# Stellar Streams in the Galactic Disk: Predicted Lifetimes and Their Utility
in Measuring the Galactic Potential

Harshil Kamdar Center for Astrophysics $|$ Harvard & Smithsonian, 60 Garden
Street, Cambridge, MA 02138, USA  Charlie Conroy Center for Astrophysics $|$
Harvard & Smithsonian, 60 Garden Street, Cambridge, MA 02138, USA  Yuan-Sen
Ting (丁源森) Institute for Advanced Study, Princeton, NJ 08540, USA  Department
of Astrophysical Sciences, Princeton University, Princeton, NJ 08544, USA
Observatories of the Carnegie Institution of Washington, 813 Santa Barbara
Street, Pasadena, CA 91101, USA  Research School of Astronomy and
Astrophysics, Mount Stromlo Observatory, Cotter Road, Weston Creek, ACT 2611,
Canberra, Australia

###### Abstract

In this paper we present a holistic view of the detection, characterization,
and origin of stellar streams in the disk of a simulated Milky Way-like
galaxy. The star-by-star simulation of the Galaxy evolves stars born in
clusters in a realistic galactic potential that includes spiral arms, a bar,
and giant molecular clouds over $5$ Gyr. We first devise a new hybrid method
to detect stellar streams that combines phase space density information along
with the action-angle space spanned by stars in our simulation. We find that
streams’ progenitor star clusters and associations are all preferentially
higher-mass ($>1000$ $M_{\odot}$) and young ($<1$ Gyr). Our stream-finding
method predicts that we might be able to find anywhere from $1$ to $10$
streams with 6D Gaia DR2 data in the solar neighborhood alone. The simulation
suggests that streams are sensitive to the initial dynamical state of
clusters, accumulated energy gain from encounters with giant molecular clouds
(GMCs), and present-day actions. We investigate what we can learn about the
Galactic potential by studying the feasiblity of rewinding stellar streams
back to their origin. Even with perfect information about the non-axisymmetric
components (spiral arms, bar) of the galactic potential, the stochastic GMC
population makes backwards integration impossible beyond one or two disk
orbital times. Streams are also sensitive to the properties of the bar, but
fairly insensitive to the properties of the non-transient two-armed spiral in
our simulation. Finally we predict that around $10$ to $30$ stellar streams
should be detectable with Gaia’s 10-year end-of-mission data. There are many
more stellar streams waiting to be discovered in the Galactic disk, and they
could hold clues about the history of the Galaxy for the past Gyr.

Galaxy: evolution – Galaxy: kinematics and dynamics – open clusters and
associations: general

††journal: ApJ

##  1 Introduction

The history of the Galaxy is encoded in the distribution of the kinematics and
the chemistry of its stars. The deluge of astrometric (Brown et al., 2018) and
spectroscopic (e.g., Kollmeier et al., 2017; Kunder et al., 2017; Buder et
al., 2019; Ahumada et al., 2019) data expected in the coming years is likely
to bring about new insights about how galaxies like ours are assembled over
cosmic time.

The study of stellar streams of stars in the Galactic halo in particular has
shown the potential of these datasets in unraveling the early history of the
Milky Way and reveal fundamental insights about the nature of dark matter (for
e.g., Helmi, 2020, and references therein). Given their cold kinematics, small
perturbation from interactions with dark matter subhaloes or the Galactic bar
could potentially leave a large imprint on the dynamical signature of streams
(e.g., Pearson et al., 2017; Bonaca et al., 2020). The kinematics and
chemistry of these stars has helped us piece together the early history of the
stellar halo of the Galaxy.

The potential utility of stellar streams in the Galactic disk from disrupting
open clusters or stellar associations on the other hand is largely unexplored.
There are two difficulties with assessing what we can learn from stellar
streams in the Galactic disk. First, perturbations from the non-axisymmetric
components of the Galaxy (spiral arms and bar) and from GMCs are far more
likely on disk-like orbits than halo-like orbits. Secondly, there is no clear
theoretical motivation for how long stellar streams in the disk will be
detectable in phase space due to the much shorter dynamical time and the
complex dynamical signature of stellar feedback and gas expulsion (e.g.,
Dinnbier & Kroupa, 2020). While moving groups were originally thought to be
disrupted clusters (e.g., Eggen, 1965), most moving groups are now thought to
be overdensities due to the resonances in the Galactic potential (e.g.,
Dehnen, 1998). Consequently, there is no real theoretical expectation for how
many stellar streams we can hope to detect with current and future data.

The first chemically homogeneous stellar stream in the disk was recently
discovered in (Meingast et al., 2019). The stream, known as Pisces-Eridanus,
is $\sim$ $120$ Myr old (Curtis et al., 2019) and extends hundreds of parsecs
in the local solar neighborhood and likely contains hundreds of stars
(Ratzenböck et al., 2020). Moreover, recent work has also detected the tidal
tails of nearby open clusters (e.g., Röser et al., 2019; Meingast & Alves,
2019; Röser & Schilbach, 2019; Oh & Evans, 2020; Meingast et al., 2021;
Jerabkova et al., 2021) and a stream originated from a past satellite
interaction (e.g., Laporte et al., 2020). These detections further beg the
question of what we can expect to learn about the nature of star formation,
the chemical evolution of stars, and the large-scale mass distribution of the
Galaxy from stellar streams in the disk.

In Kamdar et al. (2019a, hereafter K19a), we presented a star-by-star
dynamical model of the Galactic disk that takes into account the clustered
nature of star formation and the complexity of the Galactic potential. Each
resolution element in the simulation represents an individual star. The
simulation self-consistently evolves 4 billion stars over the last 5 Gyr in a
realistic potential that includes an axisymmetric component, spiral arms, a
bar, and GMCs. All stars are born in clusters with an analytical model for
cluster birth and dissolution (Lada & Lada, 2003). The simulation provides the
ideal sandbox to investigate how we can find, characterize, and learn about
the Galaxy from stellar streams.

The paper is structured as follows. In Section 2 we discuss the simulation
from Kamdar et al. (2019a), how we create mock Gaia catalogs, and the method
we use to detect stellar streams in the simulated galaxy. Section 3 discusses
why some stellar streams survive and remain visible in phase space and some do
not. In Section 4 we examine what we can learn about the Galactic potential
from stellar streams. We discuss the future of stellar streams in the disk in
Section 5 and conclude in Section 6.

##  2 Simulations

###  2.1 Simulations

In Kamdar et al. (2019a) we presented three simulations of the Galactic disk
that explore different paramterizations for clustered star formation and the
potential of the Galaxy. In this work we will focus on the “fiduical”
simulation presented in K19a. The fiducial simulation includes a comprehensive
treatment of the clustered nature of star formation and includes a realistic
potential with a bar, spiral arms, and GMCs. The fiducial simulation self-
consistently evolves 4 billion stars over the last 5 Gyr in a time-varying
potential that includes an axisymmetric component, a bar, spiral arms, and
live giant molecular clouds (GMCs). All stars’ positions and velocities are
initialized with an observationally motivated recipe for clustered star
formation.

Running direct N-body simulations for millions of star clusters comprising
billions of stars is currently computationally infeasible. In K19a we
presented a subgrid model for how to mimic star cluster initialization,
evolution, and disruption based on analytic theory and hydrodynamical & N-body
simulations (Lada & Lada, 2003; Fujii & Zwart, 2016). Our model is calibrated
to broadly agree with the cluster formation efficiency of a Milky Way-like
galaxy and the evolution of the mass-radius relation for young clusters. We
assume that stars older than $5$ Gyr are fully phase-mixed in the galaxy, and
thereby include a smooth background to match observations of the local stellar
surface density (Rix & Bovy, 2013) and recent results on radial migration
(Frankel et al., 2018).

To enable a fair comparison with observational data we create mock catalogs of
the fiducial simulation that mimic the spatial volume and errors of current
and future Gaia data releases. The solar neighborhood sphere is centered at
$(-8.2,0.0,0.025)$ kpc (Bland-Hawthorn & Gerhard, 2016). The Gaia DR2 mock
catalog sphere has a radius of $0.5$ kpc and the Gaia end-of-mission 10-year
(EOM) mock catalog has a radius of $1.5$ kpc. These values were roughly chosen
to indicate the spatial extent to which Gaia parallaxes will be of high
fidelity. We use the MIST stellar evolutionary tracks (Choi et al., 2016) and
the C3K stellar library (Conroy et al., unpublished) to derive photometry for
the simulated stars using a Kroupa IMF (Kroupa, 2001). We also calculate
$G_{\mathrm{RVS}}$ using $(G-G_{RP})$ color from Equations 2 and 3 presented
in Brown et al. (2018), and apply the $G_{\mathrm{RVS}}$ selection of
$G_{\mathrm{RVS}}<12$ for the DR2 mock catalog and $G_{\mathrm{RVS}}<14$ for
the EOM mock catalog.

Figure 1: Stellar streams in the simulated galaxy’s disk. Top-left: The
different grey histograms show the phase space density distribution for
different mock catalogs in the solar annulus. Blue histograms show the streams
that remain overdense in phase space. Orange histogram shows the phase space
density distribution of the Pisces-Eridanus stream (Meingast et al., 2019)
detected in Gaia DR2. The grey dashed line shows the $95$th percentile in the
phase space density distribution. Top-right: Number of detected streams in
Gaia DR2-like mock catalogs in the simulation. The grey dashed line in the
back shows the raw number per mock catalog and the solid red line shows the
rolling average with a window size of 4. The number of streams clearly follows
a sinusoidal pattern and seems to be correlated with the spiral arm density
maxima. Bottom: 3D distribution of the stellar streams in galactocentric
coordinates. Each star is given a unique color based on its progenitor star
cluster or stellar association.

Forecasting the number of detectable streams for Gaia DR2 and future data
releases also requires a thorough treatment of the astrometric and
spectroscopic error propagation in the simulation. The dependence of parallax,
proper motion and radial velocity errors is a complex function of several
parameters. We follow the procedure set out in Kamdar et al. (2019b, 2020) to
build the error model for the simulations. Briefly, we fit a Gaussian mixture
model (GMM) with 20 components to the combined
($G,G_{\rm{BP}}-G_{\rm{RP}},\sigma_{\varpi},\sigma_{\rm{\mu_{\alpha^{*}}}},\sigma_{\rm{\mu_{\delta}}}$)
and ($G,G_{\rm{BP}}-G_{\rm{RP}},\sigma_{\rm{RV}}$) spaces respectively for
both DR2 and EOM errors, where
$\sigma_{\varpi},\sigma_{\rm{\mu_{\alpha^{*}}}},\sigma_{\rm{\mu_{\delta}}},\sigma_{\rm{RV}}$
are the uncertainties in the parallax, proper motions and the radial
velocities. Using the $G,G_{\rm{BP}},G_{\rm{RP}}$ values derived for each star
using the procedure described above, we sample from the conditional
distributions for the respective astrometric and spectroscopic errors given
$G$ and $G_{\rm{BP}}-G_{\rm{RP}}$. The scanning law also has an impact on the
selection of stars in the solar neighborhood and their respective errors. With
recent progress on modelling the scanning law and computing the true RVS
selection function (Boubert & Everall, 2020), we plan to include a detailed
selection function in future work (as opposed to a simple magnitude cut) for
both the error model and the selection of stars.

###  2.2 Finding & Characterizing Streams in the Simulation

Only one conatal stellar stream has been definitively detected in the Galactic
disk solely using dynamical properties of stars (Meingast et al., 2019). There
is also some related recent work that suggests the existence of other such
stellar streams but these results have not been validating using chemical
information or astroseismology (Kounkel & Covey, 2019). The observational
detection of the Pisces-Eridanus stream was performed using a combination of
wavelet analysis and DBSCAN. The wavelet decomposition constructs a series of
components at different velocity scales – the authors focus on velocity
amplitudes of $\sim 1.5$ km s-1 to identify the overdensity and then perform a
clustering algorithm, DBSCAN, to select stream stars. Both analysis steps here
require hand-tuning and subsequent analysis to identify a “clean” sample of
stream stars.

We adopt a different approach in this work to minimize hand-tuning and utilize
the information content of action-angle coordinates (e.g., Trick et al.,
2019). We first use the coarse grained phase space density ($f$) to quantify
the relative overdensity of a given star in phase space in our simulation and
then perform clustering in action-angle space for stars overdense in phase
space. $f$ is the density in a finite six-dimensional volume defined by
$d^{3}xd^{3}v$, centered on the phase space position of a given star at
$(x,v)$. Phase space densities have been extensively used to study
substructure in galaxy haloes (e.g., Helmi et al., 2002; Hoffman et al.,
2007), but their use in the disk has been limited. The results presented in
this paper utilize EnBID (Sharma & Steinmetz, 2006), which builds upon
Ascasibar & Binney (2005), to numerically calculate the phase space densities
using a binary tree and an entropy-based splitting criterion.

Once the phase space density for each star has been calculated, we select
overdense stars above a certain threshold. Since the phase space density alone
cannot partition overdense stars into constituent streams, we calcualate the
actions and angles for these overdense stars using Agama (Vasiliev, 2019) and
perform clustering in action-angle space using HDBSCAN.

The detailed procedure to identify streams for the purposes of this work is
listed below.

  1. 1.

Calculate the phase space density ($f$) of all stars in a given solar
neighborhood mock catalog using EnBID (Sharma & Steinmetz, 2006)

  2. 2.

Select all stars in the given solar neighborhood that have $f$ $\geq 95$th
percentile

  3. 3.

Calculate actions and angles for these stars overdense in phase space using
Agama (Vasiliev, 2019)

  4. 4.

Run HDBSCAN (McInnes et al., 2017) on the calculated actions and angles

  5. 5.

For each detected clump by HDBSCAN, if the purity (i.e. the number of stars
from the dominant star cluster in the clump) is $>50\%$ and the number of
stars $>50$, we consider this to be a detected stellar stream

About $\sim 15-30$ % of all clumps that HDBSCAN finds at step 4 are real
detections of conatal streams. Consequently, the key caveat in our detection
method is that the purity cut requires independent information to confirm
conatality. In the simulations, the birth cluster of each star is known a
priori and makes the calculation of “purity” (i.e., how many stars in a given
clump were born from the same cluster) of each HDBSCAN-detected clump trivial.
However, performing the same calculation observationally would require some
other way to prove conatality. As shown in Hawkins et al. (2020),
spectroscopic follow-up for candidate streams can strongly indicate a common
origin by demonstrating chemical homogeneity (e.g., Bovy, 2016). Furthermore,
future spectroscopic surveys will also likely provide chemical information for
tens of millions of stars contiguously in the Galactic disk (e.g., Kollmeier
et al., 2017; Kunder et al., 2017; Buder et al., 2019; Ahumada et al., 2019).
The stream detection method above will be tested out on future Gaia and
spectroscopic data in future work (Kamdar et al. in prep).

The top-left panel of Figure 1 offers a visual demonstration of how we detect
streams in the simulation. The different black lines show the phase space
density distribution of all stars in the different solar neighborhoods in the
fiducial simulation. The dashed grey line shows the $95$th percentile of the
phase space density distribution of stars in one of the solar neighborhoods.
The different blue histograms show the phase space density distribution for
stars in our simulation that we detect as streams. The Pisces-Eridanus
stream’s phase space density distribution is shown in orange. The similarity
between the simulation streams and the observationally validated Pisces-
Eridanus stream further solidify our method of detecting streams in the
simulation.

The grey dash-dotted line in the top-right panel of Figure 1 shows the number
of detected streams in different solar neighborhoods as a function of the
solar neighborhood’s azimuthal angle along in the simulated galaxy. The red
line is a smoothed running mean with a window size of 5 points for the number
of streams. The shaded grey regions show the maxima in the density of the two-
armed spiral pattern present in our Galactic potential. The number of streams
clearly follow a sinusodial pattern as a function of the azimuthal angle of
the solar neighborhood in the galaxy.

The prescription used to initialize stars in Kamdar et al. (2019a) used the
maxima in spiral arms’ density to ensure that the bulk of star formation
occured within $\pm 30$ degrees of the spiral arms. Since most streams are
fairly young, the correlation with the spiral arms’ position is reasonable
since the stars’ memory of their birthplace is not fully lost. The streams are
likely offset due to the difference in the pattern speed for the spiral arms
($25$ km s-1 kpc-1, which translates to an orbital period of about $\sim 250$
Myr) and the circular velocity at the solar location ($\sim 240$ km s-1, which
translates to an orbital period of about $\sim 205$ Myr).

The bottom panel of Figure 1 shows a 3D view of the fiducial simulation with
different stellar streams in unique colors. The different azimuthal angles
along the solar annulus are labeled near the top of the panel. The sinusodial
pattern in the number of streams is clear in this panel as well. Streams in
the simulation shown in the Figure bear a similarity to the bead-like
structure observed in Kounkel & Covey (2019), though in a larger spatial
volume.

##  3 What Makes A Stream?

Since there has only been one detection of an unbound stellar stream in the
disk so far, it is worth asking why some streams stay overdense (hence
detectable) in phase space whereas most do not. This question requires a
suitable control sample for comparison. To that end, we use importance
sampling to select stars born in clusters that follow the same mass and age
function as the streams but are not detected as streams using the procedure
described in Section 2.2. The stars in these control clusters are of similar
masses and ages by design but are essentially phase mixed and undetectable in
phase space alone.

The current overdensity of stars in phase space that we detect as streams
could feasibly have four different explanations:

  * •

initial dynamical state of the star cluster

  * •

initial orbital properties

  * •

current orbital properties that make it easier to disentangle from background
stars

  * •

the amount of scattering or energy injection along a star cluster’s orbit

In this section we analyze these different mechanisms to understand why some
stars remain overdense in phase space up to a Gyr.

###  3.1 The Impact of Birth Conditions

Figure 2: Characterizing the massses, ages, and initial dynamical state of
stellar streams detected in the simulation. Streams preferentially originate
in higher-mass star clusters / associations and are mostly younger than $1$
Gyr. Left panel: Input cluster mass function (grey) and stream progenitor
masses (blue). Middle panel: Input cluster age function (grey) and ages of
streams (blue). Right panel:  Initial dynamical state for stream stars (blue)
and control stars (grey). The virial ratio with which star clusters are
initialized controls their initial boundedness. The bimodality in both
distributions is from the subgrid model from Kamdar et al. (2019a) where some
the majority of star clusters are born overvirialized to mimic gas expulsion
from stellar feedback. The distributions are fairly similar with stream
progenitors being slightly more likely to be dynamically bound at birth.

Figure 2 characterizes the mass, age, and initial dynamical state of the
progenitor star clusters and associations for detected stellar streams in the
simulation. The left panel shows the streams’ birth cluster masses and the
input cluster mass function. As a reminder we impose a minimum of $50$ stars
per detected stream. The panel clearly shows that the star clusters that
produce streams have a preferentially far larger mass compared to the overall
simulation. The right panel shows the streams’ birth cluster ages and the
input cluster age function (i.e., star formation history). Streams are largely
all younger than $1$ Gyr. This is similar to the result we found in (Kamdar et
al., 2019a), where we showed that phase space of the Galactic disk only
remains clumpy for about a Gyr.

In K19a we implemented a subgrid model for gas expulsion and cluster
disruption due to stellar feedback by intentionally overvirializing a majority
of birth clusters. The right panel of Figure 2 compares the initial
virialization of streams’ progenitor clusters (blue) and control clusters
(grey). The bimodality in both distributions is due to the prescription for
gas expulsion, where some star clusters are initialized as bound but the
majoirity as unbound. This panel shows that the initial dynamical state of
streams’ progenitors is slightly more bound compared to the control stars’
progenitor clusters. This initial boundedness likely translates into a higher
probability of detectability at present day. However, the large overlap in
these distributions suggest that the simulation’s prescription for gas
expulsion alone could not explain why some star clusters produce detectable
streams and some do not.

###  3.2 Initial Dynamical Properties

Figure 3 shows different dynamical properties of the progenitor star clusters
and associations that eventually produce stellar streams. The stars belonging
to the control sample are colored grey and stars belonging to streams are
colored blue. The top two panels show the birth galactocentric radius ($R$;
right panel) and the height off the midplane ($|Z|$; left panel). The bottom
two panels show the birth vertical action, $J_{z}$, and birth radial action,
$J_{r}$.

The birth $|Z|$ and $R$ distributions look fairly similar for the stream stars
and the control stars. The chosen pattern speeds for the spiral arms and bar
in the non-axisymmetric components of the simulation lead to a resonance
overlap at $\sim 8.9$ kpc (Kamdar et al., 2019a). The bimodality in the
streams’ birth $R$ distributions could perhaps indicate that star clusters
born near resonances could be more likely to create stellar streams in the
disk.

We do not observe stream or control stars born from much further away than
$1-1.5$ kpc away from the solar location. This is largely driven by the small
spatial volume of the DR2 mock catalog ($0.5$ kpc sphere). Since the control
and stream samples both contain young stars by design, the amount of radial
migration they could have experienced in the simulation is fairly low –
empirical estimates for the radial migration of similar stars from Frankel et
al. (2018) would indicate a dispersion of about $\sim 1.3$ kpc in a Gyr. The
birth $J_{z}$ and $J_{r}$ distributions also look largely identical. There is
a slight hint of the radial action having a longer tail for stream stars, but
the signal is not strong due to the small sample size.

###  3.3 Current Properties

Figure 4 shows different dynamical properties at the present time for stream
stars and control stars. It is structured similarly to Figure 3 – the top two
panels show $|Z|$ and $R$, and the bottom two panels show $J_{z}$ and $J_{r}$.
The blue histograms correspond to stream stars’ properties and the grey
histograms correspond to the control sample’s properties.

The same broad patterns are imprinted in the current dynamical properties of
stream stars as their progenitors that we saw in Figure 3. The current $|Z|$
distribution for stream stars is slightly broader than the control and
indicates that stream stars are more likely to be further away from the
midplane. The histogram for the current galactocentric radii of stream stars
seems to be tigher near the sun’s location compared to the control sample. The
narrower distribution here could be reflecting that it is easier to pick out
overdense stars closer to us because the astrometric and spectroscopic errors
for nearby stars is smaller.

Both the radial action and the vertical action for stream stars have a
noticeably longer tail than the control sample. The larger actions indicate
that they are on slightly more unique orbits compared to the field population.
This seems reasonable since our detection method prioritizes locally overdense
stars in phase space – one would expect to pick out stars on unique orbits due
to the lower background phase space density. The distributions, while notably
different, are still fairly similar. Therefore, the present-day dynamical
properties of stellar streams seem to have a small but notable difference from
the control sample. However, they do not seem to solely determine why some
stars remain overdense in phase space and some do not.

###  3.4 The Impact of GMCs

Figure 3: Birth properties of stream and control stars’ progenitor clusters.
Stream stars in blue and control stars in grey. Top-left: Birth height off the
midplane ($|Z|$) distribution for the two different samples of stars. Top-
right: Birth galactocentric radius ($R$) for stream and control stars. The
distributions are similar. Bottom-left: Vertical action distribution
($J_{z}$). Bottom-right: Radial action ($\sqrt{J_{r}}$) distributions. Figure
4: Same as Figure 3 but for current properties of stream and control stars.
Figure 5: Accumulated energy gain ($\log\frac{|\Delta E|}{E_{0}}$) from GMC
encounters along stars’ orbits. Stream stars are shown in blue and control
stars are shown in grey. Stellar streams gain almost an order-of-magnitude
less energy compared to control stars.

Interactions between star clusters and GMCs are known to be destructive (e.g.,
Spitzer, 1958; Gieles et al., 2006) and have been used in the past to explain
the dearth of old open clusters in the solar neighborhood. Relatedly, recent
work (e.g., Ting & Rix, 2019) has also shown the efficiency of GMC scattering
explains the vertical heating history of stars in the thin disk of the Milky
Way. Gieles et al. (2006, hereafter G06) show that the approximate disruption
time for an initial star cluster with mass $1000$ M⊙ in the solar neighborhood
with a uniformly distributed GMC background is about $\sim 100-200$ Myr. The
simulations in G06 suggest that young clusters are destroyed by just a few
chance GMC encounters. Therefore, individual birth clusters might have
significantly different lifetimes due to the inherent stochasticity of GMC
birth, evolution, and dispersal.

Figure 5 shows the difference between the total energy gain
($\log\frac{|\Delta E|}{E_{0}}$) from all GMC encounters for stream stars (in
blue) and for control stars (in grey) from their birth to the present day. The
two arrows near the top of the panel mark the respective peaks of the two
distributions. The difference between the peaks of the accumulated energy gain
distributions for these two samples is almost an order of magnitude. For
reference, a single encounter with a GMC of mass $10^{5}$ M⊙ and radius $\sim
15$ pc, at an impact parameter of $\sim 10$ pc and a relative velocity
difference of $\sim 10$ km s-1 would roughly correspond to $\frac{|\Delta
E|}{E_{0}}\sim 1$ and be sufficient to disrupt the stream.

The overdensity of stream stars, then, is driven by three factors – they were
initially born in a dense environment with a higher likelihood of initial
boundedness, these stars have not yet encountered any large scatterers on
their orbit, and their present-day dynamical properties seem easier to
disentangle from the background. The largest difference between stream stars
and control stars’ properties is observed in the difference in accumulated
energy from GMC encounters, which suggests that GMCs might be the primary
determinant in whether or not stars remain detectable in phase space as
stellar streams.

##  4 What Can We Learn From Streams?

###  4.1 Galactic Potential

Figure 6: Backward integration of stellar streams with perfect information
about different components of the potential but no information about the
history of GMCs in the simulation. The blue line shows the fraction of stars
rewound correctly (i.e., within $5$ pc of their birth location) when the
spiral arms and the bar are included in the backwards integration. The red
line shows the fraction of stars rewound correctly with only the axisymmetric
component of the potential. Figure 7: Impact of uncertainties in the spiral
arm parameters on the fraction of stars rewound correctly. The different
panels vary the mass density, pattern speed, or both (blue lines) and compare
with the backwards integration with perfect information from Figure 6. The
relative insensitivity of the backwards integration to the spiral arms’
parameters suggest that it would be hard to constrain the history of spiral
structure using stellar streams.  Figure 8: Same as Figure 7 but with
uncertainties in the parameters of the bar. The fraction of stars rewound
correctly does seem to be adversely affected with uncertain values for the bar
parameters. Stellar streams could potentially be used to constrain the bar’s
parameters.

While the discovery and characterization of conatal stellar streams in the
disk would have an immediate impact on the study of gyrochronology (e.g.,
Curtis et al., 2019) and the chemistry of stars (e.g., Hawkins et al., 2020),
the question of how much we can learn about the dynamical state of the disk is
unclear. The mass distribution in different components of the Galaxy is of
great importance to studies of the composition, history, and current dynamical
properties of the Galaxy (e.g., Bland-Hawthorn & Gerhard, 2016). Stellar
streams in the halo have been extensively used to constrain the potential and
the density distribution of the Galactic halo (e.g., Malhan & Ibata, 2019;
Hattori et al., 2020; Reino et al., 2020). Recent work has shown that the
tidal tails of Hyades are likely sensitive to the exact prescription for the
Galactic potential and the presence of GMCs (Jerabkova et al., 2021).

One way to probe the potential is to assess the accuracy of rewinding the
orbits of stars backwards in different potentials (e.g., Quillen et al., 2018;
Crundall et al., 2019). The destructive impact of GMCs foreshadows the
difficulty in rewinding orbits back to their birthplace. Moreover, recent work
(e.g., Beane et al., 2019) has also shown that local density variations in the
midplane could further complicate orbit integration. The number of streams
that will eventually be detected in our direct vicinity could hold intriguing
clues about the history of GMC formation and evolution in the past Gyr.

Figure 6 shows the results of backwards integration of stream stars with two
different potentials. Here we define correctly as being rewound to within $5$
pc of the given star’s birthplace. The blue line shows the fraction of stars
rewound correctly when we provide perfect information about spiral arms and
the bar, but no information about the history of the GMCs. The various blue
dots show individual streams’ correctly rewound fraction. The red line shows
the fraction of stars rewound when only the axisymmetric portion of the
potential (with the non-axisymmetric masses redistributed) is used in the
backwards integration.

The results are pessimistic even with perfect information about the input
potential. Less than half the stars can be rewound correctly after a dynamical
time ($\sim 220$ Myr) in the potential with spiral arms and bar. The
distribution of individual streams’ correctly rewound fraction seems to be
fairly bimodal; some streams are very easily rewound up to a few dynamical
times and some are poorly rewound only after $10-20$ Myr. The vast majority
stars cannot be rewound correctly after only few tens of millions of years in
the axisymmetric case.

The bimodality in Figure 6 for different streams suggests the strong
sensitivity of the backwards integration to GMC encounters. The parameters
that control the encounter probability and the destructiveness of encounters
between GMCs and stars are: (1) the mass function of GMCs, (2) the number
density of GMCs, (3) the lifetime of GMCs, and (4) the velocity dispersion of
the GMC and stellar population. Varying these parameters for the full
simulation presented in Kamdar et al. (2019a) is computationally expensive;
however, we plan to run smaller, more controlled simulations to determine
whether individual or a small collection of streams could allow us to place
constraints on these various GMC properties.

Figure 7 shows the same fraction of stars rewound correctly but with varying
uncertainties in the spiral arms of the potential. The left panel shows the
results for a $50$% uncertainty in the mass density, middle panel shows $20$%
uncertainty in the pattern speed, and the right panel shows both combined.
Surprisingly, these added uncertainties largely seem to make little difference
on the fraction of stars rewound correctly. It is worth noting that the
simulation uses a two-armed spiral pattern but recent results suggest a four-
armed spiral pattern might be more appropriate. Moreover, the simulation also
currently has steady-state spiral arms as opposed to transient spiral arms –
transient spiral arms would likely make backwards orbit integration even more
challenging. The relative insensitivity of the backwards integration to the
different spiral arm parameters would suggest that constraining the major
components of the spiral arms would likely be challenging using stellar
streams.

Figure 8 shows how different uncertainties in the potential of the bar impact
the backwards integration of stream stars. An incorrect mass for the bar leads
to a precipitous drop-off in the fraction of correctly rewound stars.
Similarly, an incorrect pattern speed also seems to have a notable impact on
the fraction. As one might expect, the bar seems to have a more tangible
impact on the immediate history of the orbits of stars in the solar
neighborhood.

##  5 The Future of Streams in the Disk

Figure 9: Number of streams as a function of the angle along the solar annulus
for Gaia DR2 and end-of-mission mock catalogs. We predict that Gaia EOM data
will likely detect a factor of $5-10$ as many streams in the Galactic disk as
we see today. Figure 10: On-sky distribution of stream stars for a single DR2
mock catalog (top panel) compared with the same location’s EOM mock catalog
(bottom panel) in equatorial coordinates. The improved errors and the far
larger spatial volume spanned by Gaia EOM data will likely have an enormous
impact on the future of stellar stream studies in the Galactic disk.

Future Gaia data releases in the coming decade will deliver many more stars
with radial velocities and far lower astrometric and spectroscopic errors. The
Gaia data improve with time as $t^{-0.5}$ for parallaxes, photometry, and
radial velocities, and as $t^{-1.5}$ for proper
motions111http://www.astro.lu.se/gaia2017/slides/Brown.pdf. To build the mock
catalogs with the error model corresponding to Gaia end-of-mission (EOM)
10-year data, we scale the parallax and the RV errors by approximately $65\%$
and the proper motion errors by approximately $90\%$ compared to the DR2 error
model. Since the parallaxes will be far more reliable further away from the
solar system and we will have radial velocities at fainter magnitudes
($G_{RVS}\sim 14$ compared to $G_{RVS}\sim 12$), we also expand the volume of
each mock catalog from a sphere with radius $0.5$ kpc to a sphere with radius
$1.5$ kpc.

We perform the same selection cuts presented in Section 2.2 on the Gaia EOM
mock catalogs. Figure 9 shows the number of detectable streams for the EOM
catalogs (blue) compared to the DR2 results presented earlier in Figure 1.
Regardless of the solar neighborhood’s position in the simulated galaxy, we
find that the number of theoretically detectable streams in the data is going
to increase by a factor of $\sim 6$ on average. The same periodic pattern
observed in Figure 1 persists with the larger mock catalogs as well.

We choose one of the simulated DR2 solar neighborhoods with only three stellar
streams currently detectable (similar to observational data today) and
compared their own-sky extent with the corresponding EOM catalog in Figure 10.
As observed in Meingast et al. (2019), these stellar streams can occupy
hundreds of degrees on the sky. The bottom panel shows the on-sky extent of
the detectable streams in the EOM catalogs.

With future Gaia data releases, the number of stars with reliable RVs and
parallaxes is likely to increase by a factor of a few. The sample could
potentially be large enough to focus on the MSTO region of the CMD with
reliable ages for stars and fold in that information into finding stellar
streams. Moreover, contiguous spectroscopic surveys such as SDSS-V (Kollmeier
et al., 2017) provide another channel of information – chemical abundances –
that were largely unexplored in this work. Recent work (e.g., Price-Jones et
al., 2020; Nelson et al., 2021) has shown that chemically tagging stars
(Freeman & Bland-Hawthorn, 2002) that were born together might indeed be
possible with current and future spectroscopic surveys. Combining dynamical
and chemical information of stars to both find and characterize stellar
streams in the disk could present the next frontier in the study of the
assembly history of the Galactic disk.

##  6 Conclusion

Several key physical processes including the clustered nature of star
formation, non-axisymmetries of the Galactic potential, and the history of
GMCs determine the fate of stars born in the Milky Way disk. The study of
dynamically cold stellar streams has yielded key insights about the nature of
dark matter, the potential of the Galaxy, and the physics of star clusters in
the Galactic halo. However, the study of stellar streams is in its relative
infancy in the Galacitc disk with only one confirmed detection and uncertainty
about what we can learn about the disk from these streams. In this paper we
used the simulations presented in Kamdar et al. (2019a) to study the
detection, characterization, and utility of stellar streams in the disk.

The streams in our simulation are detected by analyzing overdensities in phase
space. We analyzed the birth dynamical properties of streams’ progenitor star
clusters and the current dynamical properties of stream stars. We also show
what we can learn about star formation and the galactic potential from
studying these streams. Our key findings are listed below.

  * •

We find that streams’ progenitor star clusters and associations have largely
the same birth $R$, $|Z|$, $J_{z}$, and $J_{r}$ as the field population.
Present-day stream stars have a larger tail in both the vertical and radial
actions ($J_{z}$ and $J_{r}$) compared to the control sample. Moreover, stream
stars also have a slightly narrower $R$ distribution, and are slightly more
likely to be further away from the midplane.

  * •

The two primary mechanism that predict whether stars remain overdense in phase
space seems to be the accumulated energy gain for stars over their lifetime
due to interactions with GMCs and the initial dynamical state of star
clusters. Streams’ progenitor clusters are more likely to be initially more
bound compared to the control sample. We find almost an order of magnitude
smaller accumulated energy gain from GMC encounters for stream stars compared
to the field population. Consequently, only one or a few chance GMC
interactions can be wholly destructive to a dynamically cold stellar stream.

  * •

Given their large impact and stochastic nature, GMCs make studying the
dynamical state of the disk using stellar streams difficult. We find that less
than half the stream stars in our simulation can be integrated backwards in
time correctly for more than a dynanmical time ($\sim 200$ Myr) even with
perfect information about the simulated galaxy’s spiral arms and bar (but no
information about the GMC population). We also find that our chosen parameters
for steady-state, rotating spiral arms are largely insensitive to the fraction
of stars rewound correctly – consequently, constraining parameters for the
spiral arms using stellar streams will likely be frought with challenges. The
simulated galaxy’s bar mass seems to have an outsized impact on the fraction
of stars rewound correctly, which implies that we may be able to constrain the
parameters of the bar using stellar streams in the future.

  * •

Future releases of Gaia data will lead to significant improvements in the
astrometric and spectroscopic errors and will provid reliable data for a much
larger volume in the Galaxy. We predict that the number of stellar streams
detected dynamically will likely increase by a factor of $\sim 5-10$.

The future for Galactic archaeology and the study of long disrupted stellar
streams in the disk is bright. We expect significant insights into the nature
of star formation and the larger mass distribution in the Galaxy as more
streams are discovered.

We thank members of the Conroy group at Harvard for useful discussions and
helpful comments. HMK thanks Harita Koya for her continued support. HMK
acknowledges support from the DOE CSGF under grant number DE-FG02-97ER25308.
CC acknowledges support from the Packard Foundation. YST is supported by the
NASA Hubble Fellowship grant HST-HF2-51425.001 awarded by the Space Telescope
Science Institute. The computations in this paper were run on the Odyssey
cluster supported by the FAS Division of Science, Research Computing Group at
Harvard University. This work has made use of data from the European Space
Agency mission Gaia (https://www.cosmos.esa.int/gaia), processed by the Gaia
Data Processing and Analysis Consortium (DPAC,
https://www.cosmos.esa.int/web/gaia/dpac/consortium). Funding for the DPAC has
been provided by national institutions, in particular the institutions
participating in the Gaia Multilateral Agreement. The Sloan Digital Sky Survey
IV is funded by the Alfred P.Sloan Foundation, the U.S. Department of Energy
Office of Science, and the Participating Institutions and acknowledges support
and resources from the Center for High-Performance Computing at the University
of Utah. Software: IPython (Pérez & Granger, 2007), Cython (Behnel et al.,
2011), Astropy (Astropy Collaboration et al., 2013, 2018), NumPy (Van Der Walt
et al., 2011), SciPy (Jones et al., 2001–), scikit-Learn (Pedregosa et al.,
2011), Matplotlib (Hunter, 2007), HDBSCAN (McInnes et al., 2017).

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