## Friday, March 26, 2010

### Life on Other Worlds Two - The Drake Equation

[Visions of earth, as seen from Orion]

The Drake equation states that:

$N = R^{\ast} \times f_p \times n_e \times f_{\ell} \times f_i \times f_c \times L \!$

where:

N = the number of civilizations in our galaxy with which communication might be possible;

and

R* = the average rate of star formation per year in our galaxy
fp = the fraction of those stars that have planets
ne = the average number of planets that can potentially support life per star that has planets
f = the fraction of the above that actually go on to develop life at some point
fi = the fraction of the above that actually go on to develop intelligent life
fc = the fraction of civilizations that develop a technology that releases detectable signs of their existence into space
L = the length of time such civilizations release detectable signals into space.[3]

Considerable amounts of both speculation and research have gone into making estimates for each of the terms. The first three are addressable by conventional astrophysics. These are things about which quite a lot is known in general. The research is to assign particulars and quantities. Many a doctoral dissertation and research grant and paper has gone into the endless refinement of every subpart of each of these questions.

In the early stages of quantification scientists seek to put upper and lower bounds on what the quantities might be. For example even without a telescope we can determine that the lower bound of the second term, f-sub-p, must be greater than zero because we are standing on one and can see others. Simple logic tells us that f-sub-p cannot be greater than one. See, we're doing astronomical research right here at home. Nor is that entirely a joke.

Ever since the early Greek philosophers, lots has been learned just by logical thinking and commonplace observations. An example of the latter is Galileo's dropping heavier and lighter weights off the Leaning Tower of Pisa to see which would fall faster. And only a generation or two before my time came Einstein's thought experiments with a rotating bucket of water and inertial reference frames.

The lower bound of F-sub-p has been bumped up considerably by a generation of discoveries of extra-solar planets, now numbered in the hundreds. What is less obvious is that the upper bound has also been bumped down considerably by the non-discovery of planets around stars where we could have detected them if they had been there. At least large planets. Which to say that while the value of f-sub-p remains unknown, the bounds it must fall between have narrowed.

I must admit I have no idea why the first term 'R*' refers to the rate of star-formation in the galaxy and not just to the total number of stars. If anyone reading this knows why, please explain in a comment and I will copy it to a full post.

For reasons of the inverse square law, the habitable zone around a star is proportional to its brightness - the brighter the star, the wider its habitable zone both absolutely and relatively. The habitable zone used to be understood as being between where water would boil away and where it would freeze solid. The case of Jupiter's moon Europa has loused up this supposition.

The tidal effects of its proximity to Jupiter stretch and squeeze Europa with every rotation about its axis, each of its days. This stretching and squeezing heats it. Such that, though its surface is frozen, under hundreds or even thousands of feet of ice there appear to be liquid oceans. Europa, hundreds of millions of miles beyond what had been assumed to be Sol's habitable zone, is now considered the leading contender for where else in the solar system we are most likely to find liquid water - and life.

Which illustrates how even the term least difficult to calculate, the size of the habitable zone, turns out to be unexpectedly tricky. The moral of Europa is - don't assume.

The much greater relative size of habitable zones around large bright stars had led people to assume that was where life was most likely to be found. Since large stars are relatively rare, the possible loci for life were thought to be as well.

Improvements in the size and sensitivity of telescopes have revealed that the small dim stars called red dwarfs are vastly more numerous than had been previously thought. And since they last almost forever compared to larger brighter stars, the product of their habitable zone volumes times their number times their longevity makes them by far the more likely harbor life. Which means that the possible loci for life are vastly more common than previously supposed.

Further, because their surfaces nowhere near as hot as those of larger brighter stars, red dwarves emit far less ionizing radiation. For example, if you stay outside all day without protection, you will get a sunburn. Which is to say that, though your ancestry on this planet goes back at least two billion years, you will be partially roasted by your parent star's ultraviolet radiation in a few hours. And that is in spite of life on earth having created a partially oxygen atmosphere which in turn has created an ozone layer which blocks a lot of the UV from the sun.

Larger brighter stars are also hotter and a larger fraction of the radiation they emit is UV, hard UV, and X-rays. Which means that even at the same temperature range, life is more likely to be destroyed by ionizing radiation on planets around them before it can create a partially oxygen atmosphere and an ozone layer. And even then your sunburn might go all the way through if a lot of the sunshine was X-rays. So red dwarfs are looking better and better.

BUT the bastards are incredibly hard to find. They are dim compared to larger stars (the brightness of stars varies approximately with the fourth power of their mass - so a star one-tenth the mass of the sun would be one-ten-thousandth as bright) and correspondingly hard to see with even the biggest and best telescopes.

Which is a major reason astronomers are forever trying to get funding to build ever bigger and more sensitive telescopes. It isn't just mission creep or empire building, though one assumes there must be some of that too, but a genuine going where the science takes them.

In closing I would note the evolution of the thinking about the 'L' term at the end, the Length of time that civilizations broadcast detectable radiation signals into space. This used to run toward pious clucking about the prospects of the Cold War degenerating into World War III and the destruction of the world in a vast thermonuclear exchange between West and East. This included holier-than-thou holding forth about inherent aggression and instability of much of the human species, by which was meant anyone not a liberal or leftist academic.

The end of the Cold War has cut the legs out from under this argument, ripped out its guts and stomped on them, sprayed the landscape with its blood and bits of its organs as though it had swallowed a daisy cutter, have vaporized it where it stood such that its eyes boiled and burst from their sockets and... Hold on, where was I going with this?

Even as I write, the American and Russian governments are negotiating substantial further reductions in their nuclear arsenals. One would think that this would mean that the value of 'L', judging by our own case would be going up because we are less and less likely to annihilate ourselves. It isn't.

In the early days of radio and television, broadcast stations blasted sometimes up to million watt signals. We ourselves have receivers that could detect such signals if they were coming from the nearer stars. Which means that it is now possible to pick up actual live broadcasts of 'I Love Lucy' all over our immediate sector of the galaxy.

But developments in the economics and technology of broadcast have led to networks of much less powerful signals replacing the single behemoths of the middle of the century. So while Tau Ceti and Sirius-B may be able to tune into Playhouse 90 and Ed Sullivan, they probably won't be able to pick up Oprah and American Idol no matter how much they adjust their rabbit ears. Eventually they won't be able to watch the 2057 season premiere of 'Law & Order - Chico', even with a roof antenna.

Which is to say that seen from afar, earth will have winked out as a detectable civilization, and without a thermonuclear planetary suicide. There is no reason to believe that an until-then-detectable remote civilization around any given star may not have similarly winked out 17 years ago, or 17 million years ago, or 1.7 billion years ago - and yet still be there. Or not.

So our judgments on the probable value of 'L' even for our own civilization have proven slippery. For others of which we as yet know nothing, it is all but impossible to set upper or lower bounds.

All of which is to suggest that our work of answering one of the most profound questions of human existence, "Are we alone in the universe? Is anybody out there?", is a huge and daunting set of intellectual and scientific tasks. And we are just at the beginning of the work of answering it.

If you think that all matters of loaves and fishes are long since settled and that science is just about inventing new doo-dads, think again.

#### 1 comment:

1. I assume you saw this related equation: http://xkcd.com/718/