaller orbital
radii to disrupt and ultimately phase-mix more quickly than in our own Galaxy.

Future studies of stream populations in other simulations will help to further
uncover the effects of numerical resolution and feedback prescriptions on
stream formation, including analysis of streams in the higher-resolution
version of m12i (Triple Latte; Wetzel et al. in prep.). In addition, other
suites of cosmological simulations, such as the Auriga simulations (Grand et
al., 2017), with independent implementations of feedback physics, will provide
important comparisons to the results presented here. Grand et al. (2021)
conducted a comparison of the surviving satellite population in the highest
resolution Auriga simulation ($m_{\rm b}=880\mathrm{\,M_{\odot}}$, comparable
to Triple Latte) to their standard resolution simulations ($m_{\rm
b}=10^{4}\mathchar 45\relax 10^{5}\mathrm{\,M_{\odot}}$) and found that
${\sim}\,1/6$ of the satellites present at high-resolution are artificially
disrupted in the lower resolution simulations. Similar studies of stream
populations will provide further insight into the questions raised in this
work, and enable stronger tests of satellite disruption in our Galaxy and
cosmological simulations.

If the simulations considered in this paper are in fact over-disrupting
satellite galaxies, that will have implications for the comparisons of the
number and stellar mass distributions of streams as well. However, it is
unclear whether correcting for this over-disruption will lead to an increased
discrepancy between the numbers of simulated and observed stellar streams. If
the source of over-disruption is resolved, some systems that we have counted
as streams may be converted to intact satellites and, at the same time,
systems that we have classified as phase-mixed may instead form coherent tidal
streams. It is therefore necessary to conduct similar studies of stream
populations across simulations to study the full extent of the effect of
numerical resolution and feedback physics on stellar stream populations.

Another possible explanation is that the Milky Way dwarf galaxy streams
considered in this work are in fact the highest-density, most coherent
components of largely phase-mixed systems. We find that the systems classified
as phase-mixed in FIRE are on orbits more consistent with those measured for
the Milky Way stellar streams. Many of these phase-mixed systems do have
complex morphologies and include components that, when detected in the Milky
Way, could be classified as stellar streams. However, even these high-density
regions have relatively low surface brightnesses. In addition, this
explanation would not resolve the fact that the FIRE simulations are forming
streams at larger pericenters and apocenters than has been observed in the
Milky Way. Future observations of low-surface brightness features in the Milky
Way’s stellar halo will reveal whether the Milky Way dwarf galaxy streams are
in fact part of larger extended and diffuse structures that are more
consistent with the phase-mixed systems in FIRE.

##  6 Conclusion

We present the first comparison of detected dwarf galaxy streams around the
Milky Way to detectable streams in cosmological simulations. We consider the
full population of known Milky Way dwarf galaxy streams and compare them to an
analogous population identified around Milky Way-like galaxies in the FIRE
simulations.

We produce mock DES observations of the FIRE streams and estimate the
detectability of their tidal tails and their progenitors. We find that, when
taking into account detectability, the number and stellar mass distribution of
these streams is consistent between observations and simulations, resolving
the “too-big-to-fail” problem in stellar streams proposed by Li et al. (2022).

However, the orbital distributions of stellar streams differ between
observations and simulations. The Milky Way streams have small apocenters and
pericenters relative to those in the FIRE simulations. This discrepancy could
be due to properties of the Milky Way, the implementation of feedback physics
in FIRE, the resolution of the Latte and ELVIS simulations, or by other
discrepancies between the baryonic and dark matter physics that dictates tidal
disruption in our Universe and their implementation in the FIRE simulations.

Studies of additional cosmological simulations, with higher resolutions and
alternative implementations of baryonic or dark matter physics, will allow us
to disentangle simulation effects from new physics. In addition, semi-analytic
modeling of stream populations around Milky Way-like hosts may be used to
constrain the dependence of the stream population on simulation physics, as
well as host halo mass, disk properties, accretion history, and environment.
Furthermore, with high-resolution N-body simulations of individual streams, we
can test the detailed effects of changes to underlying physics models and host
properties on stream disruption.

Future observations of Milky Way stellar streams with surveys such as LSST, as
well as the Nancy Grace Roman Space Telescope (Spergel et al., 2013) and
Euclid (Laureijs et al., 2011), will enable further tests of the consistency
of the populations of tidal remnants in the Milky Way and the FIRE
simulations. In particular, the FIRE simulations predict a population of
undetected high-stellar mass, low-surface brightness stellar streams, as well
as yet-undetected tidal tails around several known satellite galaxies. Many of
these systems are predicted to be detectable in LSST. In addition, these
imaging surveys will uncover populations of stellar streams around external
galaxies (e.g. Carlin et al., 2016; Pearson et al., 2019) and enable similar
tests with a larger sample of galaxies.

This work is the first detailed comparison of stream populations in the Milky
Way and cosmological simulations. Additional studies, involving alternative
cosmological simulations, semi-analytic modeling, high-resolution N-body
simulations, and additional observations will further disentangle the effects
of numerics, baryonic physics, and dark matter on the population-level
properties of stellar streams.

##  7 Acknowledgements

We thank Sidney Mau and Alex Drlica-Wagner for help providing photometric
error estimates for DC2.

This work used the Extreme Science and Engineering Discovery Environment
(XSEDE), which is supported by National Science Foundation grant number
ACI-1548562. This work used the Stampede-2 allocation number PHY210118 to
analyze the simulations. We generated the FIRE simulations using: XSEDE,
supported by NSF grant ACI-1548562; Blue Waters, supported by the NSF;
Frontera allocations AST21010 and AST20016, supported by the NSF and TACC;
Pleiades, via the NASA HEC program through the NAS Division at Ames Research
Center.

NP and RES gratefully acknowledge support from NASA grant 19-ATP19-0068. RES
additionally acknowledges support from the Research Corporation through the
Scialog Fellows program on Time Domain Astronomy, from NSF grant AST-2007232,
and from HST-AR-15809 from the Space Telescope Science Institute (STScI),
which is operated by AURA, Inc., under NASA contract NAS5-26555. IBS received
support from NASA, through FINESST grant 80NSSC21K1845. AW received support
from: NSF via CAREER award AST-2045928 and grant AST-2107772; NASA ATP grant
80NSSC20K0513; HST grants AR-15809, GO-15902, GO-16273 from STScI. TSL
acknowledges financial support from Natural Sciences and Engineering Research
Council of Canada (NSERC) through grant RGPIN-2022-04794.

For the purpose of open access, the author has applied a Creative Commons
Attribution (CC BY) licence to any Author Accepted Manuscript version arising
from this submission.

## References

  * Abbott et al. (2021) Abbott, T. M. C., Adamów, M., Aguena, M., et al. 2021, ApJS, 255, 20, doi: 10.3847/1538-4365/ac00b3
  * Arora et al. (2022) Arora, A., Sanderson, R. E., Panithanpaisal, N., et al. 2022, arXiv e-prints, arXiv:2207.13481.  https://arxiv.org/abs/2207.13481
  * Astropy Collaboration et al. (2013) Astropy Collaboration, Robitaille, T. P., Tollerud, E. J., et al. 2013, A&A, 558, A33, doi: 10.1051/0004-6361/201322068
  * Astropy Collaboration et al. (2018) Astropy Collaboration, Price-Whelan, A. M., Sipőcz, B. M., et al. 2018, AJ, 156, 123, doi: 10.3847/1538-3881/aabc4f
  * Bechtol et al. (2015) Bechtol, K., Drlica-Wagner, A., Balbinot, E., et al. 2015, ApJ, 807, 50, doi: 10.1088/0004-637X/807/1/50
  * Behroozi et al. (2013) Behroozi, P. S., Wechsler, R. H., & Wu, H.-Y. 2013, ApJ, 762, 109, doi: 10.1088/0004-637X/762/2/109
  * Bellardini et al. (2021) Bellardini, M. A., Wetzel, A., Loebman, S. R., et al. 2021, MNRAS, 505, 4586, doi: 10.1093/mnras/stab1606
  * Binney & Knebe (2002) Binney, J., & Knebe, A. 2002, MNRAS, 333, 378, doi: 10.1046/j.1365-8711.2002.05400.x
  * Bland-Hawthorn & Gerhard (2016) Bland-Hawthorn, J., & Gerhard, O. 2016, ARA&A, 54, 529, doi: 10.1146/annurev-astro-081915-023441
  * Bonaca et al. (2018) Bonaca, A., Hogg, D. W., Price-Whelan, A. M., & Conroy, C. 2018, ArXiv e-prints.  https://arxiv.org/abs/1811.03631
  * Borukhovetskaya et al. (2022) Borukhovetskaya, A., Navarro, J. F., Errani, R., & Fattahi, A. 2022, Monthly Notices of the Royal Astronomical Society, 512, 5247, doi: 10.1093/mnras/stac653
  * Bovy (2014) Bovy, J. 2014, ApJ, 795, 95, doi: 10.1088/0004-637X/795/1/95
  * Bovy et al. (2017) Bovy, J., Erkal, D., & Sanders, J. L. 2017, MNRAS, 466, 628, doi: 10.1093/mnras/stw3067
  * Boylan-Kolchin et al. (2011) Boylan-Kolchin, M., Bullock, J. S., & Kaplinghat, M. 2011, MNRAS, 415, L40, doi: 10.1111/j.1745-3933.2011.01074.x
  * Boylan-Kolchin et al. (2012) —. 2012, MNRAS, 422, 1203, doi: 10.1111/j.1365-2966.2012.20695.x
  * Bressan et al. (2012) Bressan, A., Marigo, P., Girardi, L., et al. 2012, MNRAS, 427, 127, doi: 10.1111/j.1365-2966.2012.21948.x
  * Buck et al. (2019) Buck, T., Macciò, A. V., Dutton, A. A., Obreja, A., & Frings, J. 2019, MNRAS, 483, 1314, doi: 10.1093/mnras/sty2913
  * Bullock & Boylan-Kolchin (2017) Bullock, J. S., & Boylan-Kolchin, M. 2017, ARA&A, 55, 343, doi: 10.1146/annurev-astro-091916-055313
  * Carlberg (2009) Carlberg, R. G. 2009, ApJ, 705, L223, doi: 10.1088/0004-637X/705/2/L223
  * Carlberg (2012) —. 2012, ApJ, 748, 20, doi: 10.1088/0004-637X/748/1/20
  * Carlin et al. (2016) Carlin, J. L., Beaton, R. L., Martínez-Delgado, D., & Gabany, R. J. 2016, in Astrophysics and Space Science Library, Vol. 420, Tidal Streams in the Local Group and Beyond, ed. H. J. Newberg & J. L. Carlin, 219, doi: 10.1007/978-3-319-19336-6_9
  * Carlsten et al. (2020) Carlsten, S. G., Greene, J. E., Peter, A. H. G., Greco, J. P., & Beaton, R. L. 2020, ApJ, 902, 124, doi: 10.3847/1538-4357/abb60b
  * Chambers et al. (2016) Chambers, K. C., Magnier, E. A., Metcalfe, N., et al. 2016, arXiv e-prints, arXiv:1612.05560.  https://arxiv.org/abs/1612.05560
  * Chan et al. (2018) Chan, T. K., Kereš, D., Wetzel, A., et al. 2018, MNRAS, 478, 906, doi: 10.1093/mnras/sty1153
  * Cunningham et al. (2021) Cunningham, E. C., Sanderson, R. E., Johnston, K. V., et al. 2021, arXiv e-prints, arXiv:2110.02957.  https://arxiv.org/abs/2110.02957
  * DES Collaboration (2005) DES Collaboration. 2005, ArXiv Astrophysics e-prints
  * DES Collaboration et al. (2018) DES Collaboration, Abbott, T. M. C., Abdalla, F. B., et al. 2018, The Astrophysical Journal Supplement Series, 239, 18, doi: 10.3847/1538-4365/aae9f0
  * Dey et al. (2018) Dey, A., Schlegel, D. J., Lang, D., et al. 2018, ArXiv e-prints.  https://arxiv.org/abs/1804.08657
  * Drlica-Wagner et al. (2015) Drlica-Wagner, A., Bechtol, K., Rykoff, E. S., et al. 2015, ApJ, 813, 109, doi: 10.1088/0004-637X/813/2/109
  * Drlica-Wagner et al. (2020) Drlica-Wagner, A., Bechtol, K., Mau, S., et al. 2020, ApJ, 893, 47, doi: 10.3847/1538-4357/ab7eb9
  * Drlica-Wagner et al. (2021) Drlica-Wagner, A., Carlin, J. L., Nidever, D. L., et al. 2021, ApJS, 256, 2, doi: 10.3847/1538-4365/ac079d
  * D’Souza & Bell (2022) D’Souza, R., & Bell, E. F. 2022, MNRAS, 512, 739, doi: 10.1093/mnras/stac404
  * Du et al. (2018) Du, X., Schwabe, B., Niemeyer, J. C., & Bürger, D. 2018, Phys. Rev. D, 97, 063507, doi: 10.1103/PhysRevD.97.063507
  * El-Badry et al. (2016) El-Badry, K., Wetzel, A., Geha, M., et al. 2016, ApJ, 820, 131, doi: 10.3847/0004-637X/820/2/131
  * Epanechnikov (1969) Epanechnikov, V. 1969, Theory of Probability and its Applications, 14, 153, doi: 10.1137/1114019
  * Erkal & Belokurov (2015) Erkal, D., & Belokurov, V. 2015, MNRAS, 454, 3542, doi: 10.1093/mnras/stv2122
  * Erkal et al. (2019) Erkal, D., Belokurov, V., Laporte, C. F. P., et al. 2019, MNRAS, 487, 2685, doi: 10.1093/mnras/stz1371
  * Errani et al. (2015) Errani, R., Penarrubia, J., & Tormen, G. 2015, MNRAS, 449, L46, doi: 10.1093/mnrasl/slv012
  * Evans et al. (2020) Evans, T. A., Fattahi, A., Deason, A. J., & Frenk, C. S. 2020, MNRAS, 497, 4311, doi: 10.1093/mnras/staa2202
  * Fitts et al. (2017) Fitts, A., Boylan-Kolchin, M., Elbert, O. D., et al. 2017, MNRAS, 471, 3547, doi: 10.1093/mnras/stx1757
  * Fu et al. (2019) Fu, S. W., Simon, J. D., & Alarcón Jara, A. G. 2019, ApJ, 883, 11, doi: 10.3847/1538-4357/ab3658
  * Gaia Collaboration et al. (2016) Gaia Collaboration, Prusti, T., de Bruijne, J. H. J., et al. 2016, A&A, 595, A1, doi: 10.1051/0004-6361/201629272
  * Gaia Collaboration et al. (2018) Gaia Collaboration, Brown, A. G. A., Vallenari, A., et al. 2018, A&A, 616, A1, doi: 10.1051/0004-6361/201833051
  * Gaia Collaboration et al. (2021) —. 2021, A&A, 649, A1, doi: 10.1051/0004-6361/202039657
  * Garrison-Kimmel et al. (2017) Garrison-Kimmel, S., Wetzel, A., Bullock, J. S., et al. 2017, MNRAS, 471, 1709, doi: 10.1093/mnras/stx1710
  * Garrison-Kimmel et al. (2019a) Garrison-Kimmel, S., Hopkins, P. F., Wetzel, A., et al. 2019a, MNRAS, 487, 1380, doi: 10.1093/mnras/stz1317
  * Garrison-Kimmel et al. (2019b) Garrison-Kimmel, S., Wetzel, A., Hopkins, P. F., et al. 2019b, MNRAS, 489, 4574, doi: 10.1093/mnras/stz2507
  * Gibbons et al. (2014) Gibbons, S. L. J., Belokurov, V., & Evans, N. W. 2014, MNRAS, 445, 3788, doi: 10.1093/mnras/stu1986
  * Grand et al. (2017) Grand, R. J. J., Gómez, F. A., Marinacci, F., et al. 2017, MNRAS, 467, 179, doi: 10.1093/mnras/stx071
  * Grand et al. (2021) Grand, R. J. J., Marinacci, F., Pakmor, R., et al. 2021, MNRAS, 507, 4953, doi: 10.1093/mnras/stab2492
  * Grillmair & Carlin (2016) Grillmair, C. J., & Carlin, J. L. 2016, in Astrophysics and Space Science Library, Vol. 420, Tidal Streams in the Local Group and Beyond, ed. H. J. Newberg & J. L. Carlin, 87, doi: 10.1007/978-3-319-19336-6_4
  * Gurvich et al. (2022) Gurvich, A. B., Stern, J., Faucher-Giguère, C.-A., et al. 2022, arXiv e-prints, arXiv:2203.04321.  https://arxiv.org/abs/2203.04321
  * Hasselquist et al. (2019) Hasselquist, S., Carlin, J. L., Holtzman, J. A., et al. 2019, ApJ, 872, 58, doi: 10.3847/1538-4357/aafdac
  * Hopkins (2015) Hopkins, P. F. 2015, MNRAS, 450, 53, doi: 10.1093/mnras/stv195
  * Hopkins et al. (2013) Hopkins, P. F., Narayanan, D., & Murray, N. 2013, Mon. Not. Roy. Astron. Soc., 4, 432, doi: 10.1093/mnras/stt723
  * Hopkins et al. (2018) Hopkins, P. F., Wetzel, A., Kereš, D., et al. 2018, MNRAS, 480, 800, doi: 10.1093/mnras/sty1690
  * Ibata et al. (2020) Ibata, R., Bellazzini, M., Thomas, G., et al. 2020, ApJ, 891, L19, doi: 10.3847/2041-8213/ab77c7
  * Ibata et al. (1994) Ibata, R. A., Gilmore, G., & Irwin, M. J. 1994, Nature, 370, 194, doi: 10.1038/370194a0
  * Ibata et al. (2002) Ibata, R. A., Lewis, G. F., Irwin, M. J., & Quinn, T. 2002, MNRAS, 332, 915, doi: 10.1046/j.1365-8711.2002.05358.x
  * Ivezić et al. (2019) Ivezić, Ž., Kahn, S. M., Tyson, J. A., et al. 2019, ApJ, 873, 111, doi: 10.3847/1538-4357/ab042c
  * Ji et al. (2021) Ji, A. P., Koposov, S. E., Li, T. S., et al. 2021, arXiv e-prints, arXiv:2106.12656.  https://arxiv.org/abs/2106.12656
  * Jiang et al. (2019) Jiang, F., Dekel, A., Kneller, O., et al. 2019, MNRAS, 488, 4801, doi: 10.1093/mnras/stz1952
  * Johnson et al. (2020) Johnson, B. D., Conroy, C., Naidu, R. P., et al. 2020, ApJ, 900, 103, doi: 10.3847/1538-4357/abab08
  * Johnston et al. (2005) Johnston, K. V., Law, D. R., & Majewski, S. R. 2005, ApJ, 619, 800, doi: 10.1086/426777
  * Johnston et al. (2002) Johnston, K. V., Spergel, D. N., & Haydn, C. 2002, ApJ, 570, 656, doi: 10.1086/339791
  * Kim et al. (2018) Kim, S. Y., Peter, A. H. G., & Hargis, J. R. 2018, Phys. Rev. Lett., 121, 211302, doi: 10.1103/PhysRevLett.121.211302
  * Kirby et al. (2013) Kirby, E. N., Cohen, J. G., Guhathakurta, P., et al. 2013, ApJ, 779, 102, doi: 10.1088/0004-637X/779/2/102
  * Klypin et al. (1999) Klypin, A., Kravtsov, A. V., Valenzuela, O., & Prada, F. 1999, ApJ, 522, 82, doi: 10.1086/307643
  * Koposov et al. (2010) Koposov, S. E., Rix, H.-W., & Hogg, D. W. 2010, ApJ, 712, 260, doi: 10.1088/0004-637X/712/1/260
  * Koposov et al. (2019) Koposov, S. E., Belokurov, V., Li, T. S., et al. 2019, MNRAS, 485, 4726, doi: 10.1093/mnras/stz457
  * Kroupa (2001) Kroupa, P. 2001, MNRAS, 322, 231, doi: 10.1046/j.1365-8711.2001.04022.x
  * Laureijs et al. (2011) Laureijs, R., Amiaux, J., Arduini, S., et al. 2011, arXiv e-prints, arXiv:1110.3193.  https://arxiv.org/abs/1110.3193
  * Law & Majewski (2010) Law, D. R., & Majewski, S. R. 2010, ApJ, 714, 229, doi: 10.1088/0004-637X/714/1/229
  * Lewis et al. (2002) Lewis, I. J., Cannon, R. D., Taylor, K., et al. 2002, MNRAS, 333, 279, doi: 10.1046/j.1365-8711.2002.05333.x
  * Li et al. (2019) Li, T. S., Koposov, S. E., Zucker, D. B., et al. 2019, MNRAS, 490, 3508, doi: 10.1093/mnras/stz2731
  * Li et al. (2022) Li, T. S., Ji, A. P., Pace, A. B., et al. 2022, ApJ, 928, 30, doi: 10.3847/1538-4357/ac46d3
  * Lilleengen et al. (2022) Lilleengen, S., Petersen, M. S., Erkal, D., et al. 2022, arXiv e-prints, arXiv:2205.01688.  https://arxiv.org/abs/2205.01688
  * LSST Dark Energy Science Collaboration et al.(2021)LSST Dark Energy Science Collaboration (LSST DESC), Abolfathi, Alonso, Armstrong, Aubourg, Awan, Babuji, Bauer, Bean, Beckett, Biswas, Bogart, Boutigny, Chard, Chiang, Claver, Cohen-Tanugi, Combet, Connolly, Daniel, Digel, Drlica-Wagner, Dubois, Gangler, Gawiser, Glanzman, Gris, Habib, Hearin, Heitmann, Hernandez, Hložek, Hollowed, Ishak, Ivezić, Jarvis, Jha, Kahn, Kalmbach, Kelly, Kovacs, Korytov, Krughoff, Lage, Lanusse, Larsen, Le Guillou, Li, Longley, Lupton, Mandelbaum, Mao, Marshall, Meyers, Moniez, Morrison, Nomerotski, O’Connor, Park, Park, Peloton, Perrefort, Perry, Plaszczynski, Pope, Rasmussen, Reil, Roodman, Rykoff, Sánchez, Schmidt, Scolnic, Stubbs, Tyson, Uram, Villarreal, Walter, Wiesner, Wood-Vasey, & Zuntz (LSST DESC) LSST Dark Energy Science Collaboration (LSST DESC), Abolfathi, B., Alonso, D., et al. 2021, ApJS, 253, 31, doi: 10.3847/1538-4365/abd62c
  * LSST Science Collaboration (2009) LSST Science Collaboration. 2009, ArXiv e-prints.  https://arxiv.org/abs/0912.0201
  * Ludlow et al. (2019) Ludlow, A. D., Schaye, J., Schaller, M., & Richings, J. 2019, MNRAS, 488, L123, doi: 10.1093/mnrasl/slz110
  * Majewski et al. (2003) Majewski, S. R., Skrutskie, M. F., Weinberg, M. D., & Ostheimer, J. C. 2003, ApJ, 599, 1082, doi: 10.1086/379504
  * Majewski et al. (2017) Majewski, S. R., Schiavon, R. P., Frinchaboy, P. M., et al. 2017, AJ, 154, 94, doi: 10.3847/1538-3881/aa784d
  * Malhan et al. (2018) Malhan, K., Ibata, R. A., & Martin, N. F. 2018, MNRAS, 481, 3442, doi: 10.1093/mnras/sty2474
  * Malhan et al. (2021) Malhan, K., Yuan, Z., Ibata, R. A., et al. 2021, ApJ, 920, 51, doi: 10.3847/1538-4357/ac1675
  * Mateu (2022) Mateu, C. 2022, arXiv e-prints, arXiv:2204.10326.  https://arxiv.org/abs/2204.10326
  * Mateu et al. (2018) Mateu, C., Read, J. I., & Kawata, D. 2018, MNRAS, 474, 4112, doi: 10.1093/mnras/stx2937
  * McConnachie (2012) McConnachie, A. W. 2012, AJ, 144, 4, doi: 10.1088/0004-6256/144/1/4
  * McMillan (2017) McMillan, P. J. 2017, MNRAS, 465, 76, doi: 10.1093/mnras/stw2759
  * Moore et al. (1999) Moore, B., Ghigna, S., Governato, F., et al. 1999, ApJ, 524, L19, doi: 10.1086/312287
  * Muñoz et al. (2006) Muñoz, R. R., Majewski, S. R., Zaggia, S., et al. 2006, ApJ, 649, 201, doi: 10.1086/505620
  * Naidu et al. (2022) Naidu, R. P., Conroy, C., Bonaca, A., et al. 2022, arXiv e-prints, arXiv:2204.09057.  https://arxiv.org/abs/2204.09057
  * Navarro et al. (1996) Navarro, J. F., Frenk, C. S., & White, S. D. M. 1996, ApJ, 462, 563, doi: 10.1086/177173
  * Pace et al. (2022) Pace, A. B., Erkal, D., & Li, T. S. 2022, arXiv e-prints, arXiv:2205.05699.  https://arxiv.org/abs/2205.05699
  * Panithanpaisal et al. (2021) Panithanpaisal, N., Sanderson, R. E., Wetzel, A., et al. 2021, ApJ, 920, 10, doi: 10.3847/1538-4357/ac1109
  * Peñarrubia et al. (2012) Peñarrubia, J., Pontzen, A., Walker, M. G., & Koposov, S. E. 2012, ApJ, 759, L42, doi: 10.1088/2041-8205/759/2/L42
  * Pearson et al. (2019) Pearson, S., Starkenburg, T. K., Johnston, K. V., et al. 2019, ApJ, 883, 87, doi: 10.3847/1538-4357/ab3e06
  * Plummer (1911) Plummer, H. C. 1911, MNRAS, 71, 460, doi: 10.1093/mnras/71.5.460
  * Price-Whelan & Bonaca (2018) Price-Whelan, A. M., & Bonaca, A. 2018, ApJ, 863, L20, doi: 10.3847/2041-8213/aad7b5
  * Putman et al. (2021) Putman, M. E., Zheng, Y., Price-Whelan, A. M., et al. 2021, ApJ, 913, 53, doi: 10.3847/1538-4357/abe391
  * Ramos et al. (2020) Ramos, P., Mateu, C., Antoja, T., et al. 2020, A&A, 638, A104, doi: 10.1051/0004-6361/202037819
  * Richstein et al. (2022) Richstein, H., Patel, E., Kallivayalil, N., et al. 2022, arXiv e-prints, arXiv:2204.01917.  https://arxiv.org/abs/2204.01917
  * Rohr et al. (2022) Rohr, E., Feldmann, R., Bullock, J. S., et al. 2022, MNRAS, 510, 3967, doi: 10.1093/mnras/stab3625
  * Sales et al. (2022) Sales, L. V., Wetzel, A., & Fattahi, A. 2022, Nature Astronomy, doi: 10.1038/s41550-022-01689-w
  * Samuel et al. (2021) Samuel, J., Wetzel, A., Chapman, S., et al. 2021, MNRAS, 504, 1379, doi: 10.1093/mnras/stab955
  * Samuel et al. (2020) Samuel, J., Wetzel, A., Tollerud, E., et al. 2020, MNRAS, 491, 1471, doi: 10.1093/mnras/stz3054
  * Sanders et al. (2016) Sanders, J. L., Bovy, J., & Erkal, D. 2016, MNRAS, 457, 3817, doi: 10.1093/mnras/stw232
  * Sanders et al. (2018) Sanders, J. L., Evans, N. W., & Dehnen, W. 2018, Monthly Notices of the Royal Astronomical Society, 478, 3879, doi: 10.1093/mnras/sty1278
  * Sanderson et al. (2018) Sanderson, R. E., Garrison-Kimmel, S., Wetzel, A., et al. 2018, ApJ, 869, 12, doi: 10.3847/1538-4357/aaeb33
  * Sanderson et al. (2020) Sanderson, R. E., Wetzel, A., Loebman, S., et al. 2020, ApJS, 246, 6, doi: 10.3847/1538-4365/ab5b9d
  * Santistevan et al. (2020) Santistevan, I. B., Wetzel, A., El-Badry, K., et al. 2020, MNRAS, 497, 747, doi: 10.1093/mnras/staa1923
  * Sharma et al. (2012) Sharma, S., Bland-Hawthorn, J., Johnston, K. V., & Binney, J. 2012, in European Physical Journal Web of Conferences, Vol. 19, European Physical Journal Web of Conferences, 10001, doi: 10.1051/epjconf/20121910001
  * Sharma et al. (2011) Sharma, S., Johnston, K. V., Majewski, S. R., Bullock, J., & Muñoz, R. R. 2011, ApJ, 728, 106, doi: 10.1088/0004-637X/728/2/106
  * Sharma & Steinmetz (2011) Sharma, S., & Steinmetz, M. 2011, EnBiD: Fast Multi-dimensional Density Estimation, Astrophysics Source Code Library, record ascl:1109.012.  http://ascl.net/1109.012
  * Sharp et al. (2006) Sharp, R., Saunders, W., Smith, G., et al. 2006, in Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series, Vol. 6269, Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series, 62690G, doi: 10.1117/12.671022
  * Shen et al. (2022) Shen, X., Hopkins, P. F., Necib, L., et al. 2022, arXiv e-prints, arXiv:2206.05327.  https://arxiv.org/abs/2206.05327
  * Shipp et al. (2018) Shipp, N., Drlica-Wagner, A., Balbinot, E., et al. 2018, ApJ, 862, 114, doi: 10.3847/1538-4357/aacdab
  * Shipp et al. (2019) Shipp, N., Li, T. S., Pace, A. B., et al. 2019, ApJ, 885, 3, doi: 10.3847/1538-4357/ab44bf
  * Shipp et al. (2021) Shipp, N., Erkal, D., Drlica-Wagner, A., et al. 2021, ApJ, 923, 149, doi: 10.3847/1538-4357/ac2e93
  * Simon (2019) Simon, J. D. 2019, ARA&A, 57, 375, doi: 10.1146/annurev-astro-091918-104453
  * Simpson et al. (2018) Simpson, C. M., Grand, R. J. J., Gómez, F. A., et al. 2018, MNRAS, 478, 548, doi: 10.1093/mnras/sty774
  * Spergel et al. (2013) Spergel, D., Gehrels, N., Breckinridge, J., et al. 2013, arXiv e-prints, arXiv:1305.5422.  https://arxiv.org/abs/1305.5422
  * Springel (2005) Springel, V. 2005, MNRAS, 364, 1105, doi: 10.1111/j.1365-2966.2005.09655.x
  * The Astropy Collaboration et al. (2022) The Astropy Collaboration, Price-Whelan, A. M., Lian Lim, P., et al. 2022, arXiv e-prints, arXiv:2206.14220.  https://arxiv.org/abs/2206.14220
  * Torrealba et al. (2019) Torrealba, G., Belokurov, V., Koposov, S. E., et al. 2019, MNRAS, 488, 2743, doi: 10.1093/mnras/stz1624
  * Tulin & Yu (2018) Tulin, S., & Yu, H.-B. 2018, Phys. Rep., 730, 1, doi: 10.1016/j.physrep.2017.11.004
  * Vasiliev (2019) Vasiliev, E. 2019, MNRAS, 482, 1525, doi: 10.1093/mnras/sty2672
  * Vasiliev et al. (2021) Vasiliev, E., Belokurov, V., & Erkal, D. 2021, MNRAS, 501, 2279, doi: 10.1093/mnras/staa3673
  * Vivas et al. (2022) Vivas, A. K., Martínez-Vázquez, C. E., Walker, A. R., et al. 2022, ApJ, 926, 78, doi: 10.3847/1538-4357/ac43bd
  * Westfall et al. (2006) Westfall, K. B., Majewski, S. R., Ostheimer, J. C., et al. 2006, AJ, 131, 375, doi: 10.1086/496975
  * Wetzel et al. (2016) Wetzel, A. R., Hopkins, P. F., Kim, J.-h., et al. 2016, ApJ, 827, L23, doi: 10.3847/2041-8205/827/2/L23
  * Wheeler et al. (2019) Wheeler, C., Hopkins, P. F., Pace, A. B., et al. 2019, MNRAS, 490, 4447, doi: 10.1093/mnras/stz2887
  * Woo et al. (2008) Woo, J., Courteau, S., & Dekel, A. 2008, MNRAS, 390, 1453, doi: 10.1111/j.1365-2966.2008.13770.x
  * Yang et al. (2019) Yang, C., Xue, X.-X., Li, J., et al. 2019, ApJ, 886, 154, doi: 10.3847/1538-4357/ab48e2
  * Yoon et al. (2011) Yoon, J. H., Johnston, K. V., & Hogg, D. W. 2011, ApJ, 731, 58, doi: 10.1088/0004-637X/731/1/58
  * York et al. (2000) York, D. G., Adelman, J., Anderson, Jr., J. E., et al. 2000, AJ, 120, 1579, doi: 10.1086/301513
  * Yuan et al. (2022) Yuan, Z., Malhan, K., Sestito, F., et al. 2022, ApJ, 930, 103, doi: 10.3847/1538-4357/ac616f
  * Zhao et al. (2012) Zhao, G., Zhao, Y.-H., Chu, Y.-Q., Jing, Y.-P., & Deng, L.-C. 2012, Research in Astronomy and Astrophysics, 12, 723, doi: 10.1088/1674-4527/12/7/002

##  Appendix A Properties of Streams and Satellites in FIRE

Here we report properties of the simulated streams and satellites considered
in this work. Table A.1 lists the host halo name, the stellar mass, pericenter
and apocenter, and minimum surface brightness in DES and LSST of each stellar
stream. The stream population and the derivation of these properties is
discussed in greater detail in Section 2.2 and Section 3.1. Table A.2 includes
properties of satellites, including the host halo name, structural parameters
(half-light radius, ellipticity, position angle), distance, surface
brightness, luminosity, and density. Orbital properties of the FIRE satellites
will be published in Santistevan et al. (in prep.). In addition, we list
whether each satellite is a stream progenitor (i.e. has tidal tails) and
whether it is estimated to be detectable in DES, as discussed in Section 3.2.
For each table, we display the first ten rows here. The full tables are
included as supplemental files.

Table A.1:  FIRE stream properties. Host | $\log M_{*}$ | $r_{\rm peri}$ | $r_{\rm apo}$ |  $\mu_{\rm V,min}$ (DES) |  $\mu_{\rm V,min}$ (LSST)
---|---|---|---|---|---
| ($\mathrm{\,M_{\odot}}$) | ($\mathrm{\,kpc}$) | ($\mathrm{\,kpc}$) | $(\mathrm{mag}/\mathrm{arcsec}^{2})$ | $(\mathrm{mag}/\mathrm{arcsec}^{2})$
Romeo | 6.0 | 26.45 | 158.96 | 38 | 37
Romeo | 8.6 | 41.93 | 65.82 | 30 | 30
Romeo | 6.6 | 65.00 | 219.77 | 38 | 37
Romeo | 6.6 | 63.36 | 252.93 | $>39$ | 37
Romeo | 5.8 | 17.68 | 157.31 | 39 | 38
Romeo | 6.3 | 19.43 | 187.39 | 36 | 35
Romeo | 6.6 | 41.44 | 122.89 | 36 | 36
Romeo | 6.2 | 21.25 | 68.54 | 36 | 36
Romeo | 7.4 | 26.90 | 150.56 | 34 | 34
Juliet | 8.4 | 96.27 | 111.03 | 31 | 31
Table A.2:  FIRE satellite properties. Host |  RA, Dec Centroid | $r_{1/2}$ | $\epsilon$ | $\theta$ | $d$ | $\mu_{\rm V}$ | $M_{\rm V}$ | $\rho_{\rm 1/2}$ | Stream Progenitor | Detectable
---|---|---|---|---|---|---|---|---|---|---
| $(\deg)$ | $(\deg)$ |  | $(\deg)$ | $(\mathrm{\,kpc})$ | $(\mathrm{mag/arcsec^{2}})$ | $(\mathrm{mag})$ | $(\mathrm{\,M_{\odot}}/\mathrm{\,kpc}^{3})$ |  |
Romeo | (61.97, -13.61) | 0.28 | 0.01 | 82.54 | 136.55 | 30.41 | -8.59 | $2.50\times 10^{7}$ | True | True
Romeo | (103.54, -32.71) | 1.52 | 0.15 | 118.07 | 61.65 | 25.21 | -15.92 | $3.70\times 10^{6}$ | True | True
Romeo | (96.97, -66.55) | 0.35 | 0.13 | 138.08 | 180.30 | 29.97 | -10.29 | $9.10\times 10^{6}$ | True | True
Romeo | (109.70, 41.32) | 0.24 | 0.26 | 18.21 | 208.13 | 29.71 | -10.07 | $1.50\times 10^{7}$ | True | True
Romeo | (57.63, 51.21) | 0.51 | 0.10 | 110.09 | 95.88 | 31.72 | -7.66 | $1.56\times 10^{7}$ | True | True
Romeo | (314.97, 42.80) | 0.90 | 0.11 | 75.28 | 60.64 | 29.80 | -9.71 | $1.26\times 10^{7}$ | True | True
Romeo | (266.79, 47.80) | 0.64 | 0.17 | 86.22 | 62.64 | 31.29 | -7.55 | $2.24\times 10^{7}$ | True | True
Romeo | (247.78, 24.90) | 0.54 | 0.01 | 100.81 | 114.27 | 28.90 | -11.06 | $9.78\times 10^{6}$ | True | True
Romeo | (79.10, -39.73) | 0.15 | 0.37 | 9.16 | 254.74 | 30.59 | -8.58 | $2.47\times 10^{7}$ | False | True
Romeo | (21.18, 48.15) | 0.87 | 0.33 | 167.98 | 93.02 | 25.04 | -15.45 | $5.43\times 10^{6}$ | False | True

##  Appendix B Stream and Satellite Classification

In order to clarify the terms used in this paper, Table B.1 lists the
resulting classification of a stream or satellite system depending on the
detectability of its progenitor and tidal tails. For example, a stream with a
surviving progenitor would be classified as an intact satellite (with no tidal
tails) if only its progenitor were detectable. As discussed in Section 3.2, a
“surviving progenitor” is a progenitor that is recovered by the halo finder at
$z=0$.

Table B.1:  Classification of Streams and Satellites Depending on Detectability All Detectable | Detectable Progenitor Only | Detectable Tidal Tails Only
---|---|---
Stream with surviving progenitor | Intact satellite | Stream without surviving progenitor
Stream without surviving progenitor | N/A | Stream without surviving progenitor
Intact satellite | Intact satellite | N/A

##  Appendix C Comparison of Orbit Integration Methods

As discussed in Section 4.3, the methods used to compute pericenters and
apocenters of the FIRE and Milky Way stellar streams are not entirely
consistent. Here we discuss the differences between these calculations and the
resulting uncertainties. To compute the orbits of the FIRE streams, we trace
the positions of the simulated star particles back through the 600 output
snapshots, thereby determining the true orbital history in a fully time-
dependent potential. However, to compute the pericenters and apocenters of the
Milky Way stellar streams, we integrate the orbits of the member stars in a
time-independent potential, which is known to introduce biases into derived
orbital parameters (D’Souza & Bell, 2022; Lilleengen et al., 2022, Santisteven
et al. in prep.). In order to examine the uncertainties on the Milky Way
stream orbits due to the assumption of a time-independent potential, we also
integrate the orbits of the FIRE streams from the Latte simulations in a time-
independent potential. We use the potential models from Arora et al. (2022),
fit via basis function expansion to the host galaxy potential in each of the
Latte simulations at $z=0$. We integrate the orbits using AGAMA (Vasiliev,
2019). Figure C.1 illustrates the difference in the resulting pericenters and
apocenters of streams in the Latte simulations. The circles represent the
pericenters and apocenters derived from the fully time-dependent potentials,
which are used throughout this paper. The triangles represent the pericenter
and apocenter values derived from integrating orbits in the $z=0$ potential.
Lines connect the two values for each simulated stream. Each color represents
a different Latte host galaxy. The majority of the streams have small changes
($<10\%$) in pericenter and apocenter. Some (${\sim}\,1$ per host galaxy) have
much larger changes. The large differences in either pericenter or apocenter
are largely due to artificial fanning of the stream after the first pericenter
or apocenter when integrated backwards in the fixed time-independent
potential. Regardless of method, we find that the discrepancy remains between
the simulated and observed streams. The FIRE streams on average have
significantly larger pericenters and apocenters than the Milky Way streams.

Figure C.1: Comparison of pericenters and apocenters of Latte streams computed
in time-dependent and time-independent potentials. Each color represents
streams belonging to a single host galaxy. The circles represent the values
used throughout the paper, which were calculated in a fully time-dependent
potential. The triangles represent the pericenters and apocenters of the same
streams, calculated by integrating orbits in the time-independent $z=0$
potentials of their host galaxies. This method is analogous to that used to
compute the Milky Way stream pericenters and apocenters (black crosses). The
majority of streams have a small change in pericenter and apocenter between
methods, while a smaller number of streams have more significant changes.
These differences are not enough to resolve the discrepancy seen between the
orbits of stellar streams in FIRE and the Milky Way.