Another Factor in the Drake Formula

In 1961, Frank Drake developed a formula to estimate the number of advanced civilizations that exist in the Milky Way and that might contact us, or be detected by us.

He multiplied several factors together:

N = R_* · f_p · n_e · f_l · f_c · L

where

N =number of civilizations with which humans could communicate,
R_* = mean rate of star formation,
f_p = fraction of stars that have planets,
n_e = mean number of planets that could support life per star with planets,
f_l = fraction of life-supporting planets that develop life,
f_c = fraction of intelligent civilizations that develop communication, and
L = mean length of time that civilizations can communicate.

Carbon dioxide is necessary for most forms of life on Earth. Without it, plants die, and without plants, the only life on the Earth would be bacteria and viruses, and maybe fungi.

When the concentration of CO₂ in the Earth’s atmosphere falls below about 150 ppmv (parts per million by volume), most plants die, and with even a slightly smaller concentration, all plants die, and then all higher forms of life die.

If one studies the geological history of carbon dioxide in the Earth’s atmosphere during the last 150 million years

one sees the concentration of CO₂ in the Earth’s atmosphere declining on an almost straight line from about 2,500 ppmv 150 million years ago to 280 ppmv in 1750. Extrapolating that line to 150 ppmv, one can calculate that plants and all higher forms of life on Earth would be extinguished in nine million years.

It appears that Drake’s equation needs an additional factor:

N = R_* · f_p · n_e · f_l · f_c · T_L · φ_c

where

N =number of civilizations with which humans could communicate,
R_* = mean rate of star formation,
f_p = fraction of stars that have planets,
n_e = mean number of planets that could support life per star with planets,
f_l = fraction of life-supporting planets that develop life,
f_c = fraction of intelligent civilizations that develop communication,
T_L = mean length of time that the planet supports life, and
φ_c = fraction of the time that life exists on the planet and civilizations can communicate.

The L factor in Drake’s original equation is equal to the product of T_L and φ_c in the revised equation.

Frank Drake and Carl Sagan and others discussed L as the interval between when civilizations develop the technology that would enable them to communicate, and the time when they annihilate themselves with nuclear weapons. An optimist might assume that civilizations will eventually become civilized, not annihilate themselves with nuclear weapons, and continue indefinitely thereafter until their star destroys their planet.

But if life is extinguished on the planet, no degree of civilization can preserve communication.

On Earth, we have been running an unintended experiment. The industrial revolution has been fueled largely by at first burning coal, and later by burning petroleum and natural gas. The result is that the concentration of CO₂ in the Earth’s atmosphere has increased from 280 ppmv in 1750 to 415 ppmv today. The result is that the extermination of life has been postponed from nine million years to about eighteen million years.

Additional questions must therefore be posed in relation to the Drake equation:

1. Does life on the planet depend upon atmospheric gases that life is removing from its atmosphere??

2. Has an intelligent civilization realized that this is happening?

3. Has the intelligent civilization deployed technology to reverse it?

On Earth, the answers to the first question is “yes.”

The answers to the last two questions, so far, are unfortunately “no,” except by an accident that humans are apparently trying to reverse.