Drake’s Equation ASTR 1420 Lecture 19 Sections 12.1

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

Drake Equation (textbook version) N number of transmitting civilizations N HP number of habitable planets in our Galaxy f life fraction of planets with life f civ fraction of intelligent worlds capable of interstellar communication f now fraction of such civilizations right now N = N HP × f life × f civ × f now

Drake Equation (Carl Sagan’s version) N number of transmitting civilizations N * number of stars in our Galaxy f planet fraction of stars with planets n E number of habitable planets per star f life fraction of planets with life f intell fraction of worlds with intelligent life f civ fraction of intelligent worlds capable of interstellar communication f L the fraction of a planetary lifetime with a technological civilization N = N* N* N* N* × f planet f planet × n E n E × f life f life × f intell f intell × f civ f civ × fLfLfLfL

Drake Equation (Carl Sagan’s version) N number of transmitting civilizations N = N * × f planet × f E × f life × f intell × f civ × f L ×××× ××= N N*N* f planet f Earth f life f intell f civ f long

Drake Equation (original version) 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 N = R * × f planet × n E × f life × f intell × f civ × L

Drake Equation (original version) f planet : average fraction of stars with planets Planet formation process is universal (angular momentum conservation) 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. Exo-planets are being discovered nowadays  Doppler result indicates that at least ~20% of stars have planets. Microlensing study suggests f planet ≥ 1 Microlensing study suggests f planet ≥ 1 f planet ≈ 1 N = 20 × f planet × n E × f life × f intell × f civ × L

Drake Equation (original version) n E : average number of Earth-like planets per star system Planet formation process is universal (angular momentum conservation) Planet formation process is universal (angular momentum conservation) Rocky planets are formed closer to the central star. Rocky planets are formed closer to the central star. Close to a unity?? Close to a unity?? n E ≈ 0.5? N = 20 × 1 × n E × f life × f intell × f civ × L

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

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

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

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

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

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

Average Distance between Civilization T R Volume of our Galaxy = πR 2 × T Total number of Radio civilizations now = N Volume occupied by each civilization = πR 2 × T / N = d 3 Average distance b/w civilizations = d d d d

Average Distance between Civilizations T R 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 :  barely reached ~100 Light-years from Earth… d

Most Optimistic Estimate N  40,000,000 civilizations d  58 Light-years … 5 nearest stars to Earth Proxima Centauri4.24 Ly α Centauri A4.35 Ly α Centauri B4.35 Ly Banard’s Star5.98 Ly Wolf Ly If true, we should have already detected or been contacted or visited by them… R*R* 20 stars/yr f planet 1 nEnE 2 f life 1 f intell 1 f civ 1 L1 million yrs

Pessimistic Estimate N  1 or 2 civilizations average distance  ? R*R* 20 stars/yr f planet 0.5 nEnE f life 0.5 f intell 0.5 f civ 0.01?? L100 yrs T R bad approximation!!

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? R*R* 20 stars/yr f planet 0.5 nEnE f life 0.5 f intell 0.5 f civ 0.01?? L100 yrs d

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