Drake Equation and Earliest Alien Life

[CelesKnight]

Let's say that someone uses the Drake equation and determines that there are X radio-using species in the galaxy right now. How much would that number decrease at earlier ages? For instance, would there be X (possibly different) species 100 million years ago or would there be much less? How about 1 billion or 5 billion years ago?

At what point does the number of alien species in the galaxy (or even in the whole Universe) approach zero? (As a corollary, at what point is the conditions for life appropriate enough that we can say, "Statistically speaking, making XYZ assumptions, we can presume that there is a good chance that at least one intelligent, tool-using lifeforms exists?)

My purpose is to attempt to determine at what point is there a good chance that alien life arose, and then attempt to determine how far they could have expanded since then.

Thanks!

[Junghalli]

Too little information at present. We'll have to start seriously exploring at least the nearby solar systems and determining how many stars have habitable worlds and on average what the level of development of life on those worlds is before we can take a crack at answering your questions.
For what it's worth star formation in our galaxy dropped below replacement rate six billion years ago. There may be a large percentage of "burned out" systems which used to have life but don't anymore based on that.

[Kuroneko]

What is most unbelivable about such usage of the Drake equation is that the calculuation would have any significant degree of certainty. However, handwaving those concerns away, the most convenient form of the Drake equation is N = [Pln][Sup]*[Lif][Int][Com][Civ], where S is number of star-systems, Pln is the fraction of star-systems with planets, Sup is the number of life-supporting planets out of the systems that have planets, Lif is the fraction of those that develop life, Int is the fraction of the previous that develop intelligent life, Com is fraction of those capable and willing to communicate, and finally Civ fraction of a planet's lifetime for which such a civilization can be expected to exist. For brevity, write N = AB, where A and B are the products of the terms to the left and right of the * in the Drake equation above. These are the number of life-supporting worlds and the probability that a civilization is found among them, respectively.

To answer you question as to what is the probability that there is at least one, well, that's simply negation of the probability that none of the A world have civilizations on them: P = 1-B^A, thus the earliest civilization would occur when P = 1/2. Note that although it is reasonable for B to stay essentially constant, A is strongly varies with time, which will be very significant on the long-term scale. Another caveat is that all probability calculations are strongly dependent on the information available, so, for example, if we know with certainty that there are X worlds with civilizations satisfying those criteria in the galaxy (currently, X = 1; namely, us), then there is virtually no chance that these worlds had such civilizations in the distant past, thus they would have to be subtracted from whatever value of A would have in the past.

As to what realistic values the above can have, I am not willing to discuss. To say that any calculation would be suspect would be an understatementt, but if your goal is, say, making a consistent fictional universe, then the Drake equation could be of use.

[Quadlok]

Well, if I'm remembering correctly, the first life could not have appeared until the universe's second or third round of star formation, as before then there was almost a complete lack of elements heavier than helium. Unfortunately, I can't remember how long those first couple cycles took, only that they were on the order of millions rather than billions. Then you'd have to wait for planetary formation and cooling, and then the long crawl up from amino acid to sentient life. So I'd say about 8 billion years or so.

[GrandMasterTerwynn]

Ideally you want to start looking for the era of stars which had a metal content similar to the Sun, or higher (since stars with planets have high metallicities.) While it seems that it was possible for planets to form twelve billion years ago, these were all low-metal hydrogen and helium puffballs.

A quick Googling indicates that such stars started to be born around eight billion years ago. However, such stars were likely fairly close to the galactic center, where supernovae, and gravitational peturbations from nearby stars would shower the planets with comets and hard radiation, continually resetting their biological clocks. So you have to wait a couple billion years after that, when metal-rich stars could be born further out on the galactic disk.

So, we say stars born about 6-7 billion years ago could support life-bearing planets. If we assume that life forms immediately on those worlds, but doesn't become too complex for the first three and a half billion years of history, then we can assume that it first became possible for complex life to evolve starting about 2 or 3 billion years ago. Though on those planets, complex life will only remain possible for less than a billion more years, then the parent star becomes too hot and the world becomes like Venus.

Of course, just because complex life arises doesn't mean that there will ever be technological civilizations on those worlds. After all, the vast majority of species to ever exist on Earth never had the desire to build cities.