1997A&A...319..796S

Galactic orbits have been integrated using the Galactic potential model of Allen & Santillan (1991RMxAA..22..255A) for 280 halo stars identified in the V_rot, [Fe/H] diagram. The effects of chaos upon their orbital structure have been investigated. A "vertical" surface of section is defined, where Z is plotted versus z each time the orbit crosses the cylinder ∼ω=8.5kpc; this surface of section allows a more complete visualization of the Galactic orbits in phase space, a better understanding of the orbital chaos, and a more direct comparison with observations. "Horizontal" surfaces of section and meridional orbits have also been plotted for all of these halo stars, and have been used to classify the Galactic orbits into the categories box, chaotic, and resonant; 44.3% of the halo orbits are found to show some evidence of chaos. The observed |W'| velocities of the halo stars give poor measures of z_max for the box orbits, and especially for the chaotic orbits. Regressions of [Fe/H] against R_max and z_max, for the total sample and for the chaotic and non-chaotic subsets, show little evidence for a metallicity gradient in the Galactic halo. The surfaces of section for many of the halo stars (∼ a third) show some evidence of structure within chaos. Part of this structure is due to the "stickiness" that chaotic orbits experience near the outer KAM tori of families of periodic and quasiperiodic orbits. This "stickiness" has been discussed extensively in the literature. The phase-space clumpiness produced by this "stickiness" may help to explain the "moving groups" found in the solar vicinity and the non-Gaussian velocity distributions observed at the Galactic poles. Also, the "confinement" of the chaotic orbits by a 1:1 resonant family of tube orbits, which passes a few kpc above the Sun, may explain part of the halo duality which has been detected in several studies, such as those of Hartwick (1987, in The Galaxy, eds. G.Gilmore & B. Carswell. Reidel, dordrecht, 281) and of Kinman et al. (1994AJ....108.1722K). Histograms of the observed |W'| velocity and of the calculated orbital parameter z_max have been plotted for the 280 halo stars. Structure is seen in both histograms, due mainly to the chaotic orbits; the |W'| histogram is non-Gaussian with two peaks, and the z_max histogram has three peaks. Remarkably the structure in these two histograms is correlated and can be explained in relation to the details of the surfaces of section and the "confinement" and "stickiness" phenomena of the chaotic orbits.