Drake equation

Equation

The Drake equation is:

N = R_* \cdot f_\mathrm{p} \cdot n_\mathrm{e} \cdot f_\mathrm{l} \cdot f_\mathrm{i} \cdot f_\mathrm{c} \cdot L

where

• N = the number of civilizations in the Milky Way galaxy with which communication might be possible (i.e. which are on the current past light cone);

and

• R∗ = the average rate of star formation in our galaxy.
• fp = the fraction of those stars that have planets.
• ne = the average number of planets that can potentially support life per star that has planets.
• fl = the fraction of planets that could support life that actually develop life at some point.
• fi = the fraction of planets with life that go on to develop intelligent life (civilizations).
• fc = the fraction of civilizations that develop a technology that releases detectable signs of their existence into space.
• L = the length of time for which such civilizations release detectable signals into space. |access-date=2010-03-07

This form of the equation first appeared in Drake's 1965 paper.

History

In September 1959, physicists Giuseppe Cocconi and Philip Morrison published an article in the journal Nature with the provocative title "Searching for Interstellar Communications". |access-date=2013-04-10 |access-date=2013-04-10 |archive-url=https://web.archive.org/web/20130214073858/http://www.skyandtelescope.com/resources/seti/3304541.html |archive-date=14 February 2013 |url-status=dead

Two months later, Harvard University astronomy professor Harlow Shapley speculated on the number of inhabited planets in the universe, saying "The universe has 10 million, million, million suns (10 followed by 18 zeros) similar to our own. One in a million has planets around it. Only one in a million million has the right combination of chemicals, temperature, water, days and nights to support planetary life as we know it. This calculation arrives at the estimated figure of 100 million worlds where life has been forged by evolution." |access-date=2015-10-02

Seven months after Cocconi and Morrison published their article, Drake began searching for extraterrestrial intelligence in an experiment called Project Ozma. It was the first systematic search for signals from communicative extraterrestrial civilizations. Using the 85 foot dish of the National Radio Astronomy Observatory, Green Bank in Green Bank, West Virginia, Drake monitored two nearby Sun-like stars: Epsilon Eridani and Tau Ceti, slowly scanning frequencies close to the 21 cm wavelength for six hours per day from April to July 1960. The project was well designed, inexpensive, and simple by today's standards. It detected no signals.

Soon thereafter, Drake hosted the first search for extraterrestrial intelligence conference on detecting their radio signals. The meeting was held at the Green Bank facility in 1961. The equation that bears Drake's name arose out of his preparations for the meeting.

The ten attendees were conference organizer J. Peter Pearman, Frank Drake, Philip Morrison, businessman and radio amateur Dana Atchley, chemist Melvin Calvin, astronomer Su-Shu Huang, neuroscientist John C. Lilly, inventor Barney Oliver, astronomer Carl Sagan, and radio-astronomer Otto Struve. |trans-title=It was like a 180 degree turn from this embarrassing secret |access-date=2013-08-13 |access-date=2013-08-13

Usefulness

The Drake equation results in a summary of the factors affecting the likelihood that we might detect radio-communication from intelligent extraterrestrial life. |access-date=2013-04-17 |access-date=2013-04-17

Within the limits of existing human technology, any practical search for distant intelligent life must necessarily be a search for some manifestation of a distant technology. After about 50 years, the Drake equation is still of seminal importance because it is a 'road map' of what we need to learn in order to solve this fundamental existential question. It also formed the backbone of astrobiology as a science; although speculation is entertained to give context, astrobiology concerns itself primarily with hypotheses that fit firmly into existing scientific theories. Some 50 years of SETI have failed to find anything, even though radio telescopes, receiver techniques, and computational abilities have improved significantly since the early 1960s. SETI efforts since 1961 have conclusively ruled out widespread alien emissions near the 21 cm wavelength of the hydrogen frequency.

Estimates

Original estimates

There is considerable disagreement on the values of these parameters, but the 'educated guesses' used by Drake and his colleagues in 1961 were:

• R∗ = 1 yr−1 (1 star formed per year, on the average over the life of the galaxy; this was regarded as conservative)
• fp = 0.2 to 0.5 (one fifth to one half of all stars formed will have planets)
• ne = 1 to 5 (stars with planets will have between 1 and 5 planets capable of developing life)
• fl = 1 (100% of these planets will develop life)
• fi = 1 (100% of which will develop intelligent life)
• fc = 0.1 to 0.2 (10–20% of which will be able to communicate)
• L = somewhere between 1000 and 100,000,000 years

Inserting the above minimum numbers into the equation gives a minimum N of 20 (see: Range of results). Inserting the maximum numbers gives a maximum of 50,000,000. Drake states that given the uncertainties, the original meeting concluded that N ≈ L, and there were probably between 1000 and 100,000,000 planets with civilizations in the Milky Way Galaxy.

Current estimates

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

Rate of star creation in this Galaxy, {{math|''R''_∗}}

Calculations in 2010, from NASA and the European Space Agency indicate that the rate of star formation in this Galaxy is about of material per year. |access-date=2016-09-09

eta-earth

Fraction of those stars that have planets, {{math|''f''_p}}

Analysis of microlensing surveys, in 2012, has found that fp may approach 1—that is, stars are orbited by planets as a rule, rather than the exception; and that there are one or more bound planets per Milky Way star. |access-date=2012-01-12 |display-authors=etal

Average number of planets that might support life per star that has planets, {{math|''n''_e}}

In November 2013, astronomers reported, based on Kepler space telescope data, that there could be as many as 40 billion Earth-sized planets orbiting in the habitable zones of sun-like stars and red dwarf stars within the Milky Way Galaxy. 11 billion of these estimated planets may be orbiting sun-like stars. Since there are about 100 billion stars in the galaxy, this implies fp · ne is roughly 0.4. The nearest planet in the habitable zone is Proxima Centauri b, which is as close as about 4.2 light-years away.

The consensus at the Green Bank meeting was that ne had a minimum value between 3 and 5. Dutch science journalist Govert Schilling has opined that this is optimistic. Even if planets are in the habitable zone, the number of planets with the right proportion of elements is difficult to estimate.{{cite journal

The discovery of numerous gas giants in close orbit with their stars has introduced doubt that life-supporting planets commonly survive the formation of their stellar systems. So-called hot Jupiters may migrate from distant orbits to near orbits, in the process disrupting the orbits of habitable planets.

On the other hand, the variety of star systems that might have habitable zones is not just limited to solar-type stars and Earth-sized planets. It is now estimated that even tidally locked planets close to red dwarf stars might have habitable zones,

The authors of the rare Earth hypothesis propose a number of additional constraints on habitability for planets, including being in galactic zones with suitably low radiation, high star metallicity, and low enough density to avoid excessive asteroid bombardment. They also propose that it is necessary to have a planetary system with large gas giants which provide bombardment protection without a hot Jupiter; and a planet with plate tectonics, a large moon that creates tidal pools, and moderate axial tilt to generate seasonal variation.

Fraction of the above that actually go on to develop life, {{math|''f''_l}}

Geological evidence from the Earth suggests that fl may be high; life on Earth appears to have begun around the same time as favorable 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). From a classical hypothesis testing standpoint, without assuming that the underlying distribution of fl is the same for all planets in the Milky Way, there are zero degrees of freedom, permitting no valid estimates to be made. If life (or evidence of past life) were to be found on Mars, Europa, Enceladus or Titan that developed independently from life on Earth it would imply a value for fl close to 1. While this would raise the number of degrees of freedom from zero to one, there would remain a great deal of uncertainty on any estimate due to the small sample size, and the chance they are not really independent.

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 were more common it would be speculated to have occurred more than once on the Earth. Scientists have searched for this by looking for bacteria that are unrelated to other life on Earth, but none have been found yet.

In 2020, a paper by scholars at the University of Nottingham proposed an "Astrobiological Copernican" principle, based on the Principle of Mediocrity, and speculated that "intelligent life would form on other [Earth-like] planets like it has on Earth, so within a few billion years life would automatically form as a natural part of evolution". In the authors' framework, fl, fi, and fc are all set to a probability of 1 (certainty). Their resultant calculation concludes there are more than thirty current technological civilizations in the galaxy (disregarding error bars).

Fraction of the above that develops intelligent life, {{math|''f''_i}}

This value remains particularly controversial. Those who favor a low value, such as the biologist Ernst Mayr, point out that of the billions of species that have existed on Earth, only one has become intelligent and from this, infer a tiny value for fi. |url-status = dead |archive-url = https://web.archive.org/web/20101206171624/http://www.planetary.org/explore/topics/search_for_life/seti/mayr.html |archive-date = 6 December 2010 |url-status = dead |archive-url = https://web.archive.org/web/20110716063324/http://www.acampbell.ukfsn.org/bookreviews/r/morris.html |archive-date = 16 July 2011

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 a considerable amount of time after the formation of Earth, which suggests the possibility that special conditions were necessary. Some scenarios such as the snowball Earth or research into extinction events have raised the possibility that life on Earth is relatively fragile. Research on any past life on Mars is relevant since a discovery that life did form on Mars but ceased to exist might raise the estimate of fl but would indicate that in half the known cases, intelligent life did not develop.

Estimates of fi have 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 tens of millions of years (evading radiation from novae). Also, Earth's large moon may aid the evolution of life by stabilizing the planet's axis of rotation.

There has been quantitative work to begin to define f_\mathrm{l} \cdot f_\mathrm{i}. One example is a Bayesian analysis published in 2020. In the conclusion, the author cautions that this study applies to Earth's conditions. In Bayesian terms, the study favors the formation of intelligence on a planet with identical conditions to Earth but does not do so with high confidence. |doi-access=free |access-date=23 May 2020}}

Planetary scientist Pascal Lee of the SETI Institute proposes that this fraction is very low (0.0002). He based this estimate on how long it took Earth to develop intelligent life (1 million years since Homo erectus evolved, compared to 4.6 billion years since Earth formed).

Fraction of the above revealing their existence via signal release into space, {{math|''f''_c}}

For deliberate communication, the one example we have (the Earth) does not do much explicit communication, though there are some efforts covering only a tiny fraction of the stars that might look for human presence. (See Arecibo message, for example). There is considerable speculation why an extraterrestrial civilization might exist but choose not to communicate. However, deliberate communication is not required, and calculations indicate that current or near-future Earth-level technology might well be detectable to civilizations not too much more advanced than present day humans.

Another question is what percentage of civilizations in the galaxy are close enough for us to detect, assuming that they send out signals. For example, existing Earth radio telescopes could only detect Earth radio transmissions from roughly a light year away.

Lifetime of such a civilization wherein it communicates its signals into space, {{math|''L''}}

Michael Shermer estimated L as 420 years, based on the duration of sixty historical Earthly civilizations. |url-access=subscription

David Grinspoon has argued that once a civilization has developed enough, it might overcome all threats to its survival. It will then last for an indefinite period of time, making the value for L potentially billions of years. If this is the case, then he proposes that the Milky Way Galaxy may have been steadily accumulating advanced civilizations since it formed.

It has also been hypothesized that once a civilization has learned of a more advanced one, its longevity could increase because it can learn from the experiences of the other.

The 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. Paleobiologist Olev Vinn suggests that the lifetime of most technological civilizations is brief due to inherited behavior patterns present in all intelligent organisms. These behaviors, incompatible with civilized conditions, inevitably lead to self-destruction soon after the emergence of advanced technologies.

An intelligent civilization might not be organic, as some have suggested that artificial general intelligence may replace humanity.

Range of results

As many skeptics have pointed out, the Drake equation can give a very wide range of values, depending on the assumptions,"The value of N remains highly uncertain. Even if we had a perfect knowledge of the first two terms in the equation, there are still five remaining terms, each of which could be uncertain by factors of 1,000." from {{cite journal |title=The search for extraterrestrial intelligence |access-date = 16 April 2013 |url-status = dead |archive-url = https://web.archive.org/web/20130603043832/http://www.cosmosmagazine.com/features/are-we-alone-a-review-drake-equation/ |archive-date = 3 June 2013

As an example of a low estimate, combining NASA's star formation rates, the rare Earth hypothesis value of , Mayr's view on intelligence arising, Drake's view of communication, and Shermer's estimate of lifetime: :, , , [Drake, above], and years gives: : i.e., suggesting that we are probably alone in this galaxy, and possibly in the observable universe.

On the other hand, with larger values for each of the parameters above, values of N can be derived that are greater than 1. The following higher values that have been proposed for each of the parameters: :, , , , Use of these parameters gives: :

Monte Carlo simulations of estimates of the Drake equation factors based on a stellar and planetary model of the Milky Way have resulted in the number of civilizations varying by a factor of 100.

Possible former technological civilizations

In 2016, Adam Frank and Woodruff Sullivan modified the Drake equation to determine just how unlikely the event of a technological species arising on a given habitable planet must be, to give the result that Earth hosts the only technological species that has ever arisen, for two cases: (a) this Galaxy, and (b) the universe as a whole. By asking this different question, one removes the lifetime and simultaneous communication uncertainties. Since the numbers of habitable planets per star can today be reasonably estimated, the only remaining unknown in the Drake equation is the probability that a habitable planet ever develops a technological species over its lifetime. For Earth to have the only technological species that has ever occurred in the universe, they calculate the probability of any given habitable planet ever developing a technological species must be less than . Similarly, for Earth to have been the only case of hosting a technological species over the history of this Galaxy, the odds of a habitable zone planet ever hosting a technological species must be less than (about 1 in 60 billion). The figure for the universe implies that it is extremely unlikely that Earth hosts the only technological species that has ever occurred. On the other hand, for this Galaxy one must think that fewer than 1 in 60 billion habitable planets develop a technological species for there not to have been at least a second case of such a species over the past history of this Galaxy.

Modifications

As many observers have pointed out, the Drake equation is a very simple model that omits potentially relevant parameters, |archive-url = https://web.archive.org/web/20090205123935/http://astro.elte.hu/~hetesizs/Hetesi%20Zsolt%20cikkei/new%20interpretation%20fo%20drake%20eq.pdf |url-status = dead |archive-date = 2009-02-05 Combining the estimates of the original six factors by major researchers via a Monte Carlo procedure leads to a best value for the non-longevity factors of 0.85 1/years. This result differs insignificantly from the estimate of unity given both by Drake and the Cyclops report.

Others note that the Drake equation ignores many concepts that might be relevant to the odds of contacting other civilizations. For example, Glen David Brin states: "The Drake equation merely speaks of the number of sites at which ETIs spontaneously arise. The equation says nothing directly about the contact cross-section between an ETIS and contemporary human society".

;Colonization : Brin proposed to generalize the Drake equation to include additional effects of alien civilizations colonizing other star systems. Each original site expands with an expansion velocity v, and establishes additional sites that survive for a lifetime L. The result is a more complex set of 3 equations.

;Reappearance factor : The Drake equation may furthermore be multiplied by how many times an intelligent civilization may occur on planets where it has happened once. Even if an intelligent civilization reaches the end of its lifetime, life may still prevail on the planet for billions of years, permitting the next civilization to evolve. Thus, several civilizations may come and go during the lifespan of one and the same planet. Thus, if nr is the average number of times a new civilization reappears on the same planet where a previous civilization once has appeared and ended, then the total number of civilizations on such a planet would be 1 + nr, which is the actual reappearance factor added to the equation.

;METI factor : Alexander Zaitsev said that to be in a communicative phase and emit dedicated messages are not the same. For example, humans are in a communicative phase, but are not a communicative civilization; there are no purposeful and regular transmission of interstellar messages. For this reason, he suggested introducing the METI factor (messaging to extraterrestrial intelligence) to the classical Drake equation. He defined the factor as "fm = The fraction of communicative civilizations with clear and non-paranoid planetary consciousness (that is, those which actually engage in deliberate interstellar transmission)". |access-date=2013-04-20

;Biogenic gases : Astronomer Sara Seager proposed a revised equation that focuses on the search for planets with biosignature gases. These gases are produced by living organisms that can accumulate in a planet atmosphere to levels that can be detected with remote space telescopes.

:The Seager equation looks like: