Revisiting the Tale of Hercules: How Stars Orbiting the Lagrange Points Visit the Sun

Abstract

We propose a novel explanation for the Hercules stream consistent with recent measurements of the extent and pattern speed of the Galactic bar. We have adapted a made-to-measure dynamical model tailored for the Milky Way to investigate the kinematics of the solar neighborhood (SNd). The model matches the 3D density of the red clump giant stars (RCGs) in the bulge and bar as well as stellar kinematics in the inner Galaxy, with a pattern speed of 39 km s −1 kpc −1 . Cross-matching this model with the Gaia DR1 TGAS data combined with RAVE and LAMOST radial velocities, we find that the model naturally predicts a bimodality in the U-V-velocity distribution for nearby stars which is in good agreement with the Hercules stream. In the model, the Hercules stream is made of stars orbiting the Lagrange points of the bar which move outward from the bar's corotation radius to visit the SNd. While the model is not yet a quantitative fit of the velocity distribution, the new picture naturally predicts that the Hercules stream is more prominent inward from the Sun and nearly absent only a few 100 pc outward of the Sun, and plausibly explains that Hercules is prominent in old and metal-rich stars.

Distribution functions for resonantly trapped orbits in the Galactic disc

“…Notice that the orbits associated with the overdensity at (−vR, v φ ) ≈ (−10, 210) km s −1 in the central panel of Fig. 5 are of the same kind of those described by Pérez-Villegas et al (2017), i.e., trapped around the bar's Lagrangian points (see Fig. 6).…”

“…5) it occurs at −vR > 0, as predicted by the Eulerian linear theory, and as such conflicts with the observations. Hence, the pendulum formalism is mandatory if one seeks to explain the Hercules group as a consequence of the corotation resonance, as Pérez-Villegas et al (2017) did with made-to-measure N -body models. Notice that the orbits associated with the overdensity at (−vR, v φ ) ≈ (−10, 210) km s −1 in the central panel of Fig.…”

Orbital tori for non-axisymmetric galaxies

“…the bar's pattern speed is not greater than ωp = 40 km s −1 , with the consequence that the OLR lies well outside R0 and could only affect local velocity space at positive values of V . With the lower pattern speed we instead lie not far outside the bar's CR, and Pérez-Villegas et al (2017) have shown that the model of the bar developed by Wegg et al (2015) with ωp = 39 km s −1 kpc −1 predicts a feature rather like the Hercules stream that is caused by stars trapped into libration around the Lagrange point L4. Fig.…”

“…Sormani et al (2015) concluded that the bar's pattern speed is ωp ≃ 40 km s −1 kpc −1 , a value that coincides nicely the estimate obtained by Wegg et al (2015) by modelling the kinematics of bulge stars. Pérez-Villegas et al (2017) show that ωp = 39 km s −1 correctly predicts the kinematics of solar-neighbourhood stars because it causes stars trapped by corotation to visit the solar neighbourhood in the form of the "Hercules stream". Over the previous two decades larger values ∼ 55 km s −1 kpc −1 were favoured, in part on account of a significant under-estimate of the length of the bar by and in part through the Hercules stream being supposed to arise by trapping at the OLR rather than corotation (Dehnen 1998;).…”

“…Indeed, to extract a reasonable plot of the local U V plane from the M2M model of Wegg et al (2015), Pérez-Villegas et al (2017) had to upgrade the model significantly because the solar neighbourhood contains only a very small fraction of the Galaxy's stars. Plots such as Fig.…”