Extraterrestrial Life and the Drake Equation

Basic Ideas Number of Civilizations in our Galaxy –Product of Number of stars and fractions N(ever) = N x A x B –Multiplying by t/T gives the number now N(now) = N(ever) (t/T) Assumes “steady state” between birth and death of civilizations

Usual Drake Equation: N = R * f p n e f l f i f c L N = number of communicable civilizations in our galaxy R= Rate at which stars form f p =Fraction of stars which have planetary systems n e = Number of planets, per planetary system, which are suitable for life f l =Fraction of life bearing planets where intelligence develops f c =Fraction of planets with intelligent life which develop a technological phase during which there is a capacity for and interest in interstellar communication L= Average of lifetime of communicable civilizations r =Average distance to nearest civilization *

Harrison’s Drake Equation: N (now) = N x A x B x (t/T) N(now)= Number of communicable civilizations in our Galaxy now N= Number of stars in our Galaxy A=Astronomical factors B= Biological factors t= Average lifetime of communicable civilizations T =Age of the Galaxy

Astronomical Factors A = p 1 x p 2 x p 3 –p 1 = fraction of stars suitable –p 2 = fraction of suitable stars with earth-like planet –p 3 = fraction with that planet in habitable zone

Number of Stars in Galaxy We focus on our own Galaxy –Light travel time from others > 10 6 yr Estimates of number of stars around –(probably 4 x more accurate) –Calculated from mass of Galaxy and mass of average star.

Fraction of stars suitable for life (p 1 ) If star is much more massive than Sun –It lives on main sequence for too short a time It took 3-4 x 10 9 yr for intelligent life to evolve on Earth Requires M < 1.25 M sun If star is not massive enough –There MAY be problems with tidal lock If star in binary (2/3 of all stars) –About half of these unlikely to allow planets in stable orbits. Net result: p 1 about 0.1 to 0.5 Harrison takes p 1 = 0.1

planets Forbidden Zone Stable orbits around a Binary Star

Fraction of stars with Earth-like planet (p 2 ) About 150 known planets at this time But all are much more massive than Earth But those are the only ones we can detect yet Fraction of stars with some planet probably rather high Fraction with Earth-like totally unknown Searches planned with telescope in space Harrison takes 0.1

Successful Doppler planet search programs: ELODIE/CORALIE (H.P./La Silla) Mayor, Queloz, Udry, et al. (North/South) Hamilton/HIRES (Lick/Keck) Marcy, Butler, Fischer, et al. (North) Cs23 (McDonald 2.7m) Cochran, Hatzes (North) AFOE (Whipple) Noyes, Brown, et al. (North) ESO CES (La Silla) Kurster, Hatzes, Endl, et al. (South) UCLES (AAT) Butler, Tinney, et al. (South) - with about 80 extrasolar planet candidates identified: - more than 1000 stars examined.

Fraction with Earth-like planet in HZ (p 3 ) Habitable zone (require liquid, probably water) Fixes range of temperatures Fixes range of distances from star Also totally unknown Estimates often about 0.5 Harrison takes 0.1 Note: related to suitable star factor

Biological Factors B = p 4 x p 5 x p 6 x p 7 –p 4 = fraction of habitable planets where unicellular life arises –p 5 = fraction of those that evolve multicellular life –p 6 = fraction of those that evolve human- level intelligence –p 7 = fraction of those that develop advanced technological civilization

Fraction where life arises (p 4 ) Life arose on Earth within about 10 9 yr We don’t understand the origin of life –Lab experiments can explain first steps –But formation of self-replicating molecule is hard to understand p 4 is totally unknown Harrison takes 0.1

Miller -Urey Experiment

Fraction with life that develop multicellular life (p 5 ) This took about 1.5 x 10 9 yr on Earth Key development is origin of eukaryotes –Nucleus and organelle p 5 is totally unknown Harrison takes 1 (optimist) or 0.1 (pessimist) Note: this is usually not a separate factor

Eukaryotes and Prokaryotes First appeared ~  10 9 years ago complex structure, ~ genes First appeared ~  10 9 years ago Few thousand genes

Fraction with multicellular life that develop intelligent life (p 6 ) This took about 3.5 x 10 9 yr on Earth –Comparable to age of Galaxy (10 x 10 9 yr) Key development is rapid growth of brain –Primates, anthropoid apes, hominids p 6 is totally unknown Harrison takes 1 (optimist) or 0.1 (pessimist)

Various Family Trees

Fraction with intelligent life that develop technological civilization (p 7 ) This happened very fast compared to others –Human level intelligence has existed for perhaps 10 5 yr –Technological civilization has existed for perhaps 50 yr Key developments –Agriculture, language, science p 7 is totally unknown Harrison takes 1 (optimist) or 0.1 (pessimist)

Connections

Harrison’s Results for N(ever) Astronomical factors: N x A = 100 x 10 6 planets suitable for life Biological factors: B = 0.1 (optimist); 10 –4 (pessimist) N(ever) = 10 million (optimist); 10,000 (pessimist)

Harrison’s Results for N(now) Harrison assumes t = 1 x 10 6 yr; T = 10 x 10 9 yr –N(now) = 10 –4 N(ever) –Note that t is completely unknown According to Harrison: –N(now) = 1000 (optimist); 1 (pessimist) But, if t = 1000 years, N(now) = 10 –3 –Never two at once –We are alone

Distance to Nearest Neighbor 1. Assume civilizations spread uniformly but randomly through galaxy r = radius of imaginary sphere centered on us that touches nearest civilizaztion search vol  r 3  r = 10 4 l y N 1/3

Distance to Nearest Neighbor If N < 8000, r from previous formula is 500 l y About equal to thickness of Galaxy Use cylinder for search vol  r 2 h so r = 5  10 4 l y N 1/2

Happy Feller Rfpfp nene flfl fifi fcfc LNr Estimate   l y Birthrate out of 4 stars If N > 8000, r = 10 4 light years N 1/3 If N <8000, r = 5  10 4 light years N 1/2

Angela Angst Rfpfp nene flfl fifi fcfc LNr Estimate  10 –6 --- Birthrate x 10 –4 5  10 –6 5  10 –8 Never two civilizations at same time If N > 8000, r = 10 4 light years N 1/3 If N < 8000, r = 5  10 4 light years N 1/2

Mr. Average Guy Rfpfp nene flfl fifi fcfc LNr Estimate   Birthrate out of 4  10 5 stars If N > 8000, r = 10 4 light years N 1/3 If N < 8000, r = 5  10 4 light years N 1/2 10  10 5 = 10 6

Points to bear in mind r is based on assuming spread uniformly –Could be less in closer to center of MW r is based on averages –Could be closer but unlikely r is less uncertain than N Since signals travel at c, time = distance in ly If L < 2r, no two way messages

For More Info Website for my class on Extraterrestrial Life – tion/spring05/evans/309l.phphttp:// tion/spring05/evans/309l.php –Has links to factors in Drake Equation (usual form) –Has link to a calculator You can try your own values