One common definition of the habitable zone of a star is the range of distances from the star where liquid water could exist on the surface of a planet (where the planetary surface temperature ranges between 0° and 100° C [273.15 – 373.15 K]).
Of course, atmospheric pressure affects the temperature range for liquid water. For example, at 3% of sea level atmospheric pressure, water boils at 26.4° C, not 100° C. But at 68 atmospheres, water stays liquid until it reaches a scalding temperature of 285° C. At the other end of the liquid water spectrum of temperatures, the freezing point of water only increases to 0.01° C from 1 atm all the way down to 0.006 atm. At atmospheric pressures below 0.006 atm, liquid water can’t exist: the only phases that can be present are solid and gas. At higher pressures, all the way up to about 99 atm, the freezing point of water remains at 0° C. Then, from 99 atm up to 2,072 atm, the freezing point of water lowers to -21.9° C. Then it goes back up to 0° C again at 6,241 atm. Above 70,000 atm, H2O can exist only in solid form.
So, the range of temperature where liquid water can exist is generally smaller at lower atmospheric pressure, and greater at higher atmospheric pressure.
Substances dissolved in the water, called solutes, can also change the range of temperatures where liquid water can exist. And, who’s to say that life couldn’t exist with only water ice or water vapor in the environment?
And what about life beneath the surface of a planet, moon, asteroid, comet, etc.? It seems reasonable to suggest that subsurface liquid water exists on more worlds than liquid water on the surface.
And does life always require H2O to exist?
Determining the “habitable zone” of a star is complicated. That’s why we often narrow it down to just where terrestrial life could exist.
So, for now, let’s stick with that.
As you might expect, many factors enter into the equation: some relate to the star (e.g. size and surface temperature and hence bolometric luminosity), and some relate to the planet (e.g. atmospheric composition & density, and albedo). A liberal definition might say that the habitable zone in our solar system lies between the orbits of Venus (0.7 AU) and Mars (1.5 AU).
If one accepts this, then the calculation of the habitable zone around any other star is straightforward:
R1 is the inner radius of the habitable zone, in astronomical units
R2 is the outer radius of the habitable zone, in astronomical units
r* is the radius of the star, in solar radii
t* is the effective temperature of the star’s photosphere, in Kelvin
Here’s an example that’s made big news lately: seven planets very similar in size to the Earth have been discovered orbiting the red dwarf star TRAPPIST-1, located 39 light years from our solar system in the direction of the constellation Aquarius. The estimated size of the star is 0.117 solar radii, and the estimated effective temperature 2559 K. Using the above equations, we get R1 = 0.016 AU and R2 = 0.034 AU. Thus, using our approach, it appears that planets TRAPPIST-1d (0.772 R⊕) and TRAPPIST-1e (0.918 R⊕) are most likely to be within the star’s habitable zone.