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* fp ne fl fi fc L

N = number of communicable civilizations in our galaxy

R = Rate at which stars form

fp = Fraction of stars which have planetary systems

ne = Number of planets, per planetary system, which are suitable for life

fl = Fraction of life bearing planets where intelligence develops

fc = 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 = p1 x p2 x p3

– p1 = fraction of stars suitable

– p2 = fraction of suitable stars with earth-like planet

– p3 = fraction with that planet in habitable zone

Number of Stars in Galaxy

• We focus on our own Galaxy– Light travel time from others > 106 yr

• Estimates of number of stars around 1011

– (probably 4 x 1011 more accurate)– Calculated from mass of Galaxy and mass

of average star.

Fraction of stars suitable for life (p1)

• If star is much more massive than Sun– It lives on main sequence for too short a time

• It took 3-4 x 109 yr for intelligent life to evolve on Earth• Requires M < 1.25 Msun

• 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: p1 about 0.1 to 0.5• Harrison takes p1 = 0.1

planets

planets

Forbidden Zone

Stable orbits around a Binary Star

Fraction of stars with Earth-like planet (p2)

• 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 (p3)

• 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 = p4 x p5 x p6 x p7

– p4 = fraction of habitable planets where unicellular life arises

– p5 = fraction of those that evolve multicellular life

– p6 = fraction of those that evolve human-level intelligence

– p7 = fraction of those that develop advanced technological civilization

Fraction where life arises (p4)

• Life arose on Earth within about 109 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

• p4 is totally unknown

• Harrison takes 0.1

Miller -Urey Experiment

Fraction with life that develop multicellular life (p5)

• This took about 1.5 x 109 yr on Earth• Key development is origin of eukaryotes

– Nucleus and organelle

• p5 is totally unknown

• Harrison takes 1 (optimist) or 0.1 (pessimist)• Note: this is usually not a separate factor

Eukaryotes and Prokaryotes

First appeared ~ 1.5 - 2 109 years ago complex structure, ~ 104 - 105 genes

First appeared ~ 3 - 4 109 years agoFew thousand genes

Fraction with multicellular life that develop intelligent life (p6)

• This took about 3.5 x 109 yr on Earth– Comparable to age of Galaxy (10 x 109 yr)

• Key development is rapid growth of brain– Primates, anthropoid apes, hominids

• p6 is totally unknown

• Harrison takes 1 (optimist) or 0.1 (pessimist)

Various Family Trees

Fraction with intelligent life that develop technological civilization (p7)

• This happened very fast compared to others– Human level intelligence has existed for

perhaps 105 yr– Technological civilization has existed for

perhaps 50 yr• Key developments

– Agriculture, language, science• p7 is totally unknown• Harrison takes 1 (optimist) or 0.1 (pessimist)

Time Information Technology World View

2 Myr ago Stone tools?? Oral Language Collective hunting6500 B.C. Clay tokens Agriculture, cities6500 B.C. Wheel4000 B.C. Copper tools3000 B.C. Clay tablets Oyster World3000 B.C. Syllabic alphabet2800 B.C. Bronze tools1500 B.C. Letter alphabet Iron tools500 B.C. Natural Philosophy200 Ptolemaic Model1456 Printing Press1540 Copernican Model1610 Telescope Kepler, Galileo1665 Newton1700s Industrial Revolution1859 Darwin1895 Radio1924 Other galaxies1936 First TV Broadcast1950s Computers Transistors, microchips Miller-Urey1960 First Search for Signals1990s Internet

Connections

Harrison’s Results for N(ever)

• Astronomical factors: N x A = 100 x 106 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 106 yr; T = 10 x 109 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 Neighbor1. Assume civilizations spread uniformly

but randomly through galaxy

r = radius of imaginary sphere centered on us that touches nearest civilizaztionsearch vol r3

r = 104 ly N1/3

us

GalaxyNearest

civilization*r

Distance to Nearest Neighbor

If N < 8000, r from previous formula is 500 lyAbout equal to thickness of Galaxy

Use cylinder for search vol r 2 h

so r = 5 104 ly N1/2

rh

Nearest civilization *

Happy Feller

R fp ne fl fi fc L N r

Estimate 50 1 1 1 1 1 5 109 2.5 10111.6 ly

Birthrate 50 50 50 50 50 50

2.5 out of 4 stars

If N > 8000, r = 104 light years

N1/3

If N <8000, r = 5 104 light years

N1/2

Angela Angst

R fp ne fl fi fc L N r

Estimate 5 0.1 0.1 0.01 0.01 0.01 100 5 10–6 ---

Birthrate 5 0.5 0.05 5 x 10–4 5 10–6 5 10–8

Never two civilizations at same time

If N > 8000, r = 104 light years

N1/3

If N < 8000, r = 5 104 light years

N1/2

Mr. Average Guy

R fp ne fl fi fc L N r

Estimate 10 0.5 0.89 0.5 0.7 0.6 1 106 9.4 105 100

Birthrate 10 5 4.45 2.23 1.56 0.94

1 out of

4 105 stars

If N > 8000, r = 104 light years

N1/3

If N < 8000, r = 5 104 light years

N1/2

10 105 = 106

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– http://www.as.utexas.edu/astronomy/educa

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