  The first bright objects to form in the Universe at redshift $z \sim 10-20$
might have been Dark Stars, made primarily of hydrogen and helium but powered
by dark matter. In this study, we investigate the detectability of Supermassive
Dark Stars (SMDS) by the Roman Space Telescope. RST will be able to detect
SMDSs at redshifts as high as $z\simeq 14$. In cases with gravitational lensing
factors of $\mu\sim 100$, RST will be able to find SMDS as small as $\sim10^4
M_{\odot}$ at $z\sim 12$ with $\sim 10^6$ s of exposure. To differentiate SMDS
from early galaxies containing zero metallicity stars at similar redshifts, we
compare their spectra, photometry in RST bands, color indexes and image
morphology. With RST alone, the differentiation is possible only for limited
cases: SMDS formed via "adiabatic contraction" (DM pulled into the star via
gravity alone) with $M\gtrsim 10^5M_{\odot}$ and lensed by $\mu\gtrsim 30$ have
distinct photometric signatures from those of the first galaxies. For SMDSs
formed via "dark matter capture," their spectra are degenerate to those of many
galaxies with little to no nebular emission. Thus with RST alone, the only way
to tell them apart from first galaxies would be via image morphology: i.e.
point object (SMDSs) vs. extended object (sufficiently magnified galaxies).
However, if the same objects are further examined by JWST spectroscopy, a
"smoking gun" for detection of SMDS is the HeII $\lambda$1640 absorption line.
While RST does not cover the wavelength band required to find this line (for
$z_{\rm emi}\gtrsim 10$), JWST does. Hence the two detectors can be used
together in identifying SMDS. The confirmed detection of any SMDSs will provide
evidence for a new type of star, powered by dark matter. Moreover, such massive
stars can also be natural progenitors of the supermassive black holes powering
the extremely bright quasars observed at $z\gtrsim 6$.

Astrophysics of Galaxies;Cosmology and Nongalactic Astrophysics