Drake equation

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

This equation was devised by Dr. Frank Drake in the 1960s in an attempt to estimate the number of extraterrestrial civilizations in our galaxy with which we might come in contact. It seems to suggest that contact with extraterrestrials should not be a remarkably uncommon event.

The Drake equation is closely related to the Fermi paradox (for which, see below).

The Drake equation states that

N = R* × f_p × n_e × f_l × f_i × f_c × L

where:

N is the number of extraterrestrial civilizations in our galaxy with which we might expect to be able to communicate

and

R* is the rate of star creation in our galaxy

f_p is the fraction of those stars which have planets

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

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

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

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

L is the expected lifetime of such a civilisation

Considerable disagreement on the values of most these parameters exists, but the values used by Drake and his colleagues in 1961 are: R* = 10/year, f_p = 0.5, n_e = 2, f_l = 1, f_i = f_c = 0.01, and L = 10 years. The value of R* is the least disputed. f_p is more uncertain, 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 causes the types of mutations needed by evolution. Instead they flare violently, mostly in X-rays - a property not conducive to life as we know it (simulations also suggest that these bursts errode planetary atmospheres). The possibility of life on moons of gas giants such as Europa adds further uncertainty to this figure. What evidence is currently visible to humanity suggests that f_l is very high; life on Earth appears to have begun almost immediately after conditions arrived in which it was possible, suggesting that abiogenesis is relatively "easy" once conditions are right. But this evidence is limited in scope, and so this term remains in considerable dispute. f_i, f_c, and L are obviously little more than guesses. (Note, however, that in the year 2001 a value of 50 for L can be used with exactly the same degree of confidence that Drake had in using 10 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, namely ourselves. 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 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.

Others regard the anthropic principle as controversial, and consider the N << 1 case puzzling from the viewpoint of the Copernican principle.

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 years

N = 10 × 0.5 × 2 × 1 × 0.01 × 0.01 × 50 = 0.05

Alternatively, making some more optimistic assumptions, and assuming that 10% of civilisations 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 × 100000 = 5000

Estimates of the Drake equation parameters

This section attempts to list best current estimates for the parameters of the Drake equation. Please list new estimates for these values here, giving the rationale behind the estimate and a citation to their source.

R*, the rate of star creation in our galaxy

Estimated by Drake as 10/year

f_p, the fraction of those stars which have planets

Estimated by Drake as 0.5

n_e, the average number of planets 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 > 0.33 usng a statistical argument based on the length of time life took to evolve on Earth.

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

Estimated by Drake as 0.01

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 civilisation

Estimated by Drake as 10 years.

A lower bound on 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 2002, this gives a lower bound on L of 64 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.

References:

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

External references: