Drake’s Equation

ASTR 1420Lecture 19

Sections 12.1

Average score = 75.7

Drake Equation• Frank Drakeo currently at the SETI institute Berkeleyo 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

NHP number of habitable planets in our Galaxyflife fraction of planets with lifefciv fraction of intelligent worlds capable of interstellar

communicationfnow fraction of such civilizations right now

N = NHP × flife × fciv × fnow

Drake Equation (Carl Sagan’s version)

N number of transmitting civilizations

N* number of stars in our Galaxyfplanet fraction of stars with planetsnEnumber of habitable planets per starflife fraction of planets with lifefintell fraction of worlds with intelligent lifefciv fraction of intelligent worlds capable of interstellar communicationfL the fraction of a planetary lifetime with a technological civilization

N = N* × fplanet × nE × flife × fintell × fciv × fL

Drake Equation (Carl Sagan’s version)

N number of transmitting civilizations

N = N* × fplanet × fE × flife × fintell × fciv × fL

× × × ×

× × =

N

N* fplanet fEarth flife

fintell fciv flong

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* × fplanet × nE × flife × fintell × fciv × L

Drake Equation (original version)

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

N = 20 × fplanet × nE × flife × fintell × fciv × L

Drake Equation (original version)

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?

N = 20 × 1 × nE × flife × fintell × fciv × L

Drake Equation (original version)

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%

N = 20 × 1 × 0.5 × flife × fintell × fciv × L

Drake Equation (original version)

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%

N = 20 × 1 × 0.5 × 0.5 × fintell × fciv × L

Drake Equation (original version)

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%

N = 20 × 1 × 0.5 × 0.5 × 0.5 × fciv × 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

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 broadcastso nowadays, mostly via cableo but, telephone communications through a cable now became wireless…

• 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 = πR2 × TTotal number of Radio civilizations now = N

Volume occupied by each civilization = πR2 × T / N = d3

Average distance b/w civilizations = d

d

d

d

€

d = πR2 ×TN

⎛ ⎝ ⎜

⎞ ⎠ ⎟

1/ 3

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 : 1963. barely reached ~100 Light-years from Earth…

d

€

d = π 50,0002 ×1,00010,000

⎛ ⎝ ⎜

⎞ ⎠ ⎟

1/ 3

= π × 25 ×10,000,000( )1/ 3 = 922Ly

Most Optimistic Estimate

N 40,000,000 civilizations

d 58 Light-years …

5 nearest stars to EarthProxima Centauri 4.24 Lyα Centauri A 4.35 Lyα Centauri B 4.35 LyBanard’s Star 5.98 LyWolf 359 7.78 Ly

If true, we should have already detected or been contacted or visited by them…

R* 20 stars/yr

fplanet 1

nE 2

flife 1

fintell 1

fciv 1

L 1 million yrs

Pessimistic Estimate N 1 or 2 civilizations

average distance ?R* 20 stars/yr

fplanet 0.5

nE 0.5

flife 0.5

fintell 0.5

fciv 0.01??

L 100 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* 20 stars/yr

fplanet 0.5

nE 0.5

flife 0.5

fintell 0.5

fciv 0.01??

L 100 yrs

d

€

d ≈ R / N ≈ 25,000Ly

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 : 12.1SETI: next class