Planet Frequency and the Drake Equation

All predictions concerning the frequency of life in the universe inherently assume that planets are common. But what if the conclusions suggested by emerging studies—that Earth-like planets are rare, and planets with metal rarer still—are true?

This finding has enormous significance for the final answer to the Drake Equation. Any factor in the equation that is close to zero yields a near-zero final answer, because all the factors are multiplied together. Carl Sagan, in 1974, estimated that the average number of planets around each star is ten. Goldsmith and Owen, in their 1992 The Search for Life in the Universe, also estimated ten planets per star. But the new findings suggest greater caution. Perhaps planetary formation is much less common than these authors have speculated.

To estimate the frequency of intelligent life, the Drake Equation hinges on the abundance of Earth-like planets around sun-like stars. The most common stars in the galaxy are M stars, fainter than the sun and nearly 100 times more numerous than solar-mass stars. These stars can generally be ruled out because their "habitable zones," where surface temperatures could be conducive to life, are uninhabitable for other reasons. To be appropriately warmed by these fainter stars, planets must be so close to the star that tidal effects from the star force them into synchronous rotation. One side of the planet always faces the star, and on the permanently dark side, the ground reaches such low temperatures that the atmosphere freezes out. Stars much more massive than the sun have stable lifetimes of only a few billion years, which might be too short for the development of advanced life and evolution of an ideal atmosphere. As we noted earlier, each planetary system around a 1-solar-mass star will have space for at least one terrestrial planet in its habitable zone. But will there actually be an Earth-sized planet orbiting its star in that space? When we take into account factors such as the abundance of planets and the location and lifetime of the habitable zone, the Drake Equation suggests that only between 1% and 0.001% percent of all stars might have planets with habitats similar to those on

Earth. But many now believe that even these small numbers are overestimated. On a universal viewpoint, the existence of a galactic habitable zone vastly reduces them.

Such percentages seem very small, but considering the vastness of the Universe, applying them to the immense numbers of stars within it can still result in very large estimates. Carl Sagan and others have mulled these various figures over and over. They ultimately arrived at an estimate of one million civilizations of creatures capable of interstellar communication existing in the Milky Way galaxy at this time. How realistic is this estimate?

If microbial life forms readily, then millions to hundreds of millions of planets in the galaxy have the potential for developing advanced life. (We expect that a much higher number will have microbial life.) However, if the advancement to animal-like life requires continental drift, the presence of a large moon, and many of the other rare Earth factors discussed in this book, then it is likely that advanced life is very rare and that Carl Sagan's estimate of a million communicating civilizations is greatly exaggerated. If only one in 1000 Earth-like planets in a habitable zone really evolves as Earth did, then perhaps only a few thousand have advanced life. Although it could be argued that this is too pessimistic, it may also be much too optimistic. Even so, we cannot rule out the possibility that Earth is not unique in the galaxy as an abode of life that has just recently developed primitive technologies for space travel and interplanetary radio communication.

Perhaps we can suggest a new equation, which we can call the "Rare Earth Equation," tabulated for our galaxy:

where:

N* = stars in the Milky Way galaxy fp = fraction of stars with planets ne = planets in a star's habitable zone fi = fraction of habitable planets where life does arise fc = fraction of planets with life where complex metazoans arise fl = percentage of a lifetime of a planet that is marked by the presence of complex metazoans

And what if some of the more exotic aspects of Earth's history are required, such as plate tectonics, a large moon, and a critically low number of mass extinctions? When any term of the equation approaches zero, so too does the final result. We will return to this at the end of this chapter.

If animal life is so rare, then intelligent animal life must be rarer still. How can we define intelligence? Our favorite definition comes from Christopher McKay of NASA, an astronomer, who defines intelligence as the "ability to construct a radio telescope." Although a chemist might define intelligence as the ability to build a test tube, or an English professor as the ability to write a sonnet, let us for the moment accept McKay's definition and follow the lines of reasoning he sets out in his wonderful essay "Time for Intelligence on Other Planets," published in 1996. Much of the following discussion comes from that source.

McKay points out that if we accept the "Principle of Mediocrity" (also known as the Copernican Principle) that Earth is quite typical and common, it follows that "intelligence has a very high probability of emerging but only after 3.5 billion years of evolution." This supposition is based on a reading of Earth's geological record, which suggests to most authors that evolution has undergone a "steady progressive development of ever more complex and sophisticated forms leading ultimately to human intelligence." Yet McKay notes—as we have tried to emphasize in this book—that evolution on Earth has not proceeded in this fashion but rather has been affected by chance events, such as the mass extinctions and continental configurations produced by continental drift. Furthermore, we believe that not only events on Earth, but also the chance fashion in which the solar system was produced, with its characteristic number of planets and planetary positions, may have had a great influence on the history of life here.

McKay breaks down the critical events in the evolution of intelligence on Earth as shown in the accompanying table.

Event

When It Happened How Long It Possible on Earth (millions Took to Complete Minimum Time of years ago) (millions of years) (millions of years)

Origin of life Oxygenic photo-

3800-3500

synthesis Oxygen environments Tissue multicellularity Development of animals Land ecosystems Animal intelligence Human intelligence

< 3500 2500 550 510 400 250 3

< 500 1000 2000 5 100 150 3

Negligible 100 Negligible

We can certainly quibble with some (or all) of his numbers, especially his estimate of when life first arose on Earth, for we think it occurred far earlier than 3800 to 3500 million years ago. Yet these estimates are probably not off by orders of magnitude. McKay's point is that complex life—and even intelligence—could conceivably arise faster than it did on Earth. If we accept McKay's figures, a planet could go from an abiotic state to the home of a civilization building radio telescopes in 100 million years, as compared to the nearly 4 billion years it took on Earth. But McKay also concedes that there may be other factors that require a long period:

What is not known is whether there is some aspect of the biogeo-chemical processes on a habitable planet—for example, those dealing with the burial of organic material, the maintenance of habitable temperatures as the stellar luminosity increases gradually over its main sequence lifetime, or global recycling by tectonics—that mandates the long and protracted development of the oxygen-rich biosphere that occurred on Earth. Other important unknowns include the effect of solar system structure on the origin of life and its subsequent evolution to advanced forms.

His inference is that plate tectonics has slowed the rise of oxygen on Earth. But it also may be necessary to ensure a stable oxygenated habitat, just as having the correct types of planets in a solar system is important as well.

In their 1996 essay "Biotically Mediated Surface Cooling and Habit-ability," Schwartzman and Shore tackle this same problem and reach a different conclusion: They believe that the most critical element in determining the rate at which intelligence can be acquired is a potentially habitable planet's rate of cooling. Their point is that complex life such as animals is extremely temperature-limited, with a very well-defined upper temperature threshold. Although some forms of animal life can exist in temperatures as high as 50°C or sometimes even 60°C, most require lower temperatures, as do the complex plants necessary to underpin animal ecosystems. A maximum temperature of 45°C is probably realistic. It is thus the time necessary for a planet to cool to below this value that is critical, according to these two authors. Many factors affect the time required, including the rate at which a star increases in luminosity through time (which works against cooling), the volcanic outgassing rate (which also works against cooling, because such out-gassing puts more greenhouse gases into a planetary atmosphere), the rate at which continental land surface grows (as continents grow, planets usually cool), the weathering rate of land areas, the number of comet or asteroid impacts and their frequency, the size of a star, whether or not plate tectonics exists, the size of the initial planetary oceans, and the history of evolution on the planet.

With this in mind, let us return to our Rare Earth Equation and flesh it out a bit by adding some of the other factors featured in this book.

N* X fp X fpm X ne X ng X fi X fc X fl X fm X fj X fme = N

where:

N* = stars in the Milky Way galaxy fp = fraction of stars with planets fpm = fraction of metal-rich planets ne = planets in a star's habitable zone

Bg = stars in a galactic habitable zone fi = fraction of habitable planets where life does arise fc = fraction of planets with life where complex metazoans arise fl = percentage of a lifetime of a planet that is marked by the presence of complex metazoans fm = fraction of planets with a large moon fj = fraction of solar systems with Jupiter-sized planets fme = fraction of planets with a critically low number of mass extinction events

With our added elements, the number of planets with animal life gets even smaller. We have left out other aspects that may also be implicated: Snowball Earth and the inertial interchange event. Yet perhaps these too are necessary.

Again, as aBy term iB such aB equatioB approaches zero, so too does thefiBal product. How much stock can we put in such a calculation? Clearly, many of these terms are known in only the sketchiest detail. Years from now, after the astrobiology revolution has matured, our understanding of the various factors that have allowed animal life to develop on this planet will be much greater than it is now. Many new factors will be known, and the list of variables involved will undoubtedly be amended. But it is our contention that any strong signal can be perceived even when only sparse data are available. To us, the signal is so strong that even at this time, it appears that Earth indeed may be extraordinarily rare.

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