Ask Dr. SETI: Why Use the Rate of Stellar Formation?

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Ask Dr. SETI ®

Chapter 3: Philosophy

Why Use the Rate of Stellar Formation?

Dear Dr. SETI:
In his famous Equation, Dr. Drake uses as the first variable R*, the rate of star formation in the Galaxy. In helping to film a SETI documentary recently, I was asked why we use the rate of star formation, since it seems more logical to simply use the total number of stars in our Galaxy. I had no answer. Do you?

Lee, Arizona

The Doctor Responds:
The answer, Lee, lies in our desire to achieve dimensional consistency. Remember that the purported objective of the Drake Equation is to determine the number N of communicative civilizations in the Milky Way Galaxy. To get a pure number as the answer to the Equation, all the units in all seven of its Factors need to cancel. Describing R* in terms of the rate of stellar formation, rather than as simply the number of stars in the Galaxy, accomplishes this for us. Here's why:

Consider the Units in which each of the seven Drake Factors are expressed:

Variable	Drake Factor	Units
N	Number of Communicative Civilizations	unitless
R*	Rate of Stellar Formation	1/years
fp	Fraction of Stars with Planets	ratio
ne	Average number of Earth-like Planets	unitless
fl	Fraction with Life	ratio
fi	Fraction achieving Intelligence	ratio
fc	Fraction developing Communications	ratio
R*	Longevity in the Communicative Phase	years

Performing a dimensional analysis, you can see that:

(1/years) * (ratio) * (unitless number) * (ratio) * (ratio) * (ratio) * (years) = a unitless number.

Notice that Years in the denominator of R* cancels Years in the numerator of L. So the answer for N is a pure number, and we have achieved dimensional consistency. If instead of R* we were to use R, the number of stars in the Milky Way Galaxy, then N would come out as the number of civilization years, which means something else entirely.