Close-Up on the Kepler Mission

Many of you may have observed the transit of Venus in 2004, and almost all of you saw images on the Internet and in the news of this rare and amazing event. The next transit of Venus won't occur until June 6, 2012. After that, it will be another 115 years until the next one. If you missed it in 2004 and can't wait until 2012 or 2117, cheer up: The next transit of an Earth-sized planet will likely be observed in 2008 by the NASA Discovery Program's Kepler Mission.

This planet won't be a member of our solar system - it will be an extrasolar planet. Over 150 such planets have been discovered orbiting stars other than the Sun. Nearly all of these are comparable in mass and size to Jupiter, the giant of our solar system. Moreover, almost all of these giant extrasolar planets have been detected using ground-based, radial velocity (RV) surveys. While these discoveries have opened up a new field of inquiry, the Holy Grail for extrasolar planet searches remains the discovery of Earth-sized planets in Earth-like orbits about solar-like (late F, G and K) stars. Radial velocity surveys cannot discover small, rocky planets. The radial velocity signal from an Earth-mass planet is 317 times smaller than that of Jupiter, and 95 times smaller than that of Saturn, which is close to the limit of precision for RV surveys. The most likely technique to detect terrestrial planets in the near term is transit photometry.

Sic Transit Planet

The idea is to observe a large number of stars for several orbital periods, looking for periodic dimming of the stars corresponding to transit events in which the planet crosses its star's disk, blocking a fraction of the starlight. Central transits last from a few hours for orbital periods of several days, to 13 hours for an earth-like orbit, and 16 hours for a Mars-like orbit. The photometric signal from a terrestrial planet is small, basically the ratio of the area of the planet to the area of the star. For Earth, the transit depth is only one part in 10,000, comparable to the best precision attainable from the ground (~100 ppm for 4-m telescopes with painstaking observing protocols and great observing conditions), and well below the typical photometric precision obtained with 1-m class telescopes (>1,000 ppm). To push the limits of discovery down to Earth-sized planets requires space-based telescopes to allow continuous, low noise monitoring of a large number of stars for several years. That's where the NASA Discovery Program's Kepler Mission comes in.

Slated for launch in 2008, the Kepler photometer will observe ~130,000 solar-like stars for at least four years to detect transiting planets with orbital periods up to two years. Kepler's sensitivity allows it to probe for planets inside the circumstellar habitable zones of its target stars: that range of orbital distances within which liquid water could exist on the surface of an Earth-mass planet.

Kepler needs to observe so many stars because the chance of observing a planet actually transit its star is relatively small for randomly oriented orbits. The probability is the ratio of the radius of the star to the radius of the planet's orbit. Thus, there's a 0.5% chance of seeing an Earth-sized planet in a 1 AU (the distance from Earth to the Sun) orbit transit a Sun-like (G2) star. If every solar-like star harbored an Earth analog, Kepler would need to observe at least 200 solar-like stars to find one of these terrestrial cousins.

However, if Earth analogs are rare, we'd like to establish how rare they really are. To see this many stars requires a telescope with a large field of view (FOV), and Kepler's is 112 square degrees, somewhat more than the amount of celestial water contained in two Big Dippers. There are ~460,000 stars down to 15^th magnitude in Kepler's FOV in the constellation of Cygnus. About half of these will be subgiant or giant stars, and some solar-like stars will be too young and noisy to permit detection of transits, which leaves about 200,000 stars for Kepler to observe. We don't expect to be able to detect Earth-sized planets transiting stars dimmer than 12^th magnitude except for stars much smaller than the Sun, so Kepler could find up to 50 Earth-sized planets at 1 AU, while it may find several hundred with radii up to 2.2 Earth radii in similar orbits. A few thousand planets could be found at orbital distances less than 1 AU if such orbits are common.

The discovery of large (2.2 Earth-radius) planets would help constrain the formation mechanism for Jupiter-like planets. Currently, the two favored mechanisms are core accretion, which requires the formation of a large rocky core followed by capture of a gaseous atmosphere, and disk instabilities, where gas can be compressed into a gravitationally bound mass by dynamical mechanisms in a protoplanetary disk without the need for massive rocky cores. An absence of such cores would favor the latter method for forming Jupiter-like planets.

The Intricacies of Finding New Worlds

To detect transiting planets we correlate or "match" a transit pulse with a time series of stellar brightness measurements. We then fold the correlated time series starting with the shortest period of interest so that if the correct period is chosen, all the transits will line up and the signal strength will be boosted. After the data is folded at a particular period and all the bins are examined for evidence of transits, the trial period is incremented by a small amount, the data are re-folded, and the process continued until the range of periods of interest are covered. The results in each bin for each fold are called detection statistics. In the case of a good match at the correct phase bin and period, the corresponding detection statistic will be large and positive; otherwise it will be small.

To determine whether a result is significant, we need to estimate the number of effective independent statistical tests actually conducted in the search. For Kepler, looking for planets with periods up to two years in four years of data requires about 15 million independent statistical tests for each star. The requisite threshold for 130,000 stars, then, is about 7 sigma, where 1 sigma is the standard deviation of the observation noise. This is high enough so that less than one false alarm is expected for the entire campaign. We also know that a set of four Earth-sized transits will yield a mean detection statistic of at least 8 sigma, so that more than 84% of transiting Earth-sized planets exhibiting four or more transits will be detected.

The story won't end with the Kepler Mission, whose findings will be used to help scale NASA's ambitious Terrestrial Planet Finder (TPF) mission, which will seek to actually image Earth-like planets orbiting nearby stars. While the technology for TPF is still under development, Kepler is ready to go. Hopefully, by the year 2011, we'll have found the first of several hundred Earth-like planets and can begin asking the question of whether there exist any intelligent beings that call one of more of these planets "home". I hope to observe the next transit of Venus in 2012 as I did in 2004, but with a different perspective. I won't be wondering whether planets such as Venus and Earth are abundant in the Milky Way galaxy. I'll be wondering how many beings on the Earth-like planets we discovered might be watching similar events in their home solar systems with the same awe and delight that I experience.