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Frank Drake's equation is used to estimate $N$ the number of civilizations we might be able to communicate with in our galaxy:

$$N = R_\star f_p n_e f_l f_i f_c L$$

where:

$R_\star$ is the average rate of star formation in the galaxy

$f_p$ is the fraction of stars with planets

$n_e$ is the average number of goldilocks planets per planetary system

$f_l$ is the fraction of goldilocks planets that actually develop life

$f_i$ is the fraction of life bearing planets that develop intelligent life

$f_c$ is the fraction of civilizations that broadcast their existence into space

and $L$ is the length of time for which a civilization broadcasts their existence

Question

Have the many exoplanets we've discovered in the last several decades improved our estimates of $f_p$, and $n_e$? Are these values different than what was guessed about prior to the discovery of the first exoplanets? What is our current best estimate for $R_\star$ for the Milky Way?

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  • $\begingroup$ Have you consulted wikipedia on this? It seems there is a long discussion section about current values. $\endgroup$ – AtmosphericPrisonEscape Jan 3 at 19:43
  • $\begingroup$ @AtmosphericPrisonEscape Yeah, I'd like to see a little more detail about $f_p$ and $n_c$, particularly. Also it seems like the wikipedia entry may be a bit dated. A lot of the stuff is from 2011. $\endgroup$ – Connor Garcia Jan 3 at 19:59
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    $\begingroup$ We collected a bunch of estimates in arxiv.org/abs/1806.02404 (see the supplementary files), showing their distributions, but for a deeper discussion see Vakoch, D. A., & Dowd, M. F. (Eds.). (2015). The Drake equation: estimating the prevalence of extraterrestrial life through the ages (Vol. 8). Cambridge University Press. $\endgroup$ – Anders Sandberg Jan 3 at 20:42
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Have the many exoplanets we've discovered in the last several decades improved our estimates of 𝑓𝑝, and 𝑛𝑐?

Absolutely! The quantity $f_p n_e$ is a quantity of much interest in investigations of extrasolar planets, which effectively equates to the fraction of stars that have a habitable planet in their star's habitable zone. Plenty of studies have examined this specifically for Earth-sized extrasolar planets and place the value of $f_p n_e$ between ~$\frac{1}{6}$ (i.e. one in six stars have an earth-sized planet in a relatively close orbit to the host star) and ~$\frac{2}{5}$ [1][2]. A 2013 comprehensive study by Petigura is a great paper to get familiar with the specifics and assumptions of how the Kepler surveys are conducted and the quantities of interest calculated [3].

What is our current best estimate for 𝑅⋆ for the Milky Way?

Unfortunately the answer is: it varies. Roughly, we think that the Milky Way puts out about 3 solar masses worth of new star every year [4]. However, these don't have to be in one star. Since we think most stars are probably ~1 M$_\odot$, this works out to ~3 stars/year. However, some estimates go less, and some estimates (based on chemical decay of elements like aluminum) go as high as 7 stars/year [5].

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    $\begingroup$ Most stars are more like 0.3 solar masses. $\endgroup$ – ProfRob Jan 5 at 21:22
  • $\begingroup$ @ProfRob The justification for my statement can be found in the source I linked: "However, stars like our Sun (1 solar mass) are quite common and so we can approximate the star formation rate to be about 3 stars (like our Sun) per year in our Galaxy." However, I appreciate there are different estimates on this number, and I believe the qualifier in my answer: "However, some estimates go less, and some estimates (based on chemical decay of elements like aluminum) go as high as 7 stars/year" with appropriate citations addresses the issue. $\endgroup$ – Joseph Farah Jan 5 at 21:28

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