The Drake equation

This summer I am a mentor for a summer program for incoming undergraduate students. This program runs the two weeks right before the start of Fall semester. My official title is “Academic Facilitator”, though this just means that I will be organizing, teaching and walking students through some introductory “mini-classes” for two weeks. I will also get to play the role of ‘research advisor’ as I help a group of students work through a small project related to the theme of the program.

The theme for this year is exoplanets. While not directly related to my interests, it’s a fun introductory topic for new students with lots of possibilities for small projects. As my fellow facilitators and I think about the organization for the program, we keep on returning to the idea of the Drake equation.  This is an interesting and accessible introduction to thinking about planets outside of our solar system.

First of all, the Drake equation is not what you would typically consider an equation. Normally an equation is some relation between a few numbers, some way to mathematically represent something in the physical world; like how far do you go if you drive at a certain speed for a given amount of time;

distance = velocity * time

Instead, the Drake equation is more like a ‘thought experiment’, or more specifically a Fermi question, named after physicist Enrico Fermi. Fermi questions are questions, typically posed in physics, that aim for a quick rough estimation of some quantity that is either very difficult, or in the case of the Drake equation, impossible to measure.

So what is it that we’re trying to estimate? The Drake equation, constructed by American astronomer Frank Drake in the 1960’s, considers the number of civilizations within the universe. Specifically, what are the odds that there exists, and that we could contact, other intelligent life. There are a lot of things that can impact this number such as; how many stars have planets, how many of those planets are habitable, how long it would take for a civilization to be able to communicate, how long the civilization lasts…

Many of these kinds of quantities are impossible to measure, though we can use actual astronomical data to constrain some of them. Most of the research centered around exoplanets is attempting to constrain the first estimates concerned with how and where other civilizations could survive.

The Drake equation acts as an excellent way to peak interest in exoplanets – who doesn’t want to think about how likely it is we’ll chat with E.T.? However, it is also a great introduction into how to actually do science!

We can consider one of the estimates within the equation; how many planets are there that could have other life? What would we need to know?

Working backwards;

  1. How many planets are there that could have life?
  2. Where do planets need to be in order to possibly have life?
  3. How many planets are there per star?
  4. How many stars have planets?
  5. How many stars are in our galaxy?
  6. How fast do stars die out?
  7. How quickly are new stars born?
  8. How long to stars live?
  9. How long ago did stars begin to form?

This list covers a wide range of topics in astronomy – all to answer the one question; how many planets could have life? So let’s see what astronomers can do to answer those questions – this time we’ll work forward in time;

  • How long ago did stars begin to form?  This is a cosmology question. Astronomers consider the beginning of the universe and try to determine when processes such as star formation began. Recent experiments have measured a time of 550 million years after the Big Bang – or 13.45 billion years ago.
  • How long to stars live? This is an question for the stellar astronomers. They study how stars work and how they generate energy. Using the what they know about the physics inside stars, they can estimate how long it will take for the star to run out of fuel. A star’s lifetime depends on many factors including composition and mass but the range of stellar life times is between 3 million to 100 billion years (yes, some stars are expected to be able to live longer than our current estimate of the age of the universe – those are the really tiny ones)
  • How quickly are stars born? This question, surprisingly, is one galactic astronomers study. The rate of new star formation is something we consider when we look at other galaxies and galactic evolution. The rate at which a galaxy produces new stars can say a lot about it’s evolution. The estimate of star formation for the Milky Way is about 10 solar masses a yr – our galaxy makes about 10 brand new sun-sized stars a year.
  • How fast to stars die out? This is a question shared between the stellar and galactic astronomers. Stellar astronomers consider the stars themselves to determine how fast a star will use all of its fuel. However galactic astronomers consider stellar populations as a whole – are they all hot, bright stars and will all die out quickly around the same time? Are they all cooler stars that live much longer? Or is it a mix? Does the population recycle material efficiently with stars dying out and being born consistently?
  • How many stars are in our galaxy? Once astronomers have estimates for the rates new stars are born and old stars die out, they can get a snapshot of how many stars should exist right now. Astronomers also have to account for the fact that the rate stars are formed or die out could have varied throughout the life of the galaxy. Currently, it’s estimated that the Milky Way has between 200-400 billion stars.
  • How many stars have planets?/How many planets are there per star? These are questions for the planetary astronomers, and are still in a data-collection stage. Astronomers looking for exoplanets are still figuring out what kinds of stars are likely to have planets – which they can then use to estimate how many stars should have planets. Some of the best candidates are low mass stars, which greatly out number high mass stars. If 70% of all stars are low mass and 50% of those stars have planets, we would expect 35% of all stars to have planets. [Using the estimates from above this would mean 70 billion stars within the Milky Way would have planets.] The number of planets per star is also very sensitive to our instruments. So far, astronomers can detect the biggest and most massive planets – reliably detecting small Earth like planets requires more sensitive instruments than we currently can build.
  • Where do planets need to be in order to possibly have life? This is a question nearly all types of astronomy can influence. The main idea is determining a star’s habitable zone, or the distance from the star liquid water could exist. However there are a lot of things that go into that consideration such as the brightness of the star, the planet’s orbit, and what the planet’s atmosphere is made of. Astrobiologists would also be quick to point out that we don’t need to find a planet that looks exactly like Earth to find life. There could be life thriving in environments we would never expect.

Fermi questions like the Drake equation can be powerful tools to gain understanding of large concepts. Even so, all of the science and data can get hidden behind estimates. I’ve only considered one potential influence to the number of civilizations out there. Feel free to visit this handy calculator on BBC to play around with the Drake equation and see what other things influence the chance we could meet E.T….

4 thoughts on “The Drake equation

  1. If only I were friends with someone who had a Tardis and could take me all over the galaxy and throughout time and space….

  2. J’NEIL you have given us some very interesting information again. I learn new things each time I read your new post.

  3. “Recent experiments have measured a time of 550 million years after the Big Bang – or 13.45 billion years ago.” I’m confused, probably because I don’t understand enough about the Big Bang. Am I to understand that the stars started forming 13.45 billion years ago and that the Big Bang happened 550 million years before that? Is star formation a function of the material that was dispersed in the Big Bang? Kinda makes my head spin…..

    I’m also wondering about the possibility of alien existence outside of our perceptive reality. We perceive a physical universe in 3 or 4 dimensions, that generates carbon based life; but what of alien’s that may exist in a completely different physical perception, or life that’s based on something other than carbon. Does the equation take that into consideration? How would we even know? Or would that make them so alien as to cause interaction impossible. Too many questions for me…

    Obligatory obscure inside reference: I’ll bet Skippy knows….though he’ll probably have to figure out how to access the hidden parts of his memories….

  4. This was fun to read. I learn a lot of new info. I’m not sure which was more mind boggling for me – that there are 200-400 billion stars in our galaxy or that about 10 new stars form every year.

    Loved the BBC calculator. How nice of them to create that for us. Sounds like the incoming undergrads will learn a lot!

    …I wonder how many planets have lizards and how many have hamsters. 🙂

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