Report - School of Physics

The numbers in Table 5 are taken from the Kepler www site, and are based on
the following assumptions: 100 000 main-sequence stars observed with a precision
of better than ∼ 5 × 10 −5 ; typical variability of 75% of the stars is similar to that
of our Sun; most main-sequence stars, including binaries, have terrestrial planets
in or near the habitable zone; on average, two Earth-size or larger planets exist
between 0.5–1.5 AU; transit probability for planets in the habitable zone is 0.5% per
planet; the transit is near grazing in a 1-year orbit; each star has one giant planet
in an outer orbit; on average 1% of the main-sequence stars have giant planets in
orbits shorter than 1 week and comparable numbers in periods of 1–4 weeks and 1–
12 months; mission life time of 4 years. Results for giant planets are expected around
2007, with those on terrestrial planets (which will require more careful verification)
around 2010.
Eddington: ESA’s Eddington mission was originally proposed for launch around
2008. It entered ESA’s science programme as a ‘reserve’ mission, was approved
in 2002, but cancelled in November 2003 due to overall financial constraints. The
Eddington payload was composed of three identical, co-aligned telescopes with a
≃ 0.7 m aperture and identical 3 × 2 mosaic CCD cameras, a total collecting area of
≃ 0.75 m 2 and a field of view of ≃ 20 deg 2 . Each telescope had a slightly different
bandpass, allowing colour information to be derived for high S/N transits.
The baseline lifetime was 5 years (extended operations possible), of which three
would be dedicated to a single long observation (currently baselined in Lacerta),
and two would be used for short (one to a few months) observations of other fields.
Planet searches were to be conducted during the three years observation, in ∼ 10 5
stars, of which ∼ 10 4 would be observed with sufficient accuracy to detect Earthlike
planets. During the shorter observations, a further ∼ 4 × 10 5 stars would be
searched for planets, allowing many shorter-period planets to be discovered.
The numbers in Table 5 are the results of detailed Monte Carlo simulations, which
assume a ‘standard’ planet function of the form f(a, m|M) ∝ a α m β M γ where a is the
orbital radius of the planet, m its mass, and M the mass of the parent star, and using
the mass-radius relationship obtained from solar system objects. The simulations
used γ = 0, i.e. the planet function is independent of the stellar mass. As both the
Doppler planet population and the solar system objects are consistent with α = −1,
β = −1, the simulations have also used f(a, m) ∝ a −1 m −1 normalised to 0.01 hot
Jupiters per star (as derived from the Doppler surveys). In this assumption, each
star has 0.25 normal Jupiters (r > R J ), 0.01 hot Jupiters (r > R J , P = 3 − 5 day),
0.85 Earths (R > R ⊕ ) at any orbital distance, and 0.07 ‘habitable planets’ (with
liquid water temperatures). This is considered as a conservative mass function, as
the typical star probably has fewer rocky planets than the solar system. Also, the
simulations are stopped at R = 1R J (because of the emphasis on the smaller planets),
so that the number of gas giants is under-predicted. The result of the Monte Carlo
simulation predicts, for the single 3-year observation: 14 000 planets in total (in
12 500 planetary systems), of which 8000 hot planets, of which 5600 with R > 5R ⊕ ,
660 Earths (0.5 < R < 2.0R ⊕ ); 160 habitable zone planets, of which 20 ‘Earths’. A
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