Wednesday, March 13, 2013

How many habitable Earths are out there?

Now for the second installment of my two-part report on recent publications by Ravi Kopparapu. This time I shall report on A Revised Estimate of the Occurrence Rate of Terrestrial Planets in the Habitable Zones Around Kepler M-Dwarfs (Kopparapu 2013). This paper builds off of his previously discussed Habitable Zones paper by applying the calculated habitable zone boundaries to estimates of how many Earth-like planets are orbiting small, cool stars known as M-dwarfs, or red dwarfs. Ravi was inspired by a recent publication by Dressing & Charbonneau (2012) making very similar calculations. Dressing & Charbonneau (2012) predicted 0.15 habitable planets for each red dwarf, while Kopparapu (2013) predicted, at a minimum, three times that number. The main difference is that Dressing & Charbonneau was published before Ravi's habitable zone paper and, therefore, used the habitable zone estimates from Kasting et al. (1993). Just a month after publication, Dressing & Charbonneau (2012) was already out of date!

Man. I hope you made it through that paragraph alive! Don't worry though, it gets much more comprehensible from here.

Both of these papers used data from NASA's Kepler mission to estimate the number of planets orbiting red dwarf stars at a distance that would put them in the star's habitable zone. How they did this is particularly interesting, and definitely worth some explanation.

The Kepler mission is designed to detect exoplanets that transit (or eclipse) their host stars by looking for the decrease in light that happens when the planet is blocking some of its star's light. Of course, only a very small fraction of planets are in systems with exactly the right alignment that we can see them transit. Fortunately, we can account for this statistically. What it amounts to is determining the probability that any random planet orbiting a random star will transit its star, and turning that on its head. As a very simple example, if we knew that 1 out of every 100 stars hosting a planet would feature a transiting planet (we can calculate this probability) and we detect 4 transiting planets, we expect that there are probably around 396 planets that we can't see transiting.

Dressing & Charbonneau (2012) and Kopparapu (2013) both made this calculation specifically for planets in the habitable zones of red dwarf stars. But what is an red dwarf, you may ask, and why do we care? Red dwarfs are a class of star with the lowest possible temperature and mass range that an object can have and still be a star (any lower and it would be a brown dwarf, which I briefly discuss here). Because of their low masses, red dwarfs are also not very luminous. The advantage this has for the star is that it means the star can have a very long lifetime. The typical lifetime for an red dwarf is around 100 billion years (or more), which is 10 times longer than that of the Sun, and around 7 times longer than our universe has even existed!

Red dwarfs also have another interesting advantage in that they are, by far, the most common type of star in the Milky Way, making up an estimated 75% of all stars in our galaxy. This is due to a very interesting and surprisingly consistent trick of nature that the universe prefers to make more small things than it does large ones (stars, galaxies, planets, asteroids, etc.). Because red dwarfs are so common and have such long lifetimes, astronomers who study exoplanets have long been excited about the prospects for life on planets around red dwarfs.

In my previous post, I addressed the ways that Kopparapu et al. (2013) calculate the inner and outer edges of the habitable zone given their new climate model. But there is another way to calculate habitable zone boundaries that is also addressed in their paper that I have saved until now. These are the so called "recent Venus" and "early Mars" limits for the inner and outer edges, respectively. In short, these limits come from our observations of each planet and our inferences regarding how long they have been without liquid surface water. For Venus, this is at least 1 billion years ago and for Mars, this is about 3.8 billion years ago. A key point here is to note that the Sun has steadily increased in brightness over time for fairly well-understood reasons that will not be addressed here. (Though I may cover it in a later post; I *do* like stellar evolution.)

By combining the respective locations of Mars and Venus with the times at which we think they last had water, we can determine the solar flux on each planet in the past. Knowing this, we can scale that flux to the Sun's modern luminosity and determine the distance from today's Sun that would correspond to the received fluxes on recent Venus and early Mars. This yields an inner edge of 0.75 AU and an outer edge of 1.77 AU. Note that these limits allow for a much wider range of habitability. As such, these limits on the habitable zone boundaries are referred to as the optimistic limits. To see the actual calculations done out, you can read either of Ravi's recent publications.

For the paper I am currently addressing, Ravi did the above calculation, but replaced the Sun with a red dwarf star along with running the new climate model to get the more conservative habitable zone limits. Kopparapu (2013) also allowed for a larger range of planetary radii to count as being Earth-size. Where Dressing & Charbonneau used the range of 0.5-1.4 REarth, Ravi used the range of 0.5-2.0 REarth (where REarth is the radius of the Earth).

Given this increased size range and the new habitable zone models, Kopparapu (2013) concluded that the conservative (model-derived) limits on the habitable zone yield an estimate of 0.51 habitable Earth-like planets per red dwarf, while the optimistic estimates yield 0.61 habitable Earthlike planets per red dwarf. Even without the increased planetary size range, Kopparapu (2013) calculates a conservative estimate of 0.48 and an optimistic estimate of 0.53 habitable Earths per red dwarf.

Wow. In short, even if we're not feeling very optimistic, it seems that every other red dwarf should have an Earth-like planet orbiting in the habitable zone. As someone just itching to be able to find life elsewhere in the universe, these results seem pretty promising.

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