We show that the recently discovered binary 2M05215658+4359220 (2M0521),
comprised of a giant star (GS) orbiting a suspected black hole (BH) in a ~80
day orbit, may be instrumental in shedding light on uncertain BH-formation
physics and can be a test case for studying wind accretion models. Using binary
population synthesis with a realistic prescription for the star formation
history and metallicity evolution of the Milky Way, we analyze the evolution of
binaries containing compact objects (COs) in orbit around GSs with properties
similar to 2M0521. We find ~100-1000 CO-GS binaries in the Milky Way observable
by Gaia, and 0-12 BH-GS and 0-1 neutron star-GS binaries in the Milky Way with
properties similar to 2M0521. We find that all CO-GSs with Porb<5 yr, including
2M0521, go through a common envelope (CE) and hence form a class of higher mass
analogs to white dwarf post-CE binaries. We further show how the component
masses of 2M0521-like binaries depend strongly on the supernova-engine model we
adopt. Thus, an improved measurement of the orbit of 2M0521, imminent with
Gaia's third data release, will strongly constrain its component masses and as
a result inform supernova-engine models widely used in binary population
synthesis studies. These results have widespread implications for the origins
and properties of CO binaries, especially those detectable by LIGO and LISA.
Finally, we show that the reported X-ray non-detection of 2M0521 is a challenge
for wind accretion theory, making 2M0521-like CO-GS binaries a prime target for
further study with accretion models.Comment: 7 pages, 5 figures, Accepted for Publication in ApJ
