## Habitable Value

Planets at Kapteyn’s Star (source)

Since the last post on this blog, there have been two additional habitable planet candidates announced. First, a two-planet system orbiting the very nearby, very old red dwarf Kapteyn’s Star was reported by Anglada-Escudé et al. The inner planet, the habitable zone world, at 4.8+0.9-1.0 ME is probably a mini-Neptune or micro-Jovian planet, based on its mass — the overwhelming majority of planets of this mass whose radii are known are clearly low-density worlds. The outer world is a cold super-Earth, and probably the same type of planet. Kapteyn’s Star is a member of the Galactic halo, and is quite ancient at ~11 Gyr old. The apparent fact that the Universe was assembling habitable planets when it was less than 3 Gyr old may have interesting implications for the Fermi Paradox, but I won’t go into that here.

Next is Gliese 832 c. In 2008, Bailey et al. reported the presence of a Jupiter-analogue orbiting the nearby red dwarf system GJ 832, and then last week, we learned of second planet, a super-Earth type planet straddling the inner edge of the habitable zone, reported by Wittenmyer, et al. It is almost certain that this planet is not habitable, certainly not to life “as we know it.” The planet’s mass comes in at 5.4±1.0 ME, and therefore likely a mini-Netune / micro-Jovian, much like Kapteyn’s Star b.

Then wandering through the news as I do on a daily basis, I found this

Note the description of the planet as “among the most habitable,” with artist images depicting oceans, lush green land, and so on, despite the description of the planet in the discovery paper as

However, given the large mass of the planet, it seems likely that it would possess a massive atmosphere, which may well render the planet inhospitable. Indeed, it is perhaps more likely that GJ 832c is a “super-Venus,” featuring significant greenhouse forcing.

And this was being generous! I personally thought the discovery of planets at Kapteyn’s Star was much more interesting than the discovery of GJ 832 c, but apparently news cycles have a different standard than I do as to what amounts to an interesting world. That standard, with respect to exoplanet discoveries, is the Earth Similarity Index (ESI) that the Planetary Habitability Laboratory uses to evaluate a planet’s habitability. A quick look at their site shows that, sure enough, GJ 832 c is the third most highly ranked exoplanet.

This is not the first time I have complained about the PHL. But this time I will instead work on providing an alternative method of evaluating a planet’s habitability. A child could look at the above diagram and tell you Kepler-186f was the most “Earth-like” of those planets based on their appearance, but to be rigorous and useful, we need a system to quantify a planet’s habitability. Let’s first look at how the ESI is determined.

$\displaystyle ESI=\prod_{i=1}^n\left(1-\left|\frac{x_i-x_{i_0}}{x_i+x_{i_0}}\right|\right)^\frac{w_i}{n}$

Where $x_i$ is the n-th property of the planet — in this case, either radius, density, escape velocity or surface temperature — $x_{i_0}$ is the value of this property for Earth, and $w_i$ is the weight exponent of a property. For the parameters usually used by the ESI, these values are

 Property Reference Weight Exponent Radius 1 $R_\oplus$ 0.57 Density 1 $\rho_\oplus$ 1.07 Escape Velocity 1 $V_{e_\oplus}$ 0.70 Surface Temperature 288 K 5.58

The formula I will use to evaluate the habitability of an exoplanet will be rather anthropocentric – for all I know, solid, hot super-Earth-type planets like Kepler-10 b may be the most frequently inhabited planets in the Galaxy, but all I know of is Earth-life, and so this formula will be centered around finding Earth-like life. It will effectively be based on Guassian distributions, and will take the form

$\displaystyle H = \prod_{i=1}^4 \frac{1}{\sigma\sqrt{2\pi}}\exp\left(-\frac{(x_i-\mu)^2}{2\sigma^2}\right)$

Here, μ acts as a reference value much as in the ESI formula, σ describes the broadening of the distribution and will effectively be used to determine the tolerance of variation on a particular parameter, and $x_i$ is the parameter we look at. As the product sign suggests, we calculate this for each of four parameters and multiply the results. Here, the four parameters are the stellar temperature, planet mass, planet radius, and planetary insolation.

For the stellar temperature, I chose σ=0.001 and μ=5500, which is some 277 K cooler than our sun. It seems that early K dwarfs are probably a sort of “sweet spot” for planet habitability. As such, if you found an Earth-analogue around an early K dwarf, it would rank higher on this scale than Earth itself. For the planetary mass and radii, I chose μ=1.0 for obvious reasons, and chose σ=5 and σ=0.75, respectively — punishing radius pretty heavily. Lastly, I chose insolation values of μ=1 and σ=1. All values of σ are in terms of that of Earth. Lastly, the values were normalised to make 1 the highest achievable value.

Unsurprisingly, the Solar System is the clear winner, followed by Kepler-186 f, which I made a big deal about earlier this year. The GJ 581 system, which was celebrated as hosting the first habitable planet candidates in the latter years of the last decade, doesn’t even make it up to 10-5, nor does GJ 832 c.

 Planet H Earth 0.96635 Venus 0.61220 Kepler-186 f 0.18525 Kepler-62 f 0.09104 Mars 0.04304 Kepler-62 e 0.00530 Kepler-283 c 0.00005 Kepler-296 Af 0.00003

I would say this set-up makes a lot more sense than the one the PHL is using. Anything below 0.1 is probably not worth a raised eyebrow these days.

## 2013 Review

HD 106906 b, a directly imaged planet announced in 2013

First, foremost, and perhaps most painfully: α Centauri Bb may not really exist. What we thought was the Keplerian signal of an Earth-mass planet at our nearest neighbouring system may actually be noise in the data. While a bit painful, this is how science works – claims are rigorously tested and beaten tirelessly until they either continue to stand on the merit of the evidence, or they are refuted and disproved. This is how we keep the muck out of our pool of knowledge. Stay tuned… this could take a while to fully resolve.

The year began with direct imaging news: A new HST detection of Fomalhaut b (see here), suggesting the “planet” orbit is either not coplanar with the system disk or crosses the ring orbit and has a much lower mass than initially suspected. The imaged planet around β Pic b has also been independently confirmed. A circumbinary planet at 2MASS J01033563-5515561 became the first to be directly imaged. A planet with a mass of ~4 MJ became the lowest-mass planet directly imaged at HD 95086 (with the caveat that it isn’t clear what the nature of Fomalhaut b is). A planet perhaps of similar mass was later reported at GJ 504 (59 Vir).

Habitable zone discoveries started with the first known transiting Jupiter-sized planet in the habitable zone, PH2 b. Then things got very interesting with the simultaneous announcements of a super-Earth straddling the inner edge of the habitable zone of Kepler-69, and two habitable planet candidates at Kepler-62, which was covered here. HARPS found a nice system of planets around the M dwarf GJ 163. One of the planets is somewhat near the habitable zone, but it is my position that this planet does not deserve the attention worthy of a habitable planet candidate, with the planet receiving 40% more irradiation than Earth, and with the host star being an M-type dwarf, the atmosphere will not provide as much scattering of irradiation as Earth’s (Rayleigh scattering is increasingly efficient with decreasing wavelength), causing the surface of the planet to actually receive more than 40% more irradiation than Earth. Despite this, HARPS did provide us with another potentially exciting habitability result, with no less than three super-Earths in the habitable zone of GJ 667 C, with evidence for at least six, perhaps seven total planets there, however a reanalysis of the RV data seems to suggest that these new planets do not exist. Stay tuned…

Other noteworthy announcements included DW Lyn b, a giant planet orbiting a pulsating subdwarf B-type star. A hot Jupiter was also found orbiting a late-K/early-M dwarf by SuperWASP – a particularly rare find. A pair of super-Earths were found in a 2:3 resonance at HD 41248. A giant planet was found in a close orbit around a red giant branch star. Evidence of a second planet accompanying a newly discovered debris disk was presented for κ CrB. A super-Earth around HD 97658 was reported to be transiting (as was suspected two years ago but later dismissed due to a non-detection). The pair of planets at HIP 11952 ended up not existing – an error in compensating for the radial velocity of the observing site relative to the star.

Kepler results continued to stream in, starting with a rather interesting three-planet system at Kepler-68, with a mini-Neptune closest to the star, then an Earth-sized planet just outward of that, and a Jovian planet in a long-period orbit. It was shown that systems of multiple, low-mass planets uncovered by Kepler, like our own solar system, have orbits that are well-aligned with their host star’s equator (see here and here). Kepler results also uncovered a system with a pair of planets in a 2:1 resonance producing very strong transit timing and transit duration variations. A hot Jupiter at Kepler-76 provided strong evidence of super-rotation in the atmosphere via its secondary eclipse visible light photometry. Of particular note is the announcement of a planet smaller than Ganymede(!) at Kepler-37. A new population of small, rocky worlds in extremely short orbits was uncovered by Kepler, specifically Kepler-78 b wih its 8.5 hour orbit and KOI-1843.03 with its 4.2 hour orbit(!). Furthermore, Kepler unveiled the first transiting planets in an open cluster, NGC 6811.

Of particular note is the discovery of a transiting hot Jupiter orbiting a young, oblate, gravity-darkened T Tauri star. This remarkable system seems to imply that the formation mechanism behind hot Jupiters is fairly fast.

Exoplanet catalogues for WASP and Kepler saw their first triple digit identifiers, with WASP reaching WASP-100 and several Kepler planets being assigned triple digit Kepler-ID’s as well (e.g., Kepler-114, Kepler-128, Kepler-177, …).

While Kepler suffered another reaction wheel failure, effectively ending its primary mission, the year ended on a positive note with the launch of Gaia, which will likely find as many planets as Kepler, but in more intermediate period orbits and closer to the solar system.

## A Potentially Habitable Planet

Kepler-62 f

Recently, the Kepler-62 and Kepler-69 systems were made public. The first of these is quite interesting, with a Mars-sized planet sandwiched between two super-Earths in short period orbits, with two super-Earth-sized planets in or near the habitable zone further out.

A 1.6 Earth-radius planet, Kepler-62 e, is in the inner edge of the habitable zone. It’s impossible to be sure yet but it’s radius implies it could have a substantial amount of volatiles such as water. The planet may have a thick ocean layer going so deep that the pressure results in an ice layer between the liquid water layer and the rock layer, much as in Neptune-type planets.

Securely in the habitable zone, Kepler-62 f is a 1.4 Earth-radius planet. It gets about as much insolation from its star as Mars does from the sun. With a much larger radius and surely higher mass, it probably has a thicker atmosphere and so it all works out to where Kepler-62 f could very well be a habitable world.

The presence of multiple super-Earths inward of the f planet implies there has been some migration in the system, and it’s therefore possible that the f planet formed beyond the ice line and acquired a significant amount of volatiles. It’s possible Kepler-62f represents an ocean planet. Or for a slightly higher rock/water fraction, it could have continents and surface life on dry land. With what we know now, it is completely impossible to say.

Still, the fact that such a world has been found is greatly encouraging. It is by far the most promising habitable planet candidate.