Danchi & Lopez (2013) present a study on the evolution of the habitable zone around stars with 1.0, 1.5 and 2.0 times the mass of the Sun, for metallicities ranging from 0.0001 to 0.070. A star’s metallicity is basically the fraction of a star’s mass that is comprised of elements heavier than hydrogen and helium. For comparison, the Sun’s metallicity is 0.017. The study shows that the metallicity of a star strongly affects the amount of time a planet spends in the star’s habitable zone.
A planet located between 1.2 to 2.0 AU from the Sun will spend over 10 billion years in the habitable zone. For the Earth, which orbits the Sun at 1.0 AU, its time within the habitable zone will be somewhat less. The main sequence phase of the Sun comes to an end when it stars to burn helium in its core. This helium-burning phase occurs when the Sun is between 11.4 and 12.8 billion years old. During this period, the Sun will swell in size to become a red giant star and its luminosity will increase to many times its current value. After that, the Sun will shed its outer layers and leave behind its core as a white dwarf star which will cool into oblivion.
In the course of the Sun’s helium-burning phase, there is a period of stable helium-burning which lasts for ~200 million years when the Sun is between 12.5 to 12.7 billion years old. During this period, the habitable zone stays at a distance of between 6 to 15 AU from the Sun. For stars with 1.5 and 2.0 times the Sun’s mass that are in such a period of stable helium-burning, the habitable zone stays at distances of between 7 to 16 AU and 12 to 15 AU, respectively, for durations exceeding ~100 million years.
Stars with 1.5 and 2.0 times the Sun’s mass have shorter lifespans, resulting in a short period a planet can remain in the habitable zone. For a star with 1.5 times the Sun’s mass and whose metallicity is identical to the Sun’s metallicity, it can support a stable habitable zone for over 3 billion years. Finally, stars with 2.0 times the Sun’s mass do not host habitable zones for longer than 3 billion years.
Danchi & Lopez (2013), “Effect of Metallicity on the Evolution of the Habitable Zone from the Pre-Main Sequence to the Asymptotic Giant Branch and the Search for Life”, arXiv:1304.1464 [astro-ph.SR]