ASP1022 Topic05 HabZones 2015

Monash University School of Physics and Astronomy Topic 5

ASP1022 Topic 5 Habitable Zones

The concept of habitabilityThe main goal of our unit is to consider the question Is there intelligent life elsewhere in the Universe? Our question for this topic is How many of those planets are capable of supporting life?

We will look at the science of life and its requirements in more depth in other lectures. For now, we will assume that we are interested in looking for life as we know it.

There are five major requirements we need to consider:

The main elements required are carbon, oxygen, hydrogen and nitrogen. These are readily found throughout the Solar System , and we have no reason to assume that they are harder to find elsewhere. 1

In an earlier lecture, we determined that a star with a suitable lifetime to allow life to arise would have a mass in the range 0.4 to 2 Mʘ.

We will concentrate the rest of our deliberations on single stars as they are the simplest , and we expect that 2

they will have the majority of stable orbits. We are therefore left to consider the need for an energy source and liquid water.

Water-based life generally requires a temperature range of 0-100oC. (This range is for pressures at terrestrial sea level; planets with significantly different gravities or geography would have different temperature ranges for liquid water). Biological cells on Earth use water to dissolve other chemical compounds, to transport nutrients, and to carry off wastes. It is conceivable that life elsewhere might use other solvents. Some possibilities are given below.

Table 5.1: Physical properties of common solvents

From Table 5.1 we can see that water has a lot going for it! It is liquid over the widest range of temperatures. Ethane would probably be our second choice, and in practical terms it is liquid over a similar temperature range. There is, however, one important difference: ethane is a liquid only at very low temperatures. We need an energy source to drive the chemical reactions of life, especially in the early stages. It is difficult to

Substance Freezing point Boiling point Liquid range

Water (H2O) 0oC 100oC 100oC

Ammonia (NH3) -78oC -33oC 45oC

Methane (CH4) -182oC -164oC 18oC

Ethane (C2H6) -183oC -89oC 94oC

Amino acids have even been found on meteorites and in comet tails.1

Is this a reasonable limitation to apply to our search for life elsewhere in the Galaxy?2

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Imag

e cr

edit:

NAS

A; R

ober

t Sim

mon

& R

eto

Stöc

kli

Access to elements that make up living systems Access to a liquid solvent (e.g. water) An energy source A stable climate A long-lived host star

Fig. 5.1 Earth from space.


see temperatures of -100oC being sufficient , so again we come out in favour of water. We conclude that in 3

all likelihood, the search for a planet with a habitable surface is equivalent to looking for planets where liquid water is present on, or near, the surface.

Simple case: No atmosphereWe will define the habitable zone of a star to be the region around it where it is reasonable to expect that liquid water could exist on a planet's surface. It is a region, or zone (rather than a specific point), because there is a large temperature range over which water is a liquid, and hence a range of possible orbits where a habitable planet could be found.

The main factor which determines a particular star's habitable zone is the star's luminosity. This determines 4

the flux of radiant energy at any particular distance from the star, and hence (at least in part) determines the temperature range on the surface of any planet (or moon) residing at that distance.

Recall that the flux of energy is the amount of energy passing through a given area per unit time. For example, we can calculate the flux of energy at the Earth as follows:

Given that the luminosity of the Sun (the energy it radiates per second) is 3.8x1026 W, then we can see that the flux (F) of energy passing through each square metre, every second, at a distance 1AU from the Sun is:

Fig. 5.2: Habitable Zone diagram

where 4πd2 is the surface area of a sphere of radius d.

We will make use of this formula to estimate the surface temperature of a planet orbiting a star.

Other factors which determine the surface temperature of a planet include:

• The presence or absence of an atmosphere• The composition of such an atmosphere• The rotation rate of the planet• The albedo of the planet• The obliquity of the planet• The eccentricity of the planet's orbit

Just because it's difficult to imagine, it doesn't mean that it's impossible!3

The main factor, not the only factor!4

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F =L⇥

4�d2=

3.8� 1026

4� � � (1.49� 1011)2= 1362 J s�1 m�2

Albedo: the fraction of incident light (summed over all wavelengths) which is reflected by the planet (surface and/or atmosphere).

Obliquity: The tilt angle of the planet's spin axis with respect to its orbit around the star.

Flux: The energy per unit area measured at some point in space. Generally measured in W/m2.

Luminosity: The total energy output of the star, usually measured in Watts (Joules/second)


To get an idea of the surface temperature of a planet orbiting a star of given luminosity, we will make a few assumptions.

1. The albedo of the planet is zero: that is, it absorbs all the radiation incident upon it, and reflects none; 2. The planet has no atmosphere;3. The radiation absorbed is distributed evenly over the whole planet;4. The planet's orbit is circular.

So we are assuming that all the incident radiation from the star is absorbed by the planet, and that the planet heats up until it reaches an equilibrium temperature, T, after which it re-radiates as much energy as it absorbs (this is what is meant by being in equilibrium). The flux that it re-radiates can be written in terms of equilibrium temperature, and can be determined by the formula:

where σ is the Stefan-Boltzmann constant, 5.67x10-8 J s-1 m-2 K-4.

If we know the flux of energy from the host star, we can determine the flux re-radiated by a planet which is orbiting it (the same is true for the case of zero albedo), and we can calculate the temperature of the planet using this formula.

Again, let's use the Earth as an example. Keep in mind the simplifying assumptions made above, the first two of which don't apply to Earth!

The flux formula above gives us the flux of energy, F, at the Earth; that is, the amount of energy passing through each square metre per second. Since the star in question is the Sun, the energy is mostly in the form of yellow light. The amount of energy being absorbed by Earth during one second must be F times the area of a circle of radius R⊕, the radius of Earth. This is illustrated in Fig. 5.3.

�Fig. 5.3: Earth will intercept radiation from the Sun according to its cross-sectional area, π(R⊕)2, where R⊕ is Earth's radius.

Since the amount of energy re-radiated by Earth per second is the same as that absorbed per second (the system is in equilibrium), then we must have:

energy in / sec = energy out / sec

We don't need to know the Earth's radius because R⊕ is present on both sides of our equation, and so cancels out. We can then solve our equation for the temperature of Earth.

This is not too far from the truth!

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�R2�F = (4�R2

�)(⇥T 4)

T =�

F

4�

⇥ 14

=�

13624� 5.67� 10�8

⇥ 14

= 278 K = 5oC

FP = �T 4


The Solar System's habitable zone

The true habitable zone of a planetary system actually depends on many factors, but trying to include them can make things very complicated! For now, we'll ignore them and just estimate the habitable zone of a 5

'simplified' Solar System.

Using the equations above, we can estimate the distance of the inner edge of the Sun's habitable zone by using T=100o C (373 K).

So we have:

If we combine these (substitute for F, then rearrange for d), we get:

You should be able to rearrange the formulae. If you cant, ask your lecturer or tutor for help.

We generally measure distances within planetary systems using Astronomical Units (AU). Remember, 1 AU is the average distance from Earth to the Sun, and

is roughly 1.50x1011 m. So the inner edge of the Sun's habitable zone lies at:

This is between the orbits of Mercury and Venus. We can do a similar calculation to find the outer edge of the habitable zone. In this case, we need the temperature to be 0o C (or 273 K). Substituting this temperature into the formula gives us dout = 1.04 AU, just beyond Earth's orbit. This implies that Mars (dMars = 1.52 AU) lies outside the Sun's habitable zone.

Remember though, that we have used a number of assumptions in these calculations…

Comparative Planetology

Perhaps the next biggest influence on a planet's habitability, after its star and location, is the presence or absence of an atmosphere. We'll look at the terrestrial planets in our Solar System to see just how important an atmosphere can be.

Mercury is definitely too close to the Sun to be habitable, so we'll just consider Venus, Earth and Mars. Table 5.2 shows some of the properties of these planets.

If you'd like to see how complicated, look at the article by Tarter et al, Astrobiology 2006, 7, 30 (available here: http://5

astrobiology.ciw.edu/publications.php?id=29 (accessed 2nd Nov 2009).Page �4

F =L�

4�d2 F = 4�T4

d =

⇤�L

16�⇥T 4

⇥=

⇤�3.8� 1026

16� � � 5.67� 10�8 � (373)4

⇥= 8.3� 1010 m

It's not really as complicated as it looks!

Calculate T4, then multiply it by the other numbers on the bottom of the fraction.

8.3� 1010

1.5� 1011= 0.55AU

http://astrobiology.ciw.edu/publications.php?id=29


It quickly becomes apparent that despite the popular obsession with life on Mars, Venus is actually more similar to Earth in many of its properties. But why the big difference in temperature between the three worlds?

Table 5.2: Data for Terrestrial planets. Information from NASA Solar System Exploration pages (http://solarsystem.nasa.gov accessed 22/12/08).

The Greenhouse effectWhen light (energy) from the Sun reaches a planet, some fraction passes through the atmosphere and reaches the surface. Of this, some is absorbed and the rest is reflected back into space. The amounts absorbed and reflected at each stage depend on the wavelengths involved and the albedo of the reflectors (the atmosphere, clouds, land mass, oceans etc). The opacity of Earth's atmosphere to different wavelengths is shown in Fig. 5.4.

Fig. 5.4: Opacity/transparency of Earth's atmosphere to different wavelengths. (Image credit: NASA)

Image credits:NASA, GSFC, J. Bell (Cornell U.) and M. Wolff (SSI)

Mass (M⊕) 0.82 1 0.11

Radius (R⊕) 0.95 1 0.53

Orbit (AU) 0.72 1 1.52

Gravity (g⊕) 0.91 1 0.38

Surface temp (oC/K) 462o C (735 K) 15o C (288 K) -50o C (223 K)

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�

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http://solarsystem.nasa.gov


Much of the radiation which arrives at the Earth's surface is in the form of visible light (and lower-energy radio waves). The energy which is absorbed is re-emitted in the form of infra-red radiation.

Many gases in the atmosphere are good at absorbing infra-red radiation. Hence, when the photons try to escape Earth, they are absorbed by gases in the atmosphere. This causes the gas molecules to vibrate, which acts to heat the rest of the atmosphere. The infra-red photons are re-emitted, but there is a good chance they will be absorbed by another gas molecule before they can escape. Carbon dioxide (CO2), water vapour (H2O) and methane (CH4) all act as 'greenhouse gases'. So while the Earth is trying to establish an equilibrium by radiating away the energy which it absorbs from the Sun, the atmosphere has its own effect.

(Consider now the assumptions made in the calculations above. Were they justified?)

We can develop models to determine the magnitude of the greenhouse effect for each of the three terrestrial planets. (These are very complex so we won't reproduce them here, just the results). Similar models are being produced to make predictions about the future of Earth due to global warming and climate change.

But why is the greenhouse effect so much stronger on Venus than on Earth or Mars?

The problem with Mars is simple: it's just too small. Its low mass means that it has a low surface gravity (see Table 5.2), only about 30% that of Earth. This allows heavier molecules, such as the greenhouse gases discussed above, to escape into space. Some of the planet's water remains frozen on, or just below the surface, and there is a very thin CO2 atmosphere (the surface pressure --1 kPa-- is approximately 0.1% that of Earth), but not enough to keep the planet warm. Its small size means that most of the planet's internal heat will have been lost quickly too. A more massive planet in the same orbit could well have been habitable.

On the other hand, Venus is quite similar to Earth, yet it has no oceans and an atmosphere which is 96.5% CO2, and a surface temperature several hundred degrees hotter. There are two key factors which differ between the 'sister planets': location and the ability to store carbon.

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We always need to consider what assumptions

have gone into any calculation or model. Practice this skill when

reading news articles!

Planet Actual Taverage

Taverage (no greenhouse)

ΔTaverage

Venus 470oC -4oC +513oC

Earth 15oC -17oC +32oC

Mars -50oC -55oC +5oCTable 5.3: Data for Terrestrial planets. Information from NASA Solar System Exploration pages


�Fig. 5.5: The greenhouse effect. (http://maps.grida.no/go/graphic/greenhouse-effect).

The Carbon Cycle

On Earth, the atmosphere is largely regulated by the carbon cycle. It is likely that the Earth's early atmosphere was not too dissimilar to that of Venus, but over time it has changed. This will be discussed in more detail in another topic.

The carbon cycle is shown in Fig. 5.6, and includes five main steps (this is a massive simplification!):• CO2 from the atmosphere dissolves in the oceans• Rainfall erodes silicate rocks and carries minerals to the oceans• Silicates react with the dissolved CO2 to form carbonate minerals which sink to the ocean floor• Plate tectonics carries the carbonates to subduction zones where they are taken into the Earth's mantle. • Some rocks melt and their carbon is returned to the atmosphere in the form of CO2 through volcanoes.

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http://maps.grida.no/go/graphic/greenhouse-effect


�

Fig. 5.6: The Carbon Cycle. Values are gigatonnes (109) of carbon/year. Image credit: NASA Earth Observatory.

The carbon cycle acts as thermostat to regulate Earth's temperature. If Earth warms up, then the formation rate of carbonate minerals increases, which increases the rate at which oceans can absorb CO2. This then removes it from the atmosphere, weakening the greenhouse effect and cooling the planet. Conversely, a cooler temperature slows the rate of formation of carbonates, hence less CO2 is stored in the oceans, the atmospheric CO2 content increases, and Earth warms up again.

Water on VenusThe differences between Venus and Earth, then, appear to be mostly due to the operation of the CO2 cycle on Earth. It cannot operate on Venus because there are no oceans - but why is this?

Current estimates show that although there is some water vapour on Venus, it is less than 0.1% of the water content on Earth. Where did all the water go?

The oceans on Earth arose, we think , from outgassing of water in volcanic rocks. We would expect the 6

same to have occurred on other planets, including Venus and Mars. Mars was not massive enough to retain its atmosphere, and the gases were lost to space. Venus, however, should be able to retain its water as the surface gravity is similar to that of Earth.

The answer is location. Venus probably did look a lot like Earth initially, but being closer to the Sun it would have been hotter during the time when its atmosphere was forming from outgassing. Relative to Earth, a higher fraction of Venus's water would be in vapour form. This would add to the greenhouse effect on Venus (something also present on Earth). Neither planet would have had an ozone layer to protect the lower atmosphere from UV photons. This high-energy radiation is able to break down the bonds between hydrogen

"Who thinks?", "What assumptions did they make?", "How did they reach this conclusion?" These are all questions you 6

should be asking yourself at this point!Page �8


and oxygen atoms in water (photodissociation). Hydrogen atoms and molecules are too light to be retained in the atmosphere of either Venus or Earth, and are lost to space, preventing any further formation of water molecules. (See Lammer et al, 2006, Planetary and Space Science, 54, 1425 for a detailed discussion).

So to summarise: Venus, being closer to the Sun and hotter than Earth had a higher proportion of its water in the atmosphere, and was exposed to a higher UV flux to destroy the water. Over time the water disappears until only a tiny fraction of it is left.

On Earth, the cooler temperatures resulted in a lower fraction of water vapour in the atmosphere, and the greater distance to the Sun meant less UV to dissociate the atmospheric water molecules, allowing them to condense into rain and fall back onto the surface to form oceans.

If we were to move Earth from its current position to that of Venus we would find that:• Initial temperature of approximately 30oC• Some evaporation of water from the oceans, resulting in… • Reduced efficiency of the carbon cycle, so build up of CO2 in the atmosphere• More heating• More evaporation• More greenhouse effect

At the same time, the enhanced UV flux would break down water molecules in the atmosphere, preventing them from re-condensing. Eventually the surface would dry up and the planet would resemble Venus.

The Sun's Habitable Zone

It is not quite as simple to determine a star's habitable zone as we first thought. The effect of the atmosphere is crucial. The atmosphere, in turn, depends on the mass of the planet and its distance from the star.

For the operation of the CO2 cycle, we think we need plate tectonics. At present we don't understand the relationship between a planet's mass, radius and tectonic activity, which limits the accuracy of our predictions about habitable zones . 7

Nevertheless, we can make some progress. It is clear that Venus was too close to the Sun; a runaway greenhouse effect is likely for any planet at that distance. Theoretical models predict that a planet should not be closer than 0.84 AU if a runaway greenhouse effect is to be avoided. We will take this as the inner edge of the habitable zone.

What about the outer edge? We would probably guess that Mars was not habitable, but its problem is that it is just not massive enough. A more massive planet which could hold on to its atmosphere could have a chance at being habitable. Again, theoretical models of the greenhouse effect on planets suggest that the outer edge of the habitable zone could be 1.7 to 2 AU.

�Habitable Zones around other stars

Sun

Mercury's

Orbit

Venus'

Orbit

Earth's

Orbit

Mars'

Orbit

Work by Stamekovic et al. in 2009 (New Scientist, 7th Sept 2009 issue) suggests that planets need to be approximately 7

Earth-mass and size in order to have both magnetic fields and plate tectonics. It is possible that other mechanisms could recycle the crust though.

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Fig. 5.7: The habitable zone for the Solar System is believed to extend from just outside the orbit of Venus to just outside the orbit of Mars.


We can use the results we have derived for the Sun as a guide to the habitable zones around other stars. Stars of different mass will have different luminosities (as we have seen: more massive stars are brighter, and L∝M3). Since the luminosity will vary with the square of the distance (an inverse-square law) we can scale the results from the Sun to other stars. A star of luminosity L will therefore have a habitable zone between Rinner and Router where:

and

Recall that we are only interested in stars with masses between 0.5 Mʘ and 2 Mʘ. This corresponds to spectral types from A2 to M0. With estimates for their luminosities, we can estimate the locations of their habitable zones using the equations above. Here are the results:

You should not have too much faith in these numbers, but they provide some idea of what's happening.

One thing we have ignored in this table is what happens when a planet gets too close to its star. In this case, the planet will become tidally locked, and will always show the same face to the star . At first 8

glance this will make it a poor candidate for life . 9

The Moon is tidally locked to Earth. Mercury is tidally locked to the Sun in a 3:2 resonance - for every two orbits, it turns 8

on its axis 3 times.

We will discuss this more later. 9

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Rinner =�

(L/L�)Rinner,Sun =�

(L/L⇥)� 0.8 AU

Router =�

(L/L�)Router,Sun =�

(L/L⇥)� 1.7 AU

Spectral Type

L (Lʘ)

Rinner (AU)

Router(AU)

A5 24 4.2 8.3

F0 9 2.5 5.1

F5 4 1.7 3.4

G0 1.5 1 2

G2 1 0.84 1.7

G5 0.7 0.71 1.4

K0 0.4 0.51 1

K5 0.2 0.36 0.7

M0 0.1 0.22 0.4

Fig. 5.8: Predicted habitable zones around stars of different spectral type. The data was used to plan NASA's Kepler mission which is searching for habitable planets. Note the tidal-locking radius which also varies with the mass of the star. Image credit: Kasting et al. Icarus 1993

Make sure you remember why we use those limits, and

what we mean by spectral types!

Table 5.4: An estimate of habitable zone region for stars of different spectral type.


In addition to the complications discussed above, stellar luminosities also vary as stars age. The Sun's energy output has almost doubled since it was born. This means that the location of a habitable zone will also vary as the star ages, as can be seen in Fig. 5.9.

Fig. 5.9: The variation of habitable zones with time as the host star ages. The lines terminate when the star leaves the main sequence and becomes a red giant.

Be careful! Just because something is in a star's habitable zone, it will not automatically be habitable! Places outside a habitable zone could also sustain life if the conditions are right! A literal interpretation of these results can be dangerous if you don't think about them carefully.

Galactic habitable zones

One of the Sun's unusual features is that its orbit around the centre of the Galaxy is almost circular. It is less eccentric than many stars of similar age and type. Furthermore, it is barely inclined relative to the Galactic plane. These features prevent the Sun from plunging into the inner Galaxy where life-threatening supernovae are more common. A supernova explosion nearby would bathe Earth in high-energy radiation, which would almost certainly be fatal for most, if not all, life on the planet. Also, the small inclination to the Galactic plane avoids abrupt crossings through the plane (the Galactic disc) which could stir up the Sun's Oort cloud and bombard Earth with life-threatening comets.

In fact, the Sun is orbiting very close to what is called the co-rotation radius of the Galaxy, where the angular speed of the Galaxy's spiral arms matches the speed of the stars within. As a result, the Sun does not pass through the spiral arms very often, which again prevents additional exposure to supernovae.

These exceptional (we think!) circumstances might have made it more likely for complex life - and ultimately human intelligence - to arise on Earth. It is estimated that fewer than five percent of all stars in our Galaxy have similar orbits. This has led to the concept of a Galactic Habitable Zone where stars (and their planets) are more likely to have a 'quiet' life!

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Points to ponder• What is a habitable zone?• What factors affect the location of a habitable zone?• Why is Earth habitable while Venus and Mars are not?• How could we define different habitable zones?• Does 'in the habitable zone' mean 'definitely habitable'? Why/why not?

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ASP1022 Topic05 HabZones 2015