The Drake Equation, Fermi Paradox, and SETI

Drake Equation

N = R x fs x ne x fl x fi x fc x L

R: average rate of star formation
fs: fraction of stars with planetary systems
ne: numbers of planets in "habitable" zones
 fl: fraction of planets where life develops
 fi: fraction of planets where life becomes intelligent
fc: fraction of intelligent civilizations which want to communicate
L: lifetime of "communicative life"

People have long wondered whether we are unique or not. Frank Drake of Cornell University formulated what is now known as the Drake Equation in 1960 as a way to open the discussion on the possibility of intelligent life in the galaxy. At left is the Drake Equation and the meaning of the terms in the Drake Equation. We consider each term in the Drake Equation and come up with an answer as to the number of intelligent civilizations likely to exist in the Milky Way galaxy. The terms in blue are probabilites and facts which can be deduced from astrophysics. These terms can, in principle, be determined quantitatively. The sections in green are probabilities and numbers which come from biology, psychology, and sociology. These are much more difficult to estimate.

Fraction of Planets on Which Life Develops:

DNA

Plagiomnium

Hmmm, this is a hard one. Either it is 1 (if life arises from self-organizing process) or nearly 0 (if life arises randomly).

fl = 1 to ~0

Fraction of Living Species that Develop Intelligence:

I believe this is 1. If life starts, it will develop intelligence eventually

fi = 1

Fraction of Intelligent Species which Develops Technology and Wants to Communicate:

Again the likely answer is 1 (or could be 0, hard to judge motivation)
fc = 1 - 0

Lifetime of a Technological Civilization:

We first note that the Sun will live for over 10 billion years. The amount of time a star spends in its longest lived phase of nuclear evolution, its Main Sequence phase, is roughly

Lifetime = 10 billion years x Ms-3

where Ms, the star's mass is measured in multiple of the mass of the Sun.

This, however, is likely not the appropriate lifetime to consider. More realistically we should consider the more uncertain lifetime of the length of time an intelligent lifeform has the technological ability and desire to communicate. Using us, humanity as an example, we have had good enough technology (radio) to communicate for 100 years or so. if we use this as a lower limit, then

L = 100 years

The lifetime is hard to estimate, but strongly affects the number of possible intelligent civilizations who wish to communicate with us. If the length of the communication lifetime of a life form is the same as its Main Sequence lifetime then we would expect there to be billions of intelligent civilizations in the Milky Way.

Plugging in to the Drake Equation, we find for the pessimistic guess, N = 0, we are alone, and for the wildly optimistic guess

N = 20 stars per year x 0.5 x 4 x 1 x 1 x 1 x 10 billion years = 400 billion civilizations

where we took the lifetime of a technological civilization as the lifetime of the Sun. The more pessimistic, but likely more relevant guess is to use the lower limit of 100 years (our current technological lifetime) to give our optimistic estimate,

N > 4,000 civilizations

The Drake Equation serves to show that it is not implausible to suggest that there are many other intelligent civilizations who wish to communicate with us in the Milky Way, however, it is also conceivable that we are the only intelligent civilization with such desires.

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