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Close-Up on the Kepler Mission

Many of you may haveobserved the transit of Venus in 2004, and almost all of you saw images on theInternet and in the news of this rare and amazing event. The next transit ofVenus won't occur until June 6, 2012. After that, it will be another 115 yearsuntil 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 in2008 by the NASA Discovery Program's KeplerMission.

This planet won't be amember of our solar system - it will be an extrasolarplanet. Over 150 such planets have been discovered orbiting stars other thanthe Sun. Nearly all of these are comparable in mass and size to Jupiter, thegiant 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 newfield of inquiry, the Holy Grail for extrasolarplanet searches remains the discovery of Earth-sized planets in Earth-likeorbits about solar-like (late F, G and K) stars. Radial velocity surveys cannotdiscover small, rocky planets. The radial velocity signal from an Earth-massplanet is 317 times smaller than that of Jupiter, and 95 times smaller thanthat of Saturn, which is close to the limit of precision for RV surveys. Themost likely technique to detect terrestrial planets in the near term is transitphotometry.

Sic Transit Planet

The idea is to observe alarge number of stars for several orbital periods, looking for periodic dimmingof the stars corresponding to transit events in which the planet crosses itsstar's disk, blocking a fraction of the starlight. Central transits last from afew hours for orbital periods of several days, to 13 hours for an earth-likeorbit, and 16 hours for a Mars-like orbit. The photometric signal from aterrestrial planet is small, basically the ratio of the area of the planet tothe 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 protocolsand great observing conditions), and well below the typical photometricprecision obtained with 1-m class telescopes (>1,000 ppm).To push the limits of discovery down to Earth-sized planets requiresspace-based telescopes to allow continuous, low noise monitoring of a largenumber 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 ~130,000solar-like stars for at least four years to detect transiting planets withorbital periods up to two years. Kepler's sensitivity allows it toprobe for planets inside the circumstellar habitablezones of its target stars: that range of orbital distances within which liquidwater could exist on the surface of an Earth-mass planet.

Kepler needs to observe so many starsbecause the chance of observing a planet actually transit its star is relativelysmall for randomly oriented orbits. The probability is the ratio of the radiusof the star to the radius of the planet's orbit. Thus, there's a 0.5% chance ofseeing 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 Earthanalog, Kepler would need to observe at least200 solar-like stars to find one of these terrestrial cousins.

However, if Earth analogsare rare, we'd like to establish how rare they really are. To see this manystars requires a telescope with a large field of view (FOV), and Kepler'sis 112 square degrees, somewhat more than the amount of celestial watercontained in two Big Dippers. There are ~460,000 stars down to 15thmagnitude in Kepler'sFOV in the constellation of Cygnus. About half of these will be subgiant or giant stars, and somesolar-like stars will be too young and noisy to permit detection of transits,which leaves about 200,000 stars for Kepler toobserve. We don't expect to be able to detect Earth-sized planets transitingstars dimmer than 12th magnitude except for stars much smaller thanthe Sun, so Kepler could find up to 50Earth-sized planets at 1 AU, while it may find several hundred with radii up to2.2 Earth radii in similar orbits. A few thousand planets could be found atorbital distances less than 1 AU if such orbits are common.

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

The Intricacies ofFinding New Worlds

To detect transitingplanets we correlate or "match" a transit pulse with a time series ofstellar brightness measurements. We then fold the correlated time seriesstarting with the shortest period of interest so that if the correct period ischosen, 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 examinedfor 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 ofinterest are covered. The results in each bin for each fold are calleddetection statistics. In the case of a good match at the correct phase bin andperiod, the corresponding detection statistic will be large and positive;otherwise it will be small.

To determine whether aresult is significant, we need to estimate the number of effective independentstatistical tests actually conducted in the search. For Kepler,looking for planets with periods up to two years in four years of data requiresabout 15 million independent statistical tests for each star. The requisitethreshold for 130,000 stars, then, is about 7 sigma,where 1 sigma is the standard deviation of the observation noise. This is highenough 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 meandetection statistic of at least 8 sigma, so that morethan 84% of transiting Earth-sized planets exhibiting four or more transitswill be detected.

The story won't end withthe KeplerMission, whose findings will be used to help scale NASA's ambitiousTerrestrial Planet Finder (TPF) mission, which will seek to actually imageEarth-like planets orbiting nearby stars. While the technology for TPF is stillunder development, Kepler is ready to go.Hopefully, by the year 2011, we'll have found the first of several hundredEarth-like planets and can begin asking the question of whetherthere 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 didin 2004, but with a different perspective. I won't be wondering whether planetssuch as Venus and Earth are abundant in the Milky Way galaxy. I'll be wonderinghow many beings on the Earth-like planets we discovered might be watchingsimilar events in their home solar systems with the same awe and delight that Iexperience.

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