The thermonuclear $^{19}$F($p$,$alpha_0$)$^{16}$O reaction rate in a temperature region of 0.007--10 GK has been derived by re-evaluating the available experimental data, together with the low-energy theoretical $R$-matrix extrapolations. Our new rate deviates up to about 30% compared to the previous ones, although all rates are consistent within the uncertainties. At very low temperature (e.g. 0.01 GK) our reaction rate is about 20% smaller than the most recently published rate, because of a difference in the low energy extrapolated $S$-factor and a more accurate estimate of the reduced mass entering in the calculation of the reaction rate. At temperatures above $sim$1 GK, our rate is smaller, for instance, by about 20% around 1.75 GK, because we have re-evaluated in a meticulous way the previous data (Isoya et al., Nucl. Phys. 7, 116 (1958)). The present interpretation is supported by the direct experimental data. The uncertainties of the present evaluated rate are estimated to be about 20% in the temperature region below 0.2 GK, which are mainly caused by the lack of low-energy experimental data and the large uncertainties of the existing data. The asymptotic giant branch (AGB) star evolves at temperatures below 0.2 GK, where the $^{19}$F($p$,$alpha$)$^{16}$O reaction may play a very important role. However, the current accuracy of the reaction rate is insufficient to help to describe, in a careful way, for the fluorine overabundances phenomenon observed in AGB stars. Precise cross section (or $S$ factor) data in the low energy region are therefore mandatory for astrophysical nucleosynthesis studies.
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