Thursday, July 30, 2009

Life In The Universe, My Own Amateur Calculations (Pt 4)

It’s taken a while, but I’m back.

In the last post, I said I’d give the types of stars most likely to harbor worlds with ecosystems as complex as Earth’s, namely stars based on their expected total lifetimes (closely related to the star’s mass). This one is actually a big unknown, for Earth is the only planet known to harbor an ecosystem as remotely complex as ours. This means we have no clue as to whether even microbial life formed more quickly or less quickly than the average lifebearing world, let alone ecosystems as complex as our world’s. Therefore, this post will necessarily be speculative to at least a large degree.

NOTE: If you’re in a hurry or in a “Just the Facts, Ma’am” mood, the star must be between 1.1808 and 0.5 solar masses to be to be a serious candidate for harboring Earth-complexity ecosystems – especially those capable of harboring technologically advanced life.

Therefore, I will work from two following assumptions:

A)Assumptions biased in favor of life forming more quickly than it did on Earth.

Here, I make two more assumptions based on this core assumption

1)Life moved onto land 3 billion years after the planet’s formation was largely complete - one billion years than happened on Earth.

2)300 million years passed between the first significant land-based ecosystems and the emergence of technologically capable life (on Earth, it was 500 million years).

B) Assumption biased against the easy survival of technology-capable life.

1) Just as technology-capable life evolves, the star’s long-term brighteness reaches the point of harming the planet’s ecosystem. (Put another way, only a razor-thin margin separates the alien civilization’s death from its developing sufficient technology to escape the “roasting” of its home world.)

However easy the assumption may be, it is NOT as simple as saying the expected lifetime of the star need be 3.3 billion years (3 billion years for the land-based ecosystem to appear, 300 million more years for technology-capable life to appear). As we discussed in the previous post, the sun’s brightness is not fixed over time, even during it’s main sequence state. Our 4.5 billion year old sun still has about 5.5 billion years left in its main sequence stage, yet experts say at its birth it was only 70% as bright as it is now. That means the sun’s own habitable zone boundaries moved outward over time. The habitable zone will move beyond Earth in about half-a-billion to a billion years, which is right at the sun’s halfway point in its main sequence phase. Therefore, lets revise the 3.3 billion year assumption to say,

2)The life-bearing planet must spend at least 3.3 billion years within its sun’s habitable zone.

3)The planet will be within the star’s habitable zone for half the star’s main sequence phase.

This gives a lifetime of 3.3 billion years / 50%, or 6.6 billion years.
We know a very tight mathematical relationship exists between the star’s mass and its lifetime as a main sequence star (not 100% perfect, but close enough to it not to substantially alter our expectations). S o break out the trusty calculator with power figures (or spreadsheet, if you know how to do powers and square roots on it). The mass-lifetime formula is:

Ls = (1/Ms^2.5) X 10 billion years

Ls= Lifetime of the star on the main sequence, Ms = Mass of the star in Solar Units (i.e. our sun = 1, twice the mass of the sun is 2, half the mass of the sun is 0.5, and so forth), and 10 billion years (10^10) is our sun’s expected lifetime on the main sequence.

However, this formula only translates stellar mass to expected lifetime. We already know the expected lifetime of the highest mass star most probably capable of supporting Earth-complexity ecosystems (6.6 billion years). But we don’t know the mass of the star. To translate the star’s lifetime to its mass, the formula is:

Ms = [(1/Ls)^(1/2.5)] x 10 billion.

Now, we’re ready to solve the mystery “What’s the maximum probable mass of a star capable of sustaining a planet long enough for technology-capable life?”. In this case, Ls = 6.6 billion / 10 billion, which means Ls = 0.66. From here, we simply plug in the numbers:

Ms = (1/.66)^(1/2.5).

1/.66 = 1.515. So Ms = 1.515^(1/2.5), which in turn equals 1.1808 Solar Masses -- the maximum probable mass of a star bearing a complex ecosystem!

Therefore, any stars more massive than 1.1808 solar masses are not likely to harbor technically capable civilizations. While planets within such stars’ habitable zones can certainly support microbial or smile macroscopic life, at most, they will be “Planetary Serengetis” or “Jurassic Parks”. This is fascinating for biologists and ecologists, but disappointing for those looking for a Star Wars / Star Trek type world.

There’s also a minimum probably lower mass for such stars as well, but it’s rather complex. The basic points are

(1) As discussed previously, less massive stars have narrower life zones, thereby greatly lowering the probability (as opposed to basic possibility) of the presence of life-bearing planets of any sort.

(2) Even if the habitable zone is wide enough, planets too close to a star will experience tidal locking. This is when one side of an orbiting body permanently faces the body it orbits. Our moon is a perfect example. Until the launch of space probes to the moon, nobody ever saw the other side of the moon because the moon does not rotate relative to the earth. Why is this so? Because the differences in the Earth’s gravitational pull on the facing side of the moon and its far side are sharp enough to prevent rotation. This also accounts for Mercury’s very slow rotation (2 of its “days” last for 3 of its “years”), the sun’s gravity greatly slows down Mercury’s rotation.

Unfortunately, as discussed previously, habitable zone boundaries can overlap with the “Tidal Locking” boundary if the star is small enough. The formula is entirely to complex to explain here, and even too complex for me to understand. However, I heard (but can’t substantiate) that the star must be no less than 0.5 Solar Masses for a habitable zone planet to escape tidal locking. This establishes our lowest probable mass for a star capable of fostering technology-capable life.

Beyond the star’s mass, it also has to have a certain % of elements heavier than helium within it (the astronomy term is Metals). In short, astronomers discovered a relationship between stars known to harbor planets and their metallicities (the ratio between heavier-than-helium elements and the total mass of the star). They find that stars most likely to harbor planets at will have metalicities half that our sun or greater. A large metalicity indicates lots of material from which to form planets.

This pretty much completes our discussion of characteristics of stars that are most likely to harbor life-bearing planets of any sort. These characteristics become more strict as you travel up the life-complexity scale. From here on, we will look at the necessary characteristics of the planets themselves. Beyond the star’s metallicity, there’s no way to know whether any planet (or gas giant’s moon) is actually present within the star’s habitable zone – aside from possibly the presence of a gas giant too close to the habitable zone, which increases the odds of a planet having a dangerously skewed orbit, if not ejected from its solar system altogether.

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