Universe Today
"We found that planets - depending on how big their Sun is (the smaller the star, the longer the planet can stay habitable) - can stay nice and warm for up to 9 Billion years. That makes an old star an interesting place to look for life. It could have started sub-surface (e.g. in a frozen ocean) and then when the ice melts, the gases that life breaths in and out can escape into the atmosphere - what allows astronomers to pick them up as signatures of life. Or for the smallest stars, the time a formerly frozen planet can be nice and warm is up to 9 billion years. Thus life could potentially even get started in that time."
"We used stellar evolutionary models that tell us how stellar quantities, mainly the brightness, radius, and temperature all change with time as the star ages through the red giant phase. We also used a climate model to then compute how much energy each star is outputting at the boundaries of the habitable zone. Knowing this and the stellar brightness mentioned above, we can compute the distances to these habitable zone boundaries."
"The main result is that the maximum time that a planet can remain in this red giant habitable zone of hot stars is 200 million years. For our coolest star (M1), the maximum time a planet can stay within this red giant habitable zone is 9 billion years. Those results assume metallicity levels similar to those of our Sun. A star with a higher percentage of metals takes longer to fuse the non-metals (H, He..etc) and so these maximum times can increase some more, up to about a factor of two."