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12.3: The Probability of Life Elsewhere

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  • So. Life in the Universe? Frank Drake, a pioneer in the search for life with radio telescopes, first penned an equation in 1961 to estimate the probability that technologically capable and communicating civilizations exist in our galaxy.

    The Drake equation distills the key parameters that we need to know. Seth Shostak at the SETI institute characterizes this equation as a map, not a destination.

    \[N=R_s\cdot f_P\cdot \eta_E\cdot f_L\cdot f_I\cdot f_C\cdot L\]

    where,

    • \(N\) is the number of communicative civilizations that we could detect,
    • \(R_S\) is the rate of formation of suitable stars,
    • \(f_P\) is the fraction of stars with planets,
    • \(\eta_E\) is the number of "Earths" per planetary system,
    • \(f_L\) is the fraction of these "Earths" where life develops,
    • \(f_I\) is the fraction of the instances of life where intelligent life develops,
    • \(f_C\) is the fraction of intelligent life that develop communicating technology,
    • \(L\) is the lifetime of communicating civilizations
    alt
    Figure \(\PageIndex{1}\): The Drake equation is a way of organizing our thoughts about the probability of technological, communicating life elsewhere.

    Let us consider each of these terms. We will provide provisional numbers, but many of them are merely educated guesses (some more educated than others).

    Stars

    We can make a rough estimation of the star formation rate of the galaxy by considering what we know about the galaxy today. Currently, the galaxy holds about 100-400 billion stars. We also know the galaxy to be approximately 10 billion years old. From this, we find that on average stars have been be forming at a rate of 10-40 stars per year.

    \[\frac{100\,billion\,stars}{10\,billion\,years}\,=\,10\frac{stars}{years}\]

    \[\frac{400\,billion\,stars}{10\,billion\,years}\,=\,40\frac{stars}{year}\]

    This is a very simplistic estimate. It does not take into account how many of these stars may be suitable for life, such as short-lived O or B type stars, or whether the rate of star formation has been constant over the lifetime of the galaxy. However, this estimate gives a decent upper and lower bound.

    Planets

    Thank to discoveries over the past decade, we now have a good estimate for the fraction of stars with planets. This was completely unknown at the time Frank Drake first wrote down his equation. The discoveries from the Kepler mission provides statistical evidence that essentially every star has one or more planets. When you look up at the night sky, there are actually more unseen exoplanets there than there are stars. We can therefore assign a value of 1 for \(f_P\) and a value of 0.9, or 90%, as a more conservative estimate.

    The next parameter, \(\eta_E\), is the number of Earth-like habitable planets. The Kepler mission stopped just short of determining this value. However, astronomers have extrapolated out from the parameter space where Earth-sized planets were detected and estimate that the number of habitable Earths ranges from 0.5 to 3 per system. Maybe the requirement of an Earth-like planet is too conservative. Would a moon do? Titan, Europa and Enceladus all offer possible platforms for life in our solar system that are well outside the habitable zone.

    The Number of Habitable Worlds?

    We could stop here, at the end of verifiable science and calculate the number of habitable worlds in the Milky Way galaxy. We just need to make this estimate dimensionally correct by multiplying by the lifetime of habitable worlds (recall that the first term is the number of stars per year, so we need to multiply by years for this equation to be dimensionally correct). You know that Earth has had life for about 4 billion years. Whether homosapiens survives or not, life is likely to continue as long as our planet has liquid water on it's surface. The radius of our Sun is increasing as it ages. Without intervention, the Earth will lose its oceans of water in another billion years. So, we might estimate that planets like the Earth are habitable (distinct from being "inhabited") for roughly 5 billion years. Multiplying through these factors we get a range for the number of habitable worlds:

    10 × 0.9 × 0.5 × 5 × 109 = 22.5 × 109 (lower limit of 22.5 billion)

    40 × 1 × 3 × 5 × 109 = 600 × 109 (upper limit of 600 billion)

    If we want to estimate the probability of technological civilizations, then don't multiply by the longevity of habitable worlds (because that's not the number you want to find)... keep going!

    Life

    The term \(f_L\) asks us to consider the fraction of Earth-like planets in the habitable zone where life of any kind (including single-celled microbes) emerges. This term must be non-zero, because there exists life on Earth, but we have yet to find life anywhere else. What we do know is that the Earth formed about 4.56 Gya. We have firm evidence of life from stromatolites at 3.5 Gya, which must have been preceded by less complex organisms. These numbers indicate that life formed relatively quickly on Earth, even though it is not yet clear to us how. We can infer that perhaps life appears between 10% and 100% of the time on habitable planets, but you should make your own guess for this fraction. What is your justification?

    The Number of Planets in the Galaxy with Life of any Kind?

    We could stop here and calculate the probability that life of any kind will arise on Earth. We add in the new factor for our estimate that life arises. We could use the previous argument to guess that if life evolves, it may last for about 5 billion years. Multiplying through these factors we get a range for the number of habitable worlds:

    10 × 0.9 × 0.5 × 0.1 × 5 × 109 = 2.25 × 109 (lower limit: 2.25 billion planets in our galaxy have life of some kind)

    40 × 1 × 3 × 1 × 5 × 109 = 600 × 109 (upper limit: 600 billion sites with life in the galaxy)

    If we want to keep going, to estimate the probability of technological civilizations, then don't multiply by the longevity of life on habitable worlds (because that's not the number you want to find)

    Intelligent and communicating

    Intelligence is hard to describe, hard to quantify, and hard to detect. Besides the example of intelligent life on Earth, we have no other concrete evidence towards a true value for the fraction of life that becomes intelligent. We could again use what happened on Earth as a general guiding example - a sort of "Copernican" view for biology. Come up with your own estimates and reasoning for \(f_i\).

    Here is one possible argument: We know that bio-complexity requires energy, which requires efficient metabolism. On Earth this takes the form of aerobic respiration and the Cambrian explosion marks the time when complex life emerged. This occurred in the last 0.6 billion years in the lifespan of Earth.

    \[\frac{0.6\,billion\,years}{4.5\,billion\,years}\,=\,0.13\]

    This makes the argument time-based. Inherently, right or wrong, we are guessing that life everywhere will evolve and that statistically perhaps 0.13 of the habitable planets that we find with life will have life forms that evolved to become intelligent.

    However, we have no true understanding of how typical our planet is. We do not have a sense of whether the evolution of complex life is rare or inevitable for all Earth analogs. An upper bound might be 1, meaning all planets with life will eventually evolve the complexity that leads to intelligence or it might happen on one of a million inhabited worlds. That's a big range!

    Technology

    The next term, \(f_c\), tries to capture another attribute that is hard to estimate. On inhabited planets with intelligent life, how often will that life develop technology so that it can communicate across the galaxy? We are technological adolescents and there is the significant problem of light travel time. If we send a message to a civilization that is 10,000 light years away (a small distance in our galaxy, which is 100,000 light years in diameter), then it takes 20,000 years for the round trip reply. Will we still be here? Will anyone still be listening? The intelligent life on Earth has only had this communication technology for about 100 years. That is a tiny fraction of time for intelligent life on Earth: 100 years out of 200,000 years that homosapiens have existed.

    The example of Earth points to another possibility. We have taken our first steps out into the solar system. The Apollo-11 mission took us to the moon and Elon Musk wants to help us get to Mars. Even if the emergence of intelligent, technological, communicating civilizations are rare, they may spread to other planets.

    Lifetime

    The chance of discovering life inherently depends on how long life survives on a planet. On Earth, life has persisted for at least 3.5 billion years. At most, life on Earth will exist until the Sun evolves and the Earth loses its oceans (about 5 billion years). From the geological history, we know that life is fairly resilient. Our answer for the lifetime of microbes would be very different than our guess for the lifetime of technological civilizations.

    There is a good expectation that we have the engineering skills to mitigate certain natural disasters, such as asteroid impacts. At the same time, the development of technology can negatively impact the lifetime of a civilization. Industrialization has led to rapid climate change and nuclear weaponization that could threaten our existence on timescales of a few generations.

    Finale

    Finally, the finale. We can collect our musings from above to calculate a value for N, the number of communicating civilizations that we could detect. We should note that when we multiply these numbers together, we do not really get a low and high estimate for technological life. Because we put in the extreme limits of our guesses, we get extreme limits for the range of possibilities. Better to treat each of these as distribution functions and combine them in a statistically rigorous manner.

    Term Lower Estimate Upper Estimate
    \(R_S\) 10 stars/yr 40 stars/yr rate of star formation
    \(f_P\) 0.9 1 fraction of stars with planets
    \(\eta_E\) 1 3 number of "Earths" per planetary system
    \(f_L\) 0.1 1 fraction of "Earths" where life develops
    \(f_I\) 0.001 1 fraction of instance of life where intelligent life develops
    \(f_C\) 10-6 0.5 fraction of intelligent life that develops communicating technology
    \(L\) 200 years 10,000 yrs lifetime of communicating civilizations
    300 billion conservative estimates for the possible number of communicating civilizations that we could detect

    Some of the terms for which we have observations are quite certain. We know the rate of star formation, the fraction of stars with planets, and we have solid estimates for the number of habitable planets per planetary system. In contrast, the last four terms are extremely uncertain. But all we need to firm this up is one other example of a world where life exists.

    So where are they? The Fermi Paradox

    Particle physicist Enrico Fermi is credited with posing this question. If the universe is teaming with life, why haven't we observed it yet? There are many resolutions to this question. Watch the 6-minute animated TedEd video below to hear some resolutions to this question.