NASA’s Kepler mission has announced the discovery of 1,284 newly confirmed planets, raising the total confirmed exoplanets to more than 3,000. While this is a big step forward in exoplanet astronomy, it is also part of a shift in how exoplanets are discovered. That’s because these new planets weren’t discovered individually, but rather through an automated algorithm that gives candidate planets a statistical thumbs up or down.

Exoplanets found by Kepler. Credit: NASA/Wendy Stenzel

The Kepler spacecraft discovers planets by measuring the varying brightness of stars in a small region of sky. As a planet passes in front of a star (such as the recent transit of Mercury) the star dims by a small but measurable amount. By watching for dips in brightness that repeat on a regular basis, astronomers can verify that a planet is orbiting a star.

Raw data for a transiting planet. Credit: Cloudy Nights member btieman.

In principle the process is straight forward, but in practice it can be extremely difficult. Stars have some natural variation in brightness due to things like solar flares, and starspots moving across the surface of a star can look quite similar to a transiting planet. So there is always the potential of getting a false positive. There have been instances where a planet was added to the list of confirmed exoplanets and then later removed upon further analysis. It takes careful analysis to distinguish a real planet from a poser, and it isn’t something that can be done quickly by hand. But Kepler has observed nearly 150,000 main sequence stars, and there it simply isn’t practical to go through all of that data by hand.

Enter statistical analysis. Rather than pouring over data by hand, a team of astronomers wrote a program to determine the odds of an exoplanet being a false positive, based on a comparison to known false positives. They had the program analyze data from more than 7,000 “objects of interest” in the Kepler data, which at first glance look like planetary transits. They found that about 2,000 of them had less than 1% odds of being a false positive. Some of these had previously been confirmed by other means, but 1,284 have not been confirmed previously.

The history of exoplanet discoveries. Credits: NASA Ames/W. Stenzel; Princeton University/T. Morton

Given the odds, it is likely that about 100 of these new exoplanets will later be outed as false positives. So it’s a bit misleading to say that exactly 1,284 new exoplanets have been confirmed. However the exact number isn’t important. This method allows us to narrow down the amount of exoplanet data. Now that exoplanets number in the thousands, we have to shift our methods away from sorting through data by hand and rely on statistical algorithms. And that’s an amazing shift. We have so much exoplanet data and so many exoplanet candidates that we can’t keep up. It’s a dramatic change from just two decades ago when only a handful of exoplanets were known.

Paper: Timothy D. Morton, et al. False Positive Probabilities For All Kepler Objects Of Interest: 1284 Newly Validated Planets And 428 Likely False Positives. The Astrophysical Journal, Volume 822, Number 2 (2016) DOI:10.3847/0004-637X/822/2/86

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As of this writing there are 1,692 confirmed extra-solar planets.  These are planets for which we not only know they exist, but we know some things about them, such as their orbit, mass, etc.  The Kepler mission, a space telescope surveying nearly 150,000 main sequence stars, has found nearly 20,000 possible planets.  Of these, we have found more than 2,700 candidate planets.  These are planets for which we know some of their properties, but which haven’t completed the rigorous process of being officially confirmed. This is a huge change from just twenty years ago, when there were no confirmed main-sequence exoplanets.

With nearly 3,000 candidate planets we can now do a bit of statistics on just how common planets are, their typical masses, and the type of stars they orbit.  You can see some of these statistics in the figures below.  The first image shows the locations of candidate planets seen by Kepler, while the second shows the distribution of these planets by mass.

The distribution of planets discovered by Kepler. Credit: NASA

Of course we have to be a bit careful when looking at the statistics.  Kepler finds planets by a process known as the transit method.  It measures the brightness of 150,000 main sequence stars looking for the periodic dimming of a particular star.  There are several reasons why a star might dim, but one of them is because a planet passes in front of the star, blocking some of its light for a short period.  The bigger the planet, the easier it is to observe.  It is also easier to observe periods with shorter orbital periods than longer ones.  With shorter periods you can see more of them for a given observation time.  As a result, Kepler will find short-period planets first, and longer period planets as it keeps watching the stars.

Statistics on exoplanet sizes. Credit: NASA

Even with this observational bias we can see that planets have a range of sizes, and even Earth-sized planets are relatively common.  Popular science articles often use the term Earth-like, but that sounds like they have water and gazelles, but just because they are Earth sized doesn’t mean they are habitable.  That’s a topic for another time.

The transit method is just one way to discover extra-solar planets.  Another popular method is radial velocity method.  This method observes starlight and watches for a periodic Doppler shift.  As a planet orbits a star it causes the star to wobble a bit.  As a star wobbles, its light is red shifted or blue shifted slightly.  By measuring a star’s wobble we can detect the planets orbiting it.  Again this has a bit of bias.  Larger planets orbiting smaller stars are easier to observe than smaller planets orbiting larger stars.

So just how many planets are there in our galaxy?  A recent study estimates that most main sequence stars have planetary systems, with an average of about 1.6 planets per star in our galaxy.  Since there’s at least 200 billion stars in the Milky Way, that means more than 300 billion planets.  Another survey looked at planets orbiting M class (red dwarf) stars, and estimated about 6% of red dwarfs have Earth-mass stars in their habitable zone.  Since about 75% of stars in our galaxy are red dwarfs, that means there may be 4.5 billion Earth-like planets in the Milky Way.  Earth-like in that they have a mass similar to Earth’s and a temperature that could allow for liquid water on its surface.  Of course that’s just in our galaxy.  There are likely 500 billion galaxies in the observable universe, so there may be a sextillion planets similar to ours.  Sextillion as in 1 with 21 zeros after it.

Billions and billions indeed.

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Yesterday I talked about how some of Kepler’s data can be a bit puzzling, but there are lots of results from Kepler that are very clear.  After all, we now have more than a thousand confirmed exoplanets, many of which are from Kepler data.  This means we have enough planets to run a bit of statistics, and it leads to some interesting results.  For example, an article was published this month in the Proceedings of the National Academy of Sciences (PNAS) analyzing the statistical distribution of known exoplanets from the Kepler data.  This article is open access (woot!) and you can read it here.

The focus of the paper was Earth-like worlds.  The authors defined “Earth-like” as meeting three conditions:

First, the star the planet orbits must be Sun-like, meaning it must be a G or K type main sequence star.  The Sun is a G-type star, and K-type stars are a bit smaller than our Sun.  This criteria excludes M-type main sequence stars (red dwarfs) which are much more common, but not very Sun-like.

Second, the planet must have a diameter between 1 – 2 times that of Earth.  Because Kepler discovers planets that pass in front of a star, it is easier to determine a planet’s size than its mass.  But it is reasonable to assume that a planet about the same size as Earth will have a mass similar to Earth.

Third, the orbital period of the planet must be between 200 and 400 days.  This is a rough way of saying the planet is in the “habitable zone” of its star.  Very roughly, we can say the Sun’s habitable zone is bounded by the orbits of Venus and Mars.  Venus has an orbital period of 225 days, and Mars 687 days.  Since the K-class stars are a bit smaller and cooler than the Sun, the 200 – 400 day range is a reasonable measure of potentially habitable zone.

One of the challenges of doing statistics is making sure you account for biases in your data.  In exoplanet data there are two potential biases.  The first is that larger planets in closer orbits are easier to find than smaller planets in farther orbits.  Another is that planets that could potentially be observed are missed because of noise in the data.  We find the easy signals, but miss the hard ones.

To account for the first bias, the authors looked at data from 42,000 Sun-like stars, finding 603 planets.  From this they were able to look at the distribution of planetary distances observed and extrapolated the data to larger distances.  To account for the second bias the authors put fake planetary signals into the Kepler data and then tried to “discover” those signals in the data.  From that they could get a handle on how many planets are “missed” in the real data.  With a handle on those potential biases, the authors could calculate the fraction of Sun-like stars with Earth-like planets in their habitable zones.

The results are pretty surprising.  Based on the statistics, it’s estimated that between 14% and 30% of G and K type stars have Earth-sized planets in their habitable zone.  There are about 300 billion stars in our galaxy, and about 60 billion of them are G and K type stars.  That means there is somewhere between 8 to 20 billion potentially habitable Earth-like worlds in our galaxy alone.

It’s hard to wrap your head around those kind of numbers, so here is another way of looking at it.  Suppose the Earth were a big blue marble.  Suppose all the other potentially habitable “earths” were marbles of a similar size.  If you put Earth and all the other marbles in a single container, there would be enough to fill a volume roughly the size of the great pyramid at Giza.

It is important to note that these are “potentially” habitable, meaning that they are at a distance where temperatures could allow for things like liquid water.  That doesn’t mean they *are* habitable, or that they have life.  Many could be dry planets like Venus, or have atmospheres that are too thin to support life.  It is possible that most of them are warm and wet like Earth, or that none of them are.  Right now we just don’t know.

But we do know the potential is there.  The potential of billions of earths in our galaxy alone, and there are about 100 billion galaxies in the observable universe.

That’s a lot of worlds waiting to be explored.

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When the Higgs result hits the internet tomorrow, look for the phrase “five sigma”.  The reason is that if the Higgs is observed at five sigma it will be officially discovered.  But what is a sigma and why is five the magic number?

Suppose you suspected a coin was not evenly balanced, say instead of an even chance of heads and tails, it was 55% heads and 45% tails.  If you only tossed a coin a few times, you might not notice anything amiss.  But if you did it 100 times you might see 53 heads and 47 tails, which makes you suspicious.  It is possible that the coin is fair, and by random chance you got slightly more heads than tails.  But if you keep tossing the coin (a thousand times, a million), and you continue to see about 55% heads and 45% tails, then it is more likely that the coin isn’t fair.

But the coin tosses are still random, so it is possible that the coin is fair, and you’ve just had bad luck in your results.  The question is how likely is it that the coin is fair.  For that you need statistics.  The sigma is a measure of how likely your 55/45 spit is due to random chance.  The bigger the sigma, the less likely your observation is to be random.

So if your result had a measure of 1 sigma, then there is about a 30% chance that your coin is still fair.  At 2 sigma there is only a 4% chance of being fair.  In particle physics the threshold for observation is 5 sigma.  At that level there is only 1 chance in 1.7 million that you’ve observed a false positive.  So if the Higgs is observed at 5 sigma, that means we are 99.99994% certain that it exists.

Which in science terms is “close enough”.

Note: This was written 3 July 2012 on Google+.  I’m posting it here just to have a copy.

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