  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.
