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The Drake Equation part 2: Planets
Posted: 24 May 2010

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Life as we know it needs a planet to live on. With over 450 exoplanets currently known (keep a check on the growing tally at the Exoplanets Encyclopedeia, we take it for granted that there are planets out there, orbiting other suns, but it is all too easy to forget that back in 1960, there were no planets known beyond our Solar System. That other planets existed was a huge assumption based on no evidence whatsoever. In the 1980s indirect evidence was found thanks to IRAS (the Infrared Astronomy Satellite), which imaged dusty protoplanetary discs around the stars Vega and beta Pictoris. In 1992 the first exoplanets were announced, but these were dead worlds orbiting dead stars called pulsars. We had to wait until 1995 for the first detection of a planet around a normal, Sun-like star and only in the time since have we been able to make accurate assessments of the second term in Drake’s Equation, f(p), the fraction of stars that possess planets.

In 1960 Drake picked a value of 0.5, meaning that he reckoned half of all stars had planets, which isn’t so far off the mark. In 2008 astronomers led by Michael Meyer of the University of Arizona used the Spitzer Space Telescope to study bands of warm dust around stars. This dust had been thrown up by collisions between rocky bodies as planets formed around the star and, depending on various models of planet formation, Meyer estimates in a paper published in the 1 February 2008 edition of The Astrophysical Journal; that between 20 and 60 percent of the stars observed have rocky planets. Furthermore, an analysis of Sun-like stars with the HARPS spectrograph attached to the 3.6-metre telescope at the European Southern Observatory in Chile has led to astronomers estimating that one-in-three Sun-like stars has large rocky planets (known as ‘super-earths’) or Neptune-sized worlds orbiting them with a period less than 50 days.

On the other hand, observations of the Orion Nebula with the 15 radio dishes of the Combined Array for Research in Millimetre Astronomy (CARMA) in California’s Inyo Mountains indicate that only ten percent of 250 stars there have enough gas and dust to produce a Jupiter-sized gas giant. On the face of it, given that the vast majority of exoplanets discovered thus far have been Jupiter-sized worlds, these figures might be troubling, but it is worth remembering that both primary methods for finding planets – radial velocity measurements that detect the gravitational wobble imparted on a star by an orbiting planet, and transits as a planet passes in front of its star and blocks some of the starlight – are heavily biased towards finding the most massive worlds. There may yet be countless small, rocky planets like Earth that have simply gone unnoticed, but that may be about to change. NASA’s Kepler mission is an orbiting telescope that will track the starlight of 100,000 stars in the direction of the constellation of Cygnus, and is sensitive enough to spot transits of Earth-like worlds.

An artist’s impression of an exoplanet. Planets could appear blue because they have oceans, but they could also appear blue for other reasons such as methane abundance like in Neptune’s atmosphere. Image: NASA/ESA/G Bacon (STScI).

Single stars like the Sun shouldn’t be the only place we look for planets. To the surprise of many astronomers, binary star systems seem equally proficient at building worlds. A group of astronomers including David Trilling of the University of Arizona have found via Spitzer that forty percent of the 69 binary star systems that they searched showed scattered light from discs of dust orbiting them. This dust comes from collisions between asteroids, just like in our Asteroid Belt, implying that some form of rocky planet formation has taken place. Even more surprising is the fact that the tighter the binary system, the more likely it is to possess a dust disc, peaking with stars that are separated by just three astronomical units (i.e. three times the distance between Earth and the Sun).

Within the next few years, as the data comes flooding in from Kepler and also a potential European Space Agency mission called PLATO (Planetary Transits and Oscillations of stars) that could launch in 2017, we should finally gain an accurate assessment of what fraction of stars have planets, and 0.5 still seems like a good bet.

Earth-like worlds

That’s f(p) taken care of, but what about n(e), the number of worlds in each star system that are potentially habitable? Again, this is something that Kepler should discover, but there will be some footnotes to its answer.

Our Solar System has one planet that is definitely habitable – Earth. Yet Venus and Mars skirt the inner and outer edges of the all-important Goldilocks Zone, that habitable region at just the right distance from the Sun for temperatures to permit liquid water, essential for life as we know it. There may even have been, or there may even still be, life on both Mars and Venus. As inhospitable as the surface of the second planet from the Sun is, some astrobiologists have speculated that the disequilibrium of oxidising agents such as sulphur dioxide and oxygen in Venus’ dense carbon dioxide atmosphere could be caused by some form of primitive life drifting amongst the clouds. Spacecraft that entered Venus’ atmosphere in the 1970s even detected tiny particles a micrometre across floating in the wind, which some have speculated could be Venusian lifeforms. And if we were to extend our range across the Solar System, out of the Goldilocks Zone, we come across Europa and Enceladus, icy moons of Jupiter and Saturn respectively that are both expected to contain large oceans or reservoirs of liquid water. In a best case scenario the number of bodies in our Solar System that are habitable could be five, or at worst it could be just one.

Europa and Enceladus threaten to make a mockery of several of our assumptions regarding abodes for life, including our cherished notion of a Goldilocks Zone. Jupiter and Saturn are both way outside of the liquid water realm, but they keep at least some of their orbiting moons warm because their powerful gravity causes tidal flexing in the moons’ interiors. And there’s another footnote; the Drake Equation specifies planets, but where do moons fit into it? It’s not a stretch to imagine a gas giant in the Goldilocks Zone of another star, with one or more large rocky moons around it that are suitable for life – think of Endor in Return of the Jedi, or Pandora in Avatar. Should we treat each habitable moon as a planet in the Drake Equation?

Large moons factor into habitability in another way. Several scientists, including Peter Ward and Donald Brownlee in their book Rare Earth: Why Complex Life is Uncommon in the Universe point out that our Moon has played a major role in the development of life on our planet. Its tides help stir the oceans and create tidal pools in which life could have first developed. Its presence alongside Earth stabilises our planet’s rotational axis, so that we don’t suffer extreme changes in climate like Mars, which wobbles all over the place. Scientists think that our Moon was created in a gigantic smash with a protoplanet the size of Mars just after the Solar System had formed, but when astronomers look at other young planetary systems, they see very little evidence of similar giant collisions that would spread large amounts of dust and debris into space, scattering the starlight and making itself visible to the infrared spectrometers on the likes of Spitzer. In fact, a 2007 survey found that only one in 400 observed systems contained such dust. That’s not to say, of course, that large moons couldn’t form by other means, but our question is whether a terrestrial planet without a large moon could remain stable enough to support life? And if not should we discount these worlds from the Drake Equation? Similarly plate tectonics, which cause earthquakes and volcanoes on Earth, are vital for life because they regulate the amount of carbon dioxide in our atmosphere (belching it out in volcanoes, and sucking it underground in subduction zones) as well as helping maintain the dynamo generating Earth’s protective magnetic field thanks to their convective currents. Should we be surprised that Mars, which once had plate tectonics but no longer, is inhabitable?

Saturn’s moon Enceladus. Image: NASA/JPL/Space Science Institute.

Currently the only way to assess whether an exoplanet is possibly habitable is to guess, based on its distance from its star and what type of planet we think it is judging from its mass and radius. Some measurements of the composition of exoplanet atmospheres have been made – the Hubble and Spitzer telescopes have detected methane, carbon dioxide and water molecules in the atmosphere of the transiting hot jupiter HD 189733b, sixty-three light years distant in Vulpecula. As the planet passes in front of its sun, atoms and molecules in its atmosphere absorb some of the starlight, leaving distinctive absorption signatures. There’s no suggestion that this world is habitable – its temperature of 900 degrees Celsius could melt silver – but it shows that in principle we could measure the composition of smaller rocky exoplanets in the future, although such a measurement will be inordinately difficult. An assessment of the powers of the next generation replacement for Hubble, the James Webb Space Telescope (JWST), by Lisa Kaltenegger of the Harvard–Smithsonian Center for Astrophysics and Wesley Traub at the Jet Propulsion Laboratory, reveals that it will be sensitive enough to detect methane and ozone on only the closest transiting Earth-like planets, and then only after dozens, if not hundreds, of transits. Given that a terrestrial planet in the Goldilocks Zone around a yellow star like the Sun will take about a year to make one orbit, we could be in for a long wait. Planets around red dwarfs, where the Goldilocks Zone is much closer in, will only have to wait weeks between each transit, making them more viable targets, but then again red dwarfs may not be the best place to look for habitable worlds, as a team of European and American astronomers recently found out.

Using Spitzer, they compared the abundance of the molecule hydrogen cyanide around young red dwarfs and yellow Sun-like stars. Despite being a deadly gas used in prison gas chambers, hydrogen cyanide is actually a crucial part of the make-up of life, because it is a component of adenine, which is a fundamental building block of DNA. The astronomers, led by Ilaria Pascucci of Johns Hopkins University, found that hydrogen cyanide was completely absent around red dwarfs, but was present around 30 percent of yellow stars. They speculate that ultraviolet radiation, more of which is produced by the hotter yellow stars than the cooler red dwarfs, is in some way important to the formation of the hydrogen cyanide. Either way, it seems that DNA could not form on worlds around red dwarfs.

Maybe this isn’t a big problem. Just because life on Earth is dictated by DNA does not mean that life on other worlds that evolved independently have to run off the same system. There could be many analogues to DNA being used by alien lifeforms across the Universe, and it seems like anthropocentric chauvinism to think that DNA is the only way for life (although a recent research paper by Harvard’s Rudolf Schild and Rhawn Joseph of the Brain Research Laboratory challenges this assumption; see However, red dwarfs can also experience fatal magnetic outbursts that discharge large quantities of radiation, big daddy versions of the flares on our Sun, plus any worlds in the habitable zone around a red dwarf would be so close as to be tidally locked so they always face the same way to their star, like the Moon does to Earth. All things considered, should we omit red dwarfs from the Drake Equation?

Dodging this issue for a moment, let’s consider what Earth-sized planets in the Goldilocks Zone could be like, regardless of what kind of star they orbit. We assume they are made from silicate rock, but there’s no reason why they could not have formed from ice further away from their star and migrated inwards to become a waterworld. What they are made from will drastically alter their size. For instance, a waterworld that shares the same mass as Earth (5.97 x 1024 kilograms) will be 15,200 kilometres across, compared to Earth’s 12,756 kilometre diameter. On the other hand if a terrestrial planet with the same mass as Earth was made purely of iron, it would only be 4,800 kilometres across, which is about the size of Mercury (coincidentally, Mercury does have an anomalously large iron core). By measuring their diameter from a transit, and their mass from radial velocity measurments, it is possible to calculate a planet’s density and thus from what it is composed. Would a waterworld be more habitable than a smaller lump of solid iron with strong gravity?

Another way to assess whether a planet has oceans is to simply see whether it is blue. Earth is called the blue planet because the atmosphere scatters blue light, not because the oceans are blue. However from a distance it turns out that oceans appear bluer in contrast to continental areas that appear red or orange because they reflect those wavelengths of light more efficiently. Other properties, such as the presence of methane as on Neptune, can make a planet appear blue, but if the light of a distant planet changes from blue to reddy–orange and back again as it rotates, then it is an indication that there are oceans and continents. A Neptune-like planet, which has no continents and therefore would not show a change in it’s ‘blueness’ as it rotates would fail this test.

Dangerous hot jupiters

A prevailing but perhaps unspoken assumption amongst astronomers is that any star system where we have found giant planets will also likely possess smaller terrestrial worlds. Based on everything discussed here, however, it would be wrong to assume these planets would be habitable, and in fact the most recent exoplanet discoveries are possibly telling us that planetary systems with hot jupiters won’t have any Earth-like planets whatsoever.

More and more planets are being found in eccentric or retrograde orbits, such as this sample discovered by SuperWASP. Image: ESO/A Collier–Cameron.

Planets that orbit their stars backwards (in the sense that they are orbiting the star in the opposite direction to which the star is rotating) or which are on wild, highly eccentric orbits, are being found more and more frequently. To explain them, Andrew Collier–Cameron of the University of St Andrews and Didier Queloz from Geneva University have invoked something called the Kozai mechanism, and this is bad news for Earth-like worlds in these systems. The Kozai effect is instigated in binary systems, often where the companion star may be too small and faint to be detected. However, the two stars embark on a gravitational tug of war over their planets, which can see gas giants pulled out of the plane of the star system and into highly inclined orbits, sometimes even reversing the direction in which they orbit. Collier–Cameron and Queloz then suggest that the Kozai mechanism acts to shorten the orbits, flattening them once again until they move so close to their main star that they become hot jupiters, in the process scattering any terrestrial planets in their way to the four winds.

The previous theory behind hot jupiters described how gas giants migrate inwards towards their star because of friction with the dust disc from which they have just formed, resulting in a loss of angular momentum and eventually a hot jupiter. Many scientists still favour the traditional migration scenario over the Kozai mechanism in general, but planets on highly inclined, eccentric and backwards orbits can only be explained by the latter. If it turns out that the Kozai effect causes all hot jupiters, which is still highly debatable, we can rule out these systems as having habitable worlds.

So what kind of value can we put on n(e)? If we go by the example set by our own Solar System it could be as high as four or five, but our Solar System is turning out to be anything but typical (a recent assessment of how many Solar Systems are like ours puts the figure as low as 1 in 6, see The Drake Equation assumes that all stars and all planetary systems are the same, but as we are discovering, they are not. Perhaps it is necessary to have a separate equation for each type of star, thus mitigating the differences between red dwarfs and yellow stars, or those with hot jupiters and those without. Planetary systems are turning out to be far more complicated than we had thought in 1960, when we had assumed that they would all share the same architecture as our Solar System. For exoplanet hunters this cornucopia of varying planetary systems has helped keep the search for planets interesting, but for SETI researchers it has proven a headache, and that is unfortunate because we’ve reached the end of the factors in the equation for which we have at least a good chance of estimating accurate answers. The rest of the factors are relevant to that great unknown, the entire point of SETI itself, of which we have only one known example – life.

More SETI articles available here