concerning the uniqueness of Earth

Is Earth totally unique? Perhaps it is, as reported by a recent study covered in a few places.

This would be kind of sad, in a way. No aliens to meet, and no other planets like the Earth… an awful waste of space, as Carl Sagan called it. It’s also an odd idea, philosophically, because for hundreds of years astronomers have considered the Earth as nothing particularly special (the “Copernican Principle” from the article). This idea has been backed up by discoveries that the laws of physics and the laws of chemistry are the same everywhere in the universe… If that’s true, there should be nothing preventing the processes that formed the Earth from happening somewhere else.

Still, there has been a persistent line of thinking called the Rare Earth hypothesis, which claims the circumstances that led to the Earth are simply so uncommon that, statistically speaking, they won’t have happened anywhere else. The Rare Earth argument has been going back and forth for decades now – case against, the fact that there ARE planets (lots of planets) around other stars; case for, SETI’s complete lack of signals from aliens. There are many other arguments, but you get the idea.

The articles make it look like this paper is on the “Rare Earth” side of things… but it’s not really.

Apollo 8 image (NASA) and starfield by David DeHetre under CC2.0

The actual paper is on the astronomy preprint server and can be found here.

What Zackrisson and collaborators have done is combine the observed statistics of planets with models of how galaxies and stars form. Now that we know of thousands of planets (from radial velocity “wobble” and Kepler-style transiting planet surveys, and more exotic techniques like microlensing), there are all kinds of patterns emerging about how planets form around stars, and where, such as:

  • that Jupiter-sized planets are rare around tiny M dwarfs but Neptune- and Earth-sized ones are not.
  • or that stars with lower amounts of heavy elements (heavier than helium, anyway – carbon, nitrogen, oxygen, stuff like that, that astronomers lump together as “metals”) have fewer Earth-sized planets but their rate of having Jupiter-type planets is unaffected.

The authors have taken observed principles like those and combined them with galaxy formation models so that they can determine what kinds of planets form at every stage of a galaxy’s lifetime, and what the sum-total population should look like now. They then applied those principles to create other galaxies, and determine what the planet formation in the entire visible UNIVERSE would look like.

What they find is that most terrestrial planets (between 0.5 and 2 Earth radii, and 0.5-10 Earth masses) are probably much older than the Earth – over 8 billion years old. Most planets are in slightly larger galaxies than the Milky Way, because the conditions that are likely to form planets are more likely to occur in larger galaxies, and, well, they have more stars. Only 15% of all planets formed have been destroyed by their host star dying; that’s because most of them orbit the extremely common and rather small K and M dwarfs that can live longer than the current age of the universe (13.7 billion years).

Overall, there’s about 1 planet for every two solar masses of star, preferentially slanted toward tiny stars having LOTS of planets. And there’s 8×10^20 terrestrial planets (800,000,000,000,000,000,000) in the Universe. (I presume the press release was done with a slightly different draft that had 700 quintillion, not 800 quintillion)

The authors then whittled that down to REALLY earthlike planets. They threw out planets with radii over 1.5 Earth radii because some of them might be tiny gas giants, and planets orbiting M dwarfs because they’d be tidally locked (one side always facing the star) and probably inundated with stellar flares. This left 2×10^18 planets (basically, a quarter of a percent of the original population)

And that’s more or less where the paper ends.

The claim made in the article that the Earth is completely unique rest on two things:

One, planets are found 400 times more often around M dwarfs than FGK stars, so the fact that the Earth is around a G-type star is unusual. As many have pointed out, there may be reasons that M dwarf planets aren’t habitable, so it might NOT be so much of a surprise. Of course, if this is a violation of the Copernican Principle, it’s one we’ve sort-of been living with for a long time, because we’ve known for years that the Sun is more massive than 95% of all stars. (Yes, stars can be 100-200x more massive than the Sun, but those stars are incredibly rare).

Two, that 3/4 of the terrestrial planets should be in larger spheroidal galaxies, so having the Earth be in a disk galaxy like the Milky Way is a 1 in 4 chance. That’s not a terribly strong argument, and they say that in the paper.

So, the Earth is definitely rare. I’ll buy that. But their own math doesn’t make the sun completely unique; you’re still talking about quadrillions of planets potentially like the Earth. And that’s not accounting for the fact that their complete-universe sample was looking at the OBSERVABLE universe. In a universe that’s only 13.7 billion years old, galaxies 10 billion light years away can only be 3.7 billion years old. They haven’t had the time to get as big, or go through as many rounds of star and planet formation as the Milky Way. Quoting the paper:

A typical galaxy in the mass range of the Milky Way (stellar mass 4–6×10^10 M⊙; McMillan 2011) is expected to harbour ≈1×10^11 TPs around M stars and 2×10^9 TPs around FGK stars. (page 4, Zackrisson et al. 2016)

Two billion terrestrial planets in the Milky Way.

Let’s make some crude calculations with some assumptions. One, we’re going to assume the Milky Way is a disk-shaped cylinder (it isn’t; it’s more of a fried egg shape that tapers at the edges) with a radius of 60,000 light years and a height of 1,500 light years. Two, we’re going to assume the terrestrial planets (and their stars) are uniformly distributed throughout the volume of the Milky Way (they’re not; they’re more concentrated toward the galactic center).

The volume of a cylinder is pi x r^2 x h, so that’s pi x 60,000^2 x 1500 = 16,960,000,000,000 cubic light years.

If there are 2 billion terrestrial planets scattered throughout that volume, then that’s one terrestrial planet for every 8500 cubic light years of space.

Take the cube root of that to get the actual distance (average distance, really) between planets, and you get 20 light years. That’s much too far to travel right now, but as things go… that means (statistically speaking) one of the 200 closest star systems to Earth should have a terrestrial planet. If you throw in the hundred billion terrestrial planets around M dwarfs, you get 1 planet in every 169 cubic light years of space, and an average distance of 5.5 light years between them. That’s basically the distance between star systems. Only alpha Centauri (4.3 light years) is closer to us than that.

So… are terrestrial planets around solar-type stars rare? Technically, yes. But they’re still out there by the billions, and I think that leaves us exactly where we were before: in a universe teeming with exoplanets, waiting to be explored. If we can solve warp drive, of course.


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