Date: December 8, 2011
Title: A New Look at the Drake Equation
Podcaster: David Black
Organization: Walden School of Liberal Arts in Provo, Utah
Link: For more information on the Astrobiology class at Walden School and projects we are working on, visit our blog at: elementsunearthed.com.
Description: When Frank Drake created his famous equation in 1961, he meant it as an attempt to describe the factors involved in the rise of extra-terrestrial civilizations that could communicate with us. We’ll take another look at his equation, using our own factors and numbers based on 50 more years of astronomical research.
Bios: Walden School of Liberal Arts is a K-12 charter school in Provo, Utah. The astrobiology class is new this year. Taught by David V. Black, the course focuses on the definition of life, the ingredients that are necessary for life to begin, where those ingredients may be found in our solar system, our quest to find habitable worlds orbiting nearby stars, and the search for extra-terrestrial intelligence. In addition to researching and recording these podcasts, the astrobiology students are also working with students in our 3D animation class to create a series of animations on the origin, evolution, and selenography of Earth’s moon for the Center for Lunar Origin and Evolution in Boulder, CO.
David Black has taught astronomy, chemistry, and multimedia courses at the high school level for over 20 years. He has been a NASA/JPL Solar System Educator and an Educator Facilitator for the NASA Explorer Schools program at JPL. This year, he won third place nationally in the Mars Education Challenge sponsored by Explore Mars, Inc. and the National Science Teacher Association. He is a frequent presenter at state and national science and technology teacher conferences. To contact David Black with questions about our projects, please e-mail him at: elementsunearthed@gmail.com.
Sponsor: Distant Suns astronomy app for iPad and iPhone is proud to sponsor this episode of “365 Days of Astronomy”. Multiple award winning Distant Suns has been your guide to the cosmos for over 25 years. Distant Suns has all the features you need to make stargazing fun and easy. It’s also a great gift – for any occasion – holidays, birthdays… or anytime. And iTunes makes it simple to give Distant Suns as a gift. Get Distant Suns astronomy app on iTunes today.
Transcript:
This is David Black with the Walden School of Liberal Arts in Provo, Utah.
Astronomer Frank Drake convened the first meeting of scientists who were interested in SETI, or the search for extra-terrestrial intelligence, in 1961. His famous equation for calculating the number of detectable civilizations in our galaxy grew out of his presentation at that meeting. In his own words:
As I planned the meeting, I realized a few day[s] ahead of time we needed an agenda. And so I wrote down all the things you needed to know to predict how hard it’s going to be to detect extraterrestrial life. And looking at them it became pretty evident that if you multiplied all these together, you got a number, N, which is the number of detectable civilizations in our galaxy.
(http://www.cosmosmagazine.com/features/print/2915/are-we-alone)
Drake’s formula started with a number called R* which is the average yearly rate of new star formation in our galaxy, about 10 new stars per year. He then multiplied that by the fraction of those stars that have planets, or f sub p, which he thought would be about ½ or .5. He then multiplied that by the number of Earth-like planets found in those systems, or f sub e. Based on our own solar system, he put that factor at two. He then multiplied that answer by the fraction of those planets which actually do develop life, or f sub l. Although the verdict is still out on Mars, it does appear that Earth developed life as soon as it was able, so Drake set that factor to 1 or 100%. He then estimated the fraction of those planets with life that actually develop intelligent life, or f sub i, which he guessed was about 1%, or .01. To detect an alien civilization, the civilization would need to be at roughly our level of technology and able to send radio waves over interstellar distances. He called this factor f sub c, and guessed it would also be about .01, or 1% of the life of an intelligent species. Finally, he multiplied all of this by the number of years a civilization could and would be able to communicate, which he called L and set it at 10,000.
If you multiply all the factors out, you get an N of 10, meaning there would be about 10 alien civilizations in our galaxy that we could detect at any given time. Given that the galaxy is about 100,000 light years in diameter and about 1000 light years thick in the spiral arms, this gives a volume of the galaxy of approximately 7.85 trillion cubic light years. If we divide that by ten, we get one civilization in every 785 billion cubic light years. Enrico Fermi, the famous physicist, posited a paradox: If there are alien civilizations out there, then where are they? Why haven’t we heard from them? The answer is obvious – it’s a big galaxy and the average distance between civilizations is very great.
But we don’t have to use the same numbers as Frank Drake. Changing any of the parameters gives a range of numbers from one (that is, us) through tens of thousands. Astronomy has advanced a great deal since 1961, especially since new exoplanets have been discovered. All things considered, however, Drake did quite well, especially since he only meant his equation to be a starting point in the discussion of searching for intelligent life. He hoped that his initial guesses would become firmer numbers as we found out more. He was right.
Let’s look at an alternate form of the equation using more recent knowledge. We’ll use slightly different terms. The first is G*, equal to the number of stars in our galaxy and is estimated at between 200 and 400 billion. We’ll multiply that by the fraction of these stars that are second-generation stars like our sun. Let’s call this factor G sub two. Formed from the debris of supernova explosions from the first generation, these new star systems have a high enough metal content to generate rocky planets with metal cores like our Earth, and are found mostly in the spiral arms. That’s maybe 30% of the total stars in our galaxy, once we take out the metal-poor stars in the central bulge and the globular clusters in the galactic halo.
We also need to determine which of these stars are hospitable – factor H*. Many red dwarves, the most common type of star, give off x-ray bursts that would make life as we know it difficult. Large stars don’t last very long and may not provide enough time for an intelligent species to evolve. So maybe 30-40% of the remaining stars are hospitable, which include calm red dwarves through A type stars like Sirius.
We also have to eliminate some binary star systems, which could be half of the total. Kepler has recently discovered a planet orbiting both stars in a binary system, like Tatooine in Star Wars®. Computer simulations show that habitable planets could exist in stable orbits around Alpha Centauri B, which is a triple star system. Yet the possibility of planets around binaries is lower, so we need to eliminate maybe 25% of the remaining stars, leaving 75% for our single star factor, S*. Using what we’ve outlined so far, we take about 300 billion stars, times .3 times .35 times .75, which gives us about 23,625,000,000 potential stars. That’s still a pretty big number.
Now we’ll follow the factors outlined by Drake more closely: Of those remaining stars, perhaps 40-60% have planets based on data from recent exoplanet studies, theoretical models, and the Kepler probe. Drake was right on with his estimate of the fraction of stars with planets at 50%.
The number of those planets that are in the habitable zone is more controversial. The exoplanetary systems so far discovered are widely variable – instead of nice, nearly circular orbits, many of these have large, hot gas giants in eccentric orbits that travel very close to their parent stars. Having these eccentric giants does not bode well for smaller planets in those systems. It’s true, though, that our detection techniques so far have biased us to finding planets that are large, close to their parent stars, or in eccentric orbits, so maybe we are simply eliminating the bad choices. We are beginning to find planets in circular orbits about the size of our planet and in the habitable zone of their host stars, such as Gliese 581. So far we’ve found only 50 or so candidate planets in the Goldilocks zone of their stars out of about 1700 exoplanets either confirmed or suspected. As our techniques become refined, and as Kepler studies the light curves to find longer period planets, we’ll confirm more.
The number of possible sites for life in our own solar system is greater than the two conjectured by Drake in 1961. There is a good chance that life could exist on Europa or Enceladus, two moons outside the habitable zone which are both known to have liquid water below a crust of ice. That makes four sites in our system alone. We can reasonably set a factor we’ll call P sub h (for the fraction of stars with planets in their habitable zone) at about 10%.
We’re on the home stretch now. Of those stars with planets in the right place, they would need the three factors considered essential to life by astrobiologists, namely a liquid (probably water), an energy source, and organic molecules. Of the four places with all three criteria in our solar system, and we know for sure that life developed on one of these (possibly more). So our next factor is P sub l, for planets that actually have life. Not every planet that can have life will, but life started on Earth about 3.8 billion years ago, right after the period of late heavy bombardment ended and things settled down enough for evolution to really take hold. So let’s set this factor at 25%. If we do find life on Mars, Europa, or Enceladus, then this factor would increase dramatically.
Now for more guessing based on only one example. On Earth, it took life 3.2 billion years to develop complex multi-celled life forms and another 597 million years to develop intelligent life. Drake’s estimate of 1% for the time for intelligence to arise was very high based on these time scales. We get 3 million years out of 3.8 billion years, or .00079 for f sub i.
One last factor. Out of the 3 million years we’ve had so-called intelligent life on our planet, we’ve only been able to communicate over interstellar distances for 50 years. Within another 50 years, we may not be broadcasting signals into space randomly any more. But just because we aren’t sending signals at random into space doesn’t mean we won’t continue to have the capability as our civilization advances. Let’s use Drakes’ 10,000 years out of 3 million years, or about .00333. Admittedly this is the least precise of the numbers since we don’t even have one example yet of how long a technological civilization may last.
Now for the final calculation: we take 23.625 billion candidate stars and multiply by .5 for the fraction with planets, then by .1 for planets in the habitable zone, then .25 for habitable planets that are actually inhabited, then by .00079 for the fraction with intelligence, then by .00333 for intelligent species that can communicate, and we get – drum roll, please – 777. That’s quite a bit better than Drake’s original estimate. Obviously we’ve been a bit conservative so the number could be far greater, and we aren’t factoring in how many civilizations could spread to multiple star systems through space travel. We can’t do that yet, but if others could, then planets and moons that don’t evolve life naturally could still harbor colonies.
Our estimate may be a bit more firm than in 1961, but we still don’t know much about the factors involved in astrobiology and SETI. Putting aside the estimates and the equations, it’s reasonable to assume that we aren’t in a privileged position in the universe. Chemistry is the same everywhere, based on the same elements and physical laws. If it happened once, it will probably happen again, perhaps many times. Finding out that we are not alone would be a profound discovery. So we must keep on listening and hoping despite low chances of success.
As for astrobiologists, we’d be happy just to find even primitive life elsewhere. If we back up the calculations and take out the parts that have to do with intelligent life, then we get numbers more to our liking – maybe 300 million planets that have some form of life. The distances between life-bearing planets would still be vast, but at least the odds of finding them are much better. That’s why we’ve got to keep looking for life in our own solar system and for planets in habitable zones around other stars. The proposed Terrestrial Planet Finder mission and other attempts to image an exoplanet and characterize its atmosphere are important steps to finding answers. I expect sometime in the next 50 years that we will know, for certain, that life does exist outside Earth. We will see that if life is common in the universe, it is still the most precious thing anywhere.
And even if our nearest neighbors are far away, with over 700 civilizations in our own galaxy and over 100 billion galaxies in all, that’s a lot of life. Perhaps someday we’ll know for sure.
End of podcast:
365 Days of Astronomy
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