Drake’s Equation

1. Drake’s Equation ASTR 1420 Lecture 19 Sections 12.1

2. Average score = 75.7

3. Drake Equation • Frank Drake • currently at the SETI institute Berkeley • In 1961, at a meeting of about a dozen scholars at Green Bank, WV. • about the number of radio(?) transmitting civilizations Drake Equation • estimating the probability of communicable ET • at the moment, we only focus on our Galaxy

4. Drake Equation (textbook version) N = NHP× flife× fciv × fnow N number of transmitting civilizations NHP number of habitable planets in our Galaxy flife fraction of planets with life fciv fraction of intelligent worlds capable of interstellar communication fnow fraction of such civilizations right now

5. Drake Equation (Carl Sagan’s version) N = N* × fplanet× nE× flife× fintell× fciv × fL N number of transmitting civilizations N* number of stars in our Galaxy fplanet fraction of stars with planets nE number of habitable planets per star flife fraction of planets with life fintell fraction of worlds with intelligent life fciv fraction of intelligent worlds capable of interstellar communication fL the fraction of a planetary lifetime with a technological civilization

6. Drake Equation (Carl Sagan’s version) N = N* × fplanet× fE× flife× fintell× fciv × fL × × × × N number of transmitting civilizations fplanet fEarth flife N* × × = fintell fciv flong N

7. Drake Equation (original version) N = R* × fplanet× nE× flife× fintell× fciv × L R* : average star formation rate There are ~200 billion stars in our Galaxy. Our Galaxy is about 10 billion years old.  about 20 stars are born per year R* ≈ 20

8. Drake Equation (original version) N = 20 × fplanet× nE× flife× fintell× fciv × L fplanet: average fraction of stars with planets • Planet formation process is universal (angular momentum conservation) • Exo-planets are being discovered nowadays  Doppler result indicates that at least ~20% of stars have planets. • Microlensing study suggests fplanet ≥ 1 fplanet ≈ 1

9. Drake Equation (original version) N = 20 × 1× nE× flife× fintell× fciv × L nE: average number of Earth-like planets per star system • Planet formation process is universal (angular momentum conservation) • Rocky planets are formed closer to the central star. • Close to a unity?? nE ≈ 0.5?

10. Drake Equation (original version) N = 20 × 1× 0.5× flife× fintell× fciv × L flife: average fraction of Earth-like planets with life • Uncertain. One of the main goals of astrobiology. • Life on Earth arose very early on  implying that this fraction not so small? flife ≈ 50%

11. Drake Equation (original version) N = 20 × 1× 0.5× 0.5× fintell× fciv × L fintell: average fraction of life-bearing planets with intelligent species • Uncertain. One of the main goals of astrobiology. • Intelligence is an advantageous evolutionary niche (E.Q. evolution) fintell ≈ 50%

12. Drake Equation (original version) N = 20 × 1× 0.5× 0.5× 0.5× fciv × L fciv: average fraction of civilizations capable of interstellar communication • have to use some sort of symbolic languages. • Will intelligent life want to communicate to others? • Inputs from anthropologists, psychologists, philosophers, and theologians • Quite uncertain. fciv ≈ 50%

13. Drake Equation (original version) 1 ~ N = 20 × 1× 0.5× 0.5× 0.5× 0.5 × L N ≈ L Frank Drake’s California license plate

14. Drake Equation (original version) L average lifetime (in years) that a civilization remains technologically active • How long will the civilization use radio communication? • Will they be around long enough to send messages and get a reply? • We leaked radio communications from our TV/Radio broadcasts • nowadays, mostly via cable • but, telephone communications through a cable now became wireless… • At least for us, L~50 yrs N ≈ L

15. Average Distance between Civilization Our galaxy can be approximated as a thin disk R (50,000 Ly) T (1000 Ly)

16. Average Distance between Civilization Volume of our Galaxy = πR2 × T Total number of Radio civilizations now = N Volume occupied by each civilization = πR2 × T / N = d3 Average distance b/w civilizations = d d d d R T

17. Average Distance between Civilizations If N=10,000 and with R= 50,000 light-years, T= 1,000 light-years… First Radio broadcasting December 24, 1906 from Brant Rock, Massachusetts. First major TV broadcasting : 1963.  barely reached ~100 Light-years from Earth… d R T

18. Most Optimistic Estimate N  40,000,000 civilizations d 58 Light-years … 5 nearest stars to Earth Proxima Centauri 4.24 Ly α Centauri A 4.35 Ly α Centauri B 4.35 Ly Banard’s Star 5.98 Ly Wolf 359 7.78 Ly If true, we should have already detected or been contacted or visited by them…

19. Pessimistic Estimate N  1 or 2 civilizations average distance  ? R T bad approximation!!

20. Pessimistic Estimate N  1 or 2 civilizations If true, we may be effectively the only one. Should we set out a bold journey to the infinity and beyond? d

21. In summary… Important Concepts Important Terms Drake Equation • Drake Equation = calculating the number of communicable alien civilizations in our Galaxy • Understand each term • Logics behind all Equation Terms! • N ≈ L • Chapter/sections covered in this lecture : 12.1 • SETI: next class