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 < \textrm { [ Fe / H ] } < +0.4 .
We determine the abundances from HF lines in infrared K-band spectra ( \sim 2.3 \micron ) 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 ] \sim 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 < \textrm { [ Fe / H ] } < 0 , and that for two metal-poor ( \textrm { [ 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 < \textrm { [ 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 .