Section 3 - Habitable Zones and Extra-Solar Planets

Chapter 10


As we move to stars other than the Sun we may ask if they have planets, and if so, if these planets could harbor life.


Central question:

What determines the "suitable zones" or "habitable 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? The main criterion to define the "habitable zone" is: Temperature on the planet such that water may exist in liquid form.

Other factors, besides the requirement for liquid water, that might affect chances of forming life on a planet:
a. radiation spectrum or color of the star: 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. Star cluster M39 showing hotter (blue) stars are more luminous than cooler red 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. A long time time implies that we must have stars that can shine for a long time. We therefore need to find out how long different stars can shine. This is a matter of their mass and their energy output per unit time, which we measure as the star's LUMINOSITY or light power. We come back to this below, in the notes on Chapter 11.

Clicker question. The luminosity, or power, of a star measures (compare power of a light bulb):

a. How much light the star emits over its life time.

b. How much light the star has emitted in the past.

c. How much light the star emits per second over all wavelength.

d. How much light we receive from the star per second.



Stars become hotter and more luminous the more massive they are. This is because a higher mass star needs more pressure to balance the gravity causes by its mass and higher temperature produces higher pressure. The higher temperature and larger size makes the star much more luminous than the Sun. The light 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. As we already discussed, the amount of light intercepted per unit surface area 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 thus depends on several factors that we already discussed before:


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 but probably still inside the habitable zone. There may also be habitable zones around some of the giant planets, as we saw. We don't actually know the answer to this question all that well.

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 since the Sun's formation is about 30%; it 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 100-1000, 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. This very 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 (see further below in Chapter 11 section)

Stars like sun expelling their outer atmosphere, hourglass nebula
another example: stingray nebula
Ok, one more: Eskimo nebula


Discussion question: What will happen to the planets in the solar system as the Sun goes through the red giant and white dwarf phases?


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.

The principal factor that determines the main properties, including its life time, of a star is its MASS. Secondary to that is the CHEMICAL COMPOSITION of the star.


Mass affects: Temperature (due to equilibrium between gravity and pressure in the star); Rate of energy production so the stars "Luminosity" and hence Life Time; and the End Phase of the star.

Possible end phases of stars:

A Milky Way full of stars 


Question: How do we tell the temperatures of stars?

Question: How do we determine the luminosity of a star? What do we need to measure?

Question: How do we determine the mass of a star? This is relevant to find out how long it can shine.



What the important parameters we need to know about stars to understand how they compare to the Sun?

a. Color or detailed spectrum gives us the temperature of the star.

b. We need to know the distance to the star or else we cannot determine its total luminosity, nor its mass.

c. The apparent brightness (or flux) is the energy that we measure we get from the star at Earth. Combining that with the distance to the star, we can determine the "luminosity" of the star. This is the total energy emitted per second by the star.

d. Once we have the temperature and the luminosity, we can calculate the star's size. If you have two objects with the same temperature but one is more luminous than the other, it has to be bigger. That lets us calculate the star's diameter relative to the Sun's size.

e. The mass of the star can only be determined directly if we find something orbiting the star, just as the mass of the sun can be determined from the planets orbiting it, using Kepler's laws. Hence binary stars are important for measuring masses of stars.

f. The last important property is the chemical composition of the star. This also can be derived from the star's light, by splitting it over all its wavelengths into a detailed spectrum.


The results of our studies are that not all stars are same: we see stars of different luminosities, masses, temperatures, and sizes. What causes these differences? Why do we need to know?

What kind of stars exist in galaxies? Can all stars shine as long as the Sun? The answer is definitely NO. 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:


- Stars that are hotter and more massive than the Sun emit more UV light which may affect development of life on planets. The temperature of a normal star depends on its mass; in general, 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 star that is the case in in our solar system.

- Many stars are much cooler than the Sun which would imply the habitable zone will be much closer to the star. This implies that planets in such a habitable zone would have much shorter orbital periods than the Earth has.

- 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.



MASS-LUMINOSITY RELATIONSHIP FOR STARS


How long can a star shine? That is given by:

available energy supply divided by how much energy the star loses each second; this is thus 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:


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.

T The fate of stars

As we saw above, stars like the Sun leave "white dwarfs" as remnants when their life is over. Almost half of the star's mass is expelled back into the interstellar medium, the core is left as very dense, initally very hot, carbon-rich star, which we call a white dwarf. White dwarfs are peculiar; they are very dense, about a million times denser than ordinary matter. Even though the white dwarf that the Sun will leave behind has still about 60% of the Sun's mass, it will only be about the size of the Earth. Some planets may become unbound from the star as this happens and become lonely planets orbiting alone in the Milky Way.

The sun itself will fade to a white dwarf

More massive stars leave even more peculiar remnants. They don't end their lives as planetary nebula with a white dwarf remnant, but in violent explosions as a supernova. The supernova too expels a large amount of material from the star back into the interstellar medium. This gas is enriched with the heavy elements created by nuclear fusion in the star during its life and created during the supernova blast. There are two options for the remnant:

a. If the star is massive but not extremely massive, a neutron star will be left. This star literally consists mostly of neutrons packed densely together. The neutron star will spin rapidly (periods of milli-seconds to seconds), emitting beams of light that we can detect. A neutron star is another factor of one to hundred million times denser than a white dwarf. If we shrink the Sun to the size of a neutron star, it would be about 10 miles across. Neutron stars can only exist up to a certain mass limit, somewhere between 2 and 3 times the mass of the Sun.

b. If the star is extremely massive, it will not leave a neutron star but a black hole: the core is too massive to be supported as a neutron star, and will continue to collapse after the supernova explosion to a region of infinite density in an infinitely small volume. We have found such black holes in binary stars where a star orbits around a mysterious object which consists of a bright disk of emission surrounding the black hole.

Examples of massive star remnants:

The Crab Nebula, remnant of a supernova explosion in 1054 AD

The neutron star in the Crab nebula supernova remnant

Pulsar animation and discovery photo of supernova 1987A

1987A in the Large Magellanic Cloud

Recent supernova in the Whirlpool Galaxy



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?

There are several ways we might detect planets:

1. Direct imaging to look for planets around nearby stars.


Let's consider this: The major problem is that 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.

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 orbiting cool stars and images of several star-planet systems have now been obtained, especially with the Gemini telescopes.

2. 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?


Clicker question. The diameter of Jupiter is about one tenth of that of the Sun. Suppose that we are far away from the Solar System and could observe Jupiter transiting across the Sun. How much would the light from the Sun be dimmed during the transit, that is how much weaker would the Sun appear during the transit?

a. 10% b. 50% c. 1% d. 0.1%

Would it matter how far away Jupiter is from the Sun? In other words, if Jupiter were at the place of the Earth's orbit, would the dimming be the same or not?

a. Yes b. No


Transiting extrasolar planets light curve examples
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!

3. 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 or through its changes of position on the sky. 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 first for the case of 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?

Here is a simulation that shows how the star moves as the planet orbits it. It is not too scale, in reality the star's motion is tiny: Doppler spectroscopy.

The stars spectrum has dark absorption lines that we can measure the blue and red shift and thus measure the motion of the star as the planet orbits it.

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.



Clicker question: What planet would cause the largest "wobble" motion in its star, hence would be easiest to detect, be it through the Doppler method or the astrometry method?

a. Big planet far from star.

b. Big planet close to star.

c. Small planet far from star.

d. Small planet close to star.



For the same 4 choices above, which planet would be easiest to detect with the transit method?

And lastly, what about in the direct imaging method?



4. Yet another 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.

Here is an interesting link that Stephanie found on a massive planet detected by microlensing: New result on an extra-solar planet!


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:

- Most stars have planets. Estimates of the number of stars that has Earth-mass planets are not that accurate yet, but there are likely very many of them.

- In many stars multiple planets have been detected. 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!)

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. So many masses derived for planets are "LOWER LIMITS", except for the cases where we know the system is seen from "edge-on", which we know for sure when we see the planets transiting across their star.

- 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


Some questions to test your knowledge of the search for extra-solar planets


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? This is a tricky question that can easily lead to incorrect reasoning. It is very easy to point at any situation as being miraculous in some ways, and hence extremely unlikely. E.g. a couple may find that one split decision in their lives led their future together. But this doesn't mean they would not have had a future without that decision. It might have been a different future, but...


Likewise, we can point at many unique features of Earth and think that a miracle or at least a very non-scientifically explainable set of events must have happened for us to be here. But this ignores one important fact: if the events had not happened, we would not be here to ask the question! So, the very fact we can ask the question implies that things worked out OK so far.

Nevertheless, let us wade into this treacherous terrain...

What is special about 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 occurring 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.

However, we don't know though, if a variation in tilt axis would preclude development of (advanced) life. It may depend on the time scales of the change.



On a larger scale, we can ask the same questions about our universe. With only a small change in some of the basic physical constants, for example, matter might not have been stable. Could we imagine a universe with no stable matter, just light and a myriad of elementary particles that never formed atoms? Again, we can invoke miracles, but with only the example of one universe we can learn about so far, it can lead to a lot of philosophical speculation but no hard conclusion.

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.



As a wrap up, here is a recent video about the search for earth-like planets:

Some discussion of Kepler mission results.