Won’t most of those stars return a substantial fraction of their gas to the ISM at the end of their lives?

The sun should live long enough to weather the collision, but it will probably give back 1/4 to 1/3 of its outer, unburned hydrogen when it checks out 5 billion years from now. Why isn’t that gas available for later star formation?

In our paper from 1997 (Laughlin, Bodenheimer and Adams, ApJ 482,420) we wrote:

The 0.14 and 0.16 solar mass stars experience protracted periods during which their luminosity is relatively constant in the face of slow increases in the [stellar] temperature. For example, as the hydrogen burning nuclear shell source methodically consumes the 30% hydrogen envelope, the 0.16 solar mass star will take a leisurely 5.5 Gyr to increase its luminosity from 0.10 to 0.27 solar luminosities. Given the example the Earth, it seems quite possible that these phases would allow ample time for life to evolve on any appropriately situated terrestrial planets. Before this epoch, these planets would have languished in cold storage as their primary stars churned through trillions of years of fully convective main-sequence evolution.

A decade later, this seems a little naive. It’s likely that a functioning biosphere requires a geologically active planet to maintain the various long-term chemical and atmospheric cycles. A trillion years from now, terrestrial planets will have lost their interior heat.

There will be cases, however, in which dynamical evolution in the system triggers episodes of tidal heating while the star is stepping up to the plate. On the whole, though, these situations will be rare.

Conventional star formation will draw to a close sometime after the MW-M31 collision (which will trigger an intense period of star formation as the gas is shocked).

The remnant MW-M31 elliptical galaxy will experience X-ray cooling flow that will allow gas to eventually accrete at the galactic center. It’s possible that this gas will trigger a late period of star formation.

Brown-dwarf – Brown-dwarf collisions will generate the occasional formation of new red dwarf stars. For the next ~10^20 years, the MW-M31 elliptical galaxy will always support about 50 main-sequence red dwarfs that formed via this mechanism.

If you’re interested in the ultra-long-term future, check out my book with Fred Adams, The Five Ages of the Universe. (Order it in paperback, new or used, here.) It got a scathing review in the New York Times Book Review, which effectively brought our budding science-popularization careers to a quick end. Copies are available used starting at $3.36, so it makes a good recession-era holiday gift.

interesting point ! From your discussion one other thing comes to mind. Given the evolutionary tracks, namely the increase in luminosity and temperature, and the time scales for red dwarfs the habitable zone should move farther away from the star into a region where the planets are no longer tidally locked. Given the time scale at which they evolve this may make red dwarfs very hospitable places for life bearing planets in the distant future, if not today.

Simulations of large-scale structure formation indicate that it’s extremely unlikely that M31 has sufficient tangential velocity to be gravitationally unbound from the Milky Way. Galactic encounters are dissipative (kinetic energy of translation goes into heating up stellar orbits) so even if they miss on their next pass, M31 and MW will come together on a 10-15 Gyr from now timescale at the latest.

How sure are astronomers that M31 and The Galaxy will collide?