Friday, December 14, 2007


What will happen to the Earth in the far future? Can humanity or it's successors live forever in it? By now most of you know the lore: the sun will eventually consume all of its "fuel" (hydrogen and later helium) in 5 billion years, expand in to a red giant that will devour Mercury, Venus and the Earth. After that the Sun will eject the outers layers of its atmosphere and leave a stellar corpse: a white dwarf which is small, extremely hot object supported by the pressure of electron degeneracy. The ejected outer layers will be ionized by the radiation of the white dwarf and form a nice planetary nebula, like the Helix.

The Helix nebula is one of the best known planetary nebulae, in the astro-lore it is usually asummed that the Sun will produce a similar nebula when it dies.

Well, I recently attended a talk by Klaus Peter-Schroeder, from University of Guanajuato, in his talk he disputed this scenario. Now, let's discuss the good, the bad and the evil ...

  • The good: Previous models assumed a "naive" modeling of mass loss as the Sun ejects it's outer layers based on Reimer's Law, which is basically based on dimensional arguments. An improved version of this law applied to the Sun shows that it will loose enough mass to allow Earth's orbit to enlarge sufficiently to avoid the doomsday scenario.
  • The bad: Well, that doesn't mean that Earth will be an habitable planet. It will be too uncomfortably close to the Sun, but you might still think that we have around 5 billon years to worry about that. Well, that's wrong. The Sun will increase it's energy output in around a billion years (still a lot of time) by a sufficient amount to increase Earth's temperature around 10 K. You might think that it will be an uncomfortable but still bearable change, nonetheless climate models predict that effects of such a change will be catastrophic.

    In "The End of the World", the Doctor travels to Earth's last moments before being engulfed by the Sun. In the show the writers imagined that some "gravity satellites" held back the expansion of the Sun, we now know that it will be tidal dragging to blame for Earth's destruction.

  • The evil: Well, life on Earth will end one day, but at least will Earth survive to total destruction? Not really, despite that the Sun won't grow enough to engulf Earth, a process known as tidal dragging (you can think of it as a sort of "tidal friction" assisted by dynamical drag) will cause the Earth to spiral into the Sun! The model is extremely sensitive to little details, but we can estimate that the doomsday will happen just 500 000 years before the Sun reaches the tip of the AGB branch.
So the lore is actually quite wrong in practically every detail, but wait! There is still a final twist to this plot. The nice planetary nebula that will act as a sort of mausoleum to the star that made life on Earth possible actually requires stronger stellar winds than the Sun can provide. This is still a point of controversy, but at least among the attendants the consensus was the Sun might produce an irregular planetary nebula at best.

Addendum: It results I was being very naive with the raise of temperature. In Klaus own words:

"It is 1 Gyr for a rise of 10% in the solar irradiance, which makes the Earth leave the habitable zone. But in order to raise the temperature by just 10K, we need much less time! It is difficult to compute because a detailed knowledge of the various positive (and negative) feed-backs is required, but it should be of the order of 100 mio years. That is still very long compared to the timescale of the current climate change....! "


John Baez said...

Interesting post!

It's also possible that the Earth will get thrown out of the Solar System in only 3 billion years if the Andromeda collides with the Milky Way, as some astronomers expect. You can watch a simulation of this collision here.

I've been asked how certain people are that this collision will occur - how good is the evidence. I don't know. If any astronomers do know, I'd like to hear about it.

How long will it be before the earth's temperature rises 10 K?

Luis Sanchez said...

Hello John, we have rather good evidence that the Milky Way and Andromeda will merge.

The most obvious piece of evidence is that Andromeda is blueshifted, nonetheless the fine details are quite complicated to get because the observations only get the radial speed from the blueshift and it's hard to detect the other components of the velocity, nonetheless as far as I can tell the evidence is rather compelling, of course simulations are quite sensitive to little details, but all dynamical models of the mily way - andromeda dynamics seem to predict a merger.

Despite that, I find quite unlikely that Earth will be thrown out, the space between stars is huge (usually a parsec or more), making stellar interactions quite unlikely, it is essentially equally likely that the Sun passes near a star in it's orbit around the milky way.

About the temperature rise, it will happen in around 10^9 years. The models predict a rise of about 5-10 K.