The humanly habitable zone

If you want your little book people (otherwise known as characters) living on the surface of a planet that isn't Earth and without constant artificial support, you probably want the planet to be habitable. This is where the habitable zone (and hence this blog post) comes in.

Why is it a zone?

First let's talk about what we need from a planet. Earth is great; it gives us lots of handy life-sustaining conditions; air, water, the right amount of gravity, sunlight and radiation... Of course, the reason the Earth is so well-tuned to keeping us alive is that we evolved on Earth. It's not tuned to us, we're tuned to it. There is no reason that aliens couldn't evolve in very different conditions to those found on Earth. Even on Earth there are many forms of life such as extremophiles which live in conditions we humans couldn't survive in. There's also a good chance that life is possible on Europa or Titan (moons of Jupiter and Saturn respectively), but on the former it would have to be in a subsurface ocean and the latter has a very different atmosphere and composition to Earth, meaning that life couldn't be water-based.

Aliens are all well and good, but if we're interested in what conditions humans can live unsupported on a planet's surface, we need to be much more specific.

The things I mentioned earlier (air, water, heat, etc) depend on two things:

1. Planetary properties such as size and composition, and
2. Planetary location.

The first of those is most easily summarised as having to be similar to Earth to sustain unaided human life. The latter is the subject of this blog post.

You see, although the planet needs to be similar to Earth, its sun doesn't have to be that similar to our sun. Different stars output different amounts of light and energy (previously discussed in terms of how bright they are). If we were to pick Earth up and put it in orbit around a larger, hotter star then, if we didn't want to be burnt to a crisp while all our water boiled, we would have to put Earth in a further out orbit to compensate for the extra energy coming off the star. Similarly, if we put Earth around a smaller, cooler star, we'd need to put it in a closer orbit to stop it turning into a snowball.

The optimal region in which to put a habitable planet is called the habitable zone. It's a zone because there's no reason for life to have not evolved on Earth if it had been slightly closer or further away from the sun. I'll get back to life evolving on other planets at the end of the post, though.

There are a few different ways of defining what constitutes a habitable zone. Some definitions involve the region in which liquid water is possible, temperature-wise (since our biochemistry depends heavily on liquid water), other definitions go a bit further and include things like carbon cycles and the greenhouse effect (pdf link, sorry). For the purposes of the habitable zone calculations which follow, I'm going to use the definitions given in Selsis et al. (2007).

Before that, though, let's work out how warm a planet is based on how far from its sun it is. I am using a formula adapted from a Melbourne Uni 3rd year physics lab manual because it's simpler than the one given in Selsis et al. (2007), although they both give the same results. The approximate temperature of a planet, given a stellar temperature and radius and ignoring complex atmospheric effects (but assuming that an atmosphere exists) is:

T is the approximate temperature of the planet in Kelvin, T_* is the temperature of the star in Kelvin, A is the albedo of the planet (for reference, Earth's is 0.306, according to wiki), R_* is the radius of the star and d is the distance of the planet from the star.

The only tricky thing here is that both R_* and d have to be in the same units, so either both kilometres, or both AU etc.

According to Selsis et al. (2007), life is possible in the range where the temperature is between 277 K and 394 K. Rearranging the above equation then with these values and substituting R_* in annoying units for solar radii (the HR diagram I linked to a few weeks ago can help you estimate this much more easily than in km or AU), we find that the habitable zone for any main sequence star in AU is given by:

Quantities as above. R_☉ is solar radii (multiples of the radius of the sun) and d now must be in AU.

So all you have to do now is work out what kind of star you want, find out it's general properties (easily googleable if you're using a real star) and throw in the numbers. Unless you have plans to make your planet unusual, it's probably best to keep A as the Earth's albedo. That said, habitable distance will change with albedo so the only reason not to change it is because albedo reflects the planetary composition (and we probably want to keep a similar composition to Earth...).

For reference, Selsis et al. (2007) find the sun's habitable zone to be between 0.95 and 2.4. (Note that they use a different albedo for the Earth.) Wiki lists some other numbers which seem to vary mostly in the outer edge prediction.

I should also point out that all of this assumes that there aren't any other stars near our planet. Things get a bit more complicated with multiple stars around, something I will definitely address in a later post.

Evolving elsewhere

As well as the habitable zone, there is something known as the continuously habitable zone (or CHZ). This is the region around a star which remains habitable throughout the star's (main sequence) lifetime. (Main sequence lifetime because different stars end their main sequence lives in different ways, mist of which make the continued survival of planets complicated at best. More on this in a future post, I think.) The reason we need to worry about different times in a star's life is that stars tend to increase their rate of energy output as they age and use up fuel (because as more fuel is used up, hotter core temperatures are required to sustain fusion which leads to an increase in luminosity). The CHZ is narrower than the habitable zone calculated at any given time during the star's lifetime and it is possible that as the star's luminosity changes, the habitable zone could shift so that the planet moves into or out of it over (astronomical) time.

Of course, this doesn't matter so much if we just want to find a planet to throw humans at. Continuous habitability becomes more relevant when we're talking about life evolving. Evolution from scratch takes a long time, but human civilisation to date has lasted an insignificant amount of time, on an astronomical scale.