Drake’s Equation

Drake’s Equation

FYOSLecture 10

Exam2• Main transits : planet blocks light from the star• 2ndary transits : star blocks light from the planet• Curvature : phase of the planet

Drake Equation• Frank Drakeo currently at 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 (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.

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

Or nE > 1 (Cassan et al. 2012, Nature, 481, 167)

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 is about 50 yrs

Average Distance between Civilization

T R

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€

d = πR2 ×TN

⎛ ⎝ ⎜

⎞ ⎠ ⎟

1/ 3

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 about 10 civilizations

This few civilizations, we can no longer approximate each civilization as a cube…

d 9,000 Light-years … ?how?

If true, we may practically be the only one in our neightborhood.

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

Galactic Colonization Speed

Example 1: • speed 0.1c• settling time 150 yrs expansion speed of 0.01c. It takes only 10 Myrs!

Example 2: • speed 0.01c• settling time 5000 yrsexpansion speed of 0.001c takes only 100 Myrs!

Coral Model of Galactic colonization

Shouldn’t a cosmic exploration be dependent on rocket speeds?

“Interstellar distances are no barrier to a species which has

millions of years at its disposal”Freeman Dyson

In “Disturbing the Universe”1979

Which estimate do you like better?• N≈10 d≈9000 lyrs• N≈10,000 d≈900 lyrs• N≈40,000,000 d≈60 lyrs

If some of these alien civilizations can live long, then they should have enough time to colonize a good fraction of the Galaxy.

Where are they?

Fermi Paradox

Next week : possible solutions to the Fermi Paradox

1. We are the only one!o Rare Earth Hypothesis

2. They are here already!o Zoo Hypothesis, Sentinel Hypothesis

3. They exist (or existed) but incommunicableo unwillingness, short-lived, hostile, technical difficulties, etc.

• R. Shrestha Summarize “Fermi Paradox” again (including von Neumann probe argument)

• C. Barmore #1• Z. Rindik #1• T. West #2• G. Chant #2• J. Hedley #3• Y. Lee #3