Will Baird and
james_nicoll picked up on this 13-page paper, authored by Joseph Catanzarite and Michael Shao. Abstract below:
From page 4:
And one practical consequence of all this, taking from the conclusion:
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Kepler is a space telescope that searches Sun-like stars for planets. Its major goal is to determine {\eta}_Earth, the fraction of Sunlike stars that have planets like Earth. When a planet 'transits' or moves in front of a star, Kepler can measure the concomitant dimming of the starlight. From analysis of the first four months of those measurements for over 150,000 stars, Kepler's science team has determined sizes, surface temperatures, orbit sizes and periods for over a thousand new planet candidates. Here, we show that 1.4% to 2.7% of stars like the Sun are expected to have Earth analog planets, based on the Kepler data release of Feb 2011. The estimate will improve when it is based on the full 3.5 to 6 year Kepler data set. Accurate knowledge of {\eta}_Earth is necessary to plan future missions that will image and take spectra of Earthlike planets. Our result that Earths are relatively scarce means that a substantial effort will be needed to identify suitable target stars prior to these future missions.
From page 4:
We found that 2% of stars have an Earth in the HZ; this means 3000 of the 150,000 Kepler stars have an Earth. Of this 3000, about 1 in 250, or 12 will be edge-on, producing a transit. The Kepler data set contains 4 Earth and super-Earth planets colder than 300 K. This means that as of Feb 2011 Kepler found 30% of the transiting Earths and super-Earths that it will eventually find after 3~4 years. As a check, we created an ensemble of simulated planets at 300K with the same planet radius distribution by ‘moving’ all the transiting planets in the Kepler data to the semimajor axis where the temperature is 300K. We find that 30% of these have periods shorter than 120 days, and should have been detected in the Feb 2011 data release; the other 70% have longer periods and thus would not have been detected by Kepler as of Feb 2011. In other words if 3000 of the 150,000 Kepler stars have Earths, then after 3~4 years of monitoring Kepler should find 12 of those 3000, and by Feb 2011, Kepler should have found 4 of those 12. The Feb 2011 data release identified 4 such planets.
And one practical consequence of all this, taking from the conclusion:
Many mission concepts that have been studied could potentially succeed only if {\eta}_Earth is large, at least 20% (Savransky, Kasdin, & Cady, 2010); (Catanzarite & Shao, 2011). A significantly smaller value of {\eta}_Earth means that a mission to detect nearby Earths would have to be capable of searching 100 or more of the nearest stars instead of 10 or 15. The 2010 Astrophysics Decadal Review (New Worlds, New Horizons in Astronomy and Astrophysics, 2010) stated that “the role of target-finding for future direct detection missions (is) not universally accepted as essential.” But if {\eta}_Earth = 0.02, substantial effort may be needed to identify suitable target stars prior to these future missions, possibly using space astrometry (Shao, Catanzarite, & Pan, 2010). With an estimate of {\eta}_Earth in hand we can improve the fidelity of the science modeling for these missions, allowing meaningful ranking of their relative merits.
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