The Kapteyn moving group is not tidal debris from $omega$ Centauri

The Kapteyn moving group has been postulated as tidal debris from ω Centauri. If true, members of the group should show some of the chemical abundance patterns known for stars in the cluster. We present an optical and near-infrared high-resolution, high-signal-to-noise ratio spectroscopic study of 14 stars of the Kapteyn group, plus 10 additional stars (the ω Cen group) that, while not listed as members of the Kapteyn group as originally defined, have nevertheless been associated dynamically with ω Centauri. Abundances for Na, O, Mg, Al, Ca, and Ba were derived from the optical spectra, while the strength of the chromospheric He i 10830 Å line is studied as a possible helium abundance indicator. The resulting Na-O and Mg-Al patterns for stars of the combined Kapteyn and ω Cen group samples do not resemble those of ω Centauri, and are not different from those of field stars of the Galactic halo. The distribution of equivalent widths of the He i 10830 Å line is consistent with that found among non-active field stars. Therefore, no evidence is found for second-generation stars within our samples, which most likely rules out a globular-cluster origin. Moreover, no hint of the unique barium overabundance at the metal-rich end, well established for ω Centauri stars, is seen among stars of the combined samples. Because this specific Ba pattern is present in ω Centauri irrespective of stellar generation, this would rule out the possibility that our entire sample might be composed of only first-generation stars from the cluster. Finally, for the stars of the Kapteyn group, the possibility of an origin in the hypothetical parent galaxy of ω Centauri is disfavored by the different run of α-elements with metallicity between our targets and stars from present-day dwarf galaxies.