Drake Equation

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The Drake equation is a probabilistic expression, proposed by the American astronomer Frank Drake in 1961. The expression is an interesting, though highly speculative, attempt to determine the number of advanced intelligent civilizations that might now exist in the Milky Way galaxy and might be communicating (via radio waves) across interstellar distances. A basic assumption in Drake's formulation is the principle of mediocrity—namely that conditions in the solar system and even on Earth are nothing particularly special but rather represent common conditions found elsewhere in the Milky Way galaxy.

Just where do scientists look among the billions of stars in the galaxy for possible interstellar radio messages or signals from extraterrestrial civilizations? That was one of the main questions addressed by the attendees of the Green Bank Conference on Extraterrestrial Intelligent Life held in November 1961 at the National Radio Astronomy Observatory (NRAO), Green Bank, West Virginia. One of the most significant and widely used results from this conference is the Drake equation, which represents the first credible attempt to quantify the search for extraterrestrial intelligence. This "equation" has also been called the Sagan-Drake equation and the Green Bank equation in the SETI literature.

Although more nearly a subjective statement of probabilities than a true scientific equality, the Drake equation attempts to express the number (N) of advanced intelligent civilizations that might be communicating across interstellar distances at the present time. The equation is generally expressed as:


N is the number of intelligent communicating civilizations in the galaxy at present,

R* is the average rate of star formation in the Milky Way galaxy (stars/ year), fp is the fraction of stars that have planetary companions, ne is the number of planets per planet-bearing star that have suitable ecospheres (that is, the environmental conditions necessary to support the chemical evolution of life), fl is the fraction of planets with suitable ecospheres on which life actually starts, fi is the fraction of planetary life starts that eventually evolve to intelligent life-forms, fc is the fraction of intelligent civilizations that attempt interstellar communication, and

L is the average lifetime (in years) of technically advanced civilizations.

An inspection of the Drake equation quickly reveals that the major terms cover many disciplines and that they vary in technical content from numbers that are somewhat quantifiable (such as R*) to those that are completely subjective (such as L).

For example, astrophysics can provide a reasonably approximate value for R*. Generally, the estimate for R* used in SETI discussions is taken to fall between 1 and 20 stars per year.

The rate of planet formation in conjunction with stellar evolution is currently the subject of much interest and discussion in astrophysics. Do most stars have planets? If so, then the term fp would have a value approaching unity. On the other hand, if planet formation is rare, then fp approaches zero. Astronomers and astrophysicists now think that planets are a common occurrence in stellar-evolution processes. Furthermore, advanced extrasolar planet detection techniques (involving astrom-etry, adaptive optics, interferometry, spectrophotometry, high-precision radial velocity measurements, and several new "terrestrial planet hunter" spacecraft) will soon provide astronomers the ability to detect Earth-like planets (should such exist) around the Sun's nearest stellar neighbors. (See chapter 7.) Therefore, sometime within the next two decades, the search for extrasolar planets should provide scientists the number of direct observations needed to establish an accurate empirical value for fp. In typical SETI discussions, fp is now often assumed to fall in the range between 0.4 and 1.0. The value fp = 0.4 represents a more pessimistic view, while the value fp = 1.0 is taken as very optimistic.

Similarly, if planet formation is a normal part of stellar evolution, exobiologists must then ask how many of these planets are actually suitable for the evolution and maintenance of life? By taking ne = 1.0, the scientists are suggesting that for each planet-bearing star system, there is at least one planet located in a suitable continuously habitable zone (CHZ), or ecosphere. This is, of course, what has occurred in humans' own solar system. Earth is comfortably situated in the continuously habitable zone, while Mars resides on the outer (colder) edge, and Venus is situated on the inner (warmer) edge.

The question of life-bearing "moons" around otherwise unsuitable planets was not directly addressed in the original Drake equation, but recent discussions about the existence of liquid-water oceans on several of Jupiter's moons, most notably Europa, and the possibility that such oceans might support life encourages exobiologists to consider a slight expansion of the meaning of the factor ne. Perhaps ne should now be taken to include the number of planets in a planet-bearing star system that lie within the habitable zone and also the number of major moons with potential life-supporting environments (liquid water, an atmosphere, etc.) around otherwise uninhabitable, Jovian-type planets in that same star system.

Scientists must next ask: Given conditions suitable for life, how frequently does it start? One important major assumption usually made by exobiologists (again invoking the principle of mediocrity) is that wherever life can start, it will. If they adhere to this assumption, then fl equals unity. Similarly, most exobiologists like to assume that once life starts, it always strives toward the evolution of intelligence, making fi equal to 1 (or extremely close to unity).

This brings the alien civilization-hunting scientists to an even more challenging question: What fraction of intelligent extraterrestrial civilizations develops the technical means and then want to communicate with other alien civilizations? All anyone can do here is make a very subjective guess, referencing human history. The pessimists take fc to be 0.1 or less, while the optimists insist that all advanced civilizations desire to communicate and make fc = 1.0.

At this point, it is appropriate to pause for a moment and consider the hypothetical case of an alien scientist in a distant star system (say about 50 light-years away) that must submit numerous proposals for very modest funding to continue a detailed search for intelligent-species-generated electromagnetic signals emanating from the Sun's region of the Milky Way. Unfortunately, the Grand Scientific Collective (the leading technical organization within that alien civilization) keeps rejecting this alien scientist's proposals stating that "such his/her/its proposed 'SETI' efforts are a waste of precious zorbots (alien unit of currency), which should be used for more worthwhile research projects." The alien scientist's supersensitive radio receivers are turned off about a year before the first detectable television signals (leaking out from Earth) pass through that star system. Consequently, although this (hypothetical) alien civilization had developed the technology needed to justify use of a value of fc = 1, that particular alien civilization did not display any serious inclination towards SETI—thereby making fc « 0.

Extending the principle of mediocrity to the collective social behavior of intelligent alien beings (should they exist anywhere) is a highly speculative task. But, here is an important Drake equation-related question that should be considered. Is shortsightedness and a lack of strategic vision (especially among political leaders) a common shortcoming in otherwise intelligent creatures throughout the galaxy? If the principle of mediocrity is at work, the answer is, unfortunately, YES!

Finally, here on Earth, scientists must also speculate on how long an advanced technology civilization lasts. When they use Earth as a model, all they say is that (at a minimum) L is somewhere between 50 and 100 years. Truly high technology emerged on Earth only during the last century. Space travel, nuclear energy, computers, global telecommunications, and so on are now widely available on a planet that daily oscillates between the prospects of total destruction and a "golden age" of cultural and social maturity. Do most other evolving extraterrestrial civilizations follow a similar perilous pattern in which cultural maturity has to desperately race against new technologies that always threaten oblivion if they are unwisely used? Does the development of the technologies necessary for interstellar communication or perhaps interstellar travel also stimulate a self-destructive impulse in advanced civilizations, such that few (if any) survive? Or have many extraterrestrial civilizations learned to live with their evolving technologies, and do they now enjoy peaceful and prosperous "golden ages" that last for millennia to millions of years? In dealing with the Drake equation, the pessimists place very low values on L (perhaps a hundred or so years), while the optimists insist that L is several thousand to several million years in duration.

During any discussion concerning an appropriate value for L, it is interesting to recognize that space technology and nuclear technology also provide an intelligent species with very important tools for protecting their home planet from catastrophic destruction by an impacting "killer" asteroid or comet. (See chapter 2.) Although other solar systems will have cometary and asteroidal fluxes that are greater or less than those fluxes prevalent in humans' solar system, the threat of an extinction-level planetary collision might still be substantial. The arrival of high technology, therefore, also implies that intelligent aliens can overcome many natural hazards (including a catastrophic impact by an asteroid or comet)—

What is the lifetime of a typical advanced-technology civilization in the Milky Way galaxy? Do most (if not all) advanced civilizations end up destroying themselves with their own technologies before they learn to harness these powerful tools (including nuclear energy) and travel to other star systems? Depicted here is the atmospheric detonation of an 11-kiloton-yield nuclear device called FITZEAU, which was exploded by the United States at the Nevada Test Site on September 14, 1957. (The U.S. Department of Energy/Nevada Operations Office)

What is the lifetime of a typical advanced-technology civilization in the Milky Way galaxy? Do most (if not all) advanced civilizations end up destroying themselves with their own technologies before they learn to harness these powerful tools (including nuclear energy) and travel to other star systems? Depicted here is the atmospheric detonation of an 11-kiloton-yield nuclear device called FITZEAU, which was exploded by the United States at the Nevada Test Site on September 14, 1957. (The U.S. Department of Energy/Nevada Operations Office)

thereby extending the overall lifetime of the planetary civilization and increasing the value of L that scientists should use in the Drake equation.

Going back now to the Drake equation, some "representative" values are inserted. Taking R* = 10 stars/year, fp = 0.5 (thereby excluding multiple-star systems), ne = 1 (based on humans' solar system as a common model), fl = 1 (invoking the principle of mediocrity), fi = 1 (again invoking the principle of mediocrity), and fc = 0.2 (assuming that most advanced civilizations are introverts or have no desire for space travel), then the Drake equation yields: N « L. This particular result implies that the number of communicative extraterrestrial civilizations in the galaxy at present is approximately equal to the average lifetime (in Earth years) of such alien civilizations.

It is also instructive to take these "results" one step further. If N is about 10 million (a very optimistic Drake equation output), then the average distance between intelligent, communicating civilizations in the Milky Way galaxy is approximately 100 light-years. If N is 100,000, then these extraterrestrial civilizations on the average would be about 1,000 light-years apart. But if there were only 1,000 intelligent alien civilizations existing today, then they would typically be some 10,000 light-years apart. So, even if the Milky Way galaxy does contain a few such alien civilizations, they may be just too far apart to achieve communications within the total lifetimes of their respective civilizations. For example, at a distance of 10,000 light-years, it would take 20,000 years just to start an interstellar dialogue.

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