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 ∼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.Comment: 19 pages, 3 figures. Submitted to the NASA Roman Core Community
Surveys White Paper Cal