Impact of Orbital Eccentricity on the Detection of Transiting Extrasolar   Planets
  For extrasolar planets with orbital periods, P>10 days, radial velocity surveys find non-circular orbital eccentricities are common, <e>~0.3. Future surveys for extrasolar planets using the transit technique will also have sensitivity to detect these longer period planets. Orbital eccentricity affects the detection of extrasolar planets using the transit technique in two opposing ways: an enhancement in the probability for the planet to transit near pericenter and a reduction in the detectability of the transit due to a shorter transit duration. For an eccentricity distribution matching the currently known extrasolar planets with P>10 day, the probability for the planet to transit is ~1.25 times higher than the equivalent circular orbit and the average transit duration is ~0.88 times shorter than the equivalent circular orbit. These two opposing effects nearly cancel for an idealized field transit survey with independent photometric measurements that are dominated by Poisson noise. The net effect is a modest ~4% increase in the transiting planet yield compared to assuming all planets have circular orbits. When intrinsic variability of the star or correlated photometric measurements are the dominant source of noise, the transit detectability is independent of the transit duration. In this case the transit yield is ~25% higher than that predicted under the assumption of circular orbits. Since the Kepler search for Earth-sized planets in the habitable zone of a Solar-type star is limited by intrinsic variability, the Kepler mission is expected to have a ~25% higher planet yield than that predicted for circular orbits if the Earth-sized planets have an orbital eccentricity distribution similar to the currently known Jupiter-mass planets. 
Christopher J. Burke