Drake equation

The Drake equation (also known as the Green Bank equation or the Sagan equation) is a famous result in the speculative fields of xenobiology, astrosociobiology and the search for extraterrestrial intelligence.

This equation was devised by Dr. Frank Drake (a professor at the University of California, Santa Cruz) in the 1960s in an attempt to estimate the number of extraterrestrial civilizations in our galaxy with which we might come in contact. The main purpose of the equation is to allow scientists to quantify the uncertainty of the factors which determine the number of extraterrestrial civilizations. In recent years, the Rare Earth hypothesis, which posits that conditions for intelligent life are quite rare in the universe has been seen as a possible refutation of the equation.

The Drake equation is closely related to the Fermi paradox. It was cited by Gene Roddenberry as supporting the multiplicity of starfaring civilizations shown in Star Trek, the television show he created.

The Drake equation states that:

N = R^{*} ~ \times ~ f_{p} ~ \times ~ n_{e} ~ \times ~ f_{l} ~ \times ~ f_{i} ~ \times ~ f_{c} ~ \times ~ L

where:

N is the number of civilizations in our galaxy with which we might expect to be able to communicate at any given time

and

R* is the rate of star formation in our galaxy

f_p is the fraction of those stars that have planets

n_e is average number of planets that can potentially support life per star that has planets

f_l is the fraction of the above that actually go on to develop life

f_i is the fraction of the above that actually go on to develop intelligent life

f_c is the fraction of the above that are willing and able to communicate

L is the expected lifetime of such a civilization

Historical estimates of the Drake equation parameters

Considerable disagreement on the values of most of these parameters exists, but the values used by Drake and his colleagues in 1961 were:

R* = 10/year,
f_p = 0.5,
n_e = 2,
f_l = 1,
f_i = 0.01,
f_c = 0.01,
and L = 10,000 years.

The value of R* is the least disputed. f_p is less certain, but is still much firmer than the values following. Confidence in n_e was once higher, but the discovery of numerous gas giants in close orbit with their stars has introduced doubt that life-supporting planets commonly survive the creation of their stellar systems. In addition, most stars in our galaxy are red dwarfs, which have little of the ultraviolet radiation that has contributed to the evolution of life on Earth. Instead they flare violently, mostly in X-rays — a property not conducive to life as we know it (simulations also suggest that these bursts erode planetary atmospheres). The possibility of life on moons of gas giants (e.g. Jupiter's satellite Europa) adds further uncertainty to this figure.

Geological evidence from the Earth suggests that f_l may be very high; life on Earth appears to have begun around the same time as favourable conditions arose, suggesting that abiogenesis may be relatively common once conditions are right. However, this evidence only looks at the Earth (a single model planet), and contains anthropic bias as the planet of study was not chosen randomly, but by the living organisms that already inhabit it (ourselves). Also countering this argument is that there is no evidence for abiogenesis occurring more than once on the Earth—that is, all terrestrial life stems from a common origin. If abiogenesis was more common it would be speculated to have occurred more than once on the Earth.

Similar arguments can be made f_i and f_c by considering the Earth as a model: intelligence with the capacity of extraterrestrial communication occurs only in one species in the 4 billion year history of life on Earth. If generalised, this mean only relatively old planets may have intelligent life capabale of extrateresstrial communication. Again this model has a large anthropic bias. Note that the capacity and willingness to participate in extrateresstrial communication has come relatively "quickly", with the Earth having only a 100,000 year history of intelligent life without it.

One piece of data which would have major impact on f_l is the discovery of life on Mars or other planet or moon. If life were to be found on Mars which developed independently from life on Earth it would imply a higher value for f_l.

f_i, f_c and L, like f_l, are little more than guesses. f_i has been affected by discoveries that the solar system's orbit is circular in the galaxy, at such a distance that it remains out of the spiral arms for hundreds of millions of years (evading radiation from novae). Also, Earth's very large, unusual moon appears to aid retention of hydrogen by breaking up the crust, inducing a magnetosphere by tidal heating and stirring, and stabilizing the planet's axis of rotation. In addition while it appears that life developed soon after the formation of Earth, the Cambrian explosion in which a large variety of multicellular life forms came into being occurred considerable amounts of time after the formation of Earth, which suggests the possibility that special conditions were necessary for this to occur. In addition some scenarios such as the Snowball Earth or research into the extinction events have raised the possibility that life on Earth is relatively fragile. Again, the controversy over life on Mars is relevant since a discovery that life did form on Mars but ceased to exist would affect estimates of these terms.

The well-known astronomer Carl Sagan speculated that all of the terms, except for the lifetime of a civilization, are relatively high and the determining factor in whether there are large or small numbers of civilizations in the universe is the civilization lifetime, or in other words, the ability of technological civilizations to avoid self-destruction. In Sagan's case, the Drake equation was a strong motivating factor for his interest in environmental issues and his efforts to warn against the dangers of nuclear warfare.

(Note, however, that in the year 2001 a value of 50,000 for L can be used with exactly the same degree of confidence that Drake had in using 10,000 in the year 1961.)

The remarkable thing about the Drake equation is that by plugging in apparently fairly plausible values for each of the parameters above, the resultant expectant value of N is generally often >> 1. This has provided considerable motivation for the SETI movement. However, this conflicts with the currently observed value of N = 1; i.e., one observed civilization in the entire galaxy. Other assumptions give values of N that are << 1, in accord with the observable evidence.

This conflict is often called the Fermi paradox, after Enrico Fermi who first publicised the subject, and suggests that our understanding of what is a "conservative" value for some of the parameters may be overly optimistic or that some other factor is involved to suppress the development of intelligent space-faring life.

Other assumptions give values of N that are << 1, but some observers believe this is still compatible with observations due to the anthropic principle: no matter how low the probability that any given galaxy will have intelligent life in it, the galaxy that we are in must have at least one intelligent species by definition. There could be hundreds of galaxies in our galactic cluster with no intelligent life whatsoever, but of course we would not be present in those galaxies to observe this fact.

Some computations of the Drake equation, given different assumptions:

R* = 10/year, f_p = 0.5, n_e = 2, f_l = 1, f_i = f_c = 0.01, and L = 50,000 years

N = 10 × 0.5 × 2 × 1 × 0.01 × 0.01 × 50,000 = 50

Alternatively, making some more optimistic assumptions, and assuming that 10% of civilizations become willing and able to communicate, and then spread through their local star systems for 100,000 years (a very short period in geologic time):

R* = 20/year, f_p = 0.1, n_e = 0.5, f_l = 1, f_i = 0.5, f_c = 0.1, and L = 100,000 years

N = 20 × 0.1 × 0.5 × 1 × 0.5 × 0.1 × 100,000 = 5,000

For the values given by Drake above, N = 10 × 0.5 × 2 × 1 × 0.01 × 0.01 × 10,000 = 10.

Current estimates of the Drake equation parameters

This section attempts to list best current estimates for the parameters of the Drake equation.

R* = the rate of star creation in our galaxy

Estimated by Drake as 10/year. Latest calculations from NASA and the European Space Agency indicates that the current rate of star formation in our galaxy is about 6 per year. The Planck Institute for Extraterrestrial Physics in Germany notes, however, that our galaxy is not the biggest producer of stars and supernovae in the universe. ^*

f_p = the fraction of those stars which have planets

Estimated by Drake as 0.5.

n_e = the average number of planets (or rather satellites; moons may perhaps sometimes be just as good candidates) which can potentially support life per star that has planets

Estimated by Drake as 2.

f_l = the fraction of the above which actually go on to develop life

Estimated by Drake as 1.

In 2002, Charles H. Lineweaver and Tamara M. Davis (at the University of New South Wales and the Australian Centre for Astrobiology) estimated f_l as > 0.13 on planets that have existed for at least one billion years using a statistical argument based on the length of time life took to evolve on Earth. Lineweaver has also determined that about 10% of star systems in the Galaxy are hospitable to life, by having heavy elements, being far from supernovae and being stable themselves for sufficient time. ^*

f_i = the fraction of the above which actually go on to develop intelligent life

Estimated by Drake as 0.01.

Some estimate that solar systems in galactic orbits with radiation exposure as low as Earth's solar system may be more than 100,000 times rarer, however, giving a value of f_i = 1×10^-7.

f_c = the fraction of the above which are willing and able to communicate

Estimated by Drake as 0.01.

L = the expected lifetime of such a civilization

Estimated by Drake as 10,000 years.

The value of L can be estimated from the lifetime of our current civilization from the advent of radio astronomy in 1938 (dated from Grote Reber's parabolic dish radio telescope) to the current date. In 2006, this gives an L of 68 years.

In an article in Scientific American, Michael Shermer estimated L as 420 years, based on compiling the durations of sixty historical civilizations. Using twenty-eight civilizations more recent than the Roman Empire he calculates a figure of 304 years for "modern" civilizations. Note, however, that the fall of most of these civilizations did not destroy their technology, and they were succeeded by later civilizations which carried on those technologies, so Shermer's estimates should be regarded as pessimistic.

The equation based on current lower estimates, therefore, is thus:

R* = 6/year, f_p = 0.5, n_e = 2, f_l = 0.33, f_i = 1×10^-7, f_c = 0.01, and L = 420 years

N = 6 × 0.5 × 2 × 0.33 × 1×10^-7 × 0.01 × 420 = 8.316×10^-7 = 0.0000008

It is worth noting that the order of magnitude in the revised equation is determined primarily by the new estimate for f_i. Going back to the number estimated by Drake (1×10^-2) the result also changes to 0.08.

External links

The E.T. Equation, Recalculated - Frank Drake, December 2004
http://www.skypub.com/news/special/9812seti_aliens.html
Beyond the Drake Equation
January 2002 space.com article about estimated prevalence of extrasolar planets
Preprint by Lineweaver and Davis estimating f_l as > 0.13
Discovery of first planetary system similar to the solar system 29 January 2006 - page no longer available from this link
Macromedia Flash page allowing the user to modify Drake's values from PBS Nova

References

Frank Drake, Dava Sobel: Is Anyone Out There? The Scientific Search for Extraterrestrial Intelligence, Delacorte Pr., New York 1992, ISBN 0-385-30532-X
Robert T. Rood, James S. Trefil: Are We Alone? The Possibility of Extraterrestrial Civilizations, Scribner, New York 1981, ISBN 0-684-16826-X
Charles H. Lineweaver and Tamara M. Davis, Does the Rapid Appearance of Life on Earth Suggest that Life is Common in the Universe?, arXiv:astro-ph/0205014 v1 2 May 2002
Michael Shermer, Why ET Hasn't Called, Scientific American, August 2002, page 21
Gary Bates, Alien Intrusion,Master books, 2004 ISBN 0-89051-435-6

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Historical estimates of the Drake equation parameters

Current estimates of the Drake equation parameters

See also

External links

References