Trojans in the Solar Neighborhood
  About 20% of stars in the solar vicinity are in the Hercules stream, a bundle
of stars that move together with a velocity distinct from the Sun. Its origin
is still uncertain. Here, we explore the possibility that Hercules is made of
trojans, stars captured at L4, one the Lagrangian points of the stellar bar.
Using GALAKOS--a high-resolution N-body simulation of the Galactic disk--we
follow the motions of stars in the co-rotating frame of the bar and confirm
previous studies on Hercules being formed by stars in co-rotation resonance
with the bar. Unlike previous work, we demonstrate that the retrograde nature
of trojan orbits causes the asymmetry in the radial velocity distribution,
typical of Hercules in the solar vicinity. We show that trojans remain at
capture for only a finite amount of time, before escaping L4 without being
captured again. We anticipate that in the kinematic plane the Hercules stream
will de-populate along the bar major axis and be visible at azimuthal angles
behind the solar vicinity with a peak towards L4. This test can exclude the OLR
origin of the Hercules stream and be validated by Gaia DR3 and DR4.
