Impact of a revised $^{25}$Mg(p,$\gamma$)$^{26}$Al reaction rate on the
  operation of the Mg-Al cycle
  Proton captures on Mg isotopes play an important role in the Mg-Al cycle
active in stellar H-burning regions. In particular, low-energy nuclear
resonances in the $^{25}$Mg(p,$\gamma$)$^{26}$Al reaction affect the production
of radioactive $^{26}$Al$^{gs}$ as well as the resulting Mg/Al abundance ratio.
Reliable estimations of these quantities require precise measurements of the
strengths of low-energy resonances. Based on a new experimental study performed
at LUNA, we provide revised rates of the $^{25}$Mg(p,$\gamma$)$^{26}$Al$^{gs}$
and the $^{25}$Mg(p,$\gamma$)$^{26}$Al$^{m}$ reactions with corresponding
uncertainties. In the temperature range 50 to 150 MK, the new recommended rate
of the $^{26}$Al$^{m}$ production is up to 5 times higher than previously
assumed. In addition, at T$=100$ MK, the revised total reaction rate is a
factor of 2 higher. Note that this is the range of temperature at which the
Mg-Al cycle operates in an H-burning zone. The effects of this revision are
discussed. Due to the significantly larger $^{25}$Mg(p,$\gamma$)$^{26}$Al$^{m}$
rate, the estimated production of $^{26}$Al$^{gs}$ in H-burning regions is less
efficient than previously obtained. As a result, the new rates should imply a
smaller contribution from Wolf-Rayet stars to the galactic $^{26}$Al budget.
Similarly, we show that the AGB extra-mixing scenario does not appear able to
explain the most extreme values of $^{26}$Al/$^{27}$Al, i.e. $>10^{-2}$, found
in some O-rich presolar grains. Finally, the substantial increase of the total
reaction rate makes the hypothesis of a self-pollution by massive AGBs a more
robust explanation for the Mg-Al anticorrelation observed in Globular-Cluster
stars.
