Section 3 - Habitable Zones and Extra-Solar Planets
Study: Chapters 10 and 11

Chapter 10

General question:

What determines the "suitable zones" where life might exist on planets, in terms of the properties of the central star and the conditions on the planet.

What do we mean with suitable conditions?

Main criterion: Temperature on the planet such that water may exist in liquid form.

Other factors:
a. radiation conditions: too much UV light may be bad, depending on the planet's capability to shield the surface from UV light. So the atmosphere of the planet will matter for this too, but also the temperature of the star: hot stars emit much more UV light than cooler stars.

b. For how long will the conditions be suitable? If Earth is typical, it has taken a long time to develop advanced life forms here. We therefore need to study how long different stars can shine.
The factors that enter the life times of stars are:

How luminous and hot is the star; stars emit more light the larger and/or hotter they get. The radiation emitted by a hotter and more luminous star has more energy to heat planets further away from the star than for a less luminous star. In general, the amount of light intercepted by a planet decreases as the inverse of the distance squared to the star. This is simply a consequence of energy conservation: the light from the star is spread out over a larger area and volume as it moves away from the star.

The temperature on the planet or moon depends on several factors:

How large is the habitable zone in the Solar System? We call the distance between Earth and Sun 1 Astronomical Unit. Is the habitable zone  0.5-1.5 Astronomical Units? Or 0.95-1.05 A.U? Venus is too hot, Mars perhaps too cold. There may also be habitable zones around some of the giant planets, as we saw.

Some features of Venus:

Venus is the planet with the most extreme greenhouse effect in the solar system, due to its thick atmosphere. What happened to the water that likely was once present on Venus? Likely lost to space as any surface water  molecules evaporated into the atmosphere and were dissociated there due to the Sun's UV light (which is more intense near Venus than Earth).

Changes in solar system's habitable zone over time:

The Sun's energy output is gradually climbing from its early days of hydrogen fusion to the present. This general increase in brightness (measured in percentages, roughly 30% or so) is very important but happens very slowly so it is not something we need to worry about now. It implies the habitable zone was closer to the Sun in the past and is slowly moving outward.

A more dramatic change comes about when the Sun has exhausted the hydrogen in its core available for nuclear fusion. The center will shrink and heat up a lot, while the other layers will swell to enormous size. Eventually, in the center, helium will fuse into carbon. The Sun's luminosity will increase by factor of a 100, its diameter by a factor of a 100. The color of the Sun will turn redder, as it is cooler in the outer atmosphere. However, the higher luminosity will greatly increase temperatures throughout the solar system, with Earth getting warmer than 700 C. The luminous phase of the sun will last a billion years, and then it will expell its outer layers and slowly cool as a white dwarf.

Stars like sun expelling their outer atmosphere, hourglass nebula
another example: stingray nebula
Ok, one more: Eskimo nebula
While the sun itself will fade to a white dwarf

Thus the long time fate of the solar system is darkness and cold temperatures. A similar fate awaits the universe as a whole, as it keeps expanding and gradually converts any remaining gas clouds in stars with cold stellar remnants left at the end. This is many, many billions of years in the future.

CHAPTER 11

Properties of stars relevant to how large their habitable zones may be and how long the stars can shine.

What are stars other than Sun like? Are they all the same size and temperature? Do they emit the same amount of light per second (we call this "luminosity")? The answer is no to all questions.

A Milky Way full of stars 


A critical issue in determining stellar properties is to realize that in order to know how bright stars really are, we must be able to measure the distance to them. How doe we measure distances to stars? The simplest method is the parallax. Works only for relatively nearby distances. We use other methods for more distant stars.
Diagram to explain parallax

- Not all stars are same: we see stars of different apparent and intrinsic brightness, and different color. What causes these differences? Why do we care about it?

What kind of stars exist in galaxies. Are all stars like the Sun? Can all stars shine as long as the Sun? The answer is definitely NO to these questions. However, there are also very many stars like the Sun in the MW.

If stars are different from the Sun, how does that affect their habitable zone? There are several important effects to consider:

- hotter stars emit more UV light which may affect development of life on planets. The temperature of a normal star depends on its mass; high mass stars are hot and also much more luminous than the Sun.

- Stars that are more luminous than the Sun will have their habitable zone away further away from the case in our solar system.

- many stars are much cooler than the Sun which would imply the habitable zone is likely much closer to the star

- hot, luminous stars, as we will see, can not shine very long. Therefore, their habitable zone is also limited in the time available to develop life.

- Low luminosity small stars can shine much longer than the Sun and could still support life possibly since there is much time available.

Useful relations/knowledge learned about stars which taught us all these things:

We have learned an enormous amount of information on how stars evolve and how they shine by study of star clusters. In the Milky Way and in other galaxies we find close groups of stars. We distinguish two types:

Pleiades open star cluster: blue stars, more massive than Sun and hundreds of fainter members

Globular cluster 47 Tucanae
Hubble Space Telescope photograph of globluar cluster M15


There are two special properties that make study of star clusters so useful:

1. The stars in a cluster are all at the same distance from us. That way we can directly study brightness variations among stars and deduce that not all stars are the same or can shine for equally long times.

2. The stars in a cluster must have formed at the same time since the chance of forming a cluster of stars by random encounters of stars is negligible. By studying star clusters at different ages we can therefore infer how stars evolve over time.

The stars in clusters have taught us several things, most notably that massive stars are hot and cannot shine as long as lower mass stars. The Sun is a low mass star. The time a star can shine is demonstrated by the "Mass-Luminosity" relationship.

Explanation of the Mass-Luminosity relationship for stars.

Goal: we are trying to understand how long various stars can shine, so how long they can generate energy through nuclear fusion in their core and stay hot. This is a simple matter of supply and demand: how much energy can the star generate, and how fast is it losing energy through the light that it emits.

First an example. A pickup truck has a 40 gallon tank and gives 10 miles/gallon on average. A civic hybrid has an 11 gallon tank and gives 50 miles/gallon on average. Which car can go further on one tank? How did you calculate this?

When you study this problem, you will see that you take the energy supply (equals gas in the tank in gallons) and multiply that by the miles/gallon figure to see how many miles you can go. We can re-state this problem, by giving the energy consumption per mile rather than the miles/gallon. In that case we get for the pickup that it needs 0.1 gallons per mile, and it can travel:

40 gallons divided by (0.1 gallons/mile) = 400 miles.

Now, let's go back to stars. For stars, the available energy supply is a fraction of the star's mass, namely that fraction that is converted into energy through E=mc2. The rate at which energy is being used is the "luminosity" = "power" of the star. How long can a star last then? That is given by:

available energy supply divided by energy loss rate; this is proportional to the mass of the star divided by the stellar luminosity. The unit you get when you do this calculation is a unit of time, as it should be.


Here comes the interesting part: massive stars produce far more luminosity than low-mass stars. The relationship is not linear (in which case all stars would be able to shine equally long) but cubic, that is, the luminosity of a star scales as the mass to the power 3. The net result is that a star that is, say, 10 times more massive than the Sun will use up its total energy 100 times faster than the Sun, so it will only shine 1/100th of the time the Sun can shine, and a star that is 100 times more massive will only be able to shine for 10,000 less long than the Sun before it runs out of energy.

Conclusion: if life takes billions of years to develop to fairly advanced stages around stars like the Sun, very massive stars are unlikely to be good places to look for planets with life. A massive star's life is measured in millions of years, rather than billions of years.


Summary of what we have learned about the properties of stars that are in the main, stable phase of their life, like the Sun is:


Galaxies like our Milky Way contain many stars like the Sun, fewer massive stars, and many more low-mass stars. The low-mass stars will be cooler than our Sun but can shine much longer and they may be good places to look for planets and life.

Another interesting bit of information: as much as 50% of all stars may be occurring in binary systems, that is, two stars orbiting around each other. We also call them double stars. Some systems have 3 or even more stars orbiting each other. Finding planets is a bit like finding binary star systems, except much harder.

DETECTING PLANETS AROUND OTHER STARS

The last planet in our solar system was discovered in 1930 (ignoring the debate of whether it is a planet!). It has taken about another 65 years since then to find the first solid evidence for planets around other normal stars. Why is it so hard to find planets around other stars?

- The stars are bright, the planets are faint! Here is how hard this is:

The closest star to us other than the Sun is 4 light years away. This star's brightness as seen by us is about the same as that of a 150 Watts light bulb at a distance of 15 miles away from us. On this scale of 15 miles distance, the Earth would be a dust speck much smaller than a mm. It would be about 10 cm away from the light bulb. Imagine trying to detect a dust speck that is next to a 150 Watts light bulb from a distance of 15 miles away. That is how hard it is to detect Earth sized planets around stars. How about Jupiter? Jupiter would be about 50 cm away from the light bulb, and still be at least a billion times fainter than the light bulb.

It has been possible to find binary (=two) star systems, since both stars are visible if they are not too close to each other.

The situation may seem rather hopeless for planet detection through imaging, yet imaging techniques already have allowed detection of these planets in a few cases. Here is an example. But most of the planets now known to exist around other stars have been discovered in other ways, that are essentially methods similar to those how most close binary star systems have been discovered. The situation is slightly better for large planets and dim, cool stars, where a few images of the star-planet system have now been obtained.

Basic methods of extra-solar planet detection:

a. Through "occultations", or "transits". The planet moves in front of the star, and temporarily dims the light. What is required for this? How much would star light be dimmed?

Transiting extrasolar planet light curve for star HD149026b.
A comparison of ground-based transit and spectacular new data from the Kepler satellite.


The answer is quite simple. From our perspective, the distant star and its planet are about equally far away. Thus, the planet will cover a fraction of the area of the star that is equal to the ratio of the area of the planet to the area of the star:
(planet diameter)2/(star diameter)2. In the case of a planet like Jupiter, it would block about 1% of the star's light in the transit, while a planet like Earth would only block 0.01% of the star's light; with modern instruments we can detect the 1% dip easily, while the 0.01% dip is very difficult to measure.

Moreover, from multiple transits we can deduce the orbital period for the planet. This, together with knowledge of the size and mass of the star, will allow us to determine the distance of the planet to the star; we can tell if it is in the habitable zone or not!

b. Through motion of star. If you can't see the planet, look for the effect of the planet's motion on the star: the star wobbles due to force of gravity exerted on it by the planet. The wobble can be detected in star's velocity. What would the size of the wobble depend on?  How fast would it wobble?

The star wobbles at the same rate as the planet completes an orbit. It is easiest to imagine this as having two stars of equal mass orbiting each other. In that case, intuition tells us the stars would be moving at the same rate and would always be opposite each other in their orbit. Newton's laws can be used to show that this intuition is right. In the case of objects of very different mass, the speeds of the two objects vary inverse to their mass, but the two objects still each complete their orbit in the same time. The orbit of the more massive object is just much smaller than the orbit of the less massive object (which is why Kepler concluded that the Sun was at rest; it isn't, but it's motion is very small).

An example:

If the star is 1000 times more massive than the planet, the star's velocity in its orbit will be 1000 less than the planet's velocity. A planet like Jupiter is about 1000 times less massive than the Sun. Jupiter orbits at 750,000,000 km from the Sun, and completes one orbit in 11 years. As a result of Jupiter's motion around the Sun, the Sun completes its own little orbit in 11 years, and the radius of the orbit is 1000 times less than that of Jupiter, so 750,000 km, which is about equal to the radius of the Sun.

Doppler effect shifts light to bluer colors when star approaches us, and to redder colors when star is moving away from us. We can detect this!
Question: why not observe the Doppler effect for the planet which moves faster?

Illustration of Doppler technique for detecting binary stars (scroll down the page to see animation).

Look at the above animation. What would be different for planet? (answer: you would detect the tiny motion of the central star, not the large motion of the small planet!). In reality, the situation is more complex. The stars spectrum has dark absorption lines that we can measure the blue and red shift for. However, stars can also pulsate on their own and astronomers have to be very careful to rule out other causes of the shifting of the lines.

astrometry: in principle, we can also detect the motion of the star as a wobble on the sky compared to other distant stars. This has been tried in the past, but the motion is so small it is difficult to detect. Still, this will be an important technique in the future as our accuracy in imaging improves. Many double stars have been found this way.

c. A third technique: through gravitational lensing. The light from background stars can be amplified by a foreground system, causing a star to vary systematically in brightness. If the foreground system has planets, the light variations may be different. Here is an example:micro lensing by a star with a planet
The big curve shows the overall brightening of the background star by the amplification of the light by the foreground star, which acts like a lens and bends the light of the background star by its gravity. The little dip on the curve is due to a planet that orbits the foreground star and that causes additional amplification of the light as the gravity of the planet acts like an additional lens.

Can we take pictures of the planets that have been discovered? Only of a few so far, and more in the future, although they will be tiny pictures with not any detail. Coronographic techniques are used to block the star light as best as possible. Scattered light is a problem, so we need to go outside the Earth's atmosphere and use clever imaging techniques in space to block the light of the star. We also need larger telescopes to improve the angular resolution. This can be done through interferometry or a large ground-based telescope that is being planned.


What is the problem with finding Earth sized planets?

Both principle detection techniques (Doppler shift and occultations) produce weakest signal for low mass planets or for planets far away from the star. So, the planets that have been found are typically close to the star and massive. This was surprising (since people thought you could not form Jupiter size planets close to a star) but we have to keep in mind that there is a strong bias here, since those are the ones that can be most easily found.

What has been discovered about the extra-solar planets thus far:

- On average, in about 10% of stars more or less like the Sun planets have been found. The other 90% may have planets, but detection limits may not yet be good enough to find them

Question: can we find planets if we would see the star/planet system from above (vertical to the orbital plane)?

- Many stars have multiple planets. The ability to detect multiple planets relies on very well measured Doppler shifts for the stars (and/or patience to detect eclipses of the star by the planets!)

- Planets with mass of Earth have been found, but in a surprising place: surrounding neutron stars! These are the only objects were current techniques allowed detection of such low mass planets. There is only one such system known and it is not clear these are "normal planets".

Challenge in measuring the masses of planets: inclination of the orbit not known unless the planet transits across the star (then we know we see the system "edge-on" and not from above.

- Some knowledge of planetary atmospheres has been found too, with Hubble Space Telescope, where sodium was detected in planet's atmosphere. This technique shows great promise for future. It relies on detecting the change in the star's spectrum during a transit by the planet.

- Planets have also been found in binary star systems!

Planet searches, wrap up:

Current list of planets detected (Note that the masses are in Jupiter masses, except as noted). The most unexpected place to find them. Click on planet's and star's names and you get an overview of what these objects are and where they are.

The most peculiar objects in this list are the candidates found near a pulsar (labeled PSR in the list).

Techniques:
- transits to detect temporary and periodic dimming of starlight
- Detecting the wobble of the star resulting from the presence of the planet(s):

Doppler shift in velocities detected in light from star, could be in normal stars or in neutron star (= pulsar) where we detect Doppler shift in the frequency of the pulses of radio emission

- Gravitational lensing ("micro lensing") of normal stars, where we look for light variations in star due to lensing of background object. Presence of planet may give different light variation. Drawback: one time even for each star!

- Direct imaging to see the planet and its motion around the star. This will become more feasible in the future.

Results:
- Planets with mass of about Earth only found so far around neutron star, but planets with just a few times the mass of Earth found around normal stars with Doppler technique, only possible if they are very close to the star and the star has low mass so it wobbles more.
- Many planets found, sometimes multiple per star, up to as many as 5 per star.
- Results biased towards detecting massive planets close to stars; a large part of the search space cannot yet be explored (e.g. Earth size planets or large planets very far from star)
comparison of extra-solar planets with solar system planets

- Stars with higher abundance of "heavy elements" (meaning anything above Helium) have higher probability of having planets detected around them.

Here is a great link about extra-solar planets, courtesy of JPL and NASA

Future plans for finding smaller planets (click on Interactive Flash overview)

Is the Earth unusual? The "rare Earth hypothesis"

See section 11.3 in book.

Are conditions on Earth so special that it is likely few planets will exist that are like Earth?

a. Requirement for high abundance of heavy elements to form rocky planets. Likely not an issue, since most of the Galactic disk has abundance of heavy elements like Sun or higher.

b. Requirement for avoiding major impacts from occuring too frequently. Jupiter plays a critical role in keeping the asteroid belt where it is (between Mars and Jupiter and not crossing Earth's orbit). Also, most of comets are far from Sun in comet cloud, but they may have been formed much closer in, in region where major gas giants formed. Again, the massive planets are responsible for sweeping them to the outer orbits. The Moon may also play some role in the impact rate of asteroids and comets on earth.

Does every Earth need a Jupiter in the right place so that life has enough time to form and evolve?

We don't know enough to be sure of this. But it surely is no problem to form Jupiter size planets as the extra-solar planet results thus far show.

c. Is a stable climate rare?

The stability of the Earth's climate may be related to the Earth's ability to regulate the amount of natural greenhouse gases (notably CO2) in the atmosphere. Plate tectonics plays an important role in this cycle.

A second important factor is the presence of the Moon. The Moon is responsible for keeping the Earth's tilt at a pretty constant angle. There is some evidence that Mars's axis shows much larger variations in the tilt over long periods. The likely formation mechanism for the Moon is a giant impact of a mars-sized object with Earth early in the formation of the solar system. The Earth is not massive enough on its own to attract enough matter to form large moons like the gas giants did. Thus, the presence of the Moon could be quite rare.

We don't know though, if a variation in tilt axis would preclude development of (advanced) life.

In balance, "reasoning after the fact ("a posteriori") always can seem to point at magical coincidences for certain events to happen. But that is a dangerous thing to do from a scientific perspective. It is much better to get real data on the variation of planetary systems and from there draw the conclusions what is required for life and what is rare or common.