SETI and the Drake Equation

The Search for Extraterrestrial Intelligence (SETI) project has as its basis the fact that we could detect a beamed radio signal of the type we are able to generate now from anywhere in the Milky Way Galaxy. Detecting simple life or a non-technical civilization is expected to be considerably harder, but at least some of the factors used in generating an estimate of the possible numbers of targets are the same.

The exobiologists' definition of life is this:

A self-replicating system subject to Darwinian evolution.

This is not the same as developing radio, TV and powerful over-the-horizon radar beacons.

Frank Drake attempted to rationalize the estimation of the possible number N of communicating civilizations in our galaxy (forget other galaxies...) by dividing it up into a series of possibly easier to handle estimates:

N = R* fp ne fl fI fc Lc


N = number of technical civilizations in the Milky Way Galaxy with whom we might expect to communicate.

R* = average rate of star formation in the Milky Way, in units of stars per year.

Fp = fraction of stars with planetary systems.

ne = number of planets per system with suitable ecologies (liquid water...)

fl = fraction of such planets on which life actually occurs

fI = fraction on which intelligent life arises

fc = fraction where intelligent beings develop capability for interstellar communication

Lc = mean lifetime of such communicating civilizations

The average star formation rate and the fraction of stars with planetary systems can be estimated rather accurately from standard astronomical theory. The number of planets per system suitable for life falls under a new field called "astrobiology". While it is at present more difficult to quantify, in twenty years it should be as well-defined as the first two factors.

The fraction of suitable planets on which life actually develops is a specialized topic of organic chemistry and biochemistry, a field called exobiology, the search for the origin of life.

The remaining terms in the Drake Equation are sociological in nature and do not concern us in the simple search for any life. It has been noted that the reliability of estimates of theses various factors declines rapidly going from R* to Lc. We may, however, need an estimate for the expected lifetime, L, for any life on a planet in order to calculate the possible number of current locales of life in the Milky Way.

The estimated number of stars in the Milky Way, N*, has not changed much in the 50 years since we realized the nature and extent of our Galaxy and other galaxies. The Milky Way is a largish spiral galaxy, like its companion the Andromeda Galaxy, with about 100 billion (1011) stars. (Sometimes you see the number as 200 billion, but 100 billion is almost certainly good to within an order of magnitude.) This number is derived by counting the stars within several small patches of sky in the galactic plane and extrapolating to the whole galaxy. The age of the Milky Way, T*, is still accepted by most astronomers to be some 10 billion years, although the details of events between the condensation of matter after the Big Bang some 14 billion years ago and the formation of the first galaxies are still a little hazy. Recent Hubble images suggest galaxy (or star) formation began earlier than was previously believed. You'll probably get no arguments with a 12 billion year old Milky Way. In any case, it's the rate of star formation, R* = N*/ T* that we're after:

R* = N*/ T*

= 100/12 to 200/10

= 8-20 stars / year.

Bear in mind that this estimate for R* is by far the best estimate that we will encounter in this discussion. Also bear in mind that this average rate may be grossly different from the star formation rate 5 billion years ago when our Sun was forming. Further bear in mind that stars age at different rates and will have different habitable zones at different phases of their lifetime. None of these factors are included in our simplified accounting.

Then, using the age of life on the Earth as an estimate,

R* x L = (8-20 stars/year) x (3.9 billion years) = 30-77 billion stars

which might possibly host life forms in the Milky Way. But just how typical is our Sun and its system of planets?

The factor fp is an attempt to answer this last question: what fraction of stars have planetary systems? Startling progress in this area has been made in just the last few years.

Realizing that then-current technology would not permit the direct observation of a faint planet near a relatively dazzling (a billion times brighter!) star, astronomers plotted the positions of nearby stars for decades, hoping to measure a "wiggle" which would indicate one or more dark companions. In the best-known case, repeated observations of Barnard's star from 1940 to 1970 appeared to capture a sinusoidal oscillation of about 0.05 arcseconds amplitude in the star's proper motion of 300 arcseconds across the sky. (The moon is 1800 arcseconds wide). Five hundredths of an arcsecond was, at that time, at least 10 times better than the best seeing that was available. This acccuracy was the result of many repeated observations and statistical combination of results, some 3000 photographic plates analyzed by Van de Kamp.

This technique, like most others, is most sensitive to the case of one or two very massive planets orbiting relatively close to their star. Consequently, the theories of the day led to sets of simulated solar systems (S. Dole, 1970, Icarus, 13, 494-508) which, not too surprisingly, all looked fairly similar to our solar system, dominated by gas giants. The important point here is that the simplest interpretation of the sparse results from these studies did not require Earth-like planets. And the sparseness of the results led to fears of a low fp .

As instrumentation has improved, and particularly with the availability of observations from space, it has been possible to obtain direct images. If not yet of planets themselves, at least of the swirling gas and dust clouds around young stars, the stellar nebulae which are believed to be the precursors of planetary systems. Starting with Beta Pictoris from infrared observations and then with the sudden confirmation of some 153 such protoplanetary disks or "proplyds" in 1992 in the Orion Nebula by Hubble observations, this has been a fruitful avenue of approach. These disks are 3-8 times the size of our solar system and formed within the last million years. We still did not see any dense spots in these clouds that might be condensing planets, but the number of disks seen has raised new hopes for a large fp .

Another modern search technique has relied on spectroscopy rather than position measurements or direct imaging. Here we look at small shifts in the wavelengths of stellar spectral features, as the star is alternately pulled towards us when a massive planet is on the near side, or away from us when it is on the far side. These measurements are a bit easier in that spectral observations are routinely made to one part in 10,000. But there is the added complication of the Earth's orbital motion and the relative motion of the Sun and the subject star. A potentially more serious complication is to factor in the unknown "breathing" mode of the star, which causes the surface to pulse in and out. Jupiter causes the Sun to shift velocity by 12.5 m/sec or 28 mph. Solar breathing amounts to some 5 m/sec.

Spectrometers are subject to point-spread function (PSF) errors (the initial Hubble smear was an extreme example) and a 1% error leads to a 25 m/sec inaccuracy. Optimizing computer code to process out this error and spectrometer improvements over a period of 8 years led the team of Geoff Marcy and Paul Butler to 3 m/s accuracy. They narrowly missed discovering the first planet around a sun-like star, 51 Pegasi. This discovery, by Swiss astronomers Michel Mayor and Didier Queloz, found a half-Jupiter-mass planet closer than Mercury is to the Sun, so the orbital period was days, not years. This was not expected from the theoretical models of solar nebula condensation of Dole and others, and was a real shocker. Marcy and Butler quickly went back through their old observations and found six more cases of planets orbiting Sun-like stars. Close-in, massive planets tug harder at their stars (51 Pegasi tugs at 53 m/sec, Jupiter at 12.5 m/sec) and are thus easier to detect.

One summer day in Los Alamos in 1950 a lunchtime discussion among a few theoretical physicists (Enrico Fermi, Edward Teller, Herbert York and Emil Konopinski) had covered flying saucers. Fermi did a few quick calculations and asked, jokingly "Don't you ever wonder where everybody is?" The paradox lies in the astrophysicist's central dogma of mediocrity: we live in a time and place which are ordinary in every way. If we exist, there should exist other civilizations, and we should not be the first; some should be older and much more technically advanced than we are. If space travel is possible, then some of them should have visited us by now. As we shall see, it should only take a few million years for an advanced civilization to explore our whole galaxy. With potentially thousands of such civilizations (see Drake equation earlier), we should be swimming in extraterrestrials. Why not? Fermi concluded that some assumptions must be wrong; either there is nobody else, or the rare civilizations are very far apart, or interstellar travel is impossible, or technological civilization lifetimes are too short.