Equations II: The Seager Equation

Click to enlarge; composite of web photo with painting by Gert van Dijk

The Drake equation, discussed recently on this blog, provides an estimate of how many communicating civilisations there are in our galaxy. It does so by multiplying a series of factors; none of these is rock solid, so some say it is basically guesswork. That is true, but in the absence of hard facts an educated guess is the best evidence there is. The nice thing about the Drake equation is that it in essence falsifiable, meaning that it is, at least in theory, possible to say whether there are such civilizations or not. In theory, that is, because one of the two possibilities is that are no such civilizations, and it is usually much harder to prove the absence of something than its presence. If someone in another solar system one day decides to answer our interstellar call, for instance to ask mankind to please turn the volume down, or to stop pestering them with unwanted phone calls in the middle of dinner, then we will know for certain that there is someone out there. But at present we have not received any signal, which tell us precisely nothing. It is like fishing: as long as you haven't caught any fish, you cannot conclude there aren't any. Only when you've caught one can you say that there are fish (or, more precisely, that there was at least one fish; you may just have exterminated the species).

Habitable zones (from https://www.saraseager.com/)

Sara Seager, an astronomer at MIT, proposed a different approach. If you Google her you will find many entries, among them her own website. Her reasoning rests something much more basic then intelligent being using radio signals: is there a biosphere? Her idea starts with the concept that life requires liquid water, an concept that certainly holds water (sorry for that one). Liquid water requires a planet in the habitable zone at the right distance from its star. What I learned from an overview of the conditions under which you might get liquid water is that there might even be liquid water on runaway planets that are no longer circling a star. Anyway, take a planet, add life, stir and wait, and you might get a biosphere. It is wise to search for stars with a nice quiet long term behaviour, so the stars do not cook their planets halfway down the line. Lifeforms have metabolisms, and spew out interesting gases that provide a 'biosignature' in the atmosphere around an alien planet.

Life on Earth certainly altered the atmosphere. At one point there was a nice community of anaerobic organisms quietly doing their thing, and then some new-fangled intruders called 'plants' starting using a highly polluting process called photosynthesis, with a highly reactive dangerous poison as a by-product: oxygen. Plants may have caused the very first mass extinction. Later on, animals learned to control how to burn stuff slowly with that oxygen, making a dent in the amount of oxygen, but not a large one, so Earth's atmosphere now still consists of 20% oxygen. And that can be measured from afar.

Click to enlarge; principle of spectroscopy on transit signal

Unfortunately, the detection is not easy. The method Seager proposes rests on planets passing exactly through the line of sight from Earth to the planet's star, so they appear to transit the disk of that star. That process works well and has already resulted in the discovery of many exoplanets. The TESS satellite was launched in April of 2018 to find many more. When the planets pass the star, they alter the composition of the star's light, and that change tells you something about the planetary atmosphere. Of course, not all planets happen to pass through that line of sight, so only some are observable this way. There is another problem: many biosignature gases are destroyed by ultraviolet radiation from the star, reducing their amount. These gases will be easier to detect if they are not broken down by UV, which is why Seager proposes looking at M-type stars (red dwarfs), because that live long and put out little UV. The latter job is to be done by the James Webb satellite, to be launched in 2021 (probably).    

Here is the Seager Equation:

N = N* FQ FHZ FO FL FS

* N is the number of planets with detectable biosignature gases
* N* is the number of stars within the sample
* FQ is the fraction of quiet stars
* FHZ is the fraction with rocky planets in the habitable zone
* FO is the fraction of observable systems
* FL is the fraction with life
* FS is the fraction with detectable spectroscopic signatures

If you study the parameters, you will see that several factors have to do with the 'detectability' of a biosphere. That holds for the fractions that concern 'quiet stars', 'observable systems' and detectable 'spectroscopic signatures'. Those fractions decrease the total number appreciably.

Click to enlarge; from: https://informationisbeautiful.net/visualizations/the-drake-equation/

But what is the number? Luckily, there is a very nice website allowing you to play with all the parameters in both the Drake and the Seager Equations, so you can see how they alter the final estimate. The settings shown above are for the "today's optimistic" option. Pressing calculate will give you 750 planets, while  the "Seager original values" only give you 0.45 planets. Running the Drake equation with the original settings results in 10 communicating civilizations in our galaxy. Note that the drake and Seager equations rely of completely different detection techniques, that in part explain the differences.

Does it matter for speculative biology? Well, you could say that speculative biology has to start with astronomy, so yes. In the last of these 'equation' posts, a forthcoming post on the 'Nastrazurro Equation', I will try to apply all this astronomical reasoning to speculative biology in another way. Soon. Probably.