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| Artist's Depiction of extrasolar Earth-like planet. |
It's impossible to look up at the stars and not wonder about the ever growing possibility of life elsewhere in the universe. As I discussed in my previous blog regarding the Drake Equation, life may be as abundant as dirt in our galaxy alone. Many scientists disagree on whether or not meeting intelligent extraterrestrials will result in the wetting of our feet in the vast ocean of interstellar travelers, or the end of humanity as we know it. One thing, however, is certain; humanity is upward bound. Regardless of whether or not we have any desire to make first contact with the Vulcans from Star Trek, it is necessary that we, as a human race, find another planet hospitable for life. We are an ever growing species. Our energy, food, and resource needs will soon outpace the population (if it already hasn't) and we will be left in the devistating wake of our own needs. Furthermore, consider this. An asteroid just nine kilometers across wiped out the dinosaurs. There are at least 100,000 asteroids this big or larger in our asteroid belt alone. We all live on this one planet. Care to gamble humanity?
Besides extraterrestrial influence and safety of the human species, finding an extrasolar planet hospitable to life would be an immense impact on the scientific realm. Just think of the astrophysical and geologic knowledge we could gain from the data obtained from an entirely different star system hosting a planet similar to our own. We would gain insight on what kinds of stars are suitable for life, how planet mass, density, and temperature influence that life, and finally, how that life affects us. We may have only explored 1% of earth's oceans, but we have observed just a minuscule fraction of a percent of all the stars, clusters, and galaxies in the universe. So, where do we start?
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| Hertzprung-Russel diagram of stars. |
The first step in finding a planet that is hospitable to life surely begins with finding the right star. Many wrongly assume that size and temperature of a star do not matter in finding such a planet, citing that, 'if the star is hotter, the planet just has to be farther away'. This is not entirely true. We must first look at stellar mechanics. The first thing to know about main sequence stars (normal stars, see diagram above) is that everything about them can be determined by their mass and composition. A star that is more massive has more gravity, which crunches its contents inward towards the core. This makes the pressure very high. As the internal pressure of a star increases, so does its temperature, and in turn, its luminosity. Luminosity, or brightness of a star, can also be thought of as energy consumption. This means the brighter the star, the faster it burns up its fuel. The lifetime of a star, then, is dependent upon two things: its mass (how much fuel it has), and its luminosity (how much fuel it is burning away). Knowing that our own sun has a lifetime of 10 billion years (10^10 years. There is a formula for computing this too, but it's much longer and not necessary for this blog), the formula for the lifetime of a star is:
T = (10^10)(M/Ms)(Ls/L)
Where:
T = stellar lifetime
M = mass of star
Ms = mass of sun
L = luminosity of star
Ls = luminosity of sun
Now, I know what you're asking, "what does stellar lifetime have to do with finding a planet suitable for life?" It turns out that planets need time to form. With that formation, a planet needs time to settle and mature before it would ever be suitable for life. On Earth, it took about 2.5 billion years for our planet to develop conditions that could satisfy life. If a star burns up faster than that time frame, a suitable planet can never form around it and can thus be discluded in our search for life-harboring planets. So, stellar lifetime (T) must be greater than or equal to 2.5 billion. This leaves us with two unknowns: M and L for the star in question. Fortunately, main sequence stars have predictable luminosity for known masses. Plugging in the numbers with Ms = 1 and Ls = 1:
2.5*10^9 = (10^10)(M/L)
M/L = 0.25
For main sequence stars with M/L = 0.25, M = 1.59 Ms (solar masses) and L = 6.39 Ls (solar luminosities). This mass corresponds to a mid-sized F class star, a little larger than our G class sun. This may seem like we're really narrowing our search, however, stars much more massive than our sun are incredibly rare. It turns out that only 1% of stars exceed 1.59 solar masses, so we really haven't cut much off of our search. It would seem like the planetary hunt can begin, but (as always), there's another hurdle in the way of finding a star acceptable for planetary life. Obviously a star can't be too large, but what if a star is too small?
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| An 'A' class star, about 2-3x the mass of our sun. Burns up too fast to form habitable worlds. |
In many ways, small stars (or red dwarfs) seem even more hospitable to life than our own sun. They burn for trillions of years, allowing plenty of time for life to evolve, and they are incredibly abundant, making up about 75% of all stars in the galaxy. However, there are some unforeseen dilemmas with life sustaining planets forming around small stars. The first problem is their magnetic activity. Smaller stars tend to experience increased solar activity, such as solar storms, much more frequently and violently than our own sun. This makes the survival of life around such a star quite difficult. In more massive stars, the interior stabilizes and consequently mellows any violent solar activity that might occur.
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| Artist's depiction of a magnetically active red dwarf star. |
Another major difficulty with life in a red dwarf system is a process called tidal locking. Tidal locking is the phenomenon where one side of a planet or moon always faces its host. This occurs when that object (like our moon) orbits too closely to the host and the tidal "bulges" of the host actually tug on the object gravitationally and slow its revolution. Over millions or billions of years, the object becomes tidally locked. In our solar system, this isn't a problem because our planet orbits so far away from our sun. However, the habitable zone distance for a red dwarf is much closer to the star, leading to accelerated tidal locking. One can see where this would be a problem with a life-stable planet around a red dwarf star. If one side of the planet always faced the star, that side would always be a baked crisp while the other would be a frigid tundra, both sides devoid of life. Fortunately for us, there is a formula for how long it would take for a star to tidally lock a host planet as well! The equation is:
T = (w*(a^6)*I*Q)/(3*G*(Ms^2)*k*(R^5))
Where:
T = Time to tidal locking
w = initial radial velocity of planet
a = distance from star
I = moment of inertia of planet
Q = dissipation factor
G = gravitational constant
M = star mass
k = Love's number (no, not 'love' the phenomenon)
R = radius of planet
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| A tidally locked planet, half desert, half tundra. |
Some of these variables are difficult to explain, but basically, tidal locking depends on the distance, radius, revolution and orientation of the planet at its formation, and the mass of the star at hand. Remember, we want the planet to be stable for at least 2.5 billion years, so we will set 'T' equal to that. 'a' is the distance from the star, which is really just the habitable zone distance of a red dwarf star. You may have noticed that we can't calculate 'a' if we don't know the mass of the star, which we are trying to solve for. To overcome this, we must write out 'a' as a function of luminosity which, in itself, is a function of mass for main sequence stars. Also, the variables 'Q','G', and 'k' are all just constants for any system. These numbers can easily be found or equated from information online. Finally, for the variables 'w', 'I', and 'R', I used the equivalent Earth values (because we are solving for an Earth-like planet). The formula is rough, but it comes out with a reasonable answer:
M = 0.568*Ms
This number indicates that any star with a mass of less than 0.568 solar masses will consequently lock any earth-like planet in a death stare for the remainder of its existence, quenching all and any chances of finding life there. This is the mass of a small K type star. This number is also a devastating blow to the percentage of habitable stars systems out there. 80% of stars in our galaxy have masses of 0.568*Ms or less, meaning that there is little chance of finding a life supporting planet around this vast majority of stars. Adding this to the 1% of stars that are too big for habitable planets, this leaves us with just 19% of stars in our galaxy that can construct life harboring planets.
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| A 'G' class, sun-like host star. |
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| A quadrinary system, a very unstable environment for habitable planets. |
In the large scale of the galaxy, 5.7% isn't a small number at all. This is equivalent to roughly one stable, single star for every 18 stars around it. In our galaxy alone, this is still 17 billion stars. The math seems to hold true for our plot in the galaxy as well. Within 20 light years of our own sun burns 150 stellar objects. of these 150 stars, 9 of them are single, main sequence stars between 0.568 and 1.59 solar masses (including the sun), or 6% of them. These stars may be the hosts of planets with strange and complex extrasolar life, or these planets may serve as a second home for humanity in the distant future. Whatever the future holds the most important thing is that we, as a race, remain curious as to what might be out there. Who knows, life might surprise us after all.
THE LIST: These are the 9 single stars between 0.568 Ms and 1.59 Ms within 20 light years of Earth. Enjoy!
1) Sun
-distance: 0 ly
-mass: 1.00 Ms
2) Epsilon Eridani
-distance: 10.52 ly
-mass: 0.82 Ms
3) Tau Ceti
-distance: 11.89 ly
-mass: 0.78 Ms
4) Lacaille 8760
-distance: 12.87 ly
-mass: 0.60 Ms
5) Groombridge 1618
-distance: 15.85 ly
-mass: 0.67 Ms
6) Wolf 1453
-distance: 18.53 ly
-mass: 0.57 Ms
7) Sigma Draconis
-distance: 18.77 ly
-mass: 0.88 Ms
8) 82 Eridani
-distance: 19.71 ly
-mass: 0.97 Ms
9) Delta Pavonis
-distance: 19.92 ly
-mass: 1.05 Ms
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