"You can spend too much time wondering which of identical twins is the more alike." -Robert Brault

You've of course heard by now the news that Kepler, the most successful and prolific planet-finding mission of all time, has probably reached the end of its useful lifespan.

Image credit: NASA / Kepler Mission / Wendy Stenzel.

With nearly 3,000 planet candidates under its belt, including many approximately Earth-sized (and some even smaller), and many within their parent star's habitable zone, we now know that, at least planet-wise, we're not alone in our galaxy.

Image credit: NASA Ames / JPL-Caltech.

In fact, there are at minimum some 17 billion Earth-sized planets just in the disk of the Milky Way. But it takes a lot more than that to make a genuine twin of the Earth! Yes, we've taken some amazing steps forward in the past few years, but let's not lose sight of the ultimate goal here: to find another planet that harbors some type of advanced life.

Image credit: Museum Mensch und Natur in München / Wikimedia Commons user Ghedoghedo.

That is, chemical-based life akin to what we know on Earth. Even if it were akin to life on Earth as it was 500 million years ago, that'd be incredibly interesting! There are plenty of other possibilities than the chemical-based kind we've developed and grown accustomed to here on Earth, and in fact that may actually be more common in the Universe than the life we know.

There are some good reasons to believe this.

Image credit: the Morgan-Keenan spectral classification / Wikimedia Commons user LucasVB.

Our Sun is a 4.6 billion year-old G-class star. While you might look at the diagram above and think this makes us an "ordinary" star, the fact of the matter is our star is more massive than 95% of all stars out there! M-dwarfs, the little red guys all the way on the end, are by far the most common star type in the Universe, with three-out-of-every four stars being M-stars. In addition, our oceans will boil after another billion years or so, but M-stars burn at a stable temperature for up to tens of trillions of years!

Image credit: Expedition 13 / ISS / NASA / United States Government Works.

But that's a digression that could lead us far off course; if we're looking for Earth's twin, or a planet that's an awful lot like our own around a star that's a lot like our own, let's think about what we'll need.

First off, we'll need a star like the Sun. That means a star of both the same temperature and spectral class, but also of roughly the same age.

Image credit: Retrieved from Margaret Murray Hanson at University of Cincinnati.

It takes time for life to develop and evolve into something interesting, and that means we need a star system that's at least many billions of years old. But we also can't wait too long, because as stars age, the region of the core that fuses hydrogen into helium grows, meaning that power output (and brightness, and hence temperature) increases. Eventually, the planets (like Earth) that were once habitable will get too hot, permanently boiling the surface water and ending life-as-we-know-it.

So let's say we've got about a billion-year-window, or about 10% of the life of the star. There are some 200-400 billion stars in our galaxy, and about 7.6% of them are G-class stars, or the same type as our Sun. Even though our Sun is more accurately classified as a G2V star, that still means that around 10% of all G-class stars are the same type as our Sun.

Image credit: NASA's Solar Dynamics Observatory.

Estimating on the high end, that should tell you that there are 400 billion stars, 7.6% of which are G-class, about 10% of those are the same sub-class as our Sun, and about 10% of those are the right age to have interesting life, or some 300 million candidate stars.

Well, maybe. You see, we need something more than that.

Image credit: Nigel Sharp, NOAO / National Solar Observatory at Kitt Peak / AURA / NSF.

This is the spectrum of the Sun. Or, in other words, these lines you see are representative of all the different atoms -- and their ratios -- that come from the period table of elements. They're abundant in our Sun, and they come in very specific ratios.

The amount of everything that isn't hydrogen or helium to all the fuse-able material in the Sun is what astronomers call metallicity. If we want an Earth-like world, we need a star with a Sun-like metallicity.

Image credit: Wikimedia Commons user Rursus, based on Gunnar Larsson-Leander's work.

This isn't so bad; as many as 25% of the stars that were formed around the same time as our Sun were Intermediate Population I stars (like we are), and a great many of them (perhaps around 15% of those) have the same metallicity as our Sun, shown in green, below.

Image credit: Zeljko Ivezic/University of Washington/SDSS-II Collaboration.

That means there are some 11 million stars in our galaxy that have the same type of home star we do, with the same abundance of heavy elements, that formed at the right time that they could have complex life on their worlds the same way Earth does. (And this doesn't even take into account that many of the worlds with more or fewer metals could be more likely than Earth to have life. Like I said, just because it happened under our conditions does not mean our conditions are the most favorable for complex life to have happened!)

So out of these 11 million solar "twins," how many of them have Earth-twins in their habitable zones?

Well...

Image credit: NASA / JPL-Caltech / T. Pyle.

We need to form a rocky planet of the right size with the right elemental abundances, the right amount of water, and in the right location to be considered a twin of the Earth.

These problems are all inter-related. The first one is easy: if the central star has the right elemental abundances, then the planets it formed should have the same density-radius relationship as our Solar System does.

Image credit: Dimitar D. Sasselov, Nature 451, 29-31 (2008).

It's difficult to say how abundant this is, because Kepler wasn't really sensitive to that sort of information. If we make our best "guesstimate" using what we know, about 4% of Sun-like stars will have Earth-sized planets in the inner Solar System, and using what we know from simulations of orbital mechanics, maybe 10% of those systems will have an Earth-sized planet in a similar location to Earth around our Sun.

Illustration credit: NASA.

All of which is to say, based on the best that we know right now, there ought to be some 45,000 Earth-twins out there with the same age and the same elemental abundances as ours, and in orbit around a star virtually indistinguishable from our Sun.

To find out how many are more like identical twins than fraternal twins, we need to know a few more things we have no data about yet.

Image credit: (c) Lynette Cook. (Yes, this is artwork!)

How many of those have both significant oceans and continents like we do?

How many of those have rapid rotations between night-and-day like Earth and Mars do, but like Venus and Mercury don't?

And then, we can get to the real questions, like how many of them had life develop on them? Complex life? How many of them have oxygen-rich atmospheres? How many have magnetically active dynamos in their core?

Image credit: Joe Tucciarone.

And maybe the most restrictive in the search for an Earth-twin: How many have a substantial Moon like we do?

Regardless, what I wanted to impress upon you are the following three things, even if you take nothing else away:

Most of the planets we're finding, that we call "Earth-like" (or even Earth-twins if we're feeling poetic) are more like distant cousins, with more differences than similarities. True "twins" of the Earth, where a planet has the same size, elemental abundances, rotation period, a similar Moon, the same age, and orbiting a virtually identical star are really, really rare; there may only be a handful in the entire galaxy when all is said-and-done. But if we're looking for complex life, there's no reason to restrict ourselves to Earth-twins; much of what we adore about our planet might not even be the optimal conditions for complex life to have developed!

But -- even with Kepler in the rear-view mirror -- what we know now is incredible.

Image credit: NASA / Ames / JPL-Caltech.

Unless we're grossly wrong about a whole bunch of things, the conditions for complex life are everywhere in our galaxy, and they're there right now. An Earth-twin might be romantic, but it's a horribly restrictive way to seek out the most distant of our cosmic cousins. Our search continues.