Dependencies of Detectable Planet Size

Many factors determine if transits caused by a particular planet size are detectable. These include the:

  • Size of the star
  • Brightness of the star, photometer aperture and optical efficiency (photon shot noise)
  • Stellar variability (inherent noise of the source)
  • Instrument differential precision (instrument noise)
  • Number of transits (mission life divided by the orbital period)
  • Detection efficiency (SNR and false alarm rate) and
  • Duration of the transit (central or grazing)

The baseline sensitivity of the Kepler Mission photometer is designed to detect Earth-size, 1.0 Re, planets in 1 AU orbits around mv=12 solar-like stars in 6.5 hours (grazing transit) with a signal to noise ratio (SNR) of >8. These values can be scaled to define the range of detection possibilities. The result of modeling all of this for the Kepler Mission is shown below.

The figure below presents the minimum detectable planet size for:

  • A range of apparent stellar brightnesses (mv=9, 12 and 14);
  • A range of stellar masses (note their spectral types are indicated relative to their mass in the upper left figure); and
  • A range of planetary orbital sizes (semi-major axis).

Minimum Detectable Planet Size Dependence on Stellar Brightness, Stellar Mass and Planetary Orbit.
Planets of a given size are detectable to the left of each contour. Detections are based on a total SNR >8 sigma and >3 transits in 4 years. The detectable planet sizes are shown for a near-central transit. Each plot is for a given stellar brightness. Planet radius and area are relative to the Earth.

Note that although the mission is optimized to detect Earth-size planets in the habitable zone of solar-like stars, planets even as small as Mercury are detectable in the habitable zone of K and M stars. For shorter period orbits, more transits are observed for a given mission lifetime, thereby enabling the detection of planets smaller than Earth or enabling detection of Earth-size planets around stars larger than the Sun.

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