20 - The Drake Equation

1. 20 - The Drake Equation

2. There are many different ways to write it. In its simplest form: There are many factors that go into Ric. We shall examine these in detail

3. The Full Form (one version): R*= Rate of star formation (Astronomy) Pp = Probability of a star having planets (Astronomy) Pe = Probability that Habitable Zone lasts long enough for life to arise - Continuously Habitable Zone (CHZ) or "ecoshell" (Astronomy, Planetary Evolution, Chemical and Biological Evolution) Ne = Number of planets in the CHZ (Astronomy, Planetary Evolution, Chemical and Biological Evolution) PL = Probability that life will arise in the CHZ (Chemical and Biological Evolution) PI = Probability that the life will develop an "intelligent" civilization (Chemical and Biological Evolution) Lic= Lifetime of intelligent civilization (Speculative Sociology)

4. R*= Rate of Star Formation Here we need rate of suitable stars born/year averaged over the past 10 billion years Total rate is about 10/year BUT: MS stars hotter than F7 evolve too fast Cooler K & M stars - CHZ very small, close planets tidally locked, etc. Binary stars probably not good circumstellar orbit has to have planet too close circumbinary orbit has to have planet too far

5. Based on this, what fraction of these are likely to be “suitable” stars? Use Table 16.1 (see homework set) as a Guide: Of the 34 stars within 13 l.y. of the Sun: Only 2 (6%) are good candidates This is probably the best-determined parameter in the Drake Equation, as it involves very little speculation

6. Pp = Probability of a star having planets What fraction of single stars have planetary systems? Recent survey suggests ALL do initially (although they might not all develop real planets) But what fraction are likely to have terrestrial planets? Using the Figure of Extrasolar Planets as a Guide: Only ~9 systems (5%) have Jupiters beyond 2.2 AU, leaving “room” for terrestrial planets closer to the star. BUT this technique is biased in favor of detecting close Jupiters

7. Pe = Probability that Habitable Zone lasts long enough for life to arise - Continuously Habitable Zone (CHZ) In Hart’s models the CHZ ranges from a thickness of 0.07 AU out of ~1.25 AU for F9 to zero at K1. At G5 it is about 0.03 AU thick out of a total of 0.8 AU, roughly 8%. Given the amount of “real estate” present, this is a crude measure of the fraction that last “long enough”. Kasting’s models are more generous, maybe as large as 40%

8. Ne = Number of planets in the CHZ We have only 1 example top work from - our own solar system! We know Earth is in the CHZ for sure! Mars - dubious Venus - no way! But now we need to worry about whether a planet need a large Moon like we have (stabilize rotation axis & help with tides). If so, we need to correct this number downward, possibly by a large factor.

9. PL = Probability that life will arise in the CHZ Life was present on the Earth almost as soon as it was cool enough for substantial amounts of liquid water to be present. Suggests PL~1 ! However, different early bombardment rates and other factors might make this number considerably less.

10. PI = Probability that the life will develop an "intelligent" civilization Intelligence seems to have some survival value However, what we call “intelligence” - capable of interstellar communication, is a VERY RECENT development, occurring about half way through the total lifetime of our Sun. Evolution of terrestrial species has many branches & the number which terminate in an “intelligent” species is only one. (Although, if it hadn’t been for the KT Event, perhaps some dinosaur would be teaching this class…) But it will be the last term in the Drake Equation that is most uncertain!

11. Lic= Lifetime of intelligent civilization We have been capable of “communication” since ~1950 Is it the destiny of intelligent species to survive indefinitely by “solving all of our problems” or by colonizing a large number of worlds? If so in may be that: On the other hand, we have many means at our disposal to exterminate the human race (“bomb them/us back into the stone age”), in which case we may be overly generous in suggesting

12. Let’s Put It All Together!

13. Consequences: Using Table 16.1, and counting systems, not individual stars, we find the number of “stars” per cubic light year is: This is 1 star per 400 cubic light years

14. “Best Case” Need a volume that has ~1000 stars to include another civilization Requires a volume of 400,000 ly3 THAT means looking 50 ly “Worst Case” - we are alone, in a number of galaxies.. “Intermediate Case” Need a volume that has ~10,000,000 stars to include another civilization Requires a volume of 4,000,000,000 ly3 THAT means looking 1,000 ly (actually more..) And if Lic~1000 years, 2-way communication fails

15. Have we proven anything? How do we decide the issue? - LOOK! • WHERE DO WE LOOK? • There are a number of possible strategies: • Nearby stars with planets • Stars with CHZs • Everywhere • HOW DO WE SEARCH? • Spacecraft • Fast • Slow (Cryogenic and/or "Generation") • Robots • Remote Observations (much cheaper!) • Radio • Other Subject of Ch. 21 of Class Notes Subject of Ch. 22 of Class Notes