# 5.3: The Habitable Zone


One of the attributes that makes Earth a habitable planet is the presence of oceans of water. When the solar system formed, Earth and Venus were similar in size and composition, but today the surface of Venus is about 700 K, hot enough to melt lead with a staggering surface pressure that is 92 times that of Earth from the weight of a massive carbon dioxide atmosphere. Venus has 10,000 times more carbon dioxide in its atmosphere than the Earth and three times as much nitrogen. Earth stores carbon dioxide and nitrogen in surface rocks - after accounting for these geological reserves on Earth, the two planets have about the same abundance of both elements.

It is quite possible that for the first billion years, Venus had a moderate temperature atmosphere, surface water and perhaps even life. However, because Venus is closer to the Sun, it intercepts more energy than the Earth. Liquid water would have gradually evaporated, forming a potent greenhouse gas that trapped more solar energy, leading to a positive feedback loop that further warmed the planet, driving water out of the crust of Venus. Ultraviolet radiation dissociates water molecules into its component atoms of hydrogen and oxygen. The Venus Express spacecraft, launched in 2005 by the European Space Agency (ESA), has measured the escape of hydrogen and oxygen (roughly in a ratio of 2:1) from the upper atmosphere of Venus. Over the 4.56 billion year lifetime of the planet, Venus has lost its water. Carbon dioxide is chemically bound in the crust of Earth rocks. However, in the presence of a hot, dry Venusian climate, carbon dioxide would evaporate out of the mantle of the planet, producing the heavy CO2 atmosphere observed today. The current condition of Venus is the fate of an Earth-like planet that is too close to its star to retain liquid surface water.

Planets or moons that are very far away from the Sun have their reservoirs of water stored as frozen ice. If liquid water is a requirement for life, then a zone around the Sun can be defined such that it it not too hot and not too cold for liquid water to exist on the surface of a planet. This zone is called the "habitable zone." The location of the habitable zone depends on a number of factors including the luminosity of the host star, the mass of the planet, and the composition and thickness of the planet's atmosphere. For the Sun, a conservative range for the habitable zone has been calculated as 0.95 - 1.37 AU.

Like all stars, the Sun started out fainter, and has gradually increased in size and brightness over its lifetime. The faint, young Sun would have had habitable zone boundaries that were closer to the star and the boundaries of the habitable zone are pushed outward as the Sun evolves. Over the 4.56-billion year lifetime of the Earth, there is a narrower region that would have been a continuously habitable zone (CHZ) and this has been estimated to be 0.95 - 1.15 AU.

## Brightness matters

The location of the habitable zone depends on the brightness of the star. For fainter stars, the habitable zone moves closer in and for brighter stars the habitable zone moves farther out. In addition, the lifetime of the star depends on its mass. Faint, low mass stars live for hundreds of billions of years while the lifetime of bright, massive stars is only millions of years long.

The seeming advantage of long lifetimes for low mass stars like M dwarfs may be tempered by other challenges. The habitable zone is so close these stars that a year on a habitable planet around an M dwarf star is measured in (Earth) days. This proximity leads to two important issues. The first is tidal locking of the planet. We see the phenomenon of tidal locking with our moon: as the moon circles the Earth, the same hemisphere of the moon points toward the Earth. Habitable zone planets orbiting M dwarfs will likewise have one "day" side of the planet while the other side is in perpetual darkness. The rotation (spin) of the planet is gravitationally synchronized with the orbit. A second issue is that M dwarfs typically have strong magnetic fields that produce high velocity winds of charged particles. This stellar wind would bombard any planets in the habitable zone and could potentially strip away the planet atmosphere.

A simple way to approximate the inner boundary of the habitable zone is to calculate the distance from the star where the temperature is equal to the boiling point of water. The outer boundary of the habitable zone is calculated as the distance from the star where the temperature would equal the freezing point of water.

Recall that $$L\,=4\pi r^2\sigma T^4$$, scaling this to values for the solar system where the distance $$d_{in}\,=\,0.95\,AU$$ for the inner boundary and $$T_{in}=373\,K$$ by our definition:

$\frac{L_{\ast}}{L_{\odot}}\,=\,\frac{4\pi r^2_{in}\sigma T^4_{in}}{4\pi d^2_{in} \sigma T^4_{in}}$

After cancelling all of the constants (4,$$\pi$$,$$\sigma$$,$$T_{in}$$ ) we can estimate the distance (in units of AU) to the inner boundary of the habitable zone for a star with luminosity $$L_{\ast}$$:

$$r_{in}=0.95\sqrt{\frac{L_{\ast}}{L_{\odot}}}$$

Similarly, we can calculate the outer boundary of the habitable zone (in units of AU) for a star of luminosity $$L_{\ast}$$ with $$d_{out}=1.37\,AU$$ for the inner boundary and $$T_{out}=273\,K$$ by our definition:

$$r_{out}=1.37\sqrt{\frac{L_{\ast}}{L_{\odot}}}$$

## Limitations of the Habitable Zone Concept

The concept of the habitable zone helps to shape strategies in the search for life in the solar system and on planets around other worlds. It is not a definition of where life can exist because we do not yet know enough about the environmental limits for habitability. Indeed our active searches for life in the solar system do not focus on our Moon (which is in the habitable zone, but has no surface water). Instead our searches take place on Mars, Europa (moon of Jupiter), Titan and Enceladus (moons of Saturn).

Mars is a particularly interesting site for searches of ancient or subsurface life because there is evidence that liquid water existed on Mars. Today, dry fluvial features course the surface of Mar and sedimentation and aggregates associated with water on Earth have been discovered on the surface of Mars. These features suggest the past existence of running rivers and lake beds on young Mars. Since the Sun would have been fainter at this time, Mars must have had effective greenhouse gases, like methane in the atmosphere.

While it is understood that the concept of the habitable zone is too limiting, it is an easy and useful definition that can be applied (at least as a starting point) to planets orbiting other stars.

5.3: The Habitable Zone is shared under a CK-12 license and was authored, remixed, and/or curated by CK-12 Foundation via source content that was edited to conform to the style and standards of the LibreTexts platform; a detailed edit history is available upon request.