Astrobiology, Space

The Drake Equation

You can watch this as a YouTube video if you’d like! Linked below 🙂

After a fantastic response to my Kepler’s Laws posts, I decided to continue with my Equations of Space series, and return to one of my favourite areas of science, astrobiology!

What is the Drake Equation?

Essentially, it is a long list of variables that, upon finding their values, will output an estimate for the number of intelligent, detectable alien civilizations there are in the Milky Way.

A quick history lesson!

Like much of science, the equation gets its name from its inventor- Frank Drake. Back in the 60s, when radio astronomy was in its golden age and interest in space and aliens was at an all time high, he began to scan the skies for radio communications from nearby sun like stars, starting with Tau Ceti and Epsilon Eridani.

Unfortunately, he didn’t spot anything out of the ordinary, and nothing has been seen since, despite further detailed and lengthy observations of the stars being made. The stars may not have revealed any nearby aliens, but the observations didn’t go to waste, as both have been found to have planets and a debris disk!

Even though the first experiment didn’t find what he was looking for, it got people interested in the scientific search for aliens, and he set up a meeting to discuss the possibilities with likeminded scientists, including the likes of Carl Sagan and the founder of the computer company HP, Barney Oliver! But he needed a framework to guide the discussion, and thus the drake equation was born! To this day, each research topic at the SETI institute can be grouped under one of these variables.

The meeting was named the Green Bank meeting after the telescope it was held at

The Equation

R*

The first variable, R* is the rate of star formation in the galaxy, which we can find crudely by dividing the number of stars in the galaxy by the age of the galaxy, giving us a value of about 10 stars a year… except this doesn’t match up with the current rate of star formation as measured by the number of young stars we can see in the milky way.

This is because the original calculation doesn’t account for the changing rates of star formation over a galaxy lifetime, as a younger galaxy will have a much higher star formation rate than an older one. A more accurate rate, using the young star survey method, is about 3 stars a year, which is slightly higher than estimated by Drake.

F(p)

Next is the fraction of stars that have planets. Drake estimated this to be 20-50% as at this point we had not yet discovered any exoplanets, so it was really just a wild guestimate. However thanks to the Kepler telescope and the development of other methods of exoplanet detection, we now know that exoplanets are actually really common, and scientists have estimated that nearly every star will have at least one planet, putting F(p) at nearly one!

But not all of these exoplanets are capable of being home to life- of the 4000 discovered so far, over half are gas/ice giants (like the outer solar system planets), and only 163 are similar to the inner rocky planets.

N(e)

Originally, the N(e) variable was the number of earth-like planets per star, but now we describe it as the number of planets per star with an environment suitable for life.

The Green Bank meeting put this variable at an optimistic 3-5 habitable planets per planetary system, but the discovery of the prevalence of gas giants and exotic solar systems has cast that into doubt- the value is probably below 1. It’s easier to consider the number of habitable planets in the galaxy, which Kepler data suggests is about 40 billion habitable planets out of 100 billion stars, putting F(p) x N(e) at 0.4.

F(l)

Then the variables turn from astronomical to biological, with F(l) being the fraction of suitable planets on which life appears. Drake put this at 1, meaning that under any habitable conditions, life will arise.

Which on one hand makes sense, as life on earth appeared to develop as soon as conditions became suitable, but on the other hand it would suggest that on such a habitable planet like the earth, life surely must have arisen multiple times, and new geneses of life must be occurring all the time, but we’ve only found evidence for one origin, with all species fitting on to one tree of life.

If we find evidence of current or past life on potentially habitable worlds like Mars or Europa, then this would validate the claim that F(l) is closer to 1.

F(i)

Following from this, the next variable, F(i), is the fraction of the worlds that develop life, that go on to develop intelligent life. This is one of the most controversial variables, as it depends on what you class as intelligent. Some believe that if conditions remain habitable, then intelligent life is inevitable.

But even under that assumption, F(i) probably won’t be one, seeing as it took 3 billion years of single celled life to evolve into multicellular life here on earth, a further billion to evolve into animals and 600 million years to get to where we are today, conditions would have to remain relatively stable for a loooong time. And from looking at our own solar system, where both Mars and Venus lost their status of habitability, this isn’t always the case.

F(c)

Linked to intelligence, but put into its own variable by Drake, is the fraction of those intelligent civilisations capable of communicating by releasing a signal to space. This is very much a factor of its time, when the only method of detection would be via the radio waves that drake worked with. He put it at 10-20%. But Now we have different methods of detecting life, such as through biosignatures, so there’s some debate over the importance of this variable

We as humans have only been in this category for about 100 years, which is a tiny proportion of the history of the earth, let alone the universe! As communications only travel at the speed of light, this limits the number of detectable species. But its possible that other species developed earlier in time, so, if they continue to survive, they will have been transmitting for a much longer period of time.

L

How long they are able to transmit for is encompassed by the final variable L, the lifetime of an intelligent civilisation. There is so much uncertainty in this factor, partly because of arguments over what a civilization is. Does each dynasty or empire count as a new civilisation? Or is the entirety of the human race one civilisation? Personally I think the latter makes more sense. But what if a species manages to colonise different planets or solar systems?

All of these variables combine to give N: the number of currently technologically advanced civilizations in the galaxy!

Updating the Equation

Although the astronomical variables can be, and are being, empirically measured, the huge uncertainties in the final biological variables have made some scientists look for a replacement to the drake equation. 

Some of the proposed changes involve using the number of stars in the galaxy, rather than the rate of star formation, taking into account the galactic habitable zone, or the expansion velocity of a spacefaring civilisation. 

Alternatively we can change what we are actually looking for. The Drake Equation looks for the number of transmitting civilizations alive today, but by throwing out the L variable, and combining some of the other variables, you get a simplified or revised version that tells you the number of technological species that have formed over the history of the observable universe.

Or you can get rid of the intelligence factor altogether and simply look for the number of planets with detectable signs of life by their biosignatures. This is known as the Seager equation (named after Sara Seager, a name you may recognise from last year’s ‘Life on Venus?’ post), and is more useful given current knowledge and capabilities. 

Another thing to consider is what we regard as habitable. For a long time, we thought that only earth like planets could be home to life, but as we discover more about the outer solar system, especially the diverse moons there, we realise that this approach is probably too narrow minded! This will become more important if we find evidence of life in the outer moons, such as Europa or Titan!

Can it be solved?

Well as you may have gathered, there is a LOT of uncertainty in the variables, so it gives answers ranging between just 1 (us) and 15 million. I don’t think we will ever find a definitive answer, at least not for a long time, and I don’t think it really matters.

Instead it can be used, like its original purpose, as a guide, indicating what to look for and how to find the answers, as we discuss and research astrobiology!


Thanks for reading! This post was essentially just a neatened up version of my script for the video, which is why it may have seemed chattier than normal! You can subscribe to my youtube channel here or check out my other astrobiology videos!

Leave a comment if you enjoyed the post and tell me what equations you would like me to cover in the future!

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