## 2014 Review

Comets orbiting β Pic (Credit: ESO)

Results from Kepler data continued to stream in. We were graced with the discovery of a transiting Uranus-sized planet in a 704-day orbit. This is the first time a transiting planet has been discovered beyond its system’s ice line, and this may even be where the planet formed, instead of the typical case for transiting planets where we see them were they are today because of extensive inward migration in their past. Kepler’s 10th transiting circumbinary planet was reported, Kepler’s second multi-planet system orbiting a sdB star was announced and Kepler’s second disintegrating short-period planet was identified.
Kepler short-cadence data may have allowed for the detection of a non-spherical (oblate, like Saturn) exoplanet for the first time, by looking at photometry for Kepler-39 b. While the planet itself is unremarkable, a transiting sub-Neptune around HIP 116454 marks an exciting development: The first planet discovered by Kepler during it’s new “K2” mission.

The dramatic turn of events in the investigation of the planetary system at GJ 581 seems to have finally come to a conclusion. In 2007 a media frenzy accompanied the discovery of two new planets found to accompany the known 5-day Neptune. The innermost of the two new planets was a 5 Earth-mass planet in a 12-day orbit, and a 7 Earth-mass planet in a 80-day orbit. The 12-day planet was hailed as the first habitable planet candidate, despite getting more stellar insolation than Venus. In 2009, an Earth-mass planet at 3-days was found, and the new dataset brought the orbit of the 80-day planet closer to the star, down to ~60 days. Since most people had come to their senses regarding the habitability of the 12-day planet, the 60-day planet became the flag-bearer for habitability in the GJ 581 system. Everything changed in late 2010 when a 3 Earth-mass planet in the habitable zone was announced by the HARPS team. This was truly the most habitable exoplanet candidate known to date… if it were real. Multiple studies drawn out over the following several years debated back and forth how many planets exist around GJ 581. Three? Four? Five? Six? It depended on how you merged your datasets, how you handled noise in your data, and so on. This year, the issue seems to have been resolved by carefully examining the H-alpha lines of the star’s spectrum and finding variation in them that had affected the stellar radial velocity measurements. When corrected for, suddenly all of the habitable zone planets vanished. As of the end of 2014, there are no habitable planet candidates orbiting the star that only a few years ago was unanymously acknowledged to be the most promising extrasolar planetary system for habitability. Interestingly, a similar story may be unfolding at GJ 667, where some planet signals have turned up missing in other studies of the RV data. The morale of this story? Finding low-mass planets is hard.

HARPS continued to give us new planets, but the pace seemed somewhat slow. Some interesting results are the presence of planets in the cluster M67 (link). Planets were found orbiting the stellar companion to XO-2, as well, making the system an example of a binary system with planets orbiting both components. Interestingly, both host at least two planets, and one of each of them are a hot Jupiter. The hot Jupiter around the other star doesn’t transit, suggesting some misalignment between the two planetary systems. Other HARPS results included the identification of two families of comets around β Pictoris, with the identification of hundreds of individual comets through via transmission spectroscopy through their tails.

The news media nearly peed their pants with excitement over the discovery of a planet that, most optimistically, isn’t habitable now, nor has it ever been, in the habitable zone of the very nearby Kapteyn’s Star. Similar unwarranted attention was given to a mini-Neptune discovered in the habitable zone of GJ 832. While the excitement that planets like these get is unwarranted, it is at least gratifying to see the general public so interested in planets that vaguely resemble something habitable-ish. I just hope that when we do find more planets that are more like Earth, the interest hasn’t faded away already. HIRES also found a super-Earth orbiting the very nearby star GJ 15.

We saw first results from the Automated Planet Finder, a radial velocity based system to look for planets in the solar neighbourhood. The project gave us a nice four-planet system orbiting HD 141399 and aided in the discovery of a Neptune-mass planet at GJ 687. We also got to see first results from ESO’s SPHERE instrument.

A number of naked-eye stars were found to have planets, as well, such as planets around β Cnc, μ Leo, β UMi and one around σ Per.

On the direct imaging, we got a new planet imaged orbiting GU Psc with a mass ratio of ~30 and a separation of ~2000 AU… which seems more like a low-mass binary star than a true planetary system. Also, while not planets, ALMA observations of HL Tau have revealed increible detail showing planet formation carving out gaps in the circumstellar disk.

Microlensing gave us a hand-full of planets this year, among the most interesting is OGLE-2013-BLG-0341L Bb, a terrestrial-mass planet orbiting the secondary component of a binary system with a projected separation of 15 AU. For the microlensing event OGLE-2014-BLG-0124L, the event was observed both from the ground and from Spitzer, making the first joint ground+space detection of an exoplanet microlensing event. Observing the event from two different perspectives allowed for the distance to the lens to be accurately measured.

In early year-review posts, the hints of a planetary ring system around a planet orbiting 1SWASP J140747.93-394542.6 has been discussed. We now find that radial velocity observations of the star have place limits to the mass of the orbiting body, restricting it to a planet or brown dwarf. The rings do exist, and they extend far enough away from the planet to expect them to form moons.

2014 has been an interesting year. A thousand planets have been reported this year, mostly because of Kepler’s enormous contributions. It’s hard to know what 2015 will bring. RV surveys are continuing, and there are still thousands of Kepler candidates awaiting confirmation.

## 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.

## A Thousand Planets

Depending on where you get your information from and how much weight you lend it, we have reached a thousand known planets.

Some of the semi-official sites like exoplanet.eu and more official sites like NASA’s Exoplanet Archive show less than this number. In the case of the latter because it appears they only accept planets that have made it past peer review, which is a reasonable, if not high, standard. In the case of exoplanet.eu, while it has been a valuable asset since 1995, it has missed a few planets here and there as time has gone on (especially during a recent overhaul of the site). There’s a number of other anomalies there, but it’s a site run by a guy in his spare time so there’s a limit to how much you can expect of it. That being said, it’s still a very valuable resource.

There exists a fairly small group of people, myself shamelessly included, who keep tabs on extrasolar planet news and developments nearly religiously. The count varies from person to person, but I am not alone in asserting that there are now 1,000 known planets. By my count, we’ve passed that a couple months ago, but I’ve decided to give it more time to help cover some margin for error in the planet count.

Where does this margin of error arise? There’s a number of planets whose disposition is not very clear. They have been proposed and later disputed, but not fully disproven. There are planets that are unconfirmed, but confident enough that they can be talked about as real planets. And lastly there are Kepler candidates that have been determined to be planets, but in some cases have not even been included in a preprint on arXiv yet. As such, it is not possible for me or anyone to point to a specific planet and say “this is the thousandth known planet.”

In the big picture, humanity’s first thousand planets is only the top layer of H2O molecules of the iceburg of the planet population in the Galaxy. It is severely plagued by biases in favour of short-period and/or high-mass planets due to the nature of our detection methods and completeness of our detection surveys. We have found many hot Jupiters, but we know full well that this is a minority (less than 1% of stars have a hot Jupiter). It’s clear that small planets are more prevalent, it’s just a matter of detecting them.

Recently, it was announced that the nearby M dwarf GJ 667C hosts three super-Earths in its habitable zone. Taken together with the two habitable planet candidates at Kepler-64 and single habitable planet candidates in other systems, we have about a dozen targets for a search for life. Some of these planets are better candidates than others, and I won’t encourage any undue optimism by refraining from being outright by saying that some of them appear pretty unlikely candidates – a few of them look like we’re scraping the bottom of the barrel in desperate hope (I’m looking at you, HD 40307 g, GJ 163 c, Kepler-22 b, GJ 581 d).

Still, the fact that our first thousand planets contains at least a few planets where it’s not impossible for life to exist there is encouraging, especially when considering how biased our detection methods are against them. Combined with Kepler data that tells us that habitable planets are ubiquitous in the Galaxy, I am actually quite optimistic about the odds for there being a second biosphere in the solar neighbourhood.

We have learned so much in the first thousand planets, detected at a slow rate at first, but growing to over a hundred per year. It has taken us 20 years to detect the first thousand exoplanets. I would not be surprised if the next thousand come in only five years and feature many more habitable planet candidates.

Lastly, I have been dealing with some events in my “personal life” that have kept me busy, and so I have had less time to focous on extrasolar planet science and writing about it here. This is partly why this post doesn’t have a lot of meat to it. I look forward to writing more enlightening posts in the near future.

## The Real Ones

On the last post, we looked at recovering a periodic signal from a radial velocity plot and interpreting it as a planet. Now let’s look at a few of the complications involved in this.

A powerful statistical tool used to get an idea of what kind of periodic signals are in your radial velocity data set is a Lomb–Scargle periodogram (the mathematical details for the interested reader may be found here, but it is sufficiently complex to warrant skipping over in the interests of maintaining reader attention and reasonable post length). In the interests of brevity, further references to the Lomb-Scargle periodogram will be shortened to simply “periodogram.”

The purpose of this periodogram is to give an indication of how likely an arbitrary periodicity is in a data set whose data points need not be equally spaced (as is frequently the case in astronomy for a variety of reasons). Periodicities that are strongly represented in the data are assigned a higher “power,” where periodicities that are not present or only weakly present are given a lower power.

Let’s look at an example using a radial velocity data set for BD-08 2823 (source) If we calculate a periodogram for the data set, we come up with this

BD-08 2823 RV Data Periodogram

The dashed line represents a 0.1% false alarm probability (FAP). A clear, obvious peak is seen at 1 day, 230 days and ~700 days, implying that periodicities of 1 day, 230 days, and ~700 days are present in the data. Creating a one-planet model with a Saturn-mass planet at 238 days produces a nice fit. After subtracting this signal from the data, we’re left with the residuals. Now we may run up a periodogram of the residuals and see what’s left in the data.

BD-08 2823 Periodogram of Residuals

We see three noteworthy things. First and foremost is the emergence of a new peak in the periodogram that was not strongly present before at 5.6 days. We also see that the peak at 1 day remains. Lastly we see that the peak toward 700 days has weakened and moved further out. It would seem to suggest the 700-day signal is perhaps not real, or was an artifact of the 238-day signal.

Why was the 5.6-day signal not present in the first periodogram? The answer may lie in it’s mass: the planet has a mere 14 Earth-masses. It’s RV signal is completely dominated by the Saturn-mass planet. The giant planet forces the shape of the RV diagram and the signal of the second planet is just dragged along, superimposed on the larger signal.

On the radial velocity data plot, the two-planet fit we have come to looks like this:

BD-08 2823 Two-Planet Fit

It is important to realise that the obvious sine curve is not necessarily a bold line, but there is a second periodicity in there going up and down frantically, once every 5.6 days, compared to the Saturn-mass planet, at 237 days.

The fit has a reduced chi-squared of χ2 = 3.2, and a scatter of σO-C = 4.3 m s-1. There’s no obvious structure to the residuals and the scatter is not terribly bad, so any new signals will likely indicate planets of low mass. Let’s check in on the periodogram of the residuals to the two-planet fit and see what may be left in the data.

Periodogram of Residuals to 2-Planet Fit

That signal out toward a thousand days is stubbornly refusing to go away, despite a low χ2. It may either not be real, or it may be indicative of a low-amplitude signal with a rather long period.

Also noteworthy is that the periodicity at one day continues to exist, rather strongly. This periodicity is what’s known as an alias. Because the telescope observes only at night, the observations are roughly evenly spaced – there are (on average) twelve hour gaps between each data point. Therefore a sine curve with a period of 24 hours can be made to fit the data. To illustrate this, consider this (completely made up) data set:

Fake Signal

There’s no doubt that the data is well-fitted by the sine curve, but there is no real evidence that the periodicity proposed by it arises from a real, physical origin. What’s more, a sine curve with half this period could also equally well fit the data. So could a sine curve with a third of this period, and so on. There are mathematically an infinite number of aliases at ever-shortening periods that can be fit to this data.

Generally, if you observe a system with a frequency of $f_o$, and there exists a true signal with a frequency of $f_t$, then aliases will exist at frequencies $f_{t+i} * f_o$, where i is an integer.

Therefore we see that these aliases are caused by the sampling rate. If we could get data between the data points already available, if we could double our observation frequency, we could break this degeneracy. But the problem for telescopes on Earth is that the star is not actually up in the sky more than half the day, and a given portion of the time it is up could be during daylight hours. Therefore the radial velocity data sets of most stars can be plagued with short-period aliases since there is typically a small window of a few hours to observe any given star. It must be noted that as the seasons change and the stars are in different places in the sky at night, that window of availability will shift around a bit, allowing one some leverage in breaking these degeneracies. Ultimately, telescopes in multiple locations around the world (or one in space) would sufficiently break these degeneracies.

A real example of aliases exist in this example from an Alpha Arietis data set. In this case, the alias is not nearly so straightforward. Two signals of periods 0.445 days and 0.571 days can be modelled to fit the data.

Alpha Arietis RV Alias

So which of these two signals correspond to an actual planet? It turns out neither of them do: these radial velocity variations are caused by pulsations on the star – contracting and expansion of the star produces Keplerian-like signals in radial velocity data, too. That’s yet another thing to watch out for. This can be detected with simultaneous photometry of the star. If there is a photometric periodicity that is equivalent to your radial velocity periodicity, avoid claiming a planet at this period as if your academic credibility depends on it.

Additional observations could easily break this degeneracy, provided they are planned at times where the two signals do not overlap.

We see therefore that it is important to keep in mind that a low FAP speaks only to whether or not the signal is real, and not where or what it actually came from. The one-day periodicity is surely present in the data, but it is not of physical origin. It can also be extremely hard to tell whether or not a signal at a given period is actually an alias of another, more real period. There are times when the peak of an alias in the periodogram can be higher than the actual, real period. For reasons that include these, radial velocity fits must be considered fairly preliminary. New data may provide drastic revisions to the orbital periods of proposed planets if signals are exposed to be aliases.

Confusion over aliases have occurred before in literature. HD 156668 b and 55 Cnc e have both had their orbital periods considerably revised after it was realised that their published periods were, in fact, aliases. In the case of 55 Cnc e, the new, de-aliased orbital period ended up being vindicated after transits were detected). The GJ 581 data set, for example, is severely limited by sampling aliases that have spawned controversies over the possible existence of additional planets in that system.

In summary, periodograms are a useful tool to provide the user with a starting point when fitting Keplerian signals to radial velocity data, but they cannot distinguish real signals from aliases. Many observations with a diverse sampling rate are necessary to disentangle aliases from true planetary signals. Ultimately, a cautious approach to fitting signals to radial velocity data works best.