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Kepler and the Whole Sky

In this unit, we’ll estimate the number of habitable planets in the galaxy by walking through the required steps together. There are two main parts to this calculation. First, we will calculate the occurrence rate of planets, based on the Kepler survey: the number of stars that are orbited by at least one planet. As we have stated before, Kepler has found several thousand candidate planets, but how do we turn that number into an occurrence rate? Second, we will estimate the number of planets we expect to exist in our galaxy, by combining the planet occurrence rate with the number of stars in our galaxy.

First, one clarification: in this discussion, we will deal with the number of stars that host at least one planet. We could also calculate the number of planets per star -- because multiple planets can be found around a single star, these numbers will differ. Kepler has found about 4,200 planets or candidate planets circling 3,200 stars. In other words, the mission has found 3,200 planetary systems.

Below you can see an "orrery" created by Daniel Fabrycky showing some of the planets that Kepler has discovered. Their orbital periods range from several months to just a few hours. You can find an even more up-to-date version.

Candidate planets vs. confirmed planets

Only a quarter of the planet candidates found by Kepler have been “confirmed.” Confirmed planets, in Kepler lingo, are those that have been subjected to additional, rigorous study that is designed to test whether a transit signal is a bonafide planet or something else. If the signal is “something else,” we call it a false positive. Astronomers have calculated that about 10% of candidate planets are in fact false positives, so we’ll assume that 90% of the candidate planets are truly planets.

Given this estimate, Kepler has found ( 3200 x 0.9 ) = 2880 true planetary systems.

Planets found vs. planets not found

Kepler surveyed 140,000 stars and found, as we have estimated, about 2,880 true planetary systems. Does this mean that the occurrence rate of planets throughout the galaxy is 2880/140,000, or 2%? Not quite: there are several additional factors we need to take into account first.

While Kepler takes exquisite photometry, there is still noise in the data. We need to ask ourselves how many transiting planets we might have missed because the signals were washed out in the noise. Several recent studies have been developed to figure this out, and drawing from their results, we will assume that Kepler missed 15% of stars that actually do have transit signals.

How many transiting planetary systems are there hidden in the Kepler data? To find the answer we take our 2,800 systems and multiply by 115% to account for the missing transits. 2800 x 1.15 = 3200 systems.

Another important consideration is that having a planet cross between us and its host star takes a very particular alignment, and chances of getting the alignment right are small. The transit probability is greater the larger the star and the closer the planet orbits to its host star. For the typical Kepler planet, the transit probability is about 5%. That means that our planets represent just 5% of the total number that are out there.

How many planetary systems (transiting and non-transiting) are in the Kepler field? If our measurements show only 5% of them, we can take our previous guess of 3200 and divide by 0.05 to find ( 3200 / 0.05 ) = 64,000 systems!

Calculating the final occurrence rate

We have estimated that there are 64,000 total planetary systems amongst the 140,000 stars surveyed by Kepler. We can now estimate the planet occurrence rate: the fraction of stars that are orbited by planets.

This means that one out of every two stars are expected to host planetary systems. This agrees well with recent calculations: Fressin et al. found that 52% of stars have at least one planet with an orbital period less than 85 days (the statistics for longer periods were not well-constrained by the data).

How many of these planets are habitable?

How many of these systems include a habitable planet? This is hard to answer, even if we ignore the question of what makes a habitable planet. The problem is that most of the planets found by Kepler have short periods. Because an individual planet transit is hard to detect, we have to observe many transits to build up our confidence in the signal. This makes long period planets harder to find: a planet on a month-long orbit will have twelve transits in a year, while a planet on a year-long orbit will have just one. Because of this factor, most studies of the Kepler only consider the occurrence rates of small planets with orbital periods of less than 85 days

Nevertheless, recent estimates indicate that 20% of stars host a habitable planet, a result which seems to be consistent for Sun-like stars as well as for the smaller red dwarf stars – which comprise 80% of stars In our galaxy.

Extrapolating to the whole sky

Now that we've estimated the fraction of stars that host planetary systems per star, and discussed the fraction of stars that host habitable planets, we're ready to estimate the number of stars in our galaxy that have planetary systems and those that have habitable planets. The most difficult aspect of this calculation comes at the very beginning: determining the number of stars in our galaxy. Current estimates range from 100 billion to 1 trillion, and the truth of it is that we just don’t have a way of measuring this exactly. For the purposes of this exercise, let’s assume a number in the middle: 300 billion.

We’ve estimated that 50% of these 300 billion stars have a planet, and 20% of them have a habitable planet. That’s 150 billion planetary systems and 60 billion habitable planets in our galaxy alone.

That's a huge number of planets offering billions of possibilities for alien life to have occurred. But most of them are tens of thousands of light years away, beyond the capabilities of even the next generation of extremely powerful telescopes, so seeing them is not something we will be able to do in the near future. In the next unit, we'll talk about how close the nearest habitable planet might be.

Солнечная система и ее тайны