Expected results

As the mission duration lengthens from months to years, detection and follow-up begin with the detection of three or more transits for larger planets in short-period orbits, and then expands outward to the detection of smaller planets and longer orbital periods. For terrestrial-size planets with orbital periods of a week or less and geometrical alignment probabilities of 10%, the number of discoveries during the first 30 days of observations should be of order: (100,000 stars * 10% alignment probability * fraction of stars with such planets). The predicted number of discoveries varies from 10,000 to 100 as the fraction of stars with planets in inner orbits varies from 1 to 0.01.

To estimate the number of planet discoveries expected as the mission progresses, a model of a planetary system was convolved with both the distributions of stars in the FOV and the system response. To assess the level of resources needed to examine the expected number of candidates, the planetary model makes the optimistic assumption that each star has a planetary system with two Earth-size planets positioned outside the HZ of the star, and that there is one terrestrial-size planet in its HZ. It is assumed that planets found outside the HZ could be present with semi-major axes similar to those already found for the 150 giant planets already discovered. The model assumes that there is an equal probability of finding one of the two planets at 0.05, 0.1, 02, 0.4, 0.6, 0.8, 1.0, 1.2, or 1.5 AU. Whenever such a planet falls in or near the HZ of a star, it is removed to avoid conflict with the terrestrial-size planet already assumed to be in that position. The results shown in the figure are readily scaled to other assumptions and situations.

It is clear from Figure 6 that nearly 1300 Earth-size planets in short-period orbits will be found during the first year of operation and that approximately 4,500 will be found after four years of operation. Most of this contribution occurs for inner planets because they have a high probability of geometric alignment, and because the short-period orbits produce a large number of transits that greatly increases the SNR of the transit pattern. Although these values are probably high, they are useful for obtaining a conservative estimate of the magnitude of the analysis and follow-up observation tasks. It should also be noted that if planets larger than Earth size are common, they will produce higher SNR than assumed here, will be more easily detected around the many dim stars observed in the Kepler survey, and will thereby increase the values shown in Figure 6. Over the duration of a four-year mission, the number of transits in a pattern will exceed 400 for the shortest period orbits. The resulting increase in the SNR of the folded data will exceed eight even for planets as small as Mars or Mercury. Consequently, Kepler should produce an excellent estimate of the size distribution of terrestrial planets.

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Figure 6. The number of Earth-size planets expected to be discovered as a function of stellar spectral type and semi-major axis and mission duration.

The model treats planets in the HZ differently than those placed outside it. Here, the objective is to determine the smallest possible planet that provides an SNR greater than the 7a threshold value. The diameter of the terrestrial-size planet placed in the HZ of each star is systematically varied between values of Mars to 1.5 times the radius of Earth (0.53, 1.0, 1.3, 2.0 R®) and the smallest detectable planet size is tabulated. The capability to detect small planets is valuable, because a non-detection rules out a larger range of planet sizes, and their detection provides information on the tail of the distribution of planet sizes. Figure 7 shows how many of each size can be detected for both four- and six-year missions and for stellar types from F7 to M7. Figure 7 shows that for a mission duration of four years, no terrestrial planets can be found for stars as early as F7. This result is dictated by the requirement to have at least three transits for a valid discovery, and because planets in the HZ of early spectral types have orbital periods exceeding 1.5 years. However, when the mission duration is extended to six years, over 100 terrestrial-size planets can be discovered. A comparison of the results for a four-year versus six-year mission also shows that total number of expected discoveries increases, and that the fraction of the total discoveries that are capable of detecting the smallest planets rises. Because of the small sizes of the M dwarfs, and because planets in their HZ provide many transits per year, planets as small as Earth and Mars can be detected. Detection of a total 650 terrestrial-size planets, including approximately 100 Earth-size planets, is expected.

With the ability to discover about 650 terrestrial planets in the HZ for a four-year mission and about 900 for a six-year mission, our knowledge of terrestrial planets of a wide variety of stellar types in the HZ may exceed that of extrasolar giant planets. Even if only 10% of the stars have such planets, correlations can be obtained for the frequency of planets with stellar type and metallicity. Given that several percent of solar-like stars have orbiting giant planets, it seems unlikely that as few as 1% of such stars have terrestrial planets. Nevertheless, if that should be the case, Kepler will find hundreds of Earth-size planets in inner orbits and at least a few terrestrial-size planets in the HZ. If no terrestrial-size planets are found, then they must be very rare and theories on terrestrial planet accretion and migration will need to be re-examined.

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Figure 7. Number of terrestrial-size planets expected to be discovered as a function of stellar spectral type, semi-major axis, and planet size. It is assumed here that each target star has one terrestrial-size planet in its HZ.

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