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.

Life In the Universe: My Own Amateur Calculations (Part 3)

In the last post, we delved into the basics of star formation as it pertains to the potential for complex life to develop on an Earth-massed planet orbiting with that star’s habitable zone. We also explored the difference between low massed main sequence stars (red) and the corresponding high massed ones (blue). I already implied the advantages of low-massed stars vis-à-vis high-massed ones concerning the presence of complex life and highly developed ecosystems. Now we look more in-depth at the pros and cons of each:

RED STARS

Advantages

Enormously Long Expected Lifetimes. This is their biggest advantage. Simply put, longer lifetimes on the main sequence allow more time for life to form and develop; thereby increasing the odds of life actually existing around such stars – whether at present or in the future (particularly complex life). Life on Earth started around 4 billion years ago, shortly after our planet finished forming. Yet, only in the past half-billion years has surface-dwelling animal life existed on our planet – barely more than 10% of our planet’s existence!

As for species even potentially capable of developing technology Homo Sapiens Sapiens emerged only 200,000 or so years ago (the last 1/22,500 of Earth’s existence). Compare that to how long Television existed!!! Now you should appreciate how tiny a fraction of a planet’s lifetime is occupied by technically advanced lifeforms and therefore also appreciate the value of a long-lived star for increasing the probability life will arise on a planet around it.

Low radiation output,providing that red star has no more tendency to flare or suddenly vary in brightness as our sun(which unfortunately is not the case for many red stars, as explained next). If the red star is neither prone to flare NOR suddenly brightens at random or even frequent regular intervals (what astronomers call Variable Star), then life has all but infinitely better odds of surviving and thriving around such a red star – all other things being equal.

Disadvantages

Tendency to Flare or Vary in Brightness Suddenly. Still, red stars have their share of disadvantages, especially the lower massed red ones. As mentioned above, even if their radiation output is much less than larger and hotter stars, many red stars still tend to flare periodically (i.e. send jets or erupting gases, which emit high levels of radiation, heat, and light). In short, the smaller the star stars, the more likely they are to vary greatly in brightness. Clearly, any otherwise potentially life-friendly planet orbiting it will face irradiation and sudden increases in temperature, potentially killing what life evolved so far (and perhaps boiling off its oceans as well).

Narrower Habitable Zone. Just as small campfires on a cold night can’t provide nearly as wide a comfort zone as a large bonfire, so a cooler star can’t provides as much area suitable for life and/or liquid water that a hot star can (and light and radiation in general, too, for that matter). In other words the cooler the star, the narrower the life zone. For small stars, this significantly lowers the probability that a planet of any sort will be in the habitable zone. In our solar system, our habitable zone for an planet just like Earth ranges from just inside our orbit to near Mars’ orbit (more specifically from 0.95 to 1.4 Astronomical Units, where 1 AU = Earth to sun distance). For small stars, the problem is potentially even worse; which brings us to the next disadvantage of small red stars.

Rotation Lock Within The Habitable Zone. Rotation Lock is when a smaller body orbiting a larger body always shows the same side towards the body it orbits. This is the case with the Moon. You see only one face of the moon because it is so close to the Earth that the difference in Earth’s gravitational pull between one face of the Moon and the other is great enough to hold one side of the Moon toward Earth. The same thing can happen regarding a planet near its star.

While it’s impossible in this solar system for the habitable zone to be inside the sun’s rotation lock radius, this is certainly the case for cooler stars. It’s unfortunate that the rotation lock radius doesn’t shift inward with lower mass nearly as much as the habitable zone does. Therefore, only the more massive of red stars have much likelihood of hosting life-bearing worlds in addition such stars narrow habitable zones.

BLUE STARS

For the most part, blue star’s advantages and disadvantages are the opposite of red stars.

Advantages: Less tendency to suddenly brighten or flare, Wide habitable zones, Habitable zone well outside the star’s rotation lock radius. However, this is all that can be said about massive blue star’s ability to host life.

Disadvantages: By far the biggest ones are their incredibly short lifetimes (sometimes only a few million years!) and their enormous radiation output. The latter means that even if any Earth-sized or larger rocky-metallic planets do form within the habitable zone and keep suitable orbits, the star will severely irradiate the planet’s surface and, perhaps even, strip the planet of its atmosphere – unless the planet is lucky enough to have an unusually strong magnetic field. Even with such a field, massive blue stars will certainly explode into a supernova far too quickly to allow formation of anything more than primitive microbial life.

OTHER STARS:

Stars neither small red ones nor large blue ones offer some mix of advantages and disadvantages, all of them in a less extreme form than the stars we examined. Obviously, there is an optimal mass of a star if it is to have a reasonable probability of hosting a life-bearing world. The star must have a habitable zone outside the star’s rotation lock radius, it must not emit radiation intense enough to sterilize planets within the habitable zone, it must exist long enough to permit complex life and even more complex ecosystems to form, it must have a stable brightness regime, it must flare only a small amount if at all.

Obviously our Sun qualifies as such a star. However, other stars undoubtedly qualify as having high potential for life as well. The question is “What range of stellar masses is most optimal for a lifebearing world?” The sun does seem optimal for us. However, our star is the only one known to harbor a life-bearing world. That means the optimal mass of a life-bearing star could be either larger or smaller than ours (I’m inclined to lean toward “somewhat smaller”). The next posts will delve further into this most profound of all questions in astronomy and biology.

Life In the Universe: My Own Amateur Calculations (Part 2)

There are five basic aspects of determining if a planet is a suitable candidate for life:

* Location Within the galaxy (for many reasons, half-way between the core and the edge seems ideal)

*Type of star (largely dictated by its mass)

*Planetary Orbit (obviously)

*Planetary Mass (can’t be too small or too large, for many reasons)

*Time (the planetary system can’t be too young or too old).

The last three listed characteristics will be discussed in Part 2. For now, we’ll look at why which kind of star matters in the search for life outside this solar system.

STELLAR CHARACTERISTICS . To fully grasp why certain stars are more suitable candidates for life than others, we first have to look at the nature of stars. Not all stars are the same. In fact, they vary enormously in many characteristics – some of which either increase or decrease the odds of life arising on a planet even if that planet is similar to Earth in all other respects. For now, let’s look at the relevant characteristics that influence a star’s suitability for hosting an ecosystem of similar complexity as Earth’s.

How Stars Shine. In a sentence, stars shine by compressing their own gases. At gas pressures experienced in stars, several things come into play. Firstly, the more compressed a gas gets, the hotter it gets. Secondly, the hotter an object, the faster its atoms or molecules travel. Thirdly, at a certain very high temperature, the heat will tear the atom’s electrons from its orbits, leaving only the naked nucleus of the atom*. Fourthly, without the electron cloud surrounding the nucleus, the atoms of the gas can collide with each other given high enough temperatures and pressures.** Fifthly, all the above means that the nuclei in the hot gases travel so fast that they overpower the proton’s tendency to repel each other, and in the meantime fuse to become a new element (e.g. hydrogen nuclei fusing to form helium nuclei)**. These collisions release tremendous amounts of heat and energy, which enables the sun to give off heat, light, and other forms of radiation; and therefore enable it to supply a planet with sufficient heat to support the ecosystem.

Given the above, it’s easy to see how larger stars, which have higher pressures in their core, fuse their hydrogen fuel much faster than smaller stars and therefore much hotter. However, as should be obvious by now, the old saying “All good things must come to an end”, applies to stars along with everything else.

A perfect rule-of-thumb for telling how massive, hot, and long-lived a star is/will be is simply to look at its color. Just as with iron, red stars are the less massive, cooler, and longer live ones; the blue stars are the most massive, hotter, and live shorter lives. The color order is as follows: Red, Orange, Yellow, White, Blue.

However, this color-to-characteristic sequence holds only for stars on the so-called Main Sequence, which 85% of all known stars are on. A Main Sequence star is one that fuses hydrogen nuclei into helium nuclei. This is important because the smaller the nucleus, the more heat and pressure required to fuse that nucleus into a larger nucleus (i.e. it takes less heat and pressure to fuse hydrogen into helium than it does helium into carbon; and still more energy to fuse carbon and other nuclei into neon or calcium or other heavier nuclei). Furthermore, the heavier the nuclei involved in the fusion, the less energy they release from the collision in proportion to the energy required to produce that collision. Therefore, because, hydrogen->helium fusion is the most common reaction taking place in the cores of stars. Incidentally, it’s also the most efficient form of fusion in terms of energy output to energy input of the fusion..

In addition to a star’s expected lifetime on the Main Sequence, it’s temperature (reflected in it’s color), the star’s mass also reflects its radiation output. Not surprisingly, the larger the star, the greater its radiation output.

So far, we have the following traits associated with a star’s mass:

Low mass: red color, low temperature, long lifetime, low radiation output (with exceptions)
High mass: blue color, high temperature, short lifetime, high radiation output.

Now, let’s look

In the next post, we’ll we get to the pros and cons of each kind of star, plus delve into a few other advantages and disadvantages of a small cool star versus a large hot one:

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NOTES

*Electrons repel each other when they come close together, similar to the way some magnets sometimes repel each other if you place them closely together . That’s why your hand doesn’t pass straight through a table. It’s because the electrons in the table and the electrons in your body are pushing each other away.).

**Protons repel each other to, if they come too close together, unless the gas is so dense that the combination of speed and pressure forces the nuclei of atoms together.

Life In the Universe: My Own Amateur Calculations (Part 1)

Time for a change of pace - namely to one of my favorite hobbies: astronomy, in particular which stars other than our own might harbor planets bearing complex lifeforms. I will define “Complex Lifeforms” as having all these features: They do or have the following:

(a) Move by their own power

(b) Have specialized organs and organ systems(i.e. organs devoted to specific functions)

(c) Sense objects or other phenomena they aren’t in direct contact with– (i.e. they use, light, sound, vibration, and other phenomena or similar means).

(d) Have either a brain/nervous system or some other means of manipulating information about their environment, (i.e., gather, process, remember, and retrieve that information)

(e) Communicate with other members of their species through some specific means or variety of means.

For now, I will stick the type of complex life dependent on liquid water. I don’t doubt alternative biochemistries can exist but at the same times we've never seen such a lifeform. Therefore, to be safe, let’s stick with what we know instead of stacking hypothesis on top of hypothesis.

The next post will not be about the planets themselves, but about the stars that the life-bearing planets will most likely orbit. In fact, understanding the basics of stars is so important to calculating the probability of complex life in any one planetary system that I find it necessary to devote the next post to stars alone.