Fluorine Abundances in the Galactic Nuclear Star Cluster
  Abundances of fluorine ($^{19}$F), as well as isotopic ratios of
$^{16}$O/$^{17}$O, are derived in a sample of luminous young
($\sim$10$^{7}$--10$^{8}$ yrs) red giants in the Galactic center (with
galactocentric distances ranging from 0.6--30 pc), using high-resolution
infrared spectra and vibration-rotation lines of H$^{19}$F near
$\lambda$2.3$\mu$m. Five of the six red giants are members of the Nuclear star
cluster that orbits the central supermassive black hole. Previous
investigations of the chemical evolution of $^{19}$F in Galactic thin and thick
disk stars have revealed that the nucleosynthetic origins of $^{19}$F may be
rather complex, resulting from two, or more, astrophysical sites; fluorine
abundances behave as a primary element with respect to Fe abundances for thick
disk stars and as a secondary element in thin disk stars. The Galactic center
red giants analyzed fall within the thin disk relation of F with Fe, having
near-solar, to slightly larger, abundances of Fe ($<$[Fe/H]$>$=+0.08$\pm$0.04),
with a slight enhancement of the F/Fe abundance ratio
($<$[F/Fe]$>$=+0.28$\pm$0.17). In terms of their F and Fe abundances, the
Galactic center stars follow the thin disk population, which requires an
efficient source of $^{19}$F that could be the winds from core-He burning Wolf
Rayet stars, or thermally-pulsing AGB stars, or a combination of both. The
observed increase of [F/Fe] with increasing [Fe/H] found in thin disk and
Galactic center stars is not predicted by any published chemical evolution
models that are discussed, thus a quantitative understanding of yields from the
various possible sources of $^{19}$F remains unknown.
