Roman CCS White Paper

The Galactic Center with Roman

Roman Core Community Survey: Galactic Bulge Time Domain Survey

Scientific Categories: Supermassive black holes and active galaxies Stellar
populations and the interstellar medium Stellar physics and stellar types

Additional Keywords: Galactic center, Star clusters Exoplanets and exoplanet
formation Astronomical simulations

Submitting Author:

Name: Sean K. Terry Institution: University of California, Berkeley Email:
<EMAIL_ADDRESS>
Co-authors: Matthew W. Hosek Jr. (UCLA), Jessica R. Lu (UC Berkeley), Casey
Lam (UC Berkeley), Natasha Abrams (UC Berkeley), Arash Bahramian (Curtin U.),
Richard Barry (NASA/GSFC), Jean-Phillipe Beaulieu (IAP/UTAS), Aparna
Bhattacharya (UMD), Devin Chu (UCLA), Anna Ciurlo (UCLA), Will Clarkson (U. of
Michigan), Tuan Do (UCLA), Kareem El-Badry (Harvard), Ryan Felton (NASA/Ames),
Matthew Freeman (UC Berkeley), Abhimat Gautam (UCLA), Andrea Ghez (UCLA),
Daniel Huber (U. Hawaii), Jason Hunt (Flatiron/CCA), Macy Huston (PSU),
Tharindu Jayasinghe (UC Berkeley), Naoki Koshimoto (Osaka U.), Madeline Lucey
(UT Austin), Florian Peißker (U. Cologne), Anna Pusack (UC Berkeley), Clément
Ranc (IAP), Dominick Rowan (OSU), Robyn Sanderson (U. of Pennsylvania), Rainer
Schödel (IAA-CSIC), Richard G. Spencer (NIH), Rachel Street (LCO), Daisuke
Suzuki (Osaka U.), Aikaterini Vandorou (UMD)

Abstract: We advocate for a Galactic center (GC) field to be added to the
Galactic Bulge Time Domain Survey (GBTDS). The new field would yield high-
cadence photometric and astrometric measurements of an unprecedented $\sim$3.3
million stars toward the GC. This would enable a wide range of science cases,
such as finding star-compact object binaries that may ultimately merge as
LISA-detectable gravitational wave sources, constraining the mass function of
stars and compact objects in different environments, detecting populations of
microlensing and transiting exoplanets, studying stellar flares and
variability in young and old stars, and monitoring accretion onto the central
supermassive black hole. In addition, high-precision proper motions and
parallaxes would open a new window into the large-scale dynamics of stellar
populations at the GC, yielding insights into the formation and evolution of
galactic nuclei and their co-evolution with the growth of the supermassive
black hole. We discuss the possible trade-offs between the notional GBTDS and
the addition of a GC field with either an optimal or minimal cadence.
Ultimately, the addition of a GC field to the GBTDS would dramatically
increase the science return of Roman and provide a legacy dataset to study the
mid-plane and innermost regions of our Galaxy.

## Summary of Recommendations & Science:

In order to conduct one of the deepest wide-field surveys of the Galactic
Center (GC), we recommend:

  * •

One Roman WFI field positioned at the GC with an identical observing strategy
as the notional GBTDS.

This will maximize GC-related science and enable a wealth of high-precision,
wide-field studies previously unreachable in this region. These include:

  * •

A high cadence survey along the GC sight-line that will measure many transient
phenomena including young stellar flares, short/long-period variables, star-
compact object ellipsoidal variables, near-IR accretion flares from LMXBs,
microlensing planets/brown dwarfs/compact objects, transiting planets, and
more.

  * •

Large scale formation and dynamical evolution of stellar populations in the
environment surrounding the supermassive black hole (SMBH) SgrA*.

  * •

Long-term, high cadence monitoring of SgrA* events (accretion, close
approaches, tidal disruption, lensing, and more).

##  1 Scientific Motivation

The GC is a unique environment that allows us to study a SMBH and the
surrounding stellar populations in a resolved manner. The region is primarily
dominated by two old ($\sim$5 – 10 Gyr) populations: the Nuclear Star Cluster
(NSC), which is the densest and most massive star cluster in the galaxy
[[]]Schodel:2014zl, and the Nuclear Stellar Disk (NSD), which extends along
the Galactic plane to R $\sim$150 pc [57]. However, the GC is also a zone of
active star formation, and hosts three of the most massive young star clusters
($\lesssim$ 10 Myr) in the MW: the Young Nuclear Cluster (YNC), the Arches
cluster, and the Quintuplet cluster [[, e.g.]]Serabyn:1998hw, Figer:1999px,
Paumard:2006sh, Lu:2013wo, Stostad:2015gr. As similar structures are commonly
found in other galaxies, the GC serves as a valuable template for
understanding how galactic nuclei form and evolve. In addition to the GC
itself, this sight line also probes the MW’s inner thin disk with young and
metal-rich populations relative to the thick disk and bulge located at the
slightly higher galactic latitudes of the GBTDS. We aim to describe the
motivation for adding Roman observations of the GC with either the same
observing schedule as the notional GBTDS or at a lower cadence.

##  2 The Survey, Science Cases, and Metrics

The Nancy Grace Roman Space Telescope (Roman) will conduct one of the deepest
ever surveys toward the central region of the Milky Way (MW) during its
Galactic Bulge Time Domain Survey (GBTDS). This Core Community Survey (CCS)
will provide multi-filter high resolution imaging of a ${\sim}$2 deg2 patch of
sky at approximately $-0.5<l<1.5$ and $-2.0<b<-0.5$ (see Figure 1) for over
four years. The Galactic center (GC) lies just ${\sim}1.4$ deg away from the
notional GBTDS fields (Figure 1).

We present here an ‘optimal’ and ‘minimal’ observing strategy for the
recommended Roman GBTDS + GC survey (hereafter Roman GB+GC). Both strategies
include adding an eighth field at the GC pointing (e.g. 7 GBTDS + 1 GC field;
left panel of Figure 1). The optimal strategy involves observing the GC field
at the same cadence, exposure times, and filters as the notional GBTDS fields.
The minimal strategy involves observing the GC field at a lower cadence (e.g.
every 12 hours or more) in one wide passband filter (F146). Both of these
strategies would measure a myriad of time-domain phenomena through photometric
and astrometric monitoring.

(a)

(b)

Figure 1: Left: The notional Roman GBTDS fields from [49] (black outlines)
overlaid on an $H$-band extinction map from [19]. The additional Roman-GC
field described in this paper is shown in yellow outline. Right: Composite
image (in J, H, Ks bands) of the GC region from 2MASS. The full 0.281 deg2
Roman field covers the central supermassive black hole SgrA*, nuclear star
cluster (NSC), young nuclear cluster (YNC), nuclear stellar disk (NSD),
Arches, and Quintuplet clusters in one pointing.

A Roman GB+GC survey would uniquely probe the transient populations in the
Galactic mid-plane and center. Survey results could include a census of star-
compact object binary systems both in the NSC and in the foreground (A.1). The
NSC alone is expected to host many of these systems from star formation and
dynamical predictions ([36]; estimated yield of ${\sim}$ 250). Further, we can
conduct a census of transiting exoplanets in the innermost Galactic mid-plane
(A.2). The microlensing event rate is at least an order of magnitude larger in
the mid-plane [40], thus the addition of a GC field could add a substantial
amount of planetary and compact object detections (${\sim}$hundreds total) to
the expected microlensing yield for the GBTDS [25, 49, 51] and enable us to
study how the planet, star, and compact object mass function changes in the
Galactic mid plane and center (A.3). Lastly, we can study the occurrence rate
of young stellar flares, near-IR counterparts to LMXBs, and accretion events
and near-IR flares from SgrA* (A.4). Superb information on stellar variability
will provide unique constraints on the stellar population and formation
history of the GC. For example, the number density of RR Lyraes will provide
us with a tight constraint on the presence and distribution of an old metal-
poor population in this region.

The recommended survey would also enable revolutionary investigations of the
formation and evolution of its stellar populations through long-term proper
motion and parallax measurements. For example: how did the NSC and NSD form,
and what is their relationship to each other and to the Galactic bulge at
large (B.1)? What is the distribution of mass, and thus gravitational
potential of the region (B.2)? What is the lifecycle, internal kinematics, and
stellar Initial Mass Function (IMF) of young clusters in the GC environment
(B.3)? The outstanding spatial coverage and astrometric performance offered by
Roman makes it uniquely suited to conduct a large-scale kinematic survey of
the region to address these questions. In the case of the optimal survey, it
will be possible to make parallax-based measurements of stellar distances for
bright stars towards the GC (B.4).

Figure 2: Left panel: The distribution of transit duration for confirmed and
candidate transiting exoplanets from the NASA Exoplanet Archive3. The minimal
and optimal thresholds (black vertical bars) are shown with the cadence of 15
minutes and 12 hours, respectively. The minimal strategy shows that Roman will
measure at best one data point during transits for long period (transit
duration) planets, while the optimal strategy will measure many data points
during transit for nearly the entire population. Stacking and phase folding
transit light curves will benefit both strategies. Right panel: The Einstein
timescale distribution for predicted FFPs and low-mass stars, adapted from
[25]. The $t_{E}$ signal from stars is shown as a thick gray line. The FFP
distributions (orange, red, blue-hatched) are derived using three different
mass functions from [3] and [39]. The minimal and optimal thresholds shown
here include a requirement that Roman acquires at least five data points
during the microlensing event. The optimal strategy here will aid in
constraining the true mass function of FFPs, while the minimal strategy will
miss a significant fraction of FFPs. 00footnotetext:
https://exoplanetarchive.ipac.caltech.edu/

###  2.1 Depth, Photometric and Astrometric Requirements

We estimate that the GC field will obtain photometric and astrometric
measurements of $\sim$3.3 million stars over an area at least $\sim$7x larger
than previous proper motion studies of the GC (Fig. 3). The depth of the
survey (F146 $\sim$ 23$-$24 mag) is set by the estimated stellar confusion
limit for Roman based on HST WFC3-IR images in the GC region [[]]Hosek:2015cs,
Rui:2019ae. For an Arches-like cluster, this depth corresponds to a 0.5 – 0.7
M⊙ pre-main sequence star. For an old NSC-like population, this depth reaches
0.8 – 1.1 M⊙ stars near the main-sequence turn-off.

The primary driver for the minimal and optimal strategies is the detection and
characterization of time-domain phenomena at and along the sight-line to the
GC. The estimated photometric precision achieved by both observing strategies
is $0.03-0.06$ mag in a single F146 image. This precision allows for very
subtle light curve features to be detected in microlensing and transiting
science cases, as well as ellipsoidal variations due to star-compact object
binaries, flares from both young stellar objects (YSO) and the near-IR
counterpart to SgrA*. The range of transients the survey is sensitive to is
determined by the cadence of the observations. The optimal strategy allows for
full characterization of hour long flares (SgrA*, A.4), planets with transit
durations as low as two hours, and short timescale light curve perturbations
from low-mass planets [49]. As described in Table 2, Figure 2, and Appendix A,
the minimal strategy loses sensitivity to SgrA* flares, the shortest period
transiting planets and eclipsing binaries, as well as the lower-mass regime of
bound planets and FFPs from microlensing.

Both the minimal and optimal survey strategies will produce high-precision
stellar proper motions due to the high cadence of the observations. The
minimal strategy will achieve precisions of $\sim$25 $\mu$as/yr ($\sim$1
km/s), which enables investigations of kinematic sub-structures within the NSC
and NSD as well as the velocity dispersion profiles of the young clusters.
With the optimal survey, it becomes possible to measure stellar distances at
the GC to within $\pm$200 pc via parallax for the brighter stars in the survey
(F146 $\lesssim$ 19 mag) for the first time111This assumes that the observing
seasons will alternate between Fall and Spring windows for the GC.. This
distance resolution makes it possible to separate stars in the NSC + NSD from
those in the Galactic bulge.

Figure 3: The observed stellar density profile of the GC showing the NSC and
NSD, adopted from [4]. The Roman GB+GC survey would provide stellar proper
motions with at least 50% azimuthal coverage well into the NSD (blue line),
covering an area $\geq$7x larger than previous proper motion surveys (e.g.
[12] and HST, grey and black lines, respectively). The field would also
include the Arches and Quintuplet clusters (red star).

##  3 Discussion and Conclusions

We recommend that a GC field be added to the notional GBTDS. This Roman GB+GC
survey will produce long-baseline wide-field monitoring of SgrA*, the
surrounding GC region, and Galactic mid-plane populations along the sight-
line. A full Roman field on the GC at the GBTDS cadence will enable detection
and characterization of many transient phenomena, from young stellar flares
and short/long period variables, to transiting planets in the innermost mid-
plane. We have also shown that this survey will gather a census of star-
compact object systems that are expected to be hosted by the NSC and
surrounding environment. Monitoring of the central SMBH and its local effects
will add to the rich, decades-long history of high-precision studies of this
object and the population of stars orbiting it [17, 15]. Additionally, the
proper motions produced by the survey will allow for comprehensive kinematic
modeling of the NSC and NSD, constraining their formation and evolution, and
make the first measurements of the tidal tails and velocity dispersion
profiles of the Arches and Quintuplet clusters, revealing the lifecycle and
IMF of young clusters near the GC.

We have demonstrated that a minimal observing strategy of twice a day
observations on the GC, taken with a single wide band filter (e.g. F146),
enables many of the presented science investigations to be achieved (Table 2,
Appendix A, B). However, an optimal observing strategy will maximize the
scientific return for many of the transient populations that rely on high-
cadence photometric monitoring (transiting planets, eclipsing and star-compact
object binaries, short duration flares, microlensing planets).

Given the significant number of compelling science cases for a Roman GB+GC
survey, along with the relative ease of visiting the GC during the notional
GBTDS, we advocate that the community survey committee consider this strategy.
The addition of this GC survey at the GBTDS cadence will increase the
scientific return of the mission as a whole. The exact trade-offs between the
cadence, number of fields, and detection yields for the science cases
(including microlensing planets) should be explored with a more detailed
analysis.

Table 1: The GC Observing Strategy

Parameter | Minimal | Optimal
---|---|---
Pointing | SgrA∗ | SgrA∗
Cadence |  ${\gtrsim}$12 hours | Same as GBTDS
Depth | 23 mag $<$ F146 $<$ 24 mag | 23 mag $<$ F146 $<$ 24 mag
Total seasons | Same as GBTDS | Same as GBTDS
Total Survey Area | 0.281 deg2 | 0.281 deg2
Specific filters | F146 only | Same as GBTDS
Total Filters | one | Same as GBTDS
Subpixel Dithers | [1] | [1]
Large gap dithers | [1] | [1]
Ground-based coverage | Nightly w/ PRIME222http://www-ir.ess.sci.osaka-u.ac.jp/prime/index.html | Nightly w/ PRIME2
Photometric precision | 0.03 – 0.06 mag | 0.03 – 0.06 mag
Astrometric precision | 1 – 1.6 mas | 1 – 1.6 mas
Proper Motion precision | 15 – 25 $\mu$as/yr | 2.5 – 3.5 $\mu$as/yr

Note. Photometric and astrometric precisions are estimated for a single F146
image, while the proper motion precision is estimated for the completed
survey. All precisions correspond to the values achieved at the reported F146
depth. Magnitudes are given in the VEGAMAG photometric system.

Table 2: Summary of Science Cases, Achievable by Minimal or Optimal Strategy

Science Case | Section | Minimal | Optimal
---|---|---|---
Star-Compact Object Binaries | A.1 | ✘/✓ | ✓
Transiting Exoplanets and EB’s | A.2 | ✘ | ✓
Microlensing | A.3 | ✘/✓ | ✓
Monitoring SgrA* | A.4 | ✘ | ✓
The NSC/NSD | B.1 | ✓ | ✓
Mass Distribution of the GC | B.2 | ✓ | ✓
Lifecycle, kinematics, IMF of GC clusters | B.3 | ✓ | ✓
Parallaxes at the GC (F146 $\lesssim$ 19 mag) | B.4 | ✘ | ✓

Note. For clarity, ✓means that the given science case can be achieved with the
specified strategy, as described in the Appendices. ✘ means the science case
cannot be achieved. The mixed ✘/✓means the given science case will have
diminished sensitivity, but can be partially achieved.

##  Appendix A Transients Toward the GC

###  A.1 Star-Compact Object Binary Systems

Regardless of the minimal or optimal observing strategy, this Roman GB+GC
program will gather the largest census of star-compact object binary systems
from a single observatory to-date. For future considerations, these systems
can also be precursors to the mergers that are currently being detected by
LIGO, as well as those systems that LISA expects to detect via gravitational
waves. These objects (sometimes referred to as detached systems) can be
characterized through continuous monitoring and photometric light curve
modeling of temporal phenomena: ellipsoidal variations, Doppler beaming, and
self-lensing (e.g. Masuda & Hotokezaka 2019).

We highlight ellipsoidal variables in the NSC as an example of the power of a
Roman GB+GC program for better understanding binary systems. Dynamicists
predict that the NSC and surrounding region should host many of these systems
from mass segregation and exchange interactions occurring among these
binaries. With the minimal Roman-GC observing strategy described in Table 1,
we estimate ${\sim}275$ candidate detections with the minimal strategy, or
${\sim}350$ candidate detections with the optimal strategy during the full
mission. The optimal survey adds ${\sim}75$ short period systems that are
uniquely interesting for constraining binary merger models. Furthermore, the
additional temporal coverage provided by the optimal survey will help
constrain the true period distribution for these systems, which is unknown at
present. Confirming these candidates as true star-compact object binaries
would require spectroscopic followup.

###  A.2 Probing Binary Stars and Planets with Transit Photometry

Additionally, with the optimal observing strategy and expected photometric
precision of $0.03-0.06$ mag (Table 1), a high-cadence Roman GC field will
detect thousands of eclipsing binaries and transiting exoplanets. A simple
extrapolation from recent Roman transiting exoplanet predictions [61, 65]
(adjusting for higher surface density $+$ extinction) gives between
${\sim}8,500$ and ${\sim}28,000$ transiting exoplanets toward the GC. Most of
these planets will be giants ($R_{p}>4R_{\oplus}$) on close-in orbits ($a<0.3$
AU), however small planets ($R_{p}<4R_{\oplus}$) could make up $5-10\%$ of the
total yield. Regardless of the sizes, an exciting new window will be opened on
the population of transiting planets in the innermost mid-plane of the MW.

As shown on the left panel of Figure 2, the minimal GC observing strategy
would miss nearly all of the transiting exoplanet detections. This leaves
mostly long period eclipsing binaries as the only reachable populations
related to this science case.

###  A.3 The Mass Function of Planets, Stars, and Compact Objects via
Microlensing in the Mid-plane

The microlensing event rate is expected to increase significantly at lower
galactic latitudes. Indeed, a recent study of microlensing events found in the
VISTA Variables in the Vía Láctea (VVV) Survey shows the microlensing optical
depth rising continuously up to the GC, despite the increased extinction [40].
This large survey mapped the GC region and surrounding galactic disk with
near-IR photometry ($K_{s}$ band) at approximately nightly cadence. This
previous study represents an important demonstration that an effective near-IR
survey in this field can be profitable and detect microlensing objects with
timescales ranging from $t_{E}\,{\lesssim}\,1.5$ days (e.g. FFPs) to
$t_{E}\,{\gtrsim}\,100$ days (e.g. stellar-mass black holes.

Using predictions from [49, 25, 51] [adjusted for higher event rate $+$
extinction], we estimate a ${\sim}$five year GC survey (at the optimal
cadence) may detect as many as ${\sim}25,000$ microlensing events. Of these,
we estimate ${\sim}25$ FFPs, ${\sim}33$ bound Earth-mass planets, and at least
180 planets (total bound + FFPs). Additionally, we estimate between ${\sim}35$
and ${\sim}75$ isolated black holes and neutron stars may be detectable with
this survey. These predicted yields depend strongly on the average timescale
($t_{E}$) of microlensing events toward the bulge, which may be shorter than
the timescales in typically observed microlensing fields. Further, the exact
number of compact object lenses that will be characterizable (e.g. reliable
measurement of mass and velocity) will depend on the cadence and time baseline
between seasons. See the black hole microlensing and Roman-Rubin synergies CCS
white papers for more details [31, 60]. The minimal observing strategy
presented here would preferentially lose the lowest-mass bound planets and
FFPs (see Figure 2), as low-mass binary lens planetary perturbations and FFPs
give the shortest duration light curve features [25, 49]. However, we still
expect ${\sim}$few hundred higher-mass planet detections with the minimal
observing strategy, which will aid in constraining parts of the mass function
for stars and planets with microlensing [63].

Given the much higher and spatially variable extinction toward the GC, it will
likely prove difficult to fully characterize many of the detected planets
toward the GC due to uncertain source star properties, distances, and other
methods typically used to constrain planet and host star characteristics [55].
Nevertheless, all of the microlensing yields from the GC effectively act as a
surplus to the overall GBTDS microlensing yield and should not be considered
as part of the fixed fraction of microlensing planets that will yield mass
measurements as originally set by the administration’s requirements on
microlensing exoplanets in the GBTDS.

Ultimately, adding a GC field to the GBTDS may have both positive and negative
impacts on the overall microlensing exoplanet yields. This depends strongly on
the final slew/settle times for the program. With current slew/settle
times333https://roman.gsfc.nasa.gov/science/RRI/ROMAN_Observatory_Reference_Information_20210301.pdf,
and assuming the GBTDS fields of [49], the addition of the high-cadence GC
field would effectively lower the overall cadence for each field from
${\sim}15$ minutes to ${\sim}19$ minutes. Using equations 12, 13, and Table 6
of [49], the number of detectable Earth-mass planets for this cadence is
approximately $N_{\bigoplus,19}=0.91N_{\bigoplus,15}$. In other words,
${\sim}20$ Earth-mass planets would be missed using the assumed parameters of
[49] with no optimized slew/settle times. This assumes there are no Earth-mass
planets detected in the GC survey that would balance this loss. If it is
determined that there is extra efficiency that can be gained with faster
slew/settle times (e.g. no diminished overall cadence), then adding a field to
the GC is worth strongly considering. Finally, using the same assumptions as
above (current slew/settle + current GBTDS fields of [49]), the addition of a
low-cadence GC field would have a negligible effect on the overall cadence for
each field (e.g. from ${\sim}15$ minutes to ${\sim}15.4$ minutes). We note
there are several other possibilities for a lower cadence GC observing
strategy, beyond the stated ‘minimal’ strategy of 12 hour cadence. One
additional example would be a high cadence GC survey during only the first and
last seasons, and a lower cadence GC survey conducted during the middle
seasons. While these ’mixed’ cadence strategies do not optimize the yield for
the GC-related science described here, they may represent a reasonable
compromise while maintaining the level-1 requirements on exoplanets for the
GBTDS.

###  A.4 Monitoring SgrA*

The gravitational influence of SgrA* can be seen through monitoring of early-
type and late-type stars orbiting the central potential [48, 9], as well as
gas and dust streams orbiting at distances up to 1pc from SgrA* [38, 15]. An
intriguing filamentary gas feature, named X7, was recently reported to be
undergoing fragmentation as it approaches SgrA* [6]. This is one recent
example of intriguing dynamical interactions between SgrA* and its immediate
surroundings that are reachable by Roman.

SgrA* itself has a near-IR counterpart that can exhibit flares lasting
${\sim}$1 hour [16]. During these flares, the source flux can vary by a factor
of 100 or more [18, 16]. The duration and intensity of these flares means that
the optimal Roman GB+GC observing strategy can easily sample these events.
This high cadence monitoring will be extremely helpful for distinguishing
different emission models that have traditionally been used to describe
SgrA*’s quiescent phase. A long-standing mystery that Roman GB+GC could
address is the interpretation of SgrA*’s extremely low accretion rate that
prior multi-wavelength studies have deduced. The minimal observing strategy of
Table 1 may result in these short timescale flaring events being missed by the
survey.

Finally, with either the minimal or optimal observing strategy presented here,
long timescale evolution and other trends at the location of SgrA* can be
studied. Having continuous, long-term tracking of the source and its emission
(in near-IR) will aid in understanding the specific quiescent nature of the
SMBH.

##  Appendix B Proper Motions and Large-scale Dynamics

The recommended Roman GB+GC survey would measure high-precision stellar proper
motions over an unprecedented area of the GC, providing at least 50% azimuthal
coverage out to R $\sim$13.5’ (33 pc) from SgrA* (Figure 1). Due to the high
extinction and stellar crowding at the GC, it is very expensive to make
comparable observations from the ground (where adaptive-optics or speckle-
holography techniques are required) or from other space-based platforms (e.g.,
Roman offers a FOV 100x larger than Hubble). Thus, the Roman-GC survey is
strongly synergistic with other facilities as it provides large-scale
dynamical context for the GC as a whole.

Here we highlight three science cases enabled by this survey: the formation
and structure of the NSC and NSD, the mass distribution and gravitational
potential of the GC, and the lifecycle, kinematics, and IMF of star clusters
born in the region. We also discuss the predicted astrometric performance of
the survey in more detail.

###  B.1 The NSC and NSD: Key Components of Galactic Nuclei

Nuclear star clusters and nuclear stellar disks are commonly observed in the
central regions of spiral galaxies [13, 41], and are key components for
understanding the evolution of galactic nuclei. However, it is not yet clear
how these features form or how they relate to one another. In the Milky Way,
the distinction between the NSC and NSD is primarily based on the observed
density profile of stars [[, e.g.,]]Chatzopoulos:2015lq, Gallego-Cano:2020fx,
and there is growing evidence that they may have different star formation
histories [44, 5, 53]. Measuring the kinematics of these structures will
reveal the relationship between their formation mechanisms, as well as their
connection to gas flows along the galactic bar. Past efforts to model the
kinematics of the NSC and NSD have been limited by small sample sizes
($\lesssim$10,000 stars) and/or limited azimuthal coverage [[,
e.g.,]]Do:2013hi, Chatzopoulos:2015lq, Feldmeier-Krause:2020yk,
Sormani:2020my, Libralato:2021ck, Sormani:2022lz, Nogueras-Lara:2022cz, due to
the difficulty of measuring stellar proper motions over large regions.

The Roman GB+GC survey overcomes these challenges by measuring proper motions
for $\sim$3.3 million stars over a region at least $\sim$7x larger than
previous proper motion studies. This represents a monumental gain in terms of
both radial coverage and sample size. Reaching R = 13.5’, this survey extends
well into the regime where the NSD dominates the stellar density profile, and
thus it becomes possible to cleanly model the two components (Figure 3).

###  B.2 The Mass Distribution and Gravitational Potential of the GC

The Roman GB+GC survey will also significantly improve constraints on the mass
distribution and gravitational potential of the GC. The NSC and NSD dominate
the gravitational potential of the galaxy between 1 pc $\lesssim$ R $\lesssim$
300 pc [[, e.g.,]]Launhardt:2002hl, but since their mass distributions are not
well known, there are significant uncertainties in the gravitational potential
[56]. This has many implications for a range of physical processes in the
region, as the gravitational potential plays a major role in the
transportation of material to the GC from the galactic bar [[,
e.g.,]]Tress:2020zj, the formation of the observed ring-like structure of
dense gas [[, e.g.,]]Molinari:2011dq, the orbits of star clusters like Arches
and Quintuplet [24], and may trigger star formation in dense molecular clouds
in the region [[, e.g.,]]Kruijssen:2015mv, Kruijssen:2019kx.

The recommended survey will greatly improve measurements of the mass
distribution of the NSC and NSD, not only due to the large radial coverage,
but also because of the high azimuthal completeness it provides over the
survey region. This allows for unbiased measurements of the shape, rotation,
and velocity anisotropy of the NSC and NSD, properties which would otherwise
be assumed or approximated when deriving the mass distributions of these
populations via kinematic modeling [[, e.g.,]]Chatzopoulos:2015lq,
Sormani:2020my.

###  B.3 The Lifecycle, Kinematics, and IMF of Young Star Clusters in the GC

The Arches and Quintuplet clusters are two of the most massive young clusters
in the Galaxy. However, due to the strong tidal shear at the GC, these
clusters are predicted to dissolve on timescales of $\lesssim 20$ Myr [26,
66]. As a result, they are expected to exhibit large tidal tails that extend
some 30$-$70 pc (12’$-$30’) from the clusters [[]]Habibi:2014qf. However,
these structures have not yet been observed due to two main challenges: proper
motions must be used to detect such tidal tails, as differential extinction
makes it impossible to identify young stars in the region through photometry
alone [[, e.g.,]]Stolte:2008qy, Hosek:2015cs, and the tails are expected to be
composed of primarily lower-mass stars [[, M $\lesssim$ 2.5 M⊙;]]Park:2018fj.
The spatial coverage, astrometric accuracy, and sensitivity of the recommended
Roman GB+GC survey would offer the first opportunity to detect and
characterize the tidal tails of these clusters, testing models of cluster
evolution near the GC. This will reveal whether tidal disruption can resolve
the apparent deficit of young clusters near the GC relative to the recent star
formation history [[, the “missing cluster problem”; e.g.,]]Nogueras-
Lara:2022rt, or if additional modes of star formation other than star cluster
formation must be invoked.

In addition, characterizing the tidal tails of Arches and Quintuplet is
required to properly measure their IMFs. The IMF is a key observational
benchmark for star formation theory, as its properties are tied to the
underlying physics driving the process [[, e.g.,]]Krumholz:2014ne,
Offner:2014vn. For the Arches cluster, the IMF has been found to be
significantly different than those of star clusters in the Galactic disk for M
$\gtrsim$ 2 M⊙, possibly due to the impact of the extreme GC environment on
star formation [[, e.g.,]]Hosek:2019kk. However, several different IMF models
are allowed, and extending the measurement to lower masses is required to
determine which model (and associated physical interpretation) is correct. The
loss of stars via tidal tails is expected to become much more significant at
such lower masses, and so characterizing the tidal tails is required to infer
the IMF from the present-day cluster population.

Finally, the high astrometric precision of the Roman GB+GC survey will allow
us to probe the internal kinematics of the Arches and Quintuplet clusters.
With a proper motion accuracy of 15 - 25 $\mu$as/yr from the minimal survey,
it becomes possible to measure the velocity dispersion profiles and thus
dynamical mass of the clusters [[, e.g.,]]Clarkson:2012ty. This allows for
constraints on the mass function at stellar masses below what is possible to
observe with current telescopes.

###  B.4 Astrometric Performance of the Survey

To calculate the expected proper motion performance of the Roman GB+GC survey,
we assume that all astrometry will be extracted from the F146 images (FWHM =
0.105”), each of which have an exposure time of ${\sim}$50 s. Based on the
Roman WFI Imaging Sensitivity
Calculator444https://roman.gsfc.nasa.gov/science/WFI_technical.html;
calculated June 2023, we expect to reach a signal-to-noise ratio (SNR) of
$\sim$ 20 – 30 per image for the stars at the faint end of our sample (F146 =
23 – 24 VEGAMAG). We define the relationship between SNR and astrometric error
($\sigma_{ast}$) as:

$\sigma_{ast}=\alpha*\frac{FWHM}{SNR}$ (1)

where $\alpha$ is an empirical constant. We estimate $\alpha$ = 0.3 based on
HST WFC3-IR F153M observations of the Arches and Quintuplet clusters [23, 50,
24], which we expect to perform similarly to the recommended observations.
Thus, we predict $\sigma_{ast}$ = 1 – 1.6 mas per image at the faint end of
the sample (Table 1).

For the purposes of astrometry, we can improve the astrometric performance by
stacking multiple F146 images per astrometric epoch. Since the Point Spread
Function (PSF) of stars will begin to blur in stacked images due to their
intrinsic motion, the timescale over which we can stack images with minimal
impact on the astrometric performance is constrained by the fastest moving
stars in the sample. For the Roman GB+GC survey, the fastest stars of interest
would be hypervelocity stars produced via dynamical interactions with SgrA*
[21], which may have ejection velocities upward of $\sim$1800 km/s [[,
$\sim$47.5 mas/yr;]]Koposov:2020gz. We will stack F146 images until these
stars move $\sim$1 mas (approximately the astrometric error of an individual
image), which means that each astrometric epoch will span 7 days. Thus, for
the minimal survey strategy (1 img / 12 hrs) and optimal observing strategy (1
img / 15 mins) we will have 14 images and 672 images per epoch, respectively.

The astrometric performance per epoch ($\sigma_{ast,tot}$) is then:

$\sigma_{ast,tot}\approx\frac{\sigma_{ast}}{\sqrt{N_{img}}}$ (2)

where $N_{img}$ is the number of images per epoch [64]. This yields
$\sigma_{ast,tot}$ $\sim$ 0.3 – 0.4 mas per epoch for the minimal survey and
$\sigma_{ast,tot}$ $\sim$ 0.04 – 0.05 mas per epoch for the optimal survey.
The final proper motion precision of the survey ($\sigma_{pm}$) can then be
estimated as:

$\sigma_{pm}\approx\frac{\sigma_{ast,tot}}{\sqrt{\sum_{i=0}^{N_{ep}}(t_{i}-t_{ave})^{2}}}$
(3)

where $N_{ep}$ is the total number of epochs, $t_{ave}$ is the average time
over all epochs, and $t_{i}$ is the time of the $i$th epoch. Assuming each
observing season is 70 days long (and thus 10 epochs per season) and are
spread over 5 years, then we anticipate a final proper motion precision of
$\sigma_{pm}$ $\sim$ 15 – 25 $\mu$as / yr ($\sim$ 1 km / s) for the minimal
survey and $\sigma_{pm}$ $\sim$ 2.5 – 3.5 $\mu$as / yr ($\sim$ 0.15 km / s)
for the optimal survey.

If the observing seasons are distributed across the Fall and Spring observing
windows for the GC, then it becomes possible to measure stellar distances via
parallax for stars near the GC in the optimal survey. At a distance precision
of $\sim$200 pc, it becomes possible to begin separating stars from in the NSD
(R $\lesssim$ 200 pc from SgrA*) from those in the Galactic bulge (R
$\lesssim$ 1000 pc from SgrA*). Assuming a typical distance of 8000 pc, this
distance precision is achieved at a parallax uncertainty of approximately 3
$\mu$as. The parallax uncertainty ($\sigma_{pi}$) can be estimated as:

$\sigma_{\pi}=\frac{FWHM}{\delta_{\lambda}*SNR_{tot}}$ (4)

where $SNR_{tot}$ is the total signal-to-noise across all images and
$\delta_{\lambda}$ is a factor defined from 0 – 1 that describes how well the
parallactic ellipse is sampled across the observations [32]. Assuming
$\delta_{\lambda}$ = 0.8, then $SNR_{tot}$ $\approx$ 44000 is required to
achieve the target precision. Considering:

$SNR_{tot}=\sqrt{\sum_{i=0}^{N_{img}}(SNR_{i})^{2}}$ (5)

where $SNR_{i}$ is the SNR achieved in the $i$th of $N_{img}$ total images.
Thus, for the optimal survey ($N_{img}$ = 40320), an $SNR_{i}$ $\approx$ 200
produces the necessary $SNR_{tot}$ for a meaningful parallax measurement. This
suggests that we will be able to measure parallax-based distances to stars at
the GC for F146 $\approx$ 19 mag, which corresponds to high-mass stars (M
$\gtrsim$ 8 M⊙) in the young clusters and red clump stars in the older
populations. We note that such parallax measurements will only be possible in
the optimal survey; for the minimal survey, which has much fewer images,
$SNR_{i}$ $\approx$ 1500 is required to achieve the required precision, which
is not possible for the vast majority of stars near the GC.

## Appendix C

### Synergies with other White Papers

The previous call for community input requested ‘science pitches’ for each of
the Roman CCS programs. This call received several pitches involving GC
observations with Roman555https://rb.gy/vt2wt, which demonstrates large and
wide-ranging interest in visiting this region during the GBTDS. We note
several interesting science pitches involving near-IR surveys from large
ground-based observatories (PRIME, JASMINE) that will turn on soon and operate
during the notional GBTDS mission. PRIME will offer high cadence photometric
coverage using the same Roman chips and near-IR passbands, while JASMINE will
conduct a near-IR astrometry mission starting in 2028. This astrometry program
will measure very precise motions for mostly bright stars in the field ($H<14$
mag), this information can act as a good calibration or systematics check for
Roman if Roman acquires shallow images of these bright stars occasionally.

While it is uncertain how many of these science pitches will have accompanying
white papers submitted for the current call, we are aware of at least one
other Roman CCS white paper that specifically recommends GC observing
strategies that synergize well with the studies presented in this work. The
Bahramian CCS white paper [2] primarily focuses on black hole and neutron star
science (e.g. XRBs and detached systems), and recommends moving one of the
notional GBTDS fields to the GC and a second intervening field to connect the
GC field with the other GBTDS fields (see Figure 1 of [2]). They show the
total number of Chandra sources that can be monitored with the inclusion of
their recommended fields is nearly $5\times$ higher than the number of sources
covered by the notional GBTDS fields. We describe a similar science case in
this white paper involving star-compact object binaries (e.g. detached
systems) in Section 2 and Appendix A.

There are several synergies between our white paper and other GBTDS-related
white papers [31, 60]. The Lam paper focuses on delivering high-quality
astrometry from the data reduction pipelines and potentially increasing
temporal coverage in the seasonal GBTDS gaps with Roman or other facilities,
which would be of benefit to the GC-connected science presented here. The
Street paper focuses on coordinating the survey strategy of the GBTDS with the
Rubin observatory, by filling the GBTDS seasonal gaps with Rubin photometric
coverage. This is particularly useful for long duration microlensing events
caused by compact object lenses like black holes and neutron stars. Figure 2
of [60] shows that the very wide field of Rubin allows a deep drilling field
placed on the notional GBTDS to also cover the GC (or at least partially).
This would clearly benefit the Roman GB+GC case for long duration microlensing
events.

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