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. 2013 Nov 26;110(48):19273-8.
doi: 10.1073/pnas.1319909110. Epub 2013 Nov 4.

Prevalence of Earth-size planets orbiting Sun-like stars

Erik A Petigura  1 , Andrew W Howard, Geoffrey W Marcy
Affiliations

Prevalence of Earth-size planets orbiting Sun-like stars

Erik A Petigura et al. Proc Natl Acad Sci U S A. .

Erratum in

  • Proc Natl Acad Sci U S A. 2013 Nov 26;110(48):19652

Abstract

Determining whether Earth-like planets are common or rare looms as a touchstone in the question of life in the universe. We searched for Earth-size planets that cross in front of their host stars by examining the brightness measurements of 42,000 stars from National Aeronautics and Space Administration's Kepler mission. We found 603 planets, including 10 that are Earth size ( ) and receive comparable levels of stellar energy to that of Earth (1 - 2 R[Symbol: see text] ). We account for Kepler's imperfect detectability of such planets by injecting synthetic planet-caused dimmings into the Kepler brightness measurements and recording the fraction detected. We find that 11 ± 4% of Sun-like stars harbor an Earth-size planet receiving between one and four times the stellar intensity as Earth. We also find that the occurrence of Earth-size planets is constant with increasing orbital period (P), within equal intervals of logP up to ~200 d. Extrapolating, one finds 5.7(-2.2)(+1.7)% of Sun-like stars harbor an Earth-size planet with orbital periods of 200-400 d.

Keywords: astrobiology; extrasolar planets.

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Conflict of interest statement

The authors declare no conflict of interest.

Figures

Fig. 1.
Fig. 1.
2D domain of orbital period and planet size, on a logarithmic scale. Red circles show the 603 detected planets in our survey of 42,557 bright Sun-like stars (Kp = 10–15 mag, GK spectral type). The color scale shows survey completeness measured by injection and recovery of synthetic planets into real photometry. Dark regions represent (P, RP) with low completeness, C, where significant corrections for missed planets must be made to compute occurrence. The most common planets detected have orbital formula image and formula image (at middle left of graph). However, their detectability is favored by orbital tilt and detection completeness, C, that favors detection of such close-in, large planets.
Fig. 2.
Fig. 2.
Planet occurrence, formula image, as a function of orbital period and planet radius for P = 6.25–400 d and formula image. As in Fig. 1, detected planets are shown as red circles. Each cell spans a factor of 2 in orbital period and planet size. Planet occurrence in a cell is given by formula image, where the sum is over all detected planets within each cell. Here, formula image is the number of nontransiting planets (for each detected planet) due to large tilt of the orbital plane, formula image is the detection completeness factor, and formula image stars in the Best42k sample. Cells are colored according to planet occurrence within the cell. We quote planet occurrence within each cell. We do not color cells where the completeness is less than 25%. Among the small planets, 1–2 and 2–4 formula image, planet occurrence is constant (within a factor of 2 level) over the entire range of orbital period. This uniformity supports mild extrapolation into the P = 200–400 d, formula image domain.
Fig. 3.
Fig. 3.
The measured distributions of planet sizes (A) and orbital periods (B) for formula image and P = 5–100 d. Heights of the bars represent the fraction of Sun-like stars harboring a planet within a given P or RP domain. The gray portion of the bars show planet occurrence without correction for survey completeness, i.e., for formula image. The red region shows the correction to account for missed planets, 1/C. Bars are annotated to reflect the number of planets detected (gray bars) and missed (red bars). The occurrence of planets of different sizes rises by a factor of 10 from Jupiter-size to Earth-sized planets. The occurrence of planets with different orbital periods is constant, within 15%, between 12.5 and 100 d. Due to the small number of detected planets with formula image and P > 100 d (four detected planets), we do not include P > 100 d in these marginalized distributions.
Fig. 4.
Fig. 4.
The detected planets (dots) in a 2D domain similar to Figs. 1 and 2. Here, the 2D domain has orbital period replaced by stellar light intensity, incident flux, hitting the planet. The highlighted region shows the 10 Earth-size planets that receive an incident stellar flux comparable to the Earth: flux = 0.25–4.0 times the flux received by the Earth from the Sun. Our uncertainties on stellar flux and planet radii are indicated at the top right.
Fig. 5.
Fig. 5.
The fraction of stars having nearly Earth-size planets formula image with any orbital period up to a maximum period, P, on the horizontal axis. Only planets of nearly Earth size formula image are included. This cumulative distribution reaches 20.2% at P = 50 d, meaning 20.4% of Sun-like stars harbor a 1–2 formula image planet with an orbital period, P < 50 d. Similarly, 26.2% of Sun-like stars harbor a 1–2 formula image planet with a period of P < 100 d. The linear increase in this cumulative quantity corresponds to planet occurrence that is constant in equal intervals of logP. One may perform a modest extrapolation into the P = 200–400 d range, equivalent to assuming constant occurrence per logP interval, using all planets with P > 50 d. Such an extrapolation predicts that formula image% of Sun-like stars have a planet with size 1–2 formula image, with an orbital period between P = 200 and 400 d.
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