  The cosmic origin of fluorine is still not well constrained. Several
nucleosynthetic channels at different phases of stellar evolution have been
suggested, but these must be constrained by observations. For this, the
fluorine abundance trend with metallicity spanning a wide range is required.
Our aim is to determine stellar abundances of fluorine for -1.1<[Fe/H]<+0.4. We
determine the abundances from HF lines in infrared K-band spectra (at 2.3
microns) of cool giants, observed with the IGRINS and Phoenix high-resolution
spectrographs. We derive accurate stellar parameters for all our observed K
giants, which is important since the HF lines are very temperature sensitive.
We find that [F/Fe] is flat as a function of metallicity at [F/Fe]~0, but
increases as the metallicity increases. The fluorine slope shows a clear
secondary behavior in this metallicity range. We also find that the [F/Ce]
ratio is relatively flat for -0.6<[Fe/H]<0, and that for two metal-poor
([Fe/H]<-0.8), s-process element enhanced giants, we do not detect an elevated
fluorine abundance. We interpret all these observational constraints to
indicate that several major processes are at play for the cosmic budget of
fluorine over time; from those in massive stars at low metallicities, through
the asymptotic giant branch-star contribution at -0.6<[Fe/H]<0, to processes
with increasing yields with metallicity at super-solar metallicities. The
origins of the latter, and whether or not Wolf-Rayet stars and/or novae could
contribute at super-solar metallicities, is currently not known. To quantify
these observational results, theoretical modelling is required. More
observations in the metal-poor region are required to clarify the processes
there.
