1. NSCI 314 LIFE IN THE COSMOS 14 -THE DRAKE EQUATION Dr. Karen Kolehmainen Department of Physics, CSUSB http://physics.csusb.edu/~karen/

2. THE DRAKE EQUATION THIS EQUATION IS USED TO ESTIMATE THE NUMBER OF “TECHNOLOGICAL” CIVILIZATIONS IN THE MILKY WAY GALAXY. –WE DEFINE A “TECHNOLOGICAL” CIVILIZATION AS ONE THAT IS CAPABLE OF (AND INTERESTED IN) ENGAGING IN INTERSTELLAR COMMUNICATIONS WITH OTHER CIVILIZATIONS. –NOTE: WE ARE ONLY MAKING THIS ESTIMATE FOR OUR GALAXY, BUT THE NUMBER SHOULD BE ABOUT THE SAME FOR ANY SIMILAR SPIRAL GALAXY. THIS IS THE NUMBER OF CIVILIZATIONS THAT COULD BE SENDING OUT RADIO (OR OTHER) SIGNALS THAT WE MIGHT BE ABLE TO RECEIVE.

3. THE DRAKE EQUATION WHY TRY TO ESTIMATE THE NUMBER OF TECHNOLOGICAL CIVILIZATIONS? –IF THE ESTIMATED NUMBER IS VERY SMALL, SEARCHES FOR SIGNALS FROM ALIEN CIVILIZATIONS MIGHT NOT BE WORTH THE TIME, EFFORT, AND EXPENSE. –IF THE ESTIMATED NUMBER IS LARGE, SEARCHES ARE MORE LIKELY TO BE SUCCESSFUL. THEREFORE IT’S EASIER TO ARGUE THAT THE TIME, MONEY, AND EFFORT ARE WORTH IT. KEEP IN MIND THAT: – WE CAN’T MAKE AN EXACT CALCULATION OF THE NUMBER OF CIVILIZATIONS, ONLY A VERY ROUGH ESTIMATE. –OUR ESTIMATE WILL APPLY ONLY TO LIFE THAT IS SIMILAR TO TERRESTRIAL LIFE. IF EXOTIC LIFE EXISTS, CIVILIZATIONS MAY BE MORE COMMON.

4. DRAKE EQUATION N = N * f s n p f l f i f c f L N = Number of civilizations in the MW galaxy capable of communication (what we'd like to find)‏ N * = Number of stars in the MW galaxy f s = fraction of stars that are suitable stars (so the result of N * f s is number of suitable stars in MW galaxy)‏

5. DRAKE EQUATION N = N * f s n p f l f i f c f L n p = average number of planets that are suitable for life per each suitable star (result of N * f s n p is number of suitable planets in MW galaxy)‏ f l = fraction of suitable planets on which life actually originates (result of N * f s n p f l is number of planets with life in MW galaxy)‏

6. DRAKE EQUATION N = N * f s n p f l f i f c f L f i = fraction of those planets with life on which intelligent life evolves (result of N * f s n p f l f i is number of planets with intelligent life in MW galaxy)‏ NOTE: By “intelligent,” we mean of roughly human intelligence.

7. DRAKE EQUATION N = N * f s n p f l f i f c f L f c = fraction of planets with intelligent life on which technology sufficient for interstellar communication develops (result of N * f s n p f l f i is number of planets with technological life in MW galaxy)‏ You might think we're done, but there is one more factor!

8. DRAKE EQUATION N = N * f s n p f l f i f c f L f L = fraction of those civilizations that exist NOW (as opposed to ones that existed in the past, but don’t exist any more)‏ We find f L via f L = L/t L = average lifetime of a technological civilization t = age of Milky Way galaxy (This assumes that the probability of a civilization arising has remained constant over the lifetime of our galaxy.)‏

9. DRAKE EQUATION N = N * f s n p f l f i f c f L The Drake equation is sometimes written in a form that is different than that above. All of these other forms are equivalent. For example, the textbook uses the form: N = N HP f life f civ f now, with N HP = N * f s n p = number of suitable planets in MW, f life = f l = fraction of suitable planets on which life actually develops, f civ = f i f c = fraction of those planets with life on which a technological civilization develops, and f now = f L = fraction of civilizations that exist now.

10. FACTORS IN THE DRAKE EQUATION N = N * f s n p f l f i f c f L N = Number of technological civilizations in the Milky Way galaxy To calculate an estimated value of N, we must first estimate the other factors in the Drake Equation. Let’s go through these one by one. Many of these factors are not very well known. N * =Number of stars in the MW galaxy N * = 400 billion stars (may be off by ~30%)‏

11. SUITABLE STARS Drake Equation: N = N * f s n p f l f i f c f L f s =fraction of stars that are suitable Recall that properties of a suitable star are: - main sequence - long enough main sequence lifetime - reasonable sized habitable zone - enough heavy elements (younger star)‏ - not too close to center of galaxy - not in a binary or multiple star system?

12. SUITABLE STARS Drake Equation: N = N * f s n p f l f i f c f L f s =fraction of stars that are suitable f s = 0.1 = 1/10 (optimistic case)‏ f s = 0.001 = 1/1000 (pessimistic case)‏ f s = 0.05 = 1/20 (my best estimate)‏

13. SUITABLE PLANETS Drake Equation: N = N * f s n p f l f i f c f L n p =average number of suitable planets per suitable star Recall that properties of a suitable planet are: - in habitable zone - reasonably circular orbit - massive enough to keep an atmosphere - has a large moon?? - giant planets found in desirable locations within solar system?? -

14. SUITABLE PLANETS Drake Equation: N = N * f s n p f l f i f c f L n p =average number of suitable planets per suitable star - Our solar system has one for sure (Earth), and several others that are almost but not quite suitable (Mars and Venus). - If we consider Europa-type planets or moons (with an internal source of heat replacing the sun), the number could be higher. - If solar systems like those containing known extrasolar planets are common, the number could be lower.

15. SUITABLE PLANETS Drake Equation: N = N * f s n p f l f i f c f L n p =average number of planets that are suitable for life per each suitable star n p = 2 (optimistic case)‏ n p = 0.1 = 1/10 (pessimistic case)‏ n p = 0.5 = 1/2 (my best estimate)‏

16. DEVELOPMENT OF LIFE Drake Equation: N = N * f s n p f l f i f c f L f l =fraction of suitable planets on which life actually originates Problem: we know of only one suitable planet (Earth), so we have little information on this. But… Life got started very early on the earth, basically as soon as the earth cooled off sufficiently. This suggests that it is “easy” for life to originate.

17. DEVELOPMENT OF LIFE Drake Equation: N = N * f s n p f l f i f c f L f l =fraction of suitable planets on which life actually originates f l = 1 (optimistic case - life will always arise if the planet is suitable)‏ f l = 0.005 = 1/200 (pessimistic case)‏ f l = 1 (my best estimate)‏

18. DEVELOPMENT OF INTELLIGENCE Drake Equation: N = N * f s n p f l f i f c f L f i = fraction of those planets with life on which intelligent life evolves There are actually two (at least) steps here: first the evolution of “complex” life forms (e.g., multicellular life), and then the evolution of intelligent life. We don’t know how likely these developments are, but let’s examine some “pro and con” arguments.

19. DEVELOPMENT OF INTELLIGENCE ARGUMENTS WHY INTELLIGENCE SHOULD ARISE EASILY -Evolution produces a wide diversity of life forms, so perhaps it is inevitable that mutations leading to intelligence will eventually arise. -Intelligence bestows a tremendous selective advantage on organisms possessing it: -Better at finding food -Better at escaping from predators -Better at attracting a mate -Based on terrestrial fossil evidence over the last few tens of million years, it appears that there has been an increase in intelligence over time for many types of mammals and birds.

20. DEVELOPMENT OF INTELLIGENCE ARGUMENTS WHY INTELLIGENCE MAY NOT ARISE EASILY - The development of intelligence is not the “goal” or “purpose” of evolution. -Life on earth existed for a long time before multicellular life evolved. -Multicellular life on earth existed for a long time before intelligent life (humans) evolved. -A lot of organisms on earth have been highly successful without developing intelligence. -Perhaps the evolution of multicellularity and/or intelligence wouldn’t have happened without special circumstances (e.g., specific climate changes) that might not be common on other planets.

21. DEVELOPMENT OF INTELLIGENCE Drake Equation: N = N * f s n p f l f i f c f L f i = fraction of planets with life on which intelligent life evolves f i = 1 (optimistic case) f i = 0.001 = 1/1000 (pessimistic case) f i = 0.01 = 1/100 (my best estimate)

22. DEVELOPMENT OF TECHNOLOGY Drake Equation: N = N * f s n p f l f i f c f L f c =fraction of planets with intelligent life on which technology sufficient for interstellar communication develops - Is technology a natural consequence of intelligence? Again, in the absence of any information about what happened on other planets, let’s examine life on earth as a guide.

23. DEVELOPMENT OF TECHNOLOGY -Is technology a natural consequence of intelligence, or are other things besides intelligence also necessary in order for technology to develop? -Dolphins are probably the second smartest species on Earth (after humans). If dolphins were a little smarter, could they have developed technology? -Possible reasons why they might not: - They have no hands with which to manipulate objects. - A creature that lives in water might not be likely to develop certain types of technology (e.g., fire). - A creature that lives in water might not develop an understanding of astronomy.

24. DEVELOPMENT OF TECHNOLOGY Some human civilizations on Earth have developed technology and others have not. Why? Unfortunately, some people believe in racist explanations, i.e., innate superiority of some groups of people. More likely explanation – some locations on Earth are more conducive to the development of technology than others, due to: –Better or more varied climates –Differences in the availability of natural resources –Animals that can be domesticated –See “Guns, Germs, and Steel” by Jared Diamond

25. DEVELOPMENT OF TECHNOLOGY Therefore, in order to develop a technological civilization, other things besides intelligence might be necessary, such as: –Hands (or similar organs)‏ –Living on dry land –Better or more varied climates –Certain natural resources –Creatures that can be domesticated

26. DEVELOPMENT OF TECHNOLOGY Drake Equation: N = N * f s n p f l f i f c f L f c =fraction of planets with intelligent life on which technology sufficient for interstellar communication develops f c =1 (optimistic case)‏ f c = 0.01 = 1/100 (pessimistic case)‏ f c = 0.5 = 1/2 (my best estimate)‏

27. DO THEY EXIST NOW? Drake Equation: N = N * f s n p f l f i f c f L f L = Probability that they’re around NOW (as opposed to civilizations that existed in the past, but don’t exist any more)‏ f L = L/t t = Age of MW galaxy = 10 billion years L = Average lifetime of a technological civilization (in years) = Average lifetime of civilization with ability and desire to communicate

28. LIFETIMES OF CIVILIZATIONS L = Average lifetime of a technological civilization L = 10 billion years (optimistic case)‏ = Age of galaxy L = 100 years (pessimistic case)‏ Civilizations destroy themselves quickly or lose interest in communication! NOTE: L is the least well-known factor in the Drake equation!

29. DRAKE EQUATION EXTREME OPTIMISTIC CASE (Use optimistic values of all factors except L)‏ N = 400 billion x 0.1 x 2 x 1 x 1 x 1 x L/10 billion RESULT: N = 8 L Now look at different values of L: IF L = 100 YEARS (pessimistic case for L), THEN N = 800 IF L = 10 BILLION YRS (optimistic case for L), THEN N = 80 BILLION

30. DRAKE EQUATION MY BEST ESTIMATE N = 400 billion x 0.05 x 0.5 x 1 x 0.01 x 0.5 x L/10 billion RESULT: N = 0.005 L = L/200 Now look at different values of L: IF L = 100 YEARS (pessimistic case for L), THEN N = 0.5 IF L = 10 BILLION YRS (optimistic case for L), THEN N = 50 MILLION

31. DRAKE EQUATION EXTREME PESSIMISTIC CASE (Use pessimistic values of all factors except L)‏ N = 400 billion x 0.001 x 0.1 x 0.005 x 0.001 x 0.01 x L/10 billion RESULT: N = 0.0000000002 L = 2 X 10 -10 L Now look at different values of L: IF L = 100 YEARS (pessimistic case for L), THEN N = 0.00000002 IF L = 10 BILLION YRS (optimistic case for L) THEN N = 2

32. DRAKE EQUATION WE KNOW THAT N MUST BE AT LEAST 1 BECAUSE WE EXIST! THEREFORE: IF THE EXTREME PESSIMISTIC CASE IS CORRECT (N = 2 X 10 -10 L), WE WOULD CONCLUDE THAT L > 5 BILLION YEARS. THIS WOULD MEAN THAT CIVILIZATIONS ARE LONG-LIVED!

33. DRAKE EQUATION WE KNOW THAT N MUST BE AT LEAST 1 BECAUSE WE EXIST! THEREFORE: IF THE EXTREME OPTIMISTIC CASE IS CORRECT (N = 8L), WE CONCLUDE THAT L > 1/8 YEAR. BUT WE ALREADY KNOW THIS! (WE’VE HAD THE RELEVANT TECHNOLOGY FOR ABOUT 50 YEARS SO FAR.)‏

34. DRAKE EQUATION WE KNOW THAT N MUST BE AT LEAST 1 BECAUSE WE EXIST! THEREFORE: IF MY BEST ESTIMATE IS CORRECT (N = 0.005 L), WE CONCLUDE THAT L > 200 YEARS.

35. DRAKE EQUATION CONCLUSIONS BASED ON THE FACT THAT WE EXIST EITHER N = L IS VERY ROUGHLY CORRECT (TO WITHIN A FACTOR OF A FEW HUNDRED OR A FEW THOUSAND), AS IN THE EXTREMELY OPTIMISTIC CASE OR MY BEST ESTIMATE OR 2. IF THE EXTREMELY PESSIMISTIC VALUES OF VARIOUS FACTORS ARE CLOSE TO CORRECT, THEN L MUST BE VERY LARGE

36. DRAKE EQUATION BUT WE SUSPECT FROM HUMAN EXPERIENCE THAT L COULD EASILY BE SMALL! (MORE ON THIS LATER)‏ THEREFORE WE CAN PROBABLY EXCLUDE THE EXTREMELY PESSIMISTIC CASE. REALITY IS PROBABLY CLOSER TO THE OPTIMISTIC CASE (N ~ L) OR TO MY BEST ESTIMATE (N ~ L/200).

37. DRAKE EQUATION N = # OF CIVILIZATIONS IN MW GALAXY CAPABLE OF INTERSTELLAR COMMUNICATION L = AVERAGE LIFETIME OF SUCH A CIVILIZATION IN YEARS RESULT: N ~ L VERY ROUGHLY, (TO WITHIN A FACTOR OF A FEW 100 OR FEW 1000)‏ BUT HOW LARGE IS L?? (BIGGEST SOURCE OF UNCERTAINTY)‏

38. DRAKE EQUATION We will examine factors that affect L (the average lifetime of a “technological” civilization) later. For now, let's examine how the value of L (and therefore N, the number of “technological” civilizations) affects the possibility of interstellar communication. –The more civilizations there are, the closer together they'll be, on the average. –The distance between civilizations determines how long it takes for messages to pass back and forth. –Messages can't travel faster than the speed of light (one light year per year).

39. MILKY WAY GALAXY N=1 * THIS IS US

40. MILKY WAY GALAXY DISTRIBUTION OF CIVILIZATIONS N=10 * THIS IS US * * * * * * * * WHY ISN’T THIS REALISTIC? *

41. MILKY WAY GALAXY DISTRIBUTION OF CIVILIZATIONS N=10 THIS IS US * * * * * * * * * RANDOM DISTRIBUTION, MORE REALISTIC *

42. MILKY WAY GALAXY DISTRIBUTION OF CIVILIZATIONS N=50 * THIS IS US * * * * * * * * * * HOW HAVE THE DISTANCES BETWEEN CIVILIZATIONS CHANGED FROM N=10? * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

43. MILKY WAY GALAXY DISTRIBUTION OF CIVILIZATIONS THE LARGER THE NUMBER OF CIVILIZATIONS, THE SMALLER THE AVERAGE DISTANCE BETWEEN THEM, THE MORE FEASIBLE INTERSTELLAR COMMUNICATION BECOMES.

44. ABUNDANCE OF LIFE IN THE GALAXY (ASSUMING N = L) ‏ CASE ABUNDANT SCARCE RARE L(YEARS)‏ 1 billion 2 million 2000 N 1 billion 2 million 2000 CASE ABUNDANT SCARCE RARE Average Distance 15 LY 100 LY 1000 LY Number of 2-Way Conversations 30 million 10,000 1 NUMBER OF CONVERSATIONS: NUMBER POSSIBLE WITHIN TIME L, BASED ON THE ASSUMPTION THAT SIGNALS TRAVEL BACK AND FORTH AT THE SPEED OF LIGHT

45. SOLVING THE DRAKE EQUATION “ONCE SETI FINDS THE FIRST ONE, IT’S JUST STATISTICS.” PHILLIP MORRISON SETI = SEARCH FOR EXTRATERRESTRIAL INTELLIGENCE (METHODS TO BE DISCUSSED NEXT TIME)‏ WHAT DOES THIS STATEMENT MEAN? ONCE WE FIND THE FIRST EXTRATERRESTRIAL CIVILIZATION, WE'LL KNOW AN APPROXIMATE VALUE FOR N, AND THUS WE'LL HAVE A BETTER ESTIMATE OF L ALSO. LET'S SEE HOW THIS WORKS.

46. SOLVING THE DRAKE EQUATION SUPPOSE SETI FINDS A SIGNAL, AND ASTRONOMERS DETERMINE THE DISTANCE TO THAT CIVILIZATION TO BE 100 LY. ASSUMING THIS DISTANCE IS ALSO THE AVERAGE DISTANCE BETWEEN NEAREST- NEIGHBOR CIVILIZATIONS (STATISTICALLY A GOOD ASSUMPTION), THEN N = 2 MILLION.

47. SOLVING THE DRAKE EQUATION WITH N = 2 MILLION: IF N ~ 10 L, THEN L ~ 200,000 YEARS, TIME FOR 100 ROUND-TRIP CONVERSATIONS. IF N ~ 0.001 L, THEN L ~ 2 BILLION YEARS, TIME FOR 10 MILLION ROUND-TRIP CONVERSATIONS. THEN WE CAN FEEL CONFIDENT THAT THERE ARE A LOT OF LONG-LIVED CIVILIZATIONS, AND THAT COMMUNICATION WITH THEM IS FEASIBLE. WE CAN ALSO FEEL CONFIDENT THAT HUMAN CIVILIZATION IS LIKELY TO SURVIVE FOR A LONG TIME.

48. SOLVING THE DRAKE EQUATION WHAT IF SETI DOES NOT FIND ANY EVIDENCE OF EXTRATERRESTRIAL CIVILIZATIONS WITHIN 1,000 LY? THEN N < 2000. IF N ~ 10 L, THEN L < 200 YEARS, NO TIME FOR ANY CONVERSATIONS. IF N ~ 0.001 L, THEN L < 2,000,000 YEARS, TIME FOR <1000 ROUND TRIP CONVERSATIONS. THEN DEPENDING ON WHAT WE ASSUME ABOUT THE DRAKE EQUATION, CIVILIZATIONS MAY BE SO FEW AND FAR BETWEEN THAT COMMUNICATION WITH THEM MAY NOT BE FEASIBLE. WE ALSO MAY FEEL MORE PESSIMISTIC ABOUT THE LIKELY LIFETIME OF HUMAN CIVILIZATION.