Chapter 28. The Drake Equation

28.1 Introduction

The goals of this module: After completing this exercise, you should be able to:

1. Relate the history of the Drake Equation.
2. Explain the process by which astronomers tackle a complex problem.
3. Identify the terms of the Drake Equation and the current range of estimated values for them.

In this module you will explore:

1. How an equation can be used to focus attention on what information needs to be gathered to solve a problem.
2. What is known and what is not known about the possibilities for finding other intelligent life.

Why you are doing it: It may seem as if studying science is about knowing lots of facts and theories, but to an astronomer, science is about finding out things nobody else knows. The process is usually long and tedious - if it were easy, somebody else would have already done it! In the case of searching for life outside of Earth, the modern scientific approach is considered to have begun in the middle of the last century. Just remember, the answer to this question isn't at the end of the book!

28.2 Background

People have been fascinated with the prospect of finding extraterrestrial life for thousands of years, but not until the 1960's did a group of astronomers get together to apply the modern scientific process to this question. The scientists' purpose was not to get the 'right answer', but to determine if it was worthwhile even pursuing the question!

This group of astronomers decided that there were three disciplines that needed to be considered: astronomy, biology, and sociology. Astronomy must be considered since life needs a planet with certain conditions, a habitable planet. Biology is the guide to whether life will start, and whether it will evolve intelligence. Human social behavior is the only guide we have to whether life will develop technology and the will to contact other civilizations.

You may object that this is being very narrow-minded. Why does this scientific undertaking assume that intelligent life will be like us? This is the best way to approach the problem since science is based on predicting the unknown from what we know. We only have one example of intelligent life that is capable of contacting life outside of its solar system–our own! When tackling a problem with so many unknowns, it really helps to limit where to search. There may be plenty of time to expand the search later!

Let's take a closer look at seven relevant factors, summarized in what is now called the Drake Equation.

28.3 Astronomical Factors: Stars and their Planets

Artist's conception of a binary red dwarf system with a tidally-locked planet.

The first two factors are similar since they can be determined by astronomical observation. In fact, astronomers are making progress on getting these numbers right now!

The focus is on solar-type stars, since the lifetime of stars varies from a few million to hundreds of billions of years, with the Sun expected to last a total of 10 billion years. Since it took at least four billion years for intelligent life to arise on Earth, we assume that another star hosting intelligent life has to be giving off about the same amount of energy for at least four billion years. This rules out the massive, short-lived stars more than about 1.5 times the mass of the Sun, but there is a different problem with the long-lived stars. (The Sun will survive to 12 billion years, but its energy output and size varies so much during the last two billion years that life won't survive on its planets.)

Some astronomers point out that R* may not be the right factor, since the current rate of star formation isn't as important as the rate a few billion year ago, which was higher than it is now. There is no consensus on the best number for R*, but estimates range from one every ten years (one-tenth per year) to ten per year.

Now let's discuss the f_p term. Our current understanding of solar system formation indicates that planets form as part of the debris of the star's formation, and thus are probably common, making this factor close to 1. However, the cloud of dust and gas from which the star forms has to have the right amount of elements, like iron and silicon, to build planets, and also have oxygen for water (H₂O). So far, the stars known to have planets range from a third of the Sun's mass to more than twice its mass.

28.4 Astronomical Factors: Number of Earthlike Planets

The next factor

limits the search to only Earthlike planets - small rocky planets that have liquid water on their surfaces and an atmosphere. Earthlike planets are tiny and dim compared to their star, and we don't have the technology right now to get images of them. However, NASA and the European Space Agency (ESA) are together developing telescopes that can detect Earthlike planets in other planetary systems.

One design that is looking particularly promising to help determine this fraction is the Kepler Mission. This will search for the drop in light from a star as a planet passes in between the telescope and the star. Play this animation to see how the Kepler telescope will capture the changing light from a distant planet.

If all planetary systems are like our solar system, then there would be one Earthlike planet per system and n_e would equal 1. Simple, you would think. However, we do have some new information that infers that this number could be larger or smaller. Let's take a look at what indicates that having even one Earthlike planet per star is unusual, an indication that n_e should be less than 1.

Of the hundreds of other planetary systems we have discovered, only about 1% (one out of a hundred) have a giant planet located close to where Jupiter is located in our own solar system. Most of the exoplanets discovered so far are giant planets - not surprising, since they're easier to find - but what is surprising is that so many of them are orbiting extremely close to their star, closer even than Mercury is! There is no room for Earthlike planets in those systems.

Features on Europa resembling Earth ice floes

Other information points in the other direction, that n_e is more than 1. One reason for n_e to be large is the possibility that life like ours can survive in places that are not quite Earthlike. Specifically, life on Earth requires energy, liquid water, and carbon to make complex molecules like deoxyribonucleic acid (DNA). Notice that sunlight, oxygen, and even an atmosphere are not necessary! For example, a salty ocean under a layer of ice could support life as we know it on Earth. One of the moons of Jupiter, Europa, has these conditions and might have life under its frozen surface. This is a case where "Earthlike" may be too limited!

Additional exosolar planets are being reported every month, and the California and Carnegie Planet Search webpage is an excellent place to find the latest information

28.5 Biological Factors

The Structure of DNA

Now let's get to the factors for which we have little information, so they'll definitely be harder to determine. Given an appropriate physical environment, how frequently does intelligent life result? This depends on

We know of only one biosphere (Earth), but even that fact yields important information. For example, all life on Earth shares only one genetic lineage. That is, all life on Earth stores its reproductive information on a particular very large carbon molecule, DNA. By 'life' I mean not only animals, but plants and bacteria too. You have more in common with a tree or the bacteria in yogurt than any alien we will ever meet! One conclusion is that life arose just once.

This raises other questions, of course. Did life arise only on Earth, or was our planet seeded billions of years ago from a neighbor planet like Mars, or perhaps from another planetary system? If we find even one other example of life with a different genetic molecule than ours, then we'll know that life can arise multiple times. If you agree with the character Dr. Ian Malcolm in the movie Jurassic Park: "No, I'm simply saying that life, uh... finds a way." then you would select f_l equal to 1.

As far as the likelihood of 'intelligence', again, if we use our planet's experience, intelligence did arise. On the other hand, it did take four billion years!

If you think that all of this seems unlikely, we know that it can happen - we're here!

28.6 Technology

The 85-foot radio telescope in West Virginia used to search for exosolar signals in 1960.

Once intelligence is attained, will the technology and desire to contact other civilizations necessarily follow? This can be quantified as:

Telescopes obviously can be used to detect signals, but it is possible to reverse the light path and send signals out through them as well. Also, television antennas send out their light signals in the radio part of the electromagnetic spectrum in all directions, including toward outer space. (This fact was used in the book Contact, by Carl Sagan, and the start of the movie Contact as well.)

The one intelligent species that we recognize - humans - did develop adequate technology, and have used it to send out and search for messages from space. Although that implies that the fraction is 1 (1 divided by 1), anybody should be reluctant to make a prediction based on only one example!

The next factor, L, considers the fact that there has to be more than one intelligent species in the Galaxy at the same time for them to talk to each other. If technically advanced species evolve at different times in our galaxy, what is the likelihood that more than one would exist at the same time? This depends on how long each civilization lasts, and is stated as the factor:

Again, we're forced to use the only technological civilization we know as our guide to how long such a civilization will last. The starting point is probably when Caroline and William Herschel searched the surface of Mars for signs of life in 1784. Almost as soon as radio signals could be detected, Nikola Tesla, the inventor of the fluorescent light bulbs now being widely adopted over incandescent ones, reported interplanetary signals in 1901. (This was quickly determined to be mistaken.) Modern searches began in 1960, when Frank Drake searched radio signals from two sun-like stars.

Predicting the future is always harder - how long will our civilization retain its technology? Certainly, we have been technologically capable of self-destruction for more than seventy years, as this image shows; yet we remain technologically advanced. Perhaps a harder challenge will be to sustain a livable environment, given climate change and our use of non-renewable resources. We don't yet know the answer to L for our own civilization, much less anyone else's!

Hamburg, Germany in 1943 after Allied bombing

Based on the results of multiple SETI projects to date, the scientific community has not confirmed the existence of any alien life, either within our own solar system or anywhere else.

28.7 Finally - an Answer!

Given all of these factors to be considered, how are they put together to come up with an estimate for how many technologically advanced civilizations are in our galaxy whose messages we might be able to detect? They are simply multiplied together, which the following animation does for you. You've no doubt noticed that we don't know the exact answer for any particular factor, but can develop a range of values that are reasonable. Start the following animation, select factors, and develop your own personal estimate. Explore how the various factors interact with each other!

28.8 The Future of SETI

The Allen Telescope Array in Hat Creek, California

Organized programs are even now searching for extraterrestrial intelligence (SETI), funded primarily by groups such as the Planetary Society and individuals. Institutions conducting these studies include Harvard University, University of Western Sydney in Australia, and the University of California. In particular, the SETI Institute is a private organization that has developed the technology and carried out rigorous studies. However, a huge amount of data has been gathered that requires a tremendous amount of computer time to analyze it. You can help analyze the data by signing up for the SETI@home project, a data analysis program that also acts as a screensaver. It automatically downloads data and processes it when your screensaver is activated.

Almost all SETI projects to date have competed with other astronomy projects to use conventional telescopes. The Allen Telescope Array, named after Microsoft co-founder Paul G. Allen, is the first telescope designed and dedicated solely to SETI. It eventually will have hundreds of small radio dishes working together to detect a signal from a distant civilization!

The science you studied as a child probably included only areas we think we understand well. However, if you had been studying, for example, chemistry a few hundred years ago, there would not have been even a periodic table! Similarly, since we only now have the technology to explore outer space, not only are some answers unknown, but scientists are still working on which questions to ask. This process is not unique to astronomy, but is true for all sciences.

Go on to the Quick Check to complete this activity on searching for intelligent life.

28.9 Quick Check Quiz

Indepth Activity: The Drake Equation